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Ind. Eng. Chem. Res. 2006, 45, 1454-1465
Insulin Wave Dynamics in Size-Exclusion Simulated Moving Bed with Residence Time Control Sungyong Mun* Department of Chemical Engineering, Hanyang UniVersity, Seoul, 133-791, Korea
Nien-Hwa Linda Wang School of Chemical Engineering, Purdue UniVersity, West Lafayette, Indiana 47907
In the application of simulated moving bed (SMB) technology to a pharmaceutical purification, the residence time of a product inside the SMB should be shortened, to prevent possible aggregation or denaturation. In addition, each key concentration wave should be confined in an appropriate zone to maintain high yield and high purity throughout the SMB operation. To achieve both goals, one must first understand clearly dynamic wave propagation phenomena in connection with solute residence time in the SMB. For this purpose, a series of transient column profiles in the tandem SMB for insulin purification are generated from computer simulations based on a detailed rate model. The column profiles show that the insulin molecules take a long time to reach the product port if they stay in the zone where the insulin wave is standing (or the standing zone). This leads to a long residence time. To shorten the insulin residence time, one can reduce the amount of insulin in the standing zone or modify the zone flow rates such that the insulin wave becomes focused or pinched. The former can be realized by a partial feeding strategy and the latter by a pinched wave design (PWD) method. The wave propagation phenomena for each case are shown using a series of insulin column profiles from the rate model simulations. Based on the understanding of the insulin wave dynamics, a three-zone SMB based on the PWD condition is proposed as the most effective strategy to reduce the residence time of insulin. 1. Introduction The simulated moving bed (SMB) method is an efficient separation technique. It was first introduced for hydrocarbon purification.1 Recently, many SMB processes have been developed for pharmaceutical applications,2 including a tandem SMB process (two SMB units in series) for the separation of insulin from two impurities: high-molecular-weight proteins (HMWP) and ZnCl2.3 Figure 1 shows a schematic diagram of the tandem SMB for insulin purification.3 HMWP are removed from the raffinate port in the first ring (Ring I). Because ZnCl2 is not required to be recovered completely in the first ring, it is allowed to distribute from zone I to zone IV; thus, it is collected in both the raffinate and extract streams. The effluent from the extract port of Ring I is loaded into the second ring (Ring II), where insulin is separated from ZnCl2. Several important issues should be considered before the SMB technology is introduced into the actual industrial process. One of the issues to be considered is the long residence time of a protein in the SMB, which may result in aggregation or denaturation.4,5 Methods for estimating and reducing the residence times of proteins in the SMB are needed to control residence time. In a previous study, the equations of solute residence time in the SMB were derived and the strategies to reduce residence time were formulated.4 The results showed that residence time in the SMB is a function of the injection time, recycle ratio, dispersion due to mass transfer, selectivity, throughput, zone flow rates, and switching time. To shorten the residence time of a fast-moving solute, one can feed during the first-half of * To whom correspondence should be addressed. Tel.: +82-2-22200483. Fax: +82-2-2298-4101. E-mail:
[email protected].
Figure 1. Schematic of a tandem simulated moving bed (SMB) process for insulin purification.
the switching period, shorten the length of zone III, or increase zone II flow rate beyond the requirement of standing wave (or the so-called “pinched wave design” (PWD)). To shorten the residence time of a slow-moving solute, one can feed during the second half of the switching period, shorten the length of
10.1021/ie0507880 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/11/2006
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Figure 2. Standing waves in a four-zone SMB system with a linear isotherm. The bold/heavy line represents the slow-moving solute (extract product), and the regular line represents the fast-moving solute (raffinate product).
zone II, or decrease the zone III flow rate. High selectivity and small dispersion effects also result in a short residence time. In addition to the control of solute residence time in the SMB, high purity and high yield should also be maintained during an SMB operation. To guarantee high purity and high yield, the four key concentration waves should be confined in the appropriate zones. As shown in Figure 2, the trailing waves of a slow-moving solute and a fast-moving solute should be confined in zone I and zone II, respectively. Simultaneously, the advancing waves of a slow-moving solute and a fast-moving solute should be confined in zone III and zone IV, respectively.6,7 To address both the issue of solute residence time and the requirements of high purity and high yield, one must first understand the wave propagation phenomena in connection with solute residence time in the SMB. This is especially important in developing new strategies to reduce solute residence time in a low-selectivity SMB system. However, the previous study did not discuss the behavior of solute wave propagation from the standpoint of the residence time issue. The goal of this study is to understand how the solute wave propagation is related to its residence time in the SMB. We will also elucidate the effects of the aforementioned residence time strategies on the solute concentration waves in the SMB. Computer simulation is an efficient tool in understanding the dynamics of wave propagation. To date, there have been two approaches of computer simulation and mathematical modeling in describing the behavior of the SMB: (1) true moving bed (TMB) analysis,8-11 which assumes that the solid phase moves countercurrently, with respect to the eluent flow; and (2) periodic moving-port analysis, which assumes that individual fixed beds are connected by two inlet and two outlet ports with periodic port movement along the flow direction.12-15 Obviously, the periodic moving-port approach is more realistic for SMB systems than the TMB approach.14 In this study, the periodic moving-port approach is used for SMB modeling. A detailed rate model based on the periodic moving-port approach is solved using VERSE (versatile reaction and separation software). In this study, the tandem SMB for insulin purification3 is chosen as an example, where the residence time of insulin should be reduced. A series of transient column profiles from VERSE simulations are used to illustrate how the insulin wave dynamics is related to its residence time. Effects of the strategies to reduce residence time on the insulin wave dynamics are investigated. This study will also identify which factors have a major effect on the insulin residence time. This understanding will help devise more effective strategies to shorten residence time in the SMB. The wave dynamics for each of the strategies is illustrated and discussed. The effects of the strategies on productivity and solvent consumption are also studied, and the results are used to find optimal operating conditions.
2. Theory 2.1. Standing Wave Design. In the standing wave design (SWD),7,16 the four zone linear velocities and the average port velocity are chosen such that the four key waves are standing relative to the ports in the appropriate zones in a time-averaged sense (Figure 2). In this study, the mixture components are separated on the basis of the difference in their size-exclusion factors. This sizeexclusion system can be treated as a linear isotherm system where the isotherm constant (a) is set to zero. The SWD equations for binary linear systems with mass-transfer effects are given by
uI0 ) (1 + Pδ2)ν + ∆I2
(1a)
uII0 ) (1 + Pδ1)ν + ∆II1
(1b)
III uIII 0 ) (1 + Pδ2)ν - ∆2
(1c)
IV uIV 0 ) (1 + Pδ1)ν - ∆1
(1d)
Ffeed II ) uIII 0 - u0 bS
(1e)
where the mass-transfer correction terms of component i in zone j are defined as
∆ji )
βji Lj
[
Eb,ij +
]
P(δiν)2 j Kf,i
(2)
The subscripts 1 and 2 represent a fast-moving solute and a slow-moving solute, respectively; the superscripts I, II, III, IV represent the four zones; ν is the average port velocity (ν ) column length/switching time); u0 is the interstitial velocity; P is the phase ratio, defined as (1 - b)/b, and b is the interstitial bed voidage; δ is defined as Kep + (1 - Kep)a, where p is the porosity of the particle, a is the linear isotherm constant, and ai ) 0 for size-exclusion systems; L is the zone length; S is the cross-sectional area of the column; Eb is the axial dispersion coefficient; and Kf is a lumped mass-transfer parameter.7 β is the logarithm of the ratio of the highest concentration to the lowest concentration of a standing wave in a particular zone. β is an index of product purity and yield; the larger the β value, the higher the product purity and yield.7,16 If the yield of each component is given, the β values can be estimated from component mass-balance equations.16 The four standing wave velocities correspond to the minimum linear velocities for zones I and II and the maximum linear velocities for zones III and IV that can guarantee the desired yield and purity in the presence of mass-transfer effects. The standing wave conditions give the highest throughput and the
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lowest solvent consumption.7 However, they lead to a significant increase in solute residence time.4 2.2. Rate Model for Computer Simulations. VERSE is a useful tool for elucidating the transient and cyclic steady-state phenomena in the SMB. VERSE is based on a detailed rate model, which consists of unsteady-state mass balance equations for each solute in both the mobile phase and the stationary phase.16 For the mobile phase within each zone, the mass balance equation for each solute i includes contributions from convection, axial dispersion, and film mass transfer. j ∂Ci ∂2Ci ∂Ci 3kf,i (1 - b) j j ) Eb,i 2 - u0 (Ci - Cp,i|r)Rp) (3a) ∂t ∂z R ∂z pb j z ) zk,0, Eb,i
∂Ci ) uj0 (Ci(t, zk,0) - Cin i (t, zk,0)) ∂z
(3b) (3c)
where Ci is the mobile phase concentration of species i at time t and axial position z, Cin i represents the inlet concentration of j is the axial i, j is the zone number (I, II, III, or IV), Eb,i dispersion coefficient of component i in zone j, zk,0 represents the axial position of the inlet of column k, zk,L represents the axial position of the outlet of column k, uj0 is the mobile phase j interstitial velocity of zone j, kf,i is the film mass-transfer coefficient, Rp is the particle radius, and Cp,i|r)Rp is the particlephase solute concentration at the particle surface. The numbering of the zones and columns begins at the eluent port (z ) 0, k ) 1, and j ) I there). In the stationary phase, the mass balance equation includes contributions from adsorption and Fickian diffusion:
(
)
∂qi ∂Cp,i Dp,i ∂ 2 ∂Cp,i + (1 - p) ) Ke,ip 2 r Ke,ip ∂t ∂t ∂r r ∂r
r ) Rp, Ke,ipDp,i
HMWP Ke D∞ (cm2/min) Dp (cm2/min) kf (cm/min)a,b Eb (cm2/min)a,c column properties
insulin
0.19 4.80 × 10-5 2.00 × 10-5 0.0255-0.0306
ZnCl2
0.74 5.49 × 10-5 2.29 × 10-5 0.0279-0.0335 0.0122-0.0211 b ) 0.35, p ) 0.89
0.99 3.96 × 10-4 1.65 × 10-4 0.117-0.124
a Because k and E are functions of mobile phase interstitial velocity, f b they have different values in each zone of the SMB. Thus, the ranges of kf and Eb are given in this table. b Obtained using the Wilson and Geankoplis correlation.25 c The Eb value of insulin in zone III of Ring I is chosen to be 40 times as large as that estimated from the Chung and Wen correlation26 (the range given in the table).
Table 2. Column Dimensions and Operating Parameters of the Tandem SMB for Insulin Purification Valuea
∂Ci z ) zk,L, )0 ∂z
r ) 0,
Table 1. Intrinsic Parameter Values Used in the Design and Simulations of the Tandem SMB for Insulin Purification
∂Cp,i )0 ∂r
∂Cp,i j (Ci - Cp,i|r)Rp) ) kf,i ∂r
parameter zone configuration single-column length column diameter zone flow rates zone I zone II zone III zone IV inlet and outlet flow rates feed eluent raffinate extract switching time
Ring I SMB
Ring II SMB
2-2-4-2 15.0 cm 10.0 cm
2-3-3-2 15.0 cm 10.0 cm
30.97 mL/min 18.16 mL/min 27.30 mL/min 17.89 mL/min
30.16 mL/min 25.56 mL/min 29.94 mL/min 24.96 mL/min
9.14 mL/min 13.08 mL/min 9.41 mL/min 12.81 mL/min 30.06 min
4.38 mL/min 5.20 mL/min 4.98 mL/min 4.60 mL/min 36.20 min
a The operating parameters are obtained from the standing wave design (SWD).
Table 3. Numerical Parameters Used in the Simulations
(4a) (4b) (4c)
where Cp,i is the pore-phase concentration, qi the solid-phase concentration, r the distance in the radial direction, Ke,i the sizeexclusion factor, and Dp,i the pore (intraparticle) diffusivity. Note that, for a size-exclusion system, the value of q in eq 4a is zero. To solve the model equations for dynamic column profiles in SMB, the method of orthogonal collocation on finite elements17-19 is applied. The partial differential equations in the model are converted to ordinary differential equations (ODEs) through polynomial approximations of the spatial partial derivatives; Legendre polynomials are used in the axial direction and Jacobi polynomials are used in the particle radial direction.20 DASSL, which is a differential/algebraic system solver,21 is used to integrate the ODEs in the time domain. All of these numerical computations are performed in a VERSE simulator, which has been validated in several previous studies.3,16,20,22-24 3. Parameters The tandem SMB for insulin purification3 was chosen as an example for this study. The operating parameters of the tandem SMB were determined from the SWD.7,16 The intrinsic parameters used in the SWD and the simulations were reported by
parameter
value
number of axial elements number of collocation points per element number of collocation points per particle absolute tolerance on concentration relative tolerance on concentration maximum step time in integration
500 4 2 0.001 mg/mL 0.001 0.001 bed volumes
Xie et al.,3 and they are listed in Table 1. Note that, in the standing wave design equations, the Eb value of insulin in zone III of Ring I was chosen to be 40 times as large as that estimated from the Chung and Wen correlation.26 The large Eb was used to overcome the dispersion of insulin due to nonideal flow or other effects in zone III of Ring I.3 The resulting zone flow rates and switching time (ts) for Rings I and II are listed in Table 2 and they were used in the analysis of insulin wave dynamics. The numerical parameters used in the VERSE simulations are also listed in Table 3. 4. Results and Discussion 4.1. Overview. First, VERSE simulations are performed for the standard case, where an SMB operation follows the conventional principles7,16,27-29 that the highest throughput and the lowest solvent consumption should be achieved while maintaining the desired yield and purity. However, the residence time issue is not taken into account in the standard case. Second, VERSE simulations are used to generate insulin column profiles for a particular case, in which the partial feeding method or the PWD is applied to reduce insulin residence time. The insulin column profiles from the particular case are then compared with those from the standard case to understand
Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1457 Table 4. Simulation Results of the Standard Case SMB yield impurity level HMWP in insulin ZnCl2 in insulin
Figure 3. Column profiles of the tandem SMB based on the standard case: (a) mid-step column profiles of Ring I at cyclic steady state, and (b) mid-step column profiles of Ring II at cyclic steady state.
clearly the effect of the partial feeding method or the pinched wave design on the insulin wave evolution. This understanding leads to the development of a more effective strategy to reduce the insulin residence time. The productivity and solvent consumption for each particular case is also compared with those for the standard case. Basically, the residence time of a solute is controlled by its migration velocity and its traveling path. In a size-exclusion system, the migration velocity of a solute and its traveling path are independent of concentration. The former is thus governed only by zone flow rates for a given system. The latter is affected only by the injection time of a solute in each switching period and the operating parameters. As a result, if the zone flow rates and switching time are kept constant during the entire operation, the solute residence time will depend only on its injection time in each switching period. This means that the residence time history in a size-exclusion system is repeated in every switching time and the residence time distribution (RTD) of solutes during one switching period is representative of the RTD of all other switching periods.4 For this reason, the column profile of insulin injected during one switching period is sufficient to analyze its residence time from the viewpoint of wave dynamics. 4.2. Standard Case. The operating parameters of the standard case (Table 2) are determined from the SWD,7,16 which is one of the well-developed design methods to guarantee the highest productivity and the lowest solvent consumption in the SMB. The mode of feed injection in the standard case adopts a continuous loading to keep productivity as high as possible. On the basis of the operating parameters (Table 2) and the continuous loading, the column profiles of the tandem SMB for insulin purification3 are obtained from the rate model simulations. As shown in Figure 3, insulin is completely separated from HMWP in Ring I and ZnCl2 in Ring II. Note that insulin is the extract product in Ring I, whereas insulin is the raffinate product in Ring II.
Ring I
Ring II
>99.9%
>99.9%
