Optimal Design of Integrated SMB-Crystallization Hybrid Separation

Article pubs.acs.org/OPRD

Optimal Design of Integrated SMB-Crystallization Hybrid Separation Process Using a Binary Solvent Balamurali Sreedhar,†,§ Baochun Shen,‡ Huayu Li,† Ronald Rousseau,† and Yoshiaki Kawajiri*,† †

School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive NW, Atlanta, Georgia 30332-0100, United States ‡ School of Pharmaceutical Science & Yunnan Key Laboratory of Pharmacology for Natural Products, Kunming Medical University, 1168 West Chun Rong Road, Yu Hua Street, Cheng Gong New City, Kunming, Yunnan 650500, P.R. China ABSTRACT: Hybrid separation processes combining simulated moving bed chromatography and crystallization have been known to reduce the capital cost for enantiomer separation, but past studies have been limited to systems of single-component pure solvent. In this study, a model-based design strategy using a binary solvent is presented. Separation of D- and Lphenylalanine in a mixture of methanol and water was employed as a case study. Experimental data for solid−liquid equilibrium as well as chromatographic separation were obtained at various compositions of the solvent mixture to model the process. The experimental data were used to model and optimize the design of the hybrid separation process. The trade-offs between the solubility, temperature, chromatographic separation, and eutectic compositions were analyzed using the model-based optimization approach. In a case study, it was found that the productivity can be increased by over 18% when the temperature is increased from 10 to 50 °C because of the lower eutectic purity.

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INTRODUCTION Production of chiral drugs is a major challenge in the pharmaceutical industry. Since enantiomers are molecules that have mirror images of each other and therefore have identical chemical and physical properties, except in their interactions with optically active substances, separation techniques practiced in an industrial scale are limited. One of such technique is the simulated moving bed (SMB) chromatography process.1,2 There have been successful reports of applications of SMB to enantiomer separations.3,4 However, due to the high cost of the chiral stationary phases (adsorbents), the capital cost of SMB chromatography remains high. Another technique for enantiomer separation is chiral crystallization,5−7 where one of the enantiomers is obtained as enantiopure crystals from a racemic mixture. While the capital and operating cost of crystallization processes can be significantly lower, a crystallization process alone cannot produce pure enantiomers due to the identical solid−liquid equilibria of enantiomers, except for the limited cases of conglomerates which account for only 10% of known enantiomers.5 In recent years, there have been many studies on integration of SMB chromatography and crystallization to reduce the capital cost. In this concept of process integration, the SMB process only increases the enantiomeric excess to slightly above the eutectic composition, which improves the throughput significantly. The low-purity products from SMB are subsequently purified by a crystallization process that produce enantiopure crystals. Between these SMB and crystallization processes, a solvent removal step by evaporation can be performed. Some past studies reported substantial increase in the productivity by this integrated separation concept.3,4 However, most of the past studies are limited to a system of a mobile phase that consists of the pure solvent of a single component. Employing a mixture of solvent in the hybrid process would increase the complexity in © XXXX American Chemical Society

the design analysis significantly, because the solvent composition may change after carrying out solvent enrichment operations, which influences the solubility and chromatographic separation. The restriction of using a single-component solvent may severely limit the applications of the integrated separation concept. In this work, we analyze an integrated hybrid process of SMB chromatography by a systematic optimization approach. Separation of L- and D-phenylalanine enantiomers in a mixture of methanol and water is considered as an example. A chiral chromatography column, Astec Chirobiotic T, was used as a stationary phase (adsorbent). Using this column, pulse injection tests were carried out to characterize the elution properties as functions of the solvent compositions. From the chromatograms obtained in this manner, a mathematical model for the chiral chromatography in the binary mobile phase was developed. Furthermore, to model the crystallization process, the solubility in the binary mixture was measured experimentally and eutectic compositions were identified at different solvent compositions and temperatures. Using the model and experimental data, the integrated process was designed by model-based optimization to determine the optimal conditions, which include the temperature and solvent composition.

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BACKGROUND Chiral Separation by Crystallization. An alternative technique to chromatography for chiral separation is crystallization. In crystallization of enantiomers, the solid−liquid equilibrium between a solvent and two enantiomers is exploited. Figure 1 shows the ternary diagram for equilibrium of compound-forming systems, which is known to include about 90% of enantiomers.5 As can be seen in this figure, the phase Received: September 1, 2016 Published: December 21, 2016 A

DOI: 10.1021/acs.oprd.6b00294 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development

Article

and crystallization. In this concept, the racemic mixture is supplied to the SMB unit, which purifies the enantiomers to a purity that can be significantly lower than the final product purity. The streams from the SMB unit, referred to as intermediate (raffinate and extract) products, are fed to enrichment steps where the solvent is partially removed and the concentrations of the enantiomers are increased without changing the purities of the two enantiomers. These enriched streams are fed to crystallizers where pure crystals are removed continuously. The slurries that contain enantiopure crystals and solvents are fed to filtration and drying steps to obtain dry and pure crystals as the final products. The mother liquors from the crystallizers, which contain mixtures of the two enantiomers, are recycled to the SMB unit. The capital cost of the SMB-crystallization can be lower than that of the SMB unit alone because the amount of the adsorbent in the SMB unit can be reduced (since the purity obtained from the operation is low). In this integrated process, the burden of separation is partially given to the crystallizers, and the SMB unit is allowed to produce intermediate products at lower purities. Because of the reduced purity requirements, the SMB unit can be operated at a higher throughput, and thus the amount of the adsorbent can be reduced. When designing the SMB-crystallization hybrid process, determining the purities of the intermediate products is critical.15 There is a trade-off between the product purity and throughput, and lower purities would lead to a higher throughput. However, the enantiomeric purities in the intermediate product must be greater than that of the eutectic composition (eutectic purity line shown in Figure 1); if this condition is satisfied, pure crystals of a single enantiomer can be obtained from the crystallizer. On the other hand, if the purities of the intermediate products are lower than eutectic purities, crystals of compound enantiomers are produced. It should also be noted that an effective driving force for crystallization must be applied in the crystallizers to improve the yield of the crystals. A common choice is cooling, where reducing the temperature brings about a reduction in solubility. Nevertheless, if the concentrations of the intermediate products are too low, crystallization may be inefficient or even infeasible; the intermediate product must be cooled to a very low temperature, which can be below the freezing point of the solutions. To improve the yield of the crystals, a solvent removal step is often employed between the SMB process and crystallizers. The solvent removal step (often evaporation) increases the total

Figure 1. Triangle diagram for equilibrium of compound-forming enantiomers and a solvent.

diagram for solid−liquid equilibria of compound-forming enantiomers in a nonchiral solution is always symmetric. In the equilibrium of compound-forming systems, crystallization alone cannot produce pure crystals from racemates due to this symmetry of the equilibrium. To break the symmetry and obtain pure crystals, the mother liquor must be partially purified to exceed the eutectic purity (E and E′). For example, consider a crystallization operation for a partially purified product denoted as R. This partially purified product goes through a solventremoval step to enter the two-phase shaded region. When the system reaches equilibrium anywhere within this two-phase region in a crystallizer, pure crystals of L can be obtained as the solid phase, and the mother liquor that has the composition of E can be obtained. For maximum crystal yield, solvent has to be removed all the way up to point R′.9 Similarly, when a partially purified product Ex can reach Ex′ by removing the solvent, the maximum yield of purified crystals of D and a mother liquor at the eutectic composition E′ is obtained. As discussed above, purifying compound-forming enantiomers by crystallization requires partial purification. This partial purification can be achieved by SMB, which motivates consideration of an SMB-crystallization hybrid process, as discussed below. Design of SMB-Crystallization Hybrid Process. The hybrid SMB-crystallization process has been studied for many enantiomers. Some examples include praziquantel,10 EMD 53986,11 mandelic acid,12 Troger’s base,13 and 2′,6′-pipecoloxylidide.14 As shown in Figure 2, the concept of the hybrid process integrates the two separation principles, SMB chromatography

Figure 2. Flowsheet of SMB-crystallization hybrid process. Solvent removal and crystallization operations are shown separately for clarity of illustration, while they can be carried out simultaneously. B



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Figure 3. SMB-crystallization hybrid process using binary solvent and evaporation. Heat exchangers, except condensers for the evaporators, are omitted for clarity.

the crystallizers. The vapor streams from the evaporators are cooled and condensed into liquid streams, which are recycled to the SMB unit.

concentration of the enantiomers, while keeping the enantiomeric purities constant. Using Binary Solvent in SMB-Crystallization Hybrid Process. It has been found that the selection of the optimal solvent is a critical step.8 As pointed out by Kaspereit et al.,14 an optimal solvent must satisfy multiple requirements. For the optimal performance in the SMB unit, the solvent must have high chromatographic resolution, loading factor, and low pressure drop. On the other hand, for optimal performance of the crystallizers, the solvent must allow for high crystal yield. For example, in cooling crystallization, the solubility must be sensitive to temperature changes. These objectives are often found contradictory,11 and due to this difficulty, solvent exchange (i.e., complete removal of one solvent after the SMB separation and redissolution of enantiomers into another solvent for crystallization) must be performed, which is energy intensive and time-consuming. For this challenge of finding an ideal solvent, employing a mixture of two or more different solvents would expand the design space significantly. However, in the hybrid process that involves the enrichment step, handling a solvent mixture would increase the design complexity.14 If evaporation is employed as the enrichment, the components that have higher vapor pressure vaporizes more easily, and as a result the solvent composition changes. The change of composition by evaporation is governed by the vapor−liquid equilibria (VLE). This composition change may influence the solubility of the enantiomers and thus the crystal product yield. Furthermore, design of the hybrid process must consider the shift of eutectic composition by the change of the solvent composition.16,17 Finally, the solvent where the composition has changed cannot be recycled back to the SMB process without readjusting the composition. To avoid such complexity caused by evaporation, employing continuous nanofiltration units may partly resolve this problem if the molecular size difference between solvents is not significant. Nevertheless, attractiveness of simple evaporation would increase the applicability of this process concept to many applications of enantiomer separation. In this study, we attempt to generalize the applications of the SMB-crystallization hybrid process to binary solvent systems for the first time. The overall process flow is shown in Figure 3. In the proposed process, a binary solvent is employed as the solvent, and the solvent removal between the SMB unit and crystallizers is carried out by single-stage evaporators. Because of the difference in the vapor pressures of the solvent components, the solvent compositions in the liquid streams are changed by the evaporation, which influence the solubility of enantiomers in

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METHODS Mathematical Model. Chromatographic Separation and SMB Unit. We first note the overall mass balance equations around the SMB unit: Cfeed, iFfeed = Fraf Craf, ̅ i + FextCext, ̅ i , i = D, L

(1)

where Fm is the volumetric flow rate for the feed (m = feed), raffinate product (m = raf), and extract product (m = ext), respectively, Cfeed,i is the feed concentration of component i, and C̅ m,i is the average concentration of enantiomer in the product streams over one step (t∈[0,tstep]) given as follows: Cm, ̅ i=

∫0

tstep

Cm, i(t )dt , i = D, L, m = ext, raf

(2)

The purities of the extract and raffinate streams from the SMB units are defined as follows: PuL =

Craf,L ̅ + Craf,L Craf,D ̅ ̅

PuD =

(3)

Cext,D ̅ + Cext,L Cext,D ̅ ̅

(4)

We also define the recovery as follows: RecL =

RecD =

Fraf Craf,L ̅ FfeedCfeed,L

(5)

FextCext,D ̅ FfeedCfeed,D

(6)

The mass balance between the feed to the SMB unit, fresh racemate, and recycled mother liquor from the crystallizers are given by rec rec rec rec Craf, iFraf + Cext, iFext + M rac, i = Cfeed, iFfeed , i = D, L

(7)

Crec m,i,

where m = raf,ext is the concentration of the recycle stream, Frec m , m = raf,ext is the volumetric flow rate of the recycle stream, and Mrac,i is the feeding rate of fresh racemate. It is assumed that the feed to the SMB unit is supplied at the maximum concentration determined by the solubility of the racemate: rac Cfeed, i = Csolubility, i

C

(8) DOI: 10.1021/acs.oprd.6b00294 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

a

∂t

Ncolumn

+

+

+

−

γkext(t )Fext

−

−

,

(12) ext γcolumn (t )Fext

k+1

(11) =F

λ Nrafcolumn(t )Fraf

k = 1, 2, ..., Ncolumn − 1

−

γkraf (t )Fraf

flow rate balance

γNdes (t )Fdes column

γkdes(t )Fdes

γNfeed (t )Ffeed column

γkfeed(t )Ffeed

competitive Langmuir isotherm

Fk = 0, i = D, L, k = 1, 2, ..., Ncolumn Acolumn ∂x

, i = D, L, k = 1, 2, ..., Ncolumn

+

∂Cik

mass balance in liquid phase

(9)

D

(18)

See nomenclature for definitions of symbols.

CiNcolumn(x , tstep) = Ci1(x , 0)

Cik(x , tstep) = Cik + 1(x , 0), k = 1, 2, ..., Ncolumn − 1

(17)

cyclic steady state for liquid phase

γkraf Fraf −

k=1

∑

F ) column ext

− γNext

(16)

qiNcolumn(x , tstep) = qi1(x , 0)

(20)

(19)

cyclic steady state for adsorbent

γkmCik(L , t ), i = D, L, m = ext, raf

column

(14)

(10)

+ γNfeed CF , i = Ci1(0, t )F1

product concentration

F column raf

k = 1, 2, ..., Ncloumn − 1

+ γkfeedCF , iFF = Cik + 1(0, t )Fk + 1,

mass balance between columns

γkextFext)

qik(x , tstep) = qik + 1(x , 0), k = 1, 2, ..., Ncolumn − 1

Ck , i(t )

Ncolumn

mass balance in adsorbent

= ka, i(Cik − Cieq, k), i = D, L, k = 1, 2, ..., Ncolumn

t )(Fk −

∂t

CiNcolumn(L , t )(FNcolumn − γNraf

Cik(L ,

(1 − ε)

∂qik

(13) =F Note: γm k , m = feed, des, ext, raf is a binary variable which equals one only if the stream is supplied to or withdrawn from column k.

F

∂t

∂qlk

1 + ∑i biCieq, k

HiCieq, k

+ (1 − ε)

Ncolumn

F +

k

qik =

ε

∂Cik

Table 1. Linear Driving Force Model for Chromatography18−20a

(15)

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where Crac solubility,i is the solubility of the racemate, which is a function of the methanol composition in the mobile phase, xMeOH. The solubility dependence is determined from solubility tests. The amount of solvent makeup, shown in Figure 3, is adjusted so that eq 8 is satisfied. Now we consider the mathematical models in the SMB unit to determine the outlet concentrations from the SMB, Cm,i(t),m = ext,raf, i = D,L,t ∈[0,tstep] . In this study, the linear driving force (LDF) model is employed as summarized in Table 1.18−20 Evaporation. Two evaporators are used on the extract and raffinate streams, respectively. The flow and solvent (methanol, water) mass balance is given by vap conc Fm̂ = Fm̂ + Fm̂ , m = raf, ext vap

As a result of the evaporation operation, the concentrations of the enantiomers increases. We assume that the evaporators are large enough, or that there is an intermediate buffer tank that holds the liquid volume for an entire cycle, so that the dynamics of the concentrations in the extract and raffinate product streams from the SMB unit are averaged out (eq 2). We have mass balance equations for the enantiomers around the evaporators: conc FmconcCm, ̅ i , i = D, L, m = raf, ext i = FmCm,

The evaporators increase the concentrations of the enantiomers by removing the solvent. The enrichment ratio can be defined as follows:

(21)

conc Craf,L

En raf =

conc

Fm̂ z jSMB = Fm̂ ym, j + Fm̂ zm, j , j = MeOH, water, m = raf, ext

(22)

Craf,L ̅ conc Cext,L

Enext =

Cext,L ̅

zSMB j

where is the mole fraction of component j (water and methanol) in SMB, and zm,j and ym,j are the mole fractions in the evaporators in the liquid and vapor phases, respectively. In the conc above two equations, the volumetric flow rates Fm,Fvap m , and Fm vap conc ̂ ̂ ̂ are converted to molar flow rates Fm,Fm , and Fm . In addition, the vapor−vapor liquid equilibrium inside the evaporators are assumed to be ideal, which is modeled by the Raoult’s law, which has been found to be sufficiently accurate for mixtures of water and methanol: Pmym, j = zm, jpm, j j = MeOH, water, m = ext, raf

∑

zm, jpm, j = Pm , m = raf, ext

(23)

(27)

conc Cext,D

Cext,D ̅

(28)

(29)

where constants a,b, and c are determined from solubility experiments at each temperature for L and D enantiomers. Because of the symmetry of the equilibrium of the enantiomers, the same cubic polynomial function (eq 29) with identical coefficients a, b, and c, is used for both enantiomers when L and D enantiomers are interchanged at the same composition and temperature. These coefficients are determined from solubility tests of enantiomers at the different conditions including enantiopure and eutectic compositions. The eutectic purities Eui, i = D,L can be given by

where Tevap is the temperature of the evaporator, and Aj,Bj, and Cj are constants given in Table 2. It is assumed that the evaporator

methanol water

Craf,D ̅

i = D, L, m = ext, raf

(25)

Table 2. Parameters for Antione Equation

=

conc Craf,D

eu 3 2 Cm, i = a(xm,MeOH) + b(xm,MeOH) + c(xm,MeOH) + d ,

where Pm is the total pressure and Pm,j is the vapor pressure of the pure component j. The partial pressure of pure components is modeled by the Antoine equation: B log10(pm, j ) = Aj − , j = MeOH, water, Cj + T evap m = ext, raf

=

Crystallizers. Since we are only concerned with the steadystate mass balance, we model only the solid−liquid equilibrium but not the crystallization kinetics. In general, the solubility of an enantiomer is a function of the counter enantiomer, solvent composition, and temperature. In this study, we represent the solvent composition dependency of eutectic enantiomeric concentrations as cubic polynomials at different temperatures:

(24)

i = MeOH,water

(26)

EuL =

eu Craf,L eu eu Craf,D + Craf,L

(30)

21

Aj (log10 mmHg)

Bj (K log10 mmHg)

Cj (K)

8.0724 8.07131

1574.99 1730.63

238.87 233.426

EuD =

eu Cext,D eu eu Cext,D + Cext,L

(31)

Ceu m,i,

where m = raf,ext, i = D,L is the concentration of enantiomers at the eutectic composition (point R′ for m = raf and Ex′ for m = ext in Figure 1), which is the property determined by the crystallizer temperature Tcryst and methanol fraction xm,MeOH. It has been demonstrated that the maximum crystal yield can be obtained when enantiomeric concentration reaches the twophase boundary (points R′ and Ex′ in Figure 1) by solvent evaporation.14,23 Here we assume such a scenario, where the enantiomer concentrations in the crystallizers are at the eutectic concentrations (points E and E′ in Figure 1):

temperature Tevap is the same as that in the SMB, while the crystallizers can be operated at a different temperature Tcryst. The evaporator total pressure Pm is varied to achieve required product enrichments. Figure 4 shows the comparison of methanol−water VLE obtained assuming an ideal mixture against experimentally obtained values.22 The total pressure Pm is adjusted so that the desired enrichment is achieved. The methanol liquid and vapor mole fractions were calculated using Raoult’s law and Antoine equation at 39.76 and 49.76 °C, as described above. It can be seen that the ideal assumption is sufficiently accurate in the regime considered in this study (methanol mole fraction zMeOH of 0.35 to 1.0).

rec eu Cm, i = Cm, i , i = L, D, m = ext, raf

(32)

In the above equation, we assumed that the crystallizers are mixed uniformly and thus the concentrations in the crystallizers equal the outlet stream concentrations. Furthermore, assuming that only crystals of pure enantiomers are withdrawn from the E



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Figure 4. Accuracy of methanol−water VLE, assuming ideal mixture at (a) 39.76 °C VLE (b) 49.76 °C.

crystallizers, the undesired (counter) enantiomer remains in the liquid phase and is recycled in the mother liquor. conc eu Craf,D = Craf,D

(33)

conc Cext,L

(34)

=

eu Cext,L

MD = FfeedCfeed,DRecD

(35)

conc conc rec rec ML = Fraf Craf,L − Fraf Craf,L

(36)

conc conc rec rec 0 = Fraf Craf,D − Fraf Craf,D

(37)

conc conc rec rec MD = Fext Cext,D − Fext Cext,D

(38)

conc conc rec rec 0 = Fext Cext,L − Fext Cext,L

(39)

PuD =

PuL − EuL 1 − EuL Pu − EuD = FfeedCfeed,D D 1 − EuD

(44)

In deriving the above equation, we used the following equations:RecD = RecL = PuD = PuL which can be derived from the fact that feed is racemate (Cfeed,D = Cfeed,L). When a binary solvent is employed, the symmetric condition discussed above does not necessarily hold; this is because the eutectic purities of L and D are not necessarily identical (EuL ≠ EuD) since the methanol compositions in the two crystallizers xraf,MeOH and xext,MeOH are not necessarily the same, xraf,MeOH ≠ xext,MeOH (note that EuL and EuL are functions of xraf,MeOHand xext,MeOH, respectively). Nevertheless, as we see in Optimal Design of SMB-Cystallizer Hybrid Process Section, the symmetric condition is virtually satisfied in all cases in this study, and the SMB-crystallization hybrid process is approximately symmetric.

(40)

PuL − EuL PuL(1 − EuL)

(43)

ML = MD = FfeedCfeed,L

Here, we obtain the following equation from eq 36 with eqs 3, 5, 30, 32, 33, and 37: ML = FfeedCfeed,L RecL

1 − EuD RecL (PuL − EuL) + EuD 1 − EuL RecD

Symmetric Design. It is worth considering the special case where the purities and recoveries are identical between the raffinate and extract sides, PuD = PuL and RecD = RecL; we call this special case as the symmetric condition. It should be noted that while the ratios of enantiomers are identical, the concentration can be different between the raffinate and extract side (the extract product is usually more dilute in the system of Langmuir isotherm). It can be easily seen from eq 43 that in this special case we have EuL = EuD. We note that eqs 41−42 reduce to the following equation:

where Mi is the crystal mass production rate for component i; Fconc m , m = ext,raf is the flow rate from the evaporators on the extract and raffinate sides, respectively; Frec m , m = ext,raf is the flow rate of the recycle stream from the crystallizers to the SMB rec unit;Cconc m,i and Cm,i m = ext,raf are the concentrations in the evaporator outlet stream and recycle streams, respectively (Figure 3) . Productivity of SMB-Crystallizer Hybrid Process. The productivity of the SMB-crystallizer hybrid process can be represented by the production rate of the enantiomer crystals, ML and MD. The overall mass balance of the hybrid system gives the following equation (note that the racemic mixture is supplied to the hybrid system): ML = MD

(42)

The above two equations give the productivity of the hybrid process from the productivity of the SMB process FfeedCfeed,i. Finally, we note that from eqs 40−42, the following equation must hold:

Assuming that there is no crystal loss in the filtration and drying steps, the mass balance equations around the crystallizers are given by Fmconc = Fmrec , m = ext, raf

PuD − EuD PuD(1 − EuD)

(41)

Similarly the following equations can be obtained from eq 38 with eqs 4, 6, 31, 34, and 39: F



Article

SMB-Crystallizer Process Design and Optimization. A model-based deterministic optimization scheme was employed to design the SMB-crystallization hybrid process. We aim to maximize the production rate of the enantiomer crystals: maximize ML( = MD)

In the above approach, the outer iteration (Steps 1 and 7) explores all possible values of the methanol composition in the cryst SMB xSMB , and the SMB raffinate MeOH, crystallizer temperature T purity PuL. On the other hand, the inner iteration in Steps 2−6 above is repeated until a converged solution is found. Nevertheless, we will see in the Results Section that the consistency condition (eq 43) is always satisfied with the initial guess of PuL = PuD and the inner iteration (steps 2−6) converges immediately in the first step; i.e., the optimal design can always be approximately symmetric.

(45)

The flow rates of the solvent in chromatographic columns of the SMB unit should not exceed a certain value Fmax, which is determined by the maximum pressure drop: 0 ≤ Fk ≤ Fmax , k = 1, 2, ..., NColumn

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(46)

EXPERIMENTAL SECTION Separation of L-phenylalanine and D-phenylalanine7 (compound 1 and 2 in Figure 5) is considered as a case study. The mobile phase is a mixture of water and methanol.

where Fk is the flow rate of the solvent in column k. A model-based optimization approach was employed to design the SMB-crystallization hybrid process within the AMPL modeling environment.24 The partial differential algebraic equations, eqs 9−20, are discretized both in time and spatial domains using the Radau collocation on finite elements25−27 and centered finite difference in the second order, respectively. The degrees of freedom for the optimization are the following variables: flow rates in the SMB unit, F1,F2,F3,F4, step time tstep, the methanol composition in the SMB unit xSMB MeOH, and the crystallizer temperature Tcryst. In this study, we treat xSMB MeOH and Tcryst as discrete parameters; instead of finding the optimal values of these parameters by interpolating or regressing the experimental values, we simply enumerate optimal solutions at cryst different values of xSMB at which the solubility MeOH and T measurements and chromatographic tests were carried out. Process Flowsheet Decomposition. To reduce the size of the optimization problem above, we decompose the process flowsheet shown in Figure 1 into smaller problems and solve them sequentially. It can be seen in eqs 41−42 that the productivity of the hybrid process is proportional to the feed flow rate to the SMB, Ffeed for given values of Pui and Eui. First, we consider maximizing the productivity of the SMB process alone without the evaporators and crystallizers by replacing eq 45 by the following objective function: maximize Ffeed

Figure 5. Structures of L-phenylalanine 1 and D-phenylalanine 2.

Adsorption Isotherms. A pure enantiomer was injected to a chromatographic column to obtain model parameters for chromatographic separation. Astec Chirobiotic T (length 5 cm, internal diameter 1 cm, particle size 15 μm) from Sigma Supelco (St. Louis, MO) was employed. The column was installed in a high performance liquid chromatography (HPLC) system from Shimadzu Scientific Instruments to obtain chromatograms at various compositions of the mobile phase at 50 °C. Enantiomers, L- and D-phenylalanine, were purchased from Sigma-Aldrich (St. Louis, MO) and dissolved in the mobile phase. The volume of the dissolved enantiomers injected into the column was 100 μL. The chromatograms obtained were fitted to the mathematical models discussed above to obtain the equilibrium parameters and mass transfer coefficients. The detection of chromatograms was performed by a UV detector, Shimadzu SPD-20A (Kyoto, Japan) at the wavelength of 280 nm. Solid−Liquid Equilibrium. Solubilities at the following compositions were measured: pure enantiomers, racemate, and the eutectic composition. These solubilities must be determined from experiments at multiple methanol fractions and temperature. Sampling and analysis were carried out as follows: the solid enantiomers were mixed with the solvent in a test tube, and placed in a rotational shaker in a thermostatic water bath. After waiting for at least 24 h and confirming that the solid phase still existed in the test tube, the supernatant was sampled with a syringe through a 0.45 μm filter, and diluted immediately with the same solvent at a known dilution ratio. The diluted sample was analyzed using the same chromatographic column and analytical system as in the chromatographic pulse tests, Astec Chirobiotic T and Shimadzu HPLC unit, using the binary solvent of water and ethanol at the flow rate of 0.5 mL/min and 50 °C. To estimate the time needed for equilibration, sampling was carried out sequentially in the interval of 24 h, and found that the solid−liquid equilibrium can be reached in less than 24 h.

(47) 28

In this study, we propose a recycle tearing method to decompose the optimization problem. In the proposed approach, the stream between the extract outlet from the SMB unit and the crystallizer is torn as shown in in Figure 3, and the decomposed units are optimized individually and iteratively until the split stream converges. Our approach to optimize the SMBcrystallizer hybrid process is summarized as follows: Step 1. Assign a value to the methanol composition in the SMB xSMB MeOH, crystallizer temperature Tcryst, and the raffinate purity PuL. Step 2. As an initial guess, assume the design is symmetric. Let PuD ← PuL. Step 3. Solve the SMB throughput maximization problem, where the objective function is given by eq 47 and constraints are eqs 2−20 and 46. Note that crystallization and evaporation units are eliminated from the problem in this step. Step 4. Using the solution of 3, solve the crystallizer and evaporator models (eqs 21−39) separately at given Tcryst to obtain xm,MeOH, m = ext,raf. Note that this is a square problem (simulation) that has no degree of freedom. Step 5. Obtain the productivity of the SMB-crystallization hybrid system using eqs 41 and 42. Step 6. Check if eq 43 is satisfied. If not, let 1 − Eu Rec PuD ← 1 − EuD RecL (PuL − EuL) + EuD and go to 3. L

D

Step 7. Change the values of xSMB MeOH, Tcryst, and PuL. Go to 1. G



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Figure 6. Example of model fitting for chromatographic separation at methanol fractions xMeOH of (a) 80%, (b) 85%, (c) 90%, (d) 95%, and (e) 100% in the mobile phase.

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RESULTS Chromatographic Pulse Ttests. By fitting the experimental chromatograms to the model given by eqs 9−11, we obtain the isotherm parameters Hi and bi as well as the mass transfer coefficients ka,i at different methanol compositions xMeOH. The

nonlinear optimization solver fmincon in MATLAB was used to solve the inverse problem. The experimental chromatograms and fitted model are shown in Figure 6. The equilibrium parameters, mass transfer coefficients, and separation factor (selectivity) are summarized in Figure 7. It can H



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Figure 7. Analysis for chromatographic separation of D-,L-phenylalanine in a mixture of methanol and water using Astec Chirobiotic T: (a) Henry’s coefficient Hi; (b) affinity constant bi in Langmuir isotherm; (c) selectivity; (d) mass transfer coefficient Ka,i.

be seen from this figure that Henry’s constants of the two enantiomers increases with the increase of methanol fraction. The affinity constant b in the Langmuir isotherm (eq 11) also increases with the increase in xMeOH, which indicates stronger nonlinearity of the isotherm at a higher methanol concentration. The difference of Henry’s constants for the two enantiomers also increases for higher methanol fraction, which can be seen in Figure 7c, indicating a higher methanol fraction is desired for chromatographic separation. Finally, Figure 7d shows the mass transfer coefficients ka,i which shows that the mass transfer coefficient of D-phenylalanine decreases with xMeOH while that of L-phenylalanine remains nearly constant for the change of xMeOH. We carried out all chromatographic experiments at 50 °C. The temperature must be as high as possible to maximize the solubility, which leads to increased throughput of the SMB unit, while the stability of the adsorbent is maintained and the solvent would not boil. In this study, we assume that the SMB unit is always operated at 50 °C, which is the same temperature as that in the evaporator. We finally note that only pulse tests are performed in this study assuming a relatively simple competitive isotherm given in eq 11 without further validation. In the SMB operation where the concentrations can be significantly high, deviation from this model may be observed. Nevertheless, in this study, we will carry out only an initial design study without experimental validation using an SMB unit. Some corrections may be necessary if significant model error is observed in experimental validation using an SMB unit.19,20

Solubility Tests. The measured solubilities are shown in Figure 8a−d. As can be seen, the solubility always decreases significantly when the methanol fraction increases. The solubility of the racemic mixture (Figure 8a) is lower than those of pure enantiomers (Figure 8b) and eutectic compositions (Figure 8c). The eutectic purity was analyzed and shown in Figure 8e. As can be seen in this figure, the eutectic purity at 10 °C shows a slight increase at around 70% methanol, but is relatively insensitive to the change of methanol fraction. On the other hand, at 50 °C, the change becomes more distinctive; the eutectic purity shows the maximum between 55% and 70% of methanol fraction, and decreases at higher fraction. A similar behavior where the eutectic purity has a maximum at a certain compositionhas been also observed for bicalutamide in methanol and water17 and serine also in methanol and water.23 It can also be seen that the eutectic purity at 50 °C is significantly lower than that at 10 °C, which can be exploited in the SMBcrystallization hybrid process. Optimization of SMB Unit. To analyze the influence of the mobile phase composition on the performance of the SMB unit, the throughput of the SMB unit is maximized at varying extract and raffinate purities. In the analysis in this section, only oncethrough productivity of the SMB unit is considered; the recycle rec flow rates from the crystallizers to the SMB unit, Frec raf and Fext , are both set to zero. The design parameters considered in this study are given in Table 3. In many examples of chromatographic separation, there is a trade-off between chromatographic resolution and solubility for a I



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Figure 8. Solubility tests for phenylalanine: (a) racemate, (b) pure enantiomers, (c) eutectic compositions at 10 °C, (d) eutectic compositions at 50 °C, and (e) eutectic purity.

highest when the methanol fraction xSMB MeOH is 80% for all purities; while the higher methanol composition increases the selectivity (Figure 7c), the decrease in solubility of the racemate feed is significant when xSMB MeOH is large (Figure 8a). Optimal Design of SMB-Crystallizer Hybrid Process. The SMB-hybrid process is designed so that the overall productivity is maximized using the decomposition algorithm in the Process Flowsheet Decompositin Section. The throughput is plotted in Figure 10 as a function of the purity of the raffinate product from the SMB unit. It can be seen that the productivity has a concave trend. This trend is due to the trade-off between the crystal yield and the throughput performance as given in eq 44; the higher the purity of the raffinate (PuL) and extract (PuD) are, the higher the crystal yields become, reducing the amount of enantiomers to be recycled to the SMB unit. However, achieving

Table 3. Design Parameters for SMB Unit design parameters

Ncolumn

dcolumn(cm)

Lcolumn (cm)

Fmax (mL/min)

values

4

1

20

13.09

binary solvent of water and an organic solvent; a favorable solvent composition for chromatographic separation often has poor solubility. Finding the optimal composition for the SMB unit is not a trivial task, and systematic optimization approaches are often utilized.8 The maximized productivity is plotted in Figure 9, which is normalized by the total adsorbent volume in the SMB unit VSMB. It can be seen in this figure that for all methanol fractions (xSMB MeOH) from 0.8 to 1.0, the productivity decreases nearly linearly from 90 to 98% purity, and the decrease becomes steeper for higher purities than 99%. It can also be seen that the productivity is the J



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insensitivity allows robust and flexible process control that can deal with unpredictable disturbances.9 The enrichment ratios in the evaporators in the raffinate and extract sides, Enraf and Enext, are plotted in Figure 11 for xSMB MeOH = 0.8. As can be seen in these plots, the enrichment ratios increase sharply as the purity PuL approaches one since the products from the SMB must be more highly diluted to achieve higher purities. Furthermore, due to the higher solubility at higher temperature, the enrichment ratios are always higher at Tcryct = 50 °C than at 10 °C. Finally, it can also be seen that the enrichment ratio for the extract product plotted in Figure 11b is slightly higher than that for the raffinate product plotted in Figure 11a. This is because the extract product has a lower concentration, since it is diluted more highly by the solvent in the SMB unit. The methanol compositions in the crystallizers are plotted for the raffinate side xraf,MeOH and extract side xext,MeOH in Figure 12 for PuL = 0.992. It can be seen that while the methanol compositions in the crystallizers are highly dependent on the methanol composition in the SMB xSMB, other factors do not influence the compositions, and we can always assume that xraf,MeOH ∼ xext,MeOH, and thus the flowsheet is approximately symmetric. This is because the enrichment ratios Enraf and Enext are not significantly different, as seen in Figure 11. Thus, the symmetric assumption EuL = EuD is sufficiently accurate; we also confirm that eq 43 is always satisfied within the error of 10−3% with the assumption of PuL = PuD. Such accuracy of the symmetric approximation may not hold in other systems if a different solvent enrichment method is used, or the eutectic purity is highly sensitive to the solvent composition. In such cases, some iterations of the proposed stream tearing algorithm in the Process Flowsheet Decomposition Section may be necessary. It should be noted that the design of the SMB-crystallization hybrid process using a binary solvent requires substantial experimental effort, especially for the solubility characterization. While in this study the binary system was preselected to be a mixture of methanol and water, screening of solvents should be performed prior to the experimental investigation; an ideal solvent should achieve high solubility, efficient chromatographic separation, low pressure drop, and high yield in the crystallization process.14 The effort to screen solvents considering these ideal properties can be substantial. Furthermore, to optimize the two design parameters, Tcryst and xSMB MeOH, the solubility of the racemate and the eutectic concentration must be measured at various temperatures and methanol compositions, which requires many solubility tests. To reduce this experimental effort, a computational prediction tool and a high-throughput solubility measurement system can be exploited.17 There is also an estimation method for eutectic purities.29 There remains substantial potential for improvement by pursuing alternative designs. First, it has been known that racemization can be integrated with the hybrid process.14 In addition, there have been many alternative operating strategies30,31 which can be combined with crystallizers. Furthermore, multistage evaporation (distillation) with a reflux condenser and reboiler can change the solvent composition more flexibly. Finally, recycling the mother liquors to different columns, but not mixing them the fresh racemate (eq 7), may improve the productivity further. It should finally be noted that the shift of the eutectic composition in the example considered in this study can be exploited further to improve the process performance. In this study, the crystallizers in the optimal design are operated at 50

Figure 9. Productivity of SMB unit at different mobile phase composition as a function of product purity.

Figure 10. Maximized throughput of SMB-crystallization hybrid process plotted as a function of raffinate purity from SMB unit (a) Tcryst = 10 °C; (b) Tcryst = 50 °C.

such high purity by the SMB would require the throughput of the SMB unit be sacrificed, as observed in Figure 9. Figure 10a also compares the productivity at different operating temperatures of the crystallizers. The maximum productivity at 50 °C is 35.8 g/L-adsorbent/day at PuL = 0.983. This productivity is higher by over 18% than that at 10 °C, 30.4 g/L-adsorbent/day (Figure 10b), obtained at PuL = 0.996. It can also be seen that at 50 °C, the curvature is less sharp, which indicates that the optimal productivity is less sensitive to the purity of the SMB product. This is a significant advantage in operating the hybrid separation process, where relatively large fluctuations can be tolerated at the higher temperature. Such an K



Article

Figure 11. Enrichment ratio by the evaporator for xMeOH = 0.8: (a) raffinate side, and (b) extract side.

ORCID

Yoshiaki Kawajiri: 0000-0002-7124-1704 Present Address §

Engineering & Process Sciences, Core R&D, The Dow Chemical Company, Midland, MI, USA

Funding

Baochun Shen was supported financially by the China Scholarship Council, and National Natural Science Foundation of China (81102408). Notes

The authors declare no competing financial interest.

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NOMENCLATURE A Antoine coefficient B Antoine coefficient C Antoine coefficient C Concentration C̅ Time-averaged concentration Eu Eutectic purity F Volumetric flow rate F̂ Molar flow rate H Henry’s coefficient LColumn Length of chromatographic column in SMB M Crystal mass flow rate NColumn Number of chromatographic columns in SMB P Total pressure Pu Purity Rec Recovery VSMB Total volume of adsorbent in SMB a Constant in solubility model b Constant in solubility model b Affinity constant in Langmuir isotherm c Constant in solubility model d Constant in solubility model dColumn Diameter of chromatographic column in SMB ka Overall mass transfer coefficient p Partial pressure x Liquid-phase mass fraction y Vapor-phase mole fraction z Liquid-phase mole fraction ε Porosity in chromatographic column γ Binary variables for inlet and outlet to/from SMB

Figure 12. Methanol composition in crystallizer xm,MeOH, m = raf,ext for PuL = 0.992.

°C, at which the eutectic purity is the lowest in the feasible range of operation. The crystal yield can be improved by considering two-step temperature-swing crystallizers, where the first crystallizer is operated at a temperature to yield a low-purity eutectic mother liquor, and the second crystallizer purifies the mother liquor into pure crystals.23

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CONCLUSIONS A design approach for an SMB-crystallization hybrid process using a binary solvent has been presented. The parameters in the model for the solid−liquid equilibrium and chromatographic separation properties were obtained from experiments at various temperatures on the model system D- and L-phenylalanine and solvents with different methanol compositions. The eutectic composition was found to depend on both the temperature and solvent composition. The results facilitate identification of the optimal methanol fraction and temperature in the trade-off between constraints on crystallization (solubility) and SMB (chromatographic separation). The procedures followed for the case of D- and L-phenylalanine provide a framework that can be used to explore application of the hybrid technology to other systems. We also note that thermodynamic prediction tools may reduce the laborious experimental effort required to measure the solubility at various solvent compositions and temperatures.

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AUTHOR INFORMATION

Corresponding Author

*[email protected].

D L

SUBSCRIPTS D-Enantiomer DOI: 10.1021/acs.oprd.6b00294 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development L MeOH column conc cryst ext evap feed max raf sol solubility step vap water

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Article

(11) Ströhlein, G.; Schulte, M.; Strube, J. Hybrid Processes: Design Method for Optimal Coupling of Chromatography and Crystallization Units. Sep. Sci. Technol. 2003, 38, 3353−3383. (12) Lorenz, H.; Sheehan, P.; Seidel-Morgenstern, A. Coupling of simulated moving bed chromatography and fractional crystallisation for efficient enantioseparation. Journal of Chromatography A 2001, 908, 201−214. (13) Amanullah, M.; Mazzotti, M. Optimization of a hybrid chromatography-crystallization process for the separation of Tröger’s base enantiomers. Journal of chromatography. A 2006, 1107, 36−45. (14) Kaspereit, M.; Swernath, S.; Kienle, A. Evaluation of Competing Process Concepts for the Production of Pure Enantiomers. Org. Process Res. Dev. 2012, 16, 353−363. (15) Kaspereit, M.; Gedicke, K.; Zahn, V.; Mahoney, A. W.; SeidelMorgenstern, A. Shortcut method for evaluation and design of a hybrid processes for enantioseparations. Journal of Chromatography A 2005, 1092, 43−54. (16) Kaemmerer, H.; Tulashie, S. K.; Lorenz, H.; Seidel-morgenstern, A. Solid-Liquid Phase Equilibria of of N-Methylephedrine Enantiomers in Two Chiral Solvents. J. Chem. Eng. Data 2010, 55, 1131−1136. (17) Kaemmerer, H.; Jones, M. J.; Lorenz, H.; Seidel-Morgenstern, A. Selective crystallisation of a chiral compound-forming systemSolvent screening, SLE determination and process design. Fluid Phase Equilib. 2010, 296, 192−205. (18) Kawajiri, Y.; Biegler, L. T. Comparison of configurations of a fourcolumn simulated moving bed process by multi-objective optimization. Adsorption 2008, 14, 433−442. (19) Bentley, J.; Kawajiri, Y. Prediction-correction method for optimization of simulated moving bed chromatography. AIChE J. 2013, 59, 736−746. (20) Bentley, J.; Sloan, C.; Kawajiri, Y. Simultaneous modeling and optimization of nonlinear simulated moving bed chromatography by the prediction-correction method. Journal of Chromatography A 2013, 1280, 51−63. (21) Yaws, C. L. The Yaws handbook of vapor pressure: Antoine coefficients; Gulf Professional Publishing, 2015. (22) Bredig, O.; Bayer, R., II Dampfdrucke des ternären Systems Methylalkohol− Methylacetat− Ä thylacetat. Z. Phys. Chem. 1927, 130, 15. (23) Lorenz, H.; Le Minh, T.; Kaemmerer, H.; Buchholz, H.; SeidelMorgenstern, A. Exploitation of shifts of eutectic compositions in crystallization-based enantioseparation. Chem. Eng. Res. Des. 2013, 91, 1890−1902. (24) Fourer, R.; Gay, D. M.; Kernighan, B. W. AMPL: A Modeling Language for Mathematical Programming; Duxbury Press: Belmont, CA, 1992. (25) Biegler, L. T.; Cervantes, A. M.; Wächter, A. Advances in simultaneous strategies for dynamic process optimization. Chem. Eng. Sci. 2002, 57, 575−593. (26) Wächter, A.; Biegler, L. T. Mathematical Programming: Series B 2006, 106, 25−57. (27) Kawajiri, Y.; Biegler, L. T. Optimization strategies for simulated moving bed and powerfeed processes. AIChE J. 2006, 52, 1343−1350. (28) Biegler, L. T.; Grossmann, I. E.; Westerberg, A. W. Systematic methods of chemical process design; Prentice Hall: Upper Saddle River, NJ, 1997; pp 70−74. (29) Klussmann, M.; White, A. J.; Armstrong, A.; Blackmond, D. G. Rationalization and prediction of solution enantiomeric excess in ternary phase systems. Angew. Chem., Int. Ed. 2006, 45, 7985−9. (30) Sreedhar, B.; Kawajiri, Y. Multi-column chromatographic process development using simulated moving bed superstructure and simultaneous optimization - model correction framework. Chem. Eng. Sci. 2014, 116, 428−441. (31) Kawajiri, Y.; Biegler, L. T. Large-scale optimization strategies for zone configuration of simulated moving beds. Comput.-Aided Chem. Eng. 2006, 21, 131−136.

L-Enantiomer

Methanol Chromatographic column Concentrated stream from evaporator Crystallizer Extract Evaporator Feed to SMB Maximum Raffinate Solvent recycle Solubility limit Step time Vapor phase Water

SUPERSCRIPTS SMB SMB unit rac Racemate rec Recycle from crystallizers to SMB eu Eutectic mixture eq Equilibrium determined by isotherm

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INDEXES i Components (D and L) j Feed, desorbent, extract, and raffinate j Mobile phase components (methanol and water) k Chromatographic column m Products (raffinate and extract)

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ABBREVIATIONS SMB, simulated moving bed; VLE, vapor−liquid equilibrium REFERENCES

(1) Schmidt-Traub, H.; Schulte, M.; Seidel-Morgenstern, A. Preparative Chromatography; John Wiley & Sons, 2012. (2) Guiochon, G.; Felinger, A.; Shirazi, D. G. G. Fundamentals of Preparative and Nonlinear Chromatography; Academic Press,2006. (3) Rajendran, A.; Paredes, G.; Mazzotti, M. Simulated moving bed chromatography for the separation of enantiomers. J. Chromatogr A 2009, 1216, 709−38. (4) Kniep, H.; Mann, G.; Vogel, C.; Seidel-Morgenstern, A. Separation of enantiomers through simulated moving-bed chromatography. Chem. Eng. Technol. 2000, 23, 853−857. (5) Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, racemates, and resolutions; Wiley, 1981. (6) Svang-Ariyaskul, A.; Koros, W. J.; Rousseau, R. W. Chiral purification of glutamic acid enantiomers using a size-selective barrier membrane and dual-vessel crystallization. Chem. Eng. Sci. 2012, 77, 35− 41. (7) Encarnación-Gómez, L. G.; Bommarius, A. S.; Rousseau, R. W. Reactive crystallization of selected enantiomers: Chemo-enzymatic stereoinversion of amino acids at supersaturated conditions. Chem. Eng. Sci. 2015, 122, 416−425. (8) Fuereder, M.; Majeed, I. N.; Panke, S.; Bechtold, M. Model-based identification of optimal operating conditions for amino acid simulated moving bed enantioseparation using a macrocyclic glycopeptide stationary phase. J. Chromatogr A 2014, 1346, 34−42. (9) Swernath, S.; Kaspereit, M.; Kienle, A. Dynamics and Control of Coupled Continuous Chromatography and Crystallization Processes for the Production of Pure Enantiomers. Chem. Eng. Technol. 2013, 36, 1417−1429. (10) Lim, B.-G.; Ching, C.-B.; Tan, R. H. B.; Ng, S.-C. Recovery of (−)-praziquantel from racemic mixtures by continuous chromatography and crystallisation. Chem. Eng. Sci. 1995, 50, 2289−2298. M


Optimal Design of Integrated SMB-Crystallization Hybrid Separation

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