NUCLEAR MAGNETIC RESONANCE STUDIES OF BIOFILM – POROUS MEDIA SYSTEMS by Catherine Mullinnix Kirkland A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering MONTANA STATE UNIVERSITY Bozeman, Montana July 2017 ©COPYRIGHT by Catherine Mullinnix Kirkland 2017 All Rights Reserved ii DEDICATION To Tim, Fergus, and Liam iii ACKNOWLEDGMENTS This material is based upon work supported, in part by the US Department of Energy, Office of Science under Award DE-SC0006376 and DE-FE0024296. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Department of Energy. This work is supported by the National Science Foundation (NSF) Graduate Research Fellowship Program under Grant No. DGE-1049562. The work comprising Chapter 9 was also supported by the Netherlands Organisation for Scientific Research (NWO) in conjunction with NSF as part of the Graduate Research Opportunities Worldwide program. Experiments conducted on the 22T (950 MHz) NMR instrument were supported by uNMR-NL, an NWO-funded National Roadmap Large-Scale Facility of the Netherlands (project 184.032.207). iv TABLE OF CONTENTS 1. INTRODUCTION ...........................................................................................................1 Low-field NMR ...............................................................................................................2 High-field NMR and MRI ...............................................................................................4 Outline..............................................................................................................................5 References .......................................................................................................................8 2. INTRODUCTION TO NUCLEAR MAGNETIC RESONANCE ................................11 Quantum Mechanics NMR Theory ................................................................................11 Spin Angular Momentum ......................................................................................12 Spin Magnetism and the Zeeman Interaction ........................................................14 Classical Mechanics NMR Theory ................................................................................18 Excitation ...............................................................................................................18 Reference Frames...................................................................................................20 Relaxation ..............................................................................................................22 Auto-correlation Functions ........................................................................22 Spectral Density Functions ........................................................................24 Experimental Background .............................................................................................28 Experimental Equipment .......................................................................................28 Signal Detection .....................................................................................................29 Basic Pulse Sequences ...........................................................................................33 Inversion Recovery ....................................................................................34 Hahn Spin Echo .........................................................................................36 CPMG Echo Train .....................................................................................37 Stimulated Echo .........................................................................................38 Phase Cycling.............................................................................................39 Introduction to Magnetic Resonance Imaging ...............................................................40 Gradients and k-space ............................................................................................40 Signal Encoding .....................................................................................................46 Selective Excitation ...............................................................................................49 Introduction to Molecular Motion Measurements .........................................................52 Normalized Echo Amplitude and q-space .............................................................53 Propagators ............................................................................................................54 References .....................................................................................................................58 3. ADVANCED NMR CONCEPTS .................................................................................59 Introduction ...................................................................................................................59 Time Varying Magnetic Fields and Phase Factors ........................................................60 Coherent Flow and Moments of the Gradient................................................................61 v TABLE OF CONTENTS – CONTINUED Bloch-Torrey Equations for Diffusion and Flow ..........................................................63 The Stejskal – Tanner Experiment .................................................................................64 Generalized Translational Motion .................................................................................67 Brownstein – Tarr Theory ..............................................................................................69 Multi-dimensional PFG and Relaxation NMR ..............................................................73 References ......................................................................................................................79 4. LOW-FIELD BOREHOLE NMR APPLICATIONS IN THE NEAR-SURFACE ENVIRONMENT ..................................................................80 Contribution of Authors and Co-Authors ......................................................................80 Manuscript Information .................................................................................................81 Abstract .........................................................................................................................82 Introduction ...................................................................................................................83 Theory ....................................................................................................................87 Measurement of Soil Moisture ......................................................................................94 Characterization of Unconsolidated Aquifers ...............................................................97 Detection of Subsurface Biogeochemical Processes ...................................................100 Outlook and Conclusions ............................................................................................106 References ...................................................................................................................108 5. BIOFILM DETECTION IN A MODEL WELL-BORE ENVIRONMENT USING LOW-FIELD NMR ..........................................................113 Contribution of Authors and Co-Authors ....................................................................113 Manuscript Information ...............................................................................................115 Abstract .......................................................................................................................116 Introduction .................................................................................................................117 Theory .........................................................................................................................120 T2 Relaxation ........................................................................................................120 Materials and Methods ................................................................................................123 Bioreactor Design and Construction ....................................................................123 Bacterial Culture ..................................................................................................125 NMR Data Acquisition ........................................................................................127 Sampling and Imaging .........................................................................................129 Results and Discussion ................................................................................................130 References ...................................................................................................................142 vi TABLE OF CONTENTS – CONTINUED 6. IN-SITU DETECTION OF SUBSURFACE BIOFILM USING LOW-FIELD NMR – A FIELD STUDY ......................................................146 Contribution of Authors and Co-Authors ....................................................................146 Manuscript Information ...............................................................................................148 Abstract .......................................................................................................................149 Introduction .................................................................................................................150 Methods .......................................................................................................................152 Results and Discussion ................................................................................................159 Microbiological Data and Water Chemical Analysis ..........................................166 Supporting Information ...............................................................................................172 Site Preparation ....................................................................................................172 Bacterial Culture ..................................................................................................173 NMR Measurements ............................................................................................175 Microbiological and Water Chemical Analysis ...................................................175 Results and Discussion ........................................................................................176 References ...................................................................................................................178 7. DETECTING MICROBIALLY-INDUCED CALCITE PRECIPITATION (MICP) IN A MODEL WELL-BORE USING DOWNHOLE LOW-FIELD NMR ................................................................182 Contribution of Authors and Co-Authors ....................................................................182 Manuscript Information ...............................................................................................183 Abstract .......................................................................................................................184 Introduction .................................................................................................................185 Background ..........................................................................................................186 NMR Theory ........................................................................................................188 Materials and Methods ................................................................................................191 Bioreactor .............................................................................................................191 Media and Injection Strategy ...............................................................................192 Bacterial Culture ..................................................................................................193 NMR Measurements ............................................................................................194 Sampling ..............................................................................................................195 Results and Discussion ................................................................................................196 Water Content and Porosity .................................................................................198 Relaxation ............................................................................................................202 References ...................................................................................................................205 vii TABLE OF CONTENTS – CONTINUED 8. NMR INVESTIGATION OF WATER DIFFUSION IN DIFFERENT BIOFILM STRUCTURES ..............................................................208 Contribution of Authors and Co-Authors ....................................................................208 Manuscript Information ...............................................................................................210 Abstract .......................................................................................................................211 Introduction .................................................................................................................212 Materials and Methods ................................................................................................215 Biofilm Sample Preparation .................................................................................215 MRI and PFG-NMR ............................................................................................217 MRI ..........................................................................................................217 Diffusion Measurements ..........................................................................218 Data Processing ....................................................................................................220 (Bi)-exponential Model ............................................................................220 Gamma Distribution Model .....................................................................221 2D Inverse Laplace Transform ................................................................221 Results and Discussion ................................................................................................222 Biofilm Characterization: Comparison of Common Quantities and Images .......222 Diffusion of Water in the Presence of Biomass ...................................................225 Influence of Biofilm Structure on Water Dynamics ............................................228 Influence of Diffusion Time on Water Dynamics ...............................................232 Correlation of Diffusion and Transverse Relaxation ...........................................235 Conclusions .................................................................................................................237 References ...................................................................................................................238 9. STRUCTURE AND DIFFUSION OF AEROBIC GRANULAR SLUDGE USING MAGNETIC RESONANCE ........................................................243 Abstract ........................................................................................................................243 Introduction .................................................................................................................243 Materials and Methods ................................................................................................247 Sample Collection and Preparation ......................................................................247 NMR and MRI Measurements .............................................................................249 Data Analysis .......................................................................................................251 T2 Maps ....................................................................................................251 Diffusion Images ......................................................................................251 Multidimensional Correlation and Exchange Experiments .....................252 Results and Discussion ................................................................................................252 MRI of Granule Internal Structure .......................................................................252 T2 Maps ....................................................................................................255 viii TABLE OF CONTENTS – CONTINUED Boundary Layer .......................................................................................256 PFG and Multidimensional NMR ........................................................................259 Future Work ................................................................................................................266 Acknowledgements .....................................................................................................267 References ...................................................................................................................268 10. CONCLUSIONS .......................................................................................................271 REFERENCES CITED ....................................................................................................275 ix LIST OF TABLES Table Page 5.1 NMR experiments with well-logging probe ................................................128 6.1 Experiment overview for biofilm detection field study ...............................155 6.2 NMR experimental parameters for field study ............................................159 8.1 Characterization of biofilms used in diffusion studies ................................216 8.2 Acquisition parameters used for diffusion measurements ...........................219 8.3 Stereoscopic and MRI images of biofilms ...................................................224 8.4 Summary of diffusion coefficients measured at Δ of 200 ms ......................228 9.1 MRI measurement parameters ....................................................................250 x LIST OF FIGURES Figure Page 2.1 Schematic of the Zeeman interaction energy .................................................15 2.2 Excitation schematic ......................................................................................20 2.3 Rotating reference frame schematic...............................................................21 2.4 Relaxation times in relation to the Larmor frequency ...................................26 2.5 Free Induction Decay .....................................................................................32 2.6 Inversion recovery pulse sequence ................................................................34 2.7 Inversion recovery magnetization evolution ..................................................34 2.8 Evolution of Mz in inversion recovery ...........................................................35 2.9 Hahn echo pulse sequence and magnetization evolution ...............................36 2.10 CPMG pulse sequence .................................................................................38 2.11 Stimulated echo pulse sequence...................................................................39 2.12 Schematic of a magnetic field gradient ........................................................41 2.13 Phase evolution under the influence of a field gradient ...............................44 2.14 Gradient echo and spin echo phase evolution ..............................................45 2.15 Phase encoding to traverse k-space .............................................................47 2.16 Frequency encoding to traverse k-space ......................................................48 2.17 Fourier transform of rectangular pulses .......................................................50 2.18 Fourier transform of soft pulses ...................................................................51 2.19 Schematic of selective excitation .................................................................52 2.20 PGSE pulse sequence ...................................................................................56 xi LIST OF FIGURES – CONTINUED Figure Page 3.1 PGSE pulse sequence .....................................................................................65 3.2 PGStE pulse sequence....................................................................................66 3.3 The Stejskal-Tanner plot ................................................................................67 3.4 Multi-dimensional PFG and relaxation NMR pulse sequences .....................77 4.1 Schematic of borehole NMR logging tool .....................................................88 4.2 CPMG pulse sequence ...................................................................................89 4.3 Temporal evolution of saturation in a column ...............................................95 4.4 Soil saturation profile .....................................................................................96 4.5 NMR well logs from the Massachusetts Military Reservation ......................98 4.6 Comparison of NMR logging data and DP permeameter data ......................99 4.7 Temporal evolution of CPMG signal decay and T2 distributions ................102 4.8 Temporal evolution of T2ML data due to biofilm growth ............................103 4.9 Temporal evolution of CPMG signal decay and T2 distributions ................105 5.1 Model well-bore bioreactor..........................................................................124 5.2 Temporal evolution of CPMG signal decay and T2 distributions ................132 5.3 Square of echoes reduction ..........................................................................134 5.4 Heterotrophic plate counts ...........................................................................136 5.5 Microscopy images of biofilm and porous media........................................137 6.1 Diversion disk attachment on the low-field NMR logging tool ..................158 6.2 Evolution of T2ML during field study ...........................................................160 xii LIST OF FIGURES – CONTINUED Figure Page 6.3 T2 distributions for the higher-frequency and lower-frequency wells .........161 6.4 Well profiles measured by NMR logging tool .............................................165 6.5 Heterotrophic plate counts and pH data .......................................................167 6.6 Square of Echoes data from field study .......................................................177 7.1 Model well-bore bioreactor..........................................................................192 7.2 Biomineralized sand annulus prior during destructive sampling .................196 7.3 Evolution of CPMG signal decay curves and T2 distributions ....................197 7.4 Temporal evolution of NMR-measured water content ................................199 7.5 SEM micrographs of calcite encrusted and control sand .............................200 8.1 Diffusion measurements at 200 MHz ..........................................................227 8.2 D1 and Dmean for various biofilm structures .................................................230 8.3 Time-dependent diffusion coefficients ........................................................233 8.4 Distribution of D using Γ distribution .........................................................235 8.5 D-T2 correlation for biofilm carriers ............................................................236 9.1 Schematic of aerobic granular sludge ..........................................................244 9.2 Sample collection and preparation ...............................................................248 9.3 Image of granular sludge samples in NMR tubes ........................................249 9.4 T1- and T2-weighted image of fresh Utrecht granule ...................................253 9.5 T1-weighted images of VFA and Garmerwolde granules ............................254 9.6 T2 maps of fresh and aged Garmerwolde granules .......................................256 xiii LIST OF FIGURES – CONTINUED Figure Page 9.7 TEM of Garmerwolde granule surface ........................................................258 9.8 TEM of Garmerwolde granule interior ........................................................259 9.9 1D diffusion image of alginate beads and aged Garmerwolde granule .......260 9.10 Apparent diffusion coefficient map of anammox granules........................261 9.11 D-T2 correlation of aged Garmerwolde granules .......................................262 9.12 1D T2 distribution and T2 map of Garmerwolde granule ...........................263 9.13 T1-T2 correlation of aged Garmerwolde granules ......................................264 9.14 T2-T2 correlation of aged Garmerwolde granules ......................................265 xiv ABSTRACT Nuclear magnetic resonance (NMR) allows for in-situ non-invasive studies of opaque systems over a wide range of length and time scales, making the method uniquely suited to studies of biofilms and porous media. The research comprising this thesis uses NMR to explore biophysical, chemical, and transport properties within heterogeneous porous media systems at both a macro- and micro-scale. The macro-scale projects validate a low-field borehole NMR instrument to monitor field-scale environmental engineering applications like subsurface biofilms and microbially-induced calcite precipitation (MICP). Subsurface biofilms are central to bioremediation of chemical contaminants in soil and groundwater whereby micro-organisms degrade or sequester environmental pollutants like nitrate, hydrocarbons, chlorinated solvents and heavy metals. When composed of ureolytic microbes, subsurface biofilms can also induce calcite precipitation. MICP has engineering applications that include soil stabilization and subsurface barriers, as well as sealing of cap rocks and well-bore regions for carbon dioxide sequestration. To meet the design goals of these beneficial applications, subsurface biofilms and MICP must be monitored over space and time – a challenging task with traditional methods. The low-field borehole NMR tool recorded changes in the T2 relaxation distribution where enhanced relaxation indicated biofilm accumulation in a sand bioreactor and in subsurface soil. Additionally, the tool was able to detect MICP in a sand bioreactor. The changed mineral surface of the sand lead to an increase in T2 relaxation times. The complementary high-field NMR project investigated micro-scale internal structures and mass transport within biofilm granules used for wastewater treatment. Granular sludge, composed of spherical aggregates of biofilm grown without a carrier, is an innovative biological treatment method with the potential to vastly reduce the cost of wastewater treatment without sacrificing efficiency. Large gaps remain, however, in our understanding of the fundamental formation mechanisms and the factors that control granule activity and stability. Magnetic resonance imaging (MRI) identified heterogeneous internal structures within aerobic granular sludge where relaxation rates and diffusion coefficients vary. Ultimately, these results will help improve modeling for optimization of granular sludge wastewater treatment process design. 1 INTRODUCTION Nuclear Magnetic Resonance (NMR) is sensitive over varying length and time scales to the physical and chemical environments, as well as translational motion, that hydrogen-bearing species experience. NMR is non-invasive, non-destructive, and can be applied to opaque samples in diverse applications including subsurface biogeochemical investigations and high-resolution imaging of micro-scale structures within biofilms. Especially in these applications, magnetic resonance can measure physical features or characteristic behaviors that are challenging to directly observe with other methods. The experiments described in this thesis use NMR or Magnetic Resonance Imaging (MRI) to explore biofilm – porous media systems. The experiments can be broadly classified into two categories, of which the first represents the vast majority of this thesis: 1) low-field NMR detection of macro-scale biofilm accumulation and biomineralization in porous media for in-situ bioremediation applications, and 2) high- field NMR and MRI measurements of granular biofilms used in wastewater treatment to identify micro-scale internal structural features and their influence on reactive transport within the biofilm. These two categories rely on the same method, NMR, but use different hardware configurations and field strengths. The two categories also focus on biofilm systems, though the biofilms of interest in the two cases are cultivated for different applications. Biofilms are mixed microbial aggregates, typically adhered to a surface with a sticky hydrogel called extracellular polymeric substance, or EPS [1, 2]. EPS consists of polysaccharides, proteins, DNA, and other entangled macro-molecules [3, 4]. While 2 some biofilms pose significant challenges to human health [5] or infrastructure [6], beneficial biofilms can be cultivated to effect biogeochemical conversions or hydrodynamic changes in the subsurface as part of a bioremediation project [7, 8]. Biofilms can also be used to induce mineral precipitation in the subsurface with applications including well-bore leakage mitigation [9] and geotechnical engineering [10, 11]. In the granular sludge system studied in the final chapter of this thesis, the biofilm granules are microbial aggregates which self-assemble under specific conditions without a support material. In this case, the granule is both the biofilm and the porous media. The remainder of this introduction puts the two types of NMR measurements in to historical context and outlines the organization of the thesis. Low-field NMR In natural materials such as soils and rock formations, the use of high-field NMR, typically defined as greater than 200 MHz, poses experimental challenges. Natural porous media, in contrast to model media like glass beads, contains minerals with a wide range of magnetic susceptibilities. When placed in a background magnetic field, these contrasts in magnetic susceptibility generate internal gradients in the local, pore-scale magnetic field that broaden the spectral peaks and cause rapid signal attenuation. Reducing the strength of the applied magnetic field reduces the influence of these local gradients, allowing signal to be captured from natural materials, though with reduced signal to noise and spectral resolution than high-field methods [12]. Low-field devices typically operate in the range between several hundred kHz to 10MHz. Low-field NMR 3 devices include well-logging tools used in the oil and gas industry to measure the distribution of pore sizes in the formation and quantify fuel-bearing reservoirs [13, 14], surface probes that measure soil moisture or water intrusion into concrete surfaces [15- 18], and small diameter probes, like the Vista Clara Javelin, to measure aquifer characteristics in the near subsurface [19]. The advent of low-cost and portable low-field NMR instrumentation in the last decade has led to an expansion of potential applications for the technology. Thus far, low-field NMR devices have not been applied in practice to monitor in-situ permeability reduction due to biofilm accumulation and biomineralization. The research within this thesis demonstrates that the Javelin low-field NMR logging tool can provide spatio- temporally resolved data regarding changing physico-chemical conditions in the near subsurface to improve monitoring capabilities and inform critical decision-making. Specifically, the device detects changes in signal relaxation response indicative of biofilm accumulation or microbially-induced calcite precipitation (MICP). Current methods to determine the extent of these processes in situ are limited and indirect. Using a NMR probe as a monitoring method may improve the efficacy of subsurface engineering projects involving biofilms and or MICP by allowing for simpler and more cost-effective assessment of their integrity. 4 High-field NMR and MRI High-field NMR has a rich history of use in laboratory biofilm systems. For more than two decades, high-field NMR has been used to study mass transport and hydrodynamics in a variety of model bioreactors using relaxometry and displacement measurements [20-26]. Potter et al. used diffusion-weighted NMR to detect bacterial cells and measure cell density within porous media [27]. MRI allows researchers to spatially resolve biofilm accumulation in porous media or capillaries through mapping regions with differing relaxation rates, where faster relaxation indicates the presence of biofilm [28, 29]. MRI can identify internal structural features of spherical biofilm aggregates, called granular sludge or biofilm granules [30, 31]. The high-field NMR experiments move the research from macro-scale field applications of commercially available low-field NMR technology to micro-scale exploration of fundamental processes related to formation of, and reactive mass transport within, granular sludge. By their very nature as spherical biofilm aggregates, granules are composed of a variety of microniches—aerobic, anoxic, anaerobic —where diverse bio-chemical conversions can occur simultaneously within the same granule [32, 33]. As a result, granular sludge treatment processes have the potential to vastly reduce the costs of cleaning wastewater by minimizing the capital costs associated with construction of separate process reactors and clarifiers, as well as reducing ongoing operations costs associated with aeration [34, 35]. The ultimate goal of the high-field NMR experiments on biofilm granules is to fill the gaps in our understanding of fundamental formation 5 mechanisms and conversion processes so that full exploitation of the technology for wastewater treatment can be realized. The high-field NMR research explores the structure and function of aerobic biofilm granules using pulsed field gradient (PFG) NMR and MRI by measuring spatially-resolved relaxation rates and diffusion coefficients of single granules in a static test tube. Ongoing experiments with flow-through cells will explore the role of wastewater particulates and particulate substrate in the formation, stability, and activity of the granules by measuring the propagator, or probability of displacement, of tracer particles. The results of these experiments will be used to refine the models used to simulate granule formation and substrate removal. These models are instrumental in process design optimization and hydraulic modeling of full-scale granular sludge wastewater treatment plants. Outline First, this thesis introduces NMR theory in Chapter 2, including discussions of the quantum and classical mechanical underpinnings of the technology, as well as excitation, relaxation, signal detection, basic pulse sequences, and an introduction to imaging and measurement of motion. Chapter 3 addresses more advanced NMR concepts related to encoding for diffusive motion and coherent flow, Brownstein and Tarr’s [13] characterization of signal relaxation behavior in various pore geometries and multi- dimensional methods to measure molecular motion. 6 Chapters 4 – 7 describe the low-field NMR experiments conducted during this thesis, beginning with a review of low-field borehole NMR applications in the near subsurface. This invited manuscript is under review for publication in the Vadose Zone Journal. Chapter 5 presents results of a laboratory experiment using the low-field NMR logging tool to detect biofilm accumulation in a model well-bore reactor. T2 relaxation distributions were measured over time while biofilm was cultivated in the reactor, resulting in a shortening of the mean log T2 relaxation time. Biofilm growth was confirmed with microscopy and microbiological methods. The manuscript was published in Groundwater Monitoring and Remediation. Following the successful laboratory demonstration, the biofilm detection experiments were conducted in a field study at an engineered field-testing facility in Butte, Montana. Again, the low-field NMR logging tool detected accumulation and removal of biofilm in the soil surrounding the test wells by recording changes in the measured T2 relaxation distributions. The manuscript comprising Chapter 6 is published in Environmental Science and Technology. Chapter 7 describes a second laboratory experiment using the low-field NMR logging tool, this time applied to the detection of calcite precipitation in a sand-filled model well-bore reactor. T2 relaxation distributions recorded during the biomineralization process showed an increase in the mean log T2 time and a bifurcation of the initial single relaxation mode into a small population with very fast relaxation and a larger population with slower relaxation. This manuscript is also published in Environmental Science and Technology. Chapters 8 and 9 shift the focus from low-field borehole NMR experiments in porous media to high field NMR and MRI experiments on wastewater biofilms. Chapter 7 8 describes research the author collaborated on with Dr. Maria Pia Herrling, a summer visitor to the Montana State University Magnetic Resonance Lab from Karlsruhe Institute of Technology in Karlsruhe, Germany. As part of her research into water diffusion in various biofilm structures, including floccular sludge, granular sludge, and biofilm grown on plastic carriers, Dr. Herrling measured diffusion-relaxation correlations at MSU with the author. The manuscript has been submitted for publication in Biotechnology and Bioengineering. Finally, Chapter 9 describes ongoing experimental work on the structure and diffusion properties of aerobic granular sludge biofilms sampled from full-scale wastewater treatment plants in the Netherlands. High-field MRI was used to image the complex and heterogeneous internal structure of the granules. These data were collected in the Netherlands at Wageningen University and Research and at the national NMR facility at the University of Utrecht under the supervision of Dr. Henk Van As as part of an international collaboration with Dr. Merle de Kreuk at Delft University of Technology. Additional high field PFG NMR experiments related to diffusion and transport within the granules are currently being conducted at MSU using samples from Dutch treatment plants. As this chapter includes work still in progress, the data and results presented are preliminary and require further validation prior to publication in peer reviewed journals. This research will be presented at the International Water Association’s 10th International Conference on Biofilm Reactors in Dublin, Ireland, in May 2017. 8 References 1. Characklis, W.G. and K.C. Marshall, Eds., Biofilms. 1990, New York: John Wiley & Sons, Inc. 2. Stoodley, P., et al., Biofilms as complex differentiated communities. Annual Review of Microbiology, 2002. 56: p. 187-209. 3. Allison, D.G., The biofilm matrix. Biofouling, 2003. 19(2): p. 139-150. 4. Sutherland, I.W., Biofilm exopolysaccharides: a strong and sticky framework. Microbiology, 2001. 147: p. 3-9. 5. Costerton, J.W., P.S. Stewart, and E.P. Greenberg, Bacterial biofilms: A common cause of persistent infections. Science, 1999. 284(5418): p. 1318-1322. 6. Camper, A.K., Organic matter, pipe materials, disinfectants and biofilms in distribution systems. 2014, IWA Publishing. p. 73-94. 7. Cunningham, A.B., et al., Subsurface biofilm barriers for the containment and remediation of contaminated groundwater. Bioremediation Journal, 2003. 7(3-4): p. 151-164. 8. Taylor, S.W. and P.R. Jaffe, Enhanced in-situ biodegradation and aquifer permeability reduction. Journal of Environmental Engineering-ASCE, 1991. 117(1): p. 25-46. 9. Cunningham, A.B., et al., Abandoned well CO2 leakage mitigation using biologically induced mineralization: current progress and future directions. Greenhouse Gases-Science and Technology, 2013. 3(1): p. 40-49. 10. Dejong, J.T., et al., Biogeochemical processes and geotechnical applications: progress, opportunities and challenges. Geotechnique, 2013. 63(4): p. 287-301. 11. Phillips, A.J., et al., Engineered applications of ureolytic biomineralization: a review. Biofouling, 2013. 29(6): p. 715-733. 12. Sanderlin, A.B., et al., Biofilm detection in natural unconsolidated porous media using a low-field magnetic resonance system. Environmental Science & Technology, 2013. 47(2): p. 987-992. 13. Brownstein, K.R. and C.E. Tarr, Importance of classical diffusion in NMR studies of water in biological cells. Physical Review A, 1979. 19(6): p. 2446-2453. 9 14. Timur, A., Pulsed nuclear magnetic resonance studies of porosity, movable fluid, and permeability of sandstones. Journal of Petroleum Technology, 1969. 21(JUN): p. 775-&. 15. Blümich, B., F. Casanova, and S. Appelt, NMR at low magnetic fields. Chemical Physics Letters, 2009. 477(4–6): p. 231-240. 16. Fukushima, E., Nuclear magnetic resonance as a tool to study flow. Annual Review of Fluid Mechanics, 1999. 31(1): p. 95. 17. Marble, A.E., et al., A constant gradient unilateral magnet for near-surface MRI profiling. Journal of Magnetic Resonance, 2006. 183(2): p. 228-234. 18. Sucre, O., et al., Low-field NMR logging sensor for measuring hydraulic parameters of model soils. Journal of Hydrology, 2011. 406(1–2): p. 30-38. 19. Walsh, D., et al., A small-diameter NMR logging tool for groundwater investigations. Groundwater, 2013. 51(6): p. 914-926. 20. Gjersing, E.L., et al., Magnetic resonance microscopy analysis of advective transport in a biofilm reactor. Biotechnology and Bioengineering, 2005. 89(7): p. 822-834. 21. Hornemann, J.A., et al., Biopolymer and water dynamics in microbial biofilm extracellular polymeric substance. Biomacromolecules, 2008. 9(9): p. 2322-2328. 22. Seymour, J.D., et al., Anomalous fluid transport in porous media induced by biofilm growth. Physical Review Letters, 2004. 93(19). 23. Seymour, J.D., et al., Magnetic resonance microscopy of biofouling induced scale dependent transport in porous media. Advances in Water Resources, 2007. 30(6- 7): p. 1408-1420. 24. Wagner, M., et al., Online assessment of biofilm development, sloughing and forced detachment in tube reactor by means of magnetic resonance microscopy. Biotechnology and Bioengineering, 2010. 107(1): p. 172-181. 25. Lewandowski, Z., et al., NMR imaging of hydrodynamics near microbially colonized surfaces. Water Science and Technology, 1992. 26(3-4): p. 577-584. 26. Van As, H. and P. Lens, Use of H-1 NMR to study transport processes in porous biosystems. Journal of Industrial Microbiology & Biotechnology, 2001. 26(1-2): p. 43-52. 27. Potter, K., et al., Assay for bacteria in porous media by diffusion-weighted NMR. Journal of Magnetic Resonance. Series B, 1996. 113: p. 9-15. 10 28. Hoskins, B.C., et al., Selective imaging of biofilms in porous media by NMR relaxation. Journal of Magnetic Resonance, 1999. 139(1): p. 67-73. 29. Seymour, J.D., et al., Magnetic resonance microscopy of biofilm structure and impact on transport in a capillary bioreactor. Journal of Magnetic Resonance, 2004. 167(322-327). 30. Gonzalez-Gil, G., et al., Cluster structure of anaerobic aggregates of an expanded granular sludge bed reactor. Applied and Environmental Microbiology, 2001. 67(8): p. 3683-3692. 31. Lens, P.N.L., et al., Diffusional properties of methanogenic granular sludge: H-1 NMR characterization. Applied and Environmental Microbiology, 2003. 69(11): p. 6644-6649. 32. Da-Wen, G. and T. Yu, Versatility and application of anaerobic ammonium- oxidizing bacteria. Applied Microbiology & Biotechnology, 2011. 91(4): p. 887- 894. 33. de Kreuk, M., J.J. Heijnen, and M.C.M. van Loosdrecht, Simultaneous COD, nitrogen, and phosphate removal by aerobic granular sludge. Biotechnology and Bioengineering, 2005. 90(6): p. 761-769. 34. de Kreuk, M.K., N. Kishida, and M.C.M. van Loosdrecht, Aerobic granular sludge - state of the art. Water Science and Technology, 2007. 55(8-9): p. 75-81. 35. Lotti, T., et al., Pilot-scale evaluation of anammox-based mainstream nitrogen removal from municipal wastewater. Environmental technology, 2015. 36(9): p. 1167-77. 11 INTRODUCTION TO NUCLEAR MAGNETIC RESONANCE Nuclear magnetic resonance (NMR) relies on the quantum physical property of angular momentum intrinsic to a single nucleus and the response of that nucleus to a magnetic field to study the behavior of macroscopic systems consisting of large ensembles of nuclei over varying length and time scales. The discussion in this thesis will begin with the quantum and classical mechanical basis for NMR measurements before moving into a description of basic NMR techniques for imaging and measurement of molecular motion. This chapter relies heavily on reference works by Paul Callaghan[1, 2]. Other primary original sources are referenced in the text where applicable. Quantum Mechanics NMR Theory For any single nucleus, there is a discrete set of energy states defined by quantum mechanics. Since we are observing the behavior of a sample composed of nuclei on the order of Avogadro’s number (1023), however, the range of possibilities for the ensemble appears continuous. Because of its fundamental connection to the subject of NMR, it is necessary to first discuss the quantum mechanical basis of nuclear angular momentum, often called spin angular momentum. 12 Spin Angular Momentum The spin state of a nuclear isotope is described by the angular momentum, or spin, quantum number I, which is a fixed integer or half-integer value and characterizes the nucleus in its stable ground state. The spin quantum number I exists in a basis set of discrete values of the angular momentum, m, measured along the z-axis, where m = –I, (-I + 1), (I -1), I. For example, the 1H proton and 13C both have I = ½ . This means that 1H and 13C have two discrete energy states possible during a measurement, m = - ½ and m = + ½ , referred to as ‘spin down’ and ‘spin up’, respectively. The effect of ‘spin’ is that each nucleus has a magnetic dipole moment, μ, where μ = γs. The constant of proportionality, γ, is called the gyromagnetic ratio and is defined as the ratio of the magnetic dipole moment (μ) to the nuclear angular momentum (s). The gyromagnetic ratio for 1H is γ = 2.675 x 108 rad/(T s) and is among the highest of all nuclear isotopes. This intrinsic property of the hydrogen proton, as well as its abundance in nature, explains the predominance of 1H NMR within the larger field of magnetic resonance research and applications. NMR measurements are conducted in order to explore the system energy state. In other words, we measure an observable quantity to describe the energy state of the system we are interested in and which informs us about the molecular environment. When we make a measurement, we affect the quantum state of the system. In fact, we must affect the quantum state of the system in order to make a measurement. The quantum mechanical nature of a spin system is given by the eigenvalue equation 𝐴𝐴|𝑎𝑎⟩ = 𝑎𝑎|𝑎𝑎⟩ (2.1) 13 where A is the observable of interest, the eigenvector |𝑎𝑎⟩ is a basis state of A, and the eigenvalue 𝑎𝑎 is the observed value of measurement A. The eigenvalue is a complex number, containing both amplitude and phase information. To interpret Equation (2.1), recall that in making quantum mechanical measurements, we are faced with the Heisenberg uncertainty principle. That is, we cannot simultaneously know both the position and momentum of an atomic nucleus; we can only know the probability of a nucleus having a given position and momentum. If a measurement of A is made while the system is in state|𝑎𝑎⟩, then the observed value, or amplitude, of the measurement must be 𝑎𝑎 with certainty. If the system, however, is in a general admixed state resulting from superposition, denoted by |𝛹𝛹⟩, then the eigenvalue is returned with the probability, |𝑎𝑎𝑚𝑚|2. To apply these concepts to the spin quantum number, I, consider the case where the observable of interest is the component of angular momentum about a particular axis, 𝐼𝐼 = 〈𝐼𝐼𝑥𝑥〉𝐢𝐢 + 〈𝐼𝐼𝑦𝑦〉𝐣𝐣 + 〈𝐼𝐼𝑧𝑧〉𝐤𝐤 where i, j, and k are unit vectors along the x, y, and z-axes, respectively. In the case of the operator, 𝐼𝐼𝑧𝑧, the equation ⟨𝛹𝛹|𝐼𝐼𝑧𝑧|𝛹𝛹⟩ = � |𝑎𝑎𝑚𝑚|2 𝑚𝑚 𝑚𝑚 (2.2) gives the probability that the measurement 𝐼𝐼𝑧𝑧 resulted in a change of energy state from some initial basis state to a final basis state. Other important operators include the raising and lowering operators, 𝐼𝐼+ = 𝐼𝐼𝑥𝑥 + 𝑖𝑖𝐼𝐼𝑦𝑦 and 𝐼𝐼− = 𝐼𝐼𝑥𝑥 − 𝑖𝑖𝐼𝐼𝑦𝑦, respectively. These operators convert |−1 2 � a basis state to a | + 1 2 � state, and vice versa. 14 Since position and momentum of Heisenberg’s uncertainty principle are also components of energy, as potential and kinetic energy, respectively, it is constructive to express changes in the quantum energy state of a system in terms of the Hamiltonian, or total energy operator, H. The dynamics of the spin system are described by the Schrödinger equation 𝑖𝑖ℏ 𝜕𝜕 𝜕𝜕𝜕𝜕 |𝛹𝛹(𝜕𝜕)⟩ = 𝐻𝐻|𝛹𝛹(𝜕𝜕)⟩ (2.3) where ℏ is Planck’s constant. The Schrödinger equation shows that the change in the energy state with respect to time is related to the total energy of the system. For a Hamiltonian constant in time, the evolution of the energy state with time is |𝛹𝛹(𝜕𝜕)⟩ = 𝑒𝑒𝑒𝑒𝑒𝑒 �−𝑖𝑖𝐻𝐻 𝜕𝜕 ℏ � |𝛹𝛹(0)⟩ (2.4) Spin Magnetism and the Zeeman Interaction Outside of an applied magnetic field, nuclear magnetic dipoles are randomly oriented and no net magnetization occurs. However, in the presence of a static magnetic field, B0, we observe the Zeeman effect where the magnetic dipole moments reside in one of two quantum energy states. The nuclear magnetic dipole moments align themselves either parallel or anti-parallel to the B0 field, with a slight preference for parallel alignment. The parallel ‘spin up’ alignment corresponds to the lower energy state| + 1 2 �, while anti-parallel ‘spin down’ alignment is the higher energy state|−1 2 �. For a proton in a static magnetic field, B0, along the z-axis, the Zeeman Hamiltonian is 15 𝐻𝐻𝑍𝑍𝑍𝑍𝑍𝑍𝑚𝑚𝑍𝑍𝑍𝑍 = −𝛾𝛾ℏ𝐵𝐵0𝐼𝐼𝑧𝑧 (2.5) This means that the difference in energy between the two possible spin states is equal to 𝛥𝛥𝛥𝛥 = 𝛾𝛾ℏ𝐵𝐵𝑜𝑜 and that the spins precess about the z-axis (Figure 2.1). Figure 2.1. The two quantum spin states are separated by an energy difference of 𝜸𝜸ℏ𝑩𝑩𝒐𝒐which is also the resonant frequency of spins within the system. The slight preference for the lower energy state yields a net magnetization on the order of parts per million. Writing Equation (2.5) in terms of angular frequency and dropping Planck’s constant, it is apparent that the intrinsic frequency of the system is equal to 𝛾𝛾𝐵𝐵0, called the Larmor frequency, 𝜔𝜔0 . The Larmor frequency is both the precession frequency of all the spin states around the z-axis as seen in the Zeeman Hamiltonian, but also the frequency of spins ‘flipping’ between the two possible energy states, m = - ½ and m = + ½. For a large number of nuclei, quantum properties can be expressed using classical statistics over the ensemble. The equation ⟨𝛹𝛹|𝐼𝐼𝑧𝑧|𝛹𝛹⟩ = 12 ��𝑎𝑎12�2 − �𝑎𝑎−12�2� (2.6) demonstrates that the ensemble average energy state resulting from the observation 𝐼𝐼𝑧𝑧, ⟨𝛹𝛹|𝐼𝐼𝑧𝑧|𝛹𝛹⟩ , is the difference between the populations in the spin up and spin down m = + ½ m = - ½ 16 states, expressed by �𝑎𝑎1 2 � 2 and �𝑎𝑎−1 2 � 2 , respectively. The Boltzmann energy distribution is derived from statistical mechanics and governs the relative sizes of the two populations. The probability of a particular energy state, Pn, within a distribution of energy states is defined as 𝑃𝑃𝑍𝑍 = exp �−∆𝛥𝛥 𝑘𝑘𝐵𝐵𝑇𝑇� � ∑ exp �−∆𝛥𝛥 𝑘𝑘𝐵𝐵𝑇𝑇� �𝑍𝑍 (2.7) where ΔE is the energy associated with each state, kB is the Boltzmann constant, and T is the absolute temperature. Because of the slight preference of spins at thermal equilibrium for the lower energy state| + 1 2 �, a polarization, 𝐼𝐼𝑧𝑧, aligned with the static magnetic field develops within a sample. Since the energy difference between the two states, 𝛾𝛾ℏ𝐵𝐵𝑜𝑜, is orders of magnitude less than 𝑘𝑘𝐵𝐵𝑇𝑇, the net polarization within a sample is typically in the part per million range. Moreover, there is no phase coherence between the spins, so it is not possible to directly measure 𝐼𝐼𝑧𝑧 . Measurement of the x-component of angular momentum, however, yields ⟨𝛹𝛹|𝐼𝐼𝑥𝑥|𝛹𝛹⟩ = 12 �𝑎𝑎12∗𝑎𝑎−12 + 𝑎𝑎−12∗ 𝑎𝑎12� (2.8) where 𝑎𝑎±1 2 ∗ is the complex conjugate of a. This equation shows that the ensemble average energy state resulting from the observation 𝐼𝐼𝑥𝑥 is the sum of the off-diagonal matrix components and reflects the phase coherence between the + ½ and – ½ spin states, where the relative phase, rather than the absolute phase, is significant. 17 To handle both the polarization and phase coherence, it is useful to introduce the spin density matrix 𝜌𝜌, a hermitian quantum mechanical operator that evolves according to the Schrödinger equation and directly provides the ensemble averaged expectation value for measurement A 〈𝛹𝛹|𝐴𝐴|𝛹𝛹〉 = 𝑇𝑇𝑇𝑇|𝐴𝐴𝜌𝜌| = 〈𝐴𝐴〉 = �𝑃𝑃𝛹𝛹 𝛹𝛹 〈𝛹𝛹|𝐴𝐴|𝛹𝛹〉 (2.9) where 𝑇𝑇𝑇𝑇|𝜌𝜌| is the trace of 𝜌𝜌—the sum of all state probabilities—and is therefore equal to 1. When I is the observable of interest for spin ½ nuclei, the spin density matrix is 𝜌𝜌 = ⎣ ⎢ ⎢ ⎢ ⎡ �𝑎𝑎1 2 � 2 𝑎𝑎−1 2 ∗ 𝑎𝑎1 2 𝑎𝑎1 2 ∗𝑎𝑎 − 1 2 �𝑎𝑎 − 1 2 � 2 ⎦ ⎥ ⎥ ⎥ ⎤ = � 12 + 〈𝐼𝐼𝑧𝑧〉 〈𝐼𝐼𝑥𝑥 − 𝑖𝑖𝐼𝐼𝑦𝑦〉 〈𝐼𝐼𝑥𝑥 + 𝑖𝑖𝐼𝐼𝑦𝑦〉 12 − 〈𝐼𝐼𝑧𝑧〉 � (2.10) The major implication of the spin density matrix is that specifying the vector components of the spin quantum number 𝐈𝐈 = 〈𝐼𝐼𝑥𝑥〉𝐢𝐢 + 〈𝐼𝐼𝑦𝑦〉𝐣𝐣 + 〈𝐼𝐼𝑧𝑧〉𝐤𝐤 allows full specification of the four matrix elements and therefore defines all the energy states of an ensemble of spin ½ nuclei. Recall, these energy states are the results of a direct NMR measurement of Ix, Iy, or Iz. On a macroscopic level, the net magnetization of a sample in the laboratory reference frame can be defined as 𝐌𝐌 = 𝑁𝑁𝛾𝛾ℏ �〈𝐼𝐼𝑥𝑥〉𝐢𝐢 + 〈𝐼𝐼𝑦𝑦〉𝐣𝐣 + 〈𝐼𝐼𝑧𝑧〉𝐤𝐤� (2.11) where N is the number of spins per unit volume. Here, then, we see the connection between the macroscopic magnetization in the laboratory reference frame and the quantum energy state of a single nucleus in our sample. Since we define the direction of 18 the B0 field as the z-axis, we can directly detect the quantum states 𝐼𝐼𝑥𝑥 and 𝐼𝐼𝑦𝑦 via an NMR measurement, where 𝐼𝐼𝑥𝑥 is the real component and 𝐼𝐼𝑦𝑦 is the imaginary component. Classical Mechanics NMR Theory Moving from the scale of a single quantum mechanical nucleus to the macro-scale net magnetization allows use of the language of classical mechanics to describe NMR theory and practice. Excitation When a pulse of oscillating current in the radiofrequency (rf) range is introduced along the y-axis in the plane orthogonal to B0, a magnetic field B1 is formed along the x- axis. The B1 field generates a torque, tipping the net magnetization, M, into the transverse plane, where it precesses around the z-axis. Analogous to quantum mechanical theory where the magnetic dipole moment produces precession in a static magnetic field, on a macroscopic level the Zeeman effect also produces precession of M around B0 as the magnetic field exerts a torque on the magnetization vector according to 𝑑𝑑𝑴𝑴 𝑑𝑑𝜕𝜕 = 𝛾𝛾𝑴𝑴 × 𝑩𝑩 (2.12) When the system is ‘on resonance’, both the oscillation of B1 and the precession of M occur at the Larmor frequency, 𝜔𝜔0 = 𝛾𝛾𝐵𝐵0, and the rf field is defined as 𝑩𝑩1(𝜕𝜕) = 𝐵𝐵1 cos(𝜔𝜔0𝜕𝜕) 𝐢𝐢 − 𝐵𝐵1 sin(𝜔𝜔0𝜕𝜕) 𝐣𝐣 (2.13) Performing the cross-product produces the following expressions for the time evolution of the magnetization vector in the laboratory reference frame following excitation: 19 𝑑𝑑𝑀𝑀𝑥𝑥 𝑑𝑑𝜕𝜕 = 𝛾𝛾�𝑀𝑀𝑦𝑦𝐵𝐵0 + 𝑀𝑀𝑧𝑧𝐵𝐵1𝑠𝑠𝑖𝑖𝑠𝑠𝜔𝜔0𝜕𝜕� 𝑑𝑑𝑀𝑀𝑦𝑦 𝑑𝑑𝜕𝜕 = 𝛾𝛾[𝑀𝑀𝑧𝑧𝐵𝐵1𝑐𝑐𝑐𝑐𝑠𝑠𝜔𝜔0𝜕𝜕 − 𝑀𝑀𝑥𝑥𝐵𝐵0] (2.14) 𝑑𝑑𝑀𝑀𝑧𝑧 𝑑𝑑𝜕𝜕 = 𝛾𝛾�−𝑀𝑀𝑥𝑥𝐵𝐵1𝑠𝑠𝑖𝑖𝑠𝑠𝜔𝜔0𝜕𝜕 − 𝑀𝑀𝑦𝑦𝐵𝐵1𝑐𝑐𝑐𝑐𝑠𝑠𝜔𝜔0𝜕𝜕� Solving Equations (2.14) for the initial condition M(t) = M0k gives 𝑀𝑀𝑥𝑥 = 𝑀𝑀0𝑠𝑠𝑖𝑖𝑠𝑠(𝜔𝜔1𝜕𝜕)𝑠𝑠𝑖𝑖𝑠𝑠(𝜔𝜔0𝜕𝜕) 𝑀𝑀𝑦𝑦 = 𝑀𝑀0𝑠𝑠𝑖𝑖𝑠𝑠(𝜔𝜔1𝜕𝜕)𝑐𝑐𝑐𝑐𝑠𝑠(𝜔𝜔0𝜕𝜕) (2.15) 𝑀𝑀𝑧𝑧 = 𝑀𝑀0𝑐𝑐𝑐𝑐𝑠𝑠(𝜔𝜔1𝜕𝜕) where 𝜔𝜔1 = 𝛾𝛾𝐵𝐵1. This solution shows that in the laboratory reference frame, the precession of M is a spiral, as the magnetization vector precesses around the B0 field at ω0, and about the B1 field at ω1 (Figure 2.2). Figure 2.2 Following a 90° rf excitation pulse, the net magnetization vector, M, precesses around B0 at ω0 and around B1 at ω1 in the laboratory reference frame. x y z B1 ω0t B0 ω1t M 20 The tip angle, α, is equal to ω1t. By controlling the duration of the rf pulse, t, and the amplitude of the B1 field, the net magnetization vector will lie in the transverse plane (α = 𝜋𝜋 2 ) where the induced signal is maximized. This rf pulse is called a 90°, or 𝜋𝜋 2 pulse. Similarly, an rf pulse of duration 2t will result in M aligned with the –z-axis, called a 180°, or π pulse. The precession of M as it returns to equilibrium induces a current that is measured as a decaying signal by the rf coil. Reference Frames To simplify further descriptions of the spin dynamics that occur following excitation with a resonant rf field, it is typical to use a rotating frame of reference with angular frequency ω. Recall the Zeeman Hamiltonian for a static magnetic field, B0, 𝐻𝐻𝑍𝑍𝑍𝑍𝑍𝑍𝑚𝑚𝑍𝑍𝑍𝑍 = −𝛾𝛾𝐵𝐵0𝐼𝐼𝑧𝑧 (2.16) In the rotating reference frame, an additional term is necessary to account for the frequency of the rotating frame itself, with the result 𝐻𝐻𝑍𝑍𝑍𝑍𝑍𝑍𝑚𝑚𝑍𝑍𝑍𝑍−𝑟𝑟𝑜𝑜𝑟𝑟 = −𝛾𝛾�𝐵𝐵0 − 𝜔𝜔 𝛾𝛾� �𝐼𝐼𝑧𝑧 (2.17) For a reference frame rotating in the same sense as the precession (clockwise), the apparent longitudinal magnetic field will be reduced by ω. When an oscillating rf field is applied in the transverse plane to excite the spins from equilibrium, the Hamiltonian in the rotating frame becomes 𝐻𝐻𝑟𝑟𝑜𝑜𝑟𝑟 = −𝛾𝛾�𝐵𝐵0 − 𝜔𝜔 𝛾𝛾� �𝐼𝐼𝑧𝑧 − 𝛾𝛾𝐵𝐵1𝐼𝐼𝑥𝑥 (2.18) When the system is ‘on resonance,’ ω = ω0 and the apparent longitudinal field disappears, leaving the effective magnetic field along the rotating frame x-axis with the 21 Hamiltonian 𝐻𝐻𝑟𝑟𝑜𝑜𝑟𝑟 = −𝛾𝛾𝐵𝐵1𝐼𝐼𝑥𝑥 (Figure 2.3). Here, the Ix operator is the linear combination of the raising and lowering operators, 1 2 (𝐼𝐼+ + 𝐼𝐼−), meaning that the energy change in the system with time corresponds to the flipping of spins between the ‘spin up’ and ‘spin down’ states at a rate of γB1. Figure 2.3. In the rotating reference frame, the static B0 field is not apparent and M lies along the -y-axis following excitation with a resonant 90° rf pulse. x y z B1 ω1t M 22 Relaxation The transverse magnetization decays over time following the rf pulse as the spins return to thermal equilibrium along the z-axis. This process is termed relaxation. The rate at which the net magnetization decays in the transverse plane and re-forms along the z-axis is governed by two relaxation mechanisms, T1 and T2. T1 relaxation, also called spin-lattice relaxation or longitudinal relaxation, is caused by the exchange of energy between spins and the environment, or lattice, and is related to the timescale for the net magnetization to return to thermal equilibrium along the z-axis. T1 relaxation typically occurs on the order of seconds for protons at room temperature. T2 relaxation, also called spin-spin relaxation or transverse relaxation, is related to the timescale for the net magnetization to decay in the transverse plane due to dephasing of spin coherence caused by molecular interactions. Energy exchange between magnetic dipoles creates micro-scale magnetic fields that dephase the spins within their sphere of influence. Since some measure of phase coherence is essential for generation and measurement of the induced signal, a loss of phase coherence leads to signal attenuation with time. T2 relaxation occurs on the order of seconds for liquids at room temperature and on the order of milliseconds for biopolymers in porous media. Auto-correlation Functions. The time-dependence of relaxation processes is due to molecular motion. A constructive way to describe time-dependent behavior is with the use of auto-correlation functions. When stochastic variable A is a molecular quantity that varies as a function of time, then the auto-correlation function of A is 23 𝐺𝐺(𝜕𝜕) = � 𝐴𝐴(𝜕𝜕′)𝐴𝐴(𝜕𝜕′ + 𝜕𝜕)𝑑𝑑𝜕𝜕′∞ 0 (2.19) The auto-correlation function G(t) describes the probability that A(t’) is correlated to A(t’ + t) at some later time. When the system is stationary as is the case in most NMR measurements, the origin of time does not matter; only the interval of time over which measurements are collected is important. Further, in an ensemble of spins where any one spin is statistically equivalent to any other spin over an appropriate period of time, the average over time that is implied by Equation (2.19) can also be interpreted as an average over all particles. Incorporating these concepts and replacing terms into Equation (2.19) gives 𝐺𝐺(𝜕𝜕) = < 𝐴𝐴(0)𝐴𝐴(𝜕𝜕) > (2.20) where is the well-defined ensemble average value of A during the interval 0 to t. At time zero, G(t) is equal to the mean squared value of A, . With increasing time, the relationship between the initial and final values of A decays, as the molecule ‘loses memory’ of its previous states. The characteristic timescale over which this process occurs is called the correlation time, τc. When the experimental time, t, is greater than the correlation time, τc, then there is no correlation with the initial state. The correlation time can be understood as the time for a molecule (nucleus) to rotate about its own axis and is defined by the integral 𝜏𝜏𝑐𝑐 = ∫ < 𝐴𝐴(0)𝐴𝐴(𝜕𝜕) > 𝑑𝑑𝜕𝜕∞0 < 𝐴𝐴(0)2 > (2.21) 24 Spectral Density Functions. Relaxation is caused by local spin interactions, which vary by both magnitude and the rate of fluctuation of the dipolar Hamiltonian, HD. In a relaxation experiment where A is the fluctuation of dipolar interactions between spins resulting from molecular tumbling, spin relaxation times are sensitive to the spectrum of the auto-correlation function, its Fourier transform. This spectrum is called the spectral density function, J(ω), and describes how the magnetic field fluctuations resulting from molecular interactions depend on time and the frequency of precession, ω. For spin-½ nuclei within the Zeeman interaction created by the static magnetic field, B0, there are three possibilities for behavior between interacting spins. Both interacting spins may remain in their original energy states, described by J(0)(ω), 𝐽𝐽(0)(𝜔𝜔) = 2415𝑇𝑇𝑖𝑖𝑖𝑖6 𝜏𝜏𝑐𝑐1 + 𝜔𝜔2𝜏𝜏𝑐𝑐2 (2.22) where rij is the radial distance between spin i and spin j. When one of the two spins changes its energy state, J(1)(ω) results where 𝐽𝐽(1)(𝜔𝜔) = 415𝑇𝑇𝑖𝑖𝑖𝑖6 𝜏𝜏𝑐𝑐1 + 𝜔𝜔2𝜏𝜏𝑐𝑐2 (2.23) Finally, if both spins flip to the other energy state, the resulting spectral density is defined as J(2)(ω), 𝐽𝐽(2)(𝜔𝜔) = 1615𝑇𝑇𝑖𝑖𝑖𝑖6 𝜏𝜏𝑐𝑐1 + 𝜔𝜔2𝜏𝜏𝑐𝑐2 (2.24) Using these expressions for the spectral density function, the differences between the mechanisms for T1 relaxation as opposed to T2 relaxation is apparent. The T1 relaxation rate at the Larmor frequency, ω0, is given by the equation 25 1 𝑇𝑇1 = (𝜇𝜇04𝜋𝜋)2 𝛾𝛾4ℏ2 32 𝐼𝐼(𝐼𝐼 + 1)�𝐽𝐽(1)(𝜔𝜔0) + 𝐽𝐽(2)(2𝜔𝜔0)� (2.25) Qualitatively, this equation shows that T1 relaxation is affected by spins exchanging energy with the environment, or lattice, as they seek to return to thermal equilibrium within the Zeeman interaction. There is a contribution from spins precessing at frequency ω0 as well as a contribution at a frequency of 2ω0. There is no contribution from spins that remain in the original energy state. Conversely, the T2 relaxation rate at the Larmor frequency, ω0, is given by the equation 1 𝑇𝑇2 = (𝜇𝜇04𝜋𝜋)2 𝛾𝛾4ℏ2 32 𝐼𝐼(𝐼𝐼 + 1) �14 𝐽𝐽(0)(0) + 52 𝐽𝐽(1)(𝜔𝜔0) + 14 𝐽𝐽(2)(2𝜔𝜔0)� (2.26) From this expression, it is evident that T2 relaxation also depends on the zero-frequency spectral density term, 𝐽𝐽(0)(0), wherein spins remain in their original energy states. This term implies that there is another energy exchange mechanism aside from the Zeeman interaction that contributes to T2 relaxation. For this reason, T2 relaxation will occur at the same rate or faster than T1 relaxation, but never slower. As the precession frequency, ω0, or the correlation time of the magnetic field fluctuations, τc, increases, the contribution of the zero-frequency term also increases. Faster precession frequencies and longer correlation times, therefore, cause a divergence between the T1 and T2 relaxation times (Figure 2.4). 26 Figure 2.4. T1 and T2 relaxation times are nearly equal in liquids for a given Larmor frequency. In solids, T1 and T2 diverge with T2 becoming much shorter than T1 because of long correlation times, τc. Moving now from quantum energy states and the scale of the molecule to the macro-scale, relaxation can be described as a process affecting the net magnetization vector of the sample evolving over time. The process of T1 relaxation, acting only along the longitudinal axis and governed by the Zeeman interaction, can be described phenomenologically by the equation 𝑑𝑑𝑀𝑀𝑧𝑧 𝑑𝑑𝜕𝜕 = −𝑀𝑀𝑧𝑧 −𝑀𝑀0 𝑇𝑇1 (2.27) where 𝑀𝑀0 is the initial equilibrium magnetization. The solution is 𝑀𝑀𝑧𝑧(𝜕𝜕) = 𝑀𝑀𝑧𝑧(0) exp �− 𝜕𝜕𝑇𝑇1� + 𝑀𝑀0 �1 − exp �− 𝜕𝜕𝑇𝑇1�� (2.28) The phenomenological equation describing T2 relaxation, which occurs only in the transverse plane, is 𝑑𝑑𝑀𝑀𝑥𝑥,𝑦𝑦 𝑑𝑑𝜕𝜕 = −𝑀𝑀𝑥𝑥,𝑦𝑦 𝑇𝑇2 (2.29) lo g (T 1, T 2 ) T2 T1 log (1/ω0τc) solids 1/τc <<ω0 liquids 1/τc >>ω0 ω0τc = 1 27 with the solution for a homogeneous sample 𝑀𝑀𝑥𝑥,𝑦𝑦(𝜕𝜕) = 𝑀𝑀𝑥𝑥,𝑦𝑦(0) exp �− 𝜕𝜕𝑇𝑇2� (2.30) These equations show that the magnetization decays with time as an exponential function and applies where the interaction terms related to transverse relaxation are weak, as in the case of liquid-state molecules. Solids and macromolecules which are rotationally constrained undergo very slow motions and rapid signal decay that is better described by more complicated equations. Combining the expressions for the change in M due to both excitation and relaxation in the rotating reference frame, we obtain the Bloch equations 𝑑𝑑𝑀𝑀𝑥𝑥 𝑑𝑑𝜕𝜕 = 𝛾𝛾𝑀𝑀𝑦𝑦�𝐵𝐵0 − 𝜔𝜔 𝛾𝛾� � −𝑀𝑀𝑥𝑥𝑇𝑇2 𝑑𝑑𝑀𝑀𝑦𝑦 𝑑𝑑𝜕𝜕 = 𝛾𝛾𝑀𝑀𝑧𝑧𝐵𝐵1 − 𝛾𝛾𝑀𝑀𝑥𝑥�𝐵𝐵0 − 𝜔𝜔 𝛾𝛾� � − 𝑀𝑀𝑦𝑦𝑇𝑇2 (2.31) 𝑑𝑑𝑀𝑀𝑧𝑧 𝑑𝑑𝜕𝜕 = −𝛾𝛾𝑀𝑀𝑦𝑦𝐵𝐵1 − 𝑀𝑀𝑧𝑧 −𝑀𝑀0𝑇𝑇1 These equations describe the precession of the magnetization in the frequency terms, as well as the decay of the magnetization over time in the relaxation terms. Similarly, the induced signal contains complex phase and exponential decay terms. 28 Experimental Background Before moving into a discussion of the practice of NMR—how to manipulate spin dynamics to extract meaningful information—it is necessary to first describe briefly the components of NMR hardware that make the measurements possible. Experimental Equipment A magnetic resonance system includes, on the simplest level, a magnet to create the B0 field, a spectrometer to deliver the pulses of current, an rf coil to transmit and receive the current to and from the sample, and a computer to control the system. The high-field magnets in the College of Engineering Magnetic Resonance Lab at MSU (250 MHz and 300MHz) are super-conducting magnets made with a coil of copper wire several kilometers in length. The coil is maintained at a low temperature with liquid helium and nitrogen to minimize resistance within the wire, keeping the wire superconducting. The magnets have a vertical bore that holds samples ranging between approximately 5—25mm in diameter. The samples are loaded into the magnet within an rf coil. The coil is composed of a ‘birdcage’ of copper wire positioned so as to create an orthogonal B1 field and receive the induced signal. Gradient coils are often also included around the sample to spatially vary the magnitude of the applied magnetic field. The spectrometer delivers rf pulses of current, gated to the proper pulse design according to pulse duration and frequency of current oscillation. The same coils transmit and receive the current so hardware may impose limitations on the time resolution of 29 some NMR measurements, especially where signal relaxation occurs on the timescale of the conversion between coil modes. The low-field NMR magnets (245/290 kHz and 425/360 kHz) used in some of the experiments described later are down-the-borehole solid magnets measuring 4.5 feet long and 3.5 inches in diameter. These magnets are designed to be lowered into a well casing and project a vertical B0 field into the soil surrounding the well. The static magnetic field loses strength with radial distance from the well center, with peak sensitivity between 5— 8 inches from the well center, depending on the operating frequency. The rf coil is contained within the same probe as the solid magnet. The spectrometer and computer are housed in a surface station. Signal Detection When the net magnetization of a sample is excited from equilibrium with an infinitesimally short resonant rf pulse, the resulting precession of M at the Larmor frequency in the laboratory reference frame induces a current in the rf coil according to Faraday induction. This induced current is the basis for NMR signal detection. The rf coil, a ‘birdcage’ (though solenoid coils are more efficient), is aligned orthogonal to the z-axis such that the coil output is an oscillating voltage, 𝑉𝑉(𝜕𝜕) = 𝑉𝑉0 cos(𝜔𝜔0𝜕𝜕). The strength of the signal is proportional to the Larmor frequency, 𝛾𝛾𝐵𝐵0. Higher field magnets (large B0) or a high gyromagnetic ratio, γ, increase the measurable signal to noise ratio and thereby improve sensitivity. Hydrogen protons have the largest gyromagnetic ratio of any stable nuclear isotope which, together with their natural abundance in materials of 30 interest, helps explain the prevalence of 1H NMR within the larger field of magnetic resonance. Since the initial spin density is proportional to the equilibrium polarization, 𝜌𝜌(0)~𝐼𝐼𝑧𝑧, the resulting spin density matrix in the rotating frame following excitation has proportionality of the form 𝜌𝜌𝑟𝑟𝑜𝑜𝑟𝑟(𝜕𝜕)~𝐼𝐼𝑦𝑦 cos�(𝜔𝜔0 − 𝜔𝜔)𝜕𝜕� + 𝐼𝐼𝑥𝑥 sin�(𝜔𝜔0 − 𝜔𝜔)𝜕𝜕� (2.32) In order to separately measure the 𝐼𝐼𝑥𝑥 and 𝐼𝐼𝑦𝑦 components of the spin density matrix, corresponding to the real and imaginary parts of the signal, respectively, the rf coil uses the process of heterodyne detection. Heterodying with two quadrature detection channels involves mixing the induced signal voltage with the output from a reference rf oscillator orthogonal to both the z-axis and the receiving rf coil. Heterodyning is mathematically equivalent to multiplying the induced voltage by a complex signal, exp(𝑖𝑖𝜔𝜔𝜕𝜕), and filtering out the sum frequency term, with the result that 𝑉𝑉(𝜕𝜕) = 12𝑉𝑉0[cos(𝜔𝜔0𝜕𝜕 − 𝜔𝜔𝜕𝜕) − 𝑖𝑖 sin(𝜔𝜔0𝜕𝜕 − 𝜔𝜔𝜕𝜕)] (2.33) Thus, we directly measure �𝐼𝐼𝑥𝑥 + 𝑖𝑖𝐼𝐼𝑦𝑦� in the rotating reference frame at the heterodyne mixing frequency, ω. When ω = ω0, the measured signal consists of two components 90° out of phase. When ω ≠ ω0, the signal will oscillate at the offset frequency, ∆𝜔𝜔 = 𝜔𝜔0 − 𝜔𝜔. The resulting phase factor, exp (𝑖𝑖𝑖𝑖), can be removed during signal processing. 31 The complex signal 𝑆𝑆(𝜕𝜕) is well-suited to analysis with Fourier transforms between the conjugate variables, ω and t. The Fourier transform of the measured time- domain signal is expressed as 𝐹𝐹{𝑆𝑆(𝜕𝜕)} = 𝑠𝑠(𝜔𝜔) = � 𝑆𝑆(𝜕𝜕) exp(−𝑖𝑖𝜔𝜔𝜕𝜕) 𝑑𝑑𝜕𝜕∞ −∞ (2.34) and produces a spectrum in the frequency domain, 𝑠𝑠(𝜔𝜔). The inverse Fourier transform of the spectrum returns the original signal by 𝐹𝐹−1{𝑠𝑠(𝜔𝜔)} = 𝑆𝑆(𝜕𝜕) = 12𝜋𝜋� 𝑠𝑠(𝑓𝑓) exp(𝑖𝑖𝜔𝜔𝜕𝜕) 𝑑𝑑𝜔𝜔∞−∞ (2.35) where 𝑓𝑓 = 𝜔𝜔 2𝜋𝜋� and converts between cyclic and angular frequency. For example, the Free Induction Decay, or FID, is the simplest NMR measurement and is the result of free precession of spins that induce an oscillating, decaying signal in the time domain. The FID consists of a single 90° rf pulse followed immediately by signal acquisition (Figure 2.5). The FID decays at a rate of 1 𝑇𝑇2∗� which includes effects from an inhomogeneous magnetic field and from molecular interactions in the transverse plane. 32 The Fourier transform of the FID is, in the real spectrum, a Lorentzian with full- width-half-maximum (FWHM) of 1 𝜋𝜋𝑇𝑇2∗� , called the absorption spectrum, and an imaginary spectrum called the dispersion spectrum. The integral of the phase-corrected absorption spectrum is equal to the amplitude of the NMR signal. The FID produces a signal 𝑁𝑁𝛾𝛾𝑇𝑇𝑇𝑇 ��𝐼𝐼𝑥𝑥 + 𝑖𝑖𝐼𝐼𝑦𝑦�𝜌𝜌𝑟𝑟𝑜𝑜𝑟𝑟(𝜕𝜕)� = 𝑖𝑖𝑀𝑀0 exp(−𝑖𝑖(𝜔𝜔0 − 𝜔𝜔)𝜕𝜕) (2.36) which relates the observable 𝑁𝑁𝛾𝛾�𝐼𝐼𝑥𝑥 + 𝑖𝑖𝐼𝐼𝑦𝑦� operating on the spin density matrix in the rotating frame 𝜌𝜌𝑟𝑟𝑜𝑜𝑟𝑟 to the time and phase evolution of the magnetization. In practice, the NMR signal is not recorded as a continuous function, but is rather sampled and digitized for later processing. A finite set of N points are sampled in the time domain, spaced by the dwell-time interval, T. When Fourier transformed, the data set in the frequency domain has a spectral width equal to the inverse of the dwell time, 1 𝑇𝑇� , with a digital resolution of 1 𝑁𝑁𝑇𝑇� . FT 90° rf pulse real signal imaginary signal time t t real spectrum imaginary spectrum ω ω Δωω0 ω0 Figure 2.5. The Free Induction Decay (FID) measurement produces complex decaying signal in the time domain and a spectrum in the frequency domain. 33 Basic Pulse Sequences NMR measurements consist of orchestrated sequences of rf pulses and applied magnetic field gradients which manipulate spin dynamics and encode for observables of interest, as well as wait times and signal acquisition times to allow the evolution and collection of signal that illuminates some aspect of the physico-chemical system. There are several measurements fundamental to NMR which will be described here in some detail. These include inversion recovery, the Hahn spin echo, the Carr-Purcell echo train and the stimulated echo. Each of these experiments can be conceptualized on the macro- scale using the net magnetization vector, M, influenced by the Zeeman Hamiltonian and subject to T1 and T2 relaxation. More complicated measurements take elements of these basic techniques and re-combine them to provide additional information about the sample under study. Typically, the same measurement is performed N successive times and the signal is averaged across all the measurements to improve the signal-to-noise ratio. Signal adds coherently while noise adds in random phase where its average approaches zero. The time between experiment repetitions depends on the T1 relaxation time of the sample since it is typically desirable for the net magnetization to return to its maximum along the z-axis prior to repeating the experiment. The timing of NMR experimental elements is displayed in a pulse sequence diagram, which typically includes the rf pulse timing and sequence on the first row with time increasing to the right. Applied magnetic field gradients are included in the next rows, depending on the axis along which they are applied. Acquired signal can be shown in-line with the rf or gradient sequence or may be included separately on its own line. 34 Inversion Recovery. The inversion recovery experiment measures the T1 relaxation time of a sample by first inverting M onto the –z-axis with a 180° rf pulse (Figure 2.6). M decays in magnitude as the spins experience spin-lattice relaxation and begin to return to thermal equilibrium. After some time τ, a 90° rf pulse tips any remaining magnetization into the transverse plane where it can be measured as it precesses at the Larmor frequency (Figure 2.7). Figure 2.6. The inversion recovery pulse sequence measures T1 relaxation by inverting the magnetization and allowing T1 relaxation to occur before signal acquisition. Figure 2.7. Evolution of the magnetization vector during the inversion recovery experiment. 180x° rf pulse time 90x° τ x y z M x y z M x y z M x y z M ω0 35 Repeating the experiment for various τ times produces a curve of equation 𝑀𝑀𝑦𝑦(𝜕𝜕) = 𝑀𝑀0(1 − 2 exp �−𝜕𝜕 𝑇𝑇1� � (2.37) As seen in Figure 2.8, at τ = 0.6931T1 the measured signal amplitude is zero as the excited net magnetization crosses the transverse plane on its return to thermal equilibrium. This result is particularly useful when only one component of a sample is of interest since it allows for suppression of signal from any spins with a T1 time distinct from other spins. Applying an rf pulse at an interval τ = 0.6931T1 prior to the experimental pulse sequence effectively nulls the signal from spins with that particular T1 relaxation time and allows for selective acquisition of signal from spins relaxing at a different rate. This method is particularly useful in biological tissues where the water signal can overwhelm signal from other tissue components. Figure 2.8. The amplitude of the net magnetization is equal to zero at 0.6931T1, allowing for signal from spins with a specific T1 relaxation time to be nulled in a measurement. Hahn Spin Echo. Despite the best efforts of hardware manufacturers to design a NMR magnet with a perfectly homogenous B0 field, some degree of inhomogeneity is t (s) Mz τ = 0.6931T1 M0 -M0 36 unavoidable. Spins that experience a slightly different magnetic field will precess at a slightly different frequency from other spins in the sample. This phenomenon leads to dephasing of spins in the transverse plane, as some move either faster or slower than the Larmor frequency. In 1950, Erwin Hahn [3] demonstrated that this component of signal attenuation is reversible through the application of a 180° rf pulse in the transverse plane at some time τ after the 90° excitation pulse (Figure 2.9). Figure 2.9. The Hahn echo pulse sequence and resulting evolution of the net magnetization. A 180°y rf pulse refocuses signal to produce an echo at time 2τ following the 90°x rf excitation pulse. The evolution figures are show below the position on the pulse sequence where they occur. The 180° pulse has the effect of refocusing the signal as the faster precessing spins are placed ‘behind’ the slower moving spins. The spin coherence is maximized at 180y° rf pulse time 90x° τ 2τ x y z M x y z ω0- ω0+ x y z ω0- ω0+ x y z ω0- ω0+ x y z M 37 time 2τ, when an ‘echo’ in the signal forms. Since the signal is still subject to T2 relaxation during the time 2τ, the echo amplitude is less than the initial amplitude. Only the attenuation due to magnetic field homogeneity can be re-focused. Relaxation due to homo-nuclear spin-spin interactions within the sample cannot be reversed. CPMG Echo Train. Following Hahn’s discovery of the spin echo, Carr and Purcell in 1954 [4] expanded the concept by performing successive 180° rf pulses to produce a series of echoes. Meiboom and Gill [5] modified the echo train in 1958 by use of quadrature 180y° rf pulses to compensate for small turn-angle errors. The resulting experiment, the CPMG sequence, allows for the direct measurement of T2 relaxation time in one experiment. The echo envelope decays at a rate of 1 𝑇𝑇2� . 38 Figure 2.10. The CPMG pulse sequence, consisting of a 90° pulse followed by a series of 180° pulses, is used to measure T2 relaxation where the echo envelope decays at a rate of 1/T2. Stimulated Echo. For materials where the T2 relaxation time is much shorter than the T1 relaxation time, such as solids, phase coherence expires much faster than the sample polarization. In other words, signal is no longer measureable because of T2 relaxation though incoherent magnetization remains in the transverse plane. The stimulated echo can be used to obtain signal from materials with short T2 times, especially when molecular motion is the observable of interest. The stimulated echo experiment combines elements from the previously discussed pulse sequences—inversion recovery and the spin echo. Figure 2.11 shows the pulse sequence with the induced signal on the rf pulse line. After the initial 90x° excitation pulse tips M onto the y-axis, the spins relax according to both T1 and T2 relaxation until the time τ, when another 90x° pulse is applied. The second pulse rotates the y-component of the magnetization into the longitudinal plane where only T1 relaxation occurs. The 180y° rf pulse time 90x° τ 3τ 180y° 180y° 5τ 180y° 7τ signal time 39 remaining polarization can be ‘stored’ for a time τ’ (> τe), called fast exchange, there is a single relaxation time for the system since each spin will experience 70 a different relaxation rate in each domain sampled during the measurement, effectively averaging the relaxation rates. Intermediate exchange results in non-exponential signal decay. A second model relies on a geometric description to relate relaxation and diffusion in porous media. In this model, we distinguish between the relaxation of the bulk fluid in the pore space, TiB, and the relaxation of the fluid directly interacting with the pore surface, TiS. Here, the relaxation time can refer to either spin-lattice (T1) or spin- spin relaxtion (T2), with the general case denoted as Ti. The solid matrix introduces surface relaxation sinks that enhance relaxation of the spins nearest to the pore walls. These sinks can be paramagnetic ions within the mineral surface of the pore walls or a local hindering of rotational mobility resulting from increased dipole-dipole interactions between liquid and solid phase molecules. Clearly, the surface to volume ratio of the pore, S/V, is important in this model and is related to pore size and geometry. There are also differences in magnetic susceptibility between the solid matrix and the bulk liquid, resulting in internal magnetic field gradients near the pore walls. Diffusion of spins within these internal inhomogeneities in the magnetic field further enhance relaxation. The geometric model was developed in detail by Brownstein and Tarr in 1979.[4] The authors observed fast and multi-exponential signal decay behavior in the water within biological cells. They concluded that the multi-exponential behavior was a consequence of the geometry of the cell and that it is possible to use NMR data to make inferences about the size and shape of pores (or cells). Brownstein and Tarr approached the problem by assuming diffusion of the magnetization density, M(r,t), according to 71 Fick’s Laws. They integrated over the pore volume and applied the initial condition, M(r, 0) = M(0)/V to solve for the general normal mode solution 𝑀𝑀(𝑡𝑡) = 𝑀𝑀(0)�𝐼𝐼 𝑛𝑛 exp �−𝑡𝑡 𝑇𝑇𝑛𝑛� �∞ 𝑛𝑛=0 (3.18) where 𝐼𝐼𝑛𝑛 = 𝑎𝑎𝑛𝑛 ∫𝑑𝑑𝐫𝐫𝑉𝑉 𝑢𝑢𝑛𝑛 and describes the relative intensity. The parameter n is the mode number, un is an eigenfunction, and the decay time Tn (actually T1n or T2n) is an eigenvalue. Equation 2.15 shows that the evolution of the net magnetization proceeds as a sum of decreasing exponential functions in time—resulting in the observed multi- exponential decay. In and Tn depend on D, the self-diffusion coefficient, a, the characteristic pore size, and ?̅?𝜌, the surface relaxivity, an empirical parameter describing the average sink strength of the surface. This solution assumes that there are no relaxation sinks within the pore volume, only on the active surface of the pore. Solving for In and Tn for planar, cylindrical and spherical geometries reveals the importance of the dimensionless sink strength parameter, ?̅?𝜌𝑎𝑎/𝐷𝐷. For each geometry, the mode amplitude, In, depends on ?̅?𝜌𝑎𝑎/𝐷𝐷, which can be used to assign regimes analogous to the fast and slow exchange regimes of the first model. When there is fast diffusion and ?̅?𝜌 is weak compared to D such that ?̅?𝜌𝑎𝑎/𝐷𝐷<<1 – the fast exchange regime – there is a single relaxation mode, I0, for all geometries and the spins will experience single exponential decay with a relaxation rate, 𝑇𝑇0−1~?̅?𝜌(𝑆𝑆 𝑉𝑉)⁄ . In the slow exchange regime, when ?̅?𝜌 is strong compared to D and ?̅?𝜌𝑎𝑎/𝐷𝐷>>1, the lowest relaxation mode still dominates but there is increasing influence of the higher modes. This means that spins will exhibit multi- exponential decay during the measurement timescale. In the slow exchange regime, 72 therefore, relaxation time, 𝑇𝑇0~ 𝑎𝑎2 𝐷𝐷⁄ , corresponds to the time to diffuse across the pore since the spin will be lost to relaxation once it interacts with the surface. These results predict the same relationship between the decay behavior of the normalized echo amplitude and the relaxation and diffusion properties of a system as the first, non-geometric model – single exponential decay when the spins can sample the entire pore, and multi-exponential decay when they cannot. The higher mode decay rates, 𝑇𝑇𝑛𝑛−1, are visible only in the slow exchange/slow diffusion regime, are nearly independent of ?̅?𝜌, and are of an order 𝑎𝑎2 𝑙𝑙2𝜋𝜋2𝐷𝐷⁄ . Because of this relationship, we can estimate the range of pore sizes that may exhibit multi-exponential decay when examined with PFG NMR. Assuming D = 2.5 x 10-5 cm2/s and 𝑇𝑇𝑛𝑛 is between 1 µs (due to hardware limitations) and 2 s (the relaxation of bulk water), the pore dimension, a, is in the range of 1 – 30 µm. This is exactly the size range of biological cells and pore sizes in natural porous media like sedimentary rock. While it is difficult to independently and reliably estimate the average surface relaxivity, ?̅?𝜌, the Brownstein-Tarr model is widely used to obtain pore-size distributions from multi-exponential relaxation data and complements q-space data as a way to characterize pore structure and geometry. Multidimensional PFG and Relaxation NMR Multidimensional PFG-NMR experiments encode the induced signal in multiple independent dimensions and can take the form of correlation or exchange experiments. Correlation experiments involve the measurement of two different parameters, like 73 diffusion (D) and T2, at the same time to see how one parameter is related to the other. In the case of the D-T2 experiment, for example, we are interested in how molecular translational mobility (D) is correlated with molecular rotational mobility (T2). Exchange experiments, on the other hand, encode for one parameter at two different times to probe molecular migration between domains. The measured signal is transformed to produce a spectrum using either the Fourier or Laplace transform. Which type of transform is appropriate for a given signal depends on the information sought from the sample. Oscillating, decaying signal collected in the time domain can be Fourier transformed to produce a spectrum of the frequencies contributing to the signal in the frequency domain. When the signal is collected under the influence of time-varying gradients and coherent flow, the Fourier transformed data will produce a spectrum of displacements, the propagator. Diffusive displacements result in a signal that decays exponentially with respect to q2, the squared gradient pulse area. A Fourier transform of the diffusion data with respect to q produces a Gaussian displacement spectrum where the width depends on the diffusion coefficient, D. If data is collected from a sample exhibiting multi-exponential signal decay due to a range of relaxation domains or diffusion coefficients, Fourier transformation of the signal will result in a superposition of Gaussian distributions, making it difficult to extract the relaxation rates or diffusion coefficients associated with each domain. Equation 2.19 shows the multi-exponential signal E(q) collected from a sample with multiple diffusion coefficients. A Fourier transform of the signal produces a spectrum of displacements, 𝑃𝑃�(𝑍𝑍), rather than a spectrum of diffusion coefficients, 𝑃𝑃(𝐷𝐷). 74 𝐸𝐸(𝑞𝑞) = ∫𝑃𝑃(𝐷𝐷) exp(−𝑞𝑞2𝐷𝐷∆)𝑑𝑑𝐷𝐷 (3.19) 𝑃𝑃�(𝑍𝑍) = �𝑃𝑃(𝐷𝐷)(2𝜋𝜋𝐷𝐷∆)−1 2� exp (−𝑍𝑍2 2𝐷𝐷∆)𝑑𝑑𝐷𝐷⁄ (3.20) The inverse Laplace transform (ILT), ℒ−1{𝐸𝐸(𝑞𝑞2,∆},with respect to q2 will produce a spectrum, or distribution, of the probability of having a given diffusion coefficient, 𝑃𝑃(𝐷𝐷). 𝑃𝑃(𝐷𝐷) = ℒ−1{𝐸𝐸(𝑞𝑞2,∆} (3.21) 𝐸𝐸(𝑞𝑞2,∆) = ℒ{𝑃𝑃(𝐷𝐷)} = � 𝑃𝑃(𝐷𝐷) exp(−𝑞𝑞2𝐷𝐷∆)𝑑𝑑𝐷𝐷 ∞ 0 (3.22) Likewise with measurements involving sub-ensembles with different relaxation rates, the ILT of relaxation data, ℒ−1{𝑆𝑆(𝑡𝑡)}, returns a distribution of the relaxation decay rates that contribute to the multi-exponential decay, 𝑓𝑓(𝑅𝑅). 𝑓𝑓(𝑅𝑅) = ℒ−1{𝑆𝑆(𝑡𝑡)} (3.23) 𝑆𝑆(𝑡𝑡) = ℒ{𝑓𝑓(𝑅𝑅)} = � 𝑓𝑓(𝑅𝑅) exp(−𝑅𝑅𝑡𝑡)𝑑𝑑𝑅𝑅∞ 0 (3.24) The forward and reverse Fourier transform are well-defined, symmetric with bounds between -∞ and ∞, and easy to implement with the fast Fourier Transform (FFT) algorithm. The ILT, however, is ill-defined, asymmetric with bounds between 0 and ∞, and not easy to implement. The analytical form of the ILT, shown below for a distribution of relaxation rates, 𝑓𝑓(𝑅𝑅) = ℒ−1{𝑆𝑆(𝑡𝑡)} = 12𝜋𝜋𝑖𝑖 � 𝑆𝑆(𝑡𝑡) exp(𝑅𝑅𝑡𝑡) 𝑑𝑑𝑡𝑡𝛾𝛾+𝑖𝑖∞𝛾𝛾−𝑖𝑖∞ (3.25) is a contour integral in a complex plane where 𝛾𝛾 is a vertical contour positioned to the right of any singularities. This unstable expression can result in exponential divergence 75 when there is noise in S(t), making this analytical form not particularly useful in practice. Instead, Provencher[5] developed a regularized non-negative least squares method to perform the ILT in 1982 that uses a discrete form of the signal that allows for noise: 𝑆𝑆(𝑡𝑡𝑖𝑖) = � exp�−𝑡𝑡𝑖𝑖𝑅𝑅𝑗𝑗� 𝑓𝑓�𝑅𝑅𝑗𝑗� + 𝜖𝜖𝑖𝑖𝐷𝐷 𝑗𝑗=1 (3.26) where 𝜖𝜖𝑖𝑖 is the error or noise in the measurement, i is the discrete time interval, and j is the discrete relaxation rate domain. A priori knowledge of the system requires that 𝑓𝑓�𝑅𝑅𝑗𝑗�>0. The optimal solution will be as simple as possible and minimize the error, 𝜖𝜖𝑖𝑖, for a given range of R between Rmax and Rmin, where R is the relaxation rate associated with each domain. Provencher used the Tikhonov regularization[6] to ensure parsimony (the simplest solution) where we seek a minimum value for the solution, 𝑉𝑉(𝛼𝛼), where 𝑉𝑉(𝛼𝛼) = �𝐾𝐾𝑓𝑓 − 𝑆𝑆�2 + 𝛼𝛼2 �Γ𝑓𝑓�2 = 𝑚𝑚𝑖𝑖𝑙𝑙𝑖𝑖𝑚𝑚𝑢𝑢𝑚𝑚 (3.27) and �Γ𝑓𝑓�2 = � [𝑓𝑓"(𝑅𝑅)]2𝑑𝑑𝑅𝑅𝑅𝑅𝑚𝑚𝑎𝑎𝑥𝑥 𝑅𝑅𝑚𝑚𝑚𝑚𝑛𝑛 (3.28) In these expressions, K(t, R) is the kernel, α is regularization parameter, and Γ is a smoothing operator based on the curvature of f, the distribution, and S is the measured signal. The expression in Equation 2.27 is discretized such that a solution vector 𝑓𝑓 has values corresponding to each element, 𝑅𝑅𝑗𝑗, such that 𝑉𝑉(𝛼𝛼) = ��(𝑆𝑆𝑖𝑖 − exp�−𝑡𝑡𝑖𝑖𝑅𝑅𝑗𝑗� 𝑓𝑓𝑗𝑗)2𝐷𝐷 𝑗𝑗 + 𝛼𝛼2�(2𝑓𝑓𝑗𝑗 − 𝑓𝑓𝑗𝑗+1 − 𝑓𝑓𝑗𝑗−1)2𝐷𝐷 𝑗𝑗 𝑁𝑁 𝑖𝑖 (3.29) 76 The first summation term – the residual – is called χ2 and is minimized by selecting the value of the regularization parameter,𝛼𝛼, that minimizes the error term in the second summation. A large value of 𝛼𝛼 implies a high level of confidence in the fine details of the measurement. Too large a value of 𝛼𝛼 leads to ‘pearling’ of the data where more detail is shown in the final distribution than exists in the original data. Hence, we seek the solution that produces the least amount of curvature in the distribution while still faithfully representing the data. 77 Figure 3.4. Multi-dimensional PFG-NMR correlation and exchange pulse sequences. The T1-T2 pulse sequence (top) and D-T2 pulse sequence (bottom) correlate two different parameters in the same time step. The T2-T2 pulse sequence (middle) encodes for relaxation at two different times and gives insight to exchange between relaxation domains. The pulse sequences used to collect multi-dimensional PFG-NMR data and correlation and exchange measurements are shown in Figure 3.4. The T1-T2 experiment (top) first encodes for T1 relaxation for a given inversion time, then measures T2 decay. 78 The measurement is repeated for a range of inversion times to correlate the sample’s T1 and T2 relaxation properties. The T2-T2 exchange pulse sequence (Figure 3.4, middle) encodes for T2 relaxation at two different time periods, separated by a mixing period, τm, during which spins are free to migrate between relaxation domains. Magnetization is stored along the z-axis during the mixing period to preserve the relaxation encoding of the first CPMG train. The number of echoes produced during the first encoding period is varied to capture both long and short relaxation components of the first encoding period in the final recorded signal. The T2-T2 exchange experiment provides insight to the timescale of molecular transport between physical regions in the sample, i.e. pores, or between relaxation domains, i.e. bound vs. free water. The pulse sequence for the diffusion – relaxation, or D-T2, experiment is shown in Figure 4, bottom. After encoding for diffusion with the PGStE sequence, a CPMG echo train is collected to measure T2 relaxation. The strength of the pulsed gradient, g, is varied with each repetition of the sequence to resolve the range of effective diffusion coefficients present in the sample. Data collected with the D-T2 can be analyzed with the 2D ILT to produce distributions of both diffusion and relaxation, or the diffusion data can be analyzed with Fourier methods when sufficient positive and negative q-steps are collected. The Fourier-Laplace analysis produces a T2-resolved propagator. 79 References 1. Callaghan, P.T., Translational Dynamics & Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR. 2011, New York: Oxford University Press. 2. Torrey, H.C., Bloch Equations with Diffusion Terms. Physical Review, 1956. 104(3): p. 563-565. 3. Stejskal, E.O. and J.E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient. Journal of Chemical Physics, 1965. 42: p. 288. 4. Brownstein, K.R. and C.E. Tarr, Importance of classical diffusion in NMR studies of water in biological cells. Physical Review A, 1979. 19(6): p. 2446-2453. 5. Provencher, S.W., A constrained regularization method for inverting data represented by linear algebraic or integral equations Computer Physics Communications, 1982. 27(3): p. 213-227. 6. Tychonoff, A.N. and V.Y. Arsenin, Solution of ill-posed problems. 1977, Washington: Winston and Sons. 80 CHAPTER FOUR LOW-FIELD BOREHOLE NMR APPLICATIONS IN THE NEAR SUBSURFACE ENVIRONMENT Contribution of Authors and Co-Authors Manuscript in Chapter 4 Author: Catherine M. Kirkland Contributions: Researched and wrote manuscript. Co-Author: Sarah L. Codd Contributions: Helped write manuscript. Provided feedback and comments on the manuscript. 81 Manuscript Information Page Catherine M. Kirkland, Sarah L. Codd Vadose Zone Journal Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal __X_ Officially submitted to a peer-review journal ____ Accepted by a peer-reviewed journal _ ___ Published in a peer-reviewed journal Soil Science Society of America January, 2017 82 LOW-FIELD BOREHOLE NMR APPLICATIONS IN THE NEAR-SURFACE ENVIRONMENT Abstract The inherent heterogeneity of the near subsurface (< 200 m below the ground surface) presents challenges for agricultural water management, hydrogeologic characterization, and engineering, among other fields. Borehole nuclear magnetic resonance (NMR) has the potential not only to describe this heterogeneity in space non- destructively, but also to monitor physical and chemical changes in the subsurface over time. NMR is sensitive to parameters of interest like porosity and permeability, saturation, fluid viscosity, and formation mineralogy. Borehole NMR tools have been used to measure soil moisture in model soils and recent advances in low-field borehole NMR instrumentation allow for estimation of hydraulic properties of unconsolidated aquifers. We also present results demonstrating the potential for low-field borehole NMR tools to monitor field relevant biogeochemical processes like biofilm accumulation and microbially-induced calcite precipitation (MICP) at laboratory and field scales. Finally, this mini-review addresses some remaining challenges and areas of future research, as well as other possible applications where borehole NMR could provide valuable complementary data. 83 Introduction The inherent heterogeneity of the near subsurface, defined here as< 200 m below the ground surface, presents challenges for agricultural water management, hydrogeologic characterization, and engineering, among other fields. Knowledge of the spatial heterogeneity of unconsolidated sediments is vital to accurately estimate hydraulic properties related to storage and flow and to locate confining layers. Spatially varying hydraulic properties can cause preferential flow paths and mixing of subsurface flows where conductivity and permeability are high, or alternatively, trap contaminants and impede remediation efforts where conductivity and permeability are low. For example, the increasing consumptive pressure on groundwater reserves is stimulating managed aquifer recharge (MAR) and aquifer storage and recovery (ASR) solutions which require greater sophistication in hydrogeologic investigations and modelling than conventional wellfields [1]. These methods artificially recharge aquifers with water of a sometimes differing quality than the native water, such as fresh water stored in a brackish aquifer. Extraction of the high-quality water later for re-use is maximized only when there is minimal mixing during storage as would occur in lower transmissivity zones. Furthermore, recent years have seen increased interest in harnessing the power of biogeochemical conversions to assist diverse engineering applications, including in-situ bioremediation of subsurface contaminants [2] and microbially-induced calcite precipitation (MICP) for fracture sealing [3] or geotechnical applications to strengthen soils [4, 5]. These methods are intended to alter the physical and chemical environment 84 of the pore space; proper execution of these projects requires knowledge of both temporal and spatial variations in the subsurface. The standard reference method for obtaining the volumetric water content of porous media is gravimetric. A sample of known volume is weighed before and after oven drying to determine the water content at the time of the measurement. Gravimetric measurements are necessarily invasive, destructive, and time-consuming to perform, providing point-scale data at a single time. Neutron thermalization methods, like neutron scattering, are significantly less invasive than gravimetry and are based on a well- established, linear correlation between the sediment water content and the ratio of thermalized neutrons reaching the detector. The radioactive materials which supply the neutrons, however, impose significant regulatory barriers, making the technology less attractive as newer methods are developed [6]. Established hydrogeophysical methods for in-situ characterizations of soil and sediment rely on measurements of geophysical properties to infer hydrogeological properties, meaning that the methods do not provide direct measurement of water [6, 7]. For example, Electrical Resistivity Tomography (ERT), Ground Penetrating Radar (GPR), and seismic methods measure electrical conductivity or resistivity, acoustic impedance, and velocity and attenuation of seismic waves, respectively, to provide information about water content and porosity. The translation of measured geophysical data to hydrogeologic and hydraulic properties of interest requires non-trivial mathematical inversions and modelling. The many hydrogeophysical methods available have varying spatial scales and resolution; readers 85 should refer to several recent reviews of geophysical methods for more information [6, 7]. Nuclear magnetic resonance (NMR) methods have the potential to both characterize subsurface heterogeneity and monitor changes in the geophysical and biochemical environment over time, suggesting the importance of this technology for these fields. Low-field NMR instrumentation for field applications can take several forms – mobile single-sided instruments like the NMR MOUSE, surface NMR instruments, or borehole NMR probes. Though the focus of this mini-review is borehole NMR, single-sided NMR and surface NMR tools deserve mention. The NMR MOUSE, developed by researchers at RWTH – Aachen University in the 1990’s [8], weighs approximately 1 kg and has been used in applications ranging from biomedicine, cultural heritage preservation, materials science, and measurement of moisture in soils and building materials [9, 10]. The depth of investigation for the various single-sided NMR probes is typically on the order of centimeters. The configuration of the permanent magnets and coils of wire comprising mobile, single-sided NMR tools vary according to the application and the goals of the NMR measurement. Readers may refer to the comprehensive description given by Blumich et al. (2008). Non-invasive explorations of near surface hydrogeologic and hydraulic properties can also be performed with surface NMR. Surface NMR uses the Earth’s magnetic field and coils of wire deployed on the ground surface to collect the NMR measurement. Although surface NMR coils are easy to deploy and are entirely non-invasive, the technology faces challenges related to low signal-to-noise, a long instrument dead-time between excitation and detection which 86 means that water in small pores is not measured, and a relatively shallow depth of investigation (< 100 m) with vertical resolution on the order of 10 m [11]. Several reviews which provide a description of theory and recent advances in the technology have been published [11, 12]. Borehole NMR tools have been used in the oil and gas industry to identify and characterize hydrocarbon reserves since the 1960s [13] due to the sensitivity of NMR to hydraulic properties of interest, like pore size distribution, permeability and hydraulic conductivity, and fluid content and viscosity. The mathematics describing the relationship between the measured NMR signal response and these formation hydraulic properties developed alongside technical improvements to the instruments, such that now NMR tools are an indispensable part of the oil and gas industry [14, 15]. Despite the fact that the same hydraulic parameters are of interest in hydrogeology, geotechnical engineering, and soil science, the oilfield well-logging tools are too large, expensive, and impractical for most near-surface applications. As a result, the application of NMR tools to near- surface investigations in unconsolidated sediments has developed only in the last decade due to several independent and complimentary factors. Technical innovations have allowed down-sizing of the hardware, and developments in numerical methods and error estimation have improved the mathematical inversions needed for data processing [16- 18]. Finally, pressures on global water supplies and the need for improved monitoring methods drive innovations in borehole NMR technology. Recently, portable and lower-cost borehole NMR tools have been developed in both commercial [19] and non-commercial [20] forms. These tools vary significantly in 87 operating frequency, measurement distance from the tool, the size of the probe, vertical resolution, and the minimum echo spacing, with significant implications for the ease of use of the instrument and interpretation of the data. This paper describes recent applications of these tools related to soil water management, hydrogeology, and biogeochemical engineering in the near subsurface, as well as remaining challenges and further potential applications for the technology. Theory 1H NMR measures the response of hydrogen-bearing molecules, typically water, to perturbations in a magnetic field. As such, NMR is directly sensitive to water in soil, rock, and unconsolidated subsurface sediments. Borehole NMR tools generally consist of permanent magnets and radio-frequency (rf) induction coils. The permanent magnets create a static magnetic field, B0, in the formation. The magnetic field strength in the formation drops off with the radial distance from the tool as does the resonant frequency at which the water will respond. The resonant frequency is called the Larmor frequency, 𝜔𝜔0 = 𝛾𝛾B0, where 𝛾𝛾 is the gyromagnetic ratio, a constant with a value of 2.675 x 108 rad/(T s) for hydrogen. Pulses of current are transmitted through the rf coils, exciting hydrogen at a particular Larmor frequency. The location of the cylindrical excitation region depends on the tuning of the probe; higher Larmor, i.e. operating, frequencies produce an excitation - detection shell closer to the wellbore where the magnetic field is stronger, while lower Larmor frequencies allow measurement deeper into the undisturbed formation (Figure 4.1). The excited hydrogen protons generate a detectable signal according to Faraday induction at the Larmor frequency which is received on the rf coils. 88 Figure 4.1. Schematic of a generalized borehole NMR wire-line logging tool with a cylindrical excitation-detection shell. The magnitude of the static magnetic field, B0, decays with radial distance from the well. The NMR probe is tuned to excite protons (water) at a particular Larmor frequency, 𝜔𝜔0 = 𝛾𝛾B0, which corresponds to a particular radial distance from the well. Lower frequencies produce excitation – detection shells outside the disturbed soil zone that results from traditional well-drilling methods. The induced NMR signal amplitude decays in time as the system returns to equilibrium in a process called relaxation [21]. T1 (spin-lattice) relaxation and T2 (spin- spin) relaxation both provide information about the local physical and chemical environment. T1 relaxation is related to the timescale for system to return to thermal equilibrium as the added energy from the excitation rf pulse dissipates into the environment, or lattice. T2 relaxation is related to molecular interactions occurring between the excited water molecules and their interactions with the pore walls. Measurement of T2 relaxation is robust and faster to perform, making it preferred for low- field borehole NMR [22]. T2 relaxation is measured with the CPMG pulse sequence [23, Sensitive zone Undisturbed formation Disturbed zone Well Casing NMR Probe 𝐁0 89 24] in which a series of re-focusing rf pulses, called 180° pulses, follow the 90° rf excitation pulse (Figure 4.2). The 180° pulses create a series of signal echoes where the initial signal amplitude is proportional to the volumetric water content and echo amplitudes decay at a rate of 𝑇𝑇2−1. The time between echoes is called the echo spacing, 𝑡𝑡𝐸𝐸. Figure 4.2. The CPMG pulse sequence consists of a 90° excitation pulse and a series of refocusing 180° pulses. The induced signal consists of a series of echoes in which the decay curve (thin dashed line) has an initial amplitude proportional to the water content and an exponential decay rate of 1/T2. Data acquisition with borehole NMR tools in the field involves lowering the probe incrementally into the subsurface, either in a borehole well or in an opening made by a direct push (DP) tool. DP methods drive an instrumented steel rod into the ground using hydraulic rams and avoid the need to drill boreholes. Aside from the borehole or DP opening, NMR is non-invasive and non-destructive. An NMR measurement is collected at each depth increment to create a well log, or soil profile, describing the sediment-water relationship via T2 relaxation. The vertical resolution of the well log depends on the 180y° rf pulse time 90x° 𝑡𝑡𝐸𝐸 180y° 180y° 180y° signal time 90 dimensions of the rf coil. The logging speed is related to the signal to noise ratio, and thus, how many measurements are collected and averaged at each depth increment. Since natural porous media is composed of many pores of varying sizes and geometries, the signal collected during an NMR measurement is the sum of the signal from each individual pore. The resulting multi-exponential signal decay curve data is typically analysed with the inverse Laplace transform (ILT), producing a distribution of T2 relaxation times. The integrated amplitude of the distribution provides the volume fraction of water in the measurement region—the porosity if the sediment is saturated or the water content if it is unsaturated. Such estimates can also be obtained from the initial amplitude of the signal decay curve [25]. NMR T2 relaxation is sensitive to the physical and chemical properties of macroscopic porous media systems, including pore size, soil mineralogy, degree of water saturation, and pore fluid viscosity. The expression for the T2 relaxation rate, typically in units of ms-1, in a single pore is given by the equation 𝑇𝑇2−1 = 𝑇𝑇2𝐵𝐵−1 + 𝑇𝑇2𝑆𝑆−1 + 𝑇𝑇2𝐷𝐷−1 [1] where 𝑇𝑇2𝐵𝐵−1 is the bulk fluid relaxation rate, and 𝑇𝑇2𝑆𝑆−1 is the surface relaxation rate. The final relaxation term is related to diffusion in an inhomogeneous magnetic field and can influence NMR T2 relaxation measurements where the gradient in the local magnetic field is high or when the echo spacing, tE, of the measurement is long. Gradients, or inhomogeneities, in the static magnetic field result when the sediment is composed of materials with different magnetic susceptibilities or when the strength of the B0 field rapidly decays in the radial direction [26]. A lower operating frequency reduces the 91 static field gradient. Minimizing tE through instrument design and experimental parameter selection can reduce the impact of T2D on the NMR signal response. Many studies of porous media assume T2 relaxation is 1) independent of the self- diffusion coefficient of water as in the ‘fast diffusion’ regime [27] and 2) dominated by surface relaxation [28], which can be expressed as 𝑇𝑇2𝑆𝑆−1 = 𝜌𝜌 �𝑆𝑆𝑉𝑉� [2] where 𝜌𝜌 is the surface relaxivity [cm/s], or the capacity of the pore wall to induce relaxation, and �𝑆𝑆 𝑉𝑉 � is the surface to volume ratio of the pore [cm], typically modelled as a sphere. From this expression, it follows generally that T2 is longer in larger pores and shorter in smaller pores. Also important is the mineral surface of the solid matrix where paramagnetic species like Fe(III) and Mn lead to faster relaxation (shorter T2) via the parameter 𝜌𝜌 [29, 30]. In very coarse materials, the ‘slow diffusion’ regime [27] dominates and Eqn. [2] becomes a function of �𝑆𝑆 𝑉𝑉 � 2 with no dependence on 𝜌𝜌. The T2 relaxation time distribution can be represented by a single parameter, the arithmetic mean of log T2, T2ML. This single parameter has been shown to estimate the mean pore size and permeability with the following equations [31], 𝑇𝑇2ML−1 = 𝜌𝜌 �𝑆𝑆𝑉𝑉� [3] 𝑘𝑘NMR = 𝑏𝑏𝜑𝜑𝑚𝑚(𝑇𝑇2ML)𝑛𝑛 [4] where �𝑆𝑆 𝑉𝑉 � is the surface to volume ratio of the total pore space, ρ is the surface relaxivity, kNMR is the estimated permeability from the NMR data [31] with units typically expressed in millidarcies (1 mD ≈ 10-11 cm2), ϕ is the NMR-determined porosity, and b [mD/ms2], 92 m, and n are empirically determined constants. Eqn. [4] is commonly known as the Schlumberger-Doll Research (SDR) equation. For consolidated sediments and when T2ML is in units of milliseconds, m and n are typically 4 and 2, respectively [32, 33]. Eqn. [4] can also be written in terms of hydraulic conductivity, K, in units of m/s; in this case, the values and units of the empirical constants account for the inclusion of fluid density and viscosity terms. For further discussion of the empirical constants, refer to Knight et al. (2016). From these expressions, it is clear that accurate estimation of k or K depends on the ability of the instrument to measure T2S without the influence of diffusion relaxation, T2D, since the influence of T2B is generally insignificant when the pore fluid is water. Alternatively, diffusion effects must be quantified and decoupled from measurement of T2 relaxation by encoding the signal also for the effective self-diffusion of water. This is an ongoing area of research and will be further discussed in the final section of this article. The influence of the T2D component is reduced by lowering the tool operating frequency, i.e. static magnetic field strength, and by minimizing tE. Lower operating frequency also reduces the signal to noise ratio, requiring longer measurement times. In saturated sediments, the shape of the T2 distribution estimates the pore size distribution since T2 relaxation depends linearly on the pore size when ρ is assumed constant; the distribution yields the relative volume of water in each size pore. Typically, water in sandstone with a T2 relaxation time greater than 33 ms is considered ‘mobile’, while water relaxing faster than 33 ms is considered ‘bound’ in capillaries [34]. ‘Clay bound’ water is characterized by relaxation in less than 3 ms. Water signal decaying 93 faster than the minimum echo spacing is not detected. In the vadose zone, unlike in deeper consolidated sediments, soils have varying degrees of saturation and hydraulic conditions are dynamic on timescales ranging from hours to seasons to years. In these conditions, interpretation of the T2 distribution as a pore size distribution is more complicated. Soil drying may concentrate dissolved species in the remaining pore water and influence bulk fluid relaxation, such that the 𝑇𝑇2𝐵𝐵−1 term in Eqn. [1] may become non- trivial. Additionally, large pores drain before smaller pores. Jaeger et al. (2009) found that the relaxation time distribution of unsaturated soil samples was strongly correlated to the soil texture, i.e. relative sand, silt, and clay content, as well as the content of soil organic matter (SOM). To date, borehole NMR tools have been applied to the measurement of soil moisture in laboratory studies and hydrogeologic characterization of aquifers in the field. Building on those foundations, recent studies have used borehole NMR to detect and monitor biogeochemical changes in the near subsurface for applications related to bioremediation. Measurement of Soil Moisture Researchers at RWTH – Aachen University developed two non-commercial, small-scale, and portable borehole NMR devices for measuring soil moisture [20, 35]. Sucre et al. (2011) developed a single-sided borehole NMR probe, 4.8 cm in diameter, which operated at 11.8 MHz and produced a sensitive zone 4.7 mm from the exterior of the device on one side. The minimum echo spacing, which controls the fastest-decaying 94 signal the tool can detect, was tE = 70 μs. Subsequently, the probe was re-designed, to increase the signal to noise ratio and increase the penetration of the sensitive zone, then again applied to measurement of soil moisture [20]. The optimized probe was 4.1 cm in diameter, 18.0 cm long, and operated at a frequency of 3.32 MHz. The sensitive zone in the soil for this instrument, unlike the previous, was a cylindrical shell 220 μm thick located 4.5 cm from the central axis, or 1.8 cm from the exterior of the casing. The minimum echo spacing was tE = 250 μs. The optimized probe also significantly reduced the static field gradient from 24 T/m [35] to 3 T/m [20]. The two probes were tested in a similar manner to demonstrate performance [20, 35]. Each probe was placed in a tube within a larger column of model sandy soil. The model soil FH31 is a distribution of grain size classes 2% (>0.72mm), 8% (0.71-0.5mm), 30% (0.5-0.355mm), 41% (0.36-0.25mm), 16% (0.25-0.18mm), 3% (<0.18mm). In both studies, the soil moisture profile was measured first over the full depth of the column when the soil was fully saturated. Then, the water was allowed to drain from the column while the probe remained at a fixed depth, measuring the depletion of water over time from the soil pores. Next, Perlo et al. (2013) repeated these two steps of the experiment at different depths within the column. Figure 4.3 shows the drying of the soil column over time for 5 arbitrary and undefined vertical positions. Note that the curves have similar form and the initial water content in the saturated soil is equal within 1% for all depths measured [20]. Sucre et al. (2011) instead measured the soil moisture profile over the full column depth with the single-sided tool when the system reached hydraulic equilibrium after the draining described above (Figure 4.4). 95 Figure 4.3. Temporal evolution during the draining process for different vertical z- positions in the column filled with a model soil FH31. The z-positions are not specified in the original article, but the asymptotic saturation value increases with depth in the column. Initial saturation for all curves was measured with a precision of 1%. In the inner box a CPMG-decay with 250 echoes recorded with 58 scans is shown. Reproduced from Perlo et al. (2013). 96 Figure 4.4. Saturation profile in a model soil FH31 under full saturation conditions (before outflow) and after the soil has been drained (after outflow). Reproduced from Sucre et al. (2011). Sucre et al. (2011) then calculated the soil hydraulic parameters using the NMR data from the column drainage experiment. Vertical flow was simulated with the Richards Equation, using the Mualem-van Genuchten model [36, 37] for K(θ), the hydraulic conductivity, and h(θ), hydraulic head, where both depend on saturation, θ. The saturated hydraulic conductivity, Ks, and the pore connectivity parameter, τ, were obtained by an inversion analysis. The simulations generally conformed well to the experimental results (Figure 4.4), though the rapid dynamic regime of the outflow experiment produced a Ks of 9 mm/min in the highly conductive model soil FH31, compared to a literature value of 7 mm/min [35]. The probe was also used to measure soil moisture profile changes resulting from imbibition and precipitation. It should be noted here that the relatively high field strength and high static field gradient of these two 97 probes means that especially during soil drying, the surface relaxation component of T2 relaxation, T2S, is strongly coupled to the diffusion relaxation component, T2D [35]. More recently, Vista Clara, Inc. (Mukilteo, WA) has commercialized a backpack portable system called Dart [38] which is optimized for soil and vadose zone studies shallower than 50 m. The Dart has an outer diameter of 4.5 cm and operates between 425-475 kHz, producing a sensitive zone that is at a maximum of 5 cm from the tool surface. The static field gradient is 35 G/ cm (3.5e-5 T/m) at the sensitive zone. The system is intended to be deployed in holes made with minimal soil disturbance like DP- installed PVC or hand-augering. Recently the tool has been used to study thawing in permafrost [39]. The electronics unit running the Dart can also be used to operate a non- invasive single-sided NMR sensor called Discus, which sits on the soil surface and measures water at four levels: approximately 5, 10, 15, and 20 cm from the face of the sensor [38]. Characterization of Unconsolidated Aquifers These next studies were conducted within the saturated, unconsolidated sediments below the vadose zone. The first portable borehole NMR device reported in literature was a commercial probe called the Javelin, by Vista-Clara, Inc. [19]. The Javelin probe is a slim, borehole logging tool originally developed for hydrogeologic analysis in open or PVC-cased boreholes as small as 5 cm in diameter [40], and can also be operated in DP mode. Several versions of the probe have been commercialized, operating in the range of 250—425 kHz, placing the sensitive region in the undisturbed formation outside 98 the wellbore approximately 11 – 19 cm radially from the center of the probe. The static field gradient at the sensitive region is approximately 5 G/cm (5e-6 T/m). What is most significant about this instrument is that the low operating frequency and static field gradient, together with the minimum tE (on the order of 1 ms), allow a robust measurement of T2 relaxation without the influence of diffusion relaxation, T2D. Figure 4.5. Logs from Massachussetts Military Reservation obtained May 2010 (a) NMR logs acquired in 4-inch well 03GB1060 show the T2 distributions, the NMR measured water content, and the NMR-derived estimate of K; (b) comparison of water content measured by NMR log and neutron porosity log acquired in nearby 2-inch well FSW445. Reproduced from Walsh et al. (2013) Initial field tests of the Javelin were conducted at the Massachusetts Military Reservation, near a site of known subsurface contamination from fuel spills and other activities. The 100 m NMR logging data compared well to a porosity estimation obtained by a neutron log acquired in nearby well (Figure 4.5 (b)). The T2 distribution, NMR 99 estimation of water content, and NMR derived estimate of K – all measured as a function of depth – also allowed researchers to identify water content associated with lenses of low permeability silt which are expected to trap fluids, thereby affecting contaminant fate and transport (Figure 5 (a)). Figure 4.6. Comparison of K calculated from NMR logging data using the SDR equation (Eqn. [4]) and from DP permeameter (DPP) data obtained at the Larned field site. The figure shows logs from three different locations at Larned (a) Larned E, (b) Larned C, (c) Larned W. The dashed lines show the uncertainty in KNMR due to the distribution in b values (±1σ) when fitting Eqn. 4. Reproduced from Knight et al. (2016). More recently, researchers have used the Javelin tool to characterize hydraulic conductivity in unconsolidated aquifers at several field sites [41], where the goal of the research was to identify standard values for the empirical constants in Eqn. [4]. Data from 3 wells at the Larned Research Site of the Kansas Geological Survey in west-central 100 Kansas is shown in Figure 4.6. The NMR logging data estimation of the hydraulic conductivity, K, compared very well, generally within an order of magnitude, to the more established direct-push permeameter (DPP) estimates [42]. The authors found that, like in consolidated formations [32, 33], there was little variability in the constants between the different field sites. The value of the empirical constant, b, in Eqn. [4] when written in terms of hydraulic conductivity, varied less than 50% across 3 field sites. This result suggests that it may be possible to obtain reliable values for the empirical constants and significantly reduce the need for site specific calibration to obtain accurate estimations of K and k from NMR data [41]. Establishment of standard values for the constants will improve the cost-effectiveness and ease of use of borehole NMR technology. Previous work by the research group responsible for these measurements includes their initial demonstration in a high plains aquifer [22], groundtruthing surface NMR with the NMR logging tool [43], and determining methods to estimate uncertainties [44]. Detection of Subsurface Biogeochemical Processes As Eqn. [1] shows, T2 relaxation in porous media depends on the properties of the bulk fluid and the size and mineralogy of the pores. (Diffusion relaxation effects can be neglected due to the low operating frequency of the borehole tool used in the following studies.) It therefore follows that changing the properties of the pore fluid, or changing the pore geometry or mineralogy, should produce a change in the T2 relaxation distribution from some known initial state. In application of this premise, the research group at Montana State University has been using the Javelin NMR logging tool to 101 monitor subsurface biogeochemical processes for bioremediation applications [45-47]. The studies included in this section were designed to assess the sensitivity of borehole NMR to 1) a change in pore fluid – from water to biofilm – both at laboratory and field scale, and 2) pore structural and mineralogical changes caused by microbially induced calcite precipitation (MICP) in a laboratory bioreactor. Both biofilm growth and MICP can be used as part of a bioremediation project. Bioremediation can be an effective method to contain or degrade chemical contaminants in the subsurface by exploiting the fundamental biochemical processes of microbial metabolism. Once established, biofilms have been shown to degrade or contain contaminants through a variety of mechanisms: utilizing hydrocarbons and other contaminants directly as a substrate; inducing mineralization to trap contaminants; transforming heavy metals to insoluble forms; or acting as a bio-barrier to retard the migration of contamination or re-direct groundwater flow through a treatment zone. Depending on its physical properties, the biofilm extracellular polymeric substance (EPS) matrix can change soil pore connectivity, effective pore size, and hydraulic conductivity, thereby affecting the hydrodynamic properties of the porous media [48] and allowing the detection of the biofilm state with NMR [49]. Preliminary groundtruthing was demonstrated in a lab-scale bioreactor designed to model the near-wellbore environment [45]. The bioreactor was constructed with four concentric PVC pipes, each 0.76 m tall, and filled with 1 mm nominal quartz sand, creating a combined pore space and reservoir volume of approximately 40 L. Over an 8- day experimental period, biofilm was cultivated in the reactor sand-pack with a 102 continuously recirculating flow of substrate. Measured NMR T2ML shifted from approximately 750 to 400 ms, indicating that the pore environment and bulk fluid properties were changing due to biofilm growth (Figure 4.7). Destructive sampling employing microbial population analysis and microscopy confirmed biofilm formation. This experiment demonstrated that the NMR logging tool can detect small to moderate changes in T2 distribution associated with environmentally relevant quantities of biofilm in quartz sand. Figure 4.7. Time evolution of CPMG signal decay curves and T2 distributions. Increased signal attenuation with biofilm formation produces steeper CPMG signal decay curves (top panel). The distribution of T2 relaxation times (bottom panel) shifted to faster decay times as biofilm grew in the reactor. Data collected days 3 and 4 overlap the day 5 curve and are not shown. Likewise, the day 6 data is obscured by the day 7 curve and is not shown. Day 8 data was collected from the drained reactor. Reproduced from Kirkland et al. (2015b). In 2014, two Javelin toosl were used to measure biofilm accumulation in an engineered test cell [46]. The test cell is 55 m by 40 m at the surface and is 6 m deep 103 with 2:1 side slopes (x:z). Two measurement wells were used in the study. A Javelin probe operating at approximately 400 kHz was installed in Well 1 where the soil profile was slightly more coarse grained than in Well 2. The Javelin probe in Well 2 operated at approximately 275 kHZ and was the same tool as was used in the previous laboratory study. Measured T2ML relaxation times were reduced by 43% and 62%, respectively in Well 1 and Well 2, while biofilm was cultivated in the soil surrounding each well (Figure 4.8). Figure 4.8. Data showing T2ML measurements from two monitoring wells (triangles – Well 1 (~400 kHz), squares – Well 2 (~275 kHz)). Inoculation occurred on Day 1. Growth substrate was injected daily Days 2-10. Days 11-14, the bacteria were starved. On Day 14, the wells were flushed with high flows of groundwater from the test cell then a bleach solution was injected to oxidize remaining organics. Day 15 data was collected after flushing the bleach solution from the wells. Reproduced from Kirkland et al. (2015a). 104 Differences T2ML between the wells is due to the relatively larger pores in Well 1. The reduction in T2ML observed in both wells was confirmed to be a result of biofilm accumulation by bleaching and flushing the wells and observing the NMR signal’s return to baseline. This result provided evidence of the NMR logging technique as a direct and non-invasive method to spatio-temporally monitor biofilm accumulation in the subsurface. MICP has been widely researched recently due to its relevance for subsurface engineering applications including sealing leakage pathways and permeability modification [50, 51]. These applications of MICP are inherently difficult to monitor non-destructively in time and space. The Javelin probe was used to monitor MICP in the sand-filled bioreactor described previously, measuring NMR signal amplitude and T2 relaxation over an 8-day experimental period [47]. Following inoculation with the ureolytic bacteria, Sporosarcina pasteurii, and pulsed injections of urea and calcium substrate, the NMR measured water content in the reactor decreased to 76% of its initial value as calcite precipitation displaced pore water. Destructive sampling confirmed final porosity was approximately 88% of the original value. The overestimation of porosity reduction by NMR can be attributed primarily to the accumulation of excess CO2 gas in the reactor as a result of microbial metabolism. Signal decaying faster than the minimum echo spacing (1.3 ms) may also have reduced the measured NMR water content. T2 relaxation distributions bifurcated from a single mode centered about approximately 650 ms on Day 2 into a fast decaying population (T2 less than 10 ms) and a larger population with T2 greater than 1000 ms by Day 8 (Figure 4.9). The combination of changes in pore 105 Figure 4.9. Signal decay curves (top) and the corresponding T2 distributions (bottom) are shown with each curve representing a day. Day 2 occurred during the control period. Inoculation occurred on Day 3 (not shown). The calcium media injections occurred between Day 4 – 7. The Day 8 data was collected prior to flushing the reactor with brine and destructively sampling. Both graphs show fits to the raw data. Reproduced from Kirkland et al. (2016). volume and surface mineralogy accounted for the changes in the T2 distributions. In this system, the change in pore surface mineralogy, from quartz sand containing paramagnetic impurities to a relatively uniform calcite surface, caused a decrease in the surface relaxivity, ρ, and lead to the longer T2 relaxation times observed. The authors attribute the very fast decaying signal to water trapped within the pores of the calcite itself, where the influence of the surface to volume ratio dominated. These results indicate the low- field NMR well-logging probe is sensitive to the physical and chemical changes caused by MICP in a laboratory bioreactor. 106 Outlook and Conclusions Several technological challenges remain in the further development of low-field borehole NMR tools. As discussed above, minimizing the echo spacing, tE, is critical for obtaining an accurate estimation of k and K from NMR data by reducing the influence of relaxation due to diffusion. Reducing the minimum tE also expands the range of fast- decaying signals that can be measured by the instrument, a feature which may be particularly relevant where biogeochemical conversions are concerned. Pulsed NMR tools have been used in the oil and gas industry since the early 1990’s, allowing for measurements that simultaneously encode the signal for the effective diffusion coefficient of the pore fluid, D, and T2 relaxation. The correlation of relaxation behaviour with diffusion properties allows the separation of some of the effects which combine to influence T2 relaxation [52]. The ability to collect D-T2 correlations improves the feasibility of using borehole NMR tools to detect degradation of organic contaminants by allowing the separation of the water and hydrocarbon signal, for example, since water and hydrocarbons have different self-diffusion coefficients [53]. The latest versions of the Javelin and Dart borehole NMR probes can now encode for effective self-diffusion and record D-T2 correlations though the corroborating research is not yet published. While it is often possible to neglect the influence of T2D for simple relaxation measurements, the addition of diffusion measurements, however, would make accurate estimation of the internal field gradient strength critical. Measuring the effective diffusion coefficient requires a long echo spacing to encode for motion. The influence of 107 T2D over this interval must be known. Accurate estimation of these internal field gradients under field conditions remains a challenge [26]. In addition to the research discussed above, which used borehole NMR probes, several studies have been completed using traditional benchtop NMR instruments in the laboratory where the logical future application is in the unconsolidated sediments in the near surface. One such example is using borehole NMR as a probe of the redox condition of the aquifer. Injecting oxygen-rich water into a reduced aquifer can cause leaching of metals into the water, significantly degrading the water quality. Furthermore, iron (hydr)oxides are highly reactive geochemically and, as such, can be used to sequester or transform organic or inorganic contaminants. Both of these examples involve a change in local redox conditions that changes the mineralogical form of iron compounds [54], or other metals. NMR is sensitive not only to the quantity of iron present in the measurement region [55], but also to the form of the iron with Fe (III) producing faster relaxation rates than Fe(II) compounds [30, 56, 57]. Confirmation of these laboratory results in a complex field environment would broaden the range of potential applications of borehole NMR technology and vastly improve existing methods for monitoring changing redox conditions and iron mineralization in the subsurface. 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Journal of Applied Geophysics, 2008. 66(3-4): p. 188-196. 113 CHAPTER FIVE BIOFILM DETECTION IN A MODEL WELL-BORE ENVIRONMENT USING LOW-FIELD NMR Contribution of Authors and Co-Authors Manuscript in Chapter 5 Author: Catherine M. Kirkland Contributions: Helped conceive and implement study design. Collected and analyzed data. Wrote manuscript. Provided feedback and comments on the manuscript. Co-Author: Randy Hiebert Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. Co-Author: Adrienne J. Phillips Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. Co-Author: Elliot Grunewald Contributions: Helped conceive and implement study design. Provided supervision and oversight on data collection and analysis. Provided feedback and comments on the manuscript. Co-Author: David O. Walsh Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. Co-Author: Joseph D. Seymour Contributions: Provided feedback and comments on the manuscript. 114 Co-Author: Sarah L. Codd Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. 115 Manuscript Information Page Catherine M. Kirkland, Randy Hiebert, Adrienne Phillips, Elliot Grunewald, David O. Walsh, Joseph D. Seymour, Sarah L. Codd Groundwater Monitoring and Remediation Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-review journal ____ Accepted by a peer-reviewed journal _X___ Published in a peer-reviewed journal Wiley-Blackwell Vol. 35, No. 4, Pages 36-44, Fall 2015 116 BIOFILM DETECTION IN A MODEL WELL-BORE ENVIRONMENT USING LOW-FIELD NMR Abstract This research addresses the challenges of the lack of non-invasive methods and poor spatio-temporal resolution associated with monitoring biogeochemical activity central to bioremediation of subsurface contaminants. Remediation efforts often include growth of biofilm to contain or degrade chemical contaminants, such as nitrates, hydrocarbons, heavy metals, and some chlorinated solvents. Previous research indicates that nuclear magnetic resonance (NMR) is sensitive to the biogeochemical processes of biofilm accumulation. The current research focuses on developing methods to use low- cost NMR technology to support in-situ monitoring of biofilm growth and geochemical remediation processes in the subsurface. Biofilm was grown in a lab-scale radial flow bioreactor designed to model the near wellbore subsurface environment. The Vista Clara Javelin NMR logging device, a slim down-the-borehole probe, collected NMR measurements over the course of eight days while biofilm was cultivated in the sand- packed reactor. Measured NMR mean log T2 relaxation times decreased from approximately 710 to 389ms, indicating that the pore environment and bulk fluid properties were changing due to biofilm growth. Destructive sampling employing drop plate microbial population analysis and scanning electron and stereoscopic microscopy confirmed biofilm formation. Our findings demonstrate that the NMR logging tool can 117 detect small to moderate changes in T2 distribution associated with environmentally relevant quantities of biofilm in quartz sand. Introduction In most environments, the majority of microbial cells exist in complex communities called biofilms [1]. Bacteria preferentially attach to surfaces, anchoring themselves with a sticky gel called extracellular polymeric substance (EPS). The EPS, which consists of proteins, polysaccharides, and DNA, forms a heterogeneous matrix surrounding the bacterial cells and entrapped organic and inorganic molecules [2]. The EPS matrix has a complex structure, consisting of hydrated gel-like fibers and interconnected channels [3]. Depending on its physical properties, the EPS matrix can change soil pore connectivity, effective pore size, and hydraulic conductivity, thereby affecting the hydrodynamic properties of the porous media [4-6]. Bioremediation methods exploit these biofilm-induced changes in the soil and can be effective to contain or degrade chemical contaminants in the subsurface [7]. Once established, biofilm can consume hydrocarbons and other contaminants directly as a substrate [8-11], induce mineralization to trap contaminants [12], mediate ion exchange to remove heavy metals from aqueous solution [13] or transform heavy metals to insoluble forms [14]. In-situ bioremediation applications often require injection of appropriate nutrients into the subsurface in order to create redox conditions suitable for biofilm growth and contaminant transformation. In addition to being an integral part of the removal of toxins, biofilm can act as a bio-barrier to slow the migration of the 118 contamination or re-direct groundwater flow through a treatment zone [15] by reducing hydraulic conductivity and restricting advective flow. Furthermore, biofilms better withstand environmental stresses such as nutrient deprivation, changing pH conditions, and exposure to biocides or antimicrobial substances compared to suspended cells [16, 17], improving their effectiveness and longevity as bio-barriers. Numerous computer models have been developed in the last several decades in an effort to better understand the physical and biochemical processes of biofilm development. In general, the recent models iteratively solve partially decoupled differential equations governing conservation of momentum, mass transport, substrate utilization, and biofilm growth [18-21]. The models help describe the changing hydrodynamics and biofilm morphology, as well as confirm the overall reduced hydraulic conductivity of the porous media resulting from biofilm accumulation that is observed experimentally. This observed reduction in hydraulic conductivity is the typical method for determining whether biofilm is present in bioremediation applications [5, 22, 23]. Darcy’s Law, ν = −𝐾𝐾 𝑑𝑑ℎ 𝑑𝑑𝑑𝑑 describes the relationship between the specific discharge, ν [L/t], and the pressure gradient along a length of porous media, dh/dl [dimensionless], where the constant of proportionality is the saturated hydraulic conductivity, K [L/t]. Biofilm accumulation in pore spaces has been shown to reduce hydraulic conductivity by approximately 99% in a field setting and up to 99.99% in laboratory experiments [15, 23]. 119 In conjunction with hydraulic conductivity measurements, determination of biofilm presence is often assessed with heterotrophic plate counts (HPC) to quantify the number of viable cells in the bulk fluid [24]. Interpretation of this type of population data is not trivial since the cell count data pertains to suspended bacteria rather than those attached to surfaces as biofilm. Furthermore, how the number of suspended cells correlates to the number of cells existing within biofilm colonies is not well understood. To determine cell populations within the biofilm, samples of the porous media must be collected and analyzed. Direct destructive sampling of contaminated soils during remediation can be both costly and potentially hazardous. Moreover, cell count information in general provides no information regarding the in-situ physical characteristics of the biofilm, such as the thickness, structure, and density of the EPS component as this information is destroyed during sampling and plating. While these methods are useful to describe the hydraulic conductivity or biological community at a particular place and time, they are less useful for informing us about the spatial and temporal growth, maturation, and decay of the biofilm [25]. NMR provides an alternative method to monitor in-situ biofilm development, overcoming several of the limitations described above. The measured signal in 1H NMR comes from coherently precessing hydrogen protons, or ‘spins,’ making NMR applicable for the study of materials containing water or organic matter, including biofilm [26, 27]. Previous research indicates that NMR is sensitive to the biogeochemical processes of biofilm growth [28] and, unlike other methods of study, allows for non-invasive and non- destructive examination of the relationship between biofilm development and porous 120 media hydrodynamics and mass transport over various time and length scales [29-32]. A fundamental understanding of these related processes is critical to optimize the effectiveness of bioremediation applications, making NMR methods a useful addition to the bioremediation monitoring toolkit. The Vista Clara Javelin device is a slim, down-the-borehole NMR logging tool (4.5ft (1.37m) long, 3.5in (8.9cm) diameter) originally developed for hydrogeologic analysis in open or PVC-cased boreholes between 2 and 8in (5-20cm) in diameter [33]. Expanding from this conventional application, the research reported here uses the Javelin probe to detect changes in the signal relaxation response over time as a measurement of biofilm growth in a model sand bioreactor since biofilm accumulation enhances signal relaxation [28]. The method using a NMR logging tool as described in this article may provide an improved and non-destructive way to assess the subsurface presence of biofilm. Theory T2 relaxation Following excitation with a radio-frequency (rf) pulse, the induced NMR signal decays at a rate governed by two relaxation mechanisms—spin-lattice T1 and spin-spin T2 [34]. T1 relaxation is related to the rate at which the net magnetization grows in the longitudinal direction and returns to thermal equilibrium. T2 relaxation is related to dipolar interactions in the transverse plane and loss of phase coherence, resulting in magnetization decay and signal attenuation. 121 The statistical distribution of T2 relaxation times provides information regarding the physico-chemical environments the protons experience, since environmental factors like pore fluid type and pore size control how likely protons are to experience dipolar interactions. Typically, the signal decays more rapidly in solid-like materials due to T2 relaxation—that is, solids and gels have shorter T2 relaxation times than liquids due to low rotational mobility enhancing dipolar coupling [34]. The T2 relaxation time for pure water is on the order of 2-3 seconds in unrestricted environments, whereas it is on the order of milliseconds in porous materials due to restricted motion and surface interactions. While both T1 and T2 relaxation times can provide information about the molecular and pore-scale environment, T2 measurements require less time to conduct and are preferred. This experimental study uses measured changes in the T2 distribution to infer changes in the pore scale environment due to biofilm growth within the bioreactor. Biofilm formation in porous media leads to shorter T2 relaxation times [25, 27]. Porous media influences the NMR relaxation process in several ways. The presence of solid surfaces creates relaxation sinks and may introduce paramagnetic impurities, as well as generating susceptibility-induced magnetic field inhomogeneities. T2 in a pore is also influenced by the viscosity and chemical properties of the bulk fluid. Furthermore, diffusion of the liquid molecules between pores, and diffusion within the pore due to local magnetic field gradients also affect the T2 relaxation behavior of a porous media system. The expression for the rate of T2 relaxation in porous media 122 includes the relaxation time of the bulk media, T2B, the surface relaxation time, T2S, and relaxation time due to diffusion, T2D [35]. 1 𝑇𝑇2 = 1 𝑇𝑇2,𝐵𝐵 + 1𝑇𝑇2,𝑆𝑆 + 1𝑇𝑇2,𝐷𝐷 (5.1) When the bulk fluid is water, 1/T2B is typically very small and is often neglected in literature on relaxometry in porous materials. However, as the rotational mobility of the bulk fluid decreases due to biofilm growth in the pore space, 1/T2B increases in importance to the overall T2 relaxation rate [36]. Surface relaxation, T2S, depends on the surface relaxivity, ρ, which describes the efficiency of the mineral surface to enhance relaxation, and the surface to volume ratio, S/V [37]. 1 𝑇𝑇2,𝑆𝑆 = 𝜌𝜌 𝑆𝑆𝑉𝑉 (5.2) Since biofilm is composed of bacterial cells in a hydrated gel matrix, the T2 relaxation time of fluid contained in the biofilm is shorter than for the bulk fluid alone. As the biofilm grows into the pore spaces, proportionally more protons will be bound in, or interact with, the EPS matrix, thereby shifting the T2 distribution toward shorter relaxation times. Enhanced T2 relaxation due to biofilm formation is expected to be caused by reduced rotational mobility in the pore fluid as the EPS matrix contributes a gel phase and the cells produce biomacromolecules with shorter relaxation than bulk water (T2B). Additional relaxation effects may be due to changes in the pore structure and surface due to the biofilm growth on the grain surfaces (T2S) [38]. T2D is directly related to the echo spacing, tE, according to 123 1 𝑇𝑇2,𝐷𝐷 = 𝐷𝐷 (𝛾𝛾𝛾𝛾𝑡𝑡𝐸𝐸)212 (5.3) where D is the diffusion coefficient [L2 t-1], γ is the gyromagnetic ratio of hydrogen, 2.675 x 108 rad/(T s), and G is the local effective magnetic field gradient [Gauss L-1]. By selecting a short tE, this term can be made sufficiently small as to be neglected. Repeating the experiment with a longer tE indicates whether there are indeed enhanced relaxation effects due to diffusion to consider. Materials and Methods Bioreactor Design and Construction The lab-scale bioreactor was designed to model the near-wellbore environment and was constructed inside an aluminum Faraday cage using four concentric PVC pipe sections (Titan Industries, Paxton, NE), ranging from the inner 8in (20cm) diameter solid pipe to the outer 20in (51cm) solid pipe (Figure 1). The two middle pipe sections, 10in (25cm) and 18in (46cm) diameter respectively, were screened over the entire length with 8 rows of 0.020in (0.051cm) wide slots spaced at 0.5in (1.3cm) intervals. All of the pipes were 2.5ft (76cm) tall. Top and bottom plates were constructed from 0.5in (1.3cm) high density rigid expanded PVC sheeting with machined 0.125in (0.32cm) concentric grooves to allow nesting and sealing of the vertical pipe sections. 124 Figure 5.1. Model well-bore bioreactor. The 3.5in (8.9cm) diameter NMR logging probe was installed in the lab-scale radial flow bioreactor and Faraday cage. The purpose of the Faraday cage was to reduce external radio frequency noise caused by various electromagnetic sources in the laboratory. The 3in (7.6cm) annulus between the slotted pipes was wet-filled with approximately 2.3ft3 (0.065m3.) of No. 2095 Granusil® silica (quartz) sand (Unimin Corp., Ottowa, MN) having a nominal diameter of 1 mm and a porosity of approximately 0.37. The combined volume of the pore space and annular reservoirs was approximately 40L. The reactor was disinfected with two pore volumes (80L) of 10% bleach solution with 7g/L Tween80 (Fisher BioReagents, Waltham, MA) followed by a flush with 80L 125 sterile de-ionized (DI) water. Two pore volumes (80L) of sterile 2.52g/L sodium thiosulfate solution was pumped into the reactor to neutralize any remaining bleach. The sodium thiosulfate solution was flushed from the reactor with 80L of sterile buffer solution consisting of 3g/L NaNO3, 0.12g/L K2HPO4, and 0.04g/L KH2PO4. NMR measurements were made in the buffer-filled reactor with the NMR logging tool to establish a baseline T2 distribution for the reactor prior to any biofilm growth. Later measurements were compared to this initial condition to identify changes in T2 relaxation time distributions. Experimental constraints prevented the testing of an un- inoculated control in parallel with measurements of the biofilm reactor. These constraints are primarily associated with the uncertainties that would have been introduced by moving the NMR probe between the reactors to conduct measurements. Moving the probe during the experiment could influence the results since a slightly different shell within the reactor would be excited and measured for each placement of the probe. For these reasons, a longitudinal study of a single reactor was the preferred method for this initial experiment. Bacterial Culture One mL frozen stock of Bacillus mojavensis was cultured in 100mL of modified Brain-Heart Infusion (BHI) broth (36g/L Brain Heart Infusion (BHI) (Becton, Dickinson and Co., Sparks, MD), 3g/L NaNO3, 0.75g/L NH4Cl, 40g/L NaCl) on a shaker table at 150rpm for 48 hours. Then the 100mL inoculum was added to 10L of the modified BHI broth and mixed on a stir plate at 1150rpm for 60 hours to a concentration of 126 approximately 7log10 colony-forming units (cfu)/mL. B. mojavensis was selected because of the abundant mucoid biofilm it produces [16, 28]. The 10L inoculum was pumped into the reactor with two peristaltic pumps (Cole- Parmer Model 7553-80 with Masterflex Easy-Load 7515-00 heads) at 650-700 mL/min through eight lines of No. 16 vinyl tubing. The pumps were turned off for approximately 11 hours to allow the bacteria to attach to the sand. Following the attachment period, radial flow of substrate through the sand promoted bacterial growth and biofilm accumulation which was monitored by the NMR probe. No attempt was made to maintain a B. mojavensis monoculture within the reactor for the duration of the experiment. Following inoculation, subsequent batches of substrate were mixed and pumped into the reactor in a non-sterile manner. Sterile conditions could not be maintained due to experimental constraints imposed by the large volumes of substrate used and waste produced daily. Following inoculation, 40L of re-circulating substrate was removed daily from the system and replaced with 40L of fresh substrate. Except during no-flow NMR measurements, the substrate was re-circulated continuously at a rate of 650-700mL/min which translates to a specific discharge of approximately 0.04cm/min and a pore velocity of approximately 0.02mm/s at the radial center of the sand annulus. This flowrate corresponds to the pore volume of the reactor being replaced every 50-60 minutes. 127 NMR Data Acquisition T2 relaxation measurements used a CPMG pulse sequence [39, 40] with excitation pulses of either 245 kHz or 290 kHz corresponding to excitation regions at 19cm and 17cm (7.5in and 7in) from the center of the probe respectively. Each excitation shell is 0.5m high and several millimeters thick. Eight experiments were repeated at the same time daily (Table 5.1). Each experiment used a repetition time, Tr, of 5s to allow for T1 relaxation. Observing changes in the T2 measurement as a function of the echo spacing tE can provide an indication of the significance of NMR diffusion relaxation effects. Measurements were made under flow and no flow conditions to determine if the fluid flow affected the T2 measurement. Data was also collected under two probe tuning protocols. The first held the NMR excitation frequency constant for each experiment; the second allowed the NMR instrument to auto-tune with an adjustable excitation frequency periodically within each experiment. This allowed a determination of whether changes in probe tuning affected the T2 measurement. 128 Exp. No. Averages tE (ms) Flow Excitation Frequency Duration 1 360 6.0 No Auto-tuned 30 min 2 360 6.0 Yes Auto-tuned 30 min 3 360 1.5 No Constant 30 min 4 360 1.5 Yes Constant 30 min 5 360 6.0 No Constant 30 min 6 360 6.0 Yes Constant 30 min 7 360 1.5 No Auto-tuned 30 min 8 2880 1.5 Yes Auto-tuned 4 hours Table 5.1. NMR experiments with well-logging probe. The data processing software uses the inverse Laplace transform to generate a T2 distribution for the reactor excitation shell. Because of the generally low signal to noise ratio that is typical for a low-field NMR device in natural geologic material, the Javelin data interpretation software also calculates a noise-robust parameter based on the mean amplitude of the echoes in the record CPMG. The Square of Echoes (SOE) is calculated as the squared value of the mean of echoes. A reduction in the calculated SOE over the course of the experimental period indicates that the mean value of the T2 relaxation time is decreasing as the conductivity of the porous media in the reactor decreases. 129 Sampling and Imaging A sample of re-circulating substrate was collected daily during Experiment 6 (Table 5.1) and immediately serially diluted and plated [41] to estimate the quantity of viable cells in the reactor bulk fluid. While the suspended cell counts are not directly indicative of biofilm formation, or more specifically of EPS production, they provide a general measure of growth conditions and cell population within the reactor. On day 8, the reactor was drained and NMR measurements were acquired using Experiment 7 parameters (Table 5.1). Following the measurements, the bioreactor was destructively sampled to confirm biofilm accumulation in field-relevant quantities. The sand was removed from the reactor in layers, with samples collected in sterile, pre- weighed 15mL Falcon tubes for imaging and cell population analysis. The samples were collected from the NMR probe’s sensitive region in the annulus center at three depths— top (6in (15cm) deep from the top of pipe), middle (12-15in (30 – 38 cm) deep) and bottom (28in (71cm) deep). Six samples were collected for both population analysis with the drop plate method and imaging with stereoscopic and scanning electron microscopy. Ten mL of sterile phosphate buffered saline (PBS) solution was added to each sample of sand collected for population analysis. The samples were vortexed with a Thermolyne MaxiMix II Type 37600 mixer for 30 seconds each, then sonicated for 2 minutes (Tutthauer CSU-3). Prior to serial dilution and plating, each sample was again vortexed for 30 seconds to remove attached bacteria from the sand particles and break up clumps of cells. Following plating, the buffer solution was poured off and the sand 130 samples were dried at 65°C for until their masses stabilized. The mass of dry sand and the plate count from each sample indicate cfu/g sand in the reactor. For stereoscope microscopy analysis, biofouled sand samples from the radial flow reactor and clean control sand were stained with 300μL of 40μM Syto 9 (Molecular Probes, NY USA) for 30 minutes. The samples were rinsed with 0.2μm filtered (VWR, NJ, USA) distilled water and immediately imaged at 470nm excitation with a Niko SMZ 1500 (Nikon, NY, USA) stereoscope equipped with an EXFO Xcite 120 fluorescence illumination system. Additionally, images were acquired using a Zeiss Supra 55VP scanning electron microscope (Zeiss, USA). Sand and biofilm from the radial flow reactor and control sand samples were sputter coated with iridium and high-resolution images were taken at 1.0kV at a working distance of 3-4mm. Results and Discussion The experimental NMR data shows a shift in the T2 distribution to faster decay times, indicating that the fluid properties and pore environment changed due to biofilm growth (Figure 2). No significant relaxation enhancement due to diffusion, flow, or changes in probe tuning was observed. Therefore, unless otherwise noted, the data presented was collected during Experiment 8 where the level of background noise was lowest due to the high number of averages. The mean log T2 relaxation time decreased from approximately 710ms following the buffer pulse to approximately 390ms on day 7. 131 Figure 2 shows the signal attenuation (top) and T2 distributions (bottom) measured during the course of testing. Day 1 measurements were conducted in the disinfected sand pack saturated with a phosphate buffer solution using Experiment 7 parameters and 4560 averages. Measurements taken during the inoculation of the reactor with B. mojavensis occurred at day 1.5. Experiments conducted on day 2 represent the first potential measurement of attached biofilm within the reactor. The signal decay curves and T2 distributions collected days 3-5 show significant overlap.The data collected on days 6 and 7 likewise overlap and are shown in Figure 2 as a thick solid line. The dash-dot curve in both panels shows the data obtained on day 8 from the drained reactor (Experiment 7). 132 Figure 5.2. Time evolution of CPMG signal decay curves and T2 distributions. Increased signal attenuation with biofilm formation produces steeper CPMG signal decay curves (top panel). The distribution of T2 relaxation times (bottom panel) shifted to faster decay times as biofilm grew in the reactor. Data collected days 3 and 4 overlap the day 5 curve and are not shown. Likewise, the day 6 data is obscured by the day 7 curve and is not shown. Day 8 data was collected from the drained reactor. By day 2, the CPMG signal decay curve is notably steeper and the T2 distribution shows a narrower peak, centered at approximately 450ms (Figure 2). These data indicate an increase in the proportion of protons experiencing faster relaxation as would be expected in the event of biofilm formation. The rate of change of the signal response decreased after day 2, with little change recorded in the signal days 3-5. The day 6 and 7 data show a decreased signal amplitude in the top panel relative to day 5, indicating a decrease in the measured reactor water content. The NMR measurement from the drained reactor on day 8 reflects the presence of biofilm, as seen in the residual peak between 133 200—300ms. The smaller peak at approximately 7ms most likely originates from water or biofilm that is directly bound on and interacting with the sand surface. The lower amplitude of the signal from the drained reactor reflects the desaturation of the sandpack. The measured reactor water content decreased from 37.3% at inoculation to 32.2% on day 7. After draining the reactor on day 8, the measured water content was 7.0% and the mean log T2 relaxation time was 121ms. The decrease in measured water content during the growth phase is best explained by microbial gas production within the pores as a metabolic by-product. This biologically-driven reduction in water content of the reactor sandpack may have contributed to shorter T2 relaxation times by increasing the effective saturated surface area to fluid volume ratio (S/V) in Eqn. 2. However, the magnitude of the T2 shift between inoculation and day 7 significantly exceeds that from between day 7 and day 8 after the reactor was drained (Figure 2). The reduction in mean log T2 relaxation time by day 7 was approximately 320ms corresponding to a water content decrease of 5.1 percentage points. The 25 percentage point reduction in water content after draining the reactor produced only a further 270ms reduction in the mean log T2 relaxation time. T2 relaxation times decreased nearly six times more on a water content basis [ms/% water] during the growth phase as compared to when the reactor was drained. This suggests that decrease in water content in the reactor during the experiment was likely not the primary mechanism causing the observed shift in the T2 relaxation distribution. The best explanation for the observed decrease in T2 relaxation times is biofilm accumulation in the reactor sandpack. 134 Figure 5.3. SOE Reduction. Data for the set of long-average experiments shows a decrease of approximately 53% in the squared value of the mean of echoes over the duration of the experiment. The measured SOE, normalized with respect to water content squared, decreased 53% between day 1 and day 7 (Figure 3). The normalized SOE value shows the same trends as observed in the signal attenuation and T2 distribution data in Figure 2, where the initial change is most significant followed by stabilization in the signal response. HPC of the daily samples show an initial drop in cfu numbers after inoculation, followed by a steady increase over the duration of the experiment (Figure 4). From an inoculum concentration on the order of 7log10cfu/mL injected into the reactor on day 1.5, the day 2 HPC yielded colony counts of approximately 5.5log10cfu/mL. Combined with the NMR results showing a decrease in T2 relaxation times over the same period, this 135 decline in HPC can be attributed to bacterial attachment and initial biofilm formation on the sand particles. Planktonic cells increased in number to approximately 6.5log10cfu/mL on days 3 and 4. These higher colony counts correspond to enhanced signal attenuation and decreases in the mean log T2 relaxation time, though they are necessarily not a measurement of the cell numbers in the biofilm. The increase in SOE observed around day 5 may correspond to a biofilm sloughing event since heterotrophic plate counts from day 5 were nearly an order of magnitude higher than those from day 4, 7.4log10 versus 6.5log10 cfu/mL, respectively. After day 5, a slower rate of increase in colony numbers was observed than between days 4 and 5, suggesting a secondary attachment period may have occurred. This interpretation is supported by the NMR data which shows a decrease in the normalized SOE over the same period. In general, the HPC data and the diverse colony morphologies indicate that conditions in the bioreactor were favorable for mixed population bacterial growth. 136 Figure 5.4. Heterotrophic Plate Counts (HPC). Daily HPC data shows a strong initial attachment of cells from approximately 7log10cfu/mL in the 10L inoculum to 5.5log10cfu/mL on day 2. Increasing colony numbers resulted in a final population of approximately 8log10cfu/mL by day 8. The average biofilm HPC from the sand samples was approximately 8.5log10 cfu/g sand, shown on the secondary axis. When the bioreactor was drained and destructively sampled, the sand was sticky, consistent with presence of a biofilm bridging the pore spaces of the sand. Cell population analysis of sand samples indicates that attached bacterial concentrations in the bioreactor were approximately 7log10 to 9log10cfu/g dry sand, with an average in the reactor of 8.5log10cfu/g sand. This concentration is similar to cell counts noted in the literature for subsurface biofilms used to degrade trace organics, where populations are typically in the range of 6log10 to 9log10 cfu/g soil [15, 26]. 137 Figure 5.5. Porous media microscopy confirmed biofilm accumulation in the region of the reactor where NMR data was collected. a) Scanning electron microscope (SEM) image of mixed population bacterial cells and extracellular polymeric substance (EPS) on a sand particle collected from the middle depth of the reactor. Region 1 shows cocci bacteria while Region 2 shows rod-like cells. Bacillus mojavensis is a rod-shaped bacteria. Depth 15 in. Scale bar is 2 µm. b) Stereoscope image of EPS encasing the bacterial cells and binding grains of 1mm sand, Depth 15 in. 40X magnification. 138 SEM images (Figure 5.5) showed a mixed bacterial population of rod and cocci cells, with thicker EPS at the bottom of the reactor where the fresh nutrient supply entered the reactor. Compared to samples collected in the middle and upper regions of the reactor (Figure 5a), individual cells were less distinguishable on samples collected from the bottom due to the thicker EPS matrix (not shown). Stereoscopic microscopy qualitatively confirmed the presence of biofilm on and between sand particles (Figure 5b), where the matrix fluoresces in green and the cells are visible as bright flecks. Microscopy confirms bacterial growth and EPS production within the reactor. Population analysis indicates both quantity and diversity of heterotrophic bacteria present without directly accounting for the presence of EPS. Microscopy of the sand can confirm the presence of the EPS matrix, but does little to elucidate the in-situ characteristics and hydrodynamics of the biofouled pore space. For these reasons, characterizations of observed biofilm accumulation are qualitative and indicative of EPS formation within the NMR logging tool’s sensitive region but are not intended to quantify the total amount of EPS formed in the reactor. Several studies have demonstrated that biofilm growth in soils and rock reduces the hydraulic conductivity and permeability of the media, often by several orders of magnitude [5, 15, 42, 43]. Furthermore, biofilm itself is a porous media with an internal architecture that includes voids and channels [44-46]. The enhanced NMR relaxation observed in this study could be due to the changing surface properties if the biofilm coats the porous media, represented as an increase in 1/T2S. However, if the biopolymers are distributed throughout the pore volume then the faster relaxation could be dominated by 139 exchange of protons between the water and the biopolymers, which would be represented as an increase in 1/T2B. NMR studies on T2 decay in porous media typically focus on the influence of T2S and T2D on the overall relaxation behavior of the medium [47-50]. When the bulk fluid in the pore space changes, however, as it does during biofilm formation, the influence of T2B can no longer be neglected. In the bulk phase, the production of polymer-like EPS and biomacromolecules will enhance spin relaxation as protons bound to the polymers and dissolved organics rapidly exchange with free protons on the liquid molecules [51]. This relaxation mechanism produces shorter relaxation times than would be expected in bulk water. As the content of EPS and biomacromolecules increases within the pore space relative to the initial condition, the weighted average of ‘bound’ and ‘free’ proton T2 times will shift in the direction of the polymer relaxation time to shorter T2 decay times [3, 38]. From a macroscopic perspective, biofilm may act as a relatively impermeable surface, insofar as it is restrictive to convective flow within pores. At the molecular level, however, biofilm is composed of approximately 97% water [52]. For these reasons, we attribute the change in relaxation behavior observed in this experiment primarily to changes in the bulk relaxation of the pore fluid, which includes both a liquid and polymer-gel phase. In these experiments it is proposed that an increase in 1/T2B is the best way to conceptualize the observed enhancement in the NMR T2 relaxation. These experiments demonstrate that a commercially available low-cost NMR logging tool can detect small to moderate changes in T2 distribution due to biofilm 140 accumulation in quartz sand under laboratory conditions. Mean log T2 relaxation times decreased from 710ms when the reactor contained a sterile buffer solution to 389ms following 7 days of biofilm cultivation. Over the same period, the noise-robust SOE parameter decreased by 53%, indicating an increase in signal attenuation and shorter T2 relaxation times. Normalizing the data with respect to water content squared in the reactor indicates that the change in T2 is not primarily driven by the saturation state of the porous media in the reactor, but rather by biofilm accumulation. Heterotrophic plate counts suggest that planktonic cells in the reactor increased in abundance from approximately 5.5log10cfu/mL on day 2 to 8log10cfu/mL on day 8. Population data from destructive sampling confirmed colony counts of attached cells on the order of 8log10cfu/g dry sand. Scanning electron and stereoscope microscopy confirmed the presence of the biofilm matrix attached to the sand particles compared to control sand. Our results, therefore, show that the measured shift in the reactor T2 relaxation distribution toward faster signal decay times is best explained by biofilm accumulation in the reactor pore spaces. Our findings have the potential to improve monitoring methods for bioremediation applications involving the use of bio-barriers to slow the flow of groundwater or consume chemical contaminants. Deploying an array of the NMR probes in wells in the bio-barrier zone and recording signal changes over time could provide another measure of the robustness of the bio-barrier with respect to depth. Preparations are underway to use the NMR logging tool in situ to detect biofilm formation at an engineered field site in Butte, Montana. 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Hornemann, J.A., et al., Biopolymer and water dynamics in microbial biofilm extracellular polymeric substance. Biomacromolecules, 2008. 9(9): p. 2322-2328. 146 CHAPTER SIX IN-SITU DETECTION OF SUBSURFACE BIOFILM USING LOW-FIELD NMR – A FIELD STUDY Contribution of Authors and Co-Authors Manuscript in Chapter 6 Author: Catherine M. Kirkland Contributions: Helped conceive and implement study design. Collected and analyzed data. Wrote manuscript. Co-Author: Maria P. Herrling Contributions: Helped conceive and implement study design. Collected and analyzed data. Provided feedback and comments on the manuscript. Co-Author: Randy Hiebert Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. Co-Author: Andrew T. Bender Contributions: Collected and analyzed data. Co-Author: Elliot Grunewald Contributions: Helped conceive and implement study design. Provided supervision and oversight on data collection and analysis. Provided feedback and comments on the manuscript. Co-Author: David O. Walsh Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. 147 Co-Author: Sarah L. Codd Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. 148 Manuscript Information Page Catherine M. Kirkland, Maria P. Herrling, Randy Hiebert, Andrew T. Bender, Elliot Grunewald, David O. Walsh, Sarah L. Codd Environmental Science and Technology Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-review journal ____ Accepted by a peer-reviewed journal _X___ Published in a peer-reviewed journal American Chemical Society Vol. 49, No. 18, Pages 11045 - 11052, September 2015 149 IN-SITU DETECTION OF SUBSURFACE BIOFILM USING LOW-FIELD NMR – A FIELD STUDY Abstract Subsurface biofilms are central to bioremediation of chemical contaminants in soil and groundwater whereby micro-organisms degrade or sequester environmental pollutants like nitrate, hydrocarbons, chlorinated solvents and heavy metals. Current methods to monitor subsurface biofilm growth in-situ are indirect. Previous laboratory research conducted at MSU has indicated that low-field nuclear magnetic resonance (NMR) is sensitive to biofilm growth in porous media, where biofilm contributes a polymer gel-like phase and enhances T2 relaxation. Here we show that a small diameter NMR well logging tool can detect biofilm accumulation in the subsurface using the change in T2 relaxation behavior over time. T2 relaxation distributions were measured over an 18 day experimental period by two NMR probes, operating at approximately 275 kHz and 400 kHz, installed in 10.2 cm wells in an engineered field testing site. The mean log T2 relaxation times were reduced by 62% and 43%, respectively, while biofilm was cultivated in the soil surrounding each well. Biofilm growth was confirmed by bleaching and flushing the wells and observing the NMR signal’s return to baseline. This result provides a direct and non-invasive method to spatio-temporally monitor biofilm accumulation in the subsurface. 150 Introduction Reactive biofilm barriers, composed of attached microbial cells, extracellular polymeric substances (EPS), and entangled organic and inorganic molecules, can be cultivated in the subsurface to degrade and immobilize chemical contaminants as part of a bioremediation project [1]. Contaminants in the groundwater, including nitrates, heavy metals, hydrocarbons, and some chlorinated solvents, are consumed or transformed by bacteria attached to soil surfaces while the EPS matrix slows the groundwater flow by reducing the soil’s hydraulic conductivity [2-7]. While biobarrier technology is well- established to clean contaminated groundwater [8, 9], it is challenging with current technology to monitor the in-situ accumulation and maturation of the biofilm nondestructively. Conventional methods to infer biofilm growth in the subsurface include reduced saturated hydraulic conductivity [10-12]. While hydraulic conductivity measurements can be useful for describing how easily the soil conveys water, they are less useful for monitoring the growth, maturation and decay of the biobarrier with spatial and temporal resolution. We present results indicating a small diameter nuclear magnetic resonance (NMR) well-logging tool provides additional means of monitoring biofilm accumulation and condition over time in the subsurface by detecting changes in the NMR signal response. Chemical and physical changes in a sample can impact a wide range of NMR parameters, including NMR frequency shifts, NMR relaxation times T1 and T2, and diffusion coefficients [13]. NMR frequency shifts are typically caused by chemical changes in the fluid sample. However at very low magnetic fields (<1 MHz) even large 151 proton chemical shifts such as those between oil and water are not detectable. Diffusion coefficients require additional magnetic field gradient hardware for detection, but can be used to distinguish different viscosity fluids in a sample or determine the average pore size of a material by measuring the timescale of the restricted diffusion [9]. NMR relaxation, T1 and T2, is caused by the correlation time of the diffusing fluid with respect to the resonant frequency of the NMR signal, as well as paramagnetic molecules the fluid comes into contact with. For these reasons, NMR relaxation times are affected by pore size distributions, fluid viscosity, and chemical changes in the mineralogy of any solid matrix or dissolved ions. Measuring T2 is significantly faster than measuring T1. T2 measurements are generally considered the most robust low field measurement considering acquisition times and signal-to-noise. In a T2 measurement, the induced NMR signal echoes decay at a rate of 1/T2, where T2 is the spin-spin relaxation time associated with interactions in the fluid-pore environment. Analyzing the signal decay curve with the inverse Laplace transform produces a statistical distribution of T2 relaxation times that reflect the variety of pore- scale environments occupied by hydrogen protons in the excitation shell. The T2 relaxation time distribution in heterogeneous porous media is used, both in hydrogeologic analysis [14] and in oil and gas exploration [15-18], to estimate the pore size distribution in the formation and for fluid typing [9]. Biofilm accumulation in pores causes T2 relaxation times to decrease compared to unclogged pores as the biofilm EPS contributes a biopolymer gel-like phase [19, 20]. Water in the EPS matrix contributes a reduced NMR relaxation signal [21] and demonstrates restricted diffusion [22]. 152 The NMR well-logging tool used in this study measures T2 relaxation and was designed for use in small diameter ‘slim-line’ boreholes for groundwater exploration and aquifer characterization [14]. In preliminary work, it was shown that this NMR logging tool can detect biofilm growth [20]. The tool was tested in a laboratory-scale model well- bore bioreactor filled with silica sand and inoculated with Bacillus mojavensis. Biofilm was cultivated in the reactor over 8 days, during which the measured mean log T2 relaxation time decreased by 45%, from 710 ms to 389 ms [20]. Biofilm accumulation was confirmed with destructive sampling and subsequent heterotrophic plate counts and microscopy. The current research significantly advances previous work by showing that the same logging tool can monitor biofilm growth at field scale, 6 m underground where complex water chemical interactions exist. The NMR tool could be deployed to bioremediation sites in parallel with currently used methods to enhance the understanding of biofilm growth in-situ. Methods This study used two 8.9 cm diameter, 1.37 m long NMR well-logging probes (JP350 Javelin by Vista Clara, Inc., Mukilteo, WA) to monitor T2 relaxation distributions over time as an indication of biofilm accumulation in the soil in an engineered test cell. The test cell is 55 m by 40 m at the surface and is 6m deep with 2:1 side slopes (x:z). The cell is lined with a 30 mm polyvinylchloride (PVC) liner and contains water up to 1 - 1.2 m beneath the ground surface. The test cell contains a number of boreholes of varying dimensions that were prepared for a previous experiment [7]. Two of the 10.2 cm 153 boreholes were used for measurements of T2 relaxation over an 18-day experimental period. A bleach solution consisting of 2 lb (907 g) sodium dichloro-s-triazinetrione dihydrate (C3H4Cl2N3NaO5) (Spa Guard Chlorinating Concentrate, Bio-Lab Inc., Lawrenceville, GA) was pumped into the soil around the two wells at the beginning and end of the experiment. A 30 L inoculum of Pseudomonas fluorescens strain CPC211a was injected into each well’s measurement zone and was cultivated with a pulsed flow of molasses-based substrate (10 g/L molasses (Aunt Patty’s Blackstrap Molasses, Eugene, OR), 3 g/L sodium nitrate (SQM industrial grade prills, 98%, SQM North America, Atlanta, GA), 1 g/L yeast extract (Acros Organics, Geel, Belgium), 0.12 g/L potassium phosphate dibasic, and 0.04 g/L potassium phosphate monobasic (Thermo-Fisher Scientific, Waltham, MA)) for 10 days. A 4-day starvation period followed the growth phase. T2 measurements were conducted at the well bottom daily during the growth phase, Days 1-10, and twice during the starvation phase, Days 12 and 14. Water samples were collected prior to T2 experiments for subsequent pH measurement and microbial analysis using the drop plate method [23]. T2 relaxation measurements were also recorded over the bottom 3-3.5 m of well depth twice during the experiment; wells were logged before inoculation and during the starvation period. At the end of the experiment, the sodium dichlor bleach solution and high groundwater flows were applied to the experimental region as a validation of biofilm growth, since these stress tests would be expected to remove EPS formed during the growth phase. The experiment was designed to distinguish normal variation in signal response due to environmental noise and probe 154 placement from those changes resulting from biological activity and biofilm growth. The experimental sequence of events for a single well is shown in Table 6.1; both wells received identical treatment. Additional details regarding experimental methods are provided in Supporting Information. The two NMR probes were tuned to different frequencies, corresponding to excitation shells at different radii from the well centers. The lower frequency probe (LF) was placed in one well, called the LF well, and was tuned to 245 and 290 kHz. Two excitation shells 0.5 m in height and a few mm thick were located 17-19 cm from the LF well center. The higher frequency probe (HF), installed in the HF well, was tuned to 360 and 425 kHz, producing two excitation shells located 11-13 cm from the HF well center. The probes are identical low-field NMR tools other than the tuning frequency. 155 Day Experimental Task Purpose (-2)-( -1) Site Preparation Create a 'biofilm-free' initial condition Injection of 75 – 115 L sodium dichlor concentrate solution Flush with test cell groundwater at 45.5 L/min 0 Well logs Measure baseline T2 distribution as a function of depth T2 distributions measured in 0.5 m increments over the bottom 3-3.5 m saturated well depth 1 Inoculation Promote attachment and biofilm formation by target organism Injection of 30 L inoculum culture of Pseudomonas fluorescens CPC211a into measurement zone surrounding the NMR probe at well bottom T2 measurement in fixed location at well bottom Measure baseline T2 distribution at the well bottom 2-10 Biofilm Growth Phase Promote and measure biofilm accumulation Injection of 380-415 L molasses-based substrate daily at 1.2 L/min Measurements of T2 relaxation distributions daily in fixed location at well bottom 156 Day Experimental Task Purpose 11-14 Starvation Phase Monitor biofilm resilience Establish 'initial condition' to assess signal variation due to probe re-location Measurements of T2 relaxation distributions Day 12 and 14 at the well bottom 12 Well logs Measure T2 distribution as a function of depth after biofilm growth Evaluate signal variation due to probe re-location T2 distributions measured in 0.5 m increments over the bottom 3-3.5 m saturated well depth 14 Biofilm Stress Tests Monitor signal response to stresses intended to destroy biofilm Flush with test cell groundwater at 45.5 L/min Injection of 75-115 L sodium dichlor concentrate solution Measurements of T2 relaxation distributions in fixed location at well bottom 15 Measurement of final conditions Verify biofilm accumulation by signal restoration after detachment and removal of biofilm Flush with test cell groundwater at 45.5 L/min 157 Measurements of T2 relaxation distributions in fixed location at well bottom Table 6.1. Experiment Overview A diverter disk attachment was connected to the top of each probe to direct the substrate and high flows of water into the soil around the well-bore, rather than into the water column above the probe. A millimeter-scale gap was left between the disk and the well casing to ensure that the probe could be removed from the well. The disk was machined with an attachment for a standard garden hose to accommodate high volume flushing and four 0.1 cm holes for low-flow nutrient tubing (Figure 6.1). Pore velocity during the substrate injection was approximately 0.2 cm/min in the LF well and 0.4 cm/min in the HF well each probe’s sensitive zone. The high volume flush created a pore velocity of approximately 9.2 cm/min in the LF well and 14.8 cm/min in the HF well. 158 Figure 6.1. A diverter disk attachment on the top of each NMR logging tool directed substrate and high flow groundwater flushes into the biofilm growth region in the tool’s sensitive zone in the soil and reduced backflow up the well casing. For each probe, Experiment 1 and 2 (Table 6.2) constitute one standard Carr- Purcell-Meiboom-Gill (CPMG)[24, 25] measurement of approximately 27 minutes. This standard measurement was conducted 4 times in each well for a typical well-bottom measurement of approximately 2 hours Days 0-15, excluding Days 11 and 13. The data was averaged to obtain a single measurement for each day for each well. This standard measurement was also used at each 0.5 m depth increment when vertically logging the wells before and after biofilm growth on Day -1 and Day 12. An additional 12 standard 159 measurements were made in one or the other well on alternating days to improve the signal to noise ratio in the data collected and to confirm that 4 measurements was adequate to describe the system. LF Probe HF Probe Expt 1 Expt 2 Expt 1 Expt 2 Echo time, tE (ms) 1.5 1.5 1.3 1.3 Repetition time, Tr (ms) 1500 5000 1500 5000 Acquisition time (ms) 50 500 50 500 No. of echoes 34 334 39 385 No. of averages 600 150 600 150 Table 6.2. NMR Experimental Parameters Results and Discussion Both the LF and HF NMR logging probes recorded changing distributions of T2 relaxation times during the experiment with reductions of 62% and 43%, respectively, in the mean log T2 during the biofilm growth phase (Figure 6.2). In the LF well, the T2 relaxation time was 29 ms on Day 1 and fell to an average of 11 ms between Days 5-12. Over the same period, the HF well T2 relaxation time fell from 50 ms to an average of 28 ms. Data from both wells initially showed a T2 distribution with two peaks that transitioned to a single peak distribution by Day 6 (Figure 6.3 (a) and (b)). 160 Figure 6.2. Mean log T2. Mean log T2 relaxation times decreased 62% (LF) and 43% (HF) indicating that protons became more rotationally constrained as biofilm was cultivated in the soil. (LF well data is shown with square markers, HF well data with triangle markers). The first measurements were performed on Day -1 after bleaching and flushing both wells. Inoculation occurred on Day 1. Substrate was injected daily Days 2-10. Days 11-14, the bacteria were starved. On Day 14, T2 relaxation was measured, then the wells were flushed with high flows of groundwater from the test cell and T2 was measured again. Then a bleach solution was injected to oxidize remaining organics. Day 15 data was collected after flushing the bleach solution from the wells. 161 Figure 6.3. T2 distribution for LF well (a) and HF well (b). The curves show the transition over time of the distribution of T2 relaxation times in each well, beginning at inoculation (short dash line). As biofilm grew in the NMR probe’s sensitive region, the T2 relaxation times shifted to a single peak distribution centered about a shorter mean log T2 time (solid lines). After flushing and bleaching each well, the T2 relaxation distributions closely resembled the initial distributions (dash-dot lines). In the Day 1 data, the relaxation time distribution is bimodal. Given that there was only one fluid type at this time, the relaxation distribution peaks represent the relative pore size distribution. Water in the smaller pores relaxes more quickly due to the higher S/V ratio and the more frequent interactions of the diffusing fluid molecules with the grain surfaces [26]. Water in the larger pores experiences fewer interactions on the measurement timescale and yields slower signal decay. 162 As bacteria grow in the soil pores, the creation of gel phase EPS and the resulting exchange of hydrogen in the polymerized structure produces a secondary relaxation mechanism [21]. We attribute the collapsing the bimodal distribution to this mechanism, where the otherwise long relaxation time components shift to shorter relaxation times. In both wells, T2 distributions measured Day 6-12 show a single peak, on the order of 101 ms. The transition to shorter relaxation times is an indication of biofilm accumulation [19, 27, 28]. Data collected on Day 15 after flushing and bleaching each well shows a return to the bimodal T2 distribution that typified the system prior to biofilm growth. On Day 12, following two days of biofilm starvation, the two probes were raised from the well bottom to record T2 relaxation over 3.0-3.5 m of saturated well depth in 0.5 m increments. In the HF well data set (Figure 6.2, triangles), the two data points collected on Day 12 show the difference in the measurements due to raising and replacing the probe in its original position. In the LF well dataset, the Day 12 data point (Figure 6.2, squares) was measured prior to raising the probe. The measurement made after re- positioning the probe at the bottom of the LF well was made on Day 14. For both data sets, the open marker represents the data collected after the probe was repositioned at the bottom of the well. The variance exists both because of inherent noise in the data and because the probe was likely exciting a slightly different shell within the soil where heterogeneities exist in both the soil and biofilm. The difference is 17% and 14%, respectively, in the LF and HF wells and is significantly less than the change in signal response measured during the biofilm growth phase. The lower-value data points collected on Day 14 show that the biofilm surrounding both wells remained intact and 163 relatively robust despite four days of starvation, compared to earlier measurements during the biofilm growth phase. This is consistent with the durability of the biobarrier originally constructed in the test cell where measured conductivity remained 2 orders of magnitude lower than the initial conductivity after approximately 6 months of starvation[7]. The higher-value data points from each well on Day 14 were measured after a high-flow flush with groundwater from the test cell. The final data point, on Day 15, was collected after the wells were each treated with the same sodium dichlor solution used in the site preparation step to oxidize organics (Supporting Information). It was expected that the high shear stress and bleach solution in the soil pores would detach and remove most of the biofilm previously formed, causing the T2 distribution to return to longer relaxation times. When the test cell was constructed, coarser soil from an off-site location was used in the region where the HF well was located. The finer textured soil surrounding LF well was excavated on-site, sieved, and replaced. This variation in the soil texture between the two wells explains the differing magnitudes of the two relaxation peaks seen in the Day 1 and 15 data (Figure 6.3 (a) and (b)), with relatively more of the pore space around the HF well composed of larger pores and a more even distribution of pores sizes near the LF well. It is likely that the soil mineralogy also differs between the two wells, though examination of such parameters was beyond the scope of this experiment. More signal was recovered following removal in the HF well than in the LF well, likely due to the coarser soil and larger pores in the vicinity of the HF well. These larger 164 pores would allow for bleach solution and detached EPS to be transported more easily through the excitation shell. In the soil around the LF well, bleach solution penetration may have occurred along preferential flow paths and biofilm sloughed from one pore may have been trapped in another smaller pore where it may have still contributed to the measured signal. Furthermore, the initial bleach injection was performed prior to installing the NMR probes, so the bleach was free to migrate up the casing and may not have penetrated the target area at design strength. The final bleach injection, which occurred with the probes in place and below the diversion disks, would have more effectively isolated the biofilm growth area. Some soil pores may have experienced the second bleach pulse but not the first. The measurements collected Days 14 and 15 confirm that the mechanism responsible for the change in T2 relaxation could be reversed with flushing and bleaching the wells and is consistent with biofilm growth. T2 measurements were recorded with respect to depth in each well prior to inoculation and again on Day 12 (Figure 6.4). These well logs show notable differences. In both well logs, there was a change in T2 distribution over the entire measured depth after 10 days of substrate injection at the bottom of the well where the NMR logging tool was deployed. On Day -1, the two well logs show broad T2 distributions marked by two peaks at most depth levels. After the biofilm growth phase, the Day 12 data show a single peak distribution of T2 relaxation times centered about a shorter mean relaxation time. 165 Figure 6.4. LF and HF well profiles measured Day -1 (pre-inoculation) and Day 12 of the biofilm growth phase. T2 distribution as a function of depth shifted to faster decay times over the entire measured depth of each well when biofilm was cultivated at the well bottom. The observed changes in the well log are consistent with biofilm cultivation at the well bottom. The changes in the distributions are most pronounced at the bottom of the well, where the substrate was injected. The diversion disk attached to the top of each probe was located approximately in the middle of the distributions shown, meaning that substrate was directly accessible to the bottom half of each well log. As biofilm accumulated in the soil pores, the substrate would have encountered increased resistance to flow through the soil [10] and the gap between the casing and the diversion disk (~1mm) would have become a preferential flow pathway. Substrate would diffuse into the soil above the probe, in addition to the substrate diffusing through the soil itself. Again the difference between the LF and HF well is instructive, as the upper levels of the 166 HF well show less intensity of effect than the upper levels of the LF well. The HF well is surrounded by coarser soil, making it more difficult for the biofilm to clog the soil pores. Conversely, the LF well region had smaller soil pores initially and experienced more abundant biofilm accumulation as shown by the larger reduction in mean log T2 relaxation times. Microbiological Data and Water Chemical Analysis Heterotrophic plate counts (HPC) in both wells were approximately 1x103 colony- forming units (cfu)/mL after bleaching and prior to inoculation, representing the culturable ‘native’ heterotrophic population of the test cell (Figure 5(a)). After inoculation and substrate injection, the HPC increased in both wells to approximately 1x105 cfu/mL by Day 4. Prior to inoculation and following the injection of the sodium dichlor solution 2-3 days previously, pH measurements were approximately pH 8 (Figure 6.5 (b)). The pH in both wells was stable through Day 3 following inoculation. On Day 4, the pH measurements diverged with the HF well pH increasing to pH 9, while the LF well pH decreased to approximately pH 7. Also on Day 4, the NMR signal in both wells changed significantly, dropping to near the minimum for mean log T2 relaxation time in the LF well where the effect was more pronounced (Figure 6.3). Taken together, the higher HPC values, optimum pH conditions, and faster NMR signal decay indicate that a measureable accumulation of biofilm had grown within the pore spaces of the logging tool’s sensitive zone by Day 4 of the experiment. Since the HPC reflect bacterial cells which are necessarily not attached in biofilms, the NMR logging tool indicates itself as a 167 valuable addition to the bioremediation toolbox through its sensitivity to the biofilm EPS, which is not measurable with plate counts. Figure 6.5. Heterotrophic Plate Counts (HPC) (a) and pH data (b). Both HPC and pH measurements decreased on Day 5 in the two wells compared to earlier values, with increased variability in the measurements noted during the starvation phase when no substrate was injected (LF well data is shown with square markers, HF well data with triangle markers). This water chemical variability was not reflected in the NMR signal response which remained consistent over the same period. Water samples from days 5-10 of the experiment show a decrease in HPC to approximately 1x104 cfu/mL and a decrease in pH to approximately 4.5-5 in both wells. Lower pH promotes bacterial attachment to surfaces [29], while not significantly adversely affecting the biofilm matrix over the relatively short time frame measured [30]. This increased adhesion of bacteria may have reduced the number of suspended cells within the bulk fluid for capture during sampling or caused preferential sampling of the well casing fluid, rather than pore water, due to biofilm clogging the soil pores. It is also possible that the acidic conditions selected for other native bacterial strains that are not 168 culturable on agar plates, like autolithotrophs participating in oxidation and reduction of chemical species in the soil and water. To explore potential causes for the observed drop in pH during testing, benchtop tests were performed using isolates of the two most populous cell morphologies from the agar plates for Days 5-10. These bacteria were cultivated in 100 mL of molasses substrate in Erlenmeyer flasks. The pH of the broth decreased by more than an order of magnitude, from pH 6.2 on average to pH 5.0 on average by Day 4 of the 8-day benchtop experiment. These results are consistent with results from the field study and indicate that metabolic processes, including production of nucleic acids and CO2, contributed to the observed decrease in pH observed in the field study. Another possible explanation of the observed pH change is related to the redox chemistry of sulfur and iron cycling [31, 32]. The groundwater in the lined test cell was static for more than 10 years before the current field study was initiated, creating reducing conditions at the bottom of the test cell. The distinctive odor of hydrogen sulfide (H2S) was readily perceptible in the water pumped from the cell. When exposed to the atmosphere, the reduced Fe(II) in the groundwater oxidized to form a rust-like layer of Fe(III) compounds, likely ferrihydrite, in the large-capacity water storage tanks. The injection of the sodium dichlor solution followed by substrate containing organic carbon, nitrate, and dissolved oxygen would have promoted the oxidation of reduced species in the subsurface. Heterotrophic bacteria, like Pseudomonas fluorescens, use the electron acceptors oxygen and nitrate to oxidize the organic carbon in the media, producing new cells, EPS, and waste products. Oxidation of sulfide leads to 169 acidification, as in the case of acid mine drainage [33], and may account for some of the observed decrease in pH after the initial biofilm growth between Days 1-4. Laboratory studies have shown that NMR relaxation measurements are sensitive to changing soil redox conditions [34] as well as the mineralogic form of iron species [35, 36]. To conclude that the observed changes in relaxation response are due to biofilm growth, it is important, therefore, to consider the possible impact of geochemical changes. First, the timing of the changes is indicative of biofilm growth. Were oxidation-driven geochemical changes strongly influencing T2 during the approximately two days between the initial bleach and inoculation, we would expect to see significant changes in the T2 relaxation behavior of the two well systems Days -1 and 0. Instead we see relatively small changes—first a slight decrease in T2 which may, in fact, be due to abiotic Fe(III) precipitation, then an increase during inoculum injection (Figure 6.2). The increase is most likely due to the make-up of the inoculum broth which was made with DI water rather than water from the test cell. The tight temporal relationship at the end of the experiment between the final flush and bleach and the observed recovery of long T2 times provides further strong evidence that the oxidizing conditions themselves do not drive the shortening of the T2 response. A second reason we expect limited influence from mineralogical transformations pertains to competition for the electron acceptors in the subsurface. The 4 log reduction between the inoculum colony count and the Day 2 HPC (Figure 6.5a) indicates approximately 104 colony forming units (cfu)/mL attached to soil surfaces in the well- bore, creating strong competition for oxygen and nitrate. Oxidation of the H2S would 170 have been more thermodynamically favorable compared to oxidation of iron compounds and would have occurred preferentially [37] where the electron acceptors available exceeded bacterial demand. We therefore expect the contribution of iron precipitation to be moderated and would not expect the iron-driven T2 changes to be any larger than was observed in the small decrease between Days -1 and 0 before competing heterotrophic bacteria were present in the system. Finally, we have also considered the magnitude of the observed T2 shortening to assess whether biofilm growth or moderate changes in iron geochemistry are more likely mechanisms. The T2 shortening observed during the experiment generally shows long components, T2 > >100ms, transitioning to shorter relaxation time components, T2<<100ms. Thus, the dominant relaxation mechanism(s) must be ones that can result in T2 relaxation times much shorter than 100ms. With the exception of magnetite and hematite, the literature reports elevated, but moderate surface relaxivity for most Fe(III) minerals at a measurement frequency of 2 MHz [35]. Large reductions in relaxation times resulting from the change of Fe(II) to Fe(III) have been shown at 90 MHz [34], but this measurement frequency is more than 100 times higher than the current downhole measurements. Relaxation times exhibit significant and complex frequency dependence over this wide range. Generally, the geochemical changes are expected to show a reduced influence on T2 at lower field strengths [38] since the amplitude of internal gradients associated with diffusion relaxation are reduced at lower field. 171 With evidence suggesting moderate ferrihydrite formation is unlikely to cause the absolute T2 shortening we observe, we consider evidence of T2 shortening due to the mechanism of biofilm polymerization. Laboratory measurements at 275 kHz by Sanderlin et al. (2012) showed growth of biofilm and polymer gels resulted in T2 values as short as 50ms [21]. Furthermore, in previous laboratory work using the same LF probe [20], moderate biofilm growth in 1mm quartz sand resulted in a decrease in the mean log T2 of 45% which is similar in magnitude to the changes observed in this study. Geochemical changes in the pore fluid would have occurred slowly over the two week period, and the drop in T2 would be expected to be considerably less than was observed. Given the timing and magnitude of the T2 changes, and the evidence from previous lab work that biofilm has a large influence on NMR relaxation measurements, the experimental results provide compelling evidence that the low field NMR logging tools can detect and monitor biofilm growth in the subsurface. How biofilms interact with the geochemical environment will vary from field site to field site, as well as over space and time. Future experiments and implementation of these methods, therefore, should include an informed monitoring of the chemistry of extracted pore fluid and the changing NMR relaxation. We have shown the NMR logging tools detected significant and sustained change in signal response during the biofilm growth phase, measured by changing T2 relaxation distributions. Both the HF and LF probes were sensitive to the changes, and the differences in soil geology between the probe locations likely resulted in larger differences in the signal response than the variation between the two probes. Mean log T2 172 relaxation times decreased from 29 ms to an average of 11 ms in the LF well, and from 50 ms to an average of 28 ms in the HF well while biofilm was cultivated in the surrounding soil. We have further shown that high shear flow and oxidative stress resulting from the bleach solution, applied with the intent to denature and remove biofilm from the tool’s sensitive zone, produced a return of signal response similar to initial conditions. The timescale of these changes is consistent with biofilm formation and subsequent removal. These results provide an important demonstration of the advantages of incorporating an NMR measurement into future bioremediation toolkits. NMR T2 relaxation measurements provide unique complementary data that, together with other monitoring techniques such as hydrological conductivity measurements, can improve our ability to draw the correct conclusion about the subsurface environment with regard to biofilm growth. Supporting Information Site Preparation A bleach solution consisting of 2 lb (907 g) sodium dichloro-s-triazinetrione dihydrate (C3H4Cl2N3NaO5) (Spa Guard Chlorinating Concentrate, Bio-Lab Inc., Lawrenceville, GA) was pumped into each well to oxidize any pre-existing biofilm. The solution was mixed in a 55 gal (208 L) drum using enough water to dissolve the granules, approximately 20-30 gallons (75-115 L). The solution was pumped to the target region through a standard garden hose using a 1/3 hp centrifugal pump (AMT Pump Model 3680-975-97 by Gorman Rupp, Royersford, PA) operating at approximately 12 gpm 173 (45.5 L/min). The bleach solution was allowed to react in the wells overnight, and was followed by a 30 min high-flow (12 gpm (45.5 L/min)) flush of groundwater from the test cell to detach EPS and dead cells and purge any remaining bleach solution. Then, the probes were lowered to the bottom of the wells, approximately 18 ft (5.5 m) deep and 15 ft (4.5 m) below the water table in the test cell. Bacterial Culture The target organism, Pseudomonas fluorescens CPC211A, is the environmental isolate used in the original experiments in the test cell and, therefore, was known to grow successfully in that environment.[7] The bacteria was cultured from cryo-stock using a nutrient broth consisting of 10 g/L molasses (Aunt Patty’s Blackstrap Molasses, Eugene, OR), 3 g/L sodium nitrate (SQM industrial grade prills, 98%, SQM North America, Atlanta, GA), 1 g/L yeast extract (Acros Organics, Geel, Belgium), 0.12 g/L potassium phosphate dibasic, and 0.04 g/L potassium phosphate monobasic (Thermo-Fisher Scientific, Waltham, MA). The inoculum was cultured in successively larger volumes at ambient temperature without mixing over seven days to produce a final inoculum volume of 60 L with a viable cell count of 8.5x107 colony forming units (cfu)/mL. The active biofilm growth region of the well-bore environment was designed to be approximately 18 gal (67 L) of pore space, corresponding to the height of the NMR logging device (4.5 ft), a 9 in (22.9 cm) radius and an estimated porosity of 0.3 [7]. This active region of soil in each well was conditioned with 15 gal (56.7 L) of substrate prior to injection of the inoculum broth. The substrate was pumped at a rate of 1.2 L/min with a peristaltic pump (Masterflex L/S Model 900-1255, Cole-Parmer, Vernon Hills, IL) 174 down each well casing to the sensitive zone of the NMR probe using four lines of 1/8- inch (3.2mm) ID vinyl tubing (Clearflex, McMaster-Carr, Santa Fe Springs, CA). Then 30 L (7.9 gal) of inoculum was injected into each well, followed by 5 gal (18.9L) of fresh substrate to push the bacteria into the soil from the well casing. Finally, water from the test cell was injected for approximately 1-2 minutes to rinse the injection tubing. No attempt was made to maintain a monoculture. During the biofilm growth phase of the experiment, Days 1-10, the molasses substrate was prepared just prior to use in 50-55 gal plastic drums using groundwater from the lined test cell. Groundwater was pumped from another of the test cell’s eleven 4 inch (10.2 cm) wells located 36 ft (11 m) from the nearest experimental well and stored prior to use in a large capacity water storage tank (Ace Roto-Mold, Den Hartog Industries, Hospers, IA). Each well received approximately 100-110 gal (379-416 L) per day of substrate over a 5-6 hour period. This translates to a Darcy velocity at the logging tool’s excitation shell of approximately 4.2 cm/hr and an interstitial velocity of 14.4 cm/hr in the LF well during substrate injection, and 7.2 cm/hr and 23.4 cm/hr, respectively, in the HF well. NMR measurements were collected during the pumping of substrate. There was no pumping or flow in the wells for the remainder of each day following substrate injection. Continuous flow of substrate was not feasible given experimental constraints. 175 NMR Measurements T2 relaxation measurements were conducted using a Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence [24, 25], consisting of a 90° excitation pulse followed by a series of 180° refocusing pulses separated by the echo spacing, tE. Frequencies and echo spacings for each probe were fixed. The repetition time, Tr, which is the time between 90° rf excitation pulses, was either 1500 ms or 5000 ms for each measurement (Table 6.2). Faster repetition of the excitation pulse, with a Tr of 1500 ms, allowed for the rapid collection of data from the fastest decaying components of the NMR signal; recording 600 averages improved resolution of the early part of the decay curve [14]. A longer repetition time of 5000 ms, recorded with 150 averages, allowed signal to be collected from the slower decaying components, such as water in larger pores. Microbiological and Water Chemical Analysis Two 10-15 mL samples of water were collected daily in sterile 15 mL Falcon tubes (Becton, Dickinson and Co., Sparks, MD) from each well prior to injection of fresh substrate. Flow on the substrate injection pumps was reversed and allowed to flow for 2- 3 minutes in order to collect a water sample from each well’s biofilm growth region. The samples were placed on ice in the field and then frozen for later analysis at the conclusion of the field test. The samples were analyzed for pH (VWR sympHony benchtop SB70P pH meter) and by drop plate for heterotrophic plate count (HPC) [23]. Samples were drop plated on Difco tryptic soy agar (Becton, Dickinson and Co., Sparks, MD) plates in duplicate and cultured at room temperature on the benchtop and in anaerobic pouches (BD GasPak EZPouch, Becton, Dickinson and Co., Sparks, MD). The 176 aerobically grown plates produced higher and more consistent numbers of culturable heterotrophic cells. Results and Discussion Another measure of signal attenuation is given by the Square of Echoes (SOE) method which is used to improve the low signal to noise ratio that is typical for a low- field NMR device in natural geologic material. The SOE is the squared value of the mean echo in the signal decay curve. A reduction in the SOE value over the course of the experiment qualitatively indicates that the log mean value of T2 relaxation is also decreasing. 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Series in Water Resources and Environmental Engineering. 2002, New York, NY: McGraw-Hill. 181 38. Koenig, S.H. and K.E. Kellar, Theory of 1/T-1 and 1/T-2 NMRD profiles of solutions of magnetic nanoparticles Magnetic Resonance in Medicine, 1995. 34(2): p. 227-233. 182 CHAPTER SEVEN DETECTING MICROBIALLY-INDUCED CALCITE PRECIPITATION (MICP) IN A MODEL WELL-BORE USING DOWNHOLE LOW-FIELD NMR Contribution of Authors and Co-Authors Manuscript in Chapter 7 Author: Catherine M. Kirkland Contributions: Helped conceive and implement study design. Collected and analyzed data. Wrote manuscript. Co-Author: Sam Zanetti Contributions: Helped implement study design. Collected and analyzed data. Co-Author: Elliot Grunewald Contributions: Helped conceive and implement study design. Provided supervision and oversight on data collection and analysis. Provided feedback and comments on the manuscript. Co-Author: David O. Walsh Contributions: Provided feedback and comments on the manuscript. Co-Author: Sarah L. Codd Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. Co-Author: Adrienne J. Phillips Contributions: Helped conceive and implement study design. Provided feedback and comments on the manuscript. 183 Manuscript Information Page Catherine M. Kirkland, Sam Zanetti, Elliot Grunewald, David O. Walsh, Sarah L. Codd, Adrienne J. Phillips Environmental Science and Technology Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal ____ Officially submitted to a peer-review journal ____ Accepted by a peer-reviewed journal _X___ Published in a peer-reviewed journal American Chemical Society Vol. 51, No. 3, Pages 1537-1543, February 2017 184 DETECTING MICROBIALLY-INDUCED CALCITE PRECIPITATION (MICP) IN A MODEL WELL-BORE USING DOWNHOLE LOW-FIELD NMR Abstract Microbially-induced calcite precipitation (MICP) has been widely researched recently due to its relevance for subsurface engineering applications including sealing leakage pathways and permeability modification. These applications of MICP are inherently difficult to monitor non-destructively in time and space. Nuclear magnetic resonance (NMR) can characterize the pore size distributions, porosity, and permeability of subsurface formations. This investigation used a low-field NMR well-logging probe to monitor MICP in a sand-filled bioreactor, measuring NMR signal amplitude and T2 relaxation over an 8-day experimental period. Following inoculation with the ureolytic bacteria, Sporosarcina pasteurii, and pulsed injections of urea and calcium substrate, the NMR measured water content in the reactor decreased to 76% of its initial value. T2 relaxation distributions bifurcated from a single mode centered about approximately 650 ms into a fast decaying population (T2 less than 10 ms) and a larger population with T2 greater than 1000 ms. The combination of changes in pore volume and surface minerology accounts for the changes in the T2 distributions. Destructive sampling confirmed final porosity was approximately 88% of the original value. These results indicate the low-field NMR well-logging probe is sensitive to the physical and chemical changes caused by MICP in a laboratory bioreactor. 185 Introduction Biofilms form when bacteria secrete a matrix of extracellular polymeric substance (EPS), attaching themselves to solid surfaces in colonies akin to multicellular organisms and buffering their micro-scale environment[1]. Bacterial biofilms are known to induce metal corrosion [2], cause persistent infections [3], treat wastewater [4], or remediate contaminated groundwater [5]. When composed of ureolytic microbes, biofilms can also induce calcite precipitation [6], a process referred to as biomineralization or microbially- induced calcite precipitation (MICP). Many strains of bacteria found naturally in soil and groundwater are ureolytic, meaning they can hydrolyze urea for energy and a source of nitrogen [7]. Catalyzed by the microbially produced urease enzyme, water cleaves urea to form ammonia and carbon dioxide which, due to a pH increase, shifts the carbonate equilibrium toward bicarbonate and carbonate. Then, with sufficient calcium and carbonate activity, calcium carbonate (CaCO3 or calcite) precipitates (Eqn. 7.1). (NH2)2CO + 2H2O + Ca2+ ⇒2NH4+ + CaCO3(s) (7.1) Sporosarcina pasteurii, the ureolytic bacteria used in this experiment, forms a thin biofilm in porous media [8] where the EPS matrix, a 3-dimensional diffusion-limited hydrogel, can either facilitate or inhibit MICP over microscales. The organic molecules comprising the EPS matrix restrict mass transfer, creating localized chemical gradients within the hydrogel structure [6]. Ca2+ ions are not used in metabolic processes and accumulate near cell surfaces where ureolysis produces an alkaline environment. Thus, the microbial biofilm matrix provides nucleation sites for calcite precipitation [9]. In 186 porous media, the precipitated calcite binds together media grains and fills pore spaces [10]. MICP has engineering applications [11] that include soil stabilization [10, 12] and subsurface barriers [13], sealing of cap rocks and well-bore regions for carbon dioxide sequestration [14-16], and limestone and concrete remediation [9]. Many of these beneficial applications of MICP occur in the subsurface, raising the question of how the process can best be monitored spatio-temporally. Nuclear magnetic resonance (NMR) is commonly used non-destructively and non-invasively to characterize the pore size distributions, porosity, and permeability of subsurface geologic formations [17]. These are the same physical properties affected by MICP, indicating that NMR well-logging tools may have potential for monitoring subsurface engineering applications of MICP. This study used a low-field NMR well-logging tool designed for subsurface hydrogeologic investigations [18] to detect changes in NMR signal response indicative of MICP in the pore spaces of sand-filled radial-flow bioreactor. Background There are limited examples in the scientific literature where NMR methods have been applied to the study of biomineralization in porous media relevant for engineering applications [8, 19]. These previous studies have used high field strength magnetic resonance imaging (MRI) along with other NMR methods to probe hydrodynamic properties of biomineralization in model porous media systems. Fridjonsson et al. [8] used high-field NMR to measure changes in hydrodynamic dispersion resulting from MICP in model porous media to compare flow dynamics 187 between systems influenced by either solid precipitates or a biofilm matrix. The authors used a combination of NMR displacement measurements, relaxation mapping, MRI, and microscopy methods. Sham et al. [19] used MRI and NMR flow measurements on both a model bead pack and a Bentheimer sandstone rock core to examine structure and transport properties of each system following MICP. The authors report a reduction of 3.7% in absolute porosity in the bead pack, which correlated to a 98% reduction in permeability. In the sandstone, a 7.2% reduction in absolute porosity yielded a 96.5% reduction in permeability. In both systems, preferential fouling of the inlet region of the column was observed. The low-field NMR well-logging tool used in this study (Javelin JP350, Vista Clara, Inc., Mukilteo, WA) is sensitive to biofilm growth in the pore spaces of a sand- filled bioreactor [20] and in the subsurface soil of an engineered field testing site [21]. In both of these studies, biofilm growth caused enhanced relaxation with T2 relaxation times decreasing by approximately 40 – 60%. These previous studies show 1) NMR methods are useful for analyzing changes resulting from MICP in porous media and 2) the well-logging tool is sensitive to small changes over time in the micro-scale pore environment. To our knowledge, field scale low-field NMR instruments have not been applied to the measurement or monitoring of MICP. In the current study, CaCO3 precipitation was expected to change the NMR signal response by reducing the liquid fraction from which the signal is obtained, causing a decrease in signal amplitude over time as the pores accumulate calcite. MICP will also 188 change the pore sizes and mineral surface of the porous media, thereby influencing the signal relaxation response. A correlation between the signal response and reduction of porosity due to MICP may indicate the use of a NMR well-logging tool as a sensor for biomineralization in field applications where optical or destructive monitoring methods are not possible. This study represents a first step toward that end by demonstrating that a NMR well-logging tool is sensitive to MICP. NMR Theory The NMR well-logging tool is sensitive to the hydrogen protons in water, called ‘spins,’ such that the behavior of the NMR signal over time is related to the various micro-scale water environments in the surrounding formation. The tool measures 1.37 m long and 8.9 cm in diameter and is designed to be lowered into small-diameter cased or uncased borehole wells (Figure 7.1) [18]. The dual frequency probe used in this experiment operates at approximately 250 and 300 kHz, and is composed of an array of permanent magnets and radio-frequency (RF) induction coils [18]. The permanent magnets establish a static magnetic field, B0, along the direction of the borehole, where the field strength depends on the radial distance from the tool. The RF pulses produce two mm-scale cylindrical excitation shells at radial distances of 17-19 cm from the probe center and in the middle of the reactor’s sand annulus. The excited shells are 50 cm in height. Only spins in these two excitation shells contribute to the measured NMR signal response, which is averaged over all the spins in each shell. The initial amplitude of the NMR signal is proportional to the amount of water in the excitation shell and reflects the volumetric water content, or porosity, of the porous 189 media. The NMR signal amplitude decreases when water is displaced by mineral formation in the pores. The observed decay rate reflects spin-spin, or T2, relaxation, which occurs as protons interact with each other in the transverse plane. These interactions cause a dephasing of spin coherence and signal attenuation. In geologic materials, the observed T2 relaxation rate comprises the bulk relaxation rate of the pore fluid, 1 𝑇𝑇2𝐵𝐵 , the surface relaxation rate, 1 𝑇𝑇2𝑆𝑆 , related to interactions between the fluid and the pore walls, and the diffusion relaxation rate, 1 𝑇𝑇2𝐷𝐷 , related to diffusion of fluids within pores due to inhomogeneities in the local magnetic field (Equation 7.2) [22, 23]. 1 𝑇𝑇2 = 1 𝑇𝑇2𝐵𝐵 + 1 𝑇𝑇2𝑆𝑆 + 1 𝑇𝑇2𝐷𝐷 (7.2) At the low magnetic field strength used in this study, the experimental parameter of the echo spacing, tE, can be selected to make the influence of diffusion relaxation, T2D, sufficiently small to be neglected [20, 23]. For the current study, changes in the fluid properties of the pore liquid, such as viscosity, are not expected be a significant factor in the overall change of the system T2 relaxation time [8]. The influence of changes in T2B can therefore also be neglected. Changes in surface relaxation, 𝑇𝑇2𝑆𝑆, are expected to dominate changes in the observed T2 of this experimental system. The low-field NMR signal response in most saturated natural geologic media is dominated by surface relaxation [22, 24]. Surface relaxation occurs as excited spins approach and interact with the pore walls. Thus, the rate of surface relaxation is most 190 strongly related to pore size and the mineral surface of the solid matrix. Surface relaxation occurs faster in small pores with a high surface-area-to-volume-ratio because the diffusing water molecules are more likely to interact with the grain surface. The surface relaxation rate also depends on the propensity of the surface for inducing relaxation, a characteristic referred to as surface relaxivity, 𝜌𝜌. Greater concentrations of paramagnetic ions like Fe3+ and Mn2+ produce higher magnitudes of 𝜌𝜌 and faster relaxation rates [25, 26]. In heterogeneous materials with a range of pore sizes or variable 𝜌𝜌, there may be a distribution of relaxation rates making up the bulk response. Thus, an Inverse Laplace Transform yields a decay-time distribution that can be interpreted as a distribution of pore environments. In our experiments, we expect MICP to have several combined influences on the NMR response. First, we expect that growth of calcite within the pore space will reduce the total porosity and water content. We also expect the growth of CaCO3 to influence the observed relaxation rate due to changes in mineralogy and pore size [27-29]. The quartz sand used in this study is coarse-grained and contains small percentages of paramagnetic species including iron oxide (Fe2O3) at a mean weight percent of 0.04 (2095 Granusil® silica sand, Unimin Corp., Ottawa, MN). We expect that CaCO3 forming on the quartz grain surfaces will decrease the total macro-pore dimension which could drive faster relaxation rates. On the other hand, CaCO3 precipitating on the grain surface may shield water from the paramagnetic ions on the sand, thus decreasing the average 𝜌𝜌 of the grain surface. A lower average 𝜌𝜌 would tend to decrease the surface relaxation rate in the macro-pores, resulting in longer overall T2. Further, the CaCO3 may form 191 microcrystalline structures that incorporate significant micro-porosity of nanometer scale. We expect water in the very small geometry of these micro-pores to exhibit very short relaxation times. Thus, we anticipate these changes in the pore structure concurrent with MICP will manifest themselves as multiple changes to the NMR T2 relaxation time distribution. These observed changes are expected to indicate which mechanism dominates in the bioreactor where there exists a particular initial pore size distribution and surface minerology. Materials and Methods Bioreactor The radial flow bioreactor is designed to model the near well-bore environment and consists of four concentric polyvinyl chloride (PVC) pipe sections sealed with grooved top and bottom plates (Figure 7.1). The reactor is the same as was used in a previous study to detect biofilm growth in sand using the same NMR logging tool [20]. In the current experiment, the height of the reactor was 50 cm. The inner and outer pipes are solid while the two inner pipes are slotted to allow radial flow through the sand annulus between them. The inner and outer annuli are the influent and effluent reservoirs, respectively. The sand annulus measures 7.6 cm wide and was filled with 1 mm nominal quartz sand (2095 Granusil® silica sand, Unimin Corp., Ottawa, MN). The liquid volume of the reactor is approximately 30 L, including the sand pore volume and influent and effluent reservoirs. 192 Figure 7.1. The radial flow bioreactor and NMR logging tool were housed in a Faraday cage to reduce detection of electromagnetic noise from the laboratory. Media and Injection Strategy Two kinds of substrate media were used in this study, a bacterial growth medium (growth medium) and a calcite mineralization-promoting medium (calcium medium). Both were urea- and yeast extract-based (1 g/L yeast extract (Arcos Organics, Gheel, Belgium), 20 g/L urea, 1 g/L NH4Cl, and 24 g/L NaCl). The calcium medium contained an added 49 g/L CaCl2∙2H2O. Commercial-grade chemicals were used for urea (Urea 193 Fertilizer, Espoma, Millville, NJ), calcium chloride (various brands of commercial ice melt), and sodium chloride (Morton Table Salt, Chicago, IL). Media were mixed just prior to use in a non-sterile manner using tap water. A pulsed-flow injection strategy promoted an even distribution of CaCO3 precipitation by balancing reaction and transport rates [30]. Each 30 L pulse of substrate was pumped at a flow rate of 1 L/min, producing a pore velocity of approximately 0.4 cm/min and ensuring that the fresh substrate would penetrate the full width of the sandpack. Calcium medium was injected four times per day during the biomineralization phase Days 4 – 7. A 2-hour batch reaction period (no flow) followed each injection of calcium medium. One pulse of growth medium was injected each evening to stimulate the bacteria for the following day’s calcium medium injections. A 10 L brine rinse (24 g/L NaCl) was injected into the reactor first each morning to reduce mixing of the two substrate media in the influent reservoir and minimize clogging of the slotted pipe. Bacterial Culture The bacteria used in this experiment, Sporosarcina pasteurii (ATCC 11859), formerly known as Bacillus pasteurii, is widely used in laboratory experiments related to urea hydrolysis and biomineralization [11]. S. pasteurii is a non-pathenogenic natural soil organism capable of producing relatively large amounts of the urease enzyme needed to catalyze urea hydrolysis [11]. For the inoculum, one mL of frozen stock of S. pasteurii was cultured in 100 mL of growth medium on a shaker table at 150 rpm for 24 hours. The 100 mL culture was then added to 10 L fresh growth medium and mixed on a stir plate at 1150 rpm for 24 hours. Finally, the 10 L culture was added to 20 L of fresh 194 growth medium and mixed as before to produce a final inoculum volume of 30 L. No attempt was made to maintain a monoculture in the inoculum or in the reactor. The reactor was inoculated by first injecting 5 L of fresh growth medium to condition the reactor at a flowrate of 1 L/min, followed by the 30L inoculum. An additional 5 L of fresh growth medium was injected last. Bacteria were allowed to attach to the sand for approximately 15 hours with no flow before the first injection of calcium medium. There was no calcium present in the reactor during the 3-day control period or during inoculation. The initial period was used as the control. Note that previous experiments have shown no permeability reduction was achieved when urea and calcium containing solutions were injected into glass bead filled columns that were not inoculated with ureolytic microbes [31]. NMR Measurements Low-field NMR measurements typically consist of repeated scans which are stacked and averaged to reduce noise in the data. In this study, two experiments were conducted sequentially and together constitute one CPMG scan for measurement of T2 relaxation. Experiment 1 collects T1-weighted fast-decaying signal (tE=1.3ms, Tr=800ms, 54 echoes, 360 averages). Experiment 2, on the other hand, collects the signal from spins with longer relaxation times (tE=1.3ms, Tr=5000ms, 334 echoes, 60 averages). All NMR measurements were collected under no flow conditions. Measurements during the control period, Days 1 – 3, consisted of 24 CPMG scans. Three (3) CPMG scans were stacked and averaged for each daily measurement during the biomineralization phase, 195 Days 4 – 8, because of the timing of repeated substrate injections on a 2-hour cycle. Data presented here was collected with a noise level of approximately 1.4%. As only one tool was available on loan for a limited period, it was not possible to run replicate experiments. However, previous work with this tool [20, 21] has allowed multiple experimental runs whilst monitoring biofouling in both a sand pack and in the subsurface. The tool’s performance has been consistent and repeatable. Sampling Influent and effluent samples were collected for each injection of brine, calcium medium, and growth medium. The sample pH was measured shortly after collection, then the sample was filtered (0.2 µm membrane, VWR International, Radnor, PA) and refrigerated for later analysis with the Jung Assay [32] to evaluate the sample urea concentration. After the final measurement on Day 8, the reactor was drained and destructively sampled. The outer pipe was cut away in sections, leaving the biomineralized sand annulus exposed for sampling (Figure 7.2). Twenty-four (24) cores were collected: 2 radial cores of approximately 1 inch diameter (2.5 cm) and 3 inch length (7.5 cm) at each of 3 depths were sampled in 4 orthogonal directions. Each core sample was divided into 3 subsamples which were then weighed and subjected to nitric acid digestion to remove the solid precipitates. The liquid was extracted for calcium content analysis by ICP-MS using an Agilent 7500ce (Santa Clara, CA) with a collision cell (helium mode) and a certified environmental calibration standard from CPI International (product number 4400-12 1116NCO2). Additionally, micrograph images were acquired using a Zeiss Supra 55VP scanning electron microscope (Zeiss, USA). 196 Biomineralized sand samples from the reactor and control sand samples were sputter coated with iridium and high-resolution images were taken at 1.0 kV at a working distance of 3—4 mm. Figure 7.2. The biomineralized sand annulus was destructively sampled to quantify CaCO3 precipitation. a) The outer pipes of the bioreactor were cut away to expose the biomineralized sand annulus. A saw was used to cut the annulus into quarters, producing the large crack shown here. b) Six radial core samples were collected from each quarter. Results and Discussion The influence of CaCO3 precipitation on the NMR signal response is reflected in the daily signal decay curves and resulting T2 distributions where significant changes were observed over time. Representative data, collected on Days 2, 4, 6, and 8, are presented in Figure 7.3; the top panel shows fits to recorded signal decay curves, and the 197 bottom panel presents the T2 distributions for those decay curves. First, we will address the change in water content which corresponds to a drop in the porosity of the sandpack. Then we will discuss the relaxation distributions, which give insight to changes in the relaxation mechanism. Figure 7.3. Signal decay curves (top) and the corresponding T2 distributions (bottom) are shown with each curve representing a day. Day 2 occurred during the control period. Inoculation occurred on Day 3 (not shown). The calcium media injections occurred between Day 4 – 7. The Day 8 data was collected prior to flushing the reactor with brine and destructively sampling. Both graphs show fits to the raw data. 198 Water Content and Porosity Decreasing signal amplitude over time is an indication of CaCO3 precipitation, since CaCO3 will displace water in the pore volume. During the control period the initial porosity indicated by the NMR-measured total water content was approximately 30% which is slightly less than the 35-39% expected from a sand pack with relatively uniform grains. The observation of entrained air leaving the system after the first flow pulse following inoculation, and the subsequent increase in the water content signal on Day 4, leads us to conclude that the sand pack was not fully saturated during the control period. This also explains why the measured water content value of ~30% is less than the expected value of 35-39%. The NMR-measured total water content in the reactor decreased to approximately 76% of its original value between the control period (Day 2 data) and the end of the biomineralization phase on Day 8 (Figure 7.3, top panel, and Figure 7.4). This reduction in total water content indicates that the pore volume within the reactor decreased significantly during the biomineralization phase. If we consider Day 4 to represent full saturation, then the NMR-estimated porosity reduction is 70% of the initial value, indicating the sensitivity of the NMR measurement to partial saturation. 199 Figure 7.4. The measured total water content in the radial flow reactor decreased from approximately 29% during the control period Days 1-3 to approximately 22% by Day 8. Note that the increase on Day 4 is real and well outside expected error bounds. The increase follows the observation of entrained air leaving the bioreactor, indicating the desired fully saturated state may not have been obtained until after the control period. CaCO3 formation was confirmed by scanning electron microscopy (SEM). There appeared to be a relatively uniform CaCO3 coating on the sand samples viewed with SEM. Figure 7.5 shows an SEM micrograph showing the crystals formed on a grain of sand from the reactor (a) and the surface of a control sand grain (b). The surface of the CaCO3 -encrusted sand reveals micro-scale cavities and pores between crystals. No bacteria were visible in the sand samples viewed with SEM; it is most likely that the cells are entombed within the crystals. 200 Figure 7.5. SEM image of a) CaCO3 crystals attached to a grain of sand from the reactor following 4 days of MICP and b) control sand without CaCO3. Scale bar is 20 µm. Note that the CaCO3 crystals completely cover the sand surface and the sand is not visible in (a), whereas in (b) the smooth sand surface is observed. Several methods were applied to estimate the volume of CaCO3 formed in the reactor in order to independently determine the reduction in pore volume achieved. These methods include a mass balance on urea, ICP-MS detection of Ca2+, and gravimetric methods. An initial porosity estimate of 37%, typical for the sand in the reactor, was used in these calculations. Because the reactor was not fully saturated during the control period, the total porosity is greater than the NMR water content. The results of these three methods are in good agreement with each other and support the NMR data showing a significant pore volume reduction due to calcite precipitation. Mass balance on urea: Influent and effluent samples of each pulse of media were analyzed using the Jung Assay [32] to quantify the urea content. A mass balance on urea showed that approximately 4.2 kg of urea was consumed within the reactor, stoichiometrically producing approximately 6.9 kg of calcite. This mass of calcite would occupy at maximum approximately 15% of the pore space in the sand annulus. Since CaCO3 also 201 formed in the tubing and on the reactor walls, we consider the urea mass balance method to provide an approximation of the upper bound of CaCO3volume. ICP-MS: ICP-MS was used to measure the concentration of Ca2+ in the acid extraction liquid from 24 samples of biomineralized sand from the reactor. A mean value of 9.36 g/L Ca2+ was obtained with a sample standard deviation of 1.89 g/L, which equates to an average total mass of 6.3 kg CaCO3 within the sand. The ICP-MS data translates to an average pore volume reduction of approximately 12% (+/- 2.4%). Gravimetric method: The 24 sand samples were also weighed before and after the acid digestion removed the precipitate, resulting in an average mass of calcite of 63.6 mg CaCO3/g sand with a sample standard deviation of 13 mg/g. By this method, the average total mass within the sandpack was 5.5 kg calcite. The gravimetric method indicates that approximately 11% (+/- 2.2%) of the pore space in the sand annulus was occupied by CaCO3at the end of the experiment. Unlike the mass balance method, ICP-MS and gravimetry account only for CaCO3 attached to the sand. On the basis of these complementary and independent methods, we estimate that CaCO3 occupied approximately 11 – 12% of the pore space in the sandpack by Day 8 of the experiment. This estimated porosity reduction is significantly higher than those previously reported in other NMR/MICP studies [8, 19]. The pulsed flow injection strategy used here promotes relatively uniform CaCO3 precipitation, as evidenced by the small standard deviation of the samples collected from the reactor. The uniform calcite precipitation implies spatially uniform porosity reduction. Consequently, only an insignificant reduction in permeability was observed in this study. 202 Compared to the methods described above which found final porosity to be approximately 88% of the original value, NMR measurements of water content overestimate the porosity reduction achieved. Final NMR water content was 76% of the initial value, or 70% of the Day 4 value. The overestimation can be attributed to carbon dioxide (CO2) gas production inside the reactor. The excess CO2 produced by microbial oxidation of the yeast extract in the substrate can be trapped in the reactor pore spaces, displacing water and reducing signal amplitude without changing the pore geometry. Gas formation was also observed in previous NMR studies of MICP [8, 19]. Furthermore, signal decaying in the interval before the first echo acquisition will underestimate the water content and may explain in part the NMR overestimation of porosity reduction. Relaxation The tall initial peak (Day 2 data) in the bottom panel of Figure 7.3, centered about approximately 600-700 ms and associated with water in large pores, first increases then decreases in amplitude over time as the biomineralization phase proceeds. At the same time, there is an increase in both the occurrence of very fast T2 relaxation times less than 10 ms, and an increase in the proportion of spins experiencing very long relaxation times, greater than 1000 ms. At the left-hand limit of the T2 distribution (Figure 7.3, bottom), the NMR logging tool cannot capture NMR signal that decays faster than the measurement echo time (tE=1.3ms). We note that since the time of this study, the echo time of the Javelin tool has been reduced to 0.7 ms. At the right of the distribution, signals with T2 between 1-5 s are not tightly resolved on the T2-axis because the signal is sampled only to 500 ms. However, the amplitude of these long signals is accurately 203 measured (Figure 7.3, top). By Day 8 of the experiment, the mean log T2 time of the distribution had increased to greater than 1000 ms from approximately 650 ms during the control period. The data shows that T2 relaxation in the macro-pores of the sandpack is more significantly affected by the reduction in 𝜌𝜌 than by the decrease in the macro-pore dimension. As seen in the SEM images (Figure 7.5a), the CaCO3 crystals are on the order of 101 µm thick. In a large pore on the order of 102 µm in diameter, there is a relatively minor change in pore dimension due to calcite precipitation. On the other hand, the relatively thin and uniform coating of CaCO3 crystals is sufficient to minimize molecular interactions between the pore fluid and paramagnetic species on the sand, making the surface much less likely to induce relaxation. The combination of a large change to 𝜌𝜌 and a small change to the pore size explains the lengthening of the overall mean log T2 relaxation time. At the same time, CaCO3 precipitation also creates micro- pores between and within the crystals. In these pores, the pore size effect dominates and T2 relaxation occurs rapidly for the small population of spins within the crystals. Previous NMR/MICP studies reporting the opposite [19] or no relaxation effect [8] are not at odds with this interpretation of the data. Both previous studies used smaller diameter (~100 – 250 µm) model porous media (borosilicate or polystyrene beads, respectively) with a low initial 𝜌𝜌 and small initial pore size, where we would expect more potential influence from a change in the pore geometry than from a reduction in ρ. We expect if CaCO3 precipitation had continued to progress in the current experimental system, the reduction in the macro-pore dimension would eventually become the 204 dominate influence, driving relaxation times to decrease. Thus, the potential complexity of the relaxation response leaves open the possibility of different relaxation signatures in other porous materials where pore sizes or surface properties are more heterogeneous. Our results show that changes in NMR signal response due to MICP include 1) a decrease in signal amplitude over time, indicating a reduction in porosity, and 2) a lengthening of the overall T2 relaxation time in the quartz sand of the bioreactor. NMR measured water content in the reactor decreased to approximately 76% of the initial value, which corresponds well to the measured reduction in porosity to approximately 88% of the typical initial value. The extent of the decrease in porosity, and the corresponding minimal change in permeability, is related to the pulsed-flow injection strategy employed to achieve the MICP. T2 relaxation distributions bifurcated from a single mode centered about approximately 650 ms during the control period into a very fast decaying population (T2 less than 10 ms), associated with water in the porous CaCO3, and a larger population with relaxation times greater than 1000 ms, corresponding to the bulk water in the large crystal-coated pores. Slower relaxation is caused by CaCO3 crystals on the mineral surface of the macro-pores shielding paramagnetic species from the pore fluid, reducing 𝜌𝜌 of the pore. In the CaCO3 micro-pores, the pore size effect dominated and enhanced relaxation. Future work will evaluate the NMR signal response to MICP in natural soils and porous rock where surface relaxivity and pore sizes are more heterogeneous. This study demonstrates that a NMR well-logging tool is sensitive to MICP and has potential as a sensor for biomineralization in field applications where optical or destructive monitoring methods are not possible. 205 References 1. Stoodley, P., et al., Biofilms as complex differentiated communities. Annual Review of Microbiology, 2002. 56: p. 187-209. 2. Beech, I.B. and J. Sunner, Biocorrosion: towards understanding interactions between biofilms and metals. Current opinion in biotechnology, 2004. 15(3): p. 181-6. 3. Costerton, J.W., P.S. Stewart, and E.P. Greenberg, Bacterial biofilms: A common cause of persistent infections. Science, 1999. 284(5418): p. 1318-1322. 4. de Kreuk, M., J.J. Heijnen, and M.C.M. van Loosdrecht, Simultaneous COD, nitrogen, and phosphate removal by aerobic granular sludge. 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Jung, D., et al., New colorimetric reaction for endpoint, continuous-flow and kinetic measurement of urea Clinical Chemistry, 1975. 21(8): p. 1136-1140. 208 CHAPTER EIGHT NMR INVESTIGATION OF WATER DIFFUSION IN DIFFERENT BIOFILM STRUCTURES Contribution of Authors and Co-Authors Manuscript in Chapter 8 Author: Maria P. Herrling Contributions: Conceived the concept and designed the experiment. Conducted diffusion measurements, characterized the biomass. Analyzed the data and wrote the manuscript. Co-Author: Jessica Weisbrodt Contributions: Conducted diffusion experiments. Collected and characterized the biomass. Analyzed data. Co-Author: Catherine M. Kirkland Contributions: Assisted with data collection for D-T2 measurements. Assisted with data analysis for D-T2 measurements. Provided feedback and comments on manuscript. Co-Author: Nathan H. Williamson Contributions: Assisted with data analysis using the Gamma distribution. Provided feedback and comments on manuscript. Co-Author: Susanne Lackner Contributions: Discussed the data and Provided feedback and comments on manuscript. Co-Author: Sarah L. Codd Contributions: Provided feedback and comments on the manuscript. 209 Co-Author: Joseph D. Seymour Contributions: Provided supervision and oversight on D-T2 data collection and analysis. Provided feedback and comments on the manuscript. Co-Author: Gisela Guthausen Contributions: Conceived the concept and designed the experiment. Developed data analysis tools, analyzed the data, and discussed the data. Provided feedback and comments on the manuscript. Co-Author: Harald Horn Contributions: Designed the experiment and discussed the data. Provided feedback and comments on the manuscript. 210 Manuscript Information Page Maria P. Herrling, Jessica Weisbrodt, Catherine M. Kirkland, Nathan H. Williamson, Susanne Lackner, Sarah L. Codd, Joseph D. Seymour, Gisela Guthausen, Harald Horn. Biotechnology and Bioengineering Status of Manuscript: ____ Prepared for submission to a peer-reviewed journal __X_ Officially submitted to a peer-review journal ____ Accepted by a peer-reviewed journal ____ Published in a peer-reviewed journal Wiley-Blackwell Submitted February 10, 2017 211 NMR INVESTIGATION OF WATER DIFFUSION IN DIFFERENT BIOFILM STRUCTURES Abstract Mass transfer in biofilms is determined by diffusion. Different mostly invasive approaches have been used to measure diffusion coefficients in biofilms, however data on heterogeneous biomass under realistic conditions is still missing. To non-invasively elucidate fluid-structure-interactions in complex multispecies biofilms pulsed field gradient-nuclear magnetic resonance (PFG-NMR) was applied to measure the water diffusion in five different types of biomass aggregates: one type of sludge flocs, two types of biofilm, and two types of granules. Data analysis is an important issue when measuring heterogeneous systems and is shown to significantly influence the interpretation and understanding of water diffusion. With respect to numerical reproducibility and physico-chemical interpretation, different data processing methods were explored: (bi)-exponential data analysis and the Γ distribution model. Furthermore, the diffusion coefficient distribution in relation to relaxation was studied by D-T2 maps obtained by 2D inverse Laplace transform (2D ILT). The results show that the effective diffusion coefficients for all biofilm samples ranged from 0.36 to 0.96 relative to that of water. NMR diffusion was linked to biofilm structure (e.g. biomass density, organic and inorganic matter) as observed by magnetic resonance imaging and to traditional biofilm parameters: Diffusion was most restricted in granules with compact structures, and fast diffusion was found in heterotrophic biofilms with fluffy structures. The effective 212 diffusion coefficients in the biomass were found to be broadly distributed because of internal biomass heterogeneities, such as gas bubbles, precipitates, and locally changing biofilm densities. Thus, estimations based on biofilm bulk properties in multispecies systems can be overestimated and mean diffusion coefficients might not be sufficiently informative to describe mass transport in biofilms and the near bulk. Introduction Biofilms or more generally biomass aggregates are pervasive in natural aquatic systems [1, 2] as well as in technical systems [3]. Their substrate conversion depends on bulk and internal structures influencing the mass transfer into the matrix. Generally, this mass transfer in biomass aggregates is driven by diffusion and plays a key role for metabolic activity [4-6]. The investigation and understanding of mass transfer and substrate consumption is essential for the development of strategies to improve design and operation of biofilm-based technical applications as well as for modeling. In-depth knowledge is required - especially for multispecies biofilms under technical and realistic conditions. To experimentally explore fluid-structure-interactions, several analytical methods have been applied. Imaging techniques [7] and micro sensors [8, 9] have been used the most. Furthermore, mathematical modeling leads to mechanistic understanding of mass transfer phenomena in complex biofilm systems [10]. Biofilm modeling in combination with imaging indicates that rough biofilms show higher mass transfer of substrates compared to smooth biofilms under stagnation conditions. The larger interfacial surface 213 of a rough biofilm provides better contact to substrates [11]. The diffusion coefficient D of substrates into the biofilm is assumed constant over the biofilm depth [12]. In transport models, D is usually set to 20-30 % less than Dwater [12]. Diffusion of water and nutrients strongly varies between different biofilm systems, geometries, and growth conditions. Actual mass fluxes inside biofilms are unknown, and a generalization of mass transport is not possible. Therefore, data on heterogeneous systems is needed to address measures for mass transport in real systems. Pulsed-field gradient nuclear magnetic resonance (PFG- NMR) allows the measurement of translational diffusion completely non-invasively and non-destructively [13, 14], also in micro-porous systems and in restricted geometry. In biofilm research, alginate is often used as model system due to the chemical composition which is comparable to the biofilms’ extracellular polymeric substances (EPS). Gel heterogeneities were detected in transverse relaxation T2 maps [15]. Filtration processes have been imaged in hollow fiber membranes using alginate as model system [16]. Basic knowledge gained from investigations of artificial biofilms can be transferred to real biofilm systems. Monoculture and multispecies biofilms were investigated by NMR flow and diffusion in porous media and flow cells to study water dynamics and biofilm growth at different time and length scales [17-21]. Furthermore, combined diffusion and Magnetic Resonance Imaging (MRI) linked mass transfer to biofilm structure [7, 20]. Diffusion strongly depends on biofilm systems, growth conditions and biofilm geometries. For example, in methanogenic granular sludge internal heterogeneities significantly influenced the mass transfer [22]. Strong correlations between the diffusion of substrates and biofilm parameters have been reported [4, 23, 24]. 214 For example, Renslow et al. (2010) correlated the effective diffusion coefficient with biofilm depth by means of PFG-NMR and imaging in Shewanella oneidensis biofilms. The same was found for phototrophic Phormidium biofilms [25]. Other studies also confirm that D is biofilm-specific and depth-dependent with a linear decrease of D with biofilm depth [26, 27]. Mass transport and diffusion in biofilms are difficult to analyze and to model because of the high complexity of these biomass aggregates. Apart from the influence of specific compounds, PFG-NMR measurements and data interpretation deserve scrutiny. Different data processing approaches are summarized in Röding, Bernin [28], [29]. The most commonly used data processing approach for PFG-NMR data is the (bi)- exponential fit. Diffusion coefficients are obtained by fitting a single exponential function to the measured signal attenuation, leading to effective or apparent diffusion coefficients. An alternative and recently introduced approach is the Γ distribution model which offers mean diffusion coefficients and their distribution width. Different data processing schemes are compared for biomass aggregates in this study to show their limitations and relevance. For mathematical description we refer to [28], Röding, Williamson [29]. Water diffusion coefficients in multispecies biofilms with diverse geometries and data processing schemes are compared in this paper. To identify fluid-structure interactions, five different types of biofilms or biomass aggregates were investigated: sludge flocs, fluffy and compact biofilms grown on carriers, and aerobic and (an)aerobic granules. The goals of the study were to i) characterize the biomass by means of physico-chemical parameters and imaging, ii) compare Dwater in different structures to identify correlations 215 between biomass properties and water diffusion, iii) compare PFG-NMR data processing schemes, including (bi)-exponential fit, Γ distribution and 2D inverse Laplace transform. Materials and Methods Biofilm Sample Preparation Activated sludge flocs, carrier based biofilms, and granules were chosen to cover a broad range of physical morphologies which are technically relevant, e.g. for wastewater treatment. The properties and functionalities are summarized in Table 8.1. Sludge flocs (sludge) were collected from a full-scale wastewater treatment plant in Weinheim (Germany). The sludge is a mixed culture of auto- and heterotrophic biomass used for carbon (C), nitrogen (N) and phosphorus (P) removal from wastewater. The sludge was rinsed and sieved to a size fraction < 200 µm prior to characterization. Two different carrier based biofilms were investigated. Fluffy biofilms (biofilm_1) grown on K1 carrier materials (plastic carrier, diameter: 10 mm, AnoxKaldnes, Sweden) were cultivated in a laboratory-scale moving bed biofilm reactor fed with acetate [30]. Biofilm_1 comprised heterotrophic biomass and was mainly used for removal of easily degradable carbon compounds. Compact biofilms (biofilm_2) on K3 (plastic carrier, diameter: 25 mm, AnoxKaldnes, Sweden) were obtained from a full-scale wastewater treatment plant (AnoxKaldnes' Biofarm) in Malmö, Sweden. Biofilm_2 comprised multiple species, i.e. heterotrophs, nitrifiers, denitrifiers and anammox bacteria [31] and was mainly used for N removal. Two different types of granules, i.e. granulated biofilms, were also selected for the investigation. Aerobic granules (granules_1) were cultivated in 216 a laboratory-scale sequencing batch reactor (SBR) with acetate as the main substrate. Granules_1 were used for N, P and easily degradable C removal. Large sized granules with an approximate diameter of 10 mm were manually selected. Additionally, (an)aerobic granules (granule_2) were collected from a side-stream SBR of a full-scale wastewater treatment plant in Heidelberg (Germany). Granules_2 mainly contributed to the removal of N and some slowly degradable C compounds. Granules_2 were rinsed and sieved to a size fraction of 700-900 µm. Table 8.1: Characterization of the biofilms. The abbreviation n.m. means not measured. Data marked with asterisk (*) refer to diameter of the granules. “C” refers to carbon removal, “N” to nitrogen removal and “P” to phosphorous removal. The density of water at 20°C is 998 g/L. Parameter Sludge Biofilm_1 Biofilm_2 Granules_1 Granules_2 microbes autotrophic heterotrophic autotrophic autotrophic autotrophic removal C/N/P C N C/N/P N/C TSS 6 g/L TSS 86 mg TSS/carrier 270 mg TSS/carrier 40 mg TSS/granule 3 g/L TSS VSS [%] 80 90 69 78 80 biofilm thickness [µm] < 200* < 200 < 1000 10 000* 400-700* biofilm density [g/L] 1033 ±15 <1010 1047 ±4 1029 ±2 1046 ±14 Ca [g/kg TSS] 37 n.m. 490 97 286 P [g/kg TSS] 53 n.m. 132 49 72 Fe [g/kg TSS] 37 n.m. 590 0.6 327 S [g/kg TSS] 10 n.m. 6 6.8 84 Si [g/kg TSS] 2 n.m. 65 0.2 37 217 All biofilms were rinsed prior to the experiment to remove particulate matter and stored in tap water at 4°C. Biofilms were imaged by light microscope SMT4 (Mikroskop Technik Rathenow) in combination with a DSLR camera (Canon EOS 600D) and characterized by their total suspended solid concentration (TSS) and volatile suspended solid concentration (VSS) according to DIN-EN-12880 (2001). The biomass density was determined by pycnometer measurement (n=4, 10 ml, Blaubrand) according to DIN ISO 35079 and the solids density was calculated according to Loosdrecht, Nielsen [32]. Element analysis was conducted by atomic emission spectroscopy (ICP-OES, Varian VistaPro, Agilent Technologies, l detection limit: 10 µg/L) after acid digestion. ICP-OES data for biofilm_1 is not available due to low biofilm mass. MRI and PFG-NMR MRI. MRI experiments were performed on a 200 MHz MRI instrument (Bruker Avance 200 SWB, Bruker BioSpin GmbH, Rheinstetten, Germany) with a magnetic flux B0 of 4.7 T, 150 mm vertical bore and equipped with a Bruker gradient system micro2.5 and a 1H-NMR bird-cage (25 mm inner diameter). All measurements were performed temperature controlled at 25°C using the Bruker software ParaVision. The often used multi-slice multi-echo imaging sequence (MSME) [14, 33] was applied to acquire predominantly proton density-weighted images due to the minimum echo time used in the experiments. The biofilms were imaged using the same acquisition parameters as in a previous study [34] with TR = 10 s, τE = 50 ms, number of averages = 4, pixel matrix 128x128, slice thickness 0.8 mm. To maintain the original structure, sludge and granules_2 were filled into glass vials with 1 mL of tap water from Karlsruhe to avoid 218 osmotic stress. The Karlsruhe tap water (average values of 2015, Stadtwerke Karlsruhe) had a pH of 7.2, total organic carbon concentration of 0.84 mg/L and an electrical conductivity of 653 µS/cm (c(Ca2+) = 110 mg/L, c(Na+) = 11.1 mg/L, c(K+) = 1.7 mg/L, c(Cl-) = 22.8 mg/L, c(HCO-) = 232 mg/L). Wet biofilm_1, biofilm_2 and granules_1 were placed into plastic wrap (without bulk water) and directly inserted into the bird-cage. The measured signal intensity is encoded on a gray-scale and physically corresponds to the proton density, slightly weighted by the transverse relaxation T2. The slightly T2-weighted proton density images allow the discrimination of the main components within the biofilm system, being either 1H containing liquid (signal) or solid or gas (no signal intensity in MSME images). Additionally, materials without 1H, i.e. minerals, do not show up in the 1H images. Diffusion Measurements. Translational motion was measured by PFG-NMR, i.e. the pulsed application of magnetic field gradients which encode and decode the position across an ensemble of molecules at different times. The time between the encoding and decoding pulses is the diffusion time Δ. The PFG-NMR acquisition parameters are summarized in Table 8.2. Biomass samples were measured using the PFG stimulated echo (PFG-STE) [13] on the above described NMR spectrometer equipped with the Bruker software Topspin and a Diff30 probe, which allowed z-gradients g of up to 12 T/m. Acquisition parameters were chosen according to Table 8.2, measurement I. The logarithmic, normalized signal attenuation ln(S/S0) was measured as a function of q, where q = γδg, γ being the gyromagnetic ratio, δ the gradient pulse duration, and g the gradient amplitude. Complementary measurements were performed on a 250 MHz MRI 219 tomograph (Bruker Avance 250 SWB, Bruker BioSpin GmbH, Rheinstetten, Germany) also equipped with a Diff30 Probe (maximum gradient 17 T/m) employing acquisition parameters of measurement II and III, (Table 8.2). Images taken at the beginning and end of the experiments showed stable biofilm structure. All diffusion measurements were performed as single measurements at 25°C. Table 8.2: Acquisition parameters for PFG-NMR diffusion measurements. Measurement II and III were used to characterize biofilm_1. Acquisition Parameter Measurement I Measurement II Measurement III PFG-STE PFG-STE D_T2_STE gradient pulse duration 3 ms 1 ms 1.136 ms diffusion time 40, 100, 200, 400, 500, 800 ms 50, 100, 200 ms 100 ms first rf pulse delay 4.26 ms 21.21 ms 21.21 ms recycle delay 8 s 900 ms 12 s diffusion gradient amplitude 0.016 T/m to 0.5 T/m linear in 32 steps -0.32 T/m to +0.32 T/m linear in 64 steps 0.015 T/m to 0.2 T/m linear in 64 steps number of scans 4 16 32 number of dummy scans 1 0 4 gradient direction z z z 220 Data Processing (Bi)-exponential Model. Dwater was obtained by fitting a single exponential function to the measured signal attenuation as it is expected for a homogeneous liquid of small molecules [35]. In the biofilm matrix, the motion of water is partially restricted. The samples are highly heterogeneous; therefore, a D-distribution is expected. However, as little is known about the details and mechanisms, the question about an appropriate model is essential for a confident data interpretation. As a first approach, the commonly used (bi)-exponential function 𝑆𝑆 𝑆𝑆0 = 𝐴𝐴1 exp �−𝐷𝐷1𝑞𝑞2 �𝛥𝛥 − 𝛿𝛿3�� + 𝐴𝐴2 exp �−𝐷𝐷2𝑞𝑞2 �𝛥𝛥 − 𝛿𝛿 3 �� (eq. 1) with the gradient duration 𝛿𝛿. D1 and D2 in biofilms were obtained, meaning that there is a fast (D1) and a slow (D2) diffusion fraction described by the relative amplitudes Ai. D1 makes up more than 80 % of the signal amplitude and is the dominant part. A small portion with signal amplitudes of 4-20% can be associated with D2 (in the range of 10-10 to 10-11 m2/s), which is significantly lower than D1. Due to the dominant relative signal amplitude, the discussion focuses on D1 in the following. The relative effective diffusion coefficient is defined by fD_exp = D1/ Dwater (eq. 2), which is used to compare the diffusion properties of the samples. Data was processed using self-written scripts in Matlab® (version R2012a, Matlab Works Inc.; Natick, Massachusetts, USA) which take special care of the small amplitude of the second diffusion contribution. This (bi)-exponential rather than a mono- exponential approach is essential for accurately describing the majority of the data to avoid miss- or over interpretation due to numerical errors during data processing. Only data points with signal above the noise level were used in the fits. 221 Gamma Distribution Model. For heterogeneous systems, the Stejskal-Tanner approach for self-diffusion of homogeneous liquids composed of small molecules does not apply necessarily. D-distributions are physically more meaningful than a discrete number of D in these highly complex and heterogeneous systems. Apart from the conventionally used (bi)-exponential function for modelling the signal attenuation, a recently developed approach by Röding et al. was used to reveal the distribution of diffusion coefficients [28, 29]. The Γ distribution function is a generalization of distribution functions known in mathematical statistics. One of the advantages is that the equation for the experimentally observed magnetization as a function of q2 becomes rather simple and accurate, for details we refer to Röding et al. (2012). Data was processed using self-written scripts (Matlab®) to obtain Dmean and the distribution width σ. The relative effective diffusion coefficient within the Γ distribution is defined by fD_g = Dmean/Dmean, water (eq. 3). The ratio between Dmean/D1 listed in Table 8.4 indicates the difference between the data analysis approaches and underlines the importance of using a physical and numerically appropriate model. 2D Inverse Laplace Transform. Another approach to model data deviating from a strictly mono-exponential behavior is a purely numerical approach, the inverse Laplace transform (ILT). Diffusion measurements can additionally be combined with relaxation measurements, and the data can be Laplace transformed in two dimensions. In the present case, D-T2 maps were obtained by performing a 2D inverse Laplace transform (2D ILT) [19, 36, 37] to correlate diffusion and relaxation measurements for biofilm_1. 222 Results and Discussion Biofilm and Biomass Characterization: Comparison of Common Quantities and Images Biomass is commonly characterized by i.e. thickness, density, elemental composition, TSS, and VSS, which do not consider spatial and structural inhomogeneities. On the other hand, mass transport and diffusion properties strongly depend on these spatial inhomogeneities but are not unique in the sense of a one-to-one correspondence of structure and diffusion coefficient. In a first approach, the microscopic findings and the macroscopic chemical parameters were collected and compared to link these physical parameters to water diffusion. As evident in stereomicroscopic and MRI images (Table 8.3), sludge consisted of a complex, but loose network of flocs with a small-scale heterogeneity. The measured biomass density of 1033 g/L is within the expected biomass densities for active sludge flocs with 1020-1060 g/L [38] and is higher than pure water density (998 g/L at 20°C). The mineral content was relatively low with 37 g Ca per kg TSS. It is expected that the water diffusion is hindered in the sludge flocs, and is therefore, slower than free water. Compared to the heterogeneous structure of the sludge flocs, biofilm_1 comprised a fluffy and homogenous structure (Table 8.3). The fluffiness of the biofilm is indicative for the low biofilm density (not distinguishable from free water) and high VSS of 90%. The pycnometer measurements for biofilm_1 were not reproducible due to low density and low biomass concentration. Furthermore, spatial variation in biomass density, which influences water dynamics in the biomass, cannot be captured by a simple pycnometer 223 measurement. Another approach is to get insight into the biomass structure and density by MRI. MRI image contrast delivers qualitative information: biofilm_1 was visible in the slightly T2-weighted images due to the reduced T2 in the biofilm compared to bulk water. This effect is based mainly on the exchange of protons between EPS biopolymers (mainly OH-groups) and water molecules [39] as well as by the different molecular mobility of molecules in biofilm matrix and water. In proton-density weighted images, biofilm_1 was hardly distinguishable from bulk water because of similar proton concentration [34]. Based on this knowledge, the density was estimated to be ~1010 g/L. Biofilm_2 was cultivated for ~12 months in a WWTP, TSS and mineral accumulation were significantly higher than in all other biofilms, therefore, diffusion is expected to be highly restricted. The iron content was especially high due to iron- accumulating bacteria (anammox) [31]. The internal structure was heterogeneous: outer biofilm layers were less dense than layers close to the carrier material reflected in the gray values of corresponding MRI voxels. Solids (precipitates, possibly CaCO3) and gas bubbles (air, CO2, N2 gas due to microbial activity) appear black with the usual phase susceptibility artifacts. The local heterogeneities in biofilm structure can be related to advanced biofilm age, density and growth conditions. Those heterogeneities suggest that there are regions in the biofilm which for which water diffusion is restricted to a larger extent than in other regions. 224 Table 8.3: Summary of stereomicroscopic images and MRI (slightly T2-weighted image) of the investigated biofilms. The resolution for MRI images was approximately 100 µm x 100 µm. Biomass Stereomicroscopic Image MRI Sludge Biofilm_1 Biofilm_2 Granules_1 Granules_2 225 Under certain cultivation conditions, biofilm formation is also possible without carrier material, commonly known as granules. Due to high shear stress applied during cultivation, the surface of granules_1 and granules_2 were compact and smooth. However, in the large granules_1 strong internal heterogeneities became apparent in the MRI images, such as structural layers of microorganisms and precipitates which might lower diffusion in the biomass. The biomass density was within the conventional range for aerobic granules (1005 g/L-1070 g/L), which depends among others on the cultivation conditions and volume fraction of solid [40-42]. Granules with a high solids content of precipitates can have biomass densities up to 1200 g/L [43]. Granules_2 originated from a WWTP accumulated significantly more minerals (e.g. Ca, P, Fe, P) than granules_1, which were cultivated in a lab scale reactor. Furthermore, biomass density of granules_2 was in the same range as biofilm_2. As density is known to be one of the most important parameters for diffusion in biomass (Renslow et al. 2010) the correlation between usually measured parameters and diffusion coefficients were explored. Diffusion of Water in the Presence of Biomass To relate biofilm geometry and composition to water diffusion, PFG-NMR diffusion experiments were carried out on different biomasses. As mentioned, the biofilm’s heterogeneity poses some challenges for modelling diffusion in these systems. The logarithmic signal attenuation was measured as a function of q2, results of biofilm_2 and granules_2 are shown in Figure 8.1 together to provide examples of the data and the numerical fits. Diffusion data from the biofilms were interpreted with both the (bi)- exponential fit (indicated as (bi.)-exp.-func.) and the gamma distribution model 226 (indicated by Γ distr.). The levels for good description of the data are depicted in form of 2 % and 4 % of the maximum amplitude, respectively, corresponding to the goodness of Γ distr. fit to the data. A significant difference in the signal attenuation between the samples is evident (inset in Figure 8.1), which can be explained by the different biomass properties (see Table 8.1) influencing the water dynamics significantly. The compact morphology and low VSS lead to a reduced water diffusion in granules_2 compared to biofilm_2. The (bi.)-exp.-func. leading to D1 and D2 does not describe the measured data sufficiently well, especially the first data points (inset in Figure 8.1). The reason is found in the discrete approach which is physically not really appropriate for a multicomponent system. A discrepancy results between D1 (from the (bi.)-exp fit) compared to Dmean (from the Γ distr. fit). The Γ distr. represents the measured data above the noise level significantly better than the (bi.)-exp.-func., resulting in lower residuals leading to a better data quality and higher accuracy. The results for D1 and Dmean differ by 15 % (biofilm_2) and 5 % (granules_2) which supports the above argument. The findings are in agreement with previously published results for other heterogeneous samples such as motor oils, where a better description of measured diffusion data was achieved by Γ distr. [44]. The importance of an appropriate data analysis is obvious as the diffusion coefficients influence simulation for substrate conversion in biological systems. 227 Figure 8.1: The logarithmic signal attenuation of biofilm_2 (top) and granules_2 (bottom) are depicted exemplarily for all biofilm samples as a function of q2. The mono- and bi- exponential decay functions and the gamma distribution model were fitted to the data. The levels for good description of the data are depicted in form of 2% and 4% of the maximum amplitude, respectively, corresponding to the goodness of fit of the gamma model to the data. Deviations of the mono-exponential model are evident. 228 Influence of Biomass Structure on Water Dynamics D1 and Dmean were obtained by (bi.)-exp.-func. and Γ distr., respectively (Table 8.4). Dwater = 2.09 m2/s·10-9 was slightly lower than the reported values [19, 45] due to different water purity and temperature. When comparing the two data processing approaches, Dmean and D1 for water were similar within approximately 2%. Dmean/D1 is close to 1 for free water as expected. Table 8.4: Summary of diffusion coefficients (at Δ 200 ms) of the used biofilms gained by two different data analysis approaches. Diffusion coefficients D1 and Dmean obtained by (bi)-exponential fit (indicated by (bi.)-exp.-func.) and gamma distribution (indicated by Γ distr.), respectively. Data indicated by asterisk (*) were fitted using mono- exponential function. Dr is the relative effective diffusion coefficient for both data processing approaches, see Eq. 2 and 3. Sample (bi).- exp.- func. (bi).- exp.- func. Relative Amplitude of D1 Contribution Γdistr. Γdistr. Γ distr. width Ratio D1 [m2/s] ·10-9 Dr_exp [-] Arel [-] Dmean [m2/s] ·10-9 Dr_g [-] σ [m2/s] ·10-10 Dmean /D1 [-] Water 2.09* 1 - 2.04 1 3.19·10-3 0.98 Sludge 1.45 0.69 0.93 1.62 0.79 8.55 1.11 Biofilm_1 1.76 0.84 0.97 1.96 0.96 5.17 1.12 Biofilm_2 1.47 0.70 0.95 1.69 0.83 7.18 1.15 Granules_1 1.27 0.61 0.94 1.60 0.78 4.96 1.26 Granules_2 0.76 0.36 0.84 0.73 0.36 4.71 0.95 229 D1 and Dmean measured in the presence of biofilms deviated by 20-30 % (D1/Dmean between 0.95-1.26). This indicates a good overall agreement for both data processing approaches despite the better fitting of the measured data by Γ distribution. Dmean is typically slightly larger than D1 (Table 8.4) as in the (bi)-exponential fit only D1 with Arel > 84% was considered. The minor part of the signal is associated with D2, which is in the range of 10-10 to 10-11 m2/s. D2 might be assigned to intracellular water [46]. Previous studies have also demonstrated that water diffusion coefficients in biofilms are lower than in pure water due to restricted diffusion in the biomass matrix, cells, and EPS, resulting in a wide range of diffusion coefficients between 10−9 and 10−13 m2/s [46]. fD_exp and fD_g vary strongly with the type of biofilm. The lowest fD_g was found for granules_2 (0.36) and highest fD_g for the biofilm_1 (0.96). Diffusion was most restricted in granules_2 likely due to the compact structure and high content of inorganic matter (Table 8.1). In comparison, the diffusion coefficients in heterotrophic biofilm_1 were closest to Dwater because of the fluffy structure and high VSS of 90%. Results are within the typical range of reported relative diffusion coefficients for biofilm from 0.2 to 0.8 [47-49] except biofilm_1. In Figure 8.2, D1 and Dmean are directly compared for the different biofilm samples. The “error” bars for Dmean represent the width of the Γ distr. σ, listed in Table 8.4: σ for pure water was very small and not visible, whereas σ for all biofilms was large. Sludge and biofilm_2 show the highest σ possibly due to their highly heterogeneous internal structure (Table 8.4). The diffusion coefficients D1 and Dmean vary for all biomass, with biofilm_1 showing fastest and granules_2 showing lowest diffusion 230 coefficients. The water diffusion in sludge and biofilm_2 are similar, although the biomass structure parameters differ significantly. As visible in Table 8.3, these biomasses comprise completely different morphologies being either an open network or a compact biofilm. Furthermore, biomass structural parameters (e.g. VSS, biofilm thickness and density) differ strongly and suggest that the diffusion in biofim_2 is more hindered than in the sludge. However, this is not the case. This leads to the conclusion that the assumptions regarding mass transfer in biofilms based on bulk physical properties are not directly related to the classical parameters or optical appearance. Figure 8.2: Diffusion coefficients D1 and Dmean obtained by (bi)-exponential fit and Γ distribution for water and different biomasses measured with a diffusion time Δ= 200 ms. “Error” bars around Dmean represent not statistical errors but the width of the Γ distribution σ (Table 8.2). wa ter bio film _1 bio film _2 slu dg e gra nu les _1 gra nu les _2 0 5.0x10-10 1.0x10-9 1.5x10-9 2.0x10-9 2.5x10-9 D [m 2 /s ] Dmean D1 231 No clear correlations are found between certain integral biofilm properties and diffusion coefficients: the biofilm thickness and geometry seemed to have a minor influence on D in the present case. For example, biofilm_2 and granules_2 had similar densities, but D differed by approximately 50% when using both data processing methods. Liquid channels in biofilm_2 correspond to an enhanced water diffusion within the biomass resulting in similar apparent diffusion values as highly porous sludge. The broad range of relative diffusion coefficients highlights the fact that biofilm structure determines the mass transfer and ultimately the performance of productive biofilms, such as the mentioned wastewater biofilms or fungal bio pellets [50]. Whether the measured water diffusion can be transferred to relevant substrates for biofilms remains unclear. The substrates’ molecular weight, interaction with the surroundings as well as diffusivity and penetration into the biofilm differ from water molecules and could be explored by heteronuclear NMR diffusion measurements and theoretical models can help to answer this question. Using a simple calculation, we estimated the difference between COD (chemical oxygen demand) turnover for the highest (biofilm_1) and lowest (granule_2) diffusion coefficient. The oxygen flux can roughly be estimated by: D/Δ z * (concentration DO at biofilm surface – concentration DO at z) (eq. 4), where z is the biofilm depth and DO the dissolved oxygen concentration. Dmean was used a diffusion coefficient due to the best fit of the data. Keeping all biofilm related parameters constant (only changing D) the lower diffusion results in 20 % less turnover based on flux estimates, thus knowing the diffusion coefficient is highly relevant for biofilm modelling. Further infestations are planned in the future. 232 Besides that, the results contribute to link transport processes to biofilm structure which was shown for nanoparticle and metal transport in biofilms [27, 51]. The comparison of classical integral quantities with optical and MRI images shows that the approach of just using one measure for biofilm characterization is insufficient. A comprehensive characterization on different time and length scales is needed when aiming for an understanding of biofilms and the processes of mass transport and especially diffusion. The link between structure, diffusion and biological activity deserves further research. Influence of Diffusion Time on Water Dynamics In homogeneous liquids of small molecules, D is independent of diffusion time ∆. In porous media, D decreases with increasing ∆ due to barriers like physical restriction and adhesion of water molecules [14]. Biofilms can also be regarded as porous media consisting of biofilm matrix and bulk water. Our results show, that D1 decreased with Δ for all biofilms (Figure 8.3). D1 was selected as the trends were most pronounced. Dmean showed a similar but less marked effect. Water diffusion was most restricted in granules_2, indicated by the strong decline of D1 and low diffusion coefficient asymptote of 6.5 m2/s·10-10 at 400 ms, followed by granules_1. A different composition of EPS and microbial communities as well as the length scales of the heterogeneous internal structures are already visible in MRI images (Table 3) and are possible explanations for our observations. The mobility of water molecules may also be decreased due to entrapment in EPS molecules [46, 52]. As already mentioned, sludge and biofilm_2 both displayed fast diffusion, similar distribution width, and a small dependence on Δ. 233 Biofilm_1 did not show a strong diffusion barrier; only a slight decline of D1 relative to Dwater was found which leads to the conclusion that mainly unrestricted bulk water is observed. The calculated D also include the diffusion in the near bulk water which may be influenced by the presence of the biofilm, as has been shown for emulsions [53]. Figure 8.3: Diffusion coefficients D1 of biofilms at different diffusion times Δ. Classically, the dependence of the diffusion coefficients on diffusion time is a hint on hindered or restricted diffusion and is most pronounced in the granules. Data points for 500 ms and 800 ms are only given for sludge. The distributions of the effective diffusion coefficients obtained within Γ distr. are shown in Figure 8.4. Granule_2 exhibits the narrowest distribution (σ of 4.71 m2/s·10-10) together with the slowest Dmean. Faster diffusion was found for sludge and biofilm_2 with a broader distribution (σ of 8.55 and 7.18 m2/s·10-10). Narrow distributions, but with 0 100 200 300 400 500 600 700 800 900 6.0x10-10 8.0x10-10 1.0x10-9 1.2x10-9 1.4x10-9 1.6x10-9 1.8x10-9 sludge biofilm_1 biofilm_2 granules_1 granules_2 D 1 [m 2 /s ] ∆ [ms] 234 faster Dmean were found for biofilm_1 and granules_1. The sludge and biofilm_2 results demonstrate that increased internal heterogeneity over small length scales in the biomass tends to broader distributions. The distributions give unique indications for the estimation of the overall diffusion properties of diverse biofilm systems that single parameters determined by (bi.)-exp.-func. cannot express. However, the Γ distr. model also depicts portions of 1H-NMR signals which are diffusing significantly faster than free water (Dwater = 2.04·10-09 m2/s) highlighted in gray. This portion differed for all biofilms and was especially pronounced for biofilm_1. Possible explanations for this phenomenon are convection due to temperature or enhanced diffusion by concentration gradients. Larger bulk water compartments, which were evident for biofilm_1 (Table 8.3), are more prone to convective transport, resulting in larger influence on D. Additionally, it is known that diffusion can increase in the presence of small concentrations of nonpolar compounds, such as methanol or acetonitrile in water mixtures [54]. The convection could also be a result of vibrations induced by the large field gradients as it is difficult to immobilize the granules and biofilm carriers. 235 Figure 8.4: Distribution of the diffusion coefficients according to Γ distribution. D = Dmean for free water is 2.04·10-9 m2/s. Gray region indicates diffusion values, which are larger than free water. Correlation of Diffusion and Transverse Relaxation The effective D-T2 relaxation correlation was measured for biofilm_1 and compared to free water (Figure 8.5) using a regularization parameter α = 1*108 and 64 steps during 2D-ILT. The peak in the upper edge of the maps is an artifact of 2D-ILT due to insufficient sampling of higher gradients. To confirm the location of the main peak in the 2D distribution, a single line of data was extracted in each dimension to produce a 1D spectrum of diffusion and relaxation as the 1D ILT is numerically more stable than the 2D [55]. As expected, bulk water is characterized by Dwater = 2.4 x 10-9 m2/s with a reasonably narrow distribution width and by an average T2 of 2.6 s. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 D [m2/s] 0 2 4 6 8 10 12 pr ob ab ilit y [s /m 2 ] x10-9 x108 sludge biofilm_2 biofilm_1 granules_2 granules_1 236 Figure 8.5: Effective diffusion spin-spin relaxation correlation maps for free water (left) and biofilm_1 (right) at a diffusion time of 100 ms. Data was processed using 2D-ILT and reveals the correlation between diffusion and transverse relaxation both being influenced by the structural properties of the biomass. Compared to free water, the presence of biofilm_1 produces a significant shift of a portion of the signal to smaller D and lower T2. Typically, T2 and D in biofilms are less than that of bulk water [19, 34]. These results are consistent with previous observations. Another portion of signal attributed to the bulk water, about T2 of 3 s, shifts towards larger D. This strongly points to convection as a possible explanation for the observation of larger diffusion coefficients in 1D diffusion experiments as well as in the correlation experiment. As mentioned earlier this could well be due to vibrations induced by the gradients and enhanced by the biofilm as it is hard to immobilize the plastic carriers in the test tubes. It should be noted that the effect is well known and occurs in low viscosity liquids even at almost no temperature gradient if the solid structures in the sample cannot be completely immobilized. 237 Conclusions In this study, the water diffusion coefficients and their distributions were determined using PFG-NMR for five different biomass samples. Diffusion data was processed using conventional (bi)-exponential data analysis, the Γ distribution model and 2D ILT for data interpretation. Stereomicroscopic images are compared to MRI images and insights of D-T2 correlation maps are introduced. The experimental results lead to the following conclusions: Similar diffusion coefficients for both data processing approaches, (bi)-exponential data analysis and Γ distribution model, were obtained with 5-26% difference between Dmean and D1. A better representation of the data was achieved by the Γ distribution function with respect to numerical reproducibility and physico-chemical interpretation. No direct correlation between Dwater and typical biofilm properties (e.g. compactness, mineral content, VSS) was observed. Dmean is not sufficient to describe the mass transport in multispecies biomass. Additional information is provided by MRI images and distributions of Dwater in the biomass obtained by Γ distribution model: some areas in the biofilm seem to have exhibited more restricted transport than others, associated to gas bubbles, precipitates, and changing biofilm densities. D-T2 correlation maps confirmed these findings and proved a shift in T2. 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Journal of Magnetic Resonance, 2016. 270: p. 12-23. 243 STRUCTURE AND DIFFUSION OF AEROBIC GRANULAR SLUDGE USING MAGNETIC RESONANCE Abstract Magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) allow non-invasive measurements describing both internal structures and transport properties of opaque, complex materials like biofilms [1-3]. High-field MRI was used to image aerobic granules collected from full-scale wastewater treatment plants in the Netherlands. T1 and T2 relaxation-weighted images reveal heterogeneous internal structures that include high and low density regions and solid inclusions. Additionally, pulsed field gradient (PFG) NMR methods and multi-dimensional correlation and exchange experiments were used to measure diffusion and transport properties within undisturbed granules. Our results show differences in rates of water diffusion within the heterogeneous granule structure and suggest that models employing a single diffusion coefficient may be insufficient to capture the complexity of transport behaviour within the granules. Introduction Compared to conventional activated sludge systems where the biomass exists in dispersed flocs, aerobic granular sludge offers numerous benefits for wastewater treatment including compact design, lower energy costs, and excellent biomass retention [4]. By their very nature as spherical biofilm aggregates, granules are composed of a 244 variety of microniches—aerobic, anoxic, anaerobic —where diverse bio-chemical conversions can occur simultaneously within the same granule [5, 6] (Figure 9.1). In the last two decades, research into the formation, structure, and metabolism of granular sludge has flourished [7-12] and today full-scale reactors are in operation in several countries, including the Netherlands [13]. Figure 9.1. A conceptual model of aerobic granular sludge shows the different redox zones within the granule as concentric structural layers where distinct biochemical conversions occur simultaneously. While it is known that hydrodynamic shear, substrate type and loading rate, oxygen concentration, microbial growth rate, and microbial strain are all important parameters in the formation of aerobic biofilm granules, the governing parameter has yet to be identified [14]. Under appropriate operating conditions, floccular sludge self- assembles into millimetre-scale biofilm granules in which EPS provides a robust framework. The biofilm matrix of the granule has a complex structure [15], consisting of 245 hydrated gel-like fibers allowing for phenotypic heterogeneity and differentiation of cells within the colony analogous to a multi-cellular organism [16-18]. Early MRI experiments on anaerobic granules provided evidence of a cluster structure [19] while imaging of methanogenic granules showed that the EPS matrix is organized in concentric layers and the granules appear to have ‘hollow’ centers [20]. This complex morphology influences rates of diffusion and substrate utilization in a manner that is not entirely well-defined. Moreover, granular sludge reactors may take months or even years to reach steady state conditions, making experimental studies using parametric analysis on large scale reactors infeasible. Mathematical models have been developed to simulate substrate removal and the distribution of microbial populations and processes within the biofilm granule [21-24], but their utility is limited by a lack of knowledge. Until these models are refined with robust experimental results related to the formation and activity of granular sludge, the technology will not by fully exploited for wastewater treatment. The current research explores how the internal granular structure is related to reactive mass transport in the granule, with the goal of understanding how wastewater components move through the granule and are degraded or captured, and how granule activity is related to the structure of the aggregate. Most granules used in laboratory research have been grown on simple soluble substrates like acetate, while natural wastewaters contain complex substrates, including slowly biodegradable particulates [25- 27]. These particulates must be hydrolyzed before they are available to bacteria for conversion, which influences the granulation kinetics, the resulting granule morphology, 246 as well as reactor performance and the required operational conditions [26]. Specifically, the research will examine in the future how particulates and complex contaminants commonly found in wastewater influence the morphology and mass transport properties of aerobic granular sludge [13, 25, 27]. NMR and MRI can provide spatially-resolved data on granule structure, composition, and reaction-diffusion properties non-invasively and non-destructively under various hydrodynamic conditions. These capabilities represent a significant advantage over conventional methods like microscopy and micro-electrode studies which are necessarily invasive and destructive. These methods also tend to be limited in terms of the range of length scales that can be probed. For example, micro-electrodes provide point or 1D data. Optical methods can achieve a high spatial resolution, but over a limited field of view. NMR and MRI can better bridge multiple length scales, such as in the case of a 5 mm sample field of view with 50 µm2 pixel resolution. As the research described in this chapter is in the early stages of a multi-year international collaborative project, this chapter will focus on two main research questions, each explored with different NMR and MRI methods. The first current research question is related to the internal granule structure. Does the internal structure of aerobic granules used in practice for wastewater treatment conform to the conceptual model shown in Figure 9.1? Secondary questions are related to how consistent the observed structure is between samples from the same treatment plant, from different treatment plants, over time as the granules age, and between laboratory granules and those treating real wastewater. Imaging experiments give insight 247 to these structural questions. Secondly, the current research explores how diffusive transport varies within a granule by measuring the effective water diffusion coefficient using PFG-NMR methods. Specifically, how large is the range of Deff within the granules? Multi-dimensional diffusion – relaxation correlation (D-T2), relaxation – relaxation correlation (T1-T2), and relaxation exchange (T2-T2) experiments can also provide information about how the diffusive behaviour of water is related to structural regions with different relaxation rates, and the timescale of exchange of water between those different regions. Material and Methods Sample Collection and Preparation Samples of aerobic granular sludge were collected during the aeration phase of the treatment cycle from sequencing batch reactors at the Utrecht and Garmerwolde wastewater treatment plants in the Netherlands (Figure 9.2). The samples, which ranged in volume from several hundred millilitres to several litres, were stored in airtight plastic containers in the refrigerator without substrate addition. Granules from other sources, including anammox granules from the B-stage of the Dokhaven treatment plant, anammox granules treating the rejection water at Sluisjesdijk treatment plant, laboratory VFA-producing granules, granules produced from extracted and re-constituted EPS, and control samples of alginate beads were also imaged using the same parameters for comparison with the aerobic granules. For the MRI experiments, a single granule was added to tap water in a 5 mm NMR sample tube. The granules were elevated within the 248 sample tube by either a plug of Teflon tape, a stack of alginate beads, or a 3-D printed polymer frame (Figure 9.3). Figure 9.2. (Left to right) Samples were collected from the Utrecht wastewater treatment plant’s Nereda ™ sequencing batch reactor. The granules settle first with the floccular sludge on top. A single granule was then placed in a 5 mm NMR sample tube for imaging experiments. Samples for the PFG-NMR measurements and multi-dimensional correlation and exchange measurements were collected from Garmerwolde treatment plant as described above and stored in tap water in the refrigerator until measurements were collected, approximately 4 months after sampling. As these measurements are not spatially resolved in 2D, a stack of granules in tap water was added to the 5 mm NMR sample tube to maximize the signal obtained from the granules relative to bulk water signal. 249 Figure 9.3. The granule samples were placed in 5 mm NMR sample tubes, elevated with either Teflon tape (left), a stack of alginate beads (center), or a 3-D printed frame (right). The granules shown include an extracted EPS granule, a VFA-producing laboratory grown granule, and an anammox granule from the B-stage of Dokhaven treatment plant. NMR and MRI Measurements 1H NMR and MRI are sensitive to hydrogen protons, typically water in most biological systems. NMR relaxation rates provide information on the physico-chemical environments in which different water populations exist. Timing of the pulses which make up the NMR measurement can be adjusted to accentuate contrast between these different water populations and distinguish between intercellular water, rotationally restricted water in the EPS matrix, and free water in the bulk phase. T1 relaxation- and T2 relaxation-weighted images provide such a contrast and were collected on MRI tomographs operating at 7 T and 22 T using parameters found in Table 9.1. The MRI images were collected on both fresh granules (several days after sampling) and on aged samples (approximately 2 months after sampling). The granules were also imaged using 250 traditional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM). 22 T 7 T T1 weighted T2 weighted T2 map Repetition time, Tr (s) 0.550 5 6 Echo time, tE, (ms) 5.3 5.3 5.2 Number of echoes 16 16 128 Spatial resolution (μm) 47 x 47 47 x 47 47 x 47 Slice thickness (μm) 100 100 100 Measurement time 9 min 23 s 10 min 40 s 13 h 39 min Table 9.1. MRI measurement parameters. The 22 T MRI system at uNMR-NL, an NWO- funded National Roadmap Large-Scale Facility of the Netherlands, located at Utrecht University, produced high-resolution and high-contrast images with a minimal measurement time. The 7 T MRI system at Wageningen University achieved similar resolution with longer measurement times. Additionally, pulsed field gradient (PFG) NMR methods were used to measure diffusion coefficients in aged granules from Garmerwolde treatment plant. The samples were approximately 4 months old at the time of measurement. Experiments were performed on a 250 MHz (5T) Bruker Avance III superconducting magnet with using a high-power probe, Micro 5 gradient set (with a 2.81 T/m maximum gradient) and a 5 mm radio-frequency coil. Two-dimensional correlation and exchange experiments were also conducted to relate diffusion to T2 relaxation and to examine exchange between different T2 populations. The pulsed-gradient stimulated-echo (PGStE) experiment was used to collect diffusion data for these granules given the relatively fast signal decay rates observed for 251 the Garmerwolde granules during imaging. During the diffusion time, Δ, the stimulated echo experiment allows for the net magnetization to be stored in the longitudinal plane where it is not subject to T2 relaxation processes (Figure 3.2). Therefore, measurable signal remains following extended diffusion times in the range of tens to hundreds of milliseconds. Data Analysis T2 Maps. Multi-slice multi-echo (MSME) images produce a stack of 2-D images showing the echo amplitude per pixel in each sample slice. An image is collected of each echo in the signal decay, such that the stack of images for each slice shows the attenuation of signal in each pixel. Fitting the echo attenuation in each pixel as an exponential decay produces the effective T2 relaxation rate in each pixel. These rates, or the relaxation times, can be displayed in a 2D image of the sample where the pixel intensity corresponds to the effective relaxation rate, R2,eff, or the effective relaxation time, T2,eff. T2 map data was analysed with both IDL software at WUR by Dr. Frank Vergeldt and also at MSU by the author using Prospa v3.13. Diffusion Images. PGStE data for the 1D image was analysed first in Prospa by Fourier transforming the echo data in the read direction. The data was then exported to Matlab as a magnitude image where a fitting function was applied in the q-direction to calculate the effective diffusion coefficient at each point in the 1D image. Diffusion- weighted images collected in Paravision 5.1 were analysed in Prospa v3.13. A Prospa macro first created a matrix of q-space data for each image slice prior to using the 252 standard Prospa makeDiffMap macro to produce an image in which the pixel intensity corresponds to the apparent diffusion coefficient (ADC) in the sample. Multidimensional Correlation and Exchange Experiments. Data collected for correlation and exchange experiments were analysed in Matlab using the 2D Inverse Laplace Transform (ILT) which uses a non-negative least squares fitting function with a regularization parameter to minimize the error in the solution. Results and Discussion MRI of Granule Internal Structure The initial research goal of this project was to simply identify internal structural features within the granules and determine how consistent those features are across granule sources, types, and over time. T1 and T2 relaxation-weighted images of granules from wastewater treatment plants reveal heterogeneous internal structures that include high and low density regions and solid inclusions. Images of granules from both the Utrecht and Garmerwolde treatment plants reflected similar heterogeneity, though it was significantly more difficult to collect high quality images from the Garmerwolde granules because of rapid signal decay. For that reason, most of the images included here are of granules collected from the Utrecht wastewater treatment plant. 253 Figure 9.4. The third echo of a T1-weighted image of a Nereda® granule (Utrecht wastewater treatment plant) obtained from the 22 T MRI shows high contrast between areas of differing density within the granule. Spatial resolution is 47 x 47 x 100 μm3, echo time = 16 ms, repetition time = 550 ms. Because of the long echo time, brighter regions in the granule correspond to less dense regions where diffusion is less restricted. Darker areas indicate either decreased proton density, in the case of solid inclusions, or more rotationally restricted water as would be found in cell clusters. All granules were imaged in a 5mm tube of tap water, which is the relatively brighter fluid surrounding the granule. Figure 9.4 shows a fresh granule from the Utrecht treatment plant with characteristic dark, dense regions and brighter less dense regions. Relatively bright bulk water is visible in the sample tube outside the granule. This image is T1-weighted with a short repetition time of 550 ms to enhance signal collection from the more dense regions of the granule. It is also, however, an image of the third echo in the decay train making the image also T2-weighted. The combination of T1- and T2-weighting provides excellent contrast between regions of differing density and water mobility. 254 Figure 9.5. The first echoes of T1-weighted images of a laboratory VFA-producing granule (left) and a Nereda® granule (Garmerwolde wastewater treatment plant) obtained from the 22 T MRI show the high structural variability observed between laboratory and treatment plant granules. Spatial resolution is 47 x 47 x 100 μm3, echo time = 5.3 ms, repetition time = 550 ms. In the left image, the bright regions correspond to biomass, which is selectively highlighted with T1-weighting relative to the bulk water outside the granule. The right image, collected under the same measurement parameters, shows dense biomass in the dark regions where the signal has already decayed due to T2 relaxation during the 5.3 ms echo time. Figure 9.5 compares a laboratory-grown volatile fatty acid (VFA) producing granule with a fresh granule from the Garmerwolde treatment plant. The VFA granule appears in this image to be hollow, as was later confirmed with traditional microscopy after sectioning the granule. The Garmerwolde granule, on the other hand, exhibits a similar heterogeneous structure as seen in Figure 9.4, though more dense overall. Since the VFA and Garmerwolde granules contain different bacterial populations and grow under different operating conditions – anaerobic for the VFA granules and aerobic for the Garmerwolde granules – it is not possible with these data to draw any conclusions about the internal structural differences between laboratory and treatment plant granules in 255 general. However, as a starting point, it shows how different the internal structure can be. T2 Maps. Effective T2 maps of granules from the Utrecht treatment plant for different age granules (Figure 9.6) show the same heterogeneous internal structure observed in Figures 9.4 and 9.5. The maps were produced from MSME images (32 echoes) made on the 22 T system in the national NMR lab in Utrecht. Spatial resolution is 47 x 47 x 100 microns. The effective T2 maps also show that neither the structure nor the T2 relaxation behaviour changes significantly over the timescale of approximately 2 months. The image on the left in Figure 9.6 shows a fresh granule from Utrecht, while the right image shows a different granule from the same sample, imaged after 2 months of storage in the refrigerator. In both T2, eff maps, the bulk water T2 relaxation time is approximately 18 ms, which is approximately equal to the maximum internal T2 time in the granule ‘voids.’ In the dense biomass regions of the granules, the minimum T2 times are approximately 6 ms with the apparent transition between ‘voids’ and biomass occurring around a T2 time of 12 ms. T2 maps of alginate beads collected in the same system with the same measurement parameters produced the same bulk water relaxation time and a relatively uniform relaxation time within the bead of approximately 13 ms (not shown). 256 Figure 9.6. T2 maps of granules from Utrecht wastewater treatment plant. The image on the left was taken of a fresh aerobic granule, while the image on the right was collected from the same sample of granules after aging for 2 months. The T2 relaxation times range between approximately 18 ms in the bulk water and in the less dense regions of the granules to approximately 6 ms in the dense cell clusters of the granules. There is no discernible difference between the fresh and aged granules in terms of T2 relaxation. The spatial resolution is 47 x 47 x 100 microns. Boundary Layer. A dark apparent boundary layer is visible on the surface of both the Utrecht granule in Figure 9.4 and the Garmerwolde granule in Figure 9.5, but was not observed on any of the granules produced in laboratory reactors. This layer is very sharp and well-defined in the MRI images, particularly those from the 22 T system. Two recent studies have examined the surfaces of granular sludge and may provide insight into the nature of the material observed in the MRI images. Poot et al. recently found evidence of stratification of ammonia-oxiding bacteria (AOB) and nitritre-oxidizing bacteria (NOB) at the surface of aerobic granules grown in low-strength wastewater [28] using fluorescent in-situ hybridization (FISH). The authors suggest that the position of the AOB on the granule surface provides a competitive advantage to the AOB in terms of Ef fe ct iv e T 2 re la xa tio n t im e ( m s) 257 oxygen competition with the NOB, and also protects the NOB colonies from detachment. In order to achieve complete nitritation for subsequent anaerobic ammonium oxidation, NOB populations must be repressed relative to AOB populations. Thus, the layer may be a dense biomass region, composed primarily of nitrifiers. Manas et al. reported formation of calcium and phosphorus precipitates on the surfaces of anaerobic granules, observed using SEM-EDX imaging [29]. These authors report that ‘rings’ of the mineral were visible in the largest granules imaged, suggesting successive periods of mineralization and overgrowth. The Garmerwolde granule shown in Figure 9.5 appears to show successive rings as described by Manas et al. As part of the effort to identify the apparent boundary layer observed with MRI, SEM-EDX imaging was applied to the outer surfaces of samples of the same type of granules used in the MRI experiments. A single Garmerwolde granule was also cut with a razor blade prior to imaging with SEM-EDX to compare the internal and exterior physical properties. Results (not shown) indicate that while some mineral precipitates had formed in the granules collected from treatment plants, there was no significant precipitate layer on the surface of the granule. The sectioned granule appeared to show a more dense organic region at the surface, but the quality of the section was not high enough to make a conclusive determination. Images were also made using transmission electron microscopy (TEM) to more directly observe the surface layer of aerobic granules from Garmerwolde treatment plant. TEM imaging involves embedding an osmium-treated sample in resin which is then 258 baked until solid. The samples are then sectioned with a diamond blade to thicknesses of 70-90 nm and imaged in the electron microscope. Figure 9.7 shows dense cell clusters at the surface of a granule in the top of the image, with the embedding resin outside of the granule at the bottom. The black areas on the edges of the image are the copper frame which holds the thin sectioned sample. There is no precipitate or solid particulate debris visible on the granule surface. Figure 9.8 shows the edge of an internal cell cluster where the lower left area of the image is an internal ‘void’ space. No cells are visible in the void, though some EPS matrix material is visible in this and other TEM images of the less dense regions as imaged by MRI. When viewed at the same scale, the granule exterior exhibits greater cell density than the interior cluster, which may account for the dark apparent boundary layer. Figure 9.7. TEM image showing the outer surface of a Garmerwolde granule (top of half of image) relative to the embedding resin at the bottom. The cells shown extend approximately 20-30 microns into the granule. Scale bar is 20 µm. A (~ 5µm)2 box is shown for reference to Figure 9.8. 259 Figure 9.8. TEM image of the edge of an internal cell cluster and corresponding ‘void’ region. Scale bar is 5 µm. A (~ 5µm)2 box is shown for reference to Figure 9.7. PFG and Multidimensional NMR In addition to imaging experiments, PFG-NMR diffusion measurements and 2D correlation and exchange measurements were recently collected at MSU at 5T field strength using a stack of 4-month-old granules collected from Garmerwolde treatment plant in a 5mm sample tube. These measurements confirm the presence of multiple T2 populations, a distribution of T1 populations, and variable diffusion coefficients within the granules. The PGStE pulse sequence was used in conjunction with imaging in the read direction to produce a 1D image of the diffusion coefficients through a stack of alginate beads and one aerobic granule in tap water (Figure 9.9, top). At a diffusion time, Δ, of 100 ms, the average effective water diffusion coefficient within the granule was approximately 1 x 10-9 m2/s while the measured bulk water diffusion coefficient was 260 approximately 1.8 x 10-9 m2/s. The alginate beads exhibited slightly faster diffusion than the granule with an effective water diffusion coefficient of 1.5 x 10-9 m2/s on average. All of the measured effective diffusion coefficients are lower than the typical free water diffusion coefficient of approximately 2 x 10-9 m2/s. Figure 9.9. A 1D image of the diffusion coefficients was collected over a stack of alginate beads and a single aged Garmerwolde granule in DI water. The top 2D image shows the sample. The bottom image shows the calculated 1D diffusion coefficient for each point in the image. Diffusion-weighted images were collected of aged anammox granules sampled from the B-Stage of the Dokhaven treatment plant in the Netherlands (Figure 9.10). The images were collected on the 5 T system at MSU in a 10 mm NMR sample tube with a spatial resolution of 78 µm x 78 µm x 300 µm and 16 averages. Eight gradient values were used, ranging from 0 – 1 T/m. The resulting map of apparent diffusion coefficients (ADC) shows reduced diffusion rates in the biomass within the granules and near-free- bulk wateralginate bead granule D ( * 1 0- 9 m 2 /s ) 1 2 261 water diffusion rates in the central ‘void’ regions. Unfortuately, the spin echo-based pulse sequence and diffusion measurement parameters used were not able capture and resolve apparent diffusion coefficients in the dense outer layer of the granules. Future work will involve optimizing the diffusion-weighted imaging measurement using a stimulated echo to overcome the rapid signal loss in the outer granule layer. Figure 9.10. Two anammox granules from the B-stage of Dokhaven treatment plant were imaged on the 5 T system at MSU using diffusion weighting (left). The resulting ADC map (right) shows reduced apparent diffusion coefficients within the biofilm matrix, but was not able to quantify diffusion coefficients in the dense exterior regions of the granules due to rapid signal attenuation. Diffusion – relaxation (D-T2) correlation measurements were also collected, both on the 5 T system at MSU and on a 0.3 T system at Wageningen University (WUR) in the Netherlands (not shown). The D-T2 correlation measured at MSU with Δ = 50 ms used a stack of aged granules from Garmerwolde in DI water. The correlation (Figure 9.11) shows multiple T2 populations with the largest peak corresponding to free water. The distribution of diffusion coefficients suggests that the biomass, with the shorter 2 4 262 relaxation times, has a range of water diffusion coefficients which extends to lower values. Figure 9.11. D-T2 correlation was measured for a stack of aged Garmerwolde granules in tap water on a 5 T system at MSU. The T2 portion of the D-T2 correlation is very similar to the 1D T2 distribution measured on the stack of aged Garmerwolde granules on the 5 T system at MSU (Figure 9.12). Here, the large peak on the order of T2 = 1-2 seconds corresponds to bulk water outside the granules. When compared to T2 maps measured on the 7 T system at WUR (Figure 9.12, right), the small peak at approximately 100-200 ms corresponds to the water in the ‘void’ regions of the granules. The relatively large population with T2 relaxation times of approximately 70 – 20 ms corresponds to the water within the dense biomass regions of the granule. 263 Figure 9.12. The 1D T2 distribution measured on the 5 T system at MSU on a stack of aged (4 month old) Garmerwolde granules (left) corresponds well to the T2 map of a fresh Utrecht granule measured on the 7 T system at WUR (right) and the T2 distribution measured as part of the D- T2 correlation shown in Figure 9.11. The intensity of the free water peak is diminished in the current figure due to the loading of the sample tube to maximize sample coming from the granules and minimize the volume of bulk water. In addition to the D-T2 correlation, T1 – T2 correlation was also measured on the 5 T system at MSU (Figure 9.13). This correlation again shows the expected T2 distribution as well as a broadening of the T1 distribution relative to bulk water which indicates the presence of more solid-like material in the granule. 264 Figure 9.13. The T1-T2 correlation measured on the 5 T system at MSU on a stack of aged (4 month old) Garmerwolde granules. T2 – T2 exchange was measured on the 5 T system at MSU using mixing times, τm, of 0 ms and 150 ms (Figure 9.14). The measurement recorded at τm = 150 ms does not show the classic off-diagonal peaks that would definitively show exchange between the different T2 populations. However, since there is a distribution of T1 relaxation populations present as well, exchange may result in averaging. Further data analysis and measurement optimization is necessary to determine the extent of exchange between T2 populations. 265 Figure 9.14. T2-T2 exchange measurements conducted on the 5T MSU system using a stack of aged Garmerwolde granules in DI water do not exhibit off-diagonal exchange peaks. Measurements are ongoing at the time of thesis submission. Preliminary results indicate that aerobic granules from municipal treatment plants in the Netherlands exhibit a heterogeneous structure comprised of dense cell clusters and ‘voids’ containing diffuse EPS matrix. The structures observed are closer to the cluster structure observed in some anaerobic granules [19] than to the concentric ring schematic shown in Figure 9.1. The structures were stable over a storage period of several months. The apparent boundary layer visibile in the MRI images appears to be of organic origin, composed of dense cell clusters. The preliminary findings also suggest that a distribution of diffusion coefficients exists within each individual granule in which diffusion is slower than bulk water within the dense biomass regions and on the order of free water in the ‘voids.’ This finding suggests that models employing a single diffusion coefficient, often based on invasive -3 -2 -1 0 1 -3 -2 -1 0 1 -3 -2 -1 0 1 -3 -2 -1 0 1 Log T2 (s) Log T2 (s) Lo g T 2 (s ) τm = 0 ms τm = 150 ms 266 micro-electrode measurements on laboratory granules, may be insufficient to capture the complexity of transport behaviour within granules treating wastewater. Further work is necessary to optimize measurement parameters and pulse sequences in order to measure spatially-resolved apparent diffusion coefficients in the dense biomass regions of the granules. Rapid signal decay renders spin-echo methods ineffective, but also suggests significant differences in diffusion behavior exist in these regions. Finally, this research demonstrates that NMR and MRI methods can provide novel and reliable data regarding the structure and transport properties of aerobic granular sludge. Future Work Future experiments are planned to repeat the PFG-NMR and 2D correlation and exchange experiments described above on fresh granule samples to produce data more relevant for inclusion in mathematical models. Furthermore, propagator measurements will be collected using a flow cell with a packed bed of granules to investigate the timescale for exchange between the bulk flowing water and the intergranular water which can shed light on not only transport properties of the system but also reaction kinetics. Tracer particles will also be added to the flow to explore the fate of particulates within the granular sludge system. 267 Acknowledgements Experiments at the 22T (950 MHz) NMR instrument were supported by uNMR- NL, an NWO-funded National Roadmap Large-Scale Facility of the Netherlands (project 184.032.207) 268 References 1. Codd, S.L., et al., Magnetic Resonance Microscopy of Biofilm and Bioreactor Transport, in NMR Imaging in Chemical Engineering, S. Stapf and S.-I. Han, Editors. 2006, Wiley: USA. 2. Van As, H. and P. Lens, Use of H-1 NMR to study transport processes in porous biosystems. Journal of Industrial Microbiology & Biotechnology, 2001. 26(1-2): p. 43-52. 3. Windt, C.W., F.J. Vergeldt, and H. Van As, Correlated displacement-T-2 MRI by means of a Pulsed Field Gradient-Multi Spin Echo method. Journal of Magnetic Resonance, 2007. 185(2): p. 230-239. 4. Lin, Y., et al., Characterization of alginate-like exopolysaccharides isolated from aerobic granular sludge in pilot-plant. Water Research, 2010. 44(11): p. 3355- 3364. 5. Da-Wen, G. and T. Yu, Versatility and application of anaerobic ammonium- oxidizing bacteria. Applied Microbiology & Biotechnology, 2011. 91(4): p. 887- 894. 6. de Kreuk, M., J.J. Heijnen, and M.C.M. van Loosdrecht, Simultaneous COD, nitrogen, and phosphate removal by aerobic granular sludge. Biotechnology and Bioengineering, 2005. 90(6): p. 761-769. 7. Beun, J.J., M.C.M. van Loosdrecht, and J.J. Heijnen, Aerobic granulation in a sequencing batch airlift reactor. Water Research, 2002. 36(3): p. 702-712. 8. de Kreuk, M.K. and M.C.M. van Loosdrecht, Selection of slow growing organisms as a means for improving aerobic granular sludge stability. Water Science and Technology, 2004. 49(11-12): p. 9-17. 9. de Kreuk, M.K. and M.C.M. van Loosdrecht, Formation of aerobic granules with domestic sewage. Journal of Environmental Engineering-ASCE, 2006. 132(6): p. 694-697. 10. Liu, Y. and J.H. Tay, The essential role of hydrodynamic shear force in the formation of biofilm and granular sludge. Water Research, 2002. 36(7): p. 1653- 1665. 11. Nicolella, C., M.C.M. van Loosdrecht, and J.J. Heijnen, Wastewater treatment with particulate biofilm reactors. Journal of Biotechnology, 2000. 80(1): p. 1-33. 12. Tay, J.H., Q.S. Liu, and Y. Liu, The role of cellular polysaccharides in the 269 formation and stability of aerobic granules. Letters in Applied Microbiology, 2001. 33(3): p. 222-226. 13. Pronk, M., et al., Full scale performance of the aerobic granular sludge process for sewage treatment. Water Research, 2015. 84: p. 207-217. 14. de Kreuk, M.K., N. Kishida, and M.C.M. van Loosdrecht, Aerobic granular sludge - state of the art. Water Science and Technology, 2007. 55(8-9): p. 75-81. 15. Vogt, S.J., et al., Permeability of a growing biofilm in a porous media fluid flow analyzed by magnetic resonance displacement-relaxation correlations. Biotechnology and Bioengineering, 2013. 110(5): p. 1366-1375. 16. Stoodley, P., et al., Biofilms as complex differentiated communities. Annual Review of Microbiology, 2002. 56: p. 187-209. 17. Sauer, K., et al., Pseudomonas aeruginosa displays multiple phenotypes during development as a biofilm. Journal of Bacteriology, 2002. 184(4): p. 1140-1154. 18. Stewart, P.S. and M.J. Franklin, Physiological heterogeneity in biofilms. Nature Reviews Microbiology, 2008. 6(3): p. 199-210. 19. Gonzalez-Gil, G., et al., Cluster structure of anaerobic aggregates of an expanded granular sludge bed reactor. Applied and Environmental Microbiology, 2001. 67(8): p. 3683-3692. 20. Lens, P.N.L., et al., Diffusional properties of methanogenic granular sludge: H-1 NMR characterization. Applied and Environmental Microbiology, 2003. 69(11): p. 6644-6649. 21. Eberl, H.J., et al., A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chemical Engineering Science, 2000. 55(24): p. 6209-6222. 22. Kreft, J.U., et al., Individual-based modelling of biofilms. Microbiology-Sgm, 2001. 147: p. 2897-2912. 23. Picioreanu, C., J.U. Kreft, and M.C.M. van Loosdrecht, Particle-based multidimensional multispecies Biofilm model. Applied and Environmental Microbiology, 2004. 70(5): p. 3024-3040. 24. Picioreanu, C., M.C.M. van Loosdrecht, and J.J. Heijnen, Effect of diffusive and convective substrate transport on biofilm structure formation: A two-dimensional modeling study. Biotechnology and Bioengineering, 2000. 69(5): p. 504-515. 25. de Kreuk, M.K., et al., Behavior of polymeric substrates in an aerobic granular 270 sludge system. Water Research, 2010. 44(20): p. 5929-5938. 26. Wagner, J., et al., Effect of particulate organic substrate on aerobic granulation and operating conditions of sequencing batch reactors. Water Research, 2015. 85: p. 158-166. 27. Pronk, M., et al., Effect and behaviour of different substrates in relation to the formation of aerobic granular sludge. Applied Microbiology and Biotechnology, 2015. 99(12): p. 5257-5268. 28. Poot, V., et al., Effects of the residual ammonium concentration on NOB repression during partial nitritation with granular sludge. Water Research, 2016. 106: p. 518-530. 29. Manas, A., et al., Location and chemical composition of microbially induced phosphorus precipitates in anaerobic and aerobic granular sludge. Environmental Technology, 2012. 33(19): p. 2195-2209. 271 CONCLUSIONS The work comprising this thesis demonstrates the versatility of NMR as a method to explore complex and heterogeneous biofilm – porous media systems. NMR measurements were applied at field strengths ranging from 250 kHz to 950 MHz to study opaque systems ranging from macro-scale subsurface soils to millimeter scale granular sludge biofilms. In all cases, the NMR measurements provided data non-destructively. The low-field NMR experiments conducted during this thesis included 1) a laboratory study to detect biofilm accumulation in a laboratory model well-bore reactor, 2) a field demonstration to detect biofilm accumulation in natural subsurface soils, and 3) a laboratory study to detect microbially-induced calcite precipitation in the same model well-bore reactor. In each of these experiments, T2 relaxation distributions were measured over time to compare the signal response at the initial, clean condition to the final, biofouled condition. Identification of the typical signal response for biofilm accumulation and calcite precipitation in porous media may lead to the application of low-field borehole NMR tools as sensors for bioremediation projects involving a biobarrier. The laboratory and field-scale studies to detect biofilm accumulation measured a shortening of the mean log T2 relaxation time (T2ML) due to biofilm growth. In the lab study, T2ML decreased by approximately 50%, while in the field study the decrease was approximately 60% in the LF well (~275 kHz) and approximately 40% in the HF well (~400 kHz). Biofilm growth was confirmed with microscopy and microbiological 272 methods in the lab study and by oxidizing and flushing the biofilm from the sensitive zone in the field study. In the lab study using the low-field borehole NMR tool to detect calcite precipitation, T2 relaxation distributions recorded during the biomineralization process showed an increase in the mean log T2 time and a bifurcation of the initial single relaxation mode into a small population with very fast relaxation and a larger population with slower relaxation. This result indicates that, in the relatively large pores of the sandpack, the effect of changing the mineral surface of the pore space had a more significant impact on T2 relaxation than the reduction in the pore size. The possibility remains that a shortening of T2ML could be observed if the pores were initially smaller than those in the reactor sandpack. In addition to the change in the T2 distribution, the NMR measured water content in the reactor decreased to 76% of the initial value as calcite displaced water in the pores and as excess CO2 gas collected. Calcite precipitation was confirmed with destructive sampling followed by SEM imaging and acid digestion to quantify calcium present. These measurements indicate that approximately 12% of the pore space was occupied by calcite at the end of the experiment. The results of this experiment indicate that low-field NMR is sensitive to calcite precipitation, though further research is needed to evaluate the influence of initial pore size and mineral surface on the T2 relaxation response. The studies conducted at high magnetic field strength include collaborative work with Dr. Maria Pia Herrling, a summer visitor to the Montana State University Magnetic Resonance Lab from Karlsruhe Institute of Technology in Karlsruhe, Germany and 273 collaborative work conducted in part in the Netherlands with Dr. Merle de Kreuk and Dr. Henk Van As as part of an NSF-funded 4-month visit by the author. In both cases, the system of interest was biofilm used in wastewater treatment. As part of her research into water diffusion in various biofilm structures, including floccular sludge, granular sludge, and biofilm grown on plastic carriers, Dr. Herrling measured diffusion-relaxation correlations at MSU with the author. In this study, we found no direct correlation between the water self-diffusion coefficient, Dwater, and typical biofilm properties like biofilm density and concentration of volatile suspended solids. Additionally, the mean self-diffusion coefficient, Dmean, is not sufficient to describe diffusion behavior in multi-species biofilms. High resolution MRI found some areas in the biofilm exhibited restricted diffusion due to the presence of precipitates and differing biofilm densities. The D-T2 correlations confirmed these findings and showed shorter T2 relaxation in the carrier with biofilm attached. The final experimental work included in this thesis describes ongoing experimental work on the structure and diffusion properties of aerobic granular sludge biofilms sampled from full-scale wastewater treatment plants in the Netherlands. High- field MRI was used to image the complex and heterogeneous internal structure of the granules. Additional high field PFG NMR experiments related to diffusion and transport within the granules are currently being conducted at MSU using samples from Dutch treatment plants. Preliminary findings from this work show a heterogeneous, cluster-like structure in the aerobic granules obtained from the Utrecht treatment reactor, and a more dense, heterogeneous structure in granules collected from the Garmerwolde treatment 274 plant, where the dense biomass regions and less dense EPS regions have differing diffusive properties. These results have implications for modeling to optimize reactor performance since the presence of multiple diffusion coefficients is not currently accounted for in the models. Furthermore, the presence of inactive EPS regions may affect granule activity and performance, or serve some other useful function not yet understood. This experimental work is ongoing. Thus, this thesis demonstrates that low-field borehole NMR has potential for use as an in-situ sensor of biofilm accumulation and calcite precipitation for field applications related to bioremediation. Moreover, high field PFG NMR and MRI can provide spatially resolved data related to the structure and transport properties of aerobic granular sludge biofilms used for wastewater treatment—data that is extremely challenging, if not impossible, to obtain with other methods. 275 REFERENCES CITED Allison, D.G., The biofilm matrix. Biofouling, 2003. 19(2): p. 139-150. 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