An analysis of chemical exchange systems for the separation of boron isotopes by Ronald Scott Herbst A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering Montana State University © Copyright by Ronald Scott Herbst (1992) Abstract: Chemical exchange between gaseous BF3 and the liquid BF3 •dimethyl ether complex is currently used commercially for the fractionation of boron isotopes. Several compounds never before studied as donors in the isotope exchange reaction were examined to determine if they were viable replacements for the currently used dimethyl ether system. The evaluation of these materials as potential donors was based on experimental studies and modelling and analysis of large scale fractionation cascades. For the first time, ketones were studied as donors in the boron isotope exchange reaction. The ketones examined were: acetone, methyl isobutyl ketone (HIBK), and diisobutyl ketone (DIBK). The ideal single stage separation factor, α, for these ketones was between α = 1.038 and α = 1.043 at 30°C. The observed separation factor for a fourth donor system, nitromethane, was α = 1.067 at 30°, well above that predicted by theory or observed for any known BF3/donor system. For each of the systems studied, the separation factors were greater than the value of α = 1.027 reported for the dimethyl ether/BF3 system at 30°C. In view of the experimentally observed separation factors, these donor systems are potential replacements for dimethyl ether in large scale boron isotope fractionation schemes. Modelling and analysis of large scale fractionation cascades based on the values of a experimentally observed for the different donors indicated plant size could be greatly reduced using these donors rather than dimethyl ether. Ideal, constant recycle, and squared off cascade configurations utilizing counter current flow were examined. The two section squared off cascade reduced the ideal number of stages by 8% to 11% and required 13% more total interstage flow than the ideal cascade. Stripping in the various cascades was estimated to account for as much as 30% of total cascade size. The ideal cascade was shown to be the most energy efficient of the recycle cascade configurations studied. These results indicate the directions cascade design must take if maximally efficient large scale facilities are to be built and operated.  AN ANALYSIS OF CHEMICAL EXCHANGE SYSTEMS FOR THE SEPARATION OF JB.ORON. ISOTOPES by Ronald Scott Herbst A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering MONTANA STATE UNIVERSITY Bozeman, Montana November 1992 ii \A4 ^ APPROVAL of a thesis submitted by Ronald Scott Herbst This thesis has been read by each member of the thesis committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the College of Graduate Studies. //- Date Chairperson, Graduate Committee Approved for the Major Department / / - 3 0 - cU Date Head, Major Department Approved for the College of Graduate Studies Date Graduate Dean iii STATEMENT OF PERMISSION TO USE In presenting this thesis in partial fulfillment of the requirements for a doctoral degree at Montana State University, I agree that the Library shall make it available to borrowers under rules of the Library.• I further agree that copying of this thesis is allowable only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. Requests for extensive copying or reproduction of this thesis should be referred to University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan 48106, to whom I have granted "the exclusive right to reproduce and distribute copies of the dissertation in and from microfilm and the right to reproduce and distribute by abstract in any formats" Signature Date Z' to ■■ /99^ iv TABLE OF CONTENTS Page LIST OF T A B L E S ........................................................ vi LIST OF F I G U R E S .......................... vii A B S T R A C T ............. ■....................... ........................ ix INTRODUCTION ................................. I Historical Background .......................................... 2 Literature Review ............................................... 4 Isotope Exchange P r o c e s s e s .........................• • • 5 Selection of X ................................. -6 Donor Selection...................................... ' • • 7 Effect of Temperature and Pressure on Ke q ............. 13 Kinetics of Isotope Exchange Reactions ................ 14 Theory of Isotope Exchange Reactions .................. 15 PURPOSE AND SCOPE OF PRESENT STUDY ................................. 22 EXPERIMENTAL DETERMINATION OF SEPARATION FACTORS .................. 25 Experimental Reagents, Equipment and Procedures ............. 26 Experimental Reagents .................................... 26 Experimental Equipment and Procedures .................. 27 ■ Mass Spectroscopic Isotopic Abundance Analysis 31 Results and Discussion ........................................ 34 The Phenetole/BF3 System ............................... 34 The Acetone/BF3' S y s t e m ............................. 39 The Acetophenone/BF3 S y s t e m ............................. 42 The MIBK/BF3 S y s t e m ....................................' 43 The DIBK/BF3 S y s t e m ...................................... 47 The Nitromethane/BF3 System ............................. 50 The DMSO/BF3 System . . . 54 Comparison of Experimentally Studied Systems . . . . . 55 VTABLE OF CONTENTS— Continued . , Page MODELLING AND ANALYSIS ............................................... 61 Terminology..................................................... 62 Ideal S t a g e s .................. .. . . . '................ 62 Separation Factors ............. . . . . . ........... 64 Countercurrent Recycle Cascade ............................... 65 Material Balances . . ..................................... 68 Recycle Ratio ............................................. 69 Providing Recycle in the Cascade ■................ 72 Number of Separation Stages ............................. 73 Total Interstage F l o w .................................... 74 Practical Recycle Ratio 75 Cascade Models . ■............................................... 80 Ideal C a s c a d e .......................... 82 Heads Separation Factor ........................ 82 The Ideal Cascade Model ........................ 89 Results and Discussion of the Ideal Cascade Calculations .................................... 91 Constant Recycle Cascade 96 The Constant Recycle Model ...................... 96 Results and Discussion of the CRC Calculations . 98 Squared Off Cascade.................................... 103 The Squared Off Model ........................ 104 Results and Discussion of the SOC Calculations 108 Comparison of Cascade Models ............................... 117 Effect of the Stripping Section ............................. 124 Addition of Square Sections to the Stripper ......... 124 Elimination of the Stripping Section ................ 132 The Ideal Cascade Without Stripping ......... 134 The CRC Without Stripping .................... 136 The SOC Without Stripping .................... 138 Energy Requirements ............................... 142 Energy Requirements for Providing Recycle in the C a s c a d e .................. 143 Energy Requirements for Stagewise Separation of Components .................... 147 CONCEPTUAL BORON ISOTOPE ENRICHMENT PLANT ........................ 158 CONCLUSIONS............................... 168 RECOMMENDATIONS FOR FURTHER STUDY .................................. 170 REFERENCES C I T E D ........................................ 171 vi Table Page > LIST OF TABLES 1 Review of previously studied donor molecules in the isotopic exchange reaction ( 4 ) ................................ 8 2 Ratios of the vibrational partition function for BF3 and BF3* at 303K and 250K [ 3 2 ] ...................... ............... 19 3 Calculated and observed values of the isotopic, equilibrium constant for reaction (4) at 303K [32] .................. .19 4 Minimum ideal stage requirements with different donors for a boron isotope fractionation cascade operating at total reflux ............................. 58 5 Ideal cascade results for the various BF3/donor systems . . 92 6 Constant recycle cascade results for the various BF3/donor systems . . ..................................... 99 7 Summary of the results from the squared off cascade calculations for the various BF3/donor s y s t e m s ......... 109 8 Comparison of the various BF3/donor systems in different models .......................................... . . . . . 118 9- Comparison of the results from the SOC models with the stripping section squared off for the various BF3/donor systems...................................................... 127 10 Ideal cascade results for the various BF3/donor systems without a stripping section .......................... .135 11 Constant recycle cascade results for the various BF3/donor systems without a stripping section ..................... 137 12 Squared off cascade results for the various BF3/donor systems without a stripping section ........................... 139 13 Comparison of different types of energy input and total interstage flow for the various cascade configurations with the nitromethane/BF3 donor system ...................... 151 vii Figure Page ■ I Schematic of the test cell used to obtain experimental data . 30 2 Experimental results for the Phenetole/BF3 system ........... 36 3 Experimental results for the Acetone/BF3 system , 40 4 Experimental results for the ,MIBK/BF3 s y s t e m .......... 44 5 Experimental results for the DIBK/BF3 system ................ 48 6 Experimental results for the Nitromethane/BF3 system . . . . • 51 7 Comparison - of experimental systems studied in isotope exchange.......................................................... 56 8 Single separating stage and associated nomenclature. . . . . 63 9 Flow schematic of the countercurrent recycle cascade. . . . . . 67 10 Inverse multiplication factor vs. total interstage flow and number of ideal stages for the dimethyl ether/BF3 system . 77 11 Inverse multiplication factor vs. total interstage flow and number of ideal stages for the nitromethane/BF3 system . . 78 12 Mole ratios in a section of an ideal cascade . . . ........... 83 13 Effect of the exponential factor, q, on the recycle ratio versus stage number curve for the ideal cascade ........... 86 14 Effect of the exponential factor, q, on total interstage flow rate in the ideal casc a d e ............................... • 88 15 Recycle ratio versus stage number for the iqleal cascade with the different donors ........................................ 94 16 Recycle ratio versus stage number for the constant recycle cascade with the different donor systems . . . ......... 102 LIST OF FIGURES viii Figure Page LIST OF FIGURES— Continued 17 Recycle ratio vs. stage number for the SOC with the nitromethane/BF3 donor system ...................... 112 18 Recycle ratio vs. stage number for the SOC with the DIBK/BF3 donor s y s t e m .......................................... '.. 113 19 Recycle ratio vs. stage number for the SOC with the MIBK/BF3 donor s y s t e m ................................................. 114 20 Recycle ratio vs. stage number for the SOC with the acetone/BF3 donor system ......... .................. 115 21 Recycle ratio vs. stage number for the SOC with the dimethyl ether/BF3 donor system ..................................... 116 22 Comparison of recycle ratio versus stage number for the nitromethane/BF3 donor system with the ideal, CRC and 3 & 4 section SOC m o d e l s ............................. 121 23 Comparison of recycle ratio versus stage number for the dimethyl ether/BF3 system with the ideal, CRC and 2 Si 5 section SOC models ........................... ............. 122 24 Effect of adding square sections—to the stripping portion of the nitromethane/BF3 S O C .................. . . . . . 130 25 Effect of adding square sections to the stripping portion of the dimethyl ether/BF3 SOC .............................. 131. 26 Typical stage from a countercurrent recycle cascade . . . . 148 27 Ideal energy, separative energy and total interstage flow as a function of inverse recycle factor (1/A) for the CRC with the nitromethane/BF3 donor system ........................ 154 28 Recycle and separative energy as .a function of recycle ratio for the CRC with the nitromethane/BF3 donor system . . . 156 29 Process flow schematic for the two section SOC with the nitromethane/BF3 donor system ............................ 159 30 Process flow schematic for the two section SOC with the dimethyl ether/BF3 donor system .......................... 163 ix ABSTRACT Chemical exchange between gaseous BF3 and the liquid BF3 •dimethyl ether complex is currently used commercially for the fractionation of boron isotopes. Several compounds never before studied as donors in the isotope exchange reaction were examined to determine if they were viable replacements for the currently used dimethyl ether system. The evaluation of these materials as potential donors was based on experimental studies and modelling and analysis of large scale fractionation cascades. For the first time, ketones were studied as donors in the boron isotope exchange reaction. The ketones examined were: acetone, methyl isobutyl ketone (HIBK), and diisobutyl ketone (DIBK). The ideal single stage separation factor, a, for these ketones was between a = 1.038 and a = 1.043 at 30°C. The observed separation factor for a fourth donor system, nitromethane, was a = 1.067 at 30°, well above that predicted by theory or observed for any known BF3/donor system. For each of the systems studied, the separation factors were greater than the value of a = 1.027 reported for the dimethyl ether/BF3 system at 30°C. In view of the experimentally observed separation factors, these donor systems are potential replacements for dimethyl ether in large scale boron isotope fractionation schemes. Modelling and analysis of large scale fractionation cascades based on the values of a experimentally observed for the different donors indicated plant size could be greatly reduced using these donors rather than dimethyl ether. Ideal, constant recycle, and squared off cascade configurations utilizing counter current flow were examined. The two section squared off cascade reduced the ideal number of stages .by 8% to 11% and required 13% more total interstage flow than the ideal cascade. Stripping in the various cascades was estimated to account for as much as 30% of total cascade size. The ideal cascade was shown to be the most energy efficient of the recycle cascade configurations studied. These results indicate the directions cascade design must take if maximally efficient large scale facilities are to be built and operated. IINTRODUCTION Naturally occurring boron is comprised of two isotopic forms. The mass 10 isotope, 10B, has a relative abundance of 19.8 atom % while the remainder or 80.2% consists of the mass 11 isotope, 11B. .a" The impetus for the isotopic fractionation of boron arises primarily from a contrasting difference in thermal neutron capture cross sections. Boron-10 has a thermal neutron capture cross section of 3837 barnes, while that of 11B is only 0.005 barnes. As a composite of the two isotopes, naturally occurring boron has a thermal neutron capture cross section of approximately 750 barnes. Subsequently, 10B is roughly 5 times more effective than naturally occurring boron, 20 times more effective than lead, and nearly 500 times more effective than concrete as a neutron shielding material. It is precisely this propensity for thermal neutron capture which makes 10B enriched materials a useful commodity. The nuclear related industries are the predominant consumers of 10B. Enriched boron-10 compounds are used for standby liquid control systems in boiling water reactors. Breeder reactors use 10B enriched carbide for control rods. Boron-10 enriched boric acid is used as a chemical shim for reactivity control in pressurized water reactors. Boron-10 enriched alloys are used for criticality control in nuclear fuel casks, as construction material in storage racks, and as neutron shielding around reactors. It is also used in instrumentation for both neutron density and dosage. Medical research with 10B enriched compounds has indicated a promising method for the non-surgical removal of malignant brain tumors. 2The goals of this study included examination of several isotope exchange systems which have not been previously reported in the literature. The second objective was to examine modelling and analysis of a production scale counter current cascade process for. boron isotope separation by gas-liquid isotope exchange. Historical Background The quest for a suitable method for the large scale separation of boron isotopes began in 1943. At that time, the U.S. War Department, as a result of the war effort, requested 50 kg of crystalline boron containing not less than 90% 10B. Accordingly, research was initiated at Columbia University, under a classified program of the Manhattan Project, to develop a suitable scheme for the separation of boron isotopes. Six different separation schemes were investigated during the initial stages of the project. These were: (I) thermal diffusion of BF3; (2) distillation of BF3; (3) distillation of methyl borate, (CH3O)3B; (4) steam distillation of boric acid, H3BO3; (5) isotope exchange between dimethyl Bther-BF3 complex, (CH3)3O-BF3, and BF3,; and (6) isotope exchange between ethyl borate-BF3 complex, (C2H5O )3B-2BF3 and BF3 gas. The "distillation" of dimethyl Bther-BF3 complex was selected as the , most efficient method of separation, primarily due to a lower rate of irreversible chemical decomposition. As a result of this work, Standard Oil Company (Indiana) designed and operated the first large scale boron isotope fractionating facility. The initial order from the War Department was filled in May 1945. That plant was subsequently dismantled in 1948. A second, larger facility was constructed and operated by Hooker 3Electrochemical Corp. from 1953 to 1958 at Model City, New York. That plant successfully produced several hundred kilograms of 90-95% 10B metal utilizing the "distillation" of dimethyl ether-BF3 complex. A complete account of the above ventures is available in the open literature (1-3). It is interesting to note that the rapidity with which a suitable method for the large scale separation of boron isotopes was established is indicative that many potential methods were not investigated. In 1977, Eagle-Pitcher Industries reconstructed and began operation of the Model City plant at Quapaw, Oklahoma. This facility relies on the same gas-liquid partitioning process as its predecessors, e.g. isotope exchange between dimethyl Bther-BF3 complex and BF3 gas to fractionate the isotopes of boron. To increase capacity, two new separation cascades were designed and added to the plant. These cascades are identical, each consisting of two packed columns in series. The first column is 50.8 cm ID with a packed height of 42 meters, while the second is 30.5 cm ID with 27.4 meters of packing. The operating pressure throughout the system is 27 kPa (200 torr) with boilup at 96°C. Fourteen days are required from startup for the process to reach steady state operation. The capacity of this plant is reported to be in excess of two metric tons/year of boron metal enriched to 95% 10B with production costs of $5 to $15 per gram of 10B, depending on the degree of enrichment [4,36]. Problems associated with the process used at the Quapaw plant include irreversible decomposition of the dimethyl Bther-BF3 complex to form undesired reaction products. Furthermore, quantitative recovery of BF3 from the complex is difficult. The equilibrium constant for the (CH3)2O^BF3 exchange system is Keq = 1.027. Ideally, the single stage 4separation factor, a, would be identical to Keq. However, the gas phase contains approximately 40% undissociated complex, which effectively lowers the single stage separation factor to g = 1.014 [4]. Due to the nomenclature used in the early literature, the isotope exchange process is often referred to as "distillation". It must be emphasized that the separation is based on chemical reaction equilibrium rather than phase equilibrium. Consequently, this is not a distillation process. In fact, it is distillation (the vaporization of complex without dissociation) which is responsible for lowering the single stage, separation factor and thus decreasing the process efficiency. Literature Review Many studies have been initiated in quest of an " improved” boron isotope separation scheme. A survey of the literature indicates several active areas of study regarding boron isotope separation. These areas are conveniently divided into three categories: (1) Photochemical induced separations or laser based separations where tunable lasers are used to separate isotopes by making use of the small differences in the absorption spectra of 10B and 11B or one of their compounds. (2) Chromatographic separations where isotopic fractionation is facilitated by small differences in the retention times of boron isotopes in the liquid phase on chromatographic resins. (3) Isotopic equilibrium or isotope exchange reactions where separation is affected by the isotope exchange equilibrium between boron in a liquid and a gaseous phase. 5Numerous publications, process and process equipment patents exist in each of these three areas. Despite the fact that other technologies apparently exist for the large scale separation of boron isotopes, commercial success has been realized only with the isotope exchange process used by the Eagle-Picher Company as previously described. This study is characterized by boron isotope separation schemes involving isotope exchange reactions. Accordingly, only the literature pertinent to this area will be reviewed. Isotope Exchange Processes Isotope exchange processes are characterized by reactions of the type: 10BX3tg) + 11BX3-Donortn 11BX3(g) + 10BX3-Donortn (I) where X is generally H, CH3 or a halogen. The "complex", BX3 - Donor, is a molecular addition compound, and the donor is a Lewis base or electron pair donor. The equilibrium constant for reaction (I) is given by: [jlBX3tg)] [10BX3-Donortn] [10BZ11B] tn " [10BX3tg)] [11BX3-Donortn] [10By11B] tg) where square brackets represent the equilibrium concentrations of the respective species. Most known exchange systems pertinent to boron isotopes have values of the equilibrium constant in the range of I < Keg < 1.06. That the equilibrium lies slightly to the right in reaction (I) forms the basis for the separation. The small value of Keq suggests the need of a multistage exchange process in order to obtain a significant degree of separation. 6Utilization of the isotopic exchange reaction requires the passage of gaseous BX3 and liquid complex in a stagewise process. ' Thus, 3^0B concentrates in the liquid phase while 11B concentrates in the•gaseous phase. Pertinent considerations focus primarily on the selection of X and the donor molecule in reaction (I). These considerations include: (a) The largest possible value of the equilibrium constant, Keq, in order to minimize the necessary number of stages for a given enrichment. (b) The equilibrium must be rapidly established, e.g. isotopic exchange need be kinetically rapid, in order to maintain a high throughput in a continuous system. (c) BX3 must be readily liberated from the complex for product recovery, recirculation and reuse of the separative agent or donor. In this regard, it is desirable that the formation reaction: BF3 + Donor ** BF3-Donor (3) be quantitatively reversible.simply by addition or removal of heat. (d) The BX3•donor complex must be sufficiently stable so as not to decompose into unwanted reaction products. Such irreversible decomposition would result in 10B enriched product losses with the attendant loss of BX3 and donor. Selection of X Virtually all systems studied to date have used the first member of the halogen family, fluorine, for X in the isotopic exchange reaction. This consideration largely stems from criteria (a) and ,(d) above and is associated with the excellent electron acceptor capabilities of BF3 [6,7]. Use of BF3 as the Lewis acid in the isotope exchange reaction has been 7justified on theoretical grounds as well (vide infra). Consequently, the isotope exchange reaction may be rewritten for subsequent discussions as: 10BF3 (g) + 11BF3*Donor (,) ** 11BFf3) + 10BF3-Donorft) (4) In addition to BF3, several brief studies utilizing BCl3 as the Lewis acid in the isotopic exchange reaction have been conducted [6,7,13,15]. In all reported instances, the equilibrium constant for the BF3 systems was larger than for similar BCl3 systems. Consequently, the use of BCl3 as the acid in isotopic exchange was largely abandoned. Donor Selection The species BF3-Donor in equation (4) is a molecular adduct formed between BF3 and an electron pair donor. This type of compound formation is a classical example of Lewis acid-base chemistry. Here, the Lewis acid, BF3, accepts a lone electron pair from the basic,donor atom which is typically bound in a molecular species. Boron trifluoride has been touted as the most powerful acceptor molecule (Lewis acid) known, while the number of atomic species capable of donating electrons to BF3 is relatively small [5]. The nine elements H, N, O, F, P, S , Cl, Se, and Te, in certain of their compounds, have been found capable of donating electrons to BF3 [6]. Of the aforementioned criteria, (a) and (d) limit the donor atom to predominantly N, O, or S, although systems containing other donors have been examined [6,7]. Table I lists the donor molecules which have been studied, the associated equilibrium constants which were reported and the literature references for the pertinent study. 8Table I. Review of previously studied donor molecules in the isotopic exchange reaction (4). Keqf Donor LU O O 0?C Reference Oxygen Donors I. Methyl Ether (CH3)2O 1.027 1.034 6,7,12 2. Ethyl Ether (C2H5)20 1.031 1.037 6,7,17 3. n-Butyl Ether (C4H9)2O - - 6,7,12 4. Tetrahydrofuran (CH2)4O 1.026 1.031 6,7,13 5. Phenol C6H5OH 1.024 1.040 6,7,14,15 6. Anisole C6H5OCH3 1.030 1.039 6,7,15,16 7. Phenetole CgH5OC2H5 1.039 1.042 (25°C) 1.051 6,7,8 8. n-Butyl phenyl ether C6H5OC4H9 1.026 (25 °C) - 7,10 9. Ethyl formate HCOOC2H5 1.029 (20°C) - 7,11,12 10. Ethyl acetate CH3COOC2H5 1.033 (28°C) - 7,9 11. Ethyl propionate C2H5COOC2H5 1.019 (43°C) - 7,9 12. Sulfur dioxide SO2 - - 20,21 13. Dimethyl sulfoxide* (CH3)2SO 1.040 1.036 19 14. Diphenyl ether (C6H5)2O - - 6 15. Nitrobenzene C6H5NO2 1.03 (7°) 6,13 Sulfur Donors 16. Methyl sulfide (CH3)2S 1.037 1.046 6,7,12,23 17. Ethyl Sulfide (C2H5)2S 1.037 1.043 6,7,17 18. n-Butyl sulfide (C4H9)2S 1.032 1.040 6,7,15,18 19. Diphenyl sulfide (C6H5)2S - - 6,13 20. Thiophenol C6H5SH - — 6,13 21. Ethyl mercaptan C2H5SH - — 6 22. Butyl mercaptan Nitrogen Donors C4H9SH 6 23. Triethyl amine (C2H5)3N 1.022 1.028 6,7,17 24. N-Methyl diphenyl amine (C6H5)2NCH3 - — . 6,13 25. N fN-Dimethyl aniline C6H5N(CH3)2 6,13 Miscellaneous 26. Methyl selenide (CH3)2Se 1.032 1.039 6,7,12 27. Methyl telluride (CH3)2Te - - 6,12 28. Methyl isocyanide CH3NCO - — 6,13 ^"Equilibrium temperatures other than 30°C or 0°C are denoted by brackets. ^Isotopic equilibrium between the gas and solid phases: 10BF3 (g) + 11BF3-DMSO(S) ^ 11BF3tgj + * 10BF3-DMSO(S) 9The standard by which an "improved" isotope separation process is compared is the current production scale method involving BP3 and the BF3- . dimethyl ether complex. From Table I, the equilibrium constant at 30°C for this system is Keq = 1.027. The actual separation factor observed for the process is a = 1.014 with the reduction due primarily to incomplete dissociation of the complex in the vapor phase and solubility of BF3 in the liquid complex [1,6]. A second drawback associated with the dimethyl ether system results from irreversible decomposition of the complex. At atmospheric pressure, roughly 50% of the dimethyl ether-BF3 complex is decomposed to methyl fluoride and methyl borate in 24 hours [6] . In order to decrease the decomposition rate to tolerable levels, the process is operated at subatmospheric pressure of approximately 200 torr. Thus, in accord with criterion (d) above, an improved system would be amenable to operation at conditions of ambient temperature and pressure. With regard to irreversible decomposition, it is a forgone conclusion that water must be carefully excluded from the system [1,6]. Boron trifluoride readily reacts with water,even in the presence of atmospheric moisture, to form a number of acidic hydrolysis products such as hydrofluoric, hydrofluoroboric, fluoroboric and boric acid. Several of these are highly corrosive to process construction materials, some may cause or catalyze decomposition of the complex, and others are solids which tend to plug the process equipment [6]. The literature data presented in Table I indicates that the equilibrium constant for reaction (4) varies with temperature, donor atom, and donor substituents. Palko and Drury have indicated [7,32] that a 10 variation of donor atom and donor substituents affects the relative bond strength between the donor atom and boron in the molecular addition compound. The bond strength is therefore a measure of the relative stabilities of the various BF3 adducts. In general, the more stable or stronger the boron to donor bond for a particular adduct, the less prone the adduct is towards isotope exchange, resulting in a lower value of the equilibrium constant than for a similar, less stable complex. Palko et.al. [7] indicated that the variation in stability with different donor atoms increased in the order N > O > S and that stronger molecular addition compounds (in terms of bond strength or stability) resulted in smaller values of the equilibrium constant. Consequently, triethyl amine was more stable than diethyl ether which in turn was more stable than diethyl sulfide. As a result of this difference in stability, the value of the equilibrium constant increased in the order (C2H5)2S > (C2H5)2O > (C2H5)3N at 30°C. In accord with theoretical considerations {vide infra), the increase in Keq with different donors in the order S > O > N can be attributed to the fact that substitution of the heavier donor atom simultaneously increases the reduced mass of the molecular addition compound and decreases the donor to boron force constant resulting in a weaker or less stable adduct with a concomitant increase in the equilibrium constant [32]. The stability of BF3 adducts containing the same donor atom indicates variations with substituents attached to the basic center in the donor molecule. This variation has been explained in terms of inductive and steric effects associated with various donor substituents [7,37]. An electrophilic (electron withdrawing) group attached to the basic center 11 decreased basicity, and resulted in a weakened adduct. Consequently, (CH3)2O-BF3 is more stable than C6H5OCH3 • BF3 and (C6H5)2O-BF3 does not form at -40°C. Accordingly, t h e .largest equilibrium constant is associated with the weakest adduct, C6H5OCH3 •BF3 in this case (refer to Table I). Conversely, a nucleophilic or electron donating group attached to the basic center is expected to increase the basicity and stabilize the resulting adduct [7]. Table I indicates that the stabilities of the alkyl substituted etherates increase in the order (CH3)2O-BF3 > (C2H5)2O-BF3, apparently due to increased steric interferences.,, despite the increased inductive effect of the larger alkyl group. Apparently, the 0-carbon in the ethyl group of the latter compound interferes with the normal positioning of the fluorine atoms in the complex [7]. For the analogous thioether series, Table I indicates that the stability of the alkyl substituted thioethers increases in the order (C4H9)2S-BF3 > (C2H5)2S-BF3 > (CH3)2S-BF3 at 0°C. The fact that the expected inductive/stability order is observed in the alkyl substituted thioethers is attributed to the larger size of the central sulfur atom, which overcomes the steric hinderance encountered in the analogous ether systems. The above concepts regarding donor atom and inductive and steric effects of substituent groups on the equilibrium constant provide useful guidelines f o r .evaluating potential behavior of unstudied compounds in isotope exchange. Furthermore, these guidelines are of practical interest in the selection of potentially useful donors for experimental testing. The list of donor species presented in Table I were studied pursuant to development of an improved separation process with respect to the dimethyl Bther-BF3 system. The improved system would be subject to all 12 criteria previously outlined. Examination of Table I is indicative that a number of exchange systems possess a larger equilibrium constant (criterion a) than the dimethyl ether system. Most of these systems were dismissed based on failure to meet . one or another of the remaining criteria presented. In a number of cases, a donor was eliminated prior to obtaining experimental equilibrium data. . Studies with anisole as the donor species in the isotope exchange reaction indicated that this system was indeed superior to the dimethyl ether system [6,16]. The promising experimental results for the anisole- BF3 exchange reaction prompted both bench scale and pilot plant studies with this system [24,25]. The final conclusion from these.studies was that the anisole process was a definite improvement over the dimethyl ether system and was amenable to plant scale application. It was postulated that phenetole would be a better donor for isotope fractionation than anisole, but the appropriate bench scale and pilot plant studies have not yet been performed [7]. Despite the positive results suggesting the use of anisole as the separative agent for large scale fractionation, of the boron isotopes, its use has not been incorporated into the process. A satisfactory answer regarding why anisole has not been incorporated into the separation scheme is unavailable in the literature. It is therefore postulated that the reason involves economic considerations. 13 Effect of Temperature and Pressure on Keq Examination of the available equilibrium constant data in Table I indicates that Keq increases as temperature decreases. The only exception to this observation is for the dimethyl sulfoxide (DMSO) system. Thus, in all but this one instance, the isotopic exchange reaction is exothermic. In the case of the DMSO system, examination of the original literature [26] indicates that this data was obtained by parametric pumping studies based on isotopic, equilibrium between DMSO1BF3 complex in the solid state and gaseous BF3. This is the only known instance of equilibrium constant determination between the gaseous and solid states, and is therefore indicative that the isotope exchange reaction in such systems may indeed be endothermic. Studies regarding the effect of pressure on the equilibrium constant for isotope exchange are extremely limited. Only one literature reference to such a study was obtained [27], and the nature of this source left much to be desired. In that study, the equilibrium constant (system unknown) was measured over a pressure range of I to 4.5 atmospheres. The equilibrium constant was observed to decrease from. Keq = 1.027 at I atm to Keq = 1.017 at 4.5 atm. This decrease was'presumed to be due to increased solubility of gaseous BF3 in the liquid complex. This observation was explained in terms of competing isotope^ exchange reactions between BF3 bound in the complex with gaseous BF3 and BF3 dissolved in the liquid phase: 10BF3wl33. gaS) + 11BF3-Donor(() 10BF3tg) + 11BF3-Donort,) 11BF3 (disa.gas) + 10BF3-Donort,) 3tg) + 10BF3-Donor (5) f* 11BF (6) 14 The equilibrium constant for the liquid phase exchange (reaction 5) was reported as 1.003 at 25°C [27]. Palko et al. [6,22] has observed that BF3 is quite soluble in several of the liquid complexes studied and that the solubility generally increases with decreasing temperature. The increased solubility results in a lowering of the observed equilibrium constant. In agreement with the above pressure study, Palko indicated the equilibrium constant for the liquid phase exchange reaction (reaction 5) was small, on the order of 1.002 [6]. Based on the above discussions, the effect of pressure on the equilibrium constant may vary considerably depending on the solubility of BF3 gas in the liquid phase. Kinetics of Isotope Exchange Reactions In order to achieve a high throughput of process materials in isotope exchange, the rate of exchange in such systems must be rapids From the standpoint of process application, it is desirable that the rate of isotopic exchange be so rapid that exchange be completed as soon as the two phases are contacted in the suitable process equipment, i.e., the exchange reaction must be mass transfer limited as, opposed to kinetically limited. Literature references to kinetic studies of the isotope exchange reaction are virtually non-existent. Palko [6] examined the exchange rate for the anisole-BF3 and triethyl amine-BF3 systems. The technique used in that study was not amenable to measurement of exchange times less than 4 seconds. For the anisole-BF3 system, isotopic exchange occurred much 15 faster than 4 sec and exchange was determined to be contact limited. In the case of the triethyl amine-BF3 system a half time for exchange of about 50 minutes was reported. > Qualitative observations indicate that the rate of 10B-11B exchange for highly dissociated complexes is extremely rapid, while exchange rates for the more stable complexes were considerably slower [6], Thus, the kinetics of the isotopic exchange reaction is intimately connected to the relative strength of the BF3-donor bond. This observation is supported by kinetic studies pertaining to BF3 exchange between mixtures of oxygen containing donors in the liquid phase [28,2,9,30] . Theory of Isotope Exchange Reactions' Isotope exchange reactions are not unique to boron and are documented for the isotopes of many of the lighter elements [31]. The observed thermodynamic phenomena are a manifestation of small differences in the energy states of isotopically different molecules. Thlus, the equilibrium constant is adequately correlated with the energy states of the molecules as secured from spectral data. Statistical thermodynamics provides the medium through ,which spectral data is related to the thermodynamic equilibrium constant. The generalized theory of equilibrium constants for isotope exchange reactions has been eloquently presented by Urey [31]. Palko and Drury [32] have proposed a model of isotope exchange which adequately accounts for the observed variation in the equilibrium constant and explains the behavior of the different boron halides in isotope exchange reactions. This model is supported by theoretical calculations i 16 based on spectral data. A development of this isotope exchange model follows. Consider first the electronic and structural details of BF3 and its constituent atoms. The free boron atom has three valence shell electrons in the nominal configuration 2S2P1. The free fluorine atom has seven valence shell electrons with the nominal 2s2p5 configuration. When a molecule of BF3 is formed, the boron valence shell electrons are promoted to sp2 hybridized orbitals and three boron to fluorine bonds are formed by sharing the unpaired fluorine electrons. The resulting BF3 molecule is planar with the nominal 120° central bond angle and an empty boron p orbital protruding from the plane of the molecule at 90°. Each-fluorine atom in BF3 has three non-bonding electron pairs, and due to the small size of fluorine, the electron pairs are crowded much closer together.than in any other element. Consequently, the repulsive forces between these lone pairs are much greater in fluorine than in any other element. Due to the large repulsive forces, a fluorine lone pair of electrons occupies the empty boron p orbital in the BF3 molecule. One fluorine atom is therefore essentially double bonded to boron while the remaining two fluorines have conventional sigma bonds. There are three such configurations possible and resonance occurs between them [34]. The associated resonance energy, has been estimated to be 48 kcal/mol [35]. This resonance energy is much greater than the energy involved in formation of the BF3-donor bond upon adduct formation and is directly responsible for the enrichment of the lighter isotope in the liquid phase. The boron p orbital used for m-bondihg to one of the fluorines in BF3 must be available for formation of the coordinate covalent bond between BF3 17 and a Lewis base. Thus, the TT-bond energy associated with BF3 must be released and the energy associated with adduct formation must be absorbed when the BF3• donor molecular addition compound is formed. It is convenient to regard these energy changes as occurring in separate, discrete steps. The isotope exchange reaction discussed previously: 11BF3-Donortn + 10BF3tg) ^ 10BF3-Donortn + 11BF3(g) (4) may therefore be rewritten as a composite of the two reactions: 10BF3tgj + 11BF3V ^ 11BF3(Cj) + 10BF3V <7 ) 11BF3V ) + 10BF3-Donortn ** 10BF3* tg) + 11BF3-Donortn (8) where BF3* is a hypothetical intermediate in which no m-bonding occurs, e.g. a molecule in which all fluorines are attached to boron with a conventional sigma bond. The respective equilibrium constants for reactions (7) and (8) are given by: Q(11BF3) . Q( 11BF3*) Q(10BF3) I Q (10BF3*) K eq- (8) Q(11BF3-Donor) Q(10BF3-Donor) Q(11BF3*) Q(10BF3*) (9) (10) where Q represents the vibrational partition function of the indexed isotopic species. The ratio of these equilibrium constants is the equilibrium constant for the overall isotope exchange reaction, reaction (4): ■ Keq (7) _ Q(11BF3) Keq (8) Q(10BF3) Q(11BF3-Donor) Q(10BF3-Donor) (H) At a specific temperature, Keq (7) is fixed and the value of Keq (8) will depend on the magnitude of the vibrational partition function ratio for 18 the isotopic species in the molecular addition compound. The value of the numerator in equation (10) will depend on the specific donor and will be largest for strongly bound molecular addition compounds. Note that as Keq (8) approaches unity as a limit, the observed equilibrium Constant Keq (4) approaches Keq (7). Thus, Keq (7) represents the maximum value the observed equilibrium constant,. Keq (4) , may assume. If the appropriate spectroscopic data is available, values for the ratios of the partition functions in equations (9), (10), and (11) can be calculated using the relationships of statistical thermodynamics. In the case of the hypothetical BF3* intermediates, partition function ratios were empirically evaluated from BF3 and BF4" spectroscopic data. Thus, equations (9) through (11) provide the theoretical basis for estimating the maximum obtainable equilibrium constant, Keq (7), and the expected equilibrium constant for any BF3-donor system, Keq (4), at a specified temperature. ^ Palko and Drury [/32] have calculated values for the ratios of the vibrational partition functions in equation (9) at temperatures of 303K and 250K from the appropriate spectroscopic data and determined the theoretical maximum value the equilibrium constant may assume at these temperatures. These results are summarized in Table 2. The linear extrapolation of Keq(7) as a function of temperature through the two points listed in Table 2 is of some interest, given by: 12.233 In a = ----- +.0.00556 (12) T(K) Equation (12) represents the theoretical maximum value the equilibrium constant may assume for a specific temperature. 19 Table 2. Ratios of the vibrational partition function for BF3 and BF3* at 303K and 250K [32] . Temperature Vibrational Partition Function ' 303K 2 5 OK Q(11BF3)ZQ(10BF3) 1.2046 1.2680 Q (11BF3*) /Q (10BF3*) 1.1506 1.2006 Q(11BF3) . Q(11BF3*) 1.056 K” <7) " Q (“ BP,)- I Qt10BF3*) 1.047 Table 3. Calculated and observed values of the isotopic constant for reaction (4) at 303K [32]. equilibrium Q (11BF3 - Donor) Q(11BF3) . Q (11BF3 • Donor) Exptl. Obs. Donor Q(10BF3-Donor) Q(10BF3) I Q(10BF3-Donor) Keq(4) (CH3)2O . 1.1706 I.204671.1706 = 1.029 1.027 (CH2)4O . 1.1789 1.2046Z1.1789 = 1.022 1.026 If the spectroscopic data for the isotopic.forms of the BF3'Donor complexes are available, the equilibrium constant for reaction (4), Keq(4), may also be calculated. Begun and Palko [33] have obtained and interpreted the necessary spectra for the BF3 complexes of diethyl ether and tetrahydrofuran and calculated theoretical values of. the equilibrium constants for these systems (Table 3). The calculated and experimental values are in excellent agreement. The effect of temperature on the partition function ratios is apparent from Tables 2 and 3. As temperature increases, the ratio of the 20 partition functions decreases. The corresponding effect is a reduction of the equilibrium constant, Keq (4), as temperature increases. This trend is expected since the vibrational partition function depends inversely on temperature. Therefore, as temperature Increases, the' value of the partition function decreases and their ratio approaches unity. It is appropriate at this point to consider the substitution of one of the other boron halides for BF3 in the isotopic exchange reaction. As previously expressed, the BF3 exchange reaction proceeds as observed due to electrostatic relaxation when a fluorine electron pair occupies the empty boron p orbital. The magnitude of the electrostatic repulsions between non-bonding electron pairs progressively decreases moving down the periodic table from fluorine to iodine due to increasing atomic radius. Thus, the ratio of area to pairs for non-bonding electrons increases by factors of 2, 3, and 4, respectively. . Consequently, the 7r-bond energy and the B-X stretching force constant decreases as progressively heavier halogens are substituted for fluorine in BX3. In terms of the two step mechanism previously described for isotope exchange, the equilibrium constant for reaction (7), Keq (7), tends to unity as the B-X stretching force constant decreases. At the same time, the molecular adduct is becoming more stable due to increased strength of the Lewis acid with the heavier halogens. Thus, the equilibrium constant for reaction (8), Keq (8), is becoming larger. When Keq (8) is equal to Keq (7), isotopic fractionation will cease to occur in reaction (4) and the overall equilibrium constant, Keq (4), will be unity. It is therefore reasonable to expect that the equilibrium constant will decrease as BCl3, BBr3, or BI3 are substituted for BF3 in the isotope exchange reaction for a particular 21 donor species. Furthermore, the heavy isotope of boron, 11B, is expected to concentrate in the liquid phase at some point in this substitution process. There is little data in the literature to support the above predictions, primarily because the heavier boron trihalides are such strong Lewis acids that they tend to decompose most donors. Two systems with BCl3 as the Lewis acid have been reported [15]. The exchange reactions and equilibrium constants are: (C6H5)2O-11BCl3u, + 10BCl3(g) t* (C6H5)2O-10BCl3u, + 11BCl3tg, (12) Keq = 1.002 (28°C) CH3COCl-11BCl3tO + 10BCl3tg, ^ CH3COCl-10BCl3tO + 11BCl3tg, (13) \ Keq = 0.996 (25°C) It is apparent that the equilibrium constants for reactions (12) and (13) are much smaller than for similar BF3 reactions. Furthermore, for the acetyl chloride system, the reversal in the direction of isotopic enrichment is observed. It can be concluded that isotopic fractionation in the exchange reaction is a quantum mechanical effect. This effect is amplified with BF3 as the Lewis acid due to the unique electronic characteristics of boron and fluorine. The above described model adequately accounts for the observed behavior of the isotopic exchange reaction. It is possible to theoretically estimate the expected equilibrium constant for BF3-Donor systems solely from spectroscopic data. The theory of isotope exchange provides valuable insight regarding the expected trends in the evaluation of equilibrium constants for previously unstudied BF3-donor systems. 22 PURPOSE AND SCOPE OF PRESENT STUDY The purpose for the current study was twofold. First, several previously unstudied donors, predominately ketones, were examined to determine if such donors would be viable replacements for the dimethyl ether/BF3 system. The separation factor, a, was experimentally measured for the new donors to accomplish this goal. Secondly, modelling and analysis of large scale boron isotope separation facilities were performed to examine potential methods of increasing the efficiency of such systems. As previously mentioned, the ideal single stage separation factor, a, associated with prevalent process equipment is expected to be identical to Keq for the isotope exchange reaction. Deviations between these two values may occur due to solubility of the 11B enriched gas phase in the 10B enriched liquid phase, essentially "diluting" the isotopic constitution of the liquid complex. Furthermore, incomplete dissociation of the complex in the vapor phase can cause a dilution of the 11B enriched gas phase with 10B enriched complex. Both phenomena result in a lowering of a from the "true" value of Keq, i.e. the value of the equilibrium constant in the absence of these effects. From the standpoint of the design and operation of a large scale facility, the single stage separation factor, a, is the. more desirable quantity to have readily available since the phenomenon responsible for lowering a from the equilibrium constant would be expected to operate in the prevalent process equipment. Consequently, the scope of the experimental study focussed on the evaluation of a. and not on the measurement of the "true" equilibrium constant, Keq. 23 Besides the measurement of separation factors associated with the isotope exchange reaction, the relative stability of the BF3-donor complexes studied were qualitatively examined. In the. experimental procedure used, the various complexes were in contact with BF3 gas for several days or weeks. Thus, the mass spectroscopic analysis procedure was used to examine any irreversible decomposition of the molecular addition compounds over extended periods of time. As previously discussed in conjunction with the currently used dimethyl ether large scale fractionation system, irreversible decomposition of BF3 complex results in a number of processing problems. A goal in this portion of the study was to gain at least a qualitative idea of the relative stability of the BF3-donor complexes examined experimentally. Various large scale boron isotope fractionating facilities based on chemical exchange between BF3 and the BF3 •dimethyl ether complex have been in operation in the U.S. for nearly 50 years. Despite this fact, detailed modelling and analysis studies of these systems are nonexistent in the open literature. The need for such studies is mandatory if efficient commercial plants are to be built and operated. It is possible that the required studies have been conducted, but this information is proprietary and therefore has not appeared in the open literature. Modelling and analysis of plant scale separation cascades based on chemical exchange was therefore conducted as the second, aspect of this research program. Results from this portion of the study are expected to facilitate the design of future experiments on both the bench and pilot plant scale. Furthermore, these studies provide insight regarding, the size and design of separation columns in plant scale systems based on chemical exchange. 24 The scope of the modelling and analysis portion of this study included generating computer models for several different counter current recycle cascade configurations typically encountered in large scale isotope separations. These models were based on the separation factors evaluated for the donor systems studied experimentally. Of necessity, these models were based on the concept of ideal stages where the streams exiting each stage were in chemical equilibrium. Only ideal stages could be considered since no experimental data pertaining to stage efficiency was obtained in this research. These computer models were used to determine the ideal stage and total interstage flow requirements associated with each of the different cascade configurations. The number of ideal stages provides a measure of the height of the fractionating column while the total interstage flow is a measure of the amount of material processed by the cascade. A knowledge of the ideal stage and total interstage flow requirements indicates the relative size of the separation system associated with a given donor system. For comparison, models based on the literature value of the separation factor for the dimethyl ethef/BF3 system were also included in this study. Within the confines of the experimental data available, an analysis of plant size based on the computer models was possible. The effects that the different donor systems had on the size of the separation plant were evaluated. The analysis was also extended to examine the pros and cons of incorporating a stripping section in the separation system. Ultimately, such an analysis is beneficial in establishing an efficient cascade design for large scale boron isotope separation based on chemical exchange. 25 EXPERIMENTAL DETERMINATION OF SEPARATION FACTORS The number of molecular species capable of forming complexes with. BF3, and thus potentially useful a s ' donors in the isotope exchange reaction, is virtually limitless. As indicated previously (refer to Table I), only a select few of the vast number of potentially useful donor compounds have been examined in the isotope exchange reaction. The systematic examination of each possible donor compound would be a horrendous undertaking. Rather, a more prudent approach is the systematic examination of a number of species from characteristic classes of compounds to determine the potential usefulness of these materials in the exchange reaction. This i s .apparently the approach taken by previous researchers in this area, and a number of classes of compounds have been examined, e.g. ethers, amines, sulfides, etc. Examination of the relevant literature is indicative that carbonyl compounds have never been studied as donor species in boron isotope, exchange reactions. Furthermore, studies utilizing ketones as the donor have never been reported. Molecular addition compounds between BF3 and the carbonyl groups of acetone, acetaldehyde, trimethyl acetaldehyde, methyl nonyl ketone, and camphor are known [5]. A portion of this study was therefore directed at examining various carbonyl compounds, specifically ketones, as the donor species in the. isotope exchange reaction. Emphasis was placed on determination of the separation factors for these BF3 •donor systems. 26 . Numerous compounds were prescreened as donors to determine if the BF3 complexes with these materials actually existed. Once the existence of the complex was established, the molar ratio of BF3 absorbed per mole of donor material and the freezing point of the resultant liquid complex were also determined. These prescreening experiments provided a measure of the solubility of gaseous BF3 in the liquid complex and were used to determine the appropriate temperatures at which gas/liquid equilibrium data could be obtained. Prescreening experiments with acetone, acetophenone, methyl isobutyl ketone (MIBK),. diisobutyl ketone (DIBK), nitromethane, and dimethyl sulfoxide (DMSO) were performed. * Based on these initial experiments, the systems selected for study in equilibrium experiments were: acetone/BF3, MIBK/BF3, DIBK/BF3, and nitromethane/BF3. The acetophenone/BF3 and DMSO/BF3 systems were found to be unsuitable for boron isotope fractionation by chemical exchange methods. Experimental Reagents, Equipment and Procedures Experimental Reagents The following compounds were obtained for use, in the experimental examination of separation factors. Unless otherwise noted, materials were used as received with no attempt at further purification. Boron trifluoride, BF3, was obtained from the Matheson Gas Company, Inc. and was of chemical purity (c.p.) grade with a minimum reported purity of 99.5% BF3. This gas was used as the boron feed in a. 11 experiments. Mass spectral analysis indicated the boron isotopes were present in approximately the natural abundance (19.7% 10B, 80.3% 1 B^) . 2.7 High, purity helium was obtained from the Linde Company with a minimum reported purity of 99.995% He. The high purity helium (HP He) was used as a purge gas to eliminate entrained air, and thus atmospheric moisture, from experimental equipment prior to use of BF3. Phenetole or ethyl phenyl ether, C6H5OC2H5, was obtained from the Aldrich Chemical Company. The reported purity was 99% phenetole. Reagent grade acetone, (CH3)2CO, was obtained from the J . T . Baker Company with a minimum reported purity of 99.6% acetone. Dimethyl sulfoxide, (CH3)2SO, was obtained from the Crown Zellerbach Company Incorporated. Acetophenone or methyl phenyl ketone, C6H5COCH3, was obtained from ' ■ the Aldrich Chemical Company with a reported purity of 99.5%. Methyl isobutyl ketone (4-methyl-2-pentanone, (Ch 3)2CHCH2COCH3, or MIBK) was obtained from the Aldrich Chemical Company. Diisobutyl ketone (2,6—dimethyl—4—heptanone, (CH3) 2CHCH2COCH2CH (CH3) 2, or DISK) was obtained from the Union Carbide Corporation. Nitromethane, CH3NO2, was obtained from the Aldrich Chemical Company with a reported purity of 96%. This material was redistilled by the organic group in the Chemistry Department of Montana State University to remove residual water. This purified or redistilled material was used in all subsequent equilibrium experiments. Experimental Equipment and Procedures The separation factor for the exchange reaction being discussed: 10BF3tg.) + 11BF3-Donortn ** 11BFt3j + 10BF3-Donortn (4) is given by: 28 [10BZ11B] (t) [10BZ11B] (g) [ B Z B] (gag before equilibration) (15)a - [ B Z B ] (gag after equilibration) The approximation in the second relationship can be assumed only in the case where the amount of BF3 in the gas phase is small compared to the amount of BF3 tied up as complex in the liquid phase. This assumption is valid since it has been shown that essentially all the isotope exchange occurs in the vapor or gaseous phase [6 ], It is desirable to keep the ratio of gas to liquid as high as 1:50 or 1:100 to insure that the approximation in equation (15) is valid. Due to the difficulties associated with the quantitative recovery of BF3 from the.liquid complex, analysis of the 10BZ11B ratios of only the gas phases greatly simplifies the determination of the separation factor, a. However, caution must be used in sampling the equilibrated gas phase. The sample removed after equilibration must be small and must be rapidly removed so as not to disturb the equilibrium compositions. Otherwise, BF3 is "boiled off" of the liquid complex, contaminating the 11B enriched gas phase. Using elaborate vacuum equipment and appropriate experimental techniques, all previous investigators have determined values of a based on the approximation given in equation (15). Primarily due to equipment limitations, numerous attempts to reproduce literature values of a for the PhenetoleZBF3 system in this laboratory by the above method of sampling only the gaseous phases failed. Although isotopic fractionation occurred in the "proper" direction, e.g. 10B concentrated in the liquid phase while 11B concentrated in the gaseous phase, the experimentally determined values of a were consistently low. This problem was attributed to the inability 29 to adequately control the amount of BF3 added to the cell, thus the BF3 gas to liquid ratio was too high, and the. approximation in equation (15) was invalid. . The experimental equilibrium cell designed to obtain separation factors associated with the isotope exchange reaction is shown in Figure I. The cell consisted of a cylindrical vessel machined from 316 stainless steel. The internal volume of the cell was approximately 265 ml. The cell lid was secured by machine screws and incorporated a viton o-ring to facilitate a leak free seal. The cell lid contained gas inlet and outlet ports, a thermowell and a pressure transducer port. A liquid circulating pump withdrew the liquid phase from a port near the bottom of the cell body and returned the liquid near the top of the cell through a sparger placed in the vapor space just under the cell lid. The circulation and sparging action of the liquid phase provided agitation of the cell contents. A valved, small diameter tube placed in the circulating pump return line between the pump and the cell body provided a simple means of removing a small amount of the liquid complex for the isotopic abundance analysis {vide infra). The first step in the experimental procedure was to place a known volume (=45 ml to 65 ml) of the donor liquid into the equilibrium cell. The cell lid was then sealed in place. The cell was purged with high purity helium and evacuated under vacuum to remove any entrained air (and thus atmospheric moisture) from the cell. Once the cell was evacuated, only the pure donor material remained sealed in the equilibrium cell. Donor losses were expected during the evacuation process, but the amount of material lost was unknown. Thermowell Pressure Transducer Gas Inlet and Sampling Port Purge Gas Inlet Liquid ReturnCell Lid O-ring Seal Liquid Sample Port Sparger Cell Body Liquid Withdrawal Circulating Pump Figure I Schematic of the test cell used to obtain experimental data. 31 The cell was then placed in a constant temperature bath preset to the desired equilibrium temperature. Once the cell and its contents reached the temperature of the bath, BF3 was slowly added to the system. The internal pressure was monitored with the pressure transducer as BF3 was added to the cell. Thus, the liquid complex was formed in situ and once the pressure stabilized at between 8 to 14 psig, the complex formation process was assumed complete and the BF3 feed to the cell was shut off. The cell and its contents were then allowed to stand at the desired equilibrium temperature for an appropriate length of time. Usually 12 to 24 hours were allowed to establish the isotopic equilibrium between the two phases. Samples of both the gas and liquid phases were, withdrawn from the cell and the boron isotopic ratios determined by mass spectroscopy. The separation factor for the given BF3/donor at the specific equilibrium temperature was then evaluated from this information. The sampling/ analysis process was repeated several times at a given equilibrium temperature. The temperature, was then changed and the associated separation factor determined in an analogous manner at the new equilibration temperature. Thus, a single experiment provided the separation factor for a particular BF3/donor system as well as the temperature dependence of a. Mass■Spectroscopic Isotopic Abundance Analysis Since no attempt was made in the above outlined experimental procedure to control the BF3 ratio between the gas and liquid phases, the approximation in equation (15) could not necessarily be assumed. Thus, an analysis of the boron isotope abundance ratio for both the gas and liquid 32 phases was required, the relationship: The associated separation factor was evaluated from [10BZ11B] (<) [10BZ11B] (g) (16) which is merely the equality in equation (15). In the above outlined procedure, the value of a was determined directly by equation (16) from mass spectroscopic analysis of the two phases. Consequently, the molar quantities of BF3 and pure donor in the equilibrium cell were not required for the evaluation of a. It was only necessary that an excess amount of gaseous BF3 be present in the cell for exchange with the BF3 bound in the liquid complex. The analysis of the isotopic ratio.in the liquid phase, [10BZ11B] , presents a number of problems due to the difficulties associated,with sampling the liquid phase and quantitative recovery of BF3 from the liquid complex. Therefore, previous researchers have not attempted isotopic analysis of the liquid molecular addition compound. These problems were overcome by developing a novel analytical technique for determining the boron isotopic ratio in the equilibrated liquid phase. The liquid phase was sampled by withdrawing a small amount (= 0.6 ml) from the cell through a needle port. This sample was added to a small amount of the pure liquid donor compound (= 0.3 ml) in a sample vial. The excess liquid donor in the sample vial insured that any dissolved BF3 remained bound as complex in the sample. This measure prevented isotopic fractionation from occurring in the sample vial prior to completion of the isotopic analysis. 33 The isotopic analysis of the liquid phase was accomplished by injecting an appropriate amount of the liquid sample, taken and prepared as described, above, directly into the septum inlet port of the mass spectrometer. The mass spectrometer gas reservoir was maintained at a constant temperature of 2000C and pressure of IO"2 torr. These conditions, provided a convenient in situ method for thermally and quantitatively decomposing the liquid complex into the BF3 gas and donor compound. The analysis appeared to provide accurate and reproducible results for the isotopic abundance of boron in the liquid complex and was advantageous in that the isotopic abundance of the liquid phase could be determined directly. The evaluation of the liquid phase isotopic composition in the above manner constituted the first known attempt at such an analysis. Consequently, this work was expected to provide the actual value of a for the first time since the approximation in equation .(15) was unnecessary. The mass spectrum of the BF3 • donor liquid complex obtained in the above manner was the superimposed spectra of the donor compound and BF3. The liquid analysis procedure required that the donor compounds had no characteristic mass spectral peaks at m/z 48 and 49 , since these signals are attributed to the 10BF2* and 11BF2* ions, respectively, and are used for the isotopic abundance analysis of boron. If the donor species has contributions to the mass spectrum of the liquid complex at these masses, alternate methods must be employed for the boron isotopic abundance analysis. Such alternate methods might include correcting the signals for contributions from the donor, using high resolution mass spectroscopy to separate the donor and BF3 peaks of nearly the same mass, or calibrating the mass spectrometer to use different masses in the isotopic abundance 34 determination. Fortunately, the donor materials that were used in this study exhibited no interferences at the BF2+ positions in the mass spectra. Sampling of the equilibrated BF3 gas phase was. accomplished by removing I to 2 cc of the gas from the cell into a clean, dry gas sampling reservoir. The mass spectral procedure for the determination of isotopic abundance in gaseous BF3 was developed during the early stages of this research program. In this procedure, BF3 gas was bled into the ionization chamber of the mass spectrometer from a gas sample reservoir through a leak valve. The leak valve used was a series 203 variable leak manufactured by the Granville—Phillips Company. The variable leak is simply a very low conductance valve used for sensitive control of gas flows across the extreme pressure drop from the gas sample tube (= I atm) to the mass spectrometer ionization chamber (= IO'7 torr). Results and Discussion The Phenetole/BF3 System Since the experimental and analytical techniques used to study chemical exchange in this research were new and untested, it was necessary to establish the validity of these procedures. This task was readily accomplished by examination of a BF3/donor system studied by previous researchers with results available in the literature. Once the validity of the experimental and analysis procedures were proven, new systems could be confidently examined with these techniques. The BF3/phenetole system was chosen to further develop and test the experimental and analytical techniques. Phenetole was chosen as the donor material since the BF3-phenetole complex is reported to have a respectable 35 separation factor of a = 1.051 at 0°C [6 ]. Furthermore, this liquid complex is reportedly quite stable with regards' to irreversible decomposition [7]. N Several experiments were conducted to establish the validity of the new experimental technique and analytical procedure with the phenetole/BF3 isotope exchange system. The separation .factor was determined as a function of temperature by the above described analytical and experimental techniques for • this system^ The results of these experiments are presented in Figure 2. The best fit straight line through the experimental data is also indicated. The equation of this line, obtained by linear regression analysis, is given by: 23.94 In a = ------- - 0.03489 (17) T (K) The best fit line through the literature data taken from Table I for the phenetole/BF3 system is also shown in Figure 2. The equation of this line is given by: 30.42 In a ='------- — 0.06158 (18) T (K) As indicated in Figure 2 and by comparison of the above linear equations, the experimental and literature data show reasonable agreement. The slope of the two lines are approximately equal, indicating consistency between the two data sets. The experimental data is consistently somewhat > higher than the corresponding literature data. This may be attributed to the fact that the experimental data was obtained directly by analysis of both gas and liquid isotopic abundance ratios without the need for the approximation previously discussed in conjunction with equation (15). 1.0730.07» -1.0670.065 -1.0620.060- -1.0570.055----- Experimental -1.0510.050- -1.0460.045- -1.0410.040- 1.0360.035 1.0300.030 3.45 IOOOZT(K) Figure 2 Experimental results for the Phenetole/BFj system S e p a r a t i o n F a c t o r , 37 Consequently, the experimental data may provide a more realistic measure of the actual behavior of the BF3/phenetole system. The deviation or spread between the individual data points at each of the experimental temperatures is rather large. This discrepancy is attributed to problems associated with the sampling of the equilibrated gas phase. If too small a gas sample was removed, not enough BF3 was present for a representative mass Spectral analysis and the calculated separation factor was consistently higher than the corresponding literature value. If too much BF3 gas was removed, BF3 was "boiled" off of the liquid complex and this 10B enriched material diluted the 11B enriched gas phase. This invariably led to values of the experimental separation factors lower than the corresponding literature values. This problem was addressed by adjusting the size of the gas sample reservoirs and developing a technique to remove a consistent amount of the equilibrated gas from the equilibrium cell. The amount of equilibrated gas removed (= I cc) assured that there was an ample amount of gas for the isotopic analysis without removing enough to affect the isotopic constitution of the gas phase. The line labelled "Max" in Figure 2 is a linear extrapolation of the two data points representing the theoretical maximum value that the separation factor may assume as given by equation (1 2 ) previously presented in the theoretical section. It is slightly disconcerting that the experimental best fit line crosses the theoretical maximum line. Recall that the theoretical maximum is based on only two points, and is prone to some uncertainty. The discrepancy between experimental data and the theoretical maximum may also be attributed to the uncertainties 38 associated with the size of the equilibrated gas sample removed for analysis in the experimental procedure as previously discussed. In these experiments, gaseous BF3 and the BF3-phenetole complex were contacted in the equilibrium cell for up to 144 hours (6 days) at several different conditions of temperature and pressure. This length of time and variety of conditions allowed ample opportunity for irreversible decomposition of the liquid complex to occur. Since the gas and liquid samples are analyzed on the mass spectrometer, decomposition products would be expected to show up in the mass spectra of these samples. It was anticipated that the signal strength of peaks associated with any decomposition products would increase for samples taken at consecutively later times. Comparison of the initial mass spectra of the gas and liquid phases with those taken at all later times were indicative that no detectable decomposition of the complex had occurred. This observation is in line with literature reports attesting to the excellent stability of the BF3•phenetole complex [6,7]. The agreement between the experimental separation factors and those reported in the literature for the BF3/phenetole system was sufficient to lend credibility to the newly developed experimental technique and analytical procedure. By exercising proper care in sampling the equilibrated gas phase, these techniques appear suitable for examination of previously unstudied BF3/donor systems. the 39 Acetone was selected as the first . donor for study in isotope exchange since the existence of the acetone-BF3 complex is mentioned in the literature [5] and preliminary work in this laboratory indicated acetone readily absorbs gaseous BF3 to form a liquid molecular addition compound. Prescreening studies indicated that I mole of acetone absorbed I mole of BF3 gas. The resulting acetone-BF3 molecular addition compound was a dark brown liquid with a freezing point of 16 to 18°C. The fact that I mole of acetone absorbed I mole of BF3 is indicative that the resulting complex is a 1:1 molecular addition compound and gaseous BF3 is not excessively soluble in the liquid complex. Furthermore, equilibrium experiments between gaseous BF3 and the liquid acetone-BF3 complex could be performed only at temperatures greater than the freezing point of the complex or approximately 20°C. Thus, the temperatures selected for the determination of experimental separation factors were 25°C, 35°C, and 45°C. The experimentally determined separation factors are presented graphically in Figure 3. The best fit line through the experimental data, obtained from linear regression analysis, is also shown in Figure 3. The < equation of this line is: 59.58 In a = -------- - 0.1597 (19) T (K) Note that the experimental best fit line is consistently below the theoretical maximum. Furthermore, the slope of the experimental line is positive, indicating that a increases with decreasing temperature. Both of these observations are consistent with theoretical considerations and lend credibility to experimental data. The Acetone/BF3 System 1.087 1.0510.050 I 048 -1.041 -1.036c 0.036 1.031 -1.025 Dimethyl Ether 1.020 1.0160.016 3.25 1000/T(K) Figure 3. Experimental results for the Acetone/BFj system S e p a r a t i o n F a c t o r 41 In the experiment being discussed, the acetone-BF3 complex and gaseous BF3 were in contact in the equilibrium cell for 220 hours (= 9 days). Over this extended period of time, the appearance of decomposition products was noted in the mass spectral analysis of the liquid and gas phases. Furthermore, a lowering in the freezing point of the liquid complex present at the end of the experiment from that of the initial complex was noted. A color change of the final liquid complex was visually detected as well. These observations are indicative that.the acetone-BF3 complex undergoes slow, irreversible decomposition. No attempt was made at characterizing the decomposition mechanism or products. Mass spectral analysis of the equilibrated gas phase consistently indicated the presence of acetone in the BF3 gas samples. The presence of acetone in the equilibrated gas phase is indicative that the gaseous phase may contain undissociated acetone-BF3 complex. It is therefore possible that the ^experimental separation factors may be lower than the "true" equilibrium constant for the acetone/BF3 system in accordance with previous discussions [I]. No attempt was made to test this hypothesis or quantify these effects. The best fit line through the equilibrium constant data for the dimethyl ether/BF3 system is also indicated in Figure 3. In terms of separation factors, the acetone/BF3 system consistently out performs the dimethyl ether system. Consequently, the experimental results for the acetone/BF3 system are indicative that acetone, or perhaps other ketones, could provide superior donor properties as compared to the currently used dimethyl ether system for the large scale fractionation of boron isotopes. 42 Based on the positive results obtained in experiments with the acetone/BFg system/ the systematic examination of other ketones was warranted. Initially, acetophenone, (C6H5)COCH3, and propiophenone, (C6H5) COC2H5, were to be examined as donors in the isotope exchange reaction. These materials were selected based on the excellent properties of the homologous ethers (anisole and phenetole) in the isotope exchange reaction. It was believed that these compounds would exhibit superior qualities compared to acetone as donor materials, much as the phenyl- ethers showed enhanced properties as compared to dimethyl ether. Prior to testing these ketones in equilibrium experiments, acetophenone was. prescreened to determine if the BF3 complex even existed and if so, evaluate some of the physical properties of the resulting complex. At 25°C, acetophenone readily absorbed BF3 gas, forming a dark brown liquid. At the completion of the formation reaction, the complex was a very viscous, dark black material. Since the complex had the consistency of tar even at the elevated temperature of IOO0C, the use of acetophenone as a possible donor in isotope exchange was eliminated. Due to the chemical similarity of propiophenone, this material was not prescreened. Based on these studies, testing of phenyl ketones in the isotope exchange process was abandoned. The Acetophenone/BF3 System 43 Because the positive nature of the experimental results with the acetone/BF3 system indicated that ketones could be viable alternative donors in boron isotope exchange, 4-methyl-2-pentanone (methyl isobutyl ketone or MIBK) was prescreened as a potential donor material. The purpose for studying other ketone systems was to examine the effect substituting other functional groups for one or both of the methyl groups in acetone would have on the separation factor. The difference between acetone and MIBK is the substitution of an isobutyl group for a methyl group in acetone to form MIBK. The carbonyl oxygen provides the lone electron pair used to form the BF3 addition compound in both ketone systems. Thus, any differences in the experimentally measured separation factors associated with the two systems could be attributed to differences in the functional groups attached to the carbonyl carbon. The prescreening studies were indicative that one mole of MIBK absorbed 1.1 moles of BF3. A 1:1 molar complex is therefore indicated with slight solubility of BF3 gas in the liquid phase. The resultant MIBK/BF3 complex was a dark reddish brown liquid exhibiting a freezing point of 16 to 18°C. Based on the freezing point of the complex, equilibrium temperatures of 25°C, 35°C and 45°C were selected for the experimental determination of separation factors. The results of two separate equilibrium experiments with the MIBK/BF3 system are presented in Figure 4. Note that there is significant variation in the individual data points for a specific temperature in the first MIBK/BF3 experiment. This variation at a specified temperature results in uncertainties regarding the actual value of a and the position The MIBK/BF3 System 0.055 0.050 0.045- 0.040- 9 £ 0.035 0.030 0.025 0.020- 0.015 ■+■ Exp. #1 O Exp. #2 -r-1.057 1.051 Max -1.046 Dimethyl Ether 45C I 3.10 3.15 3.20 -H □ d -1.041 Experimental -1.036 -1.031 -1.025 - 1.020 35C I 25C I 3.25 IOOOZT(K) 3.30 3.35 -1.015 3.40 Figure 4. Experimental results for the MIBK/BF^ system. S e p a r a t i o n F a c t o r 45 of the best fit straight line.' The reasons for these variations are unclear, but inconsistencies in the sampling procedures for the equilibrated gas and liquid phases are suspect. Due to these uncertainties, the experiment was repeated with these results also indicated in Figure 4. In the second MIBK/BF3 equilibrium experiment, data was taken only a;t temperatures of 250C and 45°C. It is apparent from Figure 4 that the agreement between a ' s for a given temperature was much better in the second experiment. Furthermore, the agreement between the results from the independent experiments is very good. These observations reinforce the reliability of the individual data points and the best fit straight line through the data, also included in Figure 4. The equation of the best fit line obtained by linear regression analysis is given by: 9.504 In ex = -------- + 0.0071 (2 0 ) T (K) This line lies below the theoretical maximum.at all points. Furthermore, the slope of the best fit line is positive, indicating that a increases with decreasing temperature. Both observations are consistent with theoretical considerations and lend credibility to the experimental data. The liquid complex was in contact with gaseous BF3 for 192 hours (=8 days) in experiment #1 and for 96 hours (=4 days) in experiment #2. Decomposition products were not noted in the mass spectra of the equilibrated gas or liquid phase samples in either experiment. Further testing of the liquid phase was facilitated with gas chromatography/mass spectral (GC/MS) analysis. The GC was used to separate components in the 46 liquid phase, and the separated effluent from the GC was sent directly into the mass spectrometer such that the mass spectrum of the separated components could be obtained.' The GC/MS analysis was performed on pure MIBK used to form the complex, the MIBK/BF3 complex formed initially at the beginning of experiment #1 , and the final complex from the conclusion of experiment #1. The gas chromatographs of each of the above liquids' were identical, corresponding to pure MIBK (BF3 is so volatile that it exits the GC column with or before the solvent). Thus, irreversible decomposition products were not detected in the liquid phase. It is therefore apparent that the MIBK/BF3 system is quite stable with regards to irreversible decomposition. MIBK was not observed in the mass spectral analysis of any of the equilibrated gas phase samples. This is indicative that undissociated complex does not exist in the vapor phase for the MIBK/BF3 system. This- observation, coupled with the limited solubility of BF3 in the liquid phase are good indications that the experimentally determined a ’s should closely approximate the actual values of the equilibrium constant for this system. The best fit line based on literature data for the dimethyl ether/BF3 system is indicated in Figure 4. The MIBK/BF3 system provides larger values of the separation factor than the dimethyl ether system over the temperature range studied. Consequently, MIBK appears to be a better donor than dimethyl ether in the boron isotope exchange reaction. Furthermore, comparison of Figures 3 and 4 or equations (19) and (20) indicates that the results of the MIBK/BF3 system are slightly higher than for the acetone system. The substitution of an isobutyl group for a methyl group in acetone appears to affect the donor to boron bond 47 stability in the complex and enhances the separation factor. Thus, MIBK appears to be a viable alternative to dimethyl ether and is comparable to acetone as a donor in chemical exchange. The DIBK/BF3 System The acetone and MIBK experiments indicated that the BF3/ketone molecular addition compound was destabilized by replacing a methyl group with an isobutyl group attached at the carbonyl carbon. The manifestation of this destabilizing■effect was slightly larger separation factors at a specific temperature for the MIBK/BF3 system as compared to the acetone/BF3 system. To further examine this effect, 2,6-dimethy1-4-heptanone (diisobutyl ketqne or DISK) was selected as a donor compound for study in the exchange reaction. For DIBK, both methyl groups of acetone are replaced by isobutyl groups. It was anticipated that further destabilization of the BF3 complex with DIBK would enhance the separation factor over that obtained with either the acetone/BF3 or MIBK/BF3 systems. Prescreening studies were indicative that I mole of DIBK absorbed approximately 1.1 moles of BF3 gas. Slight solubility of gaseous BF3 in the liquid complex was therefore indicated. The resulting liquid complex was dark reddish brown in color and exhibited a freezing point of IS0C to 18°C. ' Based on the freezing point of the DIBK/BF3 complex, the selected equilibration temperatures were identical to those used with the other ketone systems. The experimental results from the equilibrium studies with the DIBK/BF3 system are shown in Figure 5. The best fit linear equation for this system is given by: 1.0570.055 1.0510.050 1.046 Experimental 1.041 1.036 1.0310.030 1.0250.025 Dimethyl Ether 1.0200.020 1.0150.016 3.25 1000/T(K) Figure 5. Experimental results for the DIBK/BFj system S e p a r a t i o n F a c t o r 49 31.785 In a = ------- - 0.0624 (21) T (K) This best fit line is also shown in Figure 5. As expected, this line lies below that of the theoretical maximum and has a positive slope. These observations are consistent with theoretical considerations and lend credibility to the experimental data. During the course of the DIBK/BF3 experiment, mass spectral analysis of the equilibrated gas indicated negligible amounts of DIBK were present in the vapor phase. This is indicative that the DIBK/BF3 complex is not present in the vapor phase. Coupled with the limited solubility of BF3 in the in the liquid complex, the experimentally measured separation factors are expected to represent the actual value of the equilibrium constant for the DIBK/BF3 system. The liquid DIBK/BF3 complex was in contact with the gas phase for 216 hours (= 9 days) during the equilibrium experiment. Decomposition products, expected to show up as increasing, time dependant signals in the mass spectra, were not detected in the equilibrated gas or liquid samples. The GC/MS analysis discussed previously was also used to examine the liquid phase for irreversible decomposition products. Samples of pure DIBK used to form the complex initially, the DIBK/BF3 complex taken at the beginning of the experiment, and of the liquid phase after 216 hours in the equilibrium cell were submitted to, the GC/MS analysis. The chromatographs and mass spectra for each sample were similar, and indicated only the DIBK donor was present in the liquid samples.. Consequently, the DIBK/BF3 complex is apparently very stable with regard to irreversible decomposition. 50 The best fit line representing literature data for the dimethyl ether/BF3 system is indicated in Figure 5. As with the other ketone systems studied, the DIBK/BF3 system exhibits separation factors larger than for the dimethyl ether system. By comparison of the available data, DIBK appears to be a significant improvement over dimethyl ether as the donor in boron isotope exchange. The Nitromethane/BFg System An interest in nitromethane (CH3NO2) as a potential donor species in boron isotope exchange developed from discussions with the organic chemistry group at Montana State University. A graduate student in that group had been working with solutions of nitromethane saturated with BF3 gas in organic synthesis reactions. The reported properties of the nitromethane/BF3 complex included excellent stability in regards to irreversible decomposition and a freezing point less than O 0C. One mole of nitromethane was reported to absorb 1.4 to 1.6 moles of BF3 gas at 0°C [38]. These properties were confirmed in this laboratory, and the light brown liquid complex exhibited a freezing point of -46°C to -48°C. The experimental • results for the nitromethane/BF3 system are presented graphically in Figure 6 . The linear equation representing the best fit line through the experimental data is also shown. The equation of this line is: 33.257 In a = -------- - .0.0452 (22) T (K) ( The slope of this line is positive in accord with theoretical considerations. The most striking aspect of these results is that they 1.0940.090 0.085 -1.088 0.080 -1.083 Experimental 0.073 1.077 0.07a -1.071 0.085- -1.065 c 0.060 1.059 0.055 -1.054 0.050 1.048 0.045 1.042 0.040 1.0360.035 1.0300.030 3.50 1000/ T(K) Figure 6 Experimental results for the NitromethaneZBF3 system S e p a r a t i o n F a c t o r , 52 are substantially greater than those predicted by the theoretical maximum. The nitromethane/BF3 system is the only known instance in BF3 gas/liquid adduct isotope exchange where a's in excess of the theoretical maximum have been observed. These extraordinary results may be justified based on the unique properties of the nitromethane molecule. The donors which have been examined in this study, and nearly all of those examined by previous researchers, have been single site donors. That is, there is only one basic center containing the required lone pair of electrons necessary for bonding in formation of the BF3-donor molecular addition compound. The nitromethane molecule contains two oxygen atoms, and consequently has two such donor sites available. It is conceivable that excess BF3 dissolved in the liquid phase beyond that mandated by a 1:1 molar complex could be associated or weakly bound to the second oxygen of the nitromethane/BF3 complex. The isotope effect between the complex and the excess BF3 could potentially result in larger values of the separation factor than for the corresponding single site donors. The only system similar to nitromethane which has been previously examined and is briefly described in the literature [13] is that of nitrobenzene, (C6H5)NO2. In that work, a separation factor for the nitrobenzene/BF3 system of 1.03 at 7°C was reported. This well below the theoretically predicted maximum of a = 1.05 at 7°C. That study also reported BF3 gas was virtually insoluble in the liquid nitrobenzene/BF3 complex. Comparison of these two systems provides some evidence regarding the existence of a double site mechanism in isotope exchange for the nitromethane/BF3 system. Furthermore, the dramatic effect of substituent groups attached to the basic donor center is indicated. 53 Any justification for such a mechanism must of course come from careful experimental observation. Determining the exact nature of the BF3^ • nitromethane bonding arrangement in the liquid complex would be the first step in evaluating the underlying principles involved. Such an undertaking is outside the scope of this project, but is strongly recommended in future work. During the nitromethane/BF3 experiment, the liquid complex was in contact with the gas phase for 435 hours (=18 days). During this extended period of time, decomposition products were never observed in the mass spectra of the equilibrated gas or liquid samples. It was concluded that this system was extremely stable with regards to irreversible decomposition of the complex. Furthermore, nitromethane was never observed in the gas phase samples, which indicated a relatively low vapor pressure for this complex. The experimental evidence outlined above for the nitromethane/BF3 system strongly suggests much potential exists for the use of nitromethane as a viable alternative donor in the boron isotope fractionation scheme. Based on the extraordinary magnitude of the separation factor, it is conceivable that a ”super donor" has been discovered in this system. Further work is certainly required and strongly suggested with the nitromethane/BF3 system to validate this supposition. 54 The DMSO/BF3 System The previously cited literature data for the dimethyl sulfoxide (DMSO) system (refer to Table I) was obtained for gas/solid isotope exchange. This is the only known instance where such a system has been examined experimentally and those results indicate that the separation factor increases with increasing temperature. This trend contradicts the theoretical predictions and experimental observations for gas/liquid exchange reactions. Based on the DMSO gas/solid data and the demonstrated behavior of similar gas/liquid systems, it was postulated that the. separation factor, a, goes through a maximum at temperatures near the phase transition of the complex from the liquid to solid states. .It is necessary to validate this hypothesis by experimental determination of the temperature dependence of a for the gas/liquid DMSO/BF3 system. The DMSO'BF3 complex freezes to form a white crystalline solid at 53°C. The experimental apparatus developed in this study proved inadequate to obtain equilibrium data.at these elevated temperatures. The complex froze in the circulating pump and pump lines external to the equilibrium cell. This complication made sampling of the liquid phase impossible since the complex solidified in the liquid sampling port as well. Consequently, experimentation with the DMSO/BF3 system, was discontinued. If experimentation is resumed at a future time, the experimental apparatus must be modified to accommodate the use of higher experimental temperatures. 55 Comparison of Experimentally Studied Systems The scope of the experimental portion of this study focussed on the experimental determination of the separation factor as a function of temperature for the various systems examined. The temperature dependence and magnitude of the separation factor for the BF3/donor systems studied in this research are presented in Figure 7. Literature data for the dimethyl ether system is also indicated in Figure 7 for comparison. As previously discussed, the separation factor, a, increases with decreasing temperature, as indicated by the positive slope of the lines shown in Figure 7. The positive slope indicates that the exchange process is exothermic. This trend is expected and predicted from theory and the results of previous researchers for similar exchange systems. Based on the slope of the experimental lines shown in Figure 7, the temperature dependence of separation factor varies from donor to donor and increases in the order: Acetone > Nitromethane > DIBK > MIBK Depending on the BF3/donor system, the variation of a with temperature may be an important consideration in the design and operation of a large scale cascade. For a strongly temperature dependent donor, such as acetone or nitromethane, a substantial increase in cascade performance may be realized by isothermal operation of the exchange column. The magnitude of the separation factor at a specific temperature varies from donor to donor. In accord with previous discussions, the variation is a result of differences in substituent groups attached to the basic center in the donor molecule. The increasing inductive effect of 1.0830.080 -1.0780.075 Nitromethane 10730.070 -1.0680.065 -1.0620.060 -1.0570.055- 9 0.050 -1.052 -1.0470.045— 1.0410.040 MIBK -1.0360.035 -1.0310.030 Dimethyl Ether -1.0260.025 - 1.0200 020 - 1.0150.015 3.40 1000/T(K) Figure 7. Comparision of experimental systems studied in isotope exchange. S e p a r a t i o n F a c t o r 57 larger alkyl groups should strengthen the BF3-donor bond and result in lower values of the separation factor. The opposite trend was observed with the ketones studied in this work, with separation factor increasing in the order DIBK- > MIBK > Acetone. This is attributed to steric interferences, presumably between the /3 or y-carbon in the isobutyl group and the normal positioning of fluorine in BF3. It is apparent in Figure.7 that the separation factors associated with the nitromethane system are dramatically larger than those for the ketones. The cause of this anomaly is uncertain, and further experimental work is necessary to enhance understanding of this phenomenon. The benefits of increasing the separation factor in large scale isotope fractionation is easily brought into perspective with a simple comparison based on the familiar Fenske-Underwood equation: ln[yP(l-xw)/(l-yP)xw] n = ---------------------- (23) In a Equation (23) provides the minimum number of ideal stages, n, required for a specified separation in a exchange column operated at total reflux. For a cascade producing 95% 10B product (yP = 0.95) and a Sjfc10B waste stream (xw = 0.05), equation (23) can be simplified: 5.889 n = -------- (24) In a Minimum stage requirements are presented in Table 4 for the dimethyl ether, acetone, MIBK, DIBK and nitromethane systems based on reported values of the separation factor and evaluated from equation (24). It is apparent from the above comparison that a slight increase in separation 58 Table 4. Minimum ideal stage requirements with different donors for a boron isotope fractionation cascade operating at total reflux. Donor a Min N6 of Ideal Staaes Dimethyl ether 1.014 424 Acetone 1.041 147 MIBK 1.041 . ■ 147 DISK 1.045 134 Nitromethane 1.081 ■ 77 factor results in a concomitant decrease in the minimum ideal stage requirements. Consequently, a dramatic reduction in the size of the required process equipment is indicated if a ketone or nitromethane is used as the donor rather than dimethyl ether.' An in-depth analysis of isotope fractionating cascades is the purpose of the second portion of this study and will be deferred to the subsequent section on modelling and analysis. Other considerations besides the magnitude of the separation factor and hence the size of the process equipment required to effect a given separation are important in the selection of the an appropriate donor. Recall that the BF3 bound in the liquid molecular addition complex must be readily liberated to effect product recovery and for the recirculation and reuse of the liquid donor. Consequently, the formation reaction: BF3 + Donor ** BF3-Donor (3) should be quantitatively reversible simply by the addition or removal of heat. Reversible decomposition of the liquid complex into BF3 and donor is tantamount to establishing the method recycle will be provided in large scale isotope fractionation. 59 Experiments to determine the reversibility of the formation reaction were undertaken in this study. The equilibrium cell previously described was fitted with a stainless steel condenser. A heating tape wrapped around the body of the cell provided a convenient method of heating the cell and its contents. The complex under consideration was formed in situ in the equilibrium cell. Then contents were then heated via the heating tape and gas was allowed to escape from the cell through the condenser under constant helium purge. In this manner, the cell was designed to operate in the fashion of a distillation flask. The idea was to thermally liberate gaseous BF3 from the complex. Liquid samples were taken at two hour intervals during the decomposition experiments for analysis of boron content. An analysis was attempted on the mass spectrometer previously used in conjunction with the isotopic abundance determinations. Boron content was to be determined by comparing the signal strength of the BF3 peak to that of the base peak from the donor in the mass spectrum of the complex. In this manner, relative amounts of BF3 present in the liquid compared to the donor were to be determined if the amount of donor in the cell was assumed constant. Unfortunately, the experimental apparatus and the analysis procedure proved inadequate for the purpose of studying reversible decomposition. Refluxing the liquid complex in the cell could not be adequately controlled, primarily since visual inspection was not possible in the stainless steel vessel. In general, the complex was irreversibly decomposed or even scorched to the cell walls due to excessive temperatures, or in some instances the donor was boiled away with the BF3 gas rendering the analysis useless. Consequently, the data obtained from 60 these experiments was very inconclusive but did indicate that the decomposition may be reversible if performed under the proper conditions. Experimental methods and analytical techniques amenable to the study of irreversible decomposition of the liquid complexes are reported in the literature [1,5,24], The appropriately modified equipment was outside the means of this project. The analytical techniques for determination of boron content in the liquid sample are extremely labor intensive and require specialized analytical equipment. Such experiments are best suited to a well equipped analytical laboratory. Consequently, a detailed study of reversible decomposition was abandoned but is strongly recommended as future work. 61 MODELLING AND ANALYSIS The purpose of the modelling and analysis portion of this study was to compare the number of ideal chemical equilibrium stages and total interstage flow requirements for different recycle cascade configurations with the various BF3/donor systems examined experimentally. Total interstage flow and ideal stage requirements provide an estimate of the size of the separation plant necessary to fractionate the isotopes of boron. The previously discussed dimethyl ether system currently in commercial use provides a convenient basis for comparison of the plant size associated with the experimentally examined exchange systems. Such a study is beneficial in estimating the effect different donors has on the size, and hence design, of the necessary process equipment. Indeed, this type of analysis is tantamount to selecting the donor system to be used in large scale separation schemes, and generally must be conducted prior to a full scale design and economic evaluation. The experimental portion of this work focussed primarily on the determination of the separation factor, a, associated with the different BF3/donor systems. With the values of a available, only ideal stages can be considered in this portion of the study since actual (non-ideal) stage requirements would rely on stage efficiency data obtained from pilot plant experiments. Furthermore, the physical properties (e.g. viscosity and density) as well as the reversibility and thermodynamics of the formation reaction for the different liquid BF3/donor complexes must be established prior to conducting a full scale design and economic evaluation. The 62 appropriate experiments and pilot plant studies necessary to.determine these important operating parameters were outside the scope of this work. Despite these limitations, the results from this portion of the study are useful in planning future bench scale experiments or pilot plant studies and to evaluate the actual requirements of plant scale boron isotope separation systems. The salient features of recycle cascades are set forth and discussed in the following sections. Detailed analysis and derivations of cascade theory can be found in the open literature [4,39,40]. These established relationships were used to propagate computer models for the stagewise behavior of several types of recycle cascades applicable to isotope fractionation. These models and the results are subsequently discussed. Terminology Ideal Stages The fundamental element of an isotope separation plant which effects a portion of the overall separation of the process materials is a separating unit or stage. The simplest type of stage is one that receives a single feed stream and produces one heads stream enriched in the desired component and a single tails stream depleted in the desired component. Such a separating stage is depicted in Figure 8 . The heads stream exits the stage with a flow rate denoted L , indicating a liquid stream in accord with chemical exchange, and is enriched in the desired isotope. The tails stream flow rate, denoted G to indicate a gas stream, is depleted in the desired isotope. The feed stream, F, is generally a mixture of two or more streams containing both gas and liquid fractions. In this study. 63 Flow Mole Abundance Stream Rate Fraction Ratio Tails Separa ting Stage Heads Figure 8 . Single separating stage and associated nomenclature. hourly molar flow rates were used exclusively, consequently L, G, and F have units of moles/hour. For binary systems, as is the case of boron isotopes, it is commonplace to express mole fractions in terms of the desired isotope. The desired isotope was defined as 10B for the purposes of this study. Accordingly, the mole fraction of 10B was denoted as y in the heads stream, x in the tails stream and z in the feed stream as indicated in Figure 8 . The mole fraction of 11B is then expressed as (1-y), (1-x), or (1-z) in the heads, tails and feed streams, respectively. Certain relationships in separation cascades are simpler when expressed as mole ratios, defined as the ratio of the mole fraction of one component in a stream to the mole fraction of the second component in the same stream. The greek letters T], e, or C are used to denote these ratios in the heads, tails, or feed streams, respectively. The mole ratios 64 corresponding to a given stream are indicated in Figure 8 and defined a s . follows: y V = -------- (25) (i - y) x e = -------- (26) (I “ x) r = -------- (27) ( 1 - z ) Emphasis in this portion of the study was placed on the concept of an equilibrium or ideal stage. In an ideal stage, the two streams exiting the stage are in equilibrium. Separation Factors The degree of separation achieved within a single ideal stage is measured by the separation factor, a. The separation factor is defined as the ratio of the heads stream mole fractions divided by the corresponding ratio in the tails stream. For the binary component mixture (10B & 11B) being discussed: n y/(i-y) y(i-x) oc = --- = -------- — (28) G x/(1-x) x(l-y) The separation factor defined in the above manner is useful since in many isotope separation processes it is independent of composition. In the models developed for this study, it was assumed that the separation factor oc was a constant and known property of each ideal stage with a magnitude determined from experiment. 65 Other useful measures of the degree of separation obtained in a single stage are the heads separation factor, /3: v y/(i-y) y(i-z) /3 = --- = -------- = ------- (29) f z/(I-Z) Z(i-y) and the tail's separation factor, yz f z/(1-z) z(l-x) e x/(1-x) x(l-z) (30) The composition differences'measured by the above defined separation factors are indicated by the dashed lines in Figure 8 . If one or more of the separation factors are known and assumed to be constant for a stage, the above definitions can be rearranged to provide equilibrium expressions relating the various mole fractions for an ideal stage: y x Z ax /Sz ax + 1 - x j S z + l - z y ______z a(l-y) + y y(l-z) + z y ax 0 (I-Y) + y ax + /3 (1-x) (31) (32) (33) Countercurrent Recycle Cascade When the degree of separation effected by a single stage is smaller than the required amount of separation between the waste and product streams, it becomes necessary to connect a number of stages together in series to perform the required separation. A group of stages connected in series is referred to as a cascade. The countercurrent recycle cascades 66 examined in this study are represented schematically in Figure 9. The process scheme in Figure 9 represents the simplest type of recycle cascade in which the tails stream from stage i-1 (G3^ 1 in Figure 9) is recycled to form a portion of the feed to stage i. Experience indicates that counter current contacting is required for the efficient separation of many mixtures; continuous distillation with reflux is .a typical example of a (-Oinmnn counter current cascade. Consequently, the recycle flow scheme is often encountered in separation processes. The countercurrent cascade shown in Figure 9 separates a feed stream with a 10B mole fraction of zF flowing at rate F into a product stream containing a mole fraction 10B of yP flowing at rate P and a tails or waste stream with a mole fraction 10B of xw flowing at rate W. These six flow rates and compositions are termed the external variables for the recycle cascade. The feed to each stage is a combination of the tails stream from the next lower stage and the heads stream from the next higher stage. The flow rates and compositions are defined in exactly the same manner as for the single stage shown in Figure 8 , except a subscript is used to indicate the stage number with which the flows and mole fractions are associated. These flow rates and compositions are referred to as the internal variables of the cascade. The portion of the cascade from the product stage up to and including the feed stage is referred to as the enriching section. The purpose of the enriching section is to make isotopically enriched material of the desired product composition. The enriching section is therefore essential in making product of the required purity. The portion of the 67 T Feed x T - I i T - I I W Waste Stripping Section I Enriching Section Figure 9. Flow schematic of the countercurrent recycle cascade. 68 cascade above the feed point is termed the stripping section. The purpose of the stripping section is to recover or strip the desired isotope from the feed stream. Therefore, the stripping section serves only to reduce the amount of fresh feed required to make a specified amount of product, and in certain instances it can be economically advantageous to eliminate this section altogether. Material Balances Two material balances may be written for the external process variables, e.g. the feed, waste and product streams, shown in Figure 9: F = P t W (34) and ZpF = yPP t xwW (35) Since there are two equations and six unknowns, it is possible to specify four of the external variables, the remaining two are fixed by the above material balance relations. If the product rate and composition, P and yP respectively, the feed composition, zF, and waste composition, xw, are specified, the feed rate, F, anjd the waste rate, W, are given by: P(Yp ~ xw) F = — - -------- (36). Zp - Xw P(Ye ~ zF) W = ------------ (37) Zp — Xw It is also possible to write two material balances on the internal process variable for any stage in the cascade. Consider a portion of the enriching section from the product end up to and including stage i. The material balances for stage i: 69 Li+1 — G1 + P (38) Yi+iLl+1 = X1G1 + ypP (39) may be combined resulting in the enriching section material balance equation valid for the heads composition exiting' any stage up to and including the feed stage. nF: Xi(GiZP) + Yp Yi+i — ( — If 2, 3,...., np.-L) (40) (GiZP) + I Equation (40) is often referred to as the operating line equation for the enriching section of a cascade. Similarly, in the stripping section for any stage above the feed stage. nF, the material balances are: Li+1 + F = G1 + P (41) yi+iLi+i + ZpF = XiGi + ypP (42) The equations can be combined to give the stripping section material balance equation valid for the heads composition exiting stages in the stripping section: X1(G1ZP) + Y p - Zf (FZP) Y1+! — ( i- — nFf nF+1 / nF+2 f • • • • f nT-I) (43) (GiZP) + I (FZP) Equation (43) is often referred.to as the stripping section operating line l - equation. Recycle Ratio The quantity G1ZP in equations (40) and (43) has special significance and was defined for the modelling purposes gf this study as the recycle ratio, R1: R 1 s G 1ZP (44) 70 The number of ideal stages required to separate feed into product and waste of the specified compositions is a minimum at Ri -» m. This condition is referred to as total reflux. The condition of total reflux is of theoretical interest since the absolute minimum number of'ideal stages, n, required for a specified separation is mathematically easy to obtain from the familiar Fenske-Underwood equation, which was presented earlier: In [ yP (l-xw)./(l-yP) xw ] n = ---------------------- (23) In a However, at total reflux, none of the product or waste is withdrawn from the cascade. Total reflux is therefore impractical in actual cascades. At total reflux, the composition difference between corresponding streams on adjacent stages is a maximum and the required number of ideal stages is minimized. As the recycle ratio is decreased, this composition difference decreases and the required number of ideal stages increases. At some point the recycle ratio reaches a minimum value where the cascade just ceases to separate. This condition is known as minimum reflux, (Ri)min, and occurs at the point within the cascade where the composition difference between corresponding streams on adjacent stages is zero. For example, in distillation of non-azeotropic mixtures a constant recycle ratio is typically used for all stages in the cascade and the minimum recycle condition occurs at the feed stage. Minimum recycle results when the operating lines for the enriching and stripping sections meet the equilibrium line. The result is an invariant zone or pinch point where an infinite number of stages are required to reach the composition at which the operating and equilibrium lines intersect. 71 For a reflux ratio approaching the minimum value, separation ceases at some point in the cascade and the desired separation cannot be obtained irregardless of the number of ideal stages used. A condition of minimum reflux for any stage i is expressed mathematically as: Yi+i = Yi (45) The minimum recycle ratio for a given stage in the enriching section, up to and including the feed stage is: Yp(QXitl-X1) - Q X 1 (R i ) min = --------------------- (4- = If 2 , 3, , nF) (46) (Q-I)X1 (I-X1) Likewise, in the stripping section, the minimum reflux ratio for any stage above the feed stage is: Wtyi-Xw) (Ri ) min — (i- — nF+1, nF+2, nF+3,...., H ^ 1 ) (47) P ( Q - I ) X 1( I - Y 1 ) Minimum reflux is impractical since no separation is obtained irregardless of the number of ideal stages used in the cascade. A knowledge of the minimum reflux for stages in the enriching or stripping sections as given by equations (46) and (47) is necessary to insure that actual values.of reflux are greater than the minimum at a given stage. This insures that fractionation actually occurs in the cascade. A salient feature of the minimum recycle ratio is that it increases as the composition departs more and more from the product or waste compositions. Thus, the maximum requirements for reflux occurs at the feed stage and these requirements decrease steadily as the ends of the cascade are approached. 72 Providing Recycle in the Cascade Two types of process equipment are required to provide recycle or alter the exiting recycle ratio at various stages in a cascade based on the isotope exchange reaction. A decomposer is required to convert the liquid complex to gaseous BF3 and liquid donor. Thus, a decomposer provides the gaseous BF3 recycle and is required at all points in the enriching section of a cascade where recycle is required or the recycle ratio is altered. A recombiner combines gaseous BF3 with the donor material to produce the liquid BF3•donor complex. Consequently, the recombiher provides liouid recycle and is associated with the stripping section of the cascade. A minimum of one recombiner and one decomposer is required for the operation of any cascade (this minimum corresponds to the constant recycle case described subsequently). Referring to Figure 9, a recombiner is. necessary at the waste end of the cascade to provide liquid recycle. A decomposer is required at the product end of the cascade to provide gaseous recycle. The design of decomposer and recombiner systems used in actual cascades requires thermodynamic data for the BF3/donor formation reaction. This data was not available, from the experimental work for the various systems studied, but was recommended for future study as previously discussed. 73 Number of Separation Stages In g e n e r a l t h e number of ideal stages required to effect a specified separation cannot be determined directly for a practical cascade. A stagewise computational scheme or graphical method must usually be employed to determine the number of stages needed to effect the required separation. The computer models utilized in this study were designed to determine stage requirements, as well as other design parameters, for the various cascade configurations. Again, it must be emphasized that the lack of stage efficiency data limits this portion of the study to the evaluation of ideal (equilibrium) stage requirements. The number of actual stages in a cascade is a basic design parameter since column cost is generally based on the unit cost of a single stage. For example, based on the previously calculated stage requirements for a cascade operating at total reflux (refer to Table 4), the currently used dimethyl ether system would require 424 ideal stages while the nitromethane system would require 77 ideal stages to perform the same separation. Assuming the cost of a single stage to be independent of the donor used and that stage size or volume remained constant, the cost of the column associated with the dimethyl ether system would be (424/77) or approximately or 5.5 times greater than for the column associated with the nitromethane system. Consequently, a knowledge of the stage requirements for a given donor system provides a rough comparison of capital cost associated with columns utilizing different donors. 74 , Total Interstage Flow The total interstage flow rate through a cascade is the total amount of material, both heads and tails,, processed by the collective stages in the cascade to produce the desired quantity and purity of product. Consequently, the total interstage flow rate is a measure of the size of the separation plant required to perform a specified separation. For example, the total volume of column internals is proportional to the total interplate vapor flow rate through a distillation column. The stagewise modelling process was used to determine the total interstage flow rates associated with the various cascade configurations and donor systems studied. The flow rate of each heads and tails stream exiting each stage in the cascade was calculated. These rates were summed over all stages to determine the total interstage flow rate. For the constant recycle cascade modelled with the dimethyl ether system (vide infra) the total . interstage flow rate was approximately 3.42*105 mols/hr. This means that 342,000 moles of material must be processed through the cascade per hour to produce 2 moles/hour of 10B product enriched to 95%. In isotope separation plants, a substantial amount of the unit production cost is derived from the enormous size of the process equipment in terms of ideal stage requirements and the inventory of process materials available in the cascade as holdup. The volume of column internals will depend on the total interstage flow through the cascade. . Therefore, the total interstage flow rate, in conjunction with the ideal stage requirements, provides a useful measure of the size of various cascade configurations operated with different donor systems. 75 Practical Recycle Ratio For a practical separation plant, the foregoing discussions clearly indicate that the recycle ratio in a cascade must lie between the minimum value and total reflux. At total reflux, the required number" of ideal stages will be a minimum while the total interstage flow is infinite. At the minimum recycle ratio, the cascade just ceases to separate and the number of ideal stages and total interstage flow are both infinite. This suggests that' the total interstage flow for a given cascade performing a specified separation goes through a minimum at some finite value of the recycle ratio between the two extremes of minimum and total reflux. For the value of the recycle ratio where total interstage flow is minimized, the number of ideal stages will be somewhere between the minimum required and an infinite number. It is of interest to examine the effect reflux has on the total interstage flow and ideal stage requirements as an aid in determining a "practical".recycle ratio for isotope separation cascades based on the chemical exchange systems of interest in this study. It is common to express the recycle ratio in a cascade as a function of the minimum reflux for a stage as given by equation (46) for the enriching section. The functional relationship between the practical and minimum recycle ratio is simplest when related by a multiplication factor: y p (QXitl-X1) - Q X 1 R1 = A* (R1)mln = A* --------------------- (48) (Q-I)X1(I-X1) The recycle multiplication factor, A, in equation (48) may take on aqy value from A = I to A = °°. Note that for A = I, R1 = (R1)mIn and as A -» R1 -, a) corresponding to total or infinite reflux. Therefore, the actual 76 or practical recycle ratio expressed by equation (48), as well as the minimum recycle ratio, is dependent upon the separation factor, a,, and the tails stream composition exiting stage i, X i. Furthermore, the practical recycle ratio is greatest at the feed stage in a countercurrent recycle cascade. Since the separation factor is close to unity (a = 1.027 to a = 1.067 @ 30°C) for the boron exchange systems under consideration, X i at the feed point is expected to approximate the feed composition, zF. As a first approximation, equation (48) can be rewritten in terms of the feed composition: yp(azF+l-zF) - azF R1 = A* (Ri)min = A* --------- - ---------- (49) (CK-I)Zf (I-Zf) It is important to note that the practical recycle ratio as expressed by equation (49) is strictly valid only in the limit as a -t I. Total interstage flow and the required number of ideal stages are plotted as a function of 1/A for a = 1.027 in Figure 10. Similarly, the same results for a = 1.067 are shown in Figure 11. The results indicated in these figures are based on the constant recycle cascade model developed and discussed in subsequent sections (vide infra). The selection of inverse multiplication factor, 1/A, as the independent variable provides a convenient method for normalizing the x-axis. Note that 1/A -t 0 as A -t co, or total reflux, and the number of ideal stages for 1/A = 0 corresponds to the minimum as given by equation (23), the Fenske equation. Similarly, as 1/A -» I, the number of stages becomes infinite in accord with the condition of minimum recycle as previously discussed. To ta l In te rs ta ge F lo w (m ol i (T ho us an ds ) I.OOE 103 1000 -C a 7.50E+02- 5.00E+02- a = 1.027 800 600 400 2.50E+02 I I I I I I I I I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/A — 200 1.0 Figure 10. Inverse multiplication factor vs. total interstage flow and number of ideal stages for the dimethyl ether/BFj system. Num ber of Ideal Stages To ta l In te rs ta ge F lo w (m ol si (T ho us an ds ) I .OOE f02 1.067a = 225 8.00E+01- 175 6.00E101 125 Figure 11. Inverse multiplication factor vs. total interstage flow and number of ideal stages for the nitromethane/BFj system. Num ber of Ideal Stages 79 Figures 10 and 11 indicate that total interstage flow indeed goes through a minimum in the vicinity of 1/A = 0.75, corresponding to a recycle ratio of Ri = I.33*(Ri)min. Comparison of these figures indicates that the minimum total interstage flow is consistent over tihe range of separation factors associated with the BF3/donor systems pertinent to this study. However, the required number of ideal stages begins to increase rather sharply in the vicinity of minimum total interstage flow. As a result, a slight increase in recycle ratio would substantially reduce the number of ideal stages without a dramatic increase in the total interstage flow. It is apparent from Figures 10 and 11 that the practical recycle ratio should lie somewhere in the range of 1/A = 0.5 to 0.8, corresponding to Ri = 1.25 to 1.7 times the minimum, respectively, in order that the total interstage flow remain in the vicinity of the minimum. However, the practical recycle ratio must be as large as possible, i.e. near 1.7 times the minimum, in order to keep the ideal stage requirements as low as possible. Obviously, a great deal of latitude exists in the selection the practical recycle ratio, and this selection is an important design and economic factor for a practical separation plant. The determination of an appropriate recycle ratio is typically dependant on the specific system, and hence separation factor, a, used to effect the given separation. Depending on the system,\values of 1.05 to 5 times the minimum recycle ratio are commonly encountered in literature sources [4,39] in accord with the above results. In fact, the selection of the practical recycle ratio will ultimately require ah in depth economic analysis for a particular separation problem and is outside the scope of this project. 80 For isotopic separations, recycle ratios of 1.5 to 1.8 times the minimum are typically reported [4,41]. For the purposes of this study, recycle ratios, where required to be specified, were set at 1.45 times the minimum. Although this value may not be the optimum for the systems under consideration, it approximates the values commonly reported for isotope separations and is likely to approximate the recycle ratio used in the design of actual boron isotope separation systems. Cascade Models Three different types of cascades were modelled in this study: the ideal cascade, the constant recycle cascade, and different squared off cascade configurations. With the ideal cascade, inefficiencies are removed and the total interstage flow rate is minimized. For a specified practical recycle ratio, the constant recycle cascade (a distillation- column is a typical example) requires the minimum number of stages of all recycle cascade configurations. The ideal and constant recycle cascades are limiting cases for the actual design of isotope separation cascades; the constant recycle case minimizes stage requirements while the ideal cascade minimizes total interstage flow. Although a detailed economic analysis is ultimately required, it is probable that both types of cascades are impractical for.the boron isotope separation problem and a balance between the two systems must be devised; such is the purpose of the squared off cascade. A squared off cascade can be designed to approach minimum interstage flow requirements associated with the ideal cascade while the number of separation stages in the squared off cascade approaches those of a constant recycle cascade. 81 If a viable comparison of total interstage flows and stage requirements for the various types of cascades operating with different donor systems is to be made, each cascade must be performing the same separation. Consequently, the external variables specified for each type of cascade in all models were as follows: 0.950 = mol fraction 10B in the product stream 0.198 = mol fraction 10B in the feed stream 0.050 = mol fraction 10B in the waste stream P =2.00 mol/hr = product stream flow rate a = the single stage separation factor for a particular donor With these external variables specified, the feed rate, F, and the waste rate, W, are fixed as specified by equations (36) and (37), respectively. These variables were selected to approximate production rates and purities associated with the currently used dimethyl ether plant as reported in the literature ['2,3,4,36]. Notice that a stripping section was required to produce a waste stream composition substantially lower than the composition of the feed stream. Recall that the stripping section is that portion of the cascade operating between the composition range zP and xw. The need for a stripping section in the design of an actual plant would, require an in depth economic analysis involving the cost of providing fresh BF3 feed and disposal of the 10B depleted waste stream. 82 Ideal Cascade An important type of cascade that is easy to treat theoretically, minimizes total interstage flow, and is generally approximated by all isotope separation plants designed for minimum equipment costs is the Ideal cascade. An ideal cascade is characterized by the following properties: 1. The compositions of the heads and tails streams forming the feed to a stage are the same, expressed mathematically: Yi+i = xi-i = zi (i = 2,3,4,--nT-l) (50) 2. The heads separation factor /3 is constant and equal to the square root of a: P = ao-5 = y (51) The first condition, corresponding to equation (50), is often termed the no-mix criteria. The mixing of streams of different isotopic compositions to form the feed to a separation stage obviously constitutes an inefficiency since it is precisely the reverse of this process that is desired and takes place within the stage itself. The no-mix criteria is a key property of the ideal cascade which fixes the recycle ratio as a function of stage number. This results in minimum equipment size, (stage volume) to separate the isotopic mixture. Heads Separation Factor The ramifications of the second condition, expressed by equation (51), are not intuitively obvious. This condition is necessary to insure minimum total interstage flow, as indicated by the following development. i 83 First, assume that the stage separation factor a is constant for each stage in the cascade. For an ideal cascade, the no-mix criteria, equation (50), may also be expressed in terms of mole ratios: ei-i = tIi-H = Ci (52) Figure 12 shows three stages of an ideal cascade for which this condition holds. First, consider the relationship between the heads separation factors for every other stage in the cascade, e.g. stages i- 1 and i+ 1 in Figure 12. From the definition of (I, equation (29), it follows that: and Pi-i 5 Pin = nil Ci-i niH CiH (53) (54) a ) a Figure 12. Mole ratios in a section of an ideal cascade. 84 Since the cascade is ideal. fi-i = Vi (55) and fi+l = «1 (56) Substituting these relations into equations .(53) and (54): Vi-i Pi-i = (57) Vi Vl+i Pi+i = (58) Ei Dividing equation (58) by equation (57): Pi+l Vl+i Vl (59) Pi-i e i Vl-i \ From equation (52) and the definition of a, equation (28) , the right hand side of (59) is simply a/a or I, thus: j6i+i = (i = 2,3,4,.... nT-l) (60.) Equation (60) indicates that for constant a, the heads separation factor jS is fixed and constant for at least every other stage in the cascade. Next consider the relationship between the heads separation factors on adiacent stages in a section of the cascade shown in Figure 12, i.e. stages i and i—I. Equation (57) is still valid: Pi-i 7i-i Vl (57) and Pi Vi Vl (61) Ti 6I-I The right hand side of (61) is a result of equation (52) for an ideal 85 cascade. Solving equations (57) and (51) for Tji, equating and rearranging: Vi-i PiPi-i = ---- = « (62) £ i-i Equation (62) provides the key result that for an ideal cascade with constant a, the product of the heads separation factors on adjacent stages of the cascade are equal to the stage separation factor a. Expressed mathematically: PlPl-i = (i — 2,3,4> . . . »nT) (63) Equations (60) and (63) suggest that it may be convenient to relate a and /3 through the relationship: /3 = a9 where 0 < q < I (64) The exponential factor q must lie in the prescribed range since it. is easily shown that for q = I or q = 0 , no fractionation occurs and the cascade ceases to separate. Note that for the case of q = 0.5, equation (64) is identical to equation (51). It is of practical interest to examine the effect q has on a plot of recycle ratio versus stage number in the ideal cascade. Such a plot is shown in Figure 13, derived from the ideal cascade computer model {vide infra) for a = 1.05. It is apparent from Figure 13 that for q = 0.5 the recycle ratio increases monotonically from either end of the cascade up to the, feed stage. For q = 0.4 the curve is becoming unstable and appears more as a band than a smooth curve. As the value of q departs further from the central value of 0.5, the curve will exhibit wider oscillations. The behavior of the cascade exhibited in Figure 13 for different values of q in equation (64) can be envisioned as follows. For q = 0.5, R ec yc le R at i 200.000 175.000- q = 0.5 150.000 q = 0.4 125.000- 100.000 ,tiiiillF.....75.000" ...... 50.000 25.000 0.000 200.00150.00100.00 250.0050.00 Stage Number Figure 13. Effect of the exponential factor, q, on the recycle ratio versus stage number curve for the ideal cascade. 87 the amount of material and hence the volume or size of each stage in the cascade decreases smoothly from the feed point toward the waste and product ends of the cascade. Thus the stage volume in an ideal cascade changes monotonically in one dimension for q = 0.5. For values of q ^ 0.5, the stage volume decreases smoothly for either adjacent or opposite stages in the cascade from the feed point to the ends of the cascade as well as from stage to stage. Consequently, stage volume varies in two dimensions for values of q ^ 0.5. This indicates that for q ^ 0.5, half of the cascade, consisting of every other stage, is processing more material than the remaining half and the work of performing the desired separation is not distributed equally between the two halves. ■ Finally, it is advantageous to discern the effect q has on the total interstage flow rate through an ideal cascade. Using.the model for the ideal cascade discussed subsequently, the total interstage flow rate was determined for a variety of q values with a = 1.05. The results are plotted in Figure 14. The important feature indicated by Figure 14 is I ■ that the total interstage flow is a minimum at q = 0.5. Furthermore, as q approaches the limiting values of 0 and I, the total interstage flow becomes infinite. This indicates that as q approaches 0 or I as limits, infinite interstage flow is required to perform the separation. Thus, an ideal cascade is one in which no mixing of streams with different compositions occurs (y1+1 = Z1 = Xvi or r)1+1 = Ti = 0.95), the product stage was located. A similar method was employed to determine the compositions of streams above the feed stage in the stripping.section. Successive use of the no-mix criteria and equation (32) in a stagewise manner provided the compositions of all streams in the stripping section. When the tails stream composition exiting a stage (xq) was less than or equal to the specified waste composition (xtf < 0.05), the waste stage was located. 90 In the above manner, the composition of each stream and the total number of stages in the ideal cascade were determined. With compositions known, the recycle.ratio for each stage required to bring about condition (50), the no-mix criteria, in the enriching section of the cascade is given by: I Yp /3 (I-Yp) Ri = ----- —--- - --- ;--- (/3-1) X 1 I-X 1 (65) Similarly, the necessary recycle ratio required in the stripping section for any stage above the feed point is given by: (W/P) (X1.! - xw) R1 = --------------- (66) (X1-I - X 1) The recycle ratio for each stage in the ideal cascade is calculated from equations (65) and (6 6 ) in the appropriate section. From the definition of recycle ratio, equation (44), the flow rate of the tails stream leaving each stage is simply the recycle ratio for the stage multiplied by the flow rate of the product stream. The heads flow rate leaving each stage is easily determined from material balance equations, (38) and (41) for stages in the enriching and stripping sections, respectively. The total interstage flow rate is the summation of all stream flows exiting the various stages throughout the cascade. The above model provided values for all the important variables throughout the ideal cascade for a given BF3/donor system. A number of these variables were then used to compare the different donor systems studied with the ideal cascade and eventually compare the performance of the other types of cascades modelled. Results and Discussion of the Ideal Cascade Calculations The important process variables from the ideal cascade models with the different donor systems studied experimentally are listed in Table 5. The currently used dimethyl ether system was also modelled based on the separation factor reported in the literature (see Table I). The dimethyl ether system was. used as a reference to compare the consequences of selecting one of the other donor systems studied experimentally for fractionation of boron isotopes. The first column of Table 5 indicates the BF3/donor system along with the appropriate separation factor, a. In order to make a viable comparison, the separation factors associated with each system were for a temperature of 30°C. Thus, isothermal operation of the separation column at this temperature was assumed. The total number of ideal stages, Nt, the number of stages in the- enriching section, Ne,- and the number of stages in the stripping section, N3, are also indicated in Table 5. There is a dramatic increase in the required number of stages as the separation factor is decreased from a = 1.067 for nitromethane to a = 1.027 for dimethyl ether. This trend is expected in. view of the previous discussion involving the Fenske equation (refer to equation (23) and Table 4). For the ideal cascade, stage requirements decrease by nearly 60% for nitromethane as compared to dimethyl ether. Stage requirements for acetone are approximately 30% less than for dimethyl ether. The total number of stages is an indication of the size or height of the column required to perform the desired separation. Note that Ne is the feed stage number as counted from the product end of the cascade. 91 Table 5. Ideal cascade results for the various BFaZdonor systems. System Nt Ne N8 ' Total Interstage Flow (mols/hr) External Process Variables Nitromethane a(30°C). = 1.067 181 134 47 41,900 Yp = 0.9501 x# = 0.0495 F = 12.128 mols/hr W = 10.128 mols/hr DIBK a(30°) = 1.043 280 207 73 99,700 Yp - 0.9507 xH = 0.0494 F = 12.132 mols/hr W - 10.132 mols/hr MIBK a(30°) = 1.039 308 228 80 120,500 yp = 0.9509 Xw = 0.0498 F = 12.161 mols/hr W = 10.161 mols/hr Acetone a(30°) - 1.038 315 233 82 126,400 Yp = 0.9501 X# = 0.0499 F = 12.156 mols/hr W = 10.156 mols/hr Dimethyl Ether a (30°) = 1.027 443 327 116 248,800 Yp = 0.9506 Xh = 0.0494 F = 12.128 mols/hr W = 10.128 mols/hr 93 The total interstage flows through the ideal cascades are also sI tabulated. The reduction of interstage flow with increasing separation factor is even more dramatic that the stage requirements. Interstage flow requirements for the nitromethane system are about 83% less than for the dimethyl ether system, decreasing by a factor of nearly six. Even for acetone, the interstage flow requirements are substantially reduced by a factor of two or roughly 50%. The interstage flows indicated are the minimum amounts required for each donor system in any possible type of recycle cascade arrangement performing the specified separation. The last column of Table 5 shows the values of the external variables yP, xw, and the feed and waste flow rates determined from the. models. These are the values necessary to satisfy external material balances, equations (34) and (35), for the particular BF3/donor systems in the ideal case. Comparison of the external variables indicates that they are close enough to insure each cascade is performing essentially the same separation. The recycle ratio as a ■ function of stage number is depicted graphically in Figure 15 for the ideal cascade with each of the different donors. The conical shape of each curve is typical of the ideal cascade. The "peak" or largest value of recycle coincides with the feed stage for each case. As the separation factor increases from that of dimethyl ether to nitromethane, the required number of ideal stages is observed to decrease. Furthermore, the area under the curve is proportional to the total interstage flow through the cascade and this area also decreases with increasing separation factor. These observations are consistent with the previous discussion of the ideal cascade. DIMETHYL ETHER 350- ACETON 300- MIBK 250- DIBK H 200- NITROM ETHANE 200 250 Stage Number Figure 15. Recycle ratio versus stage number for the ideal cascade with the different donors. 95 Figure 15 indicates that the recycle ratio is greatest at the feed stage and decreases sharply as the ends of the cascade are approached. The amount of material processed by each stage, and hence the stage volume or size, increases from the product stage up to the feed point and then decreases from the feed point to the waste end of the cascade. Therefore, each stage is of a different size and the recycle ratio must be changed at each stage in the ideal cascade. In order to alter the recycle ratio, each stage in the enriching section requires a decomposer to convert the liquid complex to BF3 gas. Similarly, each stage in the stripping section must include a recombiner to convert BF3 gas into liquid complex and alter the recycle ratio. In the ideal cascade, not only is each stage of a different size, but each must incorporate either a decomposer or recombiner for the system to operate properly. Clearly, the interconnection of stages and the operation of the ideal cascade would be extremely complex. Furthermore, the manufacturing and construction costs associated with such a system, would probably be enormous. In general, the actual use of an ideal cascade would probably not be economically feasible. The importance of the ideal cascade lies in the fact that it is theoretically the most efficient design (from the standpoint of minimum equipment size) available to perform the desired separation. This is a result of the no-mix criteria and minimum total interstage flow. For this reason, the ideal cascade provides a convenient basis for comparing the efficiency of other appropriate cascade designs and indicates the direction such designs must take to increase separation efficiency. 96 Constant Recycle Cascade The simplest’ type of recycle scheme is the constant recycle cascade (CRC). The recycle ratio, R1, is specified and constant for every stage in the CRC. For the specified recycle ratio, the constant recycle design provides the minimum number of stages to perform the desired separation for any cascade arrangement. On the other hand, total interstage flow and therefore total cascade size, is greatest in the CRC than for other cascade designs. A typical distillation column is the classical example of a constant recycle cascade. The Constant Recycle Model The general method used for modelling the constant recycle cascade was a straight forward, double iterative procedure. The product composition, yP, product flow rate, P, waste composition, xw, and feed composition, zF, were specified. The recycle ratio was also specified. In the constant recycle cascade, minimum recycle occurs at the feed point in accord with the pinch point previously described. In accord with the previous discussion of practical recycle ratio, equation (49) was used with a value of A = 1.45 to specify the value of R1 at the feed point. With the external variables specified, the feed rate, F , and waste rate, W, were fixed and calculated from equations (36) and (37), respectively. The value of the separation factor, a, was fixed for a specific donor system and was assumed constant for every stage in the cascade. Referring to Figure 9, the calculation process . started at the product stage, defined as stage number I in this study. The tails stream composition exiting the first stage, X 1, was calculated from equation (32), the equilibrium expression. The material balance relation for the 97 enriching section, equation (40), was used to determine the composition of the heads stream exiting stage 2, y2. Equation (32) was then reapplied to stage number 2, and the calculation process repeated. By successive application of the equilibrium and material balance relations in a stepwise iterative process, the number of ideal stages in the enriching section of the cascade were determined. When the composition difference between the tails stream leaving a stage (x^ p-i in Figure 9) and the fresh feed composition, zp, was minimized, the feed stage was located. Once feed stage location was determined, the stripping section material balance, equation (43), was required in the stagewise calculation procedure for all stages above the feed point. The equilibrium expression remained the same for the stripping section stages. When the tails composition exiting a stripping section stage was less than or equal to the specified waste purity, xw, the waste stage was located, all internal material balances were satisfied and the number of ideal stages was determined. However, since each stage is a discrete equilibrium step, the calculated waste composition was seldom equal to the specified value and the conditions of the overall material balances where not met. A second iterative loop around the external variables was therefore required. With the value of xw determined from the first iteration, new feed and waste flow rates were calculated from equations (36) and (37). The other external variables (yP, zF, P and a) arid the recycle ratio remained fixed at their previous values. The entire stagewise iterative process was repeated, beginning at the product stage, until the calculated waste stream composition, xw, satisfied external as well as internal material balances. I 98 From the definition of recycle ratio,. equation (44), the tails stream flow rate exiting each stage was fixed once the recycle ratio was specified. The heads stream flow rate exiting each stage was then determined by rearranging the appropriate material balance, equation (38) or (41) for the enriching or stripping section, respectively. The flow rates of. the-heads and tails streams for each stage was fixed and the total interstage flow rate was the summation of the individual stage flows over the entire cascade. The CRC model provided information regarding the required number of ideal stages, waste stream flow rate and composition, feed stream flow rate, and the total interstage flow rate for the specified separation and donor system. Results and Discussion of the CRC Calculations The important design parameters obtained from the constant recycle cascade models with the various BF3/donor systems studied are listed in Table 6 . The separation factor associated with each donor was for a temperature of 30°C and isothermal column operation was assumed. The recycle ratio indicated in Table 6 was specified for each donor at 1.45 times the minimum requirements at the feed stage in accord with the previous discussion of practical recycle ratio. It is apparent that the total number of required stages, Nt, increases as the separation factor decreases. This is also true for the stage requirements of the enriching section, Ne, and the stripping sectign, Ng. The nitromethane system requires 58% or 195 fewer ideal stages while the acetone system requires 28% or 95 fewer stages than the dimethyl ether Table 6. Constant recycle cascade results for the various BF3Zdonor systems. System Recycle Ratio N1 Ne Ns Total Interstage Flow (mols/hr) External Process Variables Hitn Fenske Eg. Nitromethane a(30°C) = 1.067 102 142 94 48 57,900 xH = 0.0483 F = 12.044 mols/hr W = 10.044 mols/hr 91 DIBK a(30°) - 1.043 160 215 144 71 136,800 xH = 0.0429 F = 12.114 mols/hr W - 10.114 mols/hr 141. MIBK a (30°) - 1.039 176 236 159 77 165,700 X# - 0.0494 F = 12.120 mols/hr W = 10.120 mols/hr 155 Acetone a (30°) = 1.038 181 242 163 79 174,400 xH = 0.0496 F = 12.118 mols/hr W = 10.118 mols/hr 159 Dimethyl Ether a(30°) = 1.027 254 337 , 227 H O 342,000 xw = 0.0494 F = 12.119 mols/hr W = 10.119 mols/hr 222 100 system to perform the specified separation. Note that for each donor system, the constant recycle cascade requires far fewer stages than the corresponding ideal case (refer to Table 5). Comparison of Table 6 with Table 5 indicates that column height is substantially reduced in the constant recycle case for donor systems with larger separation factors. However, the size or volume of each ideal stage in the CRC must be greater to accommodate the larger overall interstage flow. The total interstage flow also decreases as the separation factor is increased. Nitromethane requires approximately 83% less total interstage flow while acetone requires nearly 50% less than for the dimethyl ether system. The total interstage flow of each system in the constant recycle case is considerably more than for the corresponding ideal cascade (refer to Table 5). As a result, the total internal volume and holdup of process materials, i.e. the size of the cascade, is substantially greater for the ■( CRC than for the ideal cascade. The absolute minimum number of ideal stages required to perform the desired separation is given by equation (23), the Fenske equation, previously discussed. This minimum stage requirement, Nmln, obtained from equation (23) for the various donor systems is tabulated in the final column of Table 6 . Note that for each donor system with the specified recycle ratio of 1.45* (R1)rain, approximately 52% more ideal stages than the. absolute minimum are required. Larger recycle ratios would result from increasing the recycle multiplication factor. A, in equation (49) causing a decrease in total ideal stage requirements while increasing the total interstage flow. Conversely, lowering the recycle ratio would increase stage requirements with a concomitant decrease in the total interstage 101 flow. In a detailed economic evaluation, an optimum recycle ratio would be determined. This optimum is expected to be in accord with the specified recycle ratio of I.45*(R1)min as previously discussed. The external variables as determined from the models for the different donor systems are also indicated in Table 6 . The CRC process variables are in excellent agreement with the external process variables for the ideal cascade (Table 5). Consequently, each cascade accomplished essentially the same degree of separation and the comparison is valid. A plot of recycle ratio as a function of stage number for the CRC models with the different donor systems is shown in Figure 16. As indicated, the plot for each donor is rectangular as a result of using a constant recycle ratio. This rectangular shape is characteristic of the CRC. As the separation factor increases from that of the dimethyl ether system to that for nitromethane, both the number of ideal stages and the practical recycle ratio decreases. This results in a reduction of the area under each curve in Figure 16. This area is directly proportional to the total interstage flow through the CRC. Consequently, both the total interstage flow and the number of ideal stages, i.e. the size of the CRC, decreases as the separation factor increases. These observations are consistent with the foregoing results and discussion of the constant recycle cascade. The construction and operation of a constant recycle cascade for the fractionation of boron isotopes is conceivable. It is the simplest device that can be used to achieve the desired separation, although it may not be the best from an economic standpoint. Distillation columns containing 100 actual stages are not uncommon. The CRC would perform the prescribed 350 300- Dimethyl Ether 250 ~ 200- 8. to o & r? 150- 100 Acetone Nitromethane MIBK DIBK 150 200 Stage Number 250 300 350 Figure 16. Recycle ratio versus stage number for the constant recycle cascade with the different donors. 102 103 separation with the minimum number of stages for a specified practical recycle ratio. This property of constant recycle., cascades provides a convenient basis for , stage requirement comparisons between different cascade designs. The CRC is less efficient, in terms of total interstage flow rate, than the ideal case. A compromise between minimum total interstage flow.and minimum stage requirements may ultimately result in a more efficient and practical fractionation system. Squared Off Cascade The total interstage flow is minimized in the ideal cascade while the stage requirements are minimized for the constant recycle cascade operated at a specified recycle ratio and performing the same degree of separation. A realistic approach to the design of an efficient separation system is to find a compromise between these two minimums. Such is the function of the squared off cascade (SOC). "Squaring off" a section of the cascade is a result of utilizing a constant recycle ratio over a consecutive group of stages to perform a portion of the desired overall separation. A "square section" is therefore a portion of the cascade composed of identical stages, that is, a consecutive group of stages with the same separation factor, a, operating with the same (constant) recycle ratio. As such, a square section is typically regarded as an independent separation column which can be treated as a constant recycle cascade, but performs only a fraction of the desired overall separation. A great deal of latitude exists for specifying the number of square sections used in the SOC. Squaring off the entire cascade with a single section results in the constant recycle case. Squaring off each stage in 104 the cascade essentially results in the ideal case. Consequently, minimum f stage requirements are approached as fewer squared sections are used while minimum interstage flow requirements are approached as the number of square sections increases. The design of an efficient SOC requires a compromise between these two opposing minimums. The Squared Off Model The purpose of the SOC is to approximate the shape of the ideal cascade without the complexity of having each stage a different size. The number of possible squared off configurations capable of performing the desired separation are virtually limitless. How closely a particular SOC design approximates ideal behavior will depend on a number of design parameters. The important design variables includes the number of square sections and the number of ideal stages per square section. The CRC previously discussed utilized a specified and constant, recycle ratio (fixed by the feed and product compositions) over each stage in the cascade. As such, the CRC can be considered a squared off cascade utilizing a single square section. Various SOC configurations result by altering the CRC such that two or more constant recycle ratios are utilized. The recycle ratio in the vicinity of the feed stage of an SOC must remain fixed in accord with equation (49) to avoid a pinch point. However, the recycle ratio can be reduced towards the product or waste stages in accord with the ideal cascade concept. Changing the recycle ratio at various points between the feed and the waste or product stages is equivalent to adding square sections to the CRC. Consequently, it is convenient to view the SOC models as propagating from tAe addition of one or more square sections to the CRC model. As a limiting case, the recycle 105 ratio can be altered at every stage in a cascade, when specified in accord with the no-mix criteria and constant /3, the result is the ideal case. . As indicated in previous discussions, the enriching section is that portion of the cascade from the product stage up to and including the feed stage. The stripping section is then defined as the remainder of the cascade from the waste stage up to but not including the feed stage. The feed stage is therefore the dividing line between these two portions of any cascade. Furthermore, the largest minimum recycle ratio necessary to avoid a pinch point in a counter-current cascade will occur at the feed stage. As.a matter of practicality in this regard, square sections added adjacent to the feed stage in either the enriching or stripping section of the SOC will require approximately the same constant recycle ratio, which is fixed at the feed stage by the feed composition. Therefore, it is possible to add any number of square sections to the enriching portion of the SOC while utilizing a single square section to span a portion of the enricher ' (near the feed stage) and the entire stripping section. Conversely, several square sections can be added to the stripping portion of a SOC while including the entire enriching segment and a portion of the stripper in a single square section. Finally, square sections could be incorporated simultaneously into the enriching and stripping segments. I In accord with previous discussions, a larger recycle ratio 'is required on either side of the feed stage than in any other portion of the cascade. Obviously, a great deal of latitude exists in specifying the recycle ratio in a square section and how the square sections are added to the SOC. For simplicity, square sections were added only in the enriching segment of the SOCs for the initial modelling studies. In subsequent 106 models and discussions (vide infra), squared sections were added to the stripping portion of the SOC while maintaining a constant number (two) in the enricher. Consequently, the effects of adding square sections to the different segments of the SOCs were examined independently. By altering the number of squared sections added in the enricher of the SOC models, the impact on cascade size in terms of both ideal stage requirements and total interstage flow was examined. To this end, square cascades composed of 2, 3, 4, and 5 square sections were modelled in this part of the study. The stripping segment in these SOCs were composed of a single square section that utilized the same constant recycle ratio as the adjacent squared off enriching section and the feed stage. The method for specifying the number of ideal stages and hence size of each square section in the SOC models is less apparent. Every square section can be treated mathematically as a constant recycle cascade. In accordance with the CRC models, the recycle ratio must be specified for each squared off section and the number of stages per section depends on the selected value of the recycle ratio. Thus, ideal stage requirements and recycle ratio for a square section are directly related and were specified by the composition range spanned by each square section. The method used in all the SOC models for specifying the range over which each square section operated was to divide the enriching section composition range, as specified by the product and feed stream mole fractions, by the desired number of squared sections. The composition range covered by any square section was specified by the relation: yp - zF 0.95 - 0.198 0.752 Composition range = -------------- = ------------- = (67) # of sections # of sects. # of sects. 107 Thus, for the SOC model with two squared off sections, each section spanned the composition range of 0.752/2 = 0.376. The first section operated between mole fractions of yP = 0.95 and = 0.95 - 0.376 = 0.574. The second section covered the remaining composition range of Xi = 0.574 to zF = 0.198. The use of equation (67) results in equivalent composition ranges over each square section in the enriching segment of the cascade. The recycle ratio used in a square section of the SOC was required to be greater than the minimum, (Ri)min,. for that particular section. In accord with equation (49), the practical recycle ratio used in a square section of the' enricher was given by: yp (QXj^tl-X1) - Q X i R1 = A* (Ri)mln = A* --------------------- ' (6 8 ) (Q-I)Xi(I-Xi) Minimum recycle ,was determined for each square section as per equation (6 8 ) with a multiplication factor of A = 1.45. The composition of the tails stream exiting a square section, X i, i.e. the composition numerically closest to the feed composition, was used in equation (6 8 ) to determine the recycle ratio in that particular section. Since each square section in the SOC is itself a constant recycle cascade, the iterative methods previously discussed in accord with the CRC model were applicable to the individual sections. Using a similar stages wise iterative procedure, stream compositions and flow rates were determined for each stage in a square section. Hence, the SOC modeils required specifying the number of squared sections/ the composition range over which each square section operated, and the recycle ratio used in each section of the cascade in accord with the above methods. 108 Note that the above SOC models, based. on the specification of ! equivalent composition ranges and recycle ratios of 1.45 times the minimum for each square section, does not necessarily insure the best SOC approximation with regards to the ideal cascade. Different combinations of recycle ratios and/or composition ranges could conceivably result in SOCs which would more closely approximate ideal cascade behavior. Ultimately, an optimization procedure based on detailed system design for a specific BF3/donor system is necessary. However, the above models are suitable to establish the appropriate equipment configuration on a comparative or relative basis as opposed to absolute column design. For the specified number of squared sections, the above model provided the required number of ideal stages and the total interstage flow rate through each SOC. These results Were then compared for the different donor systems and ultimately, with the other types of cascades modelled. Results and Discussion of the SOC Calculations > Results from the squared off cascade models containing 2, 3, 4, and 5 sections are listed in Table 7 for the different BF3/donor systems studied. The tabulated results were obtained based on the experimental separation factors at 30°C. Isothermal column operation at that temperature was assumed. For comparative purposes, the results from the CRC (one square section) and the ideal cascade calculations (maximum number of square sections) are included in Table 7. The required number of total Stagesf Nt, and enriching section stages, Ne, as well as the total interstage flow rate increased as the separation factor decreased for the respective donor systems.■ This trend Table 7. Summary of the results from the squared off cascade calculations for the various __________ BF1Zdonor systems._________________________________ ________________________________ System # of Square Sections Nf Np N, Total Interstage Flow (mols/hr) ' xS Feed Rate (mols/hr) Waste Rate (mols/hr) Nitromethane CRC(I) 142 ■ 94 48 57,900 0.0483 12.044 10.044 (XOO0C) = 1.067 2 166 119 47 48,100 0.0495 12.127 10.127 3 185 138 47 47,200 0.0485 12.058 10.058 4 191 144 47 46,800 0.0485 12.062 10.062 , 5 198 151 47 46,700 0.0489 12.088 10.088 tIC(ISl) 181 134 47 41,900 0.0494 12.183 10.128 DIBK CRC(I) 215 144 71 136,800 0.0429 12.113 10.114 a(30o) = 1.043 2 253 182 71 114,100 0.0490 12.093 10.093 3 274 203 71 111,000 0.0490 12.097 10.097 4 289 218 71 110,300 0.0489 12.087 10.087 , 5 301 230 71' 110,000 0.0495 12.125 10.125 tIC(ZBO) 280 207 73 99,700 • 0.0494 12.132 10.132 MIBK CRC(I) 236 159 77 165,700 0.0494 12.120 10.120 a(30°) = 1.039 2 278 200 78 138,200 0.0489 12.088 10.088 3 301 223 78 134,200 0.0482 12.106 10.106 4 317 239 78 133,100 0.0493 12.117 10.117 , s 329 252 77 132,900 0.0495 12.128 10.128 ■ tIcooa) 308 228 80 120,500 0.0498 12.161 10.161 Acetone CRC(I) 242 163 79 174,400 0.0496 12.119 10.119 a(30°) = 1.038 2 285 205 80 145,400 0.0489 12.087 10.087 3 309 229 80 141,500 0.0488 12.083 10.083 4 325 246 79 140,100 0.0493 12.114 10.114 , 5 338 258 80 140,200 0.0492 12.107 10.107 tICOlS) 315 233 82 126,400 0.0499 . 12.156 10.156 Dimethyl Ether CRC(I) 337 227 H O 342,000 0.0494 12.119 10.119 ci(30o) = 1.027 2 396 286 H O 283,900 0.0494 12.121 10.121 3 429 319 H O 276,200 0.0492 12.109 10.109 4 452 342 H O 273,900 0.0495 12.125 10.125 , 5 469 359 H O 273,400 0.0496 12.133 10.133 tIC(443) 443 327 116 248,800 0.0494 12.128 10.128 IC(n) = Ideal Cascade with n square sections where n = Nt, the number of ideal stages. 109 H O is expected based on results from the previously discussed models, and is due to the prescribed separation becoming more difficult as the separation factor decreases. For a given donor (constant a), the total and enriching section stage requirements increased with the number of squared sections. As the number of squared sections increased, the composition range over which each section operates is reduced. This results in a reduction of minimum recycle requirements in accord with equation (6 8 ) (recall actual recycle was set at 1.45* (R1)mln, for each section). A reduction in recycle ratio results in a concomitant increase in the number of ideal stages. The fact that the total number o f 'stages increases as the number of squared sections increases is a salient feature of the squared off cascade. A comparison of the ideal stage requirements between the SOC and ideal cascade models in Table 7 indicates an interesting phenomenon. The three section SOC requires approximately the same number of stages as the ideal cascade for a particular donor system, while the four and five section SOCs require more ideal stages than the corresponding ideal cascade. This anomaly is a result of the method by which the practical recycle ratio was specified in the SOC cascades as given by equation (6 8 ) . By specifying a larger recycle, i.e. a larger value of A in equation (6 8 ), fewer ideal stages would be required in the various SOC models. At some point, the increased recycle ratio would result in all SOCs requiring fewer ideal stages than.the ideal cascades. Note, however, that in all cases, the SOCs require substantially more total interstage flow than the corresponding ideal case. Any further increase in recycle ratio would increase th,e total interstage flow in each SOC model. Ill The waste stream composition, xw, and the fresh feed and waste stream flow rates required to satisfy the external material balances are listed in the last three columns of Table 7. The slight variations in the external variables are unavoidable in the stagewise models since each stage is a discrete equilibrium step. The agreement is sufficient to insure each cascade performs essentially the same degree of overall separation; The number of stripping section stages, N3, remained constant for a given donor system as the number of squared sections changed. This is a result of adding square sections only to the enricher. Note that the total interstage flow would decrease and the ideal stage requirements would increase in the same manner indicated by Table 7 if one or more square sections had been incorporated into the stripping segment concomitantly with the enriching section. By adding square sections not only to the enriching segment, but also the stripping section, the SOCs would more closely approach the performance of the ideal cascade. The effect of adding squared off sections to the stripping portion ,in the SOC model is examined in detail in a subsequent section; The recycle ratio is plotted as a function of stage number for the SOCk with 2, 3, 4 and 5 sections for each of the five different donors in Figures 17 through 21. Regardless of the particular donor, the shape of each curve is a "staircase" with the number of "steps" corresponding directly to the number of squared sections. Consequently, the five section SOC has five "steps" between the product and waste ends of the cascade, the four section model has four steps, etc. The staircase shape of the recycle ratio versus stage number curve is typical of the SOC where 5 Sections 4 Sect Lons 3 Sections 2 Sections 100 Stage Number Figure 17. Recycle ratio versus stage number for the SOC with the nitromethane/BFj donor system. 112 5 Sections 4 Sections 3 Sections 2 Sections Stage Number Figure 18 Recycle ratio versus stage number for the SOC with the DIBK/BF^ donor system. 113 5 Sections 4 Sections 3 Sections 125 2 Sections -Si 100 Stage Number Figure 19. Recycle ratio versus stage number for the SOC with the MIBK/BF3 donor system. ti l 5 Sections 4 Section 3 Sectiont -2 ioo 2 Sections Stage Number Figure 20. Recycle ratio versus stage number for the SOC with the acetone/BFj donor system. 115 250 5 Sections 4 Sections 3 Sections 2 Sections 4: 150- 250 Stage Number Figure 21. Recycle ratio versus stage number for the SOC with the dimethyl ether/BFj donor system. 116 117 the horizontal regions correspond to the constant recycle over a number of stages, i.e. a. square section. These figures provide a graphical representation of where the square sections are located, the recycle ratio used in each square section and the number of ideal stages per section for the SOC models with the donor systems. Table 7 and the area under the curves in Figures 17 through 21 indicate that for a given donor, the total interstage flow decreased as the number of squared sections increased. As the number of sections increases, the amount of material processed by a particular enriching section stage decreases due to a reduction in recycle ratio. This results in reduced volume for each stage in the enriching section and a concomitant decrease in the total interstage flow requirements. The reduction of total interstage flow with an increased number of squared sections is a key property of the squared off cascade. An efficient system must compromise the opposing conditions of minimum stage requirements versus minimum interstage flow. The above results indicate the squared off cascade is adaptable and well suited to this purpose. Comparison of Cascade Models The total interstage flow rate and the number of ideal stages required for a particular cascade configuration are a measure of the size of the necessary process equipment. The results for the three different cascade configurations modelled are reiterated for convenience in Table 8. The total interstage flow rates are between those of the CRC and ideal cascades for each donor. The ideal stage requirements, are a minimum for the constant recycle cascade. Table 8. Comparision of the various BF3Zdonor systems in different models. Cascade Model Ideal Constant Recycle Squared Off System Nt Total Interstage Flow (mols/hr) N 1 Total Interstage Flow (mols/hr) # of Sects. Nt Total Interstage Flow (mols/hr) Nitromethane 2 166 48,100 a(30°C) = 1.067 181 41,900 142 57,900 3 185 47,200 4 191 46,800 5 198 .46,700 DIBK 2 253 114,100 a(30°) = 1.043 280 99,700 215 136,800 3 274 111,000 4 289 110,300 5 301 110,000 MIBK 2 278 138,200 a (30°) = 1.039 308 120,500 236 165,700 3 301 . 134,200 4 317 133,100 5 329 132,900 Acetone 2 285 145,400 a(30°) = 1.038 315 126,400 242 174,400 3 309 141,500 • 4 325 140,100 5 338 140,200 Dimethyl Ether 2 396 283,900 a(30°) = 1.027 443 248,800 337 342,000 3 429 276,200 4 452 273,900 5 469 273,400 I 118 119 Consider the nitromethane/BF3 donor system. With two squared sections, the SOC requires only 24 or 17% more stages than the minimum requirement of 142 stages for the CRC model. On the other hand, the total interstage flow for the two section SOC is 48,100 mols/hr or about 15% greater than the minimum requirement of 41,900 mols/hr for the ideal cascade model. With three sections, 30% more stages are required than for the CRC model and 13% more interstage flow than the ideal case is required. The four section SOC requires 35% more, stages and 12% more interstage flow than the respective minimums. Finally, with five square sections, 39% more stages and 11% more interstage flow is required. It is apparent that the greatest change in the ideal stage and total interstage flow requirements in the SOC, as compared to the constant recycle and ideal cascade minimums, respectively, occurs when two squared sections are used. Addition of the third, fourth, or fifth sections reduces the total interstage flow requirements only slightly while dramatically increasing the ideal stage requirements for the nitromethane system. For the design of a SOC operating at 10% to 15% more interstage flow than the ideal cascade, the use of two squared off sections is the logical choice. A similar comparison for each of the other donor systems listed in Table 8 indicates analogous behavior. In each case, two square sections results in a 12% to 13% increase in the minimum total interstage flow as compared to the ideal cascade or a 16% to 17% decrease as compared to the CRC. The total number of stages is 17% to 18% greater than the minimum ideal stage requirements fixed by the constant recycle model. It is instructive to compare the recycle ratio versus stage number curves for the ideal, CRC and SOC models for a given donor system. Figure 120 22 shows such a plot for the nitromethane/BP3 system with squared off cascades incorporating 3 & 4 square sections. Figure 23 presents this information for the dimethyl ether/BF3 system with the 2 and 5 square section SOC. These plots are representative of any of the donor systems with the different cascade configurations and a varying number of squared sections in the SOC model. The x-axis, indicating stage number, is altered in Figures 22 and 23 from the 'convention adopted in previous, figures representing recycle versus stage number curves. Previously, stages have been numbered consecutively from stage I at the product end of the cascade up through the waste stage. In Figures 22 and 23, the feed stage is counted as stage number zero; enriching section stages are numbered consecutively beginning at the feed point (stage nF is counted as stage 0 ) up to the product stage. The stripping section stages are numbered consecutively with negative numbers beginning with the first stage in the stripping section (stage nF_i is counted as stage number -I) to the waste end of the cascade. With this convention, the number of ideal stages required in either the enriching or. stripping sections of the different cascade configurations are indicated relative to the feed stage in the recycle ratio versus stage number plots. Thus, the feed stage for each cascade coincides with the vertical line indicated in these figures; enriching section stages lie to the right of the vertical "feed stage" line, all stripping section stages are in the region to the left. Figures 22 and 23 indicate an important aspect of the SOC models developed in this study. As previously discussed,, the specification of recycle ratio at 1 . 4 5 times the minimum for each square section and the Feed Stage EnrichingStripping SectionSection175 Ideal -S 100 3 Sections RecycleConstant Stage Number As Counted From Feed Stage Figure 22. Comparison of recycle ratio versus stage number for the nitromethane/BFj donor system with the ideal, CRC, and 3 & 4 section SOC models. 121 Feed Stage 400- EnrichingStripping SectionSection 350- Ideal 300 250- 200 Sections- 150- Sections100- Constant Recycle 25 75 125 175 225 Stage Number As Counted From Feed Stage Figure 23. Comparison of recycle ratio versus stage number for the dimethyl ether/BFj donor system with the ideal, CRC, and 2 & 5 section SOC models. 122 123 use of equal composition ranges across which each square section operates, results in SOCs which adequately approximate the taper of the ideal cascade. This is not to imply these models are the "best" approximation of ideal behavior; rather, that they are reasonably approximations of ideal behavior. It is apparent from Figures 22 and 23 that the ideal stage requirements for the CRC are at a minimum while the area under the curve (total int'erstage flow) is at a maximum as compared with the other configurations. As the number of square sections used in the SOC model increases, the stage requirements increase and the total interstage flow (area) decreases. ' Finally, in the case of the ideal cascade, the total interstage flow is minimized. These graphical presentations visually indicate the effect of using an increased number of square sections to approximate ideal cascade behavior in accord with the ideas propagated in previous discussions. The above comparison provides general guidelines for the design of fractionating columns based on the isotope exchange reaction associated with boron isotope separation. In general, for the specified recycle ratio of 1.45 times the minimum, two squared sections in the SOC arrangement will result in a cascade operating with 14% to 15% more total interstage flow than the corresponding ideal cascade. The same SOC requires 17% to 18% more ideal stages than the.constant recycle cascade. This appears to be the most logical design based on the specified parameters since'the addition of a tihird column would reduce the total interstage flow by only an additional 2% to 3%, while ideal stage requirements would increase by approximately 12% to 13%. IEffect of the Stripping Section The discussion to this point has focussed on the impact adding square sections to the enriching segment has on SOC design. As was indicated, the function of the SOC is to approximate the shape of the ideal cascade without the complexity of having each stage a different size. It is intuitively obvious from Figures 22 and 23 that incorporating two (or more) squared off sections in the stripping segment would result in an SdC design more closely approximating the ideal "taper". On the other hand, the optimum tails composition, which could in fact differ from the specified value of Xw = 0.05, must ultimately come from detailed design work outside the scope of this study. For this reason, the waste composition, and therefore the requirements of the stripping section, are uncertain. In some instances it could be economically advantageous to completely eliminate the stripping section. In light of these uncertainties, the purpose of this section is twofold. First, it is of interest to examine the impact additional squared off sections in the stripping segment has on SOC design. Secondly, it is appropriate to consider the impact complete elimination of the stripping section would have on the design, and specifically the size, of a squared off cascade. Addition of Square Sections to the Stripper It was indicated in conjunction with Figures 22 and 23 that the shape and size of the ideal cascade would be more closely approximated if additional square sections were utilized in the stripping segment of the SOC. In the previous models, the stripping section was completely \ incorporated into a single, large square section which included the feed 124 125 stage and a portion of the enricher. Based on the results previously presented, adding several squared off sections to the stripper was expected to reduce total interstage flow and increase ideal stage requirements as more square sections were incorporated into the stripping section. If the purpose of the SOC is to approximate ideal behavior, these effects must, at least briefly, be examined. The two section SOC model developed and discussed previously was taken as the base case or starting point for the squared off stripping section SOC calculations. The external variables, i.e. the external compositions and flow rates, were specified at their previous values. The composition range over which each square enriching section . operated was determined as per equation (67). A similar relationship was applied to the composition ranges for each square section in the stripper: zP - x w 0.198 - 0.05 0.148 Composition range = -------------- = ---- - ------- --------------(69) # of sections # of sects. # of sects. Equation (69) implies equivalent composition ranges over each square stripping section, just as equation (67) resulted in equivalent composition ranges in each (squared off) enriching section. Thus, by using two square sections in the stripping portion of the cascade, each section spanned the composition range of 0.148/2, = 0.074. The first 'square section operated between the feed composition, zF = 0.198, and a waste composition of x^ = 0.198 — 0.074 = 0.124. This square section actually included the feed stage and a portion of the enriching segment. The second square section covered the remaining composition range between X 1 = 0.124 and the mole fraction of the waste stream, xw = 0.05. 126 The recycle ratio in a square section of the stripper was specified by reasoning similar to the arguments which led to equation (6 8 ) for the enriching section. Thus, the recycle ratio was specified by a linear combination of (Ri)1Jin for a square stripping section, equation (47), and the recycle multiplication factor, A, whence: W ( X 1-Xw ) (^i) stripping — A * (70) P ( Q - I ) X 1(I-X1) The recycle multiplication factor in equation (70) was specified at the previously defined value of A = 1.45. The value of the tails stream, X 1, is defined as that value numerically closest to the waste composition in a square section. Using the modifications introduced, in accord with the above relationships, the calculations! procedures were the same as those discussed in conjunction with the earlier SOC models. The results from the SOC containing additional square sections in the stripper are presented in Table 9. The CRC and ideal cascade results previously tabulated .and discussed are reiterated in Table 9 for comparison. The nomenclature of Table 9, adopted for SOCs containing additional square sections in the stripper, is rather confusing and warrants further explanation. The two section SOC results are precisely the same as those presented earlier and are included in Table 9 for comparative purposes. Thus, the two square section SOC is equivalent to using a single square section in the stripping portion of the cascade. The three and four square section SOC results presented in Table 9 are not to be confused with those of the earlier models based on increasing the number of square sections in the enricher. The three section SOC includes the first square Table 9. Comparision of the results from the SOC models with the stripping section squared off for the various BF1Zdonor systems. System If of Square Sections N1 Nt N1 Total Interstage Flow (mols/hr) x* Feed Rate (mols/hr) Waste I Rate I (mols/hr) | CRC(I) .142 94 48 57,900 0.0483 12.044 10.044 Nitromethane 2 166 119 47 48,100 0.0495 12.127 10.127 a(30°C) = 1.067 3 174 119 55 47,900 0.0487 12.077 10.027 | . 4 179 119 60 47,800 0.0490 12.096 10.096 | tIC(ISl) 181 134 47 41,900 0.0494 12.183 10.128 CRC(I) 215 144 71 136,800 0.0429 12.113 10.114 DIBK 2 253 182 71 114,100 0.0490 12.093 10.093 a(30o) = 1.043 3 264 182 82 •113,200 0.0487 12.075 10.075 4 269 182 87 112,400 0.0497 12.096 10.141 tIC(280) 280 207 73 99,700 0.0494 12.132 10.132 CRC(I) 236 159 77 165,700 0.0494 12.120 10.120 MIBK 2 278 200 78 138,200 0.0489 12.088 10.088 a (30°) = 1.039 3 289 200 89 136,500 0.0487 12.094 ■ 10.094 4 296 200 96 136,200 0.0495 12.129 10.141 tICOOS) 308 228 80 120,500 0.0498 12.161 . 10.161 CRC(I) 242 163 79 ' 174,400 0.0496 12.119 10.119 Acetone 2 285 205 80 145,400 0.0489 12.087 10.087 a(30°) = 1.038 3 296 205 91 143,500 0.0492 12.105 10.105 . 4 303 205 98 143,200 0.0496 12.136 10.136 tICOlB) 315 233 82 126,400 0.0499 12.156 10.156 CRC(I) 337 227 H O 342,000 0.0494 12.119 10.119 Dimethyl Ether 2 " 396 286 H O 283,900 0.0494 12.121 10.121 a(30°) = 1.027 3 412 286 126 280,600 0.0493 12.112 10.112 . 4 422 286 136 280,200 0.0494 12.123 10.123 tIC (443) 443 327 116 248,800 0.0494 12.128 10.128 tlC(n) = Ideal Cascade with n square sections where n = N1, the number of ideal stages. 1 2 7 128 section covering a portion of the enricher; a second section which includes the remainder of the enricher, the feed stage, and a portion of the stripping section; and a final or third square section which includes the remainder of the stripper. The four section SOC is defined in the same manner as the three section SOC, but includes an additional or fourth square section as part of the stripper.. As expected from previous results and indicated in Table 9, the total number of ideal stages, Nt, and the total number of ideal stripping stages, N3, increases as more square sections are added to the SOC. Note that the number of ideal enriching stages, Ne, remains constant for the two, three, and four section SOC models. This is a consequence of using identically squared enriching sections in each of the models and varying only the 'number of squared sections utilized in the stripper. Table 9 indicates that the addition of a third or fourth section in the stripping portion of the cascade decreases the total interstage flow rate. Consequently, these SOC models more closely approximate the behavior of their ideal cascade counterparts. The greatest decrease in total interstage flow, as compared to the two section SOC, occurs when an additional square section is added to the stripping portion of the cascade. As a result, the three section SOC typically requires only 12% to 13% more total interstage flow than the ideal cascade. For the two section SOC, the total interstage flow is approximately 37% to 38% greater than for the ideal cascade, depending on the particular donor. At the same time, ideal stage requirements increase by approximately 3% to 4% for the three section SOC as compared with the two section SOC. The additional square stripping section in the four section SOC decreases 129 total interstage flow by less than 1 % while increasing, ideal stage requirements by nearly 4% as compared with the three section SOC. A comparison of the results in Table 9 with those in Table 8 for SOCs where square sections were added to the enricher, indicates that virtually the same results could have been obtained by using three square sections in the enricheri' Consequently, for the design basis of this study, the additional complication of using additional square sections in the stripping portion of the SOC is not easily justified. Furthermore, the specified waste composition of x* = 0.05 may not be the best choice from an economic standpoint. Again, it is important to note that the selected design criteria (recycle ratios and composition ranges) may not be the optimum conditions for reducing equipment size. It is instructive to compare the recycle ratio versus stage number curves for several different SOC configurations with the ideal cascade. Figure 24 is such a plot for the nitromethane/BF3 system. Figure .25 presents the corresponding results for dimethyl ether/BF3 system. These; plots are typical for each of the different donors examined. Adopting the convention discussed earlier, the x-axis in these figures is scaled such that the feed stages for the different cascade, configurations coincide with the vertical "feed stage" line. As with the previous SOC models, each vertical region of constant recycle, or "step" represents a square section in the cascade. In accord with the above discussion, these figures indicate the enriching section was unaltered in the different models. Furthermore, the difference between the two and three section SOCs with squared stripping sections and those without squared stripping sections (refer to Figures 22 and 23) can be visually emphasized. Feed Stage EnrichingStripping SectionSection 150 Ideal 100 Sections Sections Section Stage Number As Counted From Feed Stage Figure 24. Effect of adding square sections to the stripping portion of the nitromethane/BF, SOC. 130 Feed Stage 400 EnrichingStripping SectionSection 360- Ideal 300- 250 200- Sections 100 Sections Section 0 50 100 150 200 Stage Number As Counted From Feed Stage Figure 25. Effect of adding square sections to the stripping portion of the dimethyl ether/BFj SOC. 131 Figures 24 and 25 indicate the SOC model more closely approximates the shape of the ideal cascade as the number of square sections used in the stripper of the cascade is increased. The area under the curve decreases as more square sections are incorporated, resulting in decreased total interstage flow through the SOC. However, the number of ideal stripping section stages is larger for both SOC designs than for the ideal cascade. This feature results from the method the recycle ratio was specified in the squared sections. If larger recycle ratios were used, i.e. larger values of A in equation (70), fewer ideal stages would be required both for a given squared off section, and for the entire SOC. In conjunction with Figures 24 and 25, the results in Table .9 clearly indicate the effect using additional square sections in the stripper has on the SOC design. As with the previous results, the total interstage flow is reduced while the ideal stage requirements are increased as more square sections are added to the stripper in the SOC. For the comparative purposes of this study, i.e. in terms of equipment size, the same effect could be realized by adding more square sections to the enricher as opposed to the stripper. To be truly meaningful, the number and location of squared sections in a realistic SOC design would require a detailed economic evaluation and optimization procedure which is outside the scope of this study. . Elimination of the Stripping Section It is of interest to examine the impact that complete elimination of the stripping section would have on the ideal stage and total interstage flow requirements (plant size) in the different cascade configurations. 132 133 Recall that the stripping section.is not required to produce isotopically enriched material of the desired purity. However, stripping is necessary to reduce the amount of fresh feed required by the cascade and results in a concomitant decrease in the amount of waste, dr isotopically depleted material, which is produced. Intuitively, the economic optimum is expected to be somewhere between stripping to a waste composition of 5% and no stripping at all. The decision to incorporate or eliminate the stripping section in the actual design of an isotope separation facility must ultimately rely on a detailed economic evaluation of a particular system and is outside the scope of this study. Rather, the purpose here is to explore the reduction in plant size in terms of the total interstage flow and number of ideal stages in the absence of the stripping section in the different cascade configurations. The additional fresh feed requirements and waste production rates are also emphasized for cascades operated without a stripping section. In the absence of the stripping section, the feed stage of the cascade is also the waste stage. Thus, the isotopically depleted gas stream exiting the feed stage (xnF in Figure 9) is the gaseous waste stream of composition xw. Consequently, the modelling procedures’ and enriching section equations for the different cascades discussed previously are applicable with the exception that once the feed stage is located, the waste composition is then known and the stripping section material balances are not required. Except for the waste composition, which was obviously specified as approximately the feed composition, the other external variables were specified at their previous values for each of the 134 different cascade models. Specifying the same feed and 10B enriched product compositions with the same 10B enriched product rate in each case, both with and without stripping, insured a valid comparison since each cascade would produce approximately the same final purity of enriched material (yP = 0.95) for a given feed composition (zF = 0.198). As before, only ideal stages were considered in the comparison. The Ideal Cascade Without Stripping The results from the ideal cascade models without stripping sections are listed in Table 10 for the different BF3/donor systems. As before, the results are based on values of a at a temperature of 30°C for each of the donor systems. In accord with previous results, the total ideal stage requirements and total interstage flow are observed to decrease for each donor as the separation factor is increased. A comparison of the product composition, yP, and the waste composition, xw, for each of the donor systems in the ideal cascade indicates that approximately the same degree of separation was obtained in each case. A comparison of Table 5 and Table 10 for the ideal cascades with and without stripping sections, respectively, indicates that approximately 26% or over one quarter of the total ideal stage requirements are associated with the stripping section irregardless of the donor system. Furthermore, the stripping section consistently accounts for about 38% of the total interstage flow through the ideal cascade. It is apparent from this comparison that elimination of the stripping section results in an ideal cascade requiring substantially fewer ideal stages with a concomitant decrease in total interstage flow. Consequently, the total size of the separation plant can be greatly reduced if a stripping section is not Table 10. Ideal cascade results for the various BF3Zdonor systems without a stripping section. System N1 Total Interstage Flow (mols/hr) Yr Xn Feed Flow Rate (mols/hr) Waste Flow Rate (mols/hr) Nitromethane a(30°C) = 1.067 134 26,100 0.950 0.193 297 295 DIBK a(30°) = 1.043 207 61,700 0.951 0.195 455 453 MIBK a(30°) = 1.039 228 .. 74,800 . 0.951 0.195 501 499 Acetone a(30°) = 1.038 233 78,400 0.950 0.195 513 511 Dimethyl Ether a(30°) = 1.027 327 153,700 0.951 0.196 716 714 135 136 incorporated. An important consideration in the design of an actual separation system would include the equipment cost associated with providing a stripping section. Comparison of Table 5 with Table 10 for.the ideal cascades with and •O without stripping sections, respectively, indicates that the feed and waste flow rates are approximately 25 to 60 times greater, depending on the donor, for the ideal cascade without stripping. This is:a result of eliminating that portion of the cascade above the feed point (the stripping section) which recovers or strips the desired isotope from the waste stream. Consequently, a dramatic increase in fresh feed is required to supply the necessary amount of the desired isotope to meet product purity and flow specifications in accord with previous discussions. An important consideration in eliminating the stripping section would be the increased operating costs associated with supplying much larger quantities of fresh BF3 feed and disposing of larger amounts of slightly isotopically depleted BF3 gas from the waste end of the plant. This of course, assumes that the waste stream has no value, or the same value as the feed. The CRC Without Stripping The modelling results from the constant recycle cascade without a stripping section are shown in Table 11. As previously described, the recycle ratio used in these models was 1.45 times the minimum required at the feed point. As expected, the ideal stage requirements and total interstage flow rates decrease upon substitution of donors with successively larger separation factors. The waste stream compositions of xw = 0.194 to xw = 0.196 are close enough to insure that each CRC is performing approximately the same amount of isotopic fractionation. Table 11. Constant recycle cascade results for the various RF,/donor systems without a stripping section. System Recycle Ratio Nt Total Interstage Flow (mols/hr) x» Feed Flow Rate (mols/hr) Waste Flow Rate (mols/hr) Nitromethane a(30°C) = 1.067 102 94 38,100 0.194 369 367 DIBK a(30°) = 1.043 160 144 91,300 0.195 538 536 MIBK a(30°) = 1.039 176 159 111,200 0.194 39.7 395 Acetone a(30°) = 1.038 181 163 117,000 0.194 415 413 Dimethyl Ether a(30°) = 1.027 254 227 231,300 0.196 661 659 1.37 138 Comparison of Table 6 for the CRC with stripping and"Table 11 for the CRC without stripping indicates that approximately 33% to 34% of the ideal stage requirements are a result of the stripping section. This figure appears to be independent of the donor. Furthermore, about' 33% of the total interstage flow through the CRC occurs in the stripping section. As with the ideal case, the feed and waste flow rates vary from donor to donor and are roughly 30 to 55 times greater than for the constant recycle cascade that includes a stripping section. Again, comparison of the C R C s with and without stripping indicates that the size of the fractionation plant is greatly reduced if the stripping section is eliminated, but more fresh feed is required and a greater volume of waste is produced. The SOC Without Stripping The modelling results for the squared.off cascade with 2, 3, 4, and 5 square sections without stripping sections are tabulated in Table 12 for the different BF3/donor systems. The recycle ratio in each section of the different square cascades was 1.45 times the minimum required for that section as was discussed in conjunction with the earlier SOC models. As with all previous cases, the ideal stage requirements and total interstage flow through the square cascades with a given number of square sections increases as the separation factor decreases for. the different donor systems. . Thus, for the two square section SOC, nitromethane requires fewer ideal stages and less total interstage flow than for any of the other donor systems utilizing two square sections. As with the earlier SOC models, the ideal stage requirements are observed to increase as the number of square sections increased. Likewise, the total interstage flow decreases, as more sections are Table 12. Squared off cascade results for the various BFj/donor systems without a ___________ stripping section.___________________________________ System # of Square Sections Nt Total Interstage Flow (mols/hr) xB Feed Rate (mols/hr) Waste Rate (mols/hr) CRC(I) 94 38,100 0.194 369 367 2 119 .29,300 0.193 336 334 Nitromethane 3 134 28,300 0.191 230 228 a(30°C) = 1.067 4 144 28,000 0.192 248 238 , 5 151 27,900 0.192 272 270 'IC(134) 134 26,100 0.193 297 295 CRC(I) 144 91,300 0.195 540 538 , 2 182 69,500 0.195 445 443 DIBK 3 203 66,300 0.195 460 458 a(30°) = 1.043 4 218 65,700 0.194 424 422 , 5 230 65,900 0.194 350 348 ,IC(207) 207 61,700 0.195 455 453 CRC(I) 159 111,200 0.194 397 395 2 200 84,100 0.195 503 501 MIBK 3 223 80,100 0.196 . 604 602 a(30°) = 1.039 4 239 79,000 0.196 699 697 , 5 252 79,500 0.194 422 420 *IC(228) 228 74,800 0.195 501 499 CRC(I) 163 117,000 0.194 ■ 415 413 2 • 205 88,400 0.195 527 525 Acetone 3 229 84,500 0.195 507 505 a(30°) = 1.038 4 246 83,800 0.194 400 398 , 5 258 83,200 0.196 655 653 'IC(223) 223 78,400 0.195 513 511 CRC(I) 227 231,300 0.196 661 659 2 286 173,200 0.196 672 670 Dimethyl Ether 3 319 165,500 0.195 585 583 a(30°) = 1.027 4 342 163,100 0.196 696 694 , 5 359 162,700 0.196 803 801 IC(327) 327 153,700 0.196 716 714 IC(n) = Ideal Cascade with n square sections where n= Nt, the number of ideal stages. 139 utilized in the cascade. These observations are expected based on the earlier results and discussion of the previous' models incorporating stripping sections. Comparing the- results of the SOC models with stripping•sections listed in Table 7 to those without stripping sections in Table 12 indicates the relative effect the stripping section has on the squared off cascade. With the nitromethane system and the two section SOC, the stripping section requires approximately 28% more ideal stages than the same cascade without stripping. For the same donor but with three square sections, about 26% more ideal stages are required with the use of a stripping section. The four square section cascade with stripping requires about 25% more stages and the five section cascade requires approximately 24% more ideal stages than if stripping where eliminated. This trend is consistent when donors other than nitromethane are compared between the different SOC models. For the donors considered, it is apparent that the stripping section accounts for just under 30% of the total ideal stage requirements. The same type of comparison with total flow requirements indicates X . that roughly 40% of the total interstage flow occurs in the stripping section of the square cascade. Consequently, the elimination of the stripping section in the SOC reduces the total interstage flow through the cascade by approximately 40% while ideal stage requirements are reduced by nearly 30%. It is obvious that the stripping section can contribute substantially to the overall cost of a separation facility. While the size of the SOC is greatly reduced by eliminating the stripping section, Table 12 indicates that the fresh feed and waste flow 140 141 rates are dramatically increased. Depending upon the donor, the SOC without stripping requires anywhere from about 20 to 70 times more fresh feed and produces that much more waste material than the same SOC which incorporates a stripping section. Again, it is intuitively obvious that the economic optimum would occur somewhere between stripping to a waste composition of 5% and no stripping at all. For example, in the case of the nitromethane/BF3 two section SOC, it makes little sense to feed 336 moles/hr of feed with a composition of xF = 0.198 and produce 334 moles/hr of waste with a composition of xw = 0.193. The cost associated with purchasing the additional BF3 feed and disposing of the increased amount of waste must be balanced by the additional equipment and operation costs associated with providing and supporting a stripping section. It is of course possible to specify the waste composition, xw, at any value less than the feed composition, zF. In this manner, the size of the stripping section can be adjusted to any number of ideal stages and total interstage flow. For the purposes of this study only two possibilities were considered: no stripping and stripping to a waste composition of xw = 0.05. Finally, once an optimum xw is determined, squaring off the stripping . section may become an alternative. In the final analysis, a detailed economic study is required to determine the optimum between the expenses associated, with incorporating and operating a stripping section and the opposing costs of providing increased amounts of fresh feed and the production of increased amounts of isotopically depleted waste. Such an analysis is outside the scope of this project, but is necessary in the design of practical full scale isotope separation facilities. I142 Energy Requirements It is appropriate at this point to inquire about the energy input necessary to perform the desired separation of boron isotopes in the chemical exchange cascades under discussion. . All separation processes require an input of energy in order to perform the desired fractionation, and the boron isotope separation systems are no exception. Energy is utilized in the system to maintain the required flow rates of process streams through the entire cascade, to overcome frictional losses in the column, and associated piping, and to balance enthalpy changes associated with mixing, chemical reactions, etc. Finally, the overall effect of the isotope exchange system is to unmix the isotopic components in the feed stream to form relatively pure isotopic product streams, hence the entropy of the feed stream must decrease. Since the separation or unmixing process is not spontaneous and the work expended within a cascade to effect a prescribed separation typically increases with the difficulty of separation, isotopic separations are inherently energy intensive processes. The energy requirements for providing and maintaining the necessary reflux through a cascade is readily performed by an analysis developed in accord with the first law of thermodynamics. Similarly, the energy requirements associated with the ^ stagewise separation process are amenable to analysis in accord with the second law. In the absence of all effects which reduce system efficiency, e.g., for a thermodynamically reversible or "ideal" system, the energy necessary to support the separation is the sum of these two contributions. It is from this standpoint that energy requirements for the three different cascade configurations where developed in this portion of the study. Energy Requirements for Providing Recycle in the Cascade Reflux in the cascades under consideration is supplied by the formation reaction previously discussed: ^Ha3aoc BF3 (g) + Donor11) •(======* BF3 -Donor11) (71) ^^diss The formation reaction is assumed completely reversible simply by the addition or removal of heat. The energy removed from the system for equation (71) to proceed in the forward direction as written is given by the molar enthalpy of association, AHagaoc. The energy required to decompose the complex into BF3 gas and the liquid donor, the reverse of reaction (71), is the molar enthalpy of dissociation, AHdiaa. Complete reversibility of equation (71) is implied by assuming: AHlxn = AHdiaa = — AHaaaoc ) (72) For the systems studied experimentally, AHml is unknown (reaction enthalpy data does not exist) but is constant for a particular BF3/donor system. For the dimethyl ether/BF3 system, the association enthalpy is reported [6 ] to be AHaaaoc = -13.8 kcal/mol, indicating that the formation reaction is indeed exothermic. In the enriching section, recycle in the cascade is provided by dissociation of the complex in one or more decomposers. The energy input, 5Qdecompr to a single decomposer is simply: 5Qdecomp. = D * AHdiaa (73) where D is the molar flow rate of material^being decomposed and has the same units as the process streams in the cascade or moIes/hour. , The total 143 144 energy input in the enriching section, AQemichf is. the sum of the energy required by the individual decomposers: ^Qemich ~ ^ ( ^ Qdecomp.) (74) Similarly, for the stripping section, where recycle is provided by formation of the liquid complex in recombiners: ^Qrecomb = C * AHaaaoc (75) ^Qstrip ~ ^ ( ^ Qrecomb.) (76) Thus, the energy input requirements for providing recycle in the different sections of the cascade are directly proportional to the total amounts of material that must be decomposed or recombined in the appropriate process equipment. In conjunction with the appropriate cascade models, it can be shown mathematically that the total amount of material, AD, which must be decomposed in the enriching section of any counter current recycle cascade based on chemical exchange (refer to Figure 9) is given by: AD = Z(D) = (Rnp + 1)*P (77) where RnF is the recycle ratio at the feed stage in the cascade and P is the product flow rate. Furthermore, the total amount of material which must be decomposed in the stripping section of any counter current recycle cascade based on chemical exchange is: AC = Z(C) = (Rnp)*? - W (78) x, where W is the waste stream flow rate in mols/hr. Combining equations (77), (73) and (74), the total energy input to all decomposers in the enriching section is given by: 145 ^ Q e n r ic l i- • ^ ^ d i a a * ( ^ n F " ^ l J P ( 7 9 ) Similarly, in the stripping section, the total energy requirements are given by: AQscrip = AHaaaoc *(RnF*P - W) (80) Equations (79) and (80) are valid measures of the total energy required to provide recycle, independent of the number of decomposers or recombiners incorporated into the enriching or stripping sections of a countercurrent recycle cascade. Furthermore, the recycle ratio can be altered between any two consecutive stages, but a minimum of one decomposer and one recombiner is required at the waste and product ends of the cascade. The total work expended by the cascade to produce and maintain the necessary reflux are fixed once the recycle ratio at the feed stage, RnF, and the waste and product compositions are specified. As a consequence of this rather extraordinary result, the energy requirements for providing reflux in any countercurrent chemical exchange isotope separation recycle cascade are fixed and remain constant once the recycle ratio at the feed point is specified, regardless of the number of points where the recycle ratio is altered. Expressed alternatively: the amount of material decomposed and recombined to provide the specified reflux at the feed point is constant, whether produced entirely at the ends of the cascade, or at numerous points between the feed stage and the two ends. The above analysis leads to an interesting conclusion. The energy supplied to the CRC and different SOC configurations is the same for the specified recycle ratio of I.45*(R1)min at the feed point for a particular BF3/donor system. Recall however, that the recycle ratio at each stage in the ideal cascade is fixed by the no-mix criteria. Mathematically it has 146 been shown [4] that the recycle ratio at the feed point in an ideal cascade is approximately twice the minimum, or 2*(Ri)mln. As a consequence, the energy associated with providing recycle in the ideal cascade cannot be altered, but rather is fixed by the no-mix criteria. Therefore, by specifying smaller recycle ratios than 2*(R1)mln at the feed point for the CRC and SOCs, these cascades are more economical than the ideal cascade in terms of the energy required by the decomposers and recombiners to provide recycle. This result is contrary to . the fundamental concept that the ideal cascade is the most efficient design for performing a given separation. In this, regard, it is apparent that the above analysis does not account for everything that is occurring within the cascade and further consideration must be given to energy requirements of the various cascade configurations. For the models developed in this study, the size and holdup of the process equipment was substantially reduced by successively increasing the number of points where the recycle ratio was altered in the cascade. While this "tapering" action reduced overall equipment size, the energy requirements associated with providing recycle where unaltered provided the specified recycle ratio at the feed point remains constant. As a result, the energy requirements for each of the different models with a particular BF3/donor system and -constant recycle ratio at the feed stage where essentially constant. This result is consistent with literature discussions of the energy requirements for hydrogen and nitrogen isotope separation [43,44] based on chemical exchange recycle cascades. Energy Requirements for Staaewise Separation of Components While the foregoing analysis examined the energy requirements associated with providing recycle in the decomposers and recombiners, it also indicated that a CRC or SOC could be operated more economically than the corresponding ideal cascade. This result is a contradiction of the basic premise behind the ideal cascade and does not completely account for the separation process that is occurring within the system. Therefore, it is of interest to examine the stagewise separation process that is occurring as a result of "unmixing", or separating, the isotopic mixture. Consider a typical separation stage in a countercurrent recycle cascade, such as stage i shown in Figure 26. For the SOC or CRC, streams of different compositions from the stages immediately above and below are mixed to form the feed for stage i. This process is associated with the mixing point indicated in Figure 26. For the ideal cascade, the composition of the streams entering and exiting.the mixing point are equivalent due to the no-mix criteria. It is precisely the opposite of this process which is occurring within the stage. Consequently, for the SOC and CRC, the stage must overcome the effect of re-mixing streams of different compositions at the mixing point and provide a fraction of the desired overall separation. In the ideal cascade however, the inefficiency associated with the mixing point is removed and the energy required for the unmixing or separation process will be a minimum. This condition of minimum energy input is a primary basis upon which the ideal 147 cascade concept is based. 148 Mixing Point Stage i Figure 26. Typical stage from a countercurrent recycle cascade. It is advantageous to consider the mixing point and stage as shown in Figure 26 independently for an energy analysis of the stagewise separation process. The logical starting point for such an evaluation is the Gibbs Function for the mixing process: dGmix = AHmix - TASmix (81) The subscripts in the above equation indicate the respective thermodynamic quantities are considered only for mixing of streams with different isotopic compositions. The enthalpy of mixing, AHmix, is unknown for the BF3/donor systems under consideration. However, isotopic species are often considered to form the proverbial "ideal" gas or liquid mixtures, e.g., the enthalpy of mixing for gaseous 10BF3 and 11BF3 is approximately zero. Therefore, AHmix is anticipated to be relatively small and is assumed to be identically zero for the systems being studied. • 149 The entropy of mixing in equation (81) can be expressed as: ^Smix = [ (x i x i) feed — (x i x i) products] (®2) The mole fractions are those entering or leaving in the feed and product streams for either the mixing point or stage. Using the nomenclature of Figure 26, expanding equation (82) , and combining with equation (81) provides the key relation for energy requirements about the mixing point: ASmix Pt = RTiG1.![X1.^ n X1.! + .(I-Xill)In (I " xi-i) ] +Li+i[yi+iln yi+1 + (l-yi+1)ln (I - yi+i) ] (83), -F1Iz1In Z1 + (I-Z1)In (I-Z1)]) The respective flow rates (L, G, and Z) are incorporated in equation (83) to convert AS from a molar basis to that of energy consumption, or kJ/hr. With the understanding that the above relation was derived only for mixing of ideal gases or liquids, the "mix" subscript has also been dropped. In a similar fashion, the energy requirements for the separation process occurring within the stage can be derived: . ASatage = RTiF1 [Z1In Z1 + (I-Z1) ] - L1Iy1In yi + (l-y^ln (l-yj ] -GjJ x 1In X1 + (I-X1)In (I-X1) ] } ( 84) Note that the above equations derived for both the mixing point and stage are valid only for a general stage as shown in Figure 26. These equations are not valid for the feed stage nor for the waste or. product stages, and must be appropriately altered when applied at these points in the cascade. Furthermore, for the ideal cascade, mole fractions of the feed streams entering at the mixing point, Xlll and y1+1, are equal to the composition exiting the mixing point, Z1. Consequently, equation (83) is identically zero at every stage in the ideal cascade. 150 Equations (83) and (84) were derived and used to evaluate the work expended in the isotope separation process at a given stage in the cascade based on the second law of thermodynamics. In conjunction with the cascade models, the total work required by a cascade to perform the prescribed separation was determined by summing the individual energy terms about the mixing points or individual stages across the entire cascade: Emix - 2i f^flix pt, i (85) 'stage — Ei ^'stage, i (86) It is important to understand the significance of each work term as established by equations (85) and (86). The total work of mixing, Emix, as given by equation (85) can be interpreted as lost work due to the generation of entropy associated with the mixing process. Consequently, the numerical value of Emix is negative, which implies ASmix is positive about the individual mixing points. This concurs with the accepted sign convention that a (spontaneous) mixing process results in an increase in entropy. In the same manner, the sum of the work terms associated with the separation process within the individual stages, Eatage, is a measure of the actual separative work performed in the cascade and is therefore positive. Consequently, ASmix as given by equation (82) is negative for the individual stages in accord with the concept that separation or unmixing decreases the entropy of the isotopic mixture. It is therefore possible to define and evaluate the ideal or thermodynamic minimum work, sUUoir required by the cascade to accomplish the desired separation: ■Eideal = Eatage + Emix (87 ) 151 Table 13. Comparison of different types of energy input and total interstage flow for the various cascade configurations with the nitromethane/BF3 donor system. # of Sections s^tage (kJ/hr) Emix (kJ/hr) Eideal (kJ/hr) Recycle Energy (kJ/hr) Total Interstage Flow (kJ/hr) I (CRC) 11.939 -2.729 9.210 258* AHdlas 57,900 2 10.709 -1.521 9.188 258*AHdiaa 48,100 3 10.081 -0.888 9.193 258*AHdlaa 47,200 4 9.856 -0.642 9.215 258*AHdiaa 46,800 5 9.721 -0.530 9.192 258* AHdiaa 46,700 Ideal 9.183 9.183 2 97* AHdiaa 41,900 Results of calculations involving the different cascade models incorporating the above energy considerations are shown in Table 13. The calculations were performed only for the BF3Znitromethane system. Each of the other donor systems are expected to parallel these trends by analogy with previous modelling results. The total separative work, Eacage, lost work, Emix, and the thermodynamic minimum or ideal work, Eldeal are indicated in Table 13. These quantities were determined on a stage wise basis from the appropriate model and summed across the entire cascade in accord with the previous discussion. Table 13 indicates that the total separative energy, Egcage, is a maximum for'the constant recycle cascade and decreases as progressively more square sections are to the SOC. For the ideal cascade, Eslage corresponds to the thermodynamic minimum since the lost energy term, resulting from mixing streams of different compositions, is identically zero. 152 The lost work, Emix, is greatest (more negative) for the CRC, decreases as more square sections are incorporated into the SOC, and is identically zero for the ideal cascade. This is a direct consequence of removing inefficiencies associated with the mixing point as more square sections are incorporated into the SOC design. The use of additional square sections in the SOC reduces inefficiencies associated with the mixing points. Consequently, the thermodynamic minimum energy defined by the ideal cascade is approached as more sections are utilized in the SOC. The thermodynamic minimum work, Eldeal, is approximately the same for all cascade configurations when effects of the mixing process are removed. Slight differences in Eideal for the different designs are due to small differences in waste stream compositions and flow rates in the various cascades. (Recall that the waste composition and flow rate varies slightly for the different cascade configurations due to the use of discrete equilibrium stages in the modelling process.) The ramifications of the above results are apparent when the ideal cascade is considered. Due to the no—mix criteria,.Emix is identically zero for the ideal- cascade and equation (87) indicates that Eldeal = Estage. In conjunction with the above discussions, it is intuitively obvious that the ideal cascade has the potential to perform the desired separation with the minimum thermodynamic energy input for all possible countercurrent recycle cascade designs as a result of eliminating the inefficiencies of mixing. Alternatively, the CRC consumes the greatest amount of energy, and any degree of compromise between these limiting cases defined by the CRC and ideal cascade can be achieved with SOC configurations. These results were derived and are consistent with the second law of thermodynamics. / 153 Another interesting aspect in the energy analysis of recycle cascades evolves from an examination of energy requirements as a function of recycle ratio for a given cascade configuration. For the CRC and BF3/nitromethane system, energy requirements (Egcage and Eldeal) were determined as a function of inverse recycle factor, 1/A. A similar type of analysis was previously used by defining the recycle factor. A, to establish minimum total interstage flow. Separative and ideal work are plotted as a function of 1/A in Figure 27 for the CRC with nitromethane as the donor. As expected the minimum or ideal energy of separation, Eldeal, indicated by the dotted line in Figure 27, is essentially constant and independent of recycle factor. However, as the recycle ratio decreases from total reflux (1/A -» 0), the total energy requirements of the cascade decreases. The total separative work, Eacage, goes through a minimum in the vicinity of 1/A = 0.75, corresponding to a recycle ratio of Rnp = 1.34*(R1)mln, and then increases as minimum reflux (1/A = I) is approached. For comparison, total interstage flow is also indicated in Figure 27 as a function of 1/A. The interesting point is that the energy requirements of the CRC parallel the total interstage flow requirements as the recycle ratio varies. In fact, the two quantities go through a minimum at the same "optimum" recycle ratio of approximately 1.35*(R1)mln. This result lends further credibility to the selection of recycle ratio in the CRC and SOC models at 1.45* (R1)mln. Up to this point, two contributions to the energy requirements of the separation cascades under consideration have been examined: that associated with providing reflux in the decomposer/recombiner systems and that of providing the separative work within the individual stages. In 9500020.00 16.00- -65000 16.00- -75000 14.00 Total Separative Energy 65000 12.00- Ideal (Minimum) Energy Total Interstage Flow -55000 10.00 45000 Figure 27. Ideal energy, separative energy and total interstage flow as a function of inverse recycle factor (1/A) for the CRC with the nitromethane/BFj donor system. T otal Interstage Flow (m ol/hr) 155 reality, both types of energy must be provided for the cascade to function in the designed manner. Furthermore, the utilization of energy within the systems is not as efficient as the above discussion indicates and additional energy to support non-idealities in the actual process are required. As a minimum, the combination of recycle and separative energy must be provided for each of the cascade configurations to support the desired fractionation. Figure 28 shows each type of energy requirement as a function of recycle ratio for the CRC with the nitromethane/BF3 donor system. The recycle energy indicated in Figure 28 is based on equation (79) which was derived only for the decomposer. The derivation of this equation was based on the fact that AHdlaa was unknown but constant for the nitromethane/BF3 system. Note that the recycle energy is a linear function of recycle ratio, as expected from equation (79). It is apparent that the minimum work for recycle is associated with minimum reflux, while maximum recycle energy is required at total reflux. Consequently, it is economical to operate the cascade with the lowest possible recycle ratio at the feed stage. The work required to support the stagewise separation process in the cascade, Eatage, previously discussed is also indicated in Figure 28. The important point to be emphasized in Figure 28 is the required amount of energy supplied to the CRC operating at a specified recycle ratio and given donor is the sum of the two discussed contributions. For the optimum recycle ratio of 1.34*(R1)mln with the nitromethane/BF3 donor system, 11.8 kJ/hr must be provided to overcome the mixing process and separate the isotopic mixture. At the same time, roughly 190*AHdlaa kJ/hr 18.00 17.00 -450 16.00 Total Separative Energy 15.00- -400 14.00 13.00- -350 12.00- > 2 il.oo- -300 10.00- Energy of Providing Recycle -250 9.00- 8.00- -200 7.00- 125 Recycle Ratio Figure 28. Recycle and separative energy as a function of recycle ratio for the CRC with the nitromethane\BF3 donor system. rcle E nergyZ A H 4ia (kJ/hr) 157 must be provided- in the decomposer to maintain the necessary recycle ratio in the enriching section of the cascade. If AHdlaa is assumed to be 10 kJ/mol (similar to the dimethyl ether/BF3 system), the total energy input requirements for the system would be: ' ABtoeal' = 11.8 + 190*10 = 1912 kJ/hr (8 8 ) It is apparent from equation (8 8 ) that the greatest contribution to the energy requirements of the CRC result from providing the necessary recycle. As noted earlier, this energy is constant for the different cascade configurations for a constant recycle ratio at the feed stage. The above analysis and results cannot incorporate' quantitative measures for estimating all possible energy contributions in the recycle cascades under consideration. The necessary directions cascade design must take to minimize the energy requirements are apparent from the above analysis. First, the recycle ratio at the feed stage must be maintained as close as possible to the "optimum" value. Recall that consideration must be given to the required number of ideal stages to insure an inordinate number is not necessary. This criteria insures that the energy requirements of providing recycle is as low as possible. Secondly, by incorporating a number of squared off sections, the energy requirements necessary to provide separative work to the cascade will more closely approximate the thermodynamic minimum associated with the ideal case. Finally, the above analysis provides a thermodynamic basis establishing how and why the ideal cascade is potentially the most energy efficient type of cascade for a specified separation. Such an analysis has not been reported in the literature for separatipns based on chemical exchange reactions. 158 CONCEPTUAL BORON ISOTOPE ENRICHMENT PLANT The ultimate goal of research in the area of boron isotope separation (would , be to devise a large scale method' economically competitive or superior to the currently used dimethyl ether/BF3 system. The experimental portion of this study was directed at examining several different donors with the concept that any one could prove potentially useful in a large scale fractionation scheme. Based on the magnitude of the separation factor, a, the nitromethane/BF3 isotope exchange system indicates the greatest potential for achieving the desired goal. The modelling and analysis studies were conceived to examine the benefits of utilizing the various donor systems in terms of large scale plant design and to indicate the configuration of a suitable separation process. Within the confines of the specific designs considered in this study, the two section SOC, used in conjunction with nitromethane as the donor, is an appropriate system for the large scale fractionation of the isotopes of boron. A conceptual process flow schematic . for the two square section cascade utilizing the nitromethane/BF3 donor system is shown in Figure 29. This process is based entirely on the modelling and analysis results. Each column corresponds to a square section of the cascade and contains the appropriate number of identical ideal stages to perform the specified amount of separation for that section. The first section, denoted as column #1, contains the feed stage, a portion of the enriching section, and the entire stripping section. This Donor 194.8 mols/hr Waste 10.0 mols/hr x = 0.05 < 3 Donor 12.0 mols/hr Column #1 Recycle Ratio = 102.4 95 Ideal Stages 38,500 mols/hr Total Interstage Flow 12.0 mols/hr Stripping (47 Stages) Liquid Feed 12.0 mols/hr Enriching (48 Stages) Product 2.0 mols/hr y = 0.95 Donor 40.0 mols/hr Donor 166.8 mols/hr Decomposer #2 Recombiner Decomposer #1 Fresh Feed Recombiner Recycle Ratio = 33.1 9,600 mols/hr Total Interstage Flow 71 Ideal Stages Column #2 Figure 29. Process flow schematic for the two section SOC with the nitromethane/BFj donor system. 159 160 is the largest of the two sections. A fraction of the isotopically depleted BF3 gas is cut from the stream exiting the top of this column (corresponding to the stripping section) as the gaseous waste. The remainder of this gas stream is passed to a recombiner where it is reacted with an equimolar amount of the pure nitromethane donor to form the liquid complex. The nitromethane/BF3 complex formed in the recombiner is returned to the top of the column as liquid recycle. A fraction of the liquid complex exiting the bottom of the first section flows to a decomposer where it is completely dissociated (thermal reversal of the formation reaction) into equimolar amounts ,gaseous BF3 and the liquid donor. The remainder of this stream forms the liquid feed to the top of column #2, the second square section. The BF3 gas generated from the complex in decomposer # 1 is combined with the gas stream exiting the top of the second column and returned to the bottom of the first column as gaseous recycle. The donor recovered from the decomposer would, if necessary, be purified in a separate system and stored for reuse in the recombiners. The second Square section, corresponding to column #2, is the smaller of the two columns and produces the final product of the specified composition. The entire liquid stream exiting the base of this section flows to decomposer #2 where it is thermally decomposed to gaseous BF3 and nitromethane. The donor is reclaimed for reuse and a fraction of the gas stream exiting the decomposer is taken as the isotopically enriched BF3 product. The remainder is returned to the bottom of column #2 as gaseous recycle. 161 Note that the total amount of donor exiting the decomposers is equivalent to the amount of nitromethane required in the recombiners. This is a result of assuming that the formation reaction is completely reversible; the donor is neither consumed nor replaced in the exchange system. Consequently, the donor is continuously recycled and reused in the separation system. In the event of irreversible decomposition of the nitromethane/BF3 complex, the appropriate donor purification system would be incorporated into the actual plant design. The first and largest column in the cascade includes the entire stripping section. Of the 95 ideal stages included in this column, 47 of these stages located above the feed stage in the upper portion of the column, form the stripping section. The balance, or 48 ideal stages, located from the bottom of the column up to and including the feed stage, are a portion of the enriching section. In accord with previous discussions, the size of the stripping section could be reduced or even eliminated entirely, depending on the desired waste composition. If stripping were completely eliminated, the first section would contain only 48 ideal stages with a total interstage flow rate of 19,900 mols/hr through the column. Therefore, even in the absence of stripping, column #1 would still be the largest in terms of total interstage flow. Note that the recycle ratio for this section of the cascade would be the same if the size of the stripping section were reduced or even eliminated. This is a consequence of the fact that the specified recycle ratio (1.45 times the minimum) is fixed by the feed and product compositions in accord with equation (49). This specified recycle ratio through the column also fixes the energy requirements to the cascade. 162 The total interstage flow through the individual columns is greatest in the .first section or column, which includes the feed stage, a portion of the enriching section, and the entire stripping section, and smallest in the final, or product, column. Recall that the total interstage flow through the two section SOC, as determined from the model, was 48,100 mols/hr (Table 7). Of this, 38,500 mols/hr or 80% of the total interstage flow occurs in the first section. The balance, 9,600 mols/hr or roughly 2 0 % of the total interstage flow through the system, occurs in the final (and smallest) section. This is a consequence of decreasing the recycle ratio in the different sections as the product end of the cascade is approached. These ,trends are expected and consistent with previous discussions. In fact, the desired objective of the SOC design is a reduction in total interstage flow with a concomitant decrease in column size as the product end of the cascade is approached. It is of interest to compare the above conceptual design of the proposed nitromethane/BF3 two section SOC with the actual large scale facility using the dimethyl ether/BF3 system. The appropriate literature sources [2,3,36] are somewhat vague regarding the necessary operating variables (i.e. recycle ratios, actual stages, etc.) of the commercial plant to develop a detailed model. However, the actual plant is reported to perform the same separation in terms of the external compositions and flow rates as the conceptual system. The commercial facility reportedly operates with two columns [36]. Consequently, the two section SOC model for the dimethyl ether/BF3 system developed in this study was used to approximate actual plant behavior. A process flow schematic for the two section SOC based on the dimethyl ether/BF3 system is shown in Figure 30. Donor 488.4 mols/hr Waste 10.1 mols/hr X = 0.05 < 3 Donor 12.1 mols/hr Column #1 Recycle Ratio = 254 224 Ideal Stages 226,900 mols/hr Total Interstage FlowFeed 12.1 mols/hr Stripping (110 Stages) Liquid Feed 12.1 mols/hr Enriching (114 Stages) Product 2.0 mols/hr 'y = 0.95 Donor 343.7 mols/hr Donor 166.8 mols/hr Decomposer Recombiner Decomposer Fresh Feed Recombiner Recycle Ratio = 82.4 57,000 mols/hr Total Interstage Flow 172 Ideal Stages Column #2 Figure 30. Process flow schematic for the two section SOC with the dimethyl ether/BFj donor system. 163 164 The operation of the two separation schemes is essentially the same. The waste, product, and feed compositions and flow rates, or the external variables, are approximately equal for both systems.. The first section, column #1 in Figure 30, contains a portion of the enriching section, including the feed stage, and the entire stripping section. The decomposer at the base of this column serves to alter the recycle ratio between the two sections. Column #1 contains 224 ideal stages with a total interstage flow rate of 226,900 mols/hr. Consequently, this is the largest section of the cascade, providing roughly 80% of the total interstage flow through the entire system. The second column contains 172 ideal enriching section stages and produces the isotopically enriched gaseous product. This is the smallest section with a total interstage flow of 57,000 mols/hr through the column. This interstage flow accounts for the remainder or 20% of the total interstage flow through the cascade. As with the conceptual nitromethane process, the two section dimethyl ether SOC is designed with a smaller column at the product end of the system in order to the approximate behavior of an ideal cascade. A comparison of the two different conceptual designs indicates both the number of ideal stages and total interstage flow is significantly reduced with the nitromethane donor system. For two square sections with the nitromethane system, 166 ideal stages are required to perform the specified separation as compared to 396 ideal stages for the dimethyl ether design. Thus, the nitromethane/BF3 system requires 230 or 58% fewer stages than the dimethyl ether system. Furthermore, the total interstage flow is 235,800 mols/hr or 83% less for the nitromethane/BF3 system than 165 for the dimethyl ether SOC performing the same amount of isotopic fractionation. Note that for the dimethyl ether system, the decomposers process a total of 511 mols/hr as compared to 207 mols/hr for the nitromethane system. Consequently, the size of the decomposer and recombiner systems are substantially smaller when nitromethane is used as the donor. From the above discussion, it is obvious that a major benefit of incorporating nitromethane in the large scale separation system would be the immense reduction in the required size of the separation cascade. The experimental and modelling portions of this study ultimately resulted in defining the above conceptual process design for the two section SOC with the nitromethane/BF3 donor system. The major benefit (a reduction in overall cascade size) of such a design relative to the currently used dimethyl ether system was explored. In reality, the design of an actual optimum boron isotope separation plant would be quite complex. A detailed design would relate equipment size, performance and costs to several related process variables such as stream compositions, flow rates, number of stages, recycle ratios and total interstage flow rates for the different cascade designs. The main isotope fractionation system would consist of a large number of separating units or stages with the associated pumps and compressors, heat exchange equipment, connecting piping, and control systems. The entire system would require feed and withdrawal facilities, auxiliary systems, and support and operating personnel. It would probably be enclosed in a suitable structure and be surrounded by the appropriate type of land. The sizes and costs of these, and other, important items must be related to the process variables. For 166 a given design with a specified set of process -variables, the associated costs can in principle be defined. Therefore, for a given design it is possible to select many different sets of values for the process variables and solve for the optimum or minimum cost design by a trial and error procedure. Prior to embarking on a detailed and labor intensive design and economic analysis, feasibility studies similar to the procedures of this work are generally required. A complete feasibility study would include extensions of the experimental and modelling results propagated in this study. The existence and effects of irreversible decomposition of the liquid complex must be established. The reversibility and thermodynamics of the BF3/donor formation reaction must be determined. Furthermore, the kinetics of the isotope exchange reaction with each potential donor should be established. While the physical properties, such as viscosity and density of BF3 gas are tabulated in the literature [42], such data is generally unavailable for the liquid complexes under consideration. The design of process equipment, such as pumps and columns, may rely on a knowledge of these physical properties. Bench scale or pilot plant studies are required to establish stage heights and efficiencies if the number of actual (as opposed to ideal) separation stages is to be determined. The above information would then be incorporated into the design calculations of the modelling and analysis section and a better estimation of feasibility established. The above considerations are necessary and recommended in future studies. Despite the limitations imposed on a more detailed examination of production scale plant design, the results of this study indicate some 167 important directions such designs must take. Plant size is strongly dependent on the magnitude of the separation factor. Potential donors, such as nitromethane or any of the ketones examined, could substantially reduce the size of a separation facility. The cascade configuration also plays an important role regarding plant size. The constant recycle cascade minimized ideal stage requirements while maximizing total interstage flow. The ideal cascade required an increased number of ideal stages but minimized total interstage flow. A number of squared off cascade designs were propagated as a compromise between the performance of the CRC and ideal cascades. Based on these results, the most logical design was the two section SOC configuration used in conjunction with the nitromethane/BF3 exchange system. 168 CONCLUSIONS (1) Acetone, MIBK, DIBK and nitromethane are suitable donors and form relatively stable liquid complexes with BF3. (2) Each of these four donors exhibits larger values of separation factor than dimethyl ether in the boron isotope exchange reaction. In this regard, each is more amenable to large scale fractionation than the dimethyl ether/BF3 system. (3) Nitromethane exhibits separation factors substantially higher than those predicted theoretically or for any known system in boron isotope chemical exchange reactions. This anomaly is postulated to be due to a dual site exchange mechanism. An understanding for the cause of this anomaly could provide valuable insight into the isotope exchange process and donor selection. (4) The' constant recycle cascade minimizes total ideal stage requirements and maximizes total interstage flow. The ideal cascade minimizes total interstage flow with increased ideal stage requirements. Any degree of compromise between these opposing effects can be obtained in a squared off cascade by altering the number of squared sections'. (5) A logical compromise between total interstage flow and ideal stage requirements in ,the squared off cascade can be obtained by using two square sections. 169 (6) A reduction in total interstage flow and ideal stage requirements could be achieved by reducing the size of the stripping section. A reduction in stripping section size would result in an increase in the amounts of fresh feed required and waste produced. (7) The energy requirements of providing reflux in any countercurrent ,recycle cascade depends only on the recycle ratio at the feed stage. Therefore, if the recycle ratio at the feed stage is equivalent in the CRC, SOCs, and ideal cascade, the energy requirements of maintaining the necessary reflux for each of the different cascades will be equal. This condition holds only if each different cascade is performing the same overall separation. As a result of this unique property, CRCs and SOCs can be designed to be more efficient than the ideal cascade in terms of the work expended to provide and maintain the necessary recycle ratio. (8) From the standpoint of re-mixing and separating internal streams “ with different isotopic compositions, the ideal cascade is potentially the most energy efficient system. This is a result of the no—mix criteria upon which the ideal cascade is founded. In this • regard, the CRC is the least energy efficient of the recycle cascade configurations examined; 170 RECOMMENDATIONS FOR FURTHER STUDY (1) Further study with the liquid complexes formed between BF3 gas and the different.donors (acetone, MIBK, DIBK and nitromethane) is necessary to establish rates of irreversible decomposition, reversibility of the formation reaction and physical properties such as viscosity and densities associated with these complexes. (2) Studies into the mechanism of the boron isotope exchange reaction between BF3 and the nitromethane/BF3 complex are strongly suggested. These studies should examine the phenomenon responsible for the large separation factors associated with this system. The suggested starting point would be to use spectroscopic techniques, such as proton or fluorine NMR or perhaps UV-VIS spectroscopy to examine the molecular addition compound. With these techniques, it may be possible to determine the number and arrangement of BF3 molecules associated or bound to a nitromethane molecule in the liquid complex. A knowledge of the bonding arrangement in the complex could help support the dual site exchange mechanism proposed in this study. (3) Bench scale and/or pilot plant studies are required to establish the stage efficiencies and kinetics of isotope exchange with each of the four different donor compounds. Potential bench scale experimental systems readily adapted to examine these parameters have been reported in the literature [24]. REFERENCES CITED 172 • x [1] Murphy, G.M., ed., Separation of Boron Isotopes. National Nuclear Energy Series, Manhattan Project Technical Section, Division III, Vbl. 5, USAEC, Oak Ridge, TN, 1952. [2] Chilton, C.H., Chem. Engr. (Prog. & Technol.) 64(2), 148 (1957). [3] Conn, A.L., Wolf, J.E., Indust. Sc Engr. Chem., 50, No. 9, 1231 (1958). [4] Benedict, M., Pigford, T., Levi H., Nuclear Chemical Engineering, 2nd Ed., McGraw-Hill Book Co. Inc., New York, NY, 1949. [5] Booth, H.S, Martin, D.R., Boron Trifluoride and Its Derivatives, John Wiley & Sons Inc., New York, NY, 1949. [6] Palko, A.A., "The Chemical Separation of Boron Isotopes", ORNL-5418, Oak Ridge National Laboratory, Oak Ridge, TN, June 1978. [7] Palko, A.A, Drury, J.S., Advances in Chemistry Series, ACS Publication #89, 1969, pp. 40-56. [8] Katal'nikov, S.G., Paramonov, R.M., Zh. Fiz. Khim. 40, 401-6 (1966). [9] Katal'nikov, S.G., Chih-eh'in, J., Zh. Fiz, Khim. 39, 1393 (1965). [10] Katal'nikov, S.G., Vasenin, G.H., Zh. Fiz. Khim. 41, 1174 (1967). [11] S . Ribnikar, "Proceedings of the International Symposium on Isotope Separation", p. 204, Amsterdam, North Holland Publishing Co., 1958. [12] Palko, A.A, Drury, J.S., J. Chem. Phys. 46, 2297 (1967). [13] Palko, A.A., J. Inorg. Nucl. Chem. 27, 287 (1965). [14] Palko, A.A., Drury, J.S., J. Chem. Phys. 35., 103 (1961). [15] Palko, A.A., Healy, R.M., J. Chem. Phys. 28, 211 (1958). [16] Palko, A.A, Healy, R.M., Landau, L., J. Chem. Phys. 28, 214 (1958). [17] Palko, A.A., Drury, J.S., J. Chem. Phys. 40, 278 (1964). [18] Palko, A.A., J. Chem. Phys. 30, 1187 (1959). [19] Schroeder, H.G., Hamrin, C.E., AICHE Journal 21(4), 807 (1975). [20] Kurihara, O., Nakane, R., Rikagaku Kenkyusho Hikoku, 53(6), 239-44 (1977). Z 173 [21] Ibid., 54(1)* 25-32 (1978). [22] Palko, A.A., Begun,. G.M., Landau, L., J. Chem. Phys., .37(3), 552 (1962). [23] Palko, A.A, Drury, J.S., J. Chem. Phys., 33(3), 779 (1960). [24] Palko, A.A., Indust. & Engr. Chem., 51(2), 121 (1959). [25] Merriman, J.R., Pashley, J.H., Snow, N.W., "Engineering-Scale Studies of Boron Isotope Separation", ORNL Report K-1653, Oak Ridge National Laboratory, Oak Ridge, TN, April 1966. [26] Schroeder, H.G., Hamrin, C.E., "Separation of Boron Isotopes by Direct Mode, Thermal Parametric Pumping", Progress Report, Dept, of Chem. Engr., University of Kentucky, Lexington, KY, 1970. [27] Polevoi, A.S., Tsancua', 1.1., Zh. Fiz. Khim., 55.(8), 1929 (1981). [28] Rutenburg, A.C., Palko, A.A., Drury, J.S., J. Am. Chem. Soc.,85, 2702 (1963). [29] , Ibid., J. Phys. Chem., 68(4), 976 (1964). [30] Rutenburg, A.C., Palko, A.A., J. Phys. Chem., 69(2), 527 (1965). [31] Urey, H.C., J. Chem. Soc., 1947, 562. [32] Palko, A.A., Drury, J.S., J. Chem. Phys., 47(8), 2561 (1967). [33] Begun, G.M., Palko, A.A., J. Chem. Phys., 38(9), 2112 (1963). [34] Pauling, L., The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 1960. [35] Cotton, .F.A., Leto, J.R., J. Chem. Phys., 30(4), 993 (1959). [36] Kirk & Othmer, Encyclopedia of Chemical Technology, 3rd. Ed., Vol. 16, p.163, John Wiley Sc Sons Inc., New York, NY, 1981. [37] Brown, H.C., Adams, R.C., J. Am. Chem. Soc., '64, 2557 (1942). [38] Barring, S., PhD graduate student. Personal Communique, Dept, of Chemistry, Montana State University, Bozeman, MT. October, 1991. [39] McCabe, W.L., Smith, J.C., Harriott, P., Unit Operations of Chemical Engineering. 4th. Ed., McGraw-Hill Book Co. Inc., New York, NY, 1985. 174 [40] Cohen, K., The Theory Of Isotope Separation As Applied To The Large Scale Production Of U235, McGraw-Hill Book Co. Inc., New York, NY, 1951. [41] Gupta, D., Ray, S.N., IKEC Process Design And Development, 1(4), 255 (1962). [42] Reid, R.C., Prausnitz, J.M., Poling, B.E., The Properties of Gases K Liquids, 4th. Ed., McGraw-Hill Book Co. Inc., New York, NY, 1986. [43] King, C.J., Separation Processes, 2nd. Ed., McGraw-Hill Book Co., Inc., New York, NY, 1980. [44] Benedict, M., Trans. Am. Inst. Chem. Engr., 43(2), 41 (1947). MONTANA STATE UNIVERSITY LIBRARIES 3 762 101 98982 8