THE RECOVERI’OP'ORGARIC ACIDS IY'TERNARI'ARIOI'EXCHANGE BY Ali Reza Siahpush A.IHESIS snbnitted to Hichi an State University in partial fu§fillnent of the requirements for the degree of HASTER.OP SCIENCE Department of Chemical Engineering 1988 MAE]: Experimental and modeling studies were conducted to investigate ternary ion exchange of acetate, butyrate and bicarbonate. Axial mixing within the ion exchange column was described using the stirred tanks in series model, and the rate of exchange was described by the film model. Equilibrium experiments and batch kinetic experiments were used to evaluate the parameters needed for the model. The following average separation factors were measured at a pH of 7.5 and 25°C, using the Rohm and Haas Amberlite IRA 904: “22‘ 4.0, 031° - 3.5, and “Bic u Ac - 30. Under the same conditions, but at pH - 6.0 , a2: increased to 6.2 and butyrate was found to be adsorbed in excess of ion exchange capacity. The solution phase mass transfer coefficients were found to depend on liquid superficial velocity to the power of 2.2. The model accurately predicted binary exchange but did not adequately describe ternary exchange. ,' -_‘.~sv—-qsr--;V “ ~r zue . 4,. - I. II. TABLE OF CONTENTS mum PROBLEM STATEMENT OBJECTIVES W DEFINITION OF IMPORTANT TERMS Exchanger Capacity Counter Ions and Co-ions Ion Exchange Equilibrium Ion Exchange Selectivity Separation Factor ION EXCHANGE MATERIAL CHARACTERIZATION Capacity Per Unit Weight or Volume Functional Groups Resin Pkés Matrix type Degree of Cross-linking Porosity COLUMN OPERATIONS Constant Pattern Behavior Self Sharpening Behavior Nonsharpening Behavior Multi-component Column Operations iii IV. Modeling of Multicomponent Column Operations 111- w APPARATUS CHEMICALS USED AND ANALYTICAL METHODS PROCEDURES EXPERIMENTS, RESULTS AND DISCUSSION Equilibrium Experiments Non-ionic Sorption Verification of Differential Dolumn Rate Experiments W MATERIAL BALANCE Continous Integral Model Tanks in Series Model RATE THEORY Rate Controlling Step Solution Phase Mass Transfer Controlling Particle Phase Mass Transfer Controlling Particle Phase and Solution Phase Controlling NUMERICAL SOLUTION METHOD Flow Chart of Program Computer Solution of the Differential Equations Runge-Kutta and the Predictor Corrector Scheme Program Documentation Input File Cyclical Operation Data Storage iv hO b2 42 46 48 49 49 55 58 59 69 69 69 71 74 78 79 81 83 85 87 88 88 90 9O 92 93 COMPARISON OF MODEL TO EXPERIMENTAL DATA Model verification for two component systems Particle Phase Controlled Kinetics Solution Phase and Transition regime Model verification for three component systems V- W VLW VII- mm DERIVATIONS AND JUSTIFICATIONS SAMPLE CALCULATIONS 94 94 94 101 110 112 114 115 115 120 145 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 14,15. 16. 17. 18. 19. 19b. 20. 21. 22. 23. 24. 25. LIST OF FIGURES Types of equilibrium isotherms Ratio of the areas technique Acid titration curves for weak base resin Ion exchange as redistrbution of counter ions Weak acid cation exchanger Strong acid cation exchanger Typical weak base anion exchangers Strong base anion exchanger Constant pattern breakthrough Self sharpening breakthrough Non sharpening breakthrough Zone formation for multicomponent column operations Differential ion exchange column Layout for differential column verification Layout for rate experiments Acetate/butyrate equilibrium isotherm Non-ionic sorption of acetate and butyrate Acetate/bicarbonate equilibrium isotherm Butyrate/bicarbonate equilibrium isotherm Batch rate experiments for acetate/butyrate exchange at 20 mM. Calculated mass transfer coefficients for ac/bu at 20 mM. Batch rate experiments for ac/bu at 100 mM Calculated mass transfer coefficients for ac/bu at 100 mM. vi Page 13 15 17 18 20 22-4 26 34 35 36 38 43 44 45 52 57 53 54 62 62 63 63 ‘~‘ I.- l " ' Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. Batch rate experiments for ac/bu at 300 mM Calculated mass transfer coefficients for ac/bu at 300 mM. Batch rate experiments for acetate/bicarbonate at 100 mM Calculated mass transfer coefficients for ac/bic at 100 mM. Batch rate experiments for butyrate/bicarbonate at 100 mM Calculated mass transfer coefficients for bu/bic at 100 mM. Analogy between stirred tanks in series and a packed column Typical distribution of component 1 between the liquid and the resin phases Concentration profile based on the film model Flow chart of computer program Comparison of experimental data with model under particle phase kinetics at 200 mM Comparison of experimental data with model under particle phase kinetics at 300 mM Comparison of experimental data with model under particle phase kinetics at 1.5 Comparison of experimental data with model under particle phase kinetics using the measured separation factor Effect of flow rate on exchange kinetics of ac/bu at 20 mM Effect of flow rate on exchange kinetics of ac/bu at 100 mM Effect of flow rate on exchange kinetics of ac/bu at 300 mM Effect of flow rate on exchange kinetics of ac/bic at 100 mM vii 64 64 66 66 67 67 73 75 77 87 97 98 99 100 105 106 107 108 Figure Figure Figure Figure 45. Effect of flow rate on exchange kinetics of bu/bic 100 mM. Bu/Bic Comparison of experimental data with model for ternary system Example isotherm used for calculation of separation factors Computer program code viii 109 111 124 131 .1..- -—._ Table Table Table Table Table Table Table Table LIST OF‘TABLES pKa of anionic resins Concentration drop across differential column Coefficients calculated for regression fit of particle phase mass transfer coefficents Values of constants for the solution phase mass transfer coefficients Equilibrium concentrations for acetate/butyrate exchange Equilibrium equivalent fraction distribution for acetate/butyrate exchange Concentration drop across differential column Sample of spread for calculation of mass transfer coefficients ix 28 59 95 102 121 123 127 130 The Michigan Biotechnology Institute's Biomethanation Process requires the transfer of organic acids, mainly acetate and butyrate, from an acidogenic reactor to a methanogenic reactor. However, the transport of non-ionic medium components is undesirable. The “Substrate Shuttle” ion exchange unit is able to serve this purpose of substrate transfer without transferring the undesirable components. For the purpose of automation and/or process control of the Biomethanation Process, a mathematical model capable of predicting the performance of the substrate shuttle is required. The model must be able to quickly and accurately predict the behavior of the ion exchange column in two modes of operation. The first mode, termed the "charging cycle”, occurs when a stream containing the two fatty acids anions, acetate and butyrate, enters the ion exchange column and replaces bicarbonate. The second mode of operation, termed the "discharging cycle”, occurs when a stream from the methanogenic reactor containing bicarbonate ions enters the column and displaces the acetate and butyrate ions. The process can be described as the cyclical modeling of ternary ion exchange with significant mixing. OBJECTIVES The primary purpose of this investigation was to develop a mathematical model for the numerical simulation of the substrate shuttle as an integral part of Michigan Biotechnology Institute's biomethanation process. The numerical simulation involve the prediction of unsteady-state effluent concentration profiles of the substrate shuttle anion exchange unit in the exchange of acetate and butyrate for bicarbonate. The model must be capable of simulating significant mixing within the ion exchange column because the exchange of acetate and butyrate for bicarbonate at low pH involves the production of gaseous carbon dioxide which will disturb the flow within the unit. The model must also be implementable in microcomputers, able to predict column performance on a shorter time scale than the actual process, as well as capable of interface with microcomputer based control software. CHAPTER II W Before any discussion of ion exchange theory can be carried out, it is necessary to define some elementary but important terms in ion exchange. The following definitions and concepts are necessary for an understanding of the ion exchange process. DEFINITION OF IMPORTANT TERMS Exghanger gapacity The exchanger capacity describes the number of fixed charge groups in the ion exchange material per unit volume or weight of exchanger. The capacity is the theoretical limit of the exchanger for the uptake of counter ions. Counter ions and co-ions The permanently bound charges of the ion exchanger together with the ions of the same charge in solution are termed "Co-ions". The term "Counter-ions" refers to the mobile ionic species that carry a charge opposite to the fixed groups of the exchanger. Ioe ee um The phase equilibrium for two or several transferable components between a fluid phase and an ion exchanger will often depend on both the liquid phase concentration and temperature. For the simplest case of two component ion exchange a single curve can be drawn to show the relation between the concentration of one species in the exchanger to that in the liquid phase. The variance of the system is defined as the number of independent concentration variables at equilibrium. It is also equal to the difference between the total number of concentration variables and the number of independent relations connecting them. The variance of an ion exchange system of n components is (n-l). A two component system can then be represented on a two dimensional graph with only the solid phase-liquid phase relation of one component shown. Generally the concentration of an ionic species within the exchanger is expressed as ion equivalents per weight or volume of exchanger, while the liquid phase concentration is expressed as mass or moles per volume of liquid. The general convention is to have the solid phase concentration measure all solute within the outer most boundaries of the individual granules of the exchanger material, regardless of solutes chemical or physical form. For brevity, the solid and liquid phase concentrations used in equilibrium relationships or isotherms (so termed because they only apply at constant temperature) are generally given in terms of non- dimensional concentrations defined by Equations (1) and (2). -3. . x1- .91. (1) Y1- _“1_ (2) where C1 - liquid phase concentration of species i C - a reference liquid phase concentration ref Xi - non-dimensional liquid phase concentration of i q1 - exchanger phase concentration of species 1 qref- a reference exchanger phase concentration Y - non-dimensional solid phase concentration of i 1 Total liquid phase and exchanger (resin) phase concentrations are often used as reference concentrations. This convention normalizes the liquid and solid phase non-dimensional concentrations to values between zero and one. The reference concentrations are defined according to Equations (3) and (4) for the exchange of n components. (3) qref-iflqi- exchanger capacity (Q) (4) Equations (3) and (4) then enforce the following relationships: EX — 1 (5 1-1 1 ) n 2 Y1 - l (6) i-l Based upon the above definitions, a typical two component equilibrium isotherm can then be represented by a single curve of Y1 versus X1 . Equilibrium isotherms that are convex upward throughout are designated as favorable to uptake of solute. The isotherms that are concave upward throughout are designated as unfavorable to uptake of solute. Isotherms that follow a rising diagonal are termed linear. It is also possible to have inflection points in the isotherm making them favorable at one range and unfavorable at another. An example of each type of isotherm is given in Figure 1. i Figure 1. Different types of equilibriun isotherms plotted as resin phase dimensionless concentration versus limid phase diaensionless caloentration. lsn.£xsbsass.§sles£ixi£x It has long been documented that although two ions exchange with one another on an ion exchange material, they are not held by the exchanger equally strongly. Thus, at equilibrium with a liquid phase that contains equal amounts of ions A and B, the exchanger will in general not contain equal amounts of both ions, but prefer one to the other. This preference is quantified by "Selectivity". If, for example, ions A and B are in equilibrium between a liquid phase and an exchanger phase, the exchange process may be written as follows: A + B -———————l- A. + B x Y Y (7) where the subscripts x and y refer to the liquid and exchanger phases respectively. The selectivity coefficient (K's/A) is then defined as follows: 2 z B A . _ (q ) (C ) KB/A Bz AZ (8) (on) ”up A Here, 2A and 2B are the ionic charges of species A and B respectively, and the selectivity coefficient shows the exchanger selectivity for B over A. One can define a dimensionless selectivity coefficient (K' B /A) by using dimensionless concentrations. z z c o A Eli/r _9_ (Y5) (xA) (9) Q 23 2A (x3) (YA) Here, C o and Q are total liquid concenetration and the resin capacity. Any value of 1% / A different from unity measures the preference of the exchanger for one species over another. These preferences can be summarized by the term activity. The higher the activity of one component in a given phase, the greater is its escaping tendency from that phase. Activities were not used in this investigation, however, all experiments were performed at or near the concentration range of interest so that any possible nonidealities would be included in the results. There also exist "Corrected Selectivity Coefficients” which account for the preferences of the exchanger only by making use of activity coefficients of the species in the liquid and resin phases. These coefficients will not be considered in this study because it is generally the combined effect of the two phases that determines the distribution of species in the phases. JI 10 Factors affecting selectivity: Several factors affect the preference of'a resin for a given ion. Typically the exchanger prefers counter ions with the following characteristicsl’zz 1. Highest valance. 2. Smallest hydrated ionic radius. 3. Most strongly interacting with the fixed groups of the exchanger. 4. Greatest polarizability. 5. Cause the least swelling of the resin. 6. Lowest free energy of hydration in aqueous solution. The following factors also affect the selectivity of the resin. 7. The degree of cross linking of the matrix. 8. Starting ionic form of the resin; i.e. a resin starting with Cl- form has a lesser affinity for C1. than a resin predominantly saturated with HCO3- . 9. The non exchanging ion, if it in any way forms a complex with an exchanging ion that alters its charge or impedes its diffusion across the surface film of the resin bead. 10. The total ionic strength of the solution. The selectivity order is sometimes reversed in favor of ions that were not 11 preferred by the exchanger at low ionic strength as the ionic strength of the solution is increased. Separation Factor The separation factor is defined by Equation (10). a; - YA in - x13 (1 ' YB) (10) xA YB Ya (I - x3) If a: > 1, the exchanger is said to prefer ion A to ion B. By virtue of its definition, the separation factor is analogous to relative volatility in distillation. Unless the equilibrium isotherm is linear, the separation factor is not constant as it changes. Generally for the purpose of brevity, average separation factors are used which apply over the entire concentration range of the isotherm. It is therefore necessary to calculate an integrated average separation factor from the experimentally measured isotherm. Figure 2 shows a typical favorable isotherm. In this‘ study, integrated average separation factors were calculated from experimental data according to Equation (11). Please refer to the appendix or to the work of Clifford2 for a derivation of this equation and a justification for the use of separation factors rather than selectivities. _~ _a~_.-..r" .1 WW: 12 (az-a-alna) azeaIII) _ (a - 1)2 Area(I) 1 - _1Q2- a - a 1n a) (a - 1)2 (11) Jl 13 - _.__ 0““ m- 3'— mummy/fl f I I “”9 A E I : - g a i AREA ll . I f g , BELOII lSOiileI ,' ‘ . +4“ i I i on .LJ _ _._--____-__.-._ ___J 0.0 1.0 X I F Ian 2. Typical favardIle isotherm showing the reasoning med In the derivation of the average sepcrotion factor. __l| ‘-_-fi_FI-- 14 ION EXCHANGE MATERIAL WARACTERIZATION Ion exchange materials are classified by several different properties and independent variables: I. Ion exchange capacity per weight or volume. II. Functional groups. III. Resin pKa's. IV. Matrix type. V. Degree of cross linking. VI. Porosity. WW For ion exchange materials that contain permanent charges, such as strong acid and strong base ion exchangers, the capacity is constant; however, for weak acid and weak base exchangers, the functional groups are charged or neutral depending on the pH of the environment, and thus the capacity of the exchanger is a function of pH. Figure 3 shows titration curves for three different acids on a weak base resin. Since the amount of acid needed to produce a given pH change is dependent on the resin capacity, the capacity is seen to be pH dependent. 15 O n JI- 0,00 5,00 A V . RQEGQPHNEPH 0. SJ” 2,00 D j I 'l j {.00 £90 ' 5.00 2.50 «cm was). Ira/IL. 3. . . 'b.oofi 0150 Figure 3. Acid titration curves for a weak base resin lame are see. MRCROPOBOUS RESIN STYRENE—DVB HRTflIX manner-anus FUNCTIONPLIT‘! TOTRL cnracm = 1.25 MEGJflL. [From Clifford (2)]. __I| l6 Funct ional Groups The two main categories of functional groups are Cation and Anion exchangers. Cationic ion exchangers are so named because they participate in the exchange of cations. The functional groups in this type of material are negatively charged and depending on the type of the exchanger (Strong Acid, or Weak Acid), they may posses either permanent or pH dependent charges. Figure 4 shows the crosslinked polymeric matrix containing the fixed charges together with the mobile exchanging counterions. Cationic ion exchangers are themselves classified in two categories: weak acid and strong acid exchangers. Weak acid cation exchangers consist of functional groups that are weakly acidic. Functional groups such as carboxylic acids demonstrate a good example of a weak acid functionality. It is clear that such weak acids only exhibit negatively charged behavior at a pH range above their respective pKa. The molecular structure of a typical weak acid exchanger is shown in Figure 5. ~v—‘.- m _._..__, r vul— 1' T."W"’WV_. ' H ”Ti“; ' . sat-ups 17 0‘ Matrix with Fixed Charges 06 Countctions Initial State Equilibrium Figure 4. Mechanism of ion exchange, a redistribution of counterions between particle and solution. [From Marinski (1), Chap. 2]. l8 CH3 CH3 —c- CHz-C-CHZ- -CH- COOH COOH CH3 CH3 -C-CH2-CH-CHz-(:Z- COOH COOH Figure 5. Weak acid cation exchange resin Methacrylic acid-divinylbenzene capolymer “'Functional group: 0003 Acidity: pxa 8 4 to 6, ionized at pH > S Swelling: +65§ going from tt'to Na form Capacity: 10 meg/gm. 4. 3 meg/gm .__..... ++._..__ + RCOOH+Na*RCOONa+H P: denotes the resin matrix [From Clifford (2)]. 19 Strong acid cation exchangers posess rongly acidic functional groups. The molecular structure of a typical strong acid cation exchanger, Duolite C-20, is shown in Figure 6 together with its physical properties. All of the major strongly acidic cation exchangers involved. in industrial water treatment applications have a chemical matrix consisting of Styrene-divinyl benzene (STY-DVB) with sulfonic acid radical functional groups. These resins differ mainly in DVB content and pore structure32(Rohm & Haas catalog). 20 -CH'CHz-CH'CHZ- CH — ° ' ' ©©© so H u s H 3(aiz<34-(?42 OB -°---CH2-CH CH-CHZ-m- so,H $03H Figure 6. Typical strong acid cation exchange resin Sulfonated polystyrene-divinylbenzene copolymer Typical degree of crosslinking: 8% Physical form: Translucent spheres ' Specific gravity: 1.23, hydrogen form Moisture retention capacity: 50%, hydrogen form Effective size: 0.45 to 0.55 mm + Swelling: -7t when going from H to Na form Ion-exchange.capacity: 4.8 meg/gm, 2.0 meg/m1 Uniformity coefficient: 1.4 to 1.8 Functional group: R-SQ3H Acidity: pxa < 1, ionized at pH > 1 n— —— ‘. ..___-__. R-SOBH + Na* + RSO3Na + 3* 21 Anion exchangers have positively charged functional groups and anionic counter ions. Anion exchangers can be classified as either weak base or as strong base. Weakly basic anion exchange resins, similar to weak acid resins are ionized at a specific pH and therefore are primarily used to remove strong acids such as hydrochloric, and sulfuric. Unlike strongly basic anion exchange resins, weak base resins do not have the capability to remove bicarbonates, silica, or weak organic acids. The main advantage of weak base resins is that they can be regenerated with relative ease and with stoichiometric amounts of regenerant. They are therefore more efficient than strong base resins. Typical structures of weak base resins are shown in Figures 7, 8 and 9. 22 C-H C—-H,_-— CH -CH2- CH- .H,Q Q. 3.HCI ZCHZ CH’CHz HCI. -CH2- CH CH- CH2-' .@ Q CH CH3- N—CHZ CHZ- N-CH3 HCI HCI Figure 7. Typical weak base anion exchange resin tyrene-divinylbenzene copolymer with tertiary-amine functionality Typical examples: Amberlite IRA-93, Duolite 85-368 Physical from: tan, spherical particles Moisture retention: 50!, free base form Capacity: 3.8 meg/gm. 1.3 meg/ml Swelling: +23% free base to salt form Baszcity: pKa = 7 to 9, ionized at pH < 8 HNO RN (fli3)2+ 3+ RNiCli3 )2 - “210 [From Clifford (2)]. 3 23 OH HCI HCI HCI OH --°-- -CHZ-NH-Cqu-NH-CzHa-N-CHZ- / -CH2-°-~ . \l I (EH2 l CH2 Figure 8. Typical weak base anion exchange resin Phenol-formaldehyde polyamine. condensation polymer'with secondary amine functionality Typical example: Duolite A-7 Physical form: cream colored granules Specific gravity: 1.12, free base form Particle size: 0.3 to 1.2 mm Moisture retention: 60% Total capacity: 9.1 meg/gm. 2.4 meg/ml Swelling: +18% going from free base to salt form Basicity: pKé = 7 to 9, ionized at pH < 8 NH + HCl : W [From lifford (2)]. . d' 'hF-r "' 24 ------ If—CHz-CH-CHZ-IEI-CH2-—CHz—I}I—CHz—-~- CH2 OH CH2 CH2 CH2 HC-OH HC-OH HN----- CH2 CH2 -----N- CH2 -CH2- NH Epcxy-polyamine condensation polymer .. ._$H2_CH2—.... c==o . , I'vH ~CH2—CH2-NH-CH2-CH2-lél Cao ......._ CH2_CH ...... Polyacrylic-polyamine copolymer Figure 9. Other common weak base anion exchange resins. [From Clifford (2)]. 25 Strongly basic anion exchange resins can be divided into two major categories called Type I and Type II. Type I resins have the highest overall basicity and will therefore more completely adsorb weakly acidic ions such as weak organic acids. Type II resins will also remove weak acids, but are not as basic as Type I and do not require as much regenerant. They are therefore more efficient than Type I resins. Based on oral and written communication with a technical representative of The Rohm and Haas Company 33, type II strongly basic resins were chosen for the recovery of weak organic acids such as butyric and acetic acids. Some typical structures of strong base resins are shown in Figure 10. 26 W3 CI’ iii“ C'- -CHz-l'\l -CH3 “CH2_':l—C2H4OH CH3 CH3 Type 1 Type 2 Figure 10. Two typical strong base anion exchange resins. Other strong base resins include a.matrix of ST—DVB back bone. 0 Physical form: moist. cream-colored beads. opaque Morsture retention capactiy: 50%, chloride form Specific gravity: 1.07 chloride form Capacity:: 4.0 meg/gm, 1.3 meg/ml Swelling:; ~12t going from.OM'to Cl- form _. + - .— RN(Cfl3l3Cl + NO3 ‘- RNiCd3i3NO3 +C1 8" ‘4 we». 27 Resin pKa' s The pKa of the functional group indicates the pH range in which the resin can effectively operate. Ion exchangers are classified into four different categories based on pKa's. 1. Strong acid cation exchangers with an operating pH range of (0-14) and a p1(a value less than 1. 2. Weak acid cation exchangers with operating pH range of (5-14) and a pKa value of approximately 4.5. 3. Strong base anion exchangers with operating pH range of (0- 14) and a pl(a value greater than 13. 4. Weak base anion exchangers with operating pH range of (0-9) and a pKa's value between 7 and 9. The resin pl(a is not necessarily equal to pl(a of its individual functional groups, because this value is dependent on the environment of the functional groups. The functional groups in an aqueous environment may exhibit different pKa than functional groups in the interior of the resin matrix. Table 1 shows some anion exchange functional groups and their apparent pK4. 28 Table 1. pKa of anion resins [From Marinski (l), and Clifford (2)]. ION EXCHANGER STRUCTURE APPARENT pKa Type 1, Strong Base -N+(CH3)3'OH > 13 Type II, Strong Base -N+(cznaou) (CH3)2-OH >13 Secondary amine Weak base -N(CH3)H 7-9 Tertiary amine Weak base -N(CH2)2 7-9 Primary amine Weak base -NH2 7-9 Phenylamine Weak base - ~NH2 5-6 Matrix_112e Several types of polymeric matrices are used in commercial ion exchange resins. Some of the most common polymeric backbones are listed below: 1. 2. Polystyrene crosslinked with divinyl benzene (STY-DVB). Polyacrylic acid-polyamine condensation polymers (Acrylic- Amine). Phenol-Formaldehyde-Polyamine polymers (Phenol-HCHO-PA). . Epichlorohydrin-Polyamine condensation polymers (Epoxy-Amine). . Acetone-Formaldehyde-Polyamine condensation polymers (Aliphatic-Amine). 29 Degree of nggs Linking This is the product of the chemical cross-bridging between linear polymeric chains in the resin matrix. Crosslinking produces a three dimensional polymeric network with an effective ”pore” diameter. High degrees of crosslinking (>12t) produce tight structures that favor small ions and are kinetically slow, but chemically stable. Low degrees of cross linking (s 4%) produce a relatively open structure that is kinetically quick and permits easier penetration of large ions such as organic acids. For styrene-DVB resins, generally the amount of DVB in the backbone is a direct indication of the degree of crosslinking. Porosity Porosity is a measure of openness of the polymer matrix and is related to type 3nd degree of the matrix crosslinking. Three basic classifications exist in this type of physical categorization. l. W are microporous with apparent pore diameters of atomic dimensions (10-20 A). Gel resins resins containing DVB are generally 6-8% crosslinked. The matrix is usually transparent and continuous with little true porosity. 2. aggropozoug resigs, also known as macroreticular resins, have internal pores whose diameters far exceed atomic dimensions (2100 A). These type of resins generally have a high degree ...__ _..... "— _—. ggmywm-‘rm “"779" V" 30 of crosslinking, are opaque, have large surface area per unit volume, and have great physical stability when compared to gelular resins. 3. W115 have higher porosity than gel resins, but are not as porous as macroreticular resins. This type of matrix generally has a low degree of DVB crosslinking (0.5-2t) . The product is transparent . COUJHN OPERATIONS Effluent concentration profiles from packed-bed ion exchange columns are dependent upon several variables, including the liquid flow rate, number of ionic species, and phase equilibria. Favorable, unfavorable and linear isotherms produce different effluent concentration profiles as described below. Mobile ions are transported through the column by the carrier solvent, (water in most cases). The velocity of each ionic species is only equal to the solvent velocity if the ion exchange material behaves only as a nonporous packing, and does not interact with the dissolved species in any way. However, the counter ions penetrate the porous matrix of the exchanger material and engage in the process of ion exchange, thus reducing the velocity with which each individual specie travels through the column. The velocity of the concentration front is generally much less than that of the solvent and its shape is dependent on the equilibrium isotherm and the rate of mass transfer. In the following discussion it is assumed that the column is initially 31 presaturated with the counter ion (B- ) and the influent solution contains (A' ) at a certain concentration. For the purpose of brevity A' and B- will be referred to as A and B. 32 Consta t te e v or This type of behavior occurs when the equilibrium isotherm is “linear“. It is referred to as constant pattern because the velocity of the transition region is independent of concentration. In the absence of axial mixing, the shape of the concentration front remains constant throughout the column. This behavior is shown schematically in Figure 11 . S a e v Self sharpening refers to a concentration gradient that continuously increases in magnitude in the axial direction across the concentration wave that is decreasing in the direction of flow. This type of behavior occurs when the equilibrium between the exchanger and the liquid phase is favorable to uptake of counterion in the feed. The velocity of A through the column is concentration dependent. Because the isotherm is favorable to uptake of A the largest relative driving force for the uptake of A occurs at lowest equivalent fractions of A. Therefore the regions of low A composition are adsorbed more readily than regions of high A composition. The result is that the regions of the front containing lower equivalent fractions of A move at a lower velocity than regions of high A composition. This behavior is schematically shown in Figure 12. 33 Non ha e B v Non sharpening behavior occurs when the equilibrium is unfavorable to uptake of A. An inspection of the unfavorable equilibrium isotherm shows that large equivalent fractions of A in the exchanger will only exist at high liquid phase equivalent fractions of A. This results in a concentration dependent solute velocity that will cause the concentration front to stretch out. Thus, regions of the concentration front with small concentration of A will move more rapidly than the regions with a high concentration of A. This type of behavior is schematically shown in Figure 13 for comparison with the self sharpening behavior. 34 ‘ \ \ \\\ ‘\‘ \ \ \W— \o. \‘x \x v \\ \ \ 9- ‘\ \ \ ‘x \ Q Q ‘A . <__( +—( <—< lemma STIfllHIIEt Grumman FIGRE lLSElI SIIW’ENIIC W CIRVES PRMXID BY FAT/[RARE lSOlllelS. THE SITUTE VELOCITY IS [IPENINT IN SILUTE WTRMIIN. HIGH EWIVAIINT FRACTIINS 0" TH: HIGH AFFINITY SILUTE WE Tim TIE BED AT IIIG‘IfR vaccmr THAN L0! EWIVNBIT FRACTIIN IIEGIINS. 35 SIIUIITIEI WWI“ FIGIKE IZCINSTANT PATTBTIIflflKTlRIlKII-I ClleES PRGIKJED BY LIIEAR ISOTTERIIS AID IIAINTAIN TIEIR SHAPE Willi Tlf oauII. TIE STIUTE VELOCITY IS INIPEMENT 0F SITUTE CINIENTRATIIN. “WWW MTIIEI WWI“ FIMUWWIMM'W“WWW BY WAVIRAEE ISOTIERIIS. TIE SILUlE VELOCITY IS IIPENINT IN SILUTE (INIENIRATIIN. HIGH EQUIVALENT FRACTIWS (1" NE HIGH AFFINITY SMITE IANE TTRIIDI TIE BED AT LOIIER VElOCITY THAN L0! EWIVAIN FRACTIIII REGIONS. 37 Mut Com one C eatos Consider the three component system of butyrate, acetate and bicarbonate denoted as B, A, and C. Assuming that the resin is more selective for B than for A, (a2: >1). The feed contains only B and A and the resin bed (or column) is initially saturated with C. As the feed passes through the column a fraction of the more prefered ion B, greater than its equivalent fraction in the feed, is preferentially removed in the first differential bed segment, while a smaller amounts of the less prefered ion A is removed in this segment. In this way, B is removed from the liquid phase before component A, and A is subsequently removed in deeper segments of the bed. As the bed becomes saturated, the least preferred ion A shows up first in the column effluent. Once flow has commenced, zones will form that are predominantly rich with one species, as shown in Figure 15. Zone one is B rich with small amounts of A and C. Since B is the most preferred specie, it is completely removed in zone 1 so that the fluid passing through zone 2 only contains A and C. In zone 2 the more preferred ion A is preferentially removed, so that zone 2 is A rich in the resin phase. Zone 3 still contains the presaturant. 38 - INITINJJ SAME) IITII ' C FICLRE I4. INITIAL CONDITION OF THE COLUMN. Iqu MATEO may Mt NE! my BRIOI Alfll CIIOI FIGURE 15 ULLTICOIPONENT COLUMN OPERATION SHOWING TIE PLATEAU ZONES AM) THE CONCENTRAION FRONTS IN THE COLUIIN 39 With time, the resin will become saturated with B, and zone 1 will extend through the entire length of the column. Figure 15 shows two concentration fronts. One exists between zones 1 and 2 across which B disappears, and the other exists between zones 2 and 3, across which A disappears . In Figure 15, it is assumed that no axial mixing takes place in the column. Mixing would distort the wave fronts, and depending on the degree of mixing, the zones may not be observed at all. Prediction of column behavior for a multicomponent ion exchange system is exceedingly more difficult than that of a binary (two component) system. For an n component system (here n refers only to 27 the counter ions), it has been shown by Helfferich and Klein and by Tondeur, Klein and Vermeulenlathat n plateau zones will occur in the exchanger and the effluent concentration profile. There will also necessarily exist n-l transition regions between the n plateau zones. The prediction of the effluent concentration profile necessitates the prediction of the shape and location of these transition regions as a function of time and axial position in the column. 40 odelino utooet ea us The numerical simulation of multicomponent ion exchange has received considerable attention recently. However, the modeling of multicomponent ion exchange with finite rates of mass transfer and significant mixing has received little attention. 16,29 Dranoff and Lapidus applied Thomas' second order kinetic model5 to ternary exchange and numerically solved the resulting equations. The ion exchange process was treated as a chemical reaction and the resulting reaction rate constants were correlated to flowrate. This was an incorrect picture of the process because ion exchange is controlled by rates of mass transfer, which are affected by the flow dynamics as well as the diffusivities of the different components as 23 26 shown by Boyd et. al. Visawanthan et. al reported a non equilibrium analysis of multicomponent ion exchange based on 18 irreversible thermodynamics in a single bead. Klein et. al. Helfferich and Klein 27, and Rhee et. al.28 reported methods of predicting‘effluent profiles if local resin-liquid equilibrium is maintained. Sanders et. a1.30 modeled the separation of animo acids by ion exchange chromatography by calculating equilibrium liquid and resin phase concentrations of different species by various prediction methods and treating the remainder of the problem as standard chromatography modeling with the restriction of charge neutrality. Although it is generally assumed that the compositions of the resin and the liquid phases are in equilibrium at the interface, the bulk 41 liquid and resin concentrations are usually not in equilibrium. This equilibrium assumption is especially poor for dilute solutions with finite rates of mass transfer and high flowrate operations. in this latter case, the bulk concentrations of the ions in the liquid feed remains relatively constant while the liquid phase concentration of the presaturating ions vary. Bradley and Sweed 9 used the same type of driving forces as Vermeulen and Clazie 31 to predict the multicomponent effluent profiles assuming finite rates of mass transfer and axial dispersion. However, for cases with high degrees of axial mixing, other models, such as the stirred tanks in series model, may be preferable. Barba, 17 used the Nernst-Planck model for the diffusion Del Re, and Foscolo coefficients and orthogonal collocation to solve the solid phase diffusional equations. This treatment allows the particle side flux to be directly calculated from concentration gradients. Omatete 2“ successfully predicted effluent profiles for ternary ion exchange for the limiting cases of solution phase mass transfer controlling and particle phase mass transfer controlling. However, this study did not treat the range of concentrations in which both phases control the rate of mass transfer and did not include liquid phase mixing. The present study extends the film model used by Omatete to all concentration ranges by using the resistances in series model and describes different degrees of mixing by using the stirred tanks in series model. be to CHAPTER III APPARATUS. The experimental apparatus used for the various experiments is shown in Figures 16, 17, and 18. ‘The Cole-Farmer Master Flex peristaltic pump (model 7520-25) was calibrated and used in all experiments. The pump was found to deliver a relatively constant flow rate over the range of interest. Diffsmatialfialmn The differential column is shown schematically in Figure 16. The column consisted of three plexiglass parts held together by stainless steel screws. The middle part consisted of a hollow cylindrical chamber that contained the ion exchange resin. Two different middle sections were available; a 2.9 cm long section or a 5.0 cm long section were used depending on the desired amount of resin. The resin bed was held in place by stainless steel screens at the top and bottom of the middle section. Rubber o-rings were used at the top and bottom of the middle section to prevent leakage. Glass beads of the same diameter as the resin were used above and below the packed resin bed to uniformly distribute the liquid feed and to allow for the used of different quantities of resin. 42 43 Solution outlet l Stainless Steel Iire Ilesh Screen Rubber 0 Ring 0.5 cm Glass Beads Ian length 2. 2 l Ion Exolmge gig-é. Beads (1 on) géfig 2.9 an 9. 2 or g If 5'0 a“ 0.5 an S:_ Glass Beads 0 3 a length Other 0 Ring Stainless Steel lire Ileeh Screen Solution Inlet __T FIGIRE 16. SCHEMATIC 0F DIFFERENTIAL COLUMN 44 I DIFFERENTIAL com \ 0‘ CONTAINING ION EXCHANGE RESIN _> BLEED v _ FRACTION ‘ \ COLI£CTIR our PARIIER (VARIABLE FLOII) PERISTALTIC FLIP ‘h is") STIUTION RESERVOIR FICIRE 17. SCHEMATIC DIAGRAM 0F TIE DIFFERENTIAL COLUMN VERIFICATION EXPERIMENT . TIE BLEED STREAM IS USED TO PIRCE SYSTEM OF WATER BEFORE THE STEP INPUT RISE IN CONCENTRATION IS MADE. 45 autumn oLuIII E.— gomua meme. III Cole Parmcr (variable flow rate) peristaltic C) pump WELL STIRRED. RAFFLED 7 SOLUTION RESERVOIR. (solution concentratin is monitored here). Figure 18. Schematic diagram of the equipment setup for the rate experiments. System liquid holdup (pump. column, all connections, and tubing) - 3.8 ml. ..-.——.-—.-——_ I . u " . 46 CHDIICALS US. AND ANALYTICAL METHODS Analytical grade anhydrous sodium acetate, hygroscopic sodium butyrate and sodium bicarbonate were used in all solutions. Glacial acetic acid and analytical grade butyric acid were used toadj ust the pH of acetate and butyrate solutions. The pH of the sodium bicarbonate solutions was adjusted by addition of acetic or butyric acids and 0.1 N sodium hydroxide. The effluent concentration of the organic acids was determined by a Hewlett Packard 5890A gas chromatograph equipped with an auto- sampler and integrator. A 4 foot glass column was packed with 80-100 mesh Chromosorb 101 and operated under the following conditions: Carrier flowrate: 22.9 mL/min (N2) Oven temperature: 180 oC Injector temperature: 220°C Detector temperature: 250°C Under these conditions, the maximum chromatograph error observed was 4%. The bicarbonate concentration was determined by alkilametric pH titration with 0.1 M NaOH, and the maximum error observed was 2%. The main contributor to the scatter of experimental data was thought to be experimental and dilution error. 47 The resin used in all experiments was the Rohm & Haas Amberlite IRA-904 strongly basic type II resin. It belongs to the class of resins specified as macroporous and has the following general properties: Capacity: 2.4 meq/gm (dry basis) Average Particle Diameter: 0.45-0.5 mm Moisture Content as Shipped: 57% Density : 670 g/l (as shipped) nmnm-ffi " the—.4 For further information please refer to the Rohm & Haas Catalog32. L! The resin used in this study was chosen on the basis of efficiency of regeneration, ability to recover weak organic acids, low cost, and resistance to fouling. «-‘:~='--~¢-=m-r new “:«Mr-r'hwmwrww“ W. «m --'*es-E-i1-E-v£"~-== '- 48 P ocedu o esi The resin was thoroughly dried, as described below, and weighed . prior to all experiments. The rinsed, saturated resin was vacuum filtered using a Buchner funnel and air dried for several hours. The moist resin was then dried in a vacuum oven at 25 inches of Hg vacuum at 45°C to a constant weight. The resin was then stored in a vacuum desiccator until needed. The dryness of the resin was verified by comparing the measured capacity of the dried resin to manufacturer's data . Resin was initially soaked in double-distilled and deionized water for 24 hours to achieve its hydrated diameter; a vacuum was then placed upon the vessel containing the submerged resin to remove any air from the pores of the resin. The aspiration was continued until no visible bubble formation was observed and resin particles no longer floated when subjected to low pressure. The resin/water slurry was then poured into a standard 1.2 foot glass chromatography column with an inner diameter of one inch. The ion with which the resin was to be saturated was then slowly pumped through the top of the column (dilution rate 5 0.01 hr '} and the column effluent was checked for the ion initially contained in the ."5a, .1. W .I'. 49 resin. This exchange was continued until the presaturating ion could no longer be detected in the effluent. Double distilled deionized water was then pumped through the column until the column effluent contained no detectable concentration of ions. EXPERIMENTS, RESULTS AND DISCUSSION Equilibrium isotherms were experimentally measured as outlined by Cliffordz. The binary isotherm for acetate and butyrate was constructed at pH values of 7.5 and 6.0 to establish the effect of pH. However, the isotherms for the other binary systems containing bicarbonate were only constructed at a pH value of 7.5 because the bicarbonate concentration is pH dependent. Thus, a constant total concentration cannot be maintained if the‘pH changes. The following procedure was used to measure the equilibrium isotherm for acetate (A) and butyrate (B). The same approach was also used on the other binary systems. Starting with the resin presaturated with B, the weights of resin needed to give desired equilibrium liquid phase equivalent fractions of A ( XA- 0.1,0.3,0.5,0.7,0.9) were estimated using the Equation (12)given by Cliffordzz (l-a) x1,2 + (tr-2) x1,2 + 1 fl "' - _ (12) a (Bo/A0) XA 50 Where, fl - resin weight required per liter of solution to achieve XA A a - aB - separation factor - (YAXB)/(XAYB) Ao’Bo - initial concentration of A and B in liquid phase (mM/L) Ao’Bo - concentration of A and B initially in resin (meq/g) XA - equivalent fraction of A in solution at equilibrium The separation factor is not known initially and must be estimated. The initial estimates were not accurate, but subsequent guesses made use of data already acquired and were thus more accurate. The calculated amounts of resin were added to 100 mL aliquots of solution in 200 mL vials, sealed and shaken at approximately 60 RPM for 36 hours at 25°C in a New Brunswick gyrotory water bath shaker (model G76). The liquid phase was periodically assayed until the liquid phase concentration became constant. The liquid phase was then assumed to be in equilibrium with the resin. The experimentally measured resin capacity was used together with the resin weight and a material balance to calculate the resin phase concentration of each component. The average separation factor was then calculated using the "Ratio of the areas” technique described in the appendix. The equilibrium isotherms for butyrate/acetate, butyrate/bicarbonate and acetate/bicarbonate are shown in Figures 19, 20, and 21. The average separation factors were as follows: BU aAc(pH - 7.5) - 4.0 BU aAC(pH - 6.0) - 6.2 51 cage (pH - 7.5) - 0.303 3 afigo (pH - 7.5) - 0.031 3 Thus, the order of selectivity, or preference by the resin, is as follows: H003) BUTYRATE > ACETATE The increase in the resin selectivity for butyrate at the lower pH is thought to be related to the dissociation chemistry of the weak acid. At the lower pH, there is a higher concentration of the undissociated acids, and non-ionic interactions between the acids and the resin would be increased. Evidence of significant non-ionic sorption of butyrate to the resin was obtained, and is discussed in the section titled ”Non-ionic Sorption”. . . ............. 52 g; ’m [g 1.00 0 / Z /’° 0/ In _ ,2 0.80 // a: . / Cr; ,/ 3'— 0.60- / (I]<( fr 20: ct I —D 500 0.40- I <33 ’ m . I “- I I— ._ Z 0.20 S <>f ' _ o—o PH = 6.0 ._ - e—e PH = 7.5 3 0.00 - a i. g I O 1 T 1 1 a ‘ 8 0.00 0.20 0.40 0.60 0.80 I .00 X(BUTYRATE) Figure 19. Equilibrium isotherm for butyrate/acetate exchange. Equivalent fraction of butyrate in resin versus equivalent fraction of brtyrateGin the liquid phase at a total concentration CT - 270 mM. T - 25 C. EQUIV. FRACTION ACETATE IN RESIN - Y(AC) Figure 20. exchange. I .00 53 0.80- 0.60- 0.00 0'20 0.40 also 0.00 1.00 0-0 ACETATE/BICARBONATE ISOTHERM I I U I U X(AC) Equilibrium isotherm for acetate/bicarbonate Equivalent fraction of acetate in resin versus equivalent fraction of acetate in the liquid phasg at a total concentration CT - 100 mM. pH - 7.5. T - 25 C. exchange. 54 total concentration CT - 100 mM. pH = 7.5, T - 25°C. I .00 Z 1.00 , _ 3 o BU‘IYRATE/BICARBONATE ISOTHERM a: . Z 0.80- OJ ‘2 ' ,./ a: t 0.60- A :33 mm - 3.“ g 0.40- r: (J . 3‘: u. 0.20- 22 . '8 LBJ 0.00 I '- I r i I x I ; 0.00 0.20 0.40 0.60 0.80 X(BU) Figure 21. Equilibrium isotherm for butyrate/bicarbonate Equivalent fraction of butyrate in resin versus equivalent fraction of butyrate in the liquid phase at a 55 William An experiment was performed to determine if the resin would adsorb the ions of interest, mainly acetate and butyrate, by mechanisms other than ion exchange interactions. (e.g. , hydrophobic .interactions). Six different solutions were prepared at three different concentrations, three solutions of sodium acetate and three solutions of sodium butyrate. The solutions of sodium acetate and sodium butyrate were prepared at a pH - 6.0 and at concentrations of 200, 300 and 500 mM. Next 100 mL portions of each solution were placed into 125 mL vials together with 10 g samples of dry resin saturated with the same ion as it was being placed in. Thus, resin in butyrate form was sealed with solution of butyrate at three different concentrations, and resin in acetate form was sealed with solutions of acetate at three different concentrations. The vials were shaken for 36 hours at 25°C and the liquid phase concentration was once again checked. The quantity of ion adsorbed was calculated by a material balance. Sorption of acetate and butyrate in excess of resin capacity was attributed to non- ionic interactions. The results of this experiment are shown in Figure 19b. Butyrate was adsorbed to a greater extent than acetate by non ionic interactions, it is therefore logical that these interactions would account for a larger relative amount of butyrate adsorbed at lower pH. It is also possible that butyrate polymerizes similar to lactic acid in highly concentrated solutions; and the resin phase concentration of butyrate may be sufficient for such polymerization. It should also be r I 56 noted that no experiments were performed to confirm the mechanism by which these non-ionic interactions occur. ”"1 ‘: "t'f' 4!" ' ”straw“ “We. ' .""~-‘ as» g m 0“ 35“.." “3‘ - #— 57 A 1.0 g o BUTYRATE Y = 7.71x10”(X) - 1.2202 8 . ACETATE Y .. 2.16x10"(X) - 1.3775x10-= E 0.8- 0‘ ‘\~ 0' 0) .. O \E/ 0.6 / U / 0 04~ m o a. / 0? ¥ I, z 9 0.2-- /° E / m 9 _____________.._—--—--—--—C 0 e—-""'—"""—.———- m 00 . I l I r 1 I 150 200 250 300 350 400 450 500 EQUILIBRIUM LIQUID PHASE CONCENTRATION OF SPECIES (mM/ Liter) Figure 19b. Adsorption of acetate and butyrate by IRA 904 to excess of ion exchange capacity of the resin by non ionic interactions. Quantity of ion adsorbed versus equilibrium liquid phase concentration. pH - 6.0, T a 25°C. 58 WW The measurement of kinetic parameters in a packed ion exchange column is much easier if it can be assumed that the liquid phase concentration remains constant throughout the packed bed. This desirable effect is approximated in a differential column. It must therefore be verified that the small column used is in fact a differential column. The experiments discussed here were carried out in the layout shown in Figure 17. The following procedure was used to verify the assumption of a differential column and to determine the minimum flow rate at which this assumption would break down. The differential column was packed with 0.227 g of resin in the acetate form, then soaked and aspirated according to the procedures outlined in the previous sections. Five hundred mL of deionized water were then pumped through the column to ensure a clean column. Butyrate solutions of different concentrations and a pH of 6 were pumped through the column, and the effluent was collected via a fraction collector every 10 seconds. Only selected samples were analyzed. The samples were analyzed for presence of acetate, and the rate of release of acetate was calculated versus time. This information was then used to determine average concentration drops across the length of the column. The largest value of acetate flux was used to calculate the concentration drop of butyrate across the column. '4. f1 ‘ ‘- ___‘.-71— 59 Typical experimental data for adsorption of butyrate are shown in Table 2. Experimental conditions were as follows: Flow rate: 37 mL/min Total Concentration: 102 mM pH : 6.0 Resin weight: 0.50 g Resin presaturant: Acetate Table 2 . Concentration drop across the differential column versus time shown as percent of total concentration . Time (s) A C t 5 11.8 15 6.60 25 5.00 35 5.01 45 3.30 Here AC refers to the difference between the inlet and outlet concentrations of butyrate per centimeter of packed bed as calculated in the appendix . W To measure the mass transfer coefficient a series of experiments were carried out at high dilution rates in the differential column such that the largest percentage drop in liquid phase concentration across the column was 6%. The experimental setup is shown in the previous section titled Apparatus in Figure 18. The column was packed with 0.227 g of resin, and 0.5 mm glass beads were place above and below the resin to achieve uniform liquid velocity profiles passing 60 through the resin bed. The resin was then aspirated to remove trapped air and allowed to soak for 24 hours by pumping water through the column. Next, the resin was saturated with acetate using 1 liter of 50 mM sodium acetate solution at a pH of 6 and dilution rate of one min '1. The effluent was periodically checked to ensure resin saturation. Once saturated, the resin was rinsed with deionized water until no acetate was detected in the effluent. One hundred or 50 mL of a solution of sodium butyrate at a pH of 6 was placed in a baffled, well stirred, reservoir and then pumped through the column in recycle fashion as shown in Figure 18. The acetate concentration was monitored in the stirred reservoir by assaying 0.5 mL samples taken at specific intervals. This procedure was repeated at several different flow rates and concentrations and was also repeated with butyrate- saturated resin exchanging with acetate as well as with bicarbonate. The results of these experiments are presented in Figures 22-31. Figures 22, 24, and 26 show rates of exchange between acetate and butyrate at different total concentrations and flow rates. In each case the resin was initially saturated with acetate and exchanged with a liquid phase containing butyrate. Figures 23, 25, and 27 show corresponding values of overall particle phase mass transfer coefficients calculated from the rate data according to the procedure in the appendix (sample calculation D). The calculated overall mass transfer coefficients are plotted versus the concentration of butyrate in the resin, which corresponds to a progression in the ion exchange process, because the resin initially contains no butyrate. The overall mass transfer coefficients increased with increasing flow 61 rate. This result is thought to be due to improvements in the solution phase mass transfer rate, or explained in terms of the film model, thinner liquid side film. The overall mass transfer coefficients were also observed to increase as the liquid phase concentration increased. This increase is due to larger driving forces in the liquid phase improving the liquid side rates of mass transfer and forcing the process closer to particle phase controlled kinetics, and the larger mass transfer coefficients measured are due to elimination of the liquid phase resistances. A reduction in the magnitude of the overall mass transfer coefficients was observed as a function of time. Initially the resin beads contain only acetate, and butyrate ions can easily access and exchange with acetate ions near the surface of the beads. However, as time passes, the butyrate ions must penetrate deeper into the beads to access sites in the interior of the resin and the rate of mass transfer reflects this slower diffusion through the solid resin. 62 10.0-7— - o—o ZOInUfinhI 9.0- H 37 ml/min 8.0- 7.0- Acetote concentration (mM) 9‘ ‘3 0.0 100.0 200.0 TIME (s) Figure 22. Kinetic experiment run using a differential column packed with 0.227 g of IRA-904 initially saturated with acetate and exchanged‘with butyrate at CT - 20 mM.and pH - 6.0. Column volume - 0.7854 ml with void fraction - 0.35. total liquid volume - 100 ml. (1007- 0—0 20 Int/min H 37 Int/min (LOOS- (LOOS- (1004- (1003- K(BU AC) (3 (1002- (LOOI - (LO OVERALL MASS VANSFEI: fiOEFFlCIENT Y(BU) Figure 23. Experimentally calculated values of overall mass- transfer coefficients versus the solid phase concentration of butyrate in the exchange of acetate for butyrate shown in figure 22. ‘v‘. ’ “:70". ‘.‘ h. F" 63 10.0 I o—o 20 nfl/hfin A 9-0" H 37 ml/min E . E 8.0— V - .5 7-°'. ‘6 6.0— L E I q, $.0“ g . o 4.0 "' o . q) 3.0- ‘6 . ‘6 2.0 - o - <( 1_o- .0. . I . I . I . 0.0 100.0 200.0 300.0 40 3.0 TIME (s) Figure 24. Kinetic experiment run using a differential column packed with 0.227 g of IRA 904 initially saturated with acetate and exchanged with butyrate at C1- - 100 mM and pH - 6.0. Column volume - 0.7854 ml with void fraction - 0.35. Total liquid volume - 100 ml. 0.0074 0.006- 0.005- 0.004- 0.003- 0.002- \’° 0.0 . 0:1 ' 3.2 0'3 ‘ 0.4 0.5 0.6 0.7 Y(BU) OVERALL MA 5 T ANSFER OEFFICIENT Kieu/AC) (s-I‘) Figure 25. Experimentally calculated values of overall mass- transfer coefficients versus the solid phase concentration of butyrate in the exchange of acetate for butyrate shown in figure 24. 64 10.0 - - . H 38 ml/min A 9.0““ H 49 ml/min 2 . E 0.0- V 1 C .. .2 7'0. .5; 5”: 5 5.0- 0. . S 4.0- o . c 3.0- 0 . 1;, 2.0- 0 1 <2 1.0.. 0.0 . 1 . fl . fl . 0.0 100.0 200.0 _. 300.0 400.0 TIME (S) Figure 26. Kinetic experiment run using a differential column packed with 0.227 g of IRA 904 initially saturated with acetate and exchanged with butyrate at CT - 300 an and pH - 6.0. Column volume - 0.7854 ml with void fraction - 0.35. Total liquid volume - 50 ml. 0.012.] o—o 38 ail/min 0.011- H 61 ml/min 0.010- 0.009- d 0.008- 0.007- T 0.006- \ \e 0.005- 0.004- 0.003- 1 0.002 . , 0.0 0.1 V OVERALL MA 3 T NSFER OEFFICIENT 00% (.43 I ' 1 ' r ' I ‘ I ' I ' I ‘ I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Yaw) Figure 27. Experimentally calculated values of overall mass- transfer coefficients versus the solid phase concentration of butyrate in the exchange of acetate for buryrate shown in figure 26. a. . '0‘“ Jva—cnf' 65 Figures (28) and (30) show rate experiments performed with the acetate/bicarbonate, and butyrate/bicarbonate binary systems. In each case the ion exchange resin was saturated with the organic acid anion and then exchanged with bicarbonate at a pH of 7.5. As in Figure 26, the rate of mass transfer was observed to increase as the flow rate was increased up to a certain point; beyond this point, the rate of mass transfer was independent of flow rate. The calculated values of overall mass transfer coefficients at this point were assumed to be particle phase controlled mass transfer coefficients, and therefore, an intrinsic property of the resin and the exchanging ions. These overall mass transfer coefficients are plotted as a function of the resin phase concentration of the species initially in the liquid phase in Figures (29) and (31). 66 A ' IE .8, Z 9 '2 n: '— Z 8 d z 5.0- (3 O E <( ¢- 201nuhnm ti a—a JOInufinm 5% m-m 4OInUhin 0 n H ‘50 «ml/min av 1 m 1 I 14‘__1—‘— 0.0 100.0 200.0 500.0 400.0 500.0 603.0 TIME (SECONDS) Figure 28. Kinetic experiment run using a differential column packed with 0.227 g of IRA 904 initially saturated with acetate and exchanged with bicarbonate at or - 100 m“ and ph - 7.5. Column volume - 0.78510 ml with void fraction - 0.35. Total liquid volume - 50 ml. A | . damn IE ---- E! E a 0.010- O 0 0: 9:: x g 0.012- .. I ‘0 0.000- g 4 H 50 «II/min M £0 cud/min “I 1 o-o :0 cut/«1h i {”54 - «czouuhh ' I - ' . I . - u . . u - g 00 0.2 0.4 0.6 0.5 1.0 O YflNCARBONKflD Figure 29. Experimentally calculated values of overall mass- transfer coefficients versus the solid phase concentration of bicarbonate, in exchange of acetate for bicarbonaehshownnin figure 28. 67 1 0.0“ / _ J & 31mm: CONCENTRATION (mM) 5.0- ./ .2 . 37 0—4 201nuhfin ." H 30 ni/min 0 0 H” 50 val/min . e . . . . . . 0T0— 100.0 200.0 300.0 400.0 500.0 600.0 TIME (SECONDS) Figure 30. Kinetic experiment run using a differential column packed with 0.227 g of IRA,904 initially saturated with butyrate and exchanged with bicarbonate at CT - 100 mu and pH - 7.5. Column volume - 0.7854 ml with void fraction - 0.35. Total liquid volume - 50 ml. 0.0 d1'oh'oh‘ofc‘ois‘oic'oh'oia 0.: Yteucmsomrt) '1' E; can” 5 0.009- I g... t) . 0301- E m 0.005- g ‘ Hum/«a. 0.004- "40“,” d ‘ Hanna/min E 0.00: - Hanan/1.1.1 Figure 31. Experimentally calculated values of overall mass- transfer coefficients versus the solid phase concentration of vicarbonate in the exchange of butyrate for bicarbonate shown in figure 30. ........ 68 The magnitude of the calculated mass transfer coefficients in Figures (29) and (31) were observed to decrease initially as ion exchange progressed and then increased. The decrease in the mass transfer coefficients can be explained by similar reasoning as the acetate/butyrate exchange. However, the increases at large resin phase concentrations of bicarbonate are thought to be artifacts caused by numerical errors. As shown in the appendix, these values are calculated from the experimental data by several numerical differentiations and calculations. Small errors in the data introduce significant errors in these calculations. There are also larger errors introduced at high values of Y(bicarbonate), because this value is closer to the equilibrium value of Y*(bicarbonate); as the two values approach one another small errors in either Y or Y* contributes to a larger error in the inverse of their difference (l/Y*-Y), and hence in the value of the mass transfer coefficient (see appendix). CHAPTER IV 0D INC HAIERIAL BALANCE EQUAIIORS Co uous o The liquid phase material balance for each of the species in a three component, packed bed ion exchange column can be written over a differential section of the column as follow32h° (F/S)(BCi/az) +£(8Ci/at) - -pb(aq1/6t) (13) where, Ci- concentration of species 1 (mole/L) F - volumetric flowrate of feed (L/s) t - time (s) c - bed void fraction pb- packed bed density (g/L) qi- resin phase concentration of species 1 (meq/g) z - axial position (dm) Cio- feed concentration of species 1 (mole/L) qio- presaturation condition of the column for species 1 (meq/g) 69 70 With the following boundary and initial conditions: qi(z.0) - qio @ t-O, 220 (11.) Or uniform presaturation of the resin, and C1(O,t) - C10 @ z-O, tZO (15) or constant feed concentration. The following assumptions are made in arriving at Equation (13): 1. No axial Dispersion. 2. No radial concentration gradients. 3. Plug flow velocity profile. The rate of exchange of species 1 represented by (aqi/at), must then be represented by a rate equation to solve the material balance equations and predict the effluent concentration profiles. There will exist as many material balance equations as there are exchanging ions and an equal number of rate expressions. Thus, six simultaneous partial differential equations must be solved for the prediction of the effluent concentration profile for a ternary system. The total number of simultaneous partial differential equations to be solved for an n component system is Zn. In addition, effects such as axial mixing and the possible effect of co-ions and counter ions on one another and on the overall exchange process would further increase the complexity of the model. 71 Tanks In Series flodel Material balance equations can be written for the ion exchange column based on the tanks in series model. This model assumes that no radial concentration gradients exist in the column being modeled; Fujine, Saito and Shiba22 have shown this to be a valid assumption. Different degrees of backmixing are modeled via different number of stirred tanks in series. Since each tank in the model is perfectly mixed, modeling the column with a small number of tanks represents a great degree of mixing in the column, while modeling the column with a larger number of tanks represents less axial mixing and an approach to plug flow conditions. The analogy between a packed bed and N tanks in series is shown schematically in Figure (32). The material balance for each component can then be written for the Nth stirred tank as follows: VTdci(N,t)/dt - F(C1(N-l,t)-C1(N,t)) - Wrdqi(N,t)/dt (16) where: VT - liquid volume in each stirred tank (L) t - time (s) N - axial position index indicating the number of stirred tanks from the inlet. F - solution volumetric flow rate (L/s) 72 C1(N,t) - time dependent liquid phase concentration of species 1 in tank N (mole/L solution). qi(N,t) - time dependent resin phase concentration of species 1 in tank N (meq/g of dry resin). C1(N-l,t)- time dependent liquid phase concentration of species 1. in tank N-l (mole/L solution). Wt - resin weight contained in tank N (g dry). There will be three such equations in each tank for a three component system which must then be solved together with the rate equations. It should be noted that each partial differential Equation in (13) has been replaced by N ordinary differential equations; since each tank represents a fixed axial position, the composition in each tank is a function of time only. Thus, the six simultaneous partial differential equations are converted into a (GXN) system of ordinary differential equations. Generally, for rapid ion exchange processes such as this, the liquid and solid phase compositions will not be in equilibrium, and sole knowledge of the equilibrium theory of multicomponent ion exchange will produce results that will be inaccurate. It is therefore necessary to model the kinetics of the exchange process. 73 0 ,...... ME} Figure 32. The analogy between stirred tanks in series and a packed column. 74 RKTE THEORY The rate of transfer of species between phases is a traditional chemical engineering problem that has been extensively studied. Assuming that the rate of ion exchange at the resin active sites is rapid relative to diffusion of ions to the active sites, a typical concentration profile for species 1 would be expected, as shown in Figure 33. The liquid phase concentration of species 1, which is being adsorbed onto the resin, drops from a bulk value of 01(bu1k) to C1(int) at the interface. The resin phase concentration drops from an interfacial value of q1(int) to its lowest value at the center of the particle. LIQUID PHASE 0 MM! 00.1) RESIN PHASE flint) 'ufla PARTICLE CHV'TERLINE {L Figure 33. Distribution of species (i) between the resin and the liquid in contact with the resin. Species (i) is being transfered from the liquid phase to the resin phase. 76 C1(int) and qi(int) are taken to be in equilibrium and are related by the equilibrium partition coefficient. If the electrical potential due to the separation of charges between liquid phase and the resin may be disregarded, the rate of mass transfer in each phase can be represented by the product of a mass transfer coefficient and a driving force. A local mass transfer coefficient (k) can be defined based upon the assumption of an imaginary film of thickness (6) across which the concentration drop or rise occurs. This film is schematically represented in Figure (34), and the defining equations for the liquid-phase and resin-phase local mass transfer coefficients are given as Equation (17) and (18). N1 - kc(61(bulk)-Ci(int)) (17) Since no chemical reaction takes place at the interface and there is no accumulation of mass, the liquid phase flux must equal to the flux of species into the resin: N1 - kq(qi(int)-q1(avg)) (18) In Equation (18), flux of component i across the interface (Ni) is expressed in terms of local mass transfer coefficient (kq) and driving force (q1(int) - qi(avg)). fiwwmw—mg -—_ 77 LIQUID PHASE RESIN PHASE PARTICLE CENTERLINE -_._/ {— NH“ K \ “ -\qi(int) Figure 34. Distribution of species (1) between the resin and the liquid in contact with the resin represented together with the film model. 78 In general, interfacial compositions are difficult to measure; the use is therefore made of an overall mass transfer coefficent (Kc) and a corresponding overall driving force. This driving force is defined as the difference' between the bulk liquid concentration of the exchanging species and the liquid phase concentration that would be in equilibrium with the average resin phase concentration (Ci*): N - Kc(Ci(bu1k)-C 1*) (19) 1 W: The transfer of species 1 between the liquid and the resin phases can be thought of as a series of consecutive steps, each with an inherent resistance to mass transfer. This is known as the resistances in series model. These steps are listed below: 1. Diffusion of ions from the bulk liquid phase to the outer boundary of the liquid side film. 2. Diffusion of ions through the liquid film to the resin surface. (For porous particles one must also include the diffusion of ions into the pores of the resin). 3. Diffusion of ions into the solid or gel resin matrix across a particle side film to the ionic exchange groups of the resin. AF'A! 79 a. The exchange of ions for counter ions. 5. Steps 1-3 in reverse order for the counter ions diffusing back out of the resin particle and into the liquid phase. The rate controlling step is defined as the slowest step, such that the rate of mass transfer in this step adequately represents that .23 first showed the rate of the entire process. Boyd et. a1 controlling step to be diffusion either‘within the particle or in the stagnant liquid film; in some cases, both mechanisms may affect the rate. Ion exchange is said to be solution phase mass transfem' controlled when diffusion across the liquid film is rate limiting, and particle phase mass transfer controlled when the diffusion of ions within the particles is rate limiting. Wins Omateteza, has shown that for solution phase mass transfer controlled case in a ternary system, the rate of mass transfer is well represented by the following equation: n (dxi/dt)z - (Co/Q @1131 ~,j(xj*- xj> (20> jui Where Xi - solid phase average concentration expressed in terms of equivalent fractions (Y1 - qi/Q). { 80 Q - total capacity of the resin (meq/g dry resin) 00- inlet feed total concentration - (2 Ci)z-O (Mole/L) Wt - total resin weight (g dry) ”ij- liquid phase ternary overall mass transfer coefficient predicted from binary coefficients (s'l). Xj - average liquid phase composition of species j, in equivalent fractions. X] - 61/60 for constant total concentration Xj - Cj/CT for variable total concentration CT - local total concentration - (2 Ci): Xj* - liquid phase concentration in equilibrium with the resin phase of composition Xi. ref 0 I X*- j j (21) ref n £1 “1: 1k n - number of species aief- separation factor between a reference component and j ref xj xref a '— j (22) 1ref xj The ternary overall mass transfer coefficients can be calculated from binary coefficients by applying the multicomponent theory of Bird, amw.€-WT':$%, a. .. "Marta. martini-543.1” '- . A, '4 4" ~'..r._-..._- :1 v c : A 81 25 Stewart, and Lightfoot to diffusion of ions in the liquid phase. The result is shown in Equation (23)2h: _ Kij[(xj+xk)x1k + xixik] ‘3 xixjk + xjx1k + xkxij (23) Since the resin particles are spherical and a radial concentration gradient exists within them, an average Y will be defined as follows: 11 - <3/R3>0I“ vim 1:2 dr (24) 2art1sl2_2aas2_uass_Iran§fer_£2ntrnllins For the particle phase mass transfer controlling step, Omatete has shown that n «sq/dc)z ~ng 511 (1:1 - 11*) (25) jvi adequately represents the rate of mass transfer. gtl-solid.phase overall ternary mass transfer coefficient predicted from binary coefficients. 82 arefx x*- J 3 (26) J n ref kflak xk The ternary overall mass transfer coefficients for the particle phase can be calculated analogously to the liquid phase ternary coefficients by Equation (27): Kijuxjdkmik + 11511.1 Xink + 131511: + X151) (27) ‘1 The study of the pore mass transfer controlling case is ignored, and the particle phase is taken as a whole, including the pores. The corresponding particle phase mass transfer coefficient used is then the effective particle phase mass transfer coefficient. Vermeulenzo, and Vermeulen and Quilici21 have shown that for the pore mass transfer controlling case a driving force using particle side concentrations is a valid approximation. It is therefore possible to model the pore phase mass transfer controlling case by the product of a particle phase driving force and a pore phase mass transfer coefficient. The pore mass transfer equation and the particle phase mass transfer equation can then be combined as the product of the particle phase driving force and an effective particle side mass transfer coefficient. 83 c e ase nd So u 0 Phase ntro For the case where both the liquid and the particle phase control the rate of mass transfer, the so called transition regime, the overall mass transfer coefficient is calculated by a sum of the resistances model 34. 1/15ij - m/kij + 1/313 (28) Where: 1511 - overall particle side binary mass transfer coefficient 1511 - local particle side binary mass transfer coefficient kij - local solution side binary mass transfer coefficient m - slope of the equilibrium isotherm Converting the material balance Equation (16) to equivalent fraction form and assuming constant total concentration yields: vTcodx;<"'t)- FC (X1(N-1,t)-Xi(n,t)) - w QdI;(N't) (29) dt ° r dt with the boundary conditions: X:l - X1(O) N - 0, (20 X3 -Xj(0) N-O, tZO X k - l - X1(0) - X (0) N - 0, tZO J N - 0 represents the inlet to the column, or axial position (z-O) where all concentrations are that of the feed. and the following initial conditions: 11 - X1(o) t "' 0, NZ]. %-Xflm t-0.&1 1k " 1 ' 11(0) ' 11(0) ‘3 " 0. N21 Component material balances of Equation (29) must then be written for all counter ions and solved simultaneously with the rate equations shown in Equation (30): dxi(N.t> _ dt n * 30) jwi 85 NUMERICAL SOLUTION METHOD Because of the complexity of the equations defined by Equations (29) and (30), the system was solved numerically. A third-order Runge-Kutta algorithm using a predictor corrector scheme was written to solve the equations. This scheme was then combined with a fortran simulation program to model the unsteady-state performance of the substrate shuttle unit. The substrate shuttle program was designed for ease of operation and is controlled by four basic parameters that control the following: 1. The manner in which the needed constants are entered into the program, (i.e. interactively or via an input file). 2. The concentrations that need to be monitored, (i.e. liquid phase or resin phase concentrations). 3. The independent variable,(i.e. time or bed volumes). 4. Process periodicity, (i.e. whether the adsorption/desorption event is a single operation or a cyclical multiple adsorption/desorption process). A logical flow chart of the program is shown in Figure 35. firm?! , .1.‘y o~.'. ‘ Figure 35. Computer flow chart showing the logic flow for the Fortran program written to simulate the Substrate Shuttle. Please refer to the appendix for a copy of the Fortran code. 87 Figure 35. 88 m u olut e e ent E uations The computer model of this process solves the material balances equations together with the rate equations by using the method of characteristics together with a third order Runge-Kutta technique with ‘ a predictor corrector scheme. The method works as follows: given the initial conditions of known composition in the resin and the boundary conditions at the inlet to the column, (i.e. inlet to the first tank), all concentrations in the first tank are calculated for a small time step. 'The concentrations of tank (2) can then be calculated at constant time using the liquid phase concentration of tank (1) as inlet to tank (2) and so on up to tank (N). The composition of the liquid phase in tank (N) corresponds to the effluent of the column. Another time step is then taken, and the same steps are repeated until a desired length of time is reached. The predictor corrector Runge-Kutta technique works as follows: 1. All needed mass transfer coefficients and equilibrium values are calculated from the initial conditions of tank (1). 2. At constant N, assuming dXi/dt - 0, an estimate of X1(N-l,t+At) is calculated. X1(N,t+At:) + x1(N,t) 3. Based on an average X value of X - , a avg 2 first estimate of 11(N-1,t+At) is calculated. 89 4. X1(N-l,t+At) is recalculated based on the new value of 11(N-1,t+At) and again averaged. 5. The final value of 11(N-l,t+At) is calculated from the corrected value of X1(N-l,t+At). 6. If the value of Xi(N-1,t+At) is different from that in step (4), it is recorrected by using 11(N-1,t+At) from step (5). 7. The X1(N-l,t+At) is used as the inlet to tank (2) and the same steps are then repeated on tank (2) and so on up to tank (N). 8. The liquid and resin concentrations in each tank are stored as initial conditions for the next time step. 9. Starting at tank (1) the operation is repeated with new initial conditions in each tank. The time step for the solution of the differential equations must be chosen (by trial and error) to minimize computer run time while maintaining accuracy. Generally time steps between (0.5 to 5 seconds) provided stable solutions. Low liquid phase concentrations produce gentle slopes in effluent profiles and can be stable at larger time steps z 5 seconds, while high solution concentrations produce steep breakthrough curves and must be run with smaller time steps (5 0.5 seconds). It would be desirable in future work to optimize this time step size as a function of total solution concentration and total number of tanks to achieve results in shortest possible time and to program this variation into the model. In this way, depending on process conditions, an optimal step size could be calculated by the program. 90 P o r o nta on Input File: It is necessary to have an input file to enter the needed. parameters into the program if (PAR l - F), or the data is not being entered interactively. The values of the following parameters must be contained in the input file, with each value entered on a separate line. . Total resin weight (g). . weight percent water in resin (8) Inlet concentration of acetate (mM). Inlet concentration of butyrate (mH). Inlet concentration of bicarbonate (mfl). 0‘04?me . Presaturation condition of resin with acetate (equivalent fraction). 7. Presaturation condition of resin with butyrate (equivalent fraction). 8. Total process duration (8). 9. Time step size for solution of differential equations (5). 10. Resin capacity (meq/g). 11. Number of tanks in series. 12. Volumetric flow rate (mL/s). 13. Column diameter (cm). 14. Resin bed volume (mL). 15. 16. 17. 18. 19. 20. 91 Average separation factor for (Bu/HC03- ). Average separation factor for (Ac/HCOa' ). Data storage or printing frequency (number of time steps per data output). Parameter 2 (X or Y). Parameter 3 (B or T). Parameter 4 (s or C). The remaining variables (21 through 27) need to be entered for cyclical operation; if the operation is single pass, then a value of (0) can be entered for the remaining variables. 21. 22. 23. 24. 25. 26. 27. Maximum acetate concentration allowed in effluent (mM). Minimum acetate concentration allowed in effluent (mu). Maximum butyrate concentration allowed in effluent (mu). Minimum butyrate concentration allowed in effluent (mu). Acetate concentration in the discharging stream (mM). Butyrate concentration in the discharging stream (mM). Bicarbonate concentration in the discharging stream (mM) . Where, the discharging stream refers to the stream that would be used to exchange with the column saturated with the fatty acid anions and to release these ions into the methanogenic reactor during the "discharging cycle”. If (PAR l - I) then all of the above variables are prompted for by the program and must be entered interactively. 92 Cyclical Operation: Because the operation of the substrate shuttle is cyclical in nature, the program was designed to simulate continuous charging and discharging of the column as follows. The resin in the column is initially saturated with bicarbonate or mostly with bicarbonate. A stream rich in volatile fatty acid anions (from the acidogenic reactor) is passed through the ion exchange column. The volatile fatty acids are exchanged for bicarbonate and slowly, as the column begins to saturate with these acids, they begin to leak out. Since these acids are to be captured and later converted to methane, the leakage concentrations, (as indicated by the critical breakthrough concentrations), must be controlled. Once the concentration of either one of the desired products reaches the critical concentration, the program can signal a solenoid valve to divert the inlet solution into a second column and to divert another stream, rich in bicarbonate (from the methanogenic reactor) into the column. The effluent of the column can now be easily sent to the methanogenic reactor by an appropriate signal to a second solenoid valve. This discharging process continues until the effluent concentration of these acids drops below other critical values. At this time the program signals all appropriate valves to return to their initial settings and begins to ”charge" the column with the acids once again. K .‘(i iii-'77: 93 Data Storage : Since the program has not yet been connected to an actual process, its output is stored in data files in the form of nondimensional concentration versus time or bed volumes. These data files have been defined within the program with the command, “status-'OLD" and therefore must already exist before the program can be run. Initially they will ofcoarse contain no data. For the purpose of run time optimization the output is not stored at every time step at a specific interval. This data storage interval must also be optimized as a function of step size, process length, number of tanks in series and any other variable that affects the run time. This variable was found to strongly affect the computer time required to solve a process simulation. It is estimated that once the program logic has been optimized, this variable alone will most strongly affect run time. This parameter (SPC) is entered as an integer showing the number of time steps between data entries. 94 (IIIBARISON OF'HDDEL.TO EMPERIHENTAL DATA M d Ve 0 or 0 on n S ems Particle Phase Controlled Kinetics: The values of the mass transfer coefficients measured at high flow rates were assumed to be particle phase controlled mass transfer coefficients.. The calculated values of the particle phase mass transfer coefficients were then correlated with the particle phase concentration of the species initially having the lowest concentration in the resin by means of curve fitting techniques. Thus, in acetate/butyrate exchange using resin that was initially saturated with acetate, the particle phase concentration of butyrate was used as the independent variable showing the progress of ion exchange. The mathematical form of these correlations was not chosen based on theory but rather based on good fit. The acetate/butyrate particle phase controlled mass transfer coefficients were fit using Equation (31): rBU,AC- B(1) eXP(B(2)*X(BU)) + 3(3) (31) Table 3 shows the calculated values of the coefficients B(1) , B(2), and B(3) as a function of total liquid phase concentration. " \_ .-. my“. 95 Table 3. Statistically calculated values of constants for the regression fit of particle phase controlled mass transfer coefficients used in equation (31). Constant 20m“ . lOOmM 200mM 300mM l . 5M B(1) 0.006694 0.009511 0.01301 0.01297 0.01299 B(2) -7.39877 -4.89570 -1.4707 -l.1012 -0.9573 B(3) 0.001267 0.002548 -0.00016 -0.00025 -0.00012 The values of B(1), B(2), and B(3) were found to change with total concentration up to 200 mM, however, at all concentration above 200 In}! these values appeared to remain constant. A total concentration of 200 ml! appears to be the lowest concentration for the attainment of particle phase controlled kinetics, because the value of the particle phase controlled mass transfer coefficient must be independent of the liquid phase concentration. No further experiments were performed to verify the variations in the particle phase mass transfer coefficients at concentrations below 200 mM. In this investigation, the particle phase mass transfer coefficients at lower concentrations than 200 ml! were calculated by the constants given in Table 3 and were assumed to vary as measured. The particle phase controlled mass transfer coefficients for the exchange of bicarbonate with butyrate and the exchange of bicarbonate with acetate shown in Figures (28) and (30) were curve fit using equation (32): 1311 - 3(1) + B(2)*Y(HCO3) + B(3)*x(nc03)2 (32) 96 where i - bicarbonate j - acetate or butyrate For j - acetate B(1) - 0.022035 B(2) - -0.061160 B(3) - 0.0639270 For j - butyrate B(1) - 0.0120195 B(2) - ~0.024088 B(3) - 0.0240139 Figures 36-39 show the fit of the model to experimental data for the system of acetate and butyrate in the particle phase controlled regime. The values of B(1), B(2), and B(3) used for acetate butyrate exchange were those of the experiment performed at 1.5 H shown in Table 3. The total concentrations are 200 mfl, 300 mM, and 1500 mM for Figures (36), (37), and (38) respectively, while the liquid flow rate, pH, and amount of resin are held constant. In Figure (39), both charging and discharging cycles of the acetate/butyrate system are shown using the experimentally measured acetate/butyrate separation factor. 97 5.0 . acetate/butyrate exchange ACETATE CONCENTRATION (mM) ‘ IWUINCfliiPROFRE o EXPERflfliflILINfiA 0.0 ‘ ' fi 1 U I I . 0.0 1 00.0 200.0 300.0 400.0 TIME (SECONDS) Figure 36. Comparison of model prediction with experimental data in the exchange of acetate with butyrate. Total concen- tration 8 200 mM. pH = 6.0. Experiment performed in the differential column with 0.227 g of IRA 904 under particle phase controlled kinetics, i.e. flow rate = 50 mllmin. Total liquid volume - 100 m1. 98 10.0 . acetate/butyrate exchange ‘ 0 EXPERIMENTAL DATA - PREDICTED PROFILE ACETATE CONCENTRATION (mM) 200.0 300.0 400.0 TTME (SECONDS) 0.0 100.0 Figure 37. Comparison of model prediction with experimental data in the exchange of acetate with butyrate. Total concentration of liquid - 300 mM. pH - 6.0. Experiment performed in the differe" tial column with 0.227 g of IRA 904 under particle phase controlled kinetics, i.e. flow rate = 50 mllmin. Total liquid volume = 50 m1. 41) <3 EXPERMWENTAL.DAIA - PREDICIED PROFILE SJ)- ACETATE CONCENTRATION (mM) I" O l acetate/butyrate exchange 0.0.,.,., ,.,.,. 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 TIME (SECONDS) Figure 38. Comparison of model prediction with experimental data in the exchange of acetate with butyrate. Total concentration of liquid - 1.5 M, pH - 6.0. Experiment performed in the differen- tial column with 0.227 g of IRA 904 under particle phase controlled kinetics, i.e. flow rate = 50 mllmin. Total liquid volume - 50 ml. 100 8 "Jf* J acetate/butyrate exchange ’r””’ IE 7- 9” E . z .J 9 6 ,2 . 0: 5" I- . 2 id 4- o E . o 3'] .— 2: 2- g I ELUTTON OF ACETATE BY BUTYRATE _J 1.1 PREDICTED CURVE. ALPHA== (1/6.2) “J j - - PREDICTED CURVE. ALPHA= 6.2 0 o ELUTION OF BUTYRATE BY ACETATE ' l ‘ l ‘ T ' 0 100 200 300 400. TIME (SECONDS) Figure 39. Comparison of model prediction with experimental data in the exchange of acetate by butyrate and the exchange of buty- rate by acetate using the measured separation factor - 6.2. total concentration - 270 mM. pH - 6.0. Experiment performed in the differential column with 0.227 g of IRA 904 under particle phase controlled kinetics, i.e. flow rate = 50 mllmin. Total liquid volume - 50 m1. 101 As shown in Figures (36) through (39), the model predictions of experimental data at different concentrations and total volumes are very accurate. Since the particle phase controlled mass transfer coefficients are not varied between Figures (36), (37), (38), and (39), the experimentally evaluated rates of mass transfer are thought to accurately describe particle phase controlled kinetics. Solution Phase Controlled and Transition Regime: At relatively low flow rates, changes in the liquid superficial velocity were found to affect the rate of ion exchange. These effects were modeled via a solution side mass transfer coefficient. Vermeulen et. a1.20 list the following equation for the solution phase mass transfer coefficient in a column packed with spherical particles and for the case of liquid-solid contact: ks _ kl DE (F/A)k2 (33) d 1.5 P where ks - solution phase mass transfer coefficient (5'1) Df - liquid phase diffusion coefficient (cmz/s) dp - particle diameter (cm) F - volumetric flow rate (cm3/s) A - column cross sectional area (cmz) kl,k2 - empirically fitted constants. (kl - 2.62 and k2 - 0.5) 102 In this investigation the solution phase mass transfer coefficient was modeled by the same form of equation; however, different values of kl and k2 were found to better describe the data. Equation (34) was used to model variations in the solution phase mass transfer coefficient. ks - kl' (F/A)k2 (34) The value of the constant k2 was found to be the same in all cases. k2 - 2.2 However, the value of the constant kl' was found to vary, depending on the binary system studied. These constants are listed in Table 4. Table 4. Values of the first constant in the solution phase mass transfer coefficient, Equation (34). System kl' acetate/butyrate 0.11090 acetate/bicarbonate 0.16820 butyrate/bicarbonate 0.14710 The values of the constant kl' contain liquid phase diffusivities and particle phase diffusivities and therefore cannot be directly compared to the value of kl suggested by Vermeulen et. a1 20. The magnitudes of these constants are consistent with estimates of liquid phase diffusivities. These diffusivities are 2.0 X lO'ScmZ/s for 35 bicarbonate , 1.6 X 10-5 35 cm2/s for acetate , 1.0 X 10-5cm2/s for butyrate 36. The binary diffusion coefficients can then be calculated 103 by the method of Omateteza ; these binary diffusion coefficients will have a magnitude comparable to a mole fraction average of the individual diffusivities. It can therefore be predicted that the binary system of acetate and bicarbonate should have the largest kl' and that the smallest value of k1' will belong to the system of acetate and butyrate . Vermeulen et. al.20 suggest that the solution phase mass transfer coefficient is weakly dependent on the superficial velocity (square root dependence). However, the solution phase mass transfer coefficient was found to have a much stronger dependence on the superficial velocity as shown by a value of 2.2 for k2. This stronger dependence was thought to be the product of the high resin porosity, (listed as ep - 0.5 ml. pores/mL). Increases in the liquid superficial velocity are thought to affect the liquid concentration within the pores and affect the rate of mass transfer to a greater degree than for a nonporous resin. For prediction of effluent concentration profiles, overall mass transfer coefficients were calculated from the particle phase mass transfer coefficient and the solution phase mass transfer coefficient according to Equation (28). These overall mass transfer coefficients were then used with appropriate driving forces to model the effect of changes in the liquid superficial velocity on the binary exchange of acetate with butyrate. The results are shown in Figures (40) through (42). Model predictions and experimental data are in good agreement. Figure (43) compares experimental data to model predictions for the exchange of butyrate with bicarbonate, and Figure (44) shows the 104 same results for the exchange of acetate with bicarbonate. In each case the resin was initially saturated with the organic acid and then exchanged with an aqueous bicarbonate solution of 100 mM concentration at pH - 7.5. It is readily evident that the model's fit for the binary exchange of acetate/bicarbonate and butyrate/bicarbonate to experimental data is not as good as the model's fit to experimental data for the acetate/butyrate exchange. Figures (43) and (44) show that the model only predicts exchange behavior accurately for short' times, but as ion exchange progresses the model overpredicts the effluent concentrations. This overprediction of effluent concentration is another indication that the increases calculated in the overall mass transfer coefficients in Figures 29 and 31 are results of numerical and/or experimental errors. These errors are explained on page 68 and also in sample calculation D of the appendix . 105 10.0 ,_\ 1E acetate/butyrate exchange V 8.0~ Z 9 '— 3‘: 6.0- p. Z I LU ‘2’ O 4.0~ 0 d I‘.‘ < 2.0- 8 ”gag—=3 FLow RATE 0 J 8 =1? 0 37 ml/min <( o 20 l/ ° n1 nun 0.0/ .— , . , . , . 0.0 I 00.0 200.0 300.0 400.0 TIME (s) Figure 40. Comparison of model prediction with experimental data for the effect of changes in the liquid superficial velocity in the exchange of acetate with butyrate. Total concentration = 20 mM, pH - 6.0, liquid volume - 100 m1. Experiment performed in the differential column using 0.227 g of IRA 904. 106 10.0 3;. acetate/butyrate exchange E V 8.0- Z 9 ‘ '— 3‘: 6.0- I— I: 11.] ‘z’ 8 4.0- 5'9~"‘.,9 2 20- /°’ ’ : FLOW RATE . ’,,”, b /g/ 2 ‘ ’99 a 37 mI/man o 201nu0nh| OJ) . I . I . I . 0.0 1 00.0 200.0 300.0 400.0 TIME (s) Figure 41. Comparison of model prediction with experimental data for the effect of changes in the liquid superficial velocity in the exchange of acetate with butyrate. Total concentration 8 100 mM. pH - 6.0, liquid volume - 100 ml. Experiment performed in the differential column using 0.227 g of IRA 904. 107 10.0 A :2 E acetate/butyrate exchange ; 8.0- ////’é C) K45>’ I: /a’// < /¢ a: (iO- ,// E / / DU //K;/0 5:) /° 0 4.0- 0 1‘! < 2.0- FLOW RATE t] i a 61 ml/min 0 ‘ o 49 ml/mm <( 011*, o Jaunymmn ° 0.0 ‘ 100.0 ‘ 200.0 300.0 400.0 TIME (s) Figure 42. Comparison of model prediction with experimental data for the effect of changes in the liquid superficial velocity in the exchange of acetate with butyrate. Total concentration - 300 mM pH - 6.0, liquid volume = 50 m1. Experiment performed in‘fhe‘—_—_“ differential column using 0.227 g of IRA 904. 108 12.0 J butyrate/bicarbonate exchange A :2 . E 10.0d c: . :3 8.0— U L. .1 .‘J I C I (D 6.0-I I U C . 8 4.0-J Q) “6 . ‘- .. o 30 mI/min 43‘ 2.0.. " A 20 mI/min no u o 50 nfl/nfin E 40 nfl/nfln 0.0 I ‘ l ‘U l U j I l U l fl 1 1 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 TIME (s) I Figure 43. Comparison of model prediction with experimental data for the effect of changes in the liquid superficial velocity in the exchange of butyrate with bicarbonate. Total concentration =100mM pH = 7.5, liquid volume = 50 m1. Experiment performed in the differential column using 0.227 g of IRA 904. 109 12.0 acetate/bicarbonate exchange 0 A ‘ T 2 A E V c: .9 .JJ t) L. “J . c: I 0) U C O U 0 4.1 .3 o 30 ml/min 2; .a 20InhflnhI U y o 50 mI/min s 40Infl/hfln 0.0 U j t I ‘I I ‘I l U I fl l I 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 TIME (s) Figure 44. Comparison of model prediction with experimental data for the effect of changes in the liquid superficial velocity in the exchange of acetate with bicarbonate. Total concentration=100 mM pH = 7.5, liquid volume - 50 ml. Experiment performed in the differential column using 0.227 g of IRA 904. 110 MdeV cto o reeComonetStes Ternary overall particle phase mass transfer coefficients were calculated from binary ones by Equation (27) and used to predict ternary column behavior. One such prediction is shown in Figure (45). The resin was initially saturated with 100 mM sodium bicarbonate and then exchanged with an aqueous solution of 50 mM sodium acetate and 50 mM sodium butyrate at pH - 6.0. The total solution concentration was therefore 100 mM. This would place the rate of mass transfer in the transition regime where the rate is controlled by both phases. A larger quantity of resin (1.58 g) was used in the column, which occupied a volume of 4.8 mL. The concentration profiles predicted by the model rise more steeply than the experimental results shown in Figure (45). The liquid phase has a low bicarbonate solubility at a pH of 6. Once the solubility limit is reached, additional bicarbonate is converted to gaseous carbon dioxide and lost from the system. This mechanism maintains a low liquid phase bicarbonate concentration, and hence, a large driving force for ion exchange. Thus, acetate and butyrate are more effectively adsorbed at a pH of 6 than at 7.5, where the bicarbonate solubility is higher. This reasoning explains why the observed experimental concentrations were smaller than those predicted by the model . 111 00.0 -——--—-- —---——----—- 1p——°——4L——.——____. A D D D D E c I o I E I I c: I o I (3 I 8 I 0 i I 0 Ida 0 Met. 200.0 300.0 430.0 TIME (s) Figure 45. Comparison of model predictions with experimental data in the three component exchange of acetate, butyrate and bicarbonate ions. Column inlet concentration - 50 mM acetate, 50 mM butyrate, pH - 6.0. Flow rate - 20 mllmin. CHAPTERV W Experimental and modeling studies of a three component anion exchange process for the system of acetate, butyrate and bicarbonate were performed. Conclusions based on the results of this work are as follows: 1. Investigation of equilibrium behavior for the exchange of acetate with butyrate showed that the resin (Amberlite IRA 904) became more selective for butyrate ions at lower pH. This effect resulted, in part, because the resin adsorbed butyrate to excess of its ion exchange capacity. The mechanism for this non-ionic sorption was not determined. 2. Under all concentrations studied the resin prefered butyrate to acetate. The average separation factor at 25 °C and a pH of 7.5 was 0'2:- 4.0, and at a pH of 6.0 and the same temperature the average separation factor increased to aBu- 6.2. Ac 3. At a pH of 7.5 and a temperature of 25°C the resin prefered bicarbonate to both acetate and butyrate. The average separation Bic Bic Bu - 3.5) and (0 factors calculated were (a Ac - 30). 112 'I. In, 113 . At relatively low flow rates the overall rates of ion exchange were found to increase as a function of liquid superficial velocity. . The liquid phase mass transfer coefficient was found to depend on superficial velocity of the liquid by a power of 2.2 inIall cases. This was a stronger dependence than suggested by Vermeulen et. al.20 for columns packed with spherical particles. . Particle phase mass transfer coefficients were found to decrease as the ion exchange progressed for all systems. . Binary exchange behavior was predicted adequately using the film model for all systems studied. . Ternary model predictions did not fit experimental data adequately. The discrepancies were thought to be due to variations in the liquid phase concentration of bicarbonate as a function of pH, variations in equilibrium behavior as a function of pH, and also gas formation in the ion exchange column. 7- mgr-Tag?“- .1. CHAPTER VI RECOMMENDATIONS From the results of this exploratory work, the following recommendations are given for future research: 1. Investigate the mechanism of butyrate adsorption to excess of resin capacity. . Incorporation of bicarbonate chemistry to the model in predict variations in the concentration of bicarbonate as a function of pH. . Investigate effect of pH on equilibrium isotherms for the systems containing bicarbopate. . Investigation of the effect of resin fouling on ion exchange properties such as operating resin capacity and rate of mass transfer. . Comparison of model predictions to experimental data obtained from non-differential ion exchange columns. 114 APPENDICES CHAPTER‘VII mm DERIVAIIONS AND JUSTIFICATIONS De v ar t actor Using the definition of the separation factor, Equation (10), and dropping the subscripts, Equation (35) is obtained: Y - 0X (35) l + (a - l) X allow 5 - a - 1, thus a - 3 + 1 Y - (B + 1)43_ (36) 1+px Area below isotherm (II) - I; Y dX (37) Area above isotherm (I) - I; (l-Y) dX (38) This reasoning can be seen in Figure (2). The Substitution of (36) into (37) and (38) results in (39). 115 116 1 Area (11) - f (a + 1) x dx (39) 0 1+px And 1 Area (I) - 1 - f (a + 1) dX (40) 0 1 + p X The ratio of the two areas can be related to the separation factor by using an arbitrary variable (a). 1 let a - I (B + l) dX (41) 0 1 + p X then the ratio of the two areas can be related to (a) by Equation (42) . - a (42) a __ l-a Area (I) The integration of Equation (42) results in Equation (43). 2 1 a - (5 + 1) IX/fl - l/fi 1n(1 + flX)]o (43) Evaluating Equation (43) at its limits and substituting a for (13 + 1) results in an equation exclusively in terms of a. - a ln(a) (44) __9____ (a - 1) (a _ 1)2 .5 A Pvl‘u .g . 117 In terms of the ratio of the areas, a is solved to result in the 1 - a following relationship: (0:2 - a - a 1n 0:) eregglll - a — 1g - 112 (45) Area(I) 1 - a 1 _ I 2_ _ J J (a - 1)2 Equation (45) cannot be explicitly solved for 0:; however, it is quite simple to make use of root finding programs to solve for a by trial and.error once the ratio of the areas above and below the isothermIis known experimentally. The process model in this study makes use of the separation factor rather than the selectivity coefficient and the following is a justification for the use of the separation factor. J t o o s athe a ec iv The separation factor 0:: indicates directly the preference of a given phase, in this case the resin, for the superscript ion in question. It is the ratio of the distribution coefficient of ion A to that of ion B. a: - ratio of fractions of ion A between solid and liggid ratio of fractions of ion B between solid and liquid J 118 Although the experimentally determined separation factors for many exchange processes are not constant, the ratio of the areas technique has provided a means by which a best fit factor can be determined. This then represents the preference the resin has for one ion over another over the entire range of equivalent fractions at some constant total concentration. This is true even for divalent/ monovalent ion exchange. The selectivity coefficient K: at constant total concentration Co is the ratio of the squared distribution of the monovalent species to the distribution of the divalent species; as such it is influenced by the units of the resin capacity and total concentration Co. Consider the following example as demonstrated by Cliffordz. A5 + 2 3' -—————~ 2 3‘ + AF (46) y ' B [B I2 [A I KA - Y X (47) 2 [an [Ayl B C Y2 X EA - O B A (48) Q 2 x3 YA Assuming the resin has no preference for either ion, we can then write YB - xB (49) J 119 YA - XA (50) B c E - o (51) A Q It is now clear that the value of the selectivity coefficient is dependent on the units of liquid and resin phase concentrations. For example if we allow the resin capacity to be 1 (eq/L) of resin and the total concentration of the liquid to be 0.005 eq/L of solution we get: B EA. 0.005 While choosing units of (meq/L) will result in the value of selectivity coefficient 1000 times larger. EA - 5.0 Either of the above choices of units for Co yields a selectivity coefficient which infers a large preference by the resin phase, first for ion A then for B. However, neither inference is correct, as the resin has an equal affinity for each ion. The separation factor being independent of C0 and Q correctly infers no preference with OTB - 1.0. A It should be noted that all ions in this study were monovalent and that based on this factor alone the selectivity coefficient can be used in the same sense as the separation factor. However, if this work were extended to the recovery of divalent or trivalent anions "II. A‘ aha:- 120 such as citric acid, then the use of the separation factor can easily be justified. 121 EHUIPLE CALCULKTIONS A. Equilibrium Isotherm Calculations The calculations shown are from the acetate/butyrate equilibrium isotherm at pH - 7.5 shown in Figure (19). The liquid volume in each sample was 100 mL. Table 5 . Equilibrium isotherm experimental data obtained for acetate and butyrate after shaking for 36 hours. 931511;» a Initial Concentration Final Concentration Resin wt. Sample AC (mH) BU (mM) AC (mM) BU (mM) (g) 1 273.0 0.0 240.74 30.39 3.00 2 273.0 0.0 213.85 53.16 6.00 3 0.0 278.0 110.88 157.14 7.25 4 0.0 278 39.12 200.09 3.36 Calculations carried out for sample #1. 30.39 30.39+240.74 X - 0.1121 30" 3- 240.74x10'3)“le (0.1 L) - L Total acetate adsorbed - (273 X 10' 3 -3.3X10' mole 3 3.3X10- eq _ 1 1X10-3 eq _ 1 1 meq 3.0 g g g Acetate concentration in resin - Total butyrate in resin initially- (2.4 233 )X(3.0 g) - 7.2 meq 8 122 '3 I"‘°1)X(0.1 L)- Total butyrate in solution at equilibrium- (30.39X10 L - 3.04x10'3m01e - 3.04 meq Butyrate concentration in resin at equilibrium (7'2'3‘04) meq - 3.0 g - 1.38 meq/g q meq YBU - _§E - 1'38 '3' - 0.575 Q 2.4 “eq 8 The resulting equilibrium liquid phase/resin phase dimensionless concentrations of butyrate are shown in Table 6. Table 6. Equilibrium liquid phase-resin phase equivalent fractions of butyrate for the equilibrium isotherm of butyrate/acetate at T - 25°C, total concentration - 270 mM and pH - 7.5. 123 Sample XBU YBU 1 0. 1121 0. 575 2 0. 1990 0. 6308 3 0. 5863 0.6941 4 0. 7379 0.8763 124 1.00 0.75 - 0.50 1 0,5! III Iv v .Jl II 0.00 0.25 0.50 0.75 1.00 0.00 1 Figure 46. Equilibrium isotherm used for the calculation of average separation factors. 125 B. a o v e e ion acto b Rat rea's Area below isotherm - Area I+Area II+Area III+Area IV+Area V 0.575 X 0.1121 2 Area I - - 0.03223 Area II - (0'575 + 0'5308) x (0.199 - 0.1121) - 0.0524 2 Area III - (0°6308 + °°6941> x (0.5863 - 0.199) - 0.2566 2 Area IV - (0'59“1 + 0'8763) x (0.7397 - 0.5863) - 0.1204 2 Area v - (1'0 + 0'3753) x (1.0 - 0.7397) - 0.2442 2 Total area below isotherm - 0.70583 Total area above isotherm - l - 0.70583 - 0.29417 Ratio of areas - Area below - 2.399 Area above Then by trial and error a is calculated from the following equation: (a2 - a - a 1n n) Area below (a _ 1)2 (11) Area above 1 2 . - (a - a - a Inn) (4 - 1)2 BU aAC (pH - 7.5) = 4.0 126 C. Calculations for Verification Of Differential Column Experimental parameters and physical constants of the equipment and resin are listed below: Column diameter - 10 mm Particle diameter - 0.45 mm Bed void fraction as 0.35 (typical) Density of dry resin - 0.34 (g/mL) measured Resin capacity - 2.4 (meq/g dry) The equipment layout for these experiments is shown in Figure (17) . Since the column effluent was not recycled, the concentration of the effluent is a direct measure of concentration drop across the column. The results of one of the experiments for the differential column verification experiments are shown in Table 7. These experiments were carried out by first saturating the resin with acetate and then exchanging the acetate saturated resin with a solution of butyrate. The concentration drop in Table 7 was calculated per cm of packed bed eventhough the column used was 1.9 cm long, this was done because the length of the column used in the subsequent rate experiments was 1 cm, and this type of calculation will allow direct comparison of the concentration drops. Experimental conditions were as follows: Flow rate: 37 mL/min Total Concentration: 102 mM pH - 6.0 Resin weight: 0.50 g Resin presaturant: Acetate *‘mrum b 127 Table 7. Concentration drop across the differential column versus time. Concentration drop expressed per cm of packed bed because the column used for the subsequent rate experiments was 1 cm long. Time (s) [AC](mM) [BU](mH) AC(mM/cm) 5 13.63 73.29 12.12 15 9.67 88.42 6.79 25 9.59 91.78 5.11 35 8.14 91.73 5.14 45 7.47 95.22 3.39 The maximum concentration drop for butyrate is: ACBut(max) - ((102 - 73.29)/102) x 100 - 28 8 The maximum concentration rise for acetate is: ACAc§(max) - (13.63/102) x 100 - 13 s The difference between the two concentration drops could be due to non-ionic interactions of butyrate with the resin. Since the concentration drops across the column are rather large, the length of the column was reduced from 1.9 cm to 0.95 cm for all of the rate experiments by reducing the quantity of the resin in the column from 0.5 g to 0.227 g. The dilution rate in all of the rate experiments was also increased. The experiment illustrated here was carried out at a dilution rate of (17.5 min'l); The dilution rate in all of the rate experiments was maintained at a minimum of (40 min'l) , hence reducing the concentration drop across the column by a factor of z4. '—§' -1:P. ‘30 \J’W , 3‘33! 2" I 3 ‘- . ““7“" ' 128 D. t o s a s e Coe n s om E erimental A component material balance written for the experimental apparatus shown in Figure 18 is shown in Equation (52). (DH. (1Y1 V C - W Q (52) T Idt r dc The liquid phase concentration of i was measured directly as a function of time, and the initial presaturation condition of the resin was known. Variations in Y1 as a function of time were calculated from variations in Xi. The rate of ion exchange was then modeled by the product of an overall mass transfer coefficient and an overall particle phase driving force. _1. - 15,1 (Y1*- 11> (53) The value of Y1* was calculated by using the average separation factor for the binary system of i and j by Equation (28). * _ a Xi l + (a-l) Xi Yi (54) dXi dt Since the values of Yi*, Xi and could all be evaluated from experimental data, the overall mass transfer coefficient was calculated by Equation (55): (in/dt) (Yi"- Yi) R —ij - (55) Any errors in the calculation of Yi*, 11 or dXi/dt result in errors in the calculated overall mass transfer coefficients. This 129 error can be significant as Yi approaches the value of Yi‘Ir and the denominator of Equation (55) approaches zero. The calculations shown here were performed using a spread sheet for every experiment. A sample of this spread sheet is shown on the next page. .J 130 The following Table is a sample of a spread sheet used to calculate mass transfer coefficients from experimental data. Wr - 0.227 g VT - 100 mL C - 20 mM butyrate pH - 6.0 Flow rate - 20 mL/min T presaturant - acetate Subscript (s) Subscript (p) All concentrations are in mM, all mass transfer coefficients in (3-1). : solution phase : particle phase Table 8. spread sheet used for calculation of mass transfer coefficients. :3 urea) IAeI [Bu] [Totgll m E ' 0 0 20.56 20.56 0.0 L 30 0.563 21.77 22.33 0.0252 g; 60 0.919 20.72 21.64 0.0425 ‘ 120 1.342 20.96 22.30 0.0602 180 1.560 20.04 21.60 0.0722 240 1.855 19.89 21.75 0.0853 300 2.12 19.73 21.85 0.0970 Y*(Ac) dX(Ac)/dt vTcT/qu dY(Ac)/dt Y(Ac) 0 0.00000 4.0255 ---- 1.0000 0.1163 0.00084 4.3726 -0.0037 0.8898 0.0197 0.00058 4.2367 -0.0024 0.8166 0.0283 0.00030 4.3665 -0.0013 0.7393 0.0342 0.00020 4.2291 -0.0008 0.6884 0.0407 0.00022 4.2575 -0.0009 0.6327 0.0466 0.00020 4.2780 -0.0008 0.5825 * 9 Y ' Y 1SBu/Ac lsBu/Ac kBu/Ac KBu/Ac Y(Bu) -1.0000 0.00000 0.00796 0.14662 0.007551 0.00000 -0.8781 0.00418 0.00423 0.14662 0.004110 0.11023 -0.7969 0.00306 0.00299 0.14662 0.002931 0.18335 -0.7110 0.00181 0.00224 0.14662 0.002206 0.26066 -0.6541 0.00129 0.00194 0.14662 0.001909 0.31161 -0.5920 0.00157 0.00171 0.14662 0.001690 0.36732 -0.5359 0.00156 0.00157 0.14662 0.001556 0.41745 K - Experimental overall mass transfer coefficient. Bu/Ac K'Bu/Ac- Overall mass transfer coefficient from Eqn' (28). 131 Figure 47. Fortran code for the substrate shuttle program WWWRWMHRWW) C ANION EXCHANGE SUBSTRATE SHUTTLE PROCESS ) C DY: ALI R, SIAHPUSH ) 0 AUGUST, 1988, MICHIGAN STATE UNIVERSITY, DEPARTMENT OF ) C CHEMICAL ENGINEERING ) THIS PROGRAM HILL SIMULATE THREE COMPONENT ION EXCHANGE IN A ) PACKED COLUMN FOR THE AQUEOUS SYSTEM OF ACETATE-l, BUTYRAE-Z, ) AND BICARBONATE-3. IT MODELS THE ION EXCHANGE COLUMN AS A SERIES) OF STIRRED TANKS, THE NUMBER OF WHICH IS CONTROLLED BY THE ) OPERATOR TO REPRESENT DIFFERENT DEGREE'S 0F AXIAL MIXING IN THE ) COLUMN. THE SIX SIMULATNEOUS PARTIAL DIFFERENTIAL EQUATIONS ARE ) CONVERTED TO ORDINARY DIFFERENTIAL EQUATIONS BY THE METHOD OF ) 000000000 CHARACTERISTICS AND THEN SOLVED BY A THIRD ORDER RUNCE-RUTTA ) TECHNIQUE WITH A BUILT IN PREDICTOR CORECTOR. ) c***********************************************************************) c**R***g******tta**ta********atta*****R*t*******************************) VARIABLE DEFINITIONS ) ACP,BUP,BIP - PRESATURATION CONDITION OF THE RESIN ) ALP21,ALP13,ALP23 - SEPARATION FACTORS FOR BINARY.SYSTEMS ) ALPZl-(Y2*X1/X2*Yl) ACETAX,BUTYRAX,BICX - CHARACTER NAMES FOR THE FILES IN WHICH THE) COMPOSITIONS RUST BE STORED. IT SHOULD BE NOTED THAT ) THESE FILES ARE DEFINED WITH THE STATUS-'OLD' AND RUST ) THEREFORE EXIST IN THE USER DIRECTORY ) B - IDOP VARIABLE INDICATING HOV MANY TIME STEPS OF SIZE DELT ) NEED TO BE TAKEN TO COVER A PROCESS PRL LONC. C - DTSCHARCINC SOLUTION INDIVIDUAL CONCENTRATIONS OF ACETATE ) ,BUTYRATE, AND BICARBONATE (mM) ) ClMX,ClMN - THE RAxTRUR AND RINTRUR CONCENTRATIONS OF ACETATE ) . ALDDUED IN THE EFFLUENT DURING A CYCLICAL OPERATION ) C2MX,02MN - SAME AS ClMX AND MN BUT FOR BUTYRATE ) CD - DTSCHARCINC SOLUTION TOTAL CONCENTRATION (DIM) ) CT - CHARCTNC SOLUTION TOTAL CONCENTRATION (mM) ) D - COLUMN DIAMETER (CR) ) DELT - TIME STEP SIZE FOR SOLVINC THE SIX DIFFERENTIAL EQUATIONS) IN UNITS OF SECONDS. THE OPTIMAL TIME STEP HAS BEEN FOUND) TO BE BETWEEN ONE AND FIVE SECONDS, ALTHOUGH STEP SIZES ) AS LARGE AS TEN SECONDS WERE ROUND To WORK FOR MANY CASES DENOMI - DENOMINATOR OF TERNARY MASS TRANSFER COEFFICIENT EQUATION, USED TO INCREASE COMPUTATIONAL SPEED O00000OOOOOOOOOOOOOOOOOOOO vvvv ‘I “diva. "“1 'K'.~".~"‘:: " "...’Z‘fim 'M an... ' Eh 000000000000 HHHHH 132 REACTOR XSIN - INLET COMPOSITION OF THE COLUMN, REGARDLESS OF THE STATE OF THE OPERATION, WHETHER CHARGING OR DISCHARGING XXIN - CHARGING INLET COMPOSITION FOR THE COLUMN XXSIN - DISCHARGING INLEIQCOMPOSITION FOR THE COLUMN YAVG - AVERAGE SOLID PHASE COMPOSTION OF EACH COMPONENT IN THE ENTIRE COLUMN. THIS IS AN INTEGRAL POSITION AVERAGE EQUAL TO THE INTEGRAL(Y1)dN/INTECRAL(dN) YN - NEW CORRECTED ESTIMATE 0F SOLID PHASE COMPOSITIONS YO - FIRST ESTIMATE OF SOLID PHASE COMPOSITIONS YSTR - SOLID PHASE COMPOSITION IN EQUILIBRIUM WITH THE LIQUID PHASE COMPOSITION INTEGER I,J,K,L,N,SPC;M,B CHARACTER*15 ACETAX,BUTYRX,BICX,INPUT CHARACTER*1 PAR1,PAR2,PAR3,PARA INTRINSIC FLOAT DOUBLE PRECISION T,TOL,XO(3,SO).Y0(3,50),XSIN(3) ,PRL,DELT,VT.VR,VTV,VC,PE,P.QEPP,Q,QES.XN(3.50),YN(3,50) ,EP,XIN(3),VT,D,S,K12,K13,K23,KK12,KK13,ALP13,ALPZ3 ,xx23,TSTR(3.50),TAVC(3);E(3).CT.ACP,EUP.DIP,ALP21 ,XAC,xEU,xEI,Rx21,TIN(2)LxAVC(3).CD,C(3),xx1N(3),xxs1N(3) ,DENONI,DENON2,x1uN,x2NN}x1Nx,x2NX,CINN,C2NN,C1Nx,C2Nx COMMON/Bl/F,VC PROMPT USER FOR NAME OF FOLES TO STORE THE OUTPUT IN WRITE(*,'(A:)') ' NAME OF OUTPUT FILE TO STORE x OR Y(ACETATE)' WRITE(*,'(A:)') ' vs. TIME. TO STORE ON DISK: AzFILENAME' READ(*,'(A:)') ACETAx OPEN(1,FILE-ACETAX,ACCESS-'SEQUENTIAL',STATUS-‘OLD') WRITE(*,'(A:)') ’ NAME OF OUTPUT FILE T0 STORE X 0R Y(BUTYRATE)' WRITE(*,'(A:)') ' VS. TIME. TO STORE 0N DISK: AtFILENAME' READ(*,'(A:)’) BUTYRX OPEN(2,FILE-BUTYRX,ACCESS-'SEQUENTIAL',STATUS-‘OLD') WRITE(*,'(A:)') ‘ NAME OF‘OUTPUT FILE TO STORE' WRITE(*,'(A:)')‘ X OR Y(BICARBONATE) VS. TIME' WRITE(*,'(A:)') ' TO STORE ON DISK: AzFILENAME' READ(*,'(A:)') BICX OPEN(3,FILE-BICX,ACCESS-'SEQUENTIAL',STATUS-‘OLD’) PROMPT USER, ASK IF INPUT IS INTERACTIVE 0R VIA DISK FILE VVVVVVVVVVVVV C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C 133 DENOM2 - DENOMINATOR OF EQUILIBRIUM SOLID PHASE CONCENTRATION ) EQUATION, USED TO INCREASE COMPUTATIONAL SPEED ) E - CHARGING sowTION INDIVIDUAL CONCENTRATIONS OF ACETATE, ) BUTYRATE, AND BICARBONATE (nM) ) EP - BED POROSITY OF VOID FRACTION, NOT DIRECTLY USED IN THE ) PROGRAM ) F - SOLUTION FLOH RATE (Ill/sec) ) I,J,K,L,M - LOOP COUNTING VARIABLES ) K IS ALSO USED AS A COUNTER TO INDICATE HHEN IT IS TIME ) TO SAVE THE COMPOSITIONS ONCE AGAIN ) N - NUMBER OF CSTR'S (INPUT BY USER) -1 ) x12,x13.x23 - BINARY OVERALL MASS TRANSFER COEFFICIENTS (s ) ) xxlz,xx21,1