Standing-Wave Design of a Simulated Moving Bed ... - ACS Publications

Ind. Eng. Chem. Res. 2005, 44, 3249-3267

3249

Standing-Wave Design of a Simulated Moving Bed under a Pressure Limit for Enantioseparation of Phenylpropanolamine Ki Bong Lee,† Chim Y. Chin,† Yi Xie,†,‡ Geoffrey B. Cox,§ and Nien-Hwa Linda Wang*,† School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, and Chiral Technologies, Exton, Pennsylvania 19341

An improved standing-wave design method is developed for nonlinear simulated moving bed (SMB) systems with significant mass-transfer effects and an operating pressure limit. The design method was verified with rate model simulations and then tested for enantioseparation of phenylpropanolamine. High purity (>99%) and high yield (>99%) were achieved experimentally using a SMB with a pressure limit of 350 psi. The verified design method was used to find the optimal column length that gives the maximum throughput per bed volume. For a given particle size and a pressure limit, the optimal column length falls on the boundary between the masstransfer-limiting region and the pressure-limiting region. If a characteristic dispersion velocity is more than 0.2% of an interstitial velocity, mass-transfer effects must be considered in the design in order to guarantee 99% purity and yield. 1. Introduction Living organisms are composed of chiral biomolecules such as proteins, nucleic acids, amino acids, and polysaccharides. Because of chirality, which is a fundamental characteristic of biological systems, living organisms show different biological responses to each of the enantiomers in drugs, pesticides, food, and waste compounds.1 In 1992, the U.S. Food and Drug Administration issued a policy that each enantiomer of all drugs should be studied separately for its pharmacological, pharmacokinetic, and toxicological actions. To avoid possible undesirable effects, only the therapeutically active enantiomer should be commercially produced.2 Nonetheless, about 75% of the commonly used drugs are still in either racemic or diastereomeric forms.3 In many cases, the differences in physiological properties between the enantiomers of these drugs have not yet been examined because of difficulties in producing both enantiomers in optically pure (enantiopure) forms.1 Racemic mixtures have been prepared using conventional chemistry and then separated by crystallization, membrane extraction, enantioselective distillation, gel electrophoresis, or chromatography.4 Conventional batch chromatography has been widely used for laboratoryscale separation of enantiomers. For preparative or large-scale production, a simulated moving bed (SMB) is preferred because it can achieve both high purity and high yield and it is a continuous operation process with low solvent consumption and high productivity.5 A standard SMB system has two input ports (feed and desorbent) and two output ports (extract and raffinate). Although the solute bands overlap, the fast-migrating * To whom correspondence should be addressed. Tel.: +1-765-494-4081. Fax: +1-765-494-0805. E-mail: wangn@ ecn.purdue.edu. † Purdue University. ‡ Current address: Eli Lilly and Co., Lilly Corporate Center, Indianapolis, IN 46285. § Chiral Technologies.

solute and the slow-migrating solute can be obtained as high-purity products from raffinate and extract ports, respectively. To run a SMB, zone flow rates and the port velocity, defined here as operating conditions, need to be selected. The McCabe-Thiele analysis was first developed to guide the selection of SMB operating conditions.6 Later, the triangle theory was derived based on the local equilibrium theory for ideal systems, which have negligible mass-transfer resistances and axial mixing.7,8 Mazzoti et al.9 developed the triangle theory for nonlinear ideal systems and applied the theory for separation of racemic mixtures. However, for nonideal systems in which mass-transfer effects are important, the triangle theory cannot ensure high product purity and high yield. Ma and Wang10 derived the design equations for a continuous moving bed system based on the concept of standing concentration waves. A “concentration wave” is a boundary of a migrating solute band. By proper selection of the concentration velocities, one can match the velocity of a key wave in each zone with the port velocity to achieve the standing waves, which, in turn, can ensure that the products are always drawn from the pure-component regions to maintain high product purity and high yield. The standing-wave design (SWD) has been applied to linear nonideal systems including the separation of phenylalanine and tryptophan,11,12 the purification of paclitaxel,13 and the separation of multicomponents.14,15 The design method was extended to nonlinear ideal systems by Mallmann et al.16 They derived the design equations for Langmuir and anti-Langmuir isotherms and tested them for the separation of fructose from glucose. Xie et al.17 incorporated the mass-transfer correction terms from the linear nonideal systems into the nonlinear nonideal systems. This method was tested with the separation of phenylalanine and tryptophan. A dimensionless number DI, which is the ratio of a characteristic dispersion velocity to an interstitial velocity, was also derived. DI indicates the degree of deviation of a nonideal system from an ideal system. A large

10.1021/ie049413p CCC: $30.25 © 2005 American Chemical Society Published on Web 03/25/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005

Figure 1. Molecular structures: (a) 1S,2R-(+)-PPA; (b) 1R,2S(-)-PPA.

Figure 2. Molecular structure of Chiralpak AD.

DI value indicates significant dispersion effects, which must be taken into account in the design to ensure high product purity and high yield. The nonlinear nonideal SWD was also used successfully for the separation of FTC-ester [cis-(()-2′,3′-dideoxy-3-fluoro-5′-thiacytidine butyrate] enantiomers18 and the purification of lactic acid from acetic acid.19 However, pressure limits were not considered in these studies. The main objective of this study is to consider pressure limits and mass-transfer effects in the design of SMB operating conditions. The enantioseparation of phenylpropanolamine (PPA) was used to test the design method. The solution algorithm for the SWD equations for nonlinear nonideal systems was modified to improve the rate of convergence. The limit of maximum allowable pressure was incorporated into the design method. Operating conditions, the throughput per bed volume, and desorbent consumption were investigated for different particle diameters. Finally, ideal design and nonideal SWD were compared under two different pressure limits. PPA, which is also known as norephedrine, is present in two forms: 1S,2R-(+)-PPA and 1R,2S-(-)-PPA (Figure 1). PPA is a sympathomimetic drug used in the treatment of asthma, ophthalmia, colds, and allergies and also used as an adjunct to calorie restriction in short-term weight loss.20 It is widely used in over 400 products. Chiralpak AD was chosen as the chiral stationary phase (CSP). It consists of amylose tris(3,5-dimethylphenyl carbamate) coated on porous silica gel particles (Figure 2). The CSP and many other derivatized amylose and cellulose phases were invented by Okamoto et al.21 They have been widely used for preparative separations, including SMB processes.18,22,23 Methanol was chosen as the mobile phase for its compatibility with the CSP and high selectivity for PPA separation. The PPA concentration in the feed was determined based on solubility and viscosity. Langmuir isotherms were estimated from single and multiple frontal tests. Three SMB experiments were carried out using the operating conditions obtained from the nonlinear nonideal SWD. The results show that the design method can achieve both high purity (>99%) and high yield (>99%) in low-pressure systems (27 µm). Mass-transfer effects must be considered in the SWD to guarantee high purity (99%) and high yield (99%) if a characteristic dispersion velocity exceeds 0.2% of an interstitial velocity. 2. Theory 2.1. SWD for Nonlinear Ideal Systems. In the SWD, zone flow rates and switching time are selected such that the key concentration wave in each zone migrates at the average velocity of the ports. As a result, all concentration waves remain confined within each zone. Under the SWD operating conditions, the minimum desorbent consumption is achieved for a given feed flow rate.10 Mallmann et al.16 derived the SWD equations of a nonlinear ideal system for binary separation

Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005 3251

uIw,2 ) ν uII w,1

(1a)

)ν

(1b)

uIII w,2 ) ν

(1c)

uIV w,1

(1d)

j uw,i

)ν uj0

)

(2)

1 + Pδji

where the subscripts 1 and 2 denote the fast-migrating solute and the slow-migrating solute, respectively; the j is the superscripts I-IV denote the four zones; uw,i wave velocity of standing component i in zone j; ν is the average port velocity, defined as (column length)/ (switching time); uj0 is the interstitial velocity in zone j; P is the phase ratio, defined as (1 - b)/b; and b is the interparticle void fraction. The effective retention factors (δ) for the binary Langmuir isotherm system are calculated from isotherm parameters (a and b), plateau concentrations (Cs,i and Cp,i; see Figure 3), and the extracolumn dead volume (DV)

δI2 ) p + (1 - p)a2 + δII 1 ) p + (1 - p) δIII 2 ) p + (1 - p) δIV 1

(

(

DV PLcSb

)

(3a)

a1 DV + 1 + b2Cp,2 PLcSb a2

)

1 + b1Cs,1 + b2Cs,2

(

)

+

(3b)

(4)

Mallmann et al.16 estimated plateau concentrations, Cs,i and Cp,i, from an iterative procedure involving numerical solutions of partial differential equations. Xie et al.17 developed a simpler procedure, which does not require solving partial differential equations. Initial guesses of Cs,i values, which were much lower than the feed concentrations, were increased in an iteration loop until Cp,i values converged within a specified tolerance. In this study, the procedure of Xie et al.17 was modified as follows. The feed concentrations (CF,i) were used as the initial guesses of Cs,i values. To update Cp,i values, the equations based on the feed concentrations and mass balance were used. Also, the following relations of plateau concentrations in batch elution were used to update Cs,i values.

a2 - a1 - a1b2Cp,2 a2b1Cp,2

Cs,2 )

(5)

a1b2Cp,1 a1 - a2 - a2b1Cp,1

(6)

a2b1γ+γ-(a1 - a2) a1a2b1b2(γ+ + γ-) + a12b22 + a22b12γ+γa1b2(a2 - a1) a1a2b1b2(γ+ + γ-) + a12b22 + a22b12γ+γ-

(7)

(8)

The iterative procedure to solve the nonlinear ideal SWD equations is shown in Figure 4. This procedure finds converged solutions of the SWD equations faster than the procedure of Xie et al.17 2.2. SWD for Nonlinear Nonideal Systems. In a nonideal system, the concentration waves spread because of mass-transfer effects. Ma and Wang10 derived the SWD equations for linear nonideal systems. The linear velocities in zones I and II are chosen such that the key wave velocities migrate faster than the average port velocity, whereas the linear velocities in zones III and IV are chosen such that the key wave velocities migrate more slowly than the average port velocity. As such, the spread waves can be confined within the respective zones to maintain high purity and high yield. Xie et al.17 showed that the mass-transfer correction terms for the linear system can be applied to nonlinear systems. The SWD equations for a nonlinear nonideal system are given by

(3d)

where p is the intraparticle void fraction, Lc is the single column length, and S is the cross-sectional area of the column. To estimate the five unknown operating parameters III IV (uI0, uII 0 , u0 , u0 , and ν), one more equation is needed in addition to the above four equations (eqs 1a-d). For a given feed flow rate (Ffeed), the following mass balance equation at the feed port must be satisfied:

γ+ )

Cs,1 )

DV (3c) PLcSb

a1 DV ) p + (1 - p) + 1 + b1Cp,1 PLcSb

II Ffeed/bS ) uIII 0 - u0

γ- )

∆ji )

uIw,2 ) ν + ∆I2

(9a)

II uII w,1 ) ν + ∆1

(9b)

ΙΙΙ uIII w,2 ) ν - ∆2

(9c)

IV uIV w,1 ) ν - ∆1

(9d)

βji

(

(1 + Pδji)Lj

j Eb,i +

)

Pν2(δji)2 j Kf,i

(10)

where ∆ji is the mass-transfer correction term for component i in zone j, Lj is the length of zone j, Eb is the axial dispersion coefficient, and Kf is the lumped masstransfer coefficient. βji is the natural logarithm of the ratio of the highest concentration to the lowest concentration of standing-wave component i in zone j. The lumped mass-transfer coefficient can be estimated from the particle radius (Rp), the intraparticle diffusion coefficient (Dp), and the film mass-transfer coefficient (kf) by10

Rp2 Rp 1 ) + Kf 15pDp 3kf

(11)

Hritzko et al.14 derived equations that relate β values (decay factors) to the zone flow rates and the yield of each component for a linear isotherm system. However, the column profiles of a nonlinear system are different from those of a linear system, and different β equations / are needed. The zone II stream of concentration Cs,i is mixed with the feed of concentration CF,i at the junction of the feed port (Figure 3). The concentration of the mixture changes to Cs,i as the mixture flows into zone

3252


Figure 4. Flowchart of the SWD for a nonlinear ideal system.

III. Furthermore, because of competitive adsorption, the low-affinity solute is displaced by the high-affinity solute, resulting in the high plateau concentration of Cp,i. For the fast-moving solute, which is the primary product in the raffinate, the following four equations can be obtained based on component mass balances.

FfeedCF,1Y1 Fraf

(12)

FfeedCF,1(1 - Y1) Fext

(13)

CR,1 ) CE,1 ) / Cs,1

)

FIIICs,1 - FfeedCF,1 II

F CIV 1 )

FICE,1 F

IV

(14)

(15)

where CR,i is the concentration of component i at the raffinate port, Yi is the yield of component i at the

product port, Fraf is the raffinate flow rate, CE,i is the concentration of component i at the extract port, Fext is the extract flow rate, Fj is the flow rate in zone j, and CIV 1 is the concentration of component 1 in the zone IV outlet before the desorbent port. Similarly, the following four equations can be derived for the slow-moving solute, which is primarily recovered from the extract stream.

CR,2 )

FfeedCF,2(1 - Y2) Fraf

(16)

FfeedCF,2Y2 Fext

(17)

CE,2 ) / ) Cs,2

FIIICs,2 - FfeedCF,2 FII CI2 )

FIVCR,2 FI

(18)

(19)


Figure 5. Flowchart of the SWD for a nonlinear nonideal system with a pressure limit.

where CI2 is the concentration of component 2 in the zone I inlet after the desorbent port. The concentrations are time-averaged values, and the β value for each zone can be represented as follows:

with the β equations for a linear system.14 The relations are shown as II II βnonlinear e βlinear

(24)

βI2 ) ln(CE,2/CI2)

(20)

III III e βnonlinear βlinear

(25)

/ βII 1 ) ln(Cs,1/CE,1)

(21)

βIII 2 ) ln(Cs,2/CR,2)

(22)

IV βIV 1 ) ln(CR,1/C1 )

(23)

The β equations in zones II and III are different from those for linear systems in work by Hritzko et al.14 In the solution of the SWD equations, the β values can be III estimated from eqs 20-23. The values of uI0, uII 0 , u0 , IV u0 , ν, Cs,i, and Cp,i for a corresponding ideal system are used as the initial guesses of a nonideal system iteration (Figure 5). 2.3. Comparison of β Values. The β equations for a nonlinear system derived in this study are compared

where

( (

II βlinear ) ln

III ) ln βlinear

) )

FIIICR,1 - FfeedCF,1 FIICE,1

FIICE,2 + FfeedCF,2 FIIICR,2

(26)

(27)

III In the above inequalities, βII nonlinear and βnonlinear are the β values of a nonlinear system given by eqs 21 and III 22, respectively. βII linear and βlinear are the β values of a linear system.14 The β equations from the linear SWD give an upper bound to βII nonlinear and a lower bound to . βIII nonlinear

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2.5. Dimensionless Number DI (Deviation from Ideality). Xie et al.17 derived the dimensionless number DI from the SWD equations. It quantifies the importance of mass-transfer effects in a nonideal system. A larger DI means that the system deviates more from its corresponding ideal system. If the system has no mass-transfer resistances (ideal system), DI is zero. The SWD equations for nonideal systems (eq 9) can be rearranged as follows:

1-

∆I2 ν ) ) βI2DII2 uIw,2 uIw,2

(29a)

1-

∆II 1 ν II ) ) βII 1 DI1 II II uw,1 uw,1

(29b)

1-

∆III 2 ν III ) ) -βIII 2 DI2 III III uw,2 uw,2

(29c)

1-

∆IV 1 ν IV ) ) -βIV 1 DI1 IV uIV u w,1 w,1

(29d)

Figure 6. Versatile laboratory-scale SMB unit in a four-zone, open-loop configuration.

2.4. SWD with a Maximum Pressure Limit. A maximum allowable pressure in a SMB system can limit the feed and zone flow rates; therefore, a pressure limit should be considered in the design of a SMB. The Ergun equation24 has been commonly used to calculate the pressure drop in a packed bed. This equation is based on the assumption that the viscous and kinetic energy losses are additive.

( )

150µuj0Lj 1 - b ∆Pj ) b 4R 2 p

2

1.75F(uj0)2(1 - b)Lj + (28a) 2Rpb IV

∆Pmax )

∆Pj ∑ j)I

The dimensionless number DI for component i in zone j is defined as17 j Eb,i

DIji

≡

Lj

+

Pν2(δji)2 j Kf,i Lj

uj0

( )( )

ν 1 1 + jP(δji)2 j j Pei Sti u0

)

Rp Lj

(30)

where the Peclet number (Peji) and the Stanton number (Stji) are defined as

(28b)

where ∆Pj is the pressure drop in zone j, µ is the fluid viscosity, and F is the fluid density. The total pressure drop was calculated from eqs 28a and 28b for the open-loop configuration in Figure 6. The pump configuration considered in this study has the highest pressure drop compared to other pump configurations. By using intercolumn pumps, the pressure drop can be reduced for a given flow rate. However, if the dead volume due to intercolumn pumps is relatively large compared to the column volume, it can reduce the product purity and yield.18 To avoid such problems, the open-loop configuration was considered. To determine the operating conditions under the limit of a maximum allowable pressure, a low feed flow rate was used as an initial value. The feed flow rate was increased until the pressure drop calculated from eq 28 reached the maximum allowable pressure (Figure 5) or the operating conditions reached the mass-transfer limit. For efficient calculation, variable step sizes were used. First, the feed flow rate was increased with a large step size. If the calculated pressure drop exceeded the maximum limit or the operating conditions exceeded the mass-transfer limit, the feed flow rate was reduced to the former step. It was increased again with a smaller step size until the pressure drop limit or the masstransfer limit was exceeded. The procedure was repeated until the solution converged within the tolerance.

2

Peji

Stji )

j Kf,i Rp

uj0

)

)

uj0Lj

(31)

j Eb,i

1 R p 1 uj0 + 15pDp,i 3kj

(

f,i

)

(32)

Zones II and III are the key separation zones, where the desorption wave of the fast-migrating component in zone II affects the extract purity and the adsorption wave of the slow-migrating component in zone III affects the raffinate purity. Therefore, only the corresponding DI values for zones II and III are considered. DI can be taken as the ratio of a characteristic dispersion velocity to an interstitial velocity. The larger the DI value, the larger the dispersion effects on the product purity and yield. 2.6. Maximum Throughput per Bed Volume, Productivity, and Desorbent Consumption. The throughput per bed volume in this study is defined as the volume of feed processed per unit bed volume and per unit time

throughput )

Ffeed Ffeed ) BV SLcNc,tot

where Nc,tot is the total number of columns.

(33)


When the column dimension, total number of columns, and feed concentration are fixed for a given system without a pressure limit, the maximum throughput per bed volume can be obtained at the maximum feed flow rate. From eqs 4, 9b, and 9c

[

III 2 PβIII 2 (δ2 ) III KIII f,2 L

+

]

II 2 PβII 1 (δ1 ) II KII f,1L

II ν2 - P(δIII 2 - δ1 )ν +

Ffeed + bS

βIII 2 L

III Eb,2 III

+

βII 1

II Eb,1 II

L

) 0 (34)

To have a physically meaningful solution for port velocity ν

( (

II 2 P2(δIII 2 - δ1 ) - 4

III 2 PβIII 2 (δ2 ) III KIII f,2 L

+

)


×

)

III II βII Ffeed βIII 2 Eb,2 1 Eb,1 + g 0 (35) + bS LIII LII

From the above equation, the maximum feed flow rate can be found as follows:

[(

Ffeed,max ) bS

4

II 2 P2(δIII 2 - δ1 ) III 2 PβIII 2 (δ2 ) III KIII f,2 L

+

)


-

III βIII 2 Eb,2

LIII

-

]

II βII 1 Eb,1

LII

(36)

Therefore, the maximum throughput per bed volume can be derived from eqs 33 and 36 as

[(

throughputmax ) b Nc,tot

4

II 2 P(δIII 2 - δ1 ) III 2 II 2 βIII βII 2 (δ2 ) 1 (δ1 ) + III II KIII KII f,2 Nc f,1 Nc

)

-

III βIII 2 Eb,2 2 NIII c (Lc)

-

II βII 1 Eb,1 2 NII c (Lc)

]

[(

b Nc,tot

4

II 2 P(δIII 2 - δ1 )

III 2 βIII 2 (δ2 ) III KIII f,2 Nc

b throughputmax ) Nc,tot

[

II 2 15pP(δIII 2 - δ1 )

4Rp2

(

III 2 βIII 2 (δ2 )

Dp,2NIII c

+

II KII f,1 Nc

]

)

II 2 βII 1 (δ1 )

(38)

The maximum throughput per bed volume is now independent of the column length but still dependent on the particle size through the lumped mass-transfer coefficient (Kf) from eq 11. If pore diffusion is dominating, the second term of the right-hand side in eq 11 is negligible and the resulting maximum throughput per

+

Dp,1NII c

]

)

II 2 βII 1 (δ1 )

(39)

Therefore, the maximum throughput per bed volume is inversely proportional to the square of the particle size if diffusion within particles is the dominant masstransfer resistance. Smaller particles have smaller diffusion resistances and cause less concentration wave spreading. As a result, shorter zones are needed to confine the waves and a smaller bed volume is required for the separation. The throughput per bed volume here is based on the amount of feed processed. Productivity, which is based on the amount of product, is related to the throughput per bed volume as follows:

productivity )

FfeedCF,iYi throughput × CF,iYi ) FbedBV Fbed (40)

where Fbed is the bulk density of the bed. Similarly, one can derive the equation to show that desorbent consumption decreases with an increase in the column length and eventually reaches a limiting value for a fixed feed flow rate.

desorbent consumption ) bS

{

Pν(δI2

-

βIV 1

δIV 1 )

[

NIV c Lc

+

Fdes ) FfeedCF,iYi

βI2 NIcLc

IV Eb,1 +

[

I Eb,2

+

KIV f,1

]

Pν2(δI2)2

]}/

2 Pν2(δIV 1 )

KIf,2

+

FfeedCF,iYi (41)

If the column is long enough, mass-transfer effects become negligible and eq 41 can be simplified as follows:

(37)

where Njc is the number of columns in zone j. Equation 37 indicates that if the mass-transfer parameters (Kf and Eb) are constant, the maximum throughput per bed volume increases with an increase in the column length and then reaches a limiting value (see the results of the throughput per bed volume without a pressure limit). If axial dispersion is not important and/or the column length is sufficiently long, the second and third terms in eq 37 are negligible.

throughputmax )

bed volume is given by

desorbent consumption )

δI2 - δIV 1 II (δIII 2 - δ1 )CF,iYi

(42)

2.7. Taylor Dispersion. In 1953, Taylor analyzed dispersion in flow in a tube caused by axial convection and molecular diffusion in the radial direction.25 Analytical solutions of solute distribution for a pulse and a step change in the concentration were derived based on the following key assumptions: (1) Laminar flow is unchanged by the pulse input or the step change. (2) Velocity varies only with the radius. (3) Mass transfer occurs only by axial convection and radial diffusion. The governing equation for diffusion can be derived as follows:

∂2Cm ∂Cm ) Ez ∂t ∂ζ2

(43)

where Cm is the average solute concentration; t is the elution time; ζ is the new coordinate, defined as z - umt; z is the distance along the tube; um is the average linear velocity at the tube axis; Ez is the dispersion coefficient,

3256


defined as (R0um)2/48D∞; R0 is the tube radius; and D∞ is the molecular diffusivity. The solution of eq 43 for the solute concentration averaged across the tube cross section for the small pulse is

C)

M/πR02 2xπEzt

{

exp -

}

(z - umt)2 4Ezt

(44)

The solution of eq 43 for the concentration elution of a step change is

{

[ ( [ (

)] )]

C0 z - umt 1 + erf , z < umt 2 2xEzt C) C z - umt 0 1 - erf , z > umt 2 2 Et

x

z

}

(45)

where M is the total solute in the pulse, C0 is the concentration of the solute that enters a tube at time t ) 0, and erf(x) ) (2/xπ)∫x0e-t2 dt. 2.8. VERSE (VErsatile Reaction SEparation) Simulation. The VERSE simulation tool for batch and SMB chromatographies was used in this study to validate adsorption isotherms and mass-transfer parameters and to check the SMB design methods. VERSE is based on a detailed rate model, and the model equations are solved numerically.26,27 VERSE simulation has been verified by the experimental data from many previous studies.10,11,16-19 The solutions for Taylor dispersion for a pulse or a step change were incorporated into VERSE to account for the dispersion in a long injection loop in this study. 3. Experimental Method 3.1. Materials and Equipment. 1,3,5-Tri-tert-butylbenzene and the enantiomers 1S,2R-(+)-PPA (98%) and 1R,2S-(-)-PPA (99%) were purchased from Aldrich Chemical Co. (Milwaukee, WI). HPLC-grade methanol and acetonitrile were purchased from Mallinckrodt Baker Inc. (Paris, KY). An analytical column (Chiralpak AD, 250 × 4.6 mm i.d.) and semipreparative columns (Chiralpak AD, 100 × 10 mm i.d.) were obtained from Chiral Technologies Inc. (Exton, PA). The particle sizes for the analytical column and the semipreparative columns were 10 and 27 µm, respectively. A Cannon-Manning semi-microviscometer (State College, PA) was used to measure the solution viscosity. The microscopic images of Chiralpak AD particles were taken with a Nikon eclipse TE300 inverted microscope (Tokyo, Japan) equipped with a Sony CCDIRIS camera (Tokyo, Japan) using MetaVue software (Universal Imaging Corp., Downingtown, PA). A fast protein liquid chromatography (FPLC) pump (Pharmacia, Piscataway, NJ) and an FMI PD-60-LF pulse dampener (Syosset, NY) were used to measure the pressure drop in a semipreparative column at different flow rates. A Waters high-performance liquid chromatography (HPLC) system (Milford, MA) was used for pulse and frontal/elution tests and sample analysis. This HPLC system included a 515 HPLC pump, a Rheodyne 7725i injector, and a photodiode array (PDA) detector. Millennium software was used to control the HPLC and to acquire experimental data.

A laboratory-scale Versatile SMB system28 was used for preparative experiments. This system consists of eight rotary valves (VICI Valco Instruments, Houston, TX) and eight semipreparative columns in a four-zone configuration (Figure 6). A computer with LabView software (National Instruments, Austin, TX) controlled the valve switching. Four pumps were used to control the flow rates. Two FPLC pumps (Pharmacia, Piscataway, NJ) were used as feed and zone I pumps, respectively. Two dual-piston HPLC pumps (Waters, Milford, MA) were used as extract and raffinate outlets pumps, respectively. All pumps were calibrated with and without columns prior to SMB experiments. 3.2. Solvent Screening. Polar solvents, such as methanol, ethanol, 2-propanol, and acetonitrile, have been widely used as mobile phases for Chiralpak AD columns. Among these solvents, pure methanol, pure acetonitrile, and a methanol-acetonitrile mixture (50: 50, v/v) were tested for selectivity using an analytical column. Methanol was found to give the best selectivity and was selected as the mobile phase. The solubility of PPA in methanol and the viscosity of the solution were measured to determine the range of the feed concentration for batch and SMB experiments. PPA solubility in pure methanol at room temperature (20-22 °C) was measured by the shake-flask method.29 If the solution remained the same after 24 h of stirring, this solution was considered to be at equilibrium. The solubility was measured for each PPA enantiomer. The kinematic viscosity of the solution was estimated by measuring the efflux time in the viscometer. The kinematic viscosity is proportional to the efflux time, and the proportional constant was provided by the manufacturer. The dynamic viscosity was calculated by multiplying the solution density and the kinematic viscosity. 3.3. CSP and Column Characterization. The shape and size of Chiralpak AD particles were investigated with a microscope. The particles were tested under dry conditions and in methanol. The interparticle void fraction (b) was estimated from the Ergun equation (eq 28) and the pressure drop data. The pressure drop was measured at five different flow rates for three different columns. The total void fraction (t) was estimated by pulse tests with 1,3,5-tri-tertbutylbenzene as the nonretained tracer. The total void fraction was measured for each column, and the average value was used in the data analysis and simulation. The value of the intraparticle void fraction (p) was calculated from the following equation based on the measured total void fraction and interparticle void fraction.

p )

t - b 1 - b

(46)

3.4. Pulse Tests. Pulse tests were performed with analytical and semipreparative Chiralpak AD columns using an HPLC pump, an injector, and a PDA detector. The pulse size was either 5 or 20 µL, and the effluent was monitored at the wavelength of 254 nm. Pure methanol was used for the mobile phase and the solvent of PPA sample solutions. Before use, methanol was degassed through sonication for 30 min. Long pulses of 5 mL were used to test the isotherms at high-loading conditions. The flow rate was 0.5 mL/ min, and the sample concentration was 25 g/L for each


enantiomer in all experiments with single enantiomers and racemic mixtures. 3.5. Frontal/Elution Tests. Single and multiple frontal/elution tests were carried out with semipreparative columns to estimate the isotherm parameters and intraparticle diffusivities. The flow rate used was 1.0 mL/min. The flow rate was checked at the beginning of each experiment and when the solution was changed. The concentrations ranged from 1 to 50 g/L, and the test was repeated multiple times at each concentration. Frontal/elution chromatograms were obtained at 274nm UV because the plateaus in the high concentration range could not be discerned well at 254-nm UV. The extra-column dead volume in the frontal/elution tests was measured to be 0.19 mL, which was 2.4% of the column volume. In frontal chromatography, the velocity of a shock wave of a single component (ush) can be predicted from the isotherm and the interstitial velocity.30

ush )

u0 1 - b 1 - b ∆q 1+ pKe + (1 - p) b b ∆c

( )

( )

( )

(47)

where Ke, the size-exclusion factor, is the fraction of the pore volume that a solute can penetrate, q is the adsorbed solute concentration (g/L solid volume), and c is the solute concentration in the fluid (g/L). Isotherms can be estimated from the term ∆q/∆c in eq 47 or by finding the total amount adsorbed at each feed concentration from the frontal chromatogram through mass balance. The intraparticle diffusivities (Dp) were first estimated from the HETP (height equivalent to a theoretical plate)31 obtained from the pulse data and fine-tuned by comparing the experimental data with the simulated frontal chromatograms. 3.6. SMB Design and Experiments. Before any of the SMB experiments, all eight columns were tested with racemic PPA pulses to check whether the column capacities were consistent. The racemic mixture concentration was 50 g/L. The mobile-phase flow rate was kept at 1.0 mL/min. After the retention time in each column was checked, the columns were installed in the SMB system and pure methanol was used to wash all columns for more than 20 bed volumes to remove any impurity. The operating conditions for the laboratoryscale SMB experiments were obtained using the nonlinear nonideal SWD method. A 350-psi system pressure limit was used in the design. In the SMB configuration tested in this study (Figure 6), the desorbent pump controlled the flows from zones I to IV. Therefore, the system pressure was calculated from the maximum length in the flow path. The operating conditions obtained from the SWD were checked by comparing the target values of purity and yield with those obtained from the VERSE simulation. In the SMB experiments, a standard four-zone system with two columns in each zone was used. An open-loop configuration (i.e., the zone IV outlet was disconnected from the inlet of zone I) was used in order to check the flow rate and concentration in zone IV. Because the switching time was less than 3 min and the flow rates were low, the outlet samples of extract, raffinate, and zone IV were collected over a period of four steps. The samples for the column concentration profile were collected in the middle of the final step. The amount of

Table 1. Resolution of PPA Enantiomers in Different Mobile Phases retention time (min) [capacity factor] mobile phase

(+)-PPA [k′+]

methanol 6.86 [0.074] methanol7.75 [0.213] acetonitrile (50:50, v/v) acetonitrile 7.04 [0.103]

(-)-PPA [k′′-]

selectivity

7.85 [0.229] 8.67 [0.357]

3.10 1.68

8.30 [0.301]

2.93

sample collected from each column was about 1 mL (13% of the column volume). The samples were analyzed using HPLC. The isotherm and mass-transfer parameters, design method, and equipment were verified with experimental data and simulation results. 4. Results and Discussion 4.1. Pulse Tests for Solvent Screening. To select a mobile phase that has the highest selectivity, pulse tests were carried out using an analytical Chiralpak AD column. Pure methanol, pure acetonitrile, and a methanol-acetonitrile mixture (50:50, v/v) were tested, and the selectivity in pure methanol was found to be the highest (Table 1). For all of the solvents tested, (+)-PPA is the less retained enantiomer. The elution order was confirmed with pure enantiomer compounds. Capacity

Figure 7. Viscosity as a function of the PPA concentration in methanol.

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Figure 8. Microscopic images of Chiralpak AD: (a) under dry conditions; (b) soaked in methanol.

Figure 10. Isotherm plot from frontal test data: (a) (+)-PPA; (b) (-)-PPA. Table 2. Retention Time of PPA for Each Column

Figure 9. Pressure drop in a column as a function of the flow rates.

factors were calculated according to the standard chromatographic theory as k′+ ) (t+ - t0)/t0 and k′- ) (t- t0)/t0, where t+ and t- are the retention times of (+)PPA and (-)-PPA, respectively.32 The void time (t0) was measured from the elution time of an inert tracer, 1,3,5tri-tert-butylbenzene. A separation factor (or selectivity) was defined as the ratio of the two capacity factors, R ) k′-/k′+. 4.2. Solubility and Viscosity. The solubility of PPA was found to be 7.4-7.7 g of PPA/mL of methanol (9.49.7 g of PPA/g of methanol), which was identical for both enantiomers. In a low-pressure SMB system, the viscosity can be a limiting factor. In the viscosity test, the viscosity increased exponentially as the PPA concentration increased (Figure 7). For this reason, the PPA feed concentrations for the batch chromatography and SMB experiments were much lower than the solubilities. 4.3. CSP and Column Characterization. The Chiralpak AD particle size was estimated from the

retention time (min) (+)-PPA (-)-PPA

column no.

t

1 2 3 4 5 6 7 8 average

0.70 0.70 0.70 0.69 0.70 0.70 0.69 0.69 0.70 ( 0.90%

6.54 6.52 6.51 6.45 6.47 6.52 6.46 6.46 6.49 ( 0.72%

8.44 8.30 8.47 8.25 8.34 8.33 8.34 8.40 8.36 ( 1.3%

Table 3. Isotherms, Mass-Transfer Parameters, and Numerical Parameters Isotherms and Mass-Transfer Parameters (+)-PPA isotherms D∞ (cm2/min) Dp (cm2/min) kf (cm/min) Eb (cm2/min)

(-)-PPA

a ) 0.448, b ) 0.0102 a ) 1.44, b ) 0.0354 7.47 × 10-4 7.47 × 10-4 -5 7.0 × 10-5 7.0 × 10 Wilson and Geankoplis correlation34 Chung and Wen correlation35 Numerical Parameters

axial elements per column 50

collocation points axial particle 4

2

absolute tolerance

relative tolerance

0.001

0.001

microscopic images (Figure 8), and the average value was about 27 µm, which was in agreement with the value reported by the manufacturer. The particles were spherical. No difference in the size or shape was observed between the dry particles and the particles in methanol. The pressure drop in a semipreparative column increased linearly with an increase in the flow rate (Figure 9). These experimental results were compared


Figure 11. Frontal/elution tests: (a) 1 g/L of (+)-PPA; (b) 50 g/L of (+)-PPA; (c) 1 g/L of (-)-PPA; (d) 50 g/L of (-)-PPA.

Figure 13. Individual component chromatograms in the racemic mixture long-pulse simulation.

Figure 12. Long-pulse chromatograms by experiments: (a) single components; (b) racemic mixture and sum of single-component chromatograms.

with the predictions from the Ergun equation (eq 28) at different values of the interparticle void fraction. The b value of 0.32 showed the best agreement, and it was used as the interparticle void fraction. The average total void fraction t was determined from the pulse tests to be 0.70 (Table 2), and the intraparticle void fraction p was estimated to be 0.55 according to eq 46.

4.4. Frontal/Elution Tests. The frontal/elution tests were performed to estimate the isotherm parameters at high concentrations. The isotherms between 1 and 50 g/L are Langmuirian (Figure 10). The adsorbed solute concentration was based on the solid volume. In the isotherm calculation, the delay due to the extracolumn dead volume was subtracted from the retention time. Figure 11 shows the comparison of experimental chromatograms and simulation results at 1 and 50 g/L. VERSE simulation results based on the isotherm parameters obtained from frontal tests are in reasonable agreement with the experimental data. The inlet concentration was simulated as a step change, and the extra-column dead volume was treated as a continuous stirred tank reactor in the simulations. The estimated isotherms, mass-transfer parameters, and numerical parameters are listed in Table 3. The Wilke and Chang correlation33 was used to estimate the molecular diffusivities. 4.5. Long-Pulse Tests. Long-pulse tests were performed to validate the isotherm parameters estimated

3260


Figure 14. Comparison of experimental long-pulse chromatograms with VERSE simulations with Taylor dispersion (solid thick line) and without Taylor dispersion (solid thin line): (a) long pulse without column; (b) (+)-PPA only; (c) (-)-PPA only; (d) racemic mixture. Table 4. Operating Conditions and Results of the SMB Experiments extra-column DV (mL/column)a inlet and outlet flow rates (mL/min)

zone flow rates (mL/min)

switching time (min) purity (%)

feed desorbent raffinate extract zone I zone II zone III zone IV

extract raffinate yield (%) (+)-PPA (-)-PPA product concentration (g/L) (+)-PPA (-)-PPA throughput per bed volume (mL of feed/ mL of BV/min) desorbent consumption (+)-PPA (L/g of product) (-)-PPA productivity (+)-PPA (g of product/ g of CSP/day) (-)-PPA

run 1

run 2

run 3

0.50

0.45

0.45

0.40b

0.50

0.90

1.10 1.38 2.63 0.35 0.44 0.82 1.15 1.44 2.71 3.88 4.85 9.07 2.73 3.41 6.36 3.13 3.91 7.26 2.78 3.47 6.44 2.43 1.94 1.04 100 98.1 100 100 100 99.1 94.6 97.6 99.1 99.9 100 99.4 25.0 27.5 27.2 8.03 8.68 8.14 0.0059 0.0080 0.014 0.13

0.11

0.12

0.12 0.33

0.11 0.46

0.12 0.85

0.35

0.48

0.84

a

The listed extra-column dead volume is a value that was considered in the SMB design. b The feed flow rate of 0.4 mL/min in run 1 was the value used in the design. After mass balance adjustment, 0.37 mL/min was used for simulation and other calculations.

from frontal tests and to examine the elution chromatograms of racemic mixtures under high-loading conditions. Figure 12 shows the experimental chromatograms of the long-pulse tests. The chromatograms of single components are shown in Figure 12a, and the comparison of the racemic mixture and the sum of singlecomponent chromatograms is shown in Figure 12b. The sum of the single-component chromatograms was obtained from the data in Figure 12a. If there was no interaction or competition between (+)-PPA and (-)PPA, the sum of the single-component chromatograms would be the same as the racemic mixture chromato-

Figure 15. Experimental data and simulation results of run 1: (a) column profile (middle of the 120th step); (b) extract history; (c) raffinate history. Concentrations in the effluent history are averaged over one switching period.

gram. Long-pulse chromatograms from the racemic mixture and the sum of single components are similar except for the frontal part of (+)-PPA. The frontal curve of (+)-PPA in the racemic mixture showed a higher concentration than that of the single component. This “roll-up” phenomenon is predicted by VERSE.


Figure 16. Experimental data and simulation results of run 1 (the simulated feed flow rate was decreased to 0.37 mL/min): (a) column profile (middle of the 120th step); (b) extract history; (c) raffinate history. Concentrations in the effluent history are averaged over one switching period.

Figure 13 shows the VERSE-simulated elution profile of each individual component in the long pulse of a racemic mixture. Note that the concentration of (+)-PPA increased to higher than the feed concentration and then decreased to the feed concentration. The low-affinity solute, (+)-PPA, was displaced by the high-affinity solute, (-)-PPA, and eluted earlier. Figure 14 shows the comparison of experimental longpulse chromatograms with the VERSE simulation results. When only inlet concentration step changes (a step up followed by a step down in concentration) were assumed in the simulation, the adsorption curves agreed closely but the desorption curves did not agree (Figure 14b-d). When the adsorption column was removed from the experimental setup, the chromatogram still showed sharp frontal but long tailing (Figure 14a). This result indicates that the long tailing was not due to slow diffusion of the solute in the adsorbent particles. In the long-pulse tests, the injection loop was 5 mL in volume and the length of the loop was approximately 6 m. The long tube in the loop might have caused the long tailing. To investigate this possibility, Taylor dispersion was considered in the VERSE simulations. With the inclusion of Taylor dispersion, the experimental chromatograms and the simulation results agree closely (Figure 14a-d). 4.6. SMB Experiments. Three laboratory-scale SMB experiments for the separation of racemic PPA were performed. Before the experiments, pulse tests were

Figure 17. Sensitivity analysis of the extra-column dead volume of the run 1 column profile: (a) 0.4-mL DV; (b) 0.45-mL DV; (c) 0.55-mL DV.

carried out to check the consistency of column packing. The results show that the deviation in the pulse retention time was within 1.3% (Table 2). The racemic feed concentration for SMB experiments was kept at 50 g/L. The operating conditions obtained by the SWD method are listed in Table 4. The first two SMB experiments were performed below the pressure limit of 350 psi. In the third experiment, the feed flow rate was increased until the system pressure reached the pressure limit. As the feed flow rate increases, zone flow rates also increase, causing an increase in the system pressure. Prior to each SMB experiment, the conditions determined by the SWD were confirmed by the VERSE simulation. In all cases, the simulated purity and yield were in close agreement with the purity and yield targeted in the SWD. Figure 15 shows the results of the first SMB experiment (run 1). The experimental column profile and effluent history were lower than the predicted values. The total amount of output solute was only 93% of the input solute in mass balance. During the experiment, the flow rates of extract, raffinate, and zone IV were monitored and corrected such that the deviation from the design flow rates was kept within 1-2%. However, the flow rates of the feed and desorbent were not monitored in run 1. The FPLC feed pump has been observed to deliver a lower flow rate than that expected in other experiments (not shown here). To examine the hypothesis of the inaccurate feed flow rate in run 1, the simulated feed flow rate was decreased from the design

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flow rate of 0.40 mL/min until the input and output mass balances agreed. Figure 16 shows the adjusted results with the lower feed flow rate of 0.37 mL/min. The simulation results agreed better with the experimental data. However, there were still deviations between the simulation result and the experimental column profile. To investigate the effect of an inaccurate extra-column dead volume on the SMB result, a sensitivity analysis of the extra-column dead volume was carried out (Figure 17). In the sensitivity analysis of the extra-column dead volume, operating conditions and other parameters were kept constant while the extracolumn dead volume was changed. If the extra-column dead volume is smaller than the value used in the design, 0.5 mL per column, the solute waves move faster. This effect is seen more clearly in the (+)-PPA wave. The slow-moving component, (-)-PPA, is more robust to the inaccuracy in the extra-column dead volume than the fast-moving component, (+)-PPA. The extra-column dead volume that gave the best agreement was 0.45 mL per column. The reported purity and yield of run 1 in Table 4 include adjustment of the feed flow rate. Pure enantiomers could be obtained from both the extract and raffinate. However, the yield of (+)-PPA was 94.6%. About 5% of (+)-PPA was lost through zone IV because the SMB was designed with an inaccurate extra-column dead volume. In the SMB design and simulation of the second SMB experiment (run 2), the extra-column dead volume was set at 0.45 mL. During the experiment, all input and


Figure 20. Effects of the column length on (a) throughput per bed volume and (b) desorbent consumption for 10-µm particles.

output flow rates were monitored and corrected such that the deviation from the design flow rates was kept




Figure 24. Representation of the operating conditions obtained from the nonideal SWD in a triangle diagram for 27-µm particles and a 350-psi pressure limit. Table 5. Optimal Column Lengths To Achieve the Highest Throughput per Bed Volume for Four Particle Sizes under Two Different Pressure Limits (Target Purity ) 99%, Yield ) 99%) optimal condition considering throughput particle pressure column column column diameter limit length diameter volume throughput (µm) (psi) (cm) (cm) (mL) (mL/mL/min) Figure 22. Effects of the column length on (a) throughput per bed volume and (b) desorbent consumption for 50-µm particles.

10 27

within 1-2%. Figure 18 shows the results of run 2. The simulation results agree well with the experimental data. Also, relatively high purity (>98.1%) and high yield (>97.6%) could be achieved. The reasonable agreement between the simulation results and the experimental data indicates that the isotherms and masstransfer parameters are accurate. In the third SMB experiment (run 3), the feed flow rate was increased to 0.9 mL/min. Because the particle

50 100

350 2000 350 2000 350 2000 350 2000

0.55 1.26 3.84 9.02 12.99 30.67 51.45 121.38

38.15 23.87 36.74 23.45 36.37 23.37 36.15 23.37

629 564 4072 3897 13 494 13 153 52 815 52 048

0.4776 0.5326 0.0738 0.0770 0.0223 0.0228 0.0057 0.0058

size was small (27 µm in diameter), the increase in the flow rates increased the system pressure almost to the limit (350 psi). The results of run 3 are shown in Figure 19. The simulation results and the experimental data

3264


Figure 25. Product purities obtained from VERSE simulation as a function of the dimensionless number DI for the operating conditions obtained from (a) the nonideal SWD, (b) the ideal design, and (c) the ideal design (enlargement of the square part in part b). The closed symbols are for DIII and the corresponding extract purity, and the open symbols are for DIIII and the corresponding raffinate purity.

agree well, and high purity (>99.1%) and high yield (>99.1%) were achieved. There were some fluctuations in the extract and raffinate outputs because of the pump instability caused by the increased pressure. The increase in the feed flow rate increases both throughput per bed volume and productivity (Table 4). Relatively high productivity could be achieved by the laboratoryscale experiments. The typical productivities reported for enantioseparation using SMBs range from 0.1 to 1 g of enantiomer/g of CSP/day.36,37 4.7. Optimal Column Length for the Highest Throughput per Bed Volume. Figures 20-23 show the effects of the column length on the throughput per bed volume and desorbent consumption. Without any pressure limit, the feed flow rate and the zone flow rates are limited only by mass-transfer effects. In this case,

as the column length increases, the throughput per bed volume increases and eventually approaches a limiting value, as expected from the SWD equation (eq 37). If a pressure limit exists, the flow rates are limited by masstransfer effects for short columns and by the maximum pressure for long columns. In the pressure-limiting region, the throughput per bed volume decreases exponentially with an increase in the column length. This is because pressure drop increases with an increase in the column length and the feed flow rate must be reduced to satisfy the pressure limit. As the column length increases, mass-transfer effects become less important, as expected from eq 10. As a result, a low desorbent flow rate is needed to maintain the required purity and yield. In the pressure-limiting region, des-


orbent consumption further decreases because the feed flow rate is reduced by the pressure limit (Figures 2023). The results in Table 5 show the optimal column length to achieve the highest throughput per bed volume for four different particle sizes. The zone and pump configurations and the total number of columns were kept the same as those in the experimental conditions. The production rate and the downtime were assumed to be 25 000 kg/year and 20%, respectively. The production rate was based on typical production rates of lowmolecular-weight pharmaceuticals, ranging from 10 000 to 50 000 kg/year.38 The optimal column length for the highest throughput per bed volume falls on the boundary between the mass-transfer-limiting region and the pressure-limiting region. For larger particles, longer columns are needed to achieve the highest throughput per bed volume. Both the low-pressure system (350 psi) and the high-pressure system (2000 psi) can achieve more than 99% purity and yield for a wide range of particle sizes (10-100 µm). The purity and yield were confirmed by the VERSE simulations. For 27 µm or larger particles, the high-pressure SMB equipment has no significant advantages in the throughput per bed volume over the low-pressure SMB. Larger particles allow a higher flow rate for a given pressure limit. However, the maximum throughput per bed volume is proportional to 1/Rp2, as predicted from the SWD equation (eq 39). Thus, larger particles intrinsically have lower throughput per bed volume. However, if large particles are considerably cheaper than small particles, SMB processes based on large particles are expected to be more economical despite the low throughput per bed volume. The correlation provided by Pynnonen39 suggested that the price of adsorbent generally decreases with an increase in the particle size. However, at present, there is no large particle CSP based on derivatized polysaccharide, and the relative costs of the larger particle CSPs versus those of the small particles are not yet known. The cost issue is beyond the scope of this study and remains an open question for future studies. The operating conditions determined from the nonideal SWD for a 27-µm particle size and a 350-psi pressure limit at different column lengths are shown in the triangle diagram9 in Figure 24. As the column length increases from 5 to 30 cm, the operating conditions approach the vertex point from the inner region of the triangle. Operating conditions near the vertex point imply that the system is close to an ideal system, which requires less solvent than nonideal systems. However, to satisfy the pressure limit, the feed flow rate and, consequently, the throughput per bed volume must be reduced as the column length increases, as shown in Figure 21a. The system with 5-cm columns, although it has the highest throughput per bed volume for the 27-µm particle size and the 350-psi pressure limit, needs more solvent to overcome mass-transfer limitation to maintain product purity and yield. 4.8. Comparison of Ideal and Nonideal Designs under a Pressure Limit. Table 6 shows the purity and yield obtained from VERSE simulations and the DI values calculated for systems using the operating conditions obtained from ideal design and nonideal SWDs with two different particle sizes (27 and 50 µm) and three different column lengths (5, 10, and 30 cm) under two different pressure limits (350 and 2000 psi). Target

Table 6. Comparison of the Simulation Results Designed by Ideal and Nonideal SWDs with a Pressure Limit (Target Purity ) 99%, Yield ) 99%) column length (cm) 5

10

30

1.10

0.36

(a) 27-µm Particle Size 350-psi Pressure Limit ideal design feed flow rate 2.20 (mL/min) purity (%) extract 98.1 raffinate 99.9 yield (%) (+)-PPA 98.1 (-)-PPA 99.9 DI zone II 0.0038 zone III 0.0050 nonideal feed flow rate 1.71 design (mL/min) purity (%) extract 99.1 raffinate 100 yield (%) (+)-PPA 99.1 (-)-PPA 100 DI zone II 0.0037 zone III 0.0052

99.4 99.7 100 100 99.4 99.7 100 100 0.0011 0.0002 0.0014 0.0002 1.03 0.36 99.7 99.8 100 100 99.7 99.8 100 100 0.0011 0.0002 0.0014 0.0002

2000-psi Pressure Limit ideal design feed flow rate 12.57 6.29 (mL/min) purity (%) extract 80.8 93.4 raffinate 94.0 99.8 yield (%) (+)-PPA 82.7 92.9 (-)-PPA 93.6 99.8 DI zone II 0.0194 0.0050 zone III 0.0260 0.0067 nonideal feed flow rate 1.91 3.97 design (mL/min) purity (%) extract 98.9 99.0 raffinate 100 100 yield (%) (+)-PPA 98.9 99.0 (-)-PPA 99.8 100 DI zone II 0.0043 0.0042 zone III 0.0060 0.0060

2.10 99.6 100 99.6 100 0.0006 0.0008 2.03 99.7 100 99.7 100 0.0006 0.0008

(b) 50-µm Particle Size 350-psi Pressure Limit ideal design feed flow rate 7.55 3.78 (mL/min) purity (%) extract 71.0 88.4 raffinate 83.7 98.7 yield (%) (+)-PPA 67.0 87.8 (-)-PPA 86.2 98.8 DI zone II 0.0399 0.0102 zone III 0.0535 0.0137 nonideal feed flow rate 0.52 1.12 design (mL/min) purity (%) extract 98.9 98.9 raffinate 100 100 yield (%) (+)-PPA 98.9 98.9 (-)-PPA 100 100 DI zone II 0.0044 0.0042 zone III 0.0061 0.0060

1.26 99.1 100 99.1 100 0.0012 0.0016 1.17 99.4 100 99.4 100 0.0012 0.0016

2000-psi Pressure Limit ideal design feed flow rate 42.85 21.55 7.20 (mL/min) purity (%) extract 52.3 65.6 92.0 raffinate 54.8 76.8 99.7 yield (%) (+)-PPA 40.1 60.0 91.7 (-)-PPA 66.5 80.8 99.7 DI zone II 0.2210 0.0559 0.0064 zone III 0.2976 0.0752 0.0085 nonideal feed flow rate 0.52 1.12 3.53 design (mL/min) purity (%) extract 98.9 98.9 98.9 raffinate 100 100 100 yield (%) (+)-PPA 98.9 98.9 98.9 (-)-PPA 100 100 100 DI zone II 0.0044 0.0042 0.0041 zone III 0.0061 0.0060 0.0059

purity and yield were 99% for the design. Compared to the ideal design, the nonideal design could achieve higher purity and higher yield. For the ideal design under a pressure limit, the flow rates are limited only by the maximum pressure and the mass-transfer effects are not considered. Therefore, the target purity and yield cannot be guaranteed when the mass-transfer

3266


effects are significant. This can be seen more clearly for the cases with short columns, a large particle size (50 µm), or a high pressure limit (2000 psi). A high pressure limit allows high flow rates, resulting in significant mass-transfer effects. The dimensionless number DI can predict whether mass-transfer effects are significant and need to be considered in the design. Figure 25a shows the purities obtained from VERSE simulation as a function of the dimensionless number DI for the operating conditions obtained from the nonideal SWD. In this design, DIII is kept below 0.004-0.005 to achieve the target purity and yield of 99%. Figure 25b shows the purities obtained from VERSE simulation as a function of the dimensionless number DI for the operating conditions obtained from the ideal design. As the DI value increases with a decrease in the column length or an increase in the particle size or zone flow rates, the deviation from the ideal system increases and the product purity and yield decrease. If the DIII value is greater than 0.002, the product purity and yield fall below the target value, 99%. This critical DI value is similar to that for the phenylalanine-tryptophan system.17 Furthermore, for the same value of DIII and DIIII, higher purity can be obtained in the raffinate than in the extract. This is because self-sharpening effects are ignored in the derivation of DI. In a Langmuir system, the adsorption waves in zones III and IV are self-sharpening (Figure 3), which reduces the masstransfer spreading. Therefore, DIII is the critical DI value. 5. Conclusions The Taylor dispersion in the injection loop for a long pulse can contribute to significant tailing. Such a dispersion effect must be considered for an accurate estimation of intraparticle diffusivities using frontal or elution tests. An improved design method for a SMB with a pressure limit was developed for nonlinear nonideal systems. The design method was verified with VERSE simulations and tested with SMB experiments using semipreparative columns (27-µm particles) and low-pressure equipment (99%) and high yield (>99%) could be achieved experimentally. The experimental results showed that the isotherm and mass-transfer parameters are accurate, and the SWD method can ensure high purity and high yield in lowpressure SMB systems. The separation of racemic PPA with a laboratory-scale SMB was sensitive to the extra-column dead volume, which is about 6% of the column volume. An accurate extra-column dead volume should be measured and considered in the SWD to guarantee high purity and high yield. The optimal column length to achieve the highest throughput per bed volume for a given particle size and a pressure limit can be found from the SWD. The optimal column length falls on the boundary of the mass-transfer-limiting region and the pressure-limiting region. The feed and zone flow rates in a SMB are limited by mass-transfer effects in a short column and

by the maximum pressure in a long column. If a column length is optimized, the high-pressure SMB equipment has no significant advantage in the throughput per bed volume over the low-pressure SMB for large particles (>27 µm). In general, desorbent consumption decreases with an increase in the column length or a decrease in the feed and zone flow rates because mass-transfer effects become less important for long columns or low flow rates. The nonideal SWD can guarantee high purity and high yield for both low- and high-pressure systems with a wide range of particle sizes, column lengths, and flow rates. The ideal design can guarantee high purity and high yield only for systems with small particles and long columns operated at low flow rates. If the characteristic dispersion velocity exceeds 0.2% of the interstitial velocity in zone II (i.e., DIII > 0.002), the nonideal design is needed to achieve 99% purity and yield. Acknowledgment This study is supported by grants from Chiral Technologies, the 21st Century Research and Technology Fund, and Purdue Technology Transfer InitiativeInnovation Realization Laboratory fellowship (NSF IGERT 9987576). The authors are grateful to Dr. Zidu Ma and Jim Berninger for their help in incorporating Taylor dispersion in VERSE simulations and to Jinwon Park for his help in taking the microscopic images. Nomenclature ai ) Langmuir isotherm parameter of component i, L/L solid volume bi ) Langmuir isotherm parameter of component i, L/g BV ) bed volume, cm3 c ) solute concentration in the fluid, g/L CE,i ) extract concentration of component i CF,i ) feed concentration of component i Cp,i ) plateau concentration of component i CR,i ) raffinate concentration of component i Cs,i ) dilution concentration of component i at the feed port / ) concentration of component i in the zone II outlet Cs,i before the feed port Dp,i ) intraparticle diffusivity of component i, cm2/min D∞,i ) molecular diffusivity of component i, cm2/min DIji ) dimensionless number of component i in zone j defined in eq 30 DV ) extra-column dead volume, cm3 j Eb,i ) axial dispersion coefficient of component i in zone j, cm2/min Ez ) dispersion coefficient defined as (R0um)2/48D∞, cm2/ min Fdes ) desorbent flow rate, mL/min Fext ) extract flow rate, mL/min Ffeed ) feed flow rate, mL/min Fraf ) raffinate flow rate, mL/min Fj ) flow rate in zone j, mL/min Ke ) size-exclusion factor j ) film mass-transfer coefficient of component i in zone kf,i j, cm/min j Kf,i ) lumped mass-transfer coefficient of component i in zone j, min-1 Lc ) length of a single column, cm Lj ) length of zone j, cm M ) total solute in the pulse, g/L Nc ) number of columns P ) phase ratio defined as (1 - b)/b Peji ) Peclet number of component i in zone j

Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005 3267 q ) solute concentration adsorbed, g/L solid volume Rp ) particle radius, cm R0 ) tube radius, cm S ) cross-sectional area of a column, cm2 Stji ) Stanton number of component i in zone j t ) elution time, min uj0 ) liquid interstitial velocity in zone j, cm/min j ) wave velocity of standing component i in zone j, cm/ uw,i min ush ) shock wave velocity, cm/min Yi ) yield of component i z ) distance along the tube, cm Greek Letters βji ) decay factor of standing component i in zone j ∆ji ) mass-transfer correction term for component i in zone j ∆P ) pressure drop, g/cm/min2 δji ) effective retention factor for component i in zone j b ) interparticle void fraction p ) intraparticle void fraction t ) total void fraction F ) fluid density, g/cm3 Fbed ) bulk density of the bed, g/cm3 µ ) fluid viscosity, g/cm/min ν ) average port velocity, cm/min

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Received for review July 4, 2004 Revised manuscript received February 11, 2005 Accepted February 21, 2005 IE049413P

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