Comparative analysis of single-cascade five-zone and two-zone SMB systems for the separation of a ternary amino acid mixture.

Jo, Se-Hee ; Kim, Jeung Kun ; Yoo, Chang Geun 等

INTRODUCTION

Simulated moving bed (SMB) technology has drawn a lot of attention as a continuous counter-current separation process for the last few decades. SMB was first developed for petrochemical purification by UOP in 1961 (Broughton and Gerhold, 1961). Since then, many researches have been performed on the optimal design of SMB and its applications to highly valuable products such as chiral drugs, biochemical products, and pharmaceutical products (Ma and Wang, 1997; Juza et al., 2000; Schulte and Strube, 2001). Until the middle of 1990s, most of SMB researches have been focused on a standard four-zone SMB for binary separations (Figure 1). If such standard four-zone SMB is used as it is, more than one SMB unit is needed either (1) for the separation of a ternary mixture into three different pure fractions (or "ternary separation") or (2) for the recovery of only an intermediate-affinity component in a ternary mixture (or "centre-cut separation"). The demand for such separation tasks occurs frequently in bio-product purification processes. The use of one more SMB unit, however, results in much higher operation and maintenance costs, compared to the use of a single SMB unit. It is obvious that the application of a single SMB unit is more advantageous if it can meet the product specification such as product purities.

Recently, there have been several studies on the use of a single SMB unit for ternary separation or centre-cut separation. Among them, major attention has been paid to a single SMB unit with five zones (hereafter "five-zone SMB") (Beste and Arlt, 2002; Kim et al., 2003; Wang and Ching, 2005) and a single SMB unit with two zones (hereafter "two-zone SMB") (Hur and Wankat, 2005, 2006; Hur et al., 2006). The structure of a five-zone SMB is briefly explained below while the details of a two-zone SMB can be obtained elsewhere (Hur and Wankat, 2005, 2006; Hur et al., 2006).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

A five-zone SMB for ternary separation usually consists of five or more chromatographic columns, which are connected to form a circular flow path. The circle is divided into five zones of constant flow rates by five ports, one each for the feed, the desorbent, the lowest-affinity component, the intermediate-affinity component, and the highest-affinity component (Figure 2). The ports are switched periodically along the circular path to allow the ports to follow the migrating solute bands. The periodic port movement achieves "simulated" counter-current movement of the adsorbent relative to the fluid. The average port movement velocity and the zone flow rates are designed to allow feed to be added in the mixed region (where three solute bands overlap) and allow three pure products to be drawn from the pure component regions (where there is no overlap between different solute bands). Such configuration and operation make more efficient use of the adsorbent and the solvent than conventional batch chromatography. A five-zone SMB has thus been a major topic in several previous publications so far. However, no previous studies have hitherto compared the separation performance of a five-zone SMB with that of a two-zone SMB for the system of a ternary mixture.

The goal of this study is to investigate the process merits of a five-zone SMB over a two-zone SMB. The system of a ternary amino acid mixture (glycine, L-phenylalanine, L-tryptophan) at 50[degrees]C, whose centre-cut separation has been lately performed using a two-zone SMB by Hur et al. (2006), was chosen as a model system for the aforementioned comparative studies. The adsorbent used for the separation of the model system was PVP resin (poly-4-vinylpyrinde cross-linked, Reillex HP polymer), where glycine has the lowest-affinity, L-phenylalanine the intermediate-affinity, and L-tryptophan the highest affinity (Hur et al., 2006).

The results of this study showed that a five-zone SMB, if well designed using the safety margin method, can achieve a better separation performance than the previous centre-cut two-zone SMB at its optimal state. Moreover, a well-designed five-zone SMB on the basis of the safety margin method can recover three products with much higher purities than the optimized two-zone SMB for ternary separation.

SMB DESIGNS FOR THE SEPARATION OF A TERNARY AMINO ACID MIXTURE

Consider a mixture of three components (A, B, C) arranged according to their adsorption affinity, where component A has the lowest adsorption affinity and component C has the highest adsorption affinity. Among the three amino acid components under examination, glycine corresponds to component A while L-phenylalanine and L-tryptophan correspond to components B and C, respectively.

In general, a ternary separation requires the use of two SMB units in series (or a tandem SMB). However, in some circumstances, a single SMB unit such as a five-zone SMB or a two-zone SMB can be satisfactorily applied to the separation of a ternary mixture as stated above.

Five-Zone SMB System for Ternary Separation

A five-zone SMB system has three product ports as shown in Figure 2. Among them, the product ports for the lowest-affinity (A) and the highest-affinity (C) components are located on the other side of the feed port as in a standard four-zone SMB. An additional product port, which is used to obtain the intermediate-affinity component, can be located upstream or downstream from the feed port (Beste and Arlt, 2002; Kim et al., 2003; Wang and Ching, 2005).

In the first configuration (Figure 2), the additional product port is located upstream from the feed port such that the five-zone SMB has two extract ports. To achieve the desired separation in such configuration, the process should be designed to make component A migrate downstream from the feed port and approach the raffinate port. Simultaneously, components B and C should be made to migrate upstream from the feed port and exit from the extract-2 and the extract-1 ports, respectively. These conditions are indicated by the arrows in Figure 2. Additionally, the following requirement on component C should be satisfied; most of the component C molecules injected into the feed port should be confined within one column until they enter zone I by a series of port switchings. This is to prevent the elution of component C through the extract-2 port, thereby obtaining high purity of B in the extract-2 stream and high yield of C in the extract-1 stream. Because of such a requirement on the component C migration behaviour, the feasibility of the aforementioned five-zone SMB is usually subject to the selectivity between B and C.

In the second configuration of a five-zone SMB (not shown), the additional product port for component B is located downstream from the feed port. Such configuration results in two raffinate streams and one extract stream. Unlike the first configuration, the second configuration always causes the contamination of product B stream, because component A must pass through the port of product B stream before exiting from the port of product A stream. The five-zone SMB based on the second configuration is thus infeasible for complete ternary separation. In this study, only a five-zone SMB based on the first configuration is applied to the separation of the ternary amino acid mixture.

Single Cascade Two-Zone SMB for Ternary Separation

A single cascade two-zone SMB, which has been developed by Hur and Wankat (2005), is shown in Figure 3. In this process, each switching period comprises two consecutive operation steps, each of which lasts for a half of the switching time. During the first step of each switching period, a feed mixture containing the three amino acids is loaded into the connection between zones I and II while the highest-affinity component (C) is withdrawn from zone I (Figure 3). The second step begins with the stop of feed injection and the disconnection of the two zones, followed by collecting two purified components A and B from the outlets of zones I and II, respectively (Figure 3).

[FIGURE 3 OMITTED]

This process is designed to recycle the overlapping portion of A and B back to SMB. At the same time, the zone flow rates and the switching time are adjusted such that the feed is always loaded into the overlapping region of A and B. On the other hand, the overlapping portion of B and C is not recycled back to SMB. The presence of a little overlapping region between B and C can thus directly leads to the contamination of two product streams B and C. For this reason, the separation performance of a two-zone SMB is governed by the following two factors: (1) the selectivity between B and C and (2) the spreading of the two component bands due to mass-transfer effects.

SIMULATION MODEL

There have been two approaches of computer simulation in describing the behaviour of SMB: (1) moving-bed approach (Rhee et al., 1971; Ruthven, 1983; Ching and Ruthven, 1985; Storti et al., 1993) and (2) fixed bed approach (Storti et al., 1989; Hashimoto et al., 1988; Charton and Nicoud, 1995; Chu and Hashim, 1995).

The moving-bed approach is based on the assumption that the adsorbent phase moves continuously in the opposite direction to the desorbent flow. The moving-bed approach simplifies the model equations and reduces the calculation time. This approach is, however, inappropriate for the simulation of a two-zone SMB, which has partially a chromatographic separation behaviour. The approach also has some limitations in the simulation of a five-zone SMB (Figure 2). The reason is that the separation between components B and C, which attainable in a well-designed five-zone SMB, cannot be described under continuous counter-current movement of the adsorbent phase (Kim et al., 2003). To be brief, the moving-bed approach cannot reflect the actual operation modes of a five-zone SMB (Figure 2) and a two-zone SMB (Figure 3) as it is.

On the other hand, the fixed bed approach is based on the actual SMB operation principle that individual fixed beds are connected with inlet and outlet ports while the ports are periodically moved along the direction of desorbent flow. Because such principle can describe more accurately the separation behaviours occurring in the SMB systems of our interest, the fixed bed approach is used for modelling in this study.

The simulation model consists of unsteady state mass balance equation for the mobile phase and the mass-transfer equation between mobile phase and solid surface. For the mobile phase within each zone, the single porosity model (Wankat, 1990) was used for the mass balance of component i as follows:

[partial derivative][C.sub.i]/[partial derivative]t + p[partial derivative][q.sub.i]/[partial derivative]t = [E.sub.b,i.sup.j][[partial derivative].sup.2][C.sub.i]/[partial derivative][z.sup.] - [u.sub.0.sup.j] [partial derivative][C.sub.i]/[partial derivative]z (1)

where [C.sub.i] is the mobile phase concentration of species i at time t and axial position z; j is the zone number (I, II, III, IV, or V); P is the phase ratio, defined as (1-[epsilon])/[epsilon], where [epsilon] is the total void fraction; [E.sup.j.sub.b,i], is the axial dispersion coefficient of component i in zone j; and [u.sup.j.sub.0] is the mobile phase interstitial velocity in zone j. For the mass-transfer equation, a linear lumped resistance model was used as follows:

[partial derivative][q.sub.i]/[partial derivative]t = [k.sub.m][a.sub.p] ([C.sub.i] - [C.sup.*.sub.i]) (2)

where [k.sub.m] is the mass-transfer coefficient; [C.sup.*.sub.i] * is the equilibrium liquid concentration corresponding to the solid concentration; and [a.sub.p] is the external surface area per particle volume and [a.sub.p] = 3/[R.sub.p] for spherical particles.

The feed concentrations of the three amino acids ([C.sub.F,A] = 0.577 g/L, [C.sub.F,B] = 0.963 g/L, [C.sub.F,C] = 0.415 g/L), which are kept the same as those in the previous study (Hur et al., 2006), are in the region of a linear isotherm relation. The linear isotherm parameter and the other intrinsic parameters at 50[degrees]C were reported by Hur et al. (2006), and they are summarized in Table 1.

To solve the aforementioned model equations for the product purities, a biased upwind differencing scheme (BUDS) was employed in conjunction with Implicit Euler integration having a step size of 0.01. The number of nodes in each column was set at 60. All of these numerical computations are carried out in Aspen Chromatography 12.1. simulator, which has been validated in several previous studies (Zang and Wankat, 2003; Kim et al., 2003; Hur and Wankat, 2005; Hur and Wankat, 2006).

APPROACH

First, a two-zone SMB is optimized for the centre-cut separation or ternary separation of the three amino acid components (A, B, C). The optimized two-zone SMB is then used as a criterion for evaluating the separation performance of a five-zone SMB. The comparative merits of a five-zone SMB are also discussed in terms of the purity index and the purity of B while the productivity and the constraints on zone flow rates are kept the same as in the two-zone SMB. The purity index (PI), which has been often used to indicate the separation performance of a given process (Hur and Wankat, 2005; Hur and Wankat, 2006), is defined as the average of the purities of three components as follows:

PI = (purity of A) + (purity of B) + (purity of C)/ 3 (3)

and the productivity is defined as

Productivity = Feed flow rate/Total bed volume x (fraction of feed-injection time over one switching period) (4)

The constraints set on both the two-zone and the five-zone SMBs are as follows:

(yield of B) [greater than or equal to] 90 % and (zone flow rate) [less than or equal to] 10 mL/min (5)

where a maximum limit is placed on the zone flow rate because of the stability of the packing bed (Hur et al., 2006). Note that the two above constraints (Equation (5)) are taken from the literature (Hur et al., 2006) as they are. This is to make fair comparison between a five-zone SMB and a two-zone SMB.

RESULTS AND DISCUSSION

Determination of Optimal Two-Zone SMB System

Since the details of the centre-cut two-zone SMB have been reported in the literature (Hur et al., 2006), only an optimization of the two-zone SMB for ternary separation was carried out in this study. All the optimization conditions of the two-zone SMB for ternary separation were kept the same as those of the previous centre-cut two-zone SMB (Hur et al., 2006) only except for the following two points. First, the purity index instead of the B purity was used as an objective function during the process optimization. Second, a waste stream for the collection of A and C was split into two separate product streams in order to purify the ternary amino acid mixture into three different pure fractions. For convenience sake, the centre-cut two-zone SMB is called hereafter "two-zone SMB-c" while the two-zone SMB for ternary separation is called hereafter "two-zone SMB-t".

During the optimization of the two-zone SMB-t, three desorbent flow rates and the switching time were chosen as the decision variables (or the variables to be optimized) while the feed flow rate was fixed at 0.5 mL/min and the zone flow rates were constrained to be less then 10 mL/min. Note that such feed flow rate and zone flow rate constraint were equal to those of the previous two-zone SMB-c reported in the literature (Hur et al., 2006).

For the optimization of the two-zone SMB-t, a binary coded genetic algorithm was applied to Excel VBA, which has the function of controlling Aspen Chromatography. The concept of genetic algorithm (GA) is based on the imitation of the process of natural selection and natural genetics (Kasat and Gupta, 2003), and the successful applications of GA to SMB optimizations have been reported in several previous publications (Zhang et al., 2002; Hur and Wankat, 2006). The GA optimization begins with the specification of several GA parameters such as population size, the length of chromosome, the number of generations, crossover probability, and mutation probability. Table 2 lists the GA parameters used in the optimization of the two-zone SMB-t. Considering both accuracy and calculation time, we chose 50 chromosomes and stopped the iteration after 40 generations. In order to ensure that the global optimum is obtained, three optimization runs were performed with different sets of initial pool of chromosomes. The computational time in obtaining the optimum values was 5 d on a 2.8 GHz Pentium 4 computer with 512 MB of RAM.

The optimization results are presented in Table 3. We see that the highest purity index obtainable from the two-zone SMB-t amounts to 85.7%. This value is about 11% higher than that of the two-zone SMB-c, whose optimization results were reported in the previous literature (Hur et al., 2006). On the other hand, the B purity (or purity of the intermediate product B) of the optimized two-zone SMB-t is reduced by 6%, compared to that of the optimized two-zone SMB-c. Comparison of the two processes in Table 3 reveals that the two-zone SMB-t improves the purities of A and C at the cost of the B purity. It is evident that the optimization results match with its corresponding objective function used in the optimization.

However, the purity index of the two-zone SMB-t and the B-purity of the two-zone SMB-c are still lower than 90% although both the processes were optimized under its corresponding objective function. These phenomena indicate that the use of only two zones is not sufficient to ensure high product purity against the mass-transfer spreading of each amino acid component. Aside from a tandem SMB (or two SMB units in series), a single cascade SMB (or single SMB unit) with more than two zones is therefore expected to be suitable for the separation of the three amino acid components.

Design of a Five-Zone SMB System Based on the Safety Margin Method

In this section, a single cascade five-zone SMB is applied to separate the ternary amino acid mixture into three different fractions. The five-zone SMB of this separation task was designed with the safety margin method, which has been effectively used for the design of SMB with mass-transfer resistances in several previous studies (Ching et al., 1985; Ruthven and Ching, 1989; Zhong and Guiochon, 1996; Zhong et al., 1997; Yun et al., 1997; Wang and Ching, 2005).

The safety margin method for the five-zone SMB (Figure 2) is based on the following relationship between the migration velocity of a key solute in each zone and the average port velocity.

[u.sup.I.sub.C] = [u.sup.I.sub.0]/1 + P x [K.sub.C] > v (6a)

[u.sup.II.sub.B] = [u.sup.II.sub.0]/1 + P x [K.sub.B] > v (6b)

[u.sup.III.sub.A] = [u.sup.III.sub.0]/1 + P x [K.sub.A] > v (6c)

[u.sup.IV.sub.B] = [u.sup.IV.sub.0]/1 + P x [K.sub.B]< v (6d)

[u.sup.V.sub.A] = [u.sup.V.sub.0]/1 + P x [K.sub.A] < v (6e)

where [u.sup.j.sub.i] is the migration velocity of component i in zone j; v is the port movement velocity (= single column length/switching time); and [K.sub.i] is the linear isotherm parameter of component i. Equations (6a) to (6e) define all the feasible zone linear velocities and the port movement velocities that guarantee separation in the five-zone SMB. These equations must be satisfied in order to have separation for systems with or without mass-transfer resistances.

The aforementioned five conditions can be re-expressed into mass flow rate ratios ([m.sub.j]), linear isotherm parameters ([K.sub.i]), and safety factor ([beta]) based on the safety margin method as follows:

[m.sub.1] = [beta] [K.sub.C] (7a)

[m.sub.2] = [beta] [K.sub.B] (7b)

[m.sub.3] = [beta] [K.sub.A] (7c)

[m.sub.4] = [K.sub.B] / [beta] (7d)

[m.sub.5] = [K.sub.A] / [beta] (7e)

where [m.sub.j] is the ratio of liquid flow rate to solid phase flow rate in zone j and it is related to the interstitial linear velocity and port movement velocity as follows (Storti et al., 1989):

[m.sub.j] = [u.sup.j.sub.0] - v/Pv = [u.sup.j.sub.0] [t.sub.s] - [L.sub.C]/P [L.sub.C] (8)

where [t.sub.s] and [L.sub.C] are the switching time and the single column length, respectively. The safety factor value ([beta]) in the above equation is usually chosen to be greater than unity in order to maintain desired product purities against mass-transfer resistances. Note that instead of different safety factors, the same safety factors were used in each zone for simplicity. Although this approach may have some possibility of losing the global optimum, it is able to show a series of intermediate changes in the operating parameters that finally lead to near-optimal solutions. The method of allocating the same safety margin to each zone has been satisfactorily employed in several previous studies for the design of SMB (Ching et al., 1985; Ruthven and Ching, 1989; Zhong and Guiochon, 1996; Wang and Ching, 2005).

Five-Zone SMB with One Column per Each Zone

Design Method

Table 4 lists the fixed parameter values in the design of the five-zone SMB with one column per each zone. One of the fixed parameter parameters is the column dimension, which was kept the same as that of the two-zone SMB in the previous section. To compare the two processes containing different number of zones under the same productivity, the feed flow rate of the five-zone SMB ([F.sup.feed.sub.5-zone]) was set to be higher than that of the two-zone SMB ([F.sup.feed.sub.2-zone]) as follows:

[F.sup.feed.sub.5-zone] = [F.sup.feed.sub.2-zone] x (5 columns/2 columns) x (0.5 [t.sub.s] loading/1 [t.sub.s] loading) = 0.625 mL/min (9)

where [F.sup.feed.sub.2-zone] was set at 0.5 mL/min in the previous section.

While the column dimension and the feed flow rate were fixed as above, the switching time of the five-zone SMB was calculated for a given [beta] value as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [V.sub.C] is the volume of a single column. The resulting switching time was then used to determine the five zone linear velocities from Equations (7) and (8). Repetition of these procedures based on the gradual increase of [beta] value leads to the five-zone SMB systems with more robustness against possible mass-transfer resistances.

However, the increase of [beta] value causes an increase in the zone flow rate. Since the zone flow rate is limited to 10 mL/min for the given column dimension in this study, the [beta] value has its maximum accordingly. Equations (7), (8), and (10) can be solved simultaneously for the maximum [beta] value, which results in

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where [F.sup.I.sub.max] is the maximum flow rate in zone I. Because the flow rate in zone I is the highest among the five zones, the value of [F.sup.I.sub.max] can be used to estimate [[beta].sub.max] from the above equation. Overall, a key issue in the design of the five-zone SMB will be the determination of an optimal value of [beta] resulting in the highest objective function value under the zone flow rate limit.

Design Results

The five-zone SMB with one column per each zone was designed by varying the magnitude of safety factor ([beta]). Detailed simulations were carried out for each designed five-zone SMB. The simulation results are presented in Figure 4, where the purities of the three product streams are plotted as a function of [beta] value. The range of x-axis in this figure is 1 [less than or equal to] [beta] [less than or equal to] [[beta].sub.max], where [[beta].sub.max] comes from the zone flow rate limit.

Figure 4 shows that the purity of A in the raffinate stream increases with increasing [beta] value. As expected from Equations (7a) and (7d), an increase in [beta] value decreases the zone IV flow rate and increases the zone I flow rate, which in turn affects the solute wave velocities of B and C as follows. The adsorption wave of B in zone IV migrates slower and thus becomes farther away from the raffinate port. The desorption wave of C in zone I migrates faster, which can enhance the efficiency of regenerating the column in zone I. These two factors help prevent a possible contamination of product A with B and C components, respectively, resulting in higher purity of A in the raffinate stream.

The purity of C in the extract-1 stream was also found to increase with increasing [beta] value (Figure 4). This trend is mostly due to the changes in the flow rates of zone II and zone V. As [beta] value increases, the zone II flow rate increases and the zone V flow rate decreases (Equations (7b) and (7e)). Such changes in the zone flow rates are favourable for the purity of C because the desorption wave of B in zone II and the adsorption wave of A in zone V become farther away from the extract-1 port.

[FIGURE 4 OMITTED]

In contrast to the purities of A and C, the purity of B in the extract-2 stream shows almost no change as [beta] value increases within the same range as above. To understand this result, the effects of increasing [beta] value on the migration behaviours of the two other solute waves (A and C waves) are examined from the standpoint of the purity of B in the extract-2 stream. As [beta] value increases, the desorption wave of A in zone III migrates faster and becomes farther away from the extract-2 port, which leads to the increase of the B purity in the extract-2 stream. In case of the adsorption wave of C, it also migrates faster in zones II and III while shifted upstream from the feed port by port switching. Such migration behaviour, however, makes the separation of B and C more unfavourable because the adsorption wave of C reaches the extract-2 port earlier and contaminates the extract-2 stream more significantly. In view of the results so far achieved, the migration behaviours of A and C solute waves seems to act on the purity of B in the opposite direction, resulting in no substantial change in the purity of B.

Five-Zone SMB with More Than Five Columns

Design Method

Until now we have considered only the case of one column per each zone in a five-zone SMB. In this section, one more column is added in some of the five zones in order to improve the separation performance of a five-zone SMB. The selection of the zones containing two columns among the five zones was carried out in accordance with the general principle that an increase in the number of columns per zone usually leads to a better separation performance in a standard four-zone SMB for binary separation. According to such principle, zones II to V in a five-zone SMB should have two columns because these four zones are responsible for the separation between A and B in the same manner as in a standard four-zone SMB for binary separation. Such column allocations, however, may be unfavourable for the separation between B and C. The reason is that the column containing component C needs one more switching period to be shifted toward zone II, thereby increasing the possibility of contaminating the product B stream with component C. Hence, the best column allocation strategy based on the aforementioned two considerations can be to assign two columns in zones II, IV, and V but one column in zone III. The five-zone SMB of study in this section is thus determined to have the column configuration of 1 - 2 - 1 - 2 - 2.

In the design of the above five-zone SMB, the column dimension was kept the same as in the previous sections (Table 4). On the other hand, the feed flow rate was further decreased to keep the productivity of the five-zone SMB equal to that of the two-zone SMB as follows (Table 4).

[F.sup.feed.sub.5-zone] = [F.sup.feed.sub.2-zone] x {8 columns/2 columns) x (0.5 [t.sub.s] loading/1 [t.sub.s] loading) = 1.0 mL/min (12)

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Under the feed flow rate determined from the above equation, the five-zone SMB with the configuration of 1 - 2 - 1 - 2 - 2 was designed using the same procedures as those in the design of the five-zone SMB with one column per each zone.

Design Results

The separation performance of the five-zone SMB, which was designed with the safety margin method under the column configuration of 1 - 2 - 1 - 2 - 2, was examined by increasing [beta] value from 1 to [[beta].sub.max]. The results are presented in Figure 5. It is easily seen that the purities of A and C increases with increasing [beta] value whereas the purity of B is little affected by a change in [beta] value. Such trends almost concur with those observed in the five-zone SMB with one column per each zone. The reason for such phenomenon has already been explained in the previous section by illustrating the wave migrations resulting from a change in [beta] value.

Comparing Figures 4 and 5, we can see that the purities of all the three product streams are improved by using the configuration of 1 - 2 - 1 - 2 - 2. This is due to the fact that the zone containing two columns can confine the solute wave better than the zone containing only one column. In other words, an SMB with more columns per zone becomes more robust against the spreading of a solute wave, which is usually caused by mass-transfer effects.

Comparison of Five-Zone SMB and Two-Zone SMB

In this section, all the processes studied so far are compared in terms of the purity index, the purity of B, and the yield of B under the same productivity and zone flow rate limit. Keep in mind that the five-zone SMB used in this section is what comes from [beta] = [[beta].sub.max] of the safety margin method. As shown in Figure 6, the five-zone SMB is superior to the two-zone SMB in all the aspects. In particular, the purity index of the five-zone SMB is much higher than that of the two-zone SMB.

Considering the separation goal of each process, the process for a centre-cut separation must be more favourable for the attainment of higher purity of B than the process for ternary separation. It is thus expected that the two-zone SMB for the centre-cut separation gives higher purity of B than the two-zone SMB for ternary separation as shown in Figure 6.

In case of the five-zone SMBs, they were both designed for ternary separation. Nevertheless, the five-zone SMBs lead to higher purity of B than the two-zone SMB for the centre-cut separation. This result indicates that the five-zone SMB can be effectively utilized for the centre-cut separation as well as for ternary separation.

Overall, the five-zone SMB turned out to produce much purer products than the two-zone SMB for the system of the ternary amino acid mixture. Of course, the use of more zones makes the process more complex, which may increase the operation and maintenance costs. However, the high purity attainable from the five-zone SMB more than compensates the cost associated with the use of additional zones.

CONCLUSIONS

The separation of a ternary mixture into three different pure fractions or the recovery of only an intermediate-affinity component in a ternary mixture usually requires a tandem SMB (two SMB units in series). Because the use of two SMB units leads to a highly expensive process, it is better to use a single SMB unit with some modifications in the number of zones or the locations of product ports. Such a modified single SMB unit has been hitherto represented by a five-zone SMB with three product ports or a two-zone SMB with two different operation steps in each switching period.

The separation performances of the five-zone SMB and the two-zone SMB were compared in this study for the separation of the ternary amino acid mixture comprising glycine, L-phenylalanine, and L-tryptophan at 50[degrees]C. Prior to the comparative study, the two-zone SMB was optimized using genetic algorithm, which is a robust optimization tool of searching the global optimum solution. On the other hand, the five-zone SMB was designed with the safety margin method by varying the magnitude of safety factor, demonstrating that an increase in the magnitude of safety factor leads to a better separation performance. Hence, the five-zone SMB based on the maximum safety factor value, which was determined by the zone flow rate constraint, was chosen for comparative study.

The results showed that the five-zone SMB designed by the safety margin method based on the maximum allowable safety factor led to much better separation performance than the two-zone SMB at its global optimum state. The average of the three product purities, namely, the purity index of the five-zone SMB is about 8% higher than that of the two-zone SMB for ternary separation, and about 19% higher than that of the two-zone SMB for the centre-cut separation. The purity of the intermediate-affinity component is also higher in the five-zone SMB than in the two-zone SMB for the centre-cut separation. Therefore, if a single SMB unit rather than a tandem SMB is to be employed for the separation of the ternary amino acid mixture with high purity, a five-zone SMB can be a better alternative than a two-zone SMB.

ACKNOWLEDGEMENT

This work was supported by the research fund of Hanyang University (HY-2006-S). The authors are also grateful to the ERC for Advanced Bioseparation Technology, KOSEF.

NOMENCLATURE

[a.sub.p] external surface area per particle volume,
 [cm.sup.2]/[cm.sup.3]
[C.sub.i] mobile phase concentration of species i,
 g/L
[E.sup.j.sub.b,i,] axial dispersion coefficient of component i
 in zone j, [cm.sup.2]/min
[F.sup.feed.sub.2-zone] feed flow rate of the two-zone SMB, mL/min
[F.sup.feed.sub.2-zone] feed flow rate of the five-zone SMB, mL/min
[F.sup.I.sub.max] maximum flow rate in zone I, mL/min
[k.sub.m] mass-transfer coefficient, cm/min
[K.sub.i] linear isotherm parameter, L/L S.V.
[L.sub.C] single column length, cm
[m.sub.j] ratio of liquid flow rate to solid phase
 flow rate in zone j
P phase ratio
S.V. solid volume, [cm.sub.3]
[t.sub.s] switching time, min
[u.sup.j.sub.i] migration velocity of component i in zone j,
 cm/min
[u.sup.j.sub.0] mobile phase interstitial velocity in zone
 j, cm/min
[epsilon] total void fraction
v port movement velocity, cm/min
[beta] safety factor
[[beta].sub.max] maximum allowable safety factor

Manuscript received December 16, 2006; revised manuscript received March 23, 2007; accepted for publication April 24, 2007.

REFERENCES

Beste, Y. A. and W. Arlt, "Side-Stream Simulated Moving-Bed Chromatography for Multicomponent Separation," Chem. Eng. Technol. 25, 956-962 (2002).

Broughton, D. B. and C. G. Gerhold, "Continuous Sorption Process Employing Fixed Bed of Sorbent and Moving Inlets and Outlets," U.S. Patent, 2,985,589 (1961).

Charton, F. and R. M. Nicoud, "Complete Design of a Simulated Moving Bed," J. Chromatogr. A 702, 97-112 (1995).

Ching, C. B. and D. M. Ruthven, "An Experimental Study of a Simulated Countercurrent Adsorption System: I. Isothermal Steady-State Operation," Chem. Eng. Sci., 40, 877-885 (1985).

Ching, C. B., D. M. Ruthven and K. Hidajat, "Experimental Study of a Simulated Moving Bed Counter-Current Adsorption System-III. Sorbex Operation," Chem. Eng. Sci. 40, 1411-1417 (1985).

Chu, K. H. and M. A. Hashim, "Simulated Countercurrent Adsorption Processes: A Comparison of Modeling Strategies," Chem. Eng. J. Bioch. Eng. 56, 59-65 (1995).

Chung, S. F. and C. Y. Wen, "Longitudinal Dispersion of Liquid Flowing through Fixed and Fluidized Beds," AIChE J. 14, 857-866 (1968).

Hashimoto, K., S. Adachi and Y. Shirai, "Continuous Desalting of Proteins with a Simulated Moving Bed Adsorber," Agr. Biol. Chem. 52, 2161-2167 (1998).

Hur, J. S., J. I. Kim, J. K. Kim, P. C. Wankat and Y. M. Koo, "Separation of L-Phenylalanine from a Ternary Amino Acid Mixture Using Two-Zone SMB/Chromatography Hybrid System," in "Theories and Applications of Chemical Engineering," Daegu, Korea, April 20-21, 2006, Korean Inst. Chem. Eng., Seoul (2006), pp. 300.

Hur, J. S. and P. C. Wankat, "New Design of Simulated Moving Bed for Ternary Separations," Ind. Eng. Chem. Res. 44, 1906-1913 (2005).

Hur, J. S. and P. C. Wankat, "Two Zone SMB/Chromatography for Center-Cut Separation from Ternary Mixtures: Linear Isotherm Systems," Ind. Eng. Chem. Res. 45, 1426-1433 (2006).

Juza, M., M. Mazzotti and M. Morbidelli, "Simulated Moving Bed Chromatography and Its Application to Chirotechnology," Trends Biotechnol. 18, 108-118 (2000).

Kasat, R. B. and S. K. Gupta, "Multi-Objective Optimization of an Industrial Fluidized-Bed Catalytic Cracking Unit (FCCU) Using Genetic Algorithm (GA) with the Jumping Genes Operator," Comput. Chem. Eng. 27, 1785-1800 (2003).

Kim, J. K., Y. Zang and P. C. Wankat, "Single-Cascade Simulated Moving Bed Systems for the Separation of Ternary Mixtures," Ind. Eng. Chem. Res. 42, 4849-4860 (2003).

Ma, Z. and N. H. L. Wang, "Standing Wave Analysis of SMB Chromatography: Linear Systems," AIChE J. 43, 2488-2508 (1997).

Rhee, H. K., R. Aris and N. R. Amundson, "Multicomponent Adsorption in Continuous Countercurrent Exchangers," Phil. Trans. Roy. Soc. London A. 269, 187-215 (1971).

Ruthven, D. M., "The Axial Dispersed Plug Flow Model for Continuous Countercurrent Adsorbers," Can. J. Chem. Eng., 61, 881-883 (1983).

Ruthven, D. M. and C. B. Ching, "Counter-Current and Simulated Counter-Current Adsorption Separation Processes," Chem. Eng. Sci., 44, 1011-1038 (1989).

Schulte, M and J. Strube, "Preparative Enantioseparation by Simulated Moving Bed Chromatography," J. Chromatogr. A 906, 399-416 (2001).

Storti, G., M. Mazzotti, M. Morbidelli and S. Carra, "Robust Design of Binary Countercurrent Adsorption Separation Processes," AIChE J. 39, 471-492 (1993).

Storti, G., M. Mazzotti, S. Carra and M. Morbidelli, "Optimal Design of Multicomponent Counter-Current Adsorption Separation Processes Involving Nonlinear Equilibria," Chem. Eng. Sci. 44, 1329-1345 (1989).

Wang, X. and C. B. Ching, "Chiral Separation of ?-blocker Drug (Nadolol) by Five-Zone Simulated Moving Bed Chromatography," Chem. Eng. Sci. 60, 1337-1347 (2005).

Wankat, P. C., "Rate-Controlled Separations," Kluwer, Amsterdam, The Netherlands (1990), pp. 268-272.

Yun, T., G. Zhong and G. Guiochon, "Experimental Study of the Influence of the Flow Rates in SMB Chromatography," AIChE J. 43, 2970-2983 (1997).

Zang, Y. F. and P. C. Wankat, "Variable Flow Rate Operation for Simulated Moving Bed Separation Systems: Simulation and Optimization," Ind. Eng. Chem. Res. 42, 4840-4848 (2003).

Zhang, Z. Y., K. Hidajat, A. K. Ray and M. Morbidelli, "Multiobjective Optimization of SMB and Varicol Process for Chiral Separation," AIChE J. 48, 2800-2816 (2002).

Zhong, G. M. and G. Guiochon, "Analytical Solution for the Linear Ideal Model of Simulated Moving Bed Chromatography," Chem. Eng. Sci. 51, 4307-4319 (1996).

Zhong, G., M. S. Smith and G. Guiochon, "Effect of the Flow Rates in Linear, Ideal Simulated Moving-Bed Chromatography," AIChE J. 43, 2960-2969 (1997).

Se-Hee Jo (1), Jeung Kun Kim (2), Chang Geun Yoo (1), Jin-Il Kim (3), Yoon-Mo Koo (2,3) and Sunyong Mun (1) *

(1.) Department of Chemical Engineering, Hanyang University, Seoul, 133-791, Korea

(2.) Center for Advanced Bioseparation Technology, Inha University, Incheon, 402-751, Korea

(3.) Department of Biological Engineering, Inha University, Incheon, 402-751, Korea

* Author to whom correspondence may be addressed. E-mail address: [email protected]

Table 1. Isotherm parameters and intrinsic parameters of the three
amino acid components at 50[degrees]C

 L-phenylalanine L-tryptophan
 Glycine (a) (b) (C)

Linear isotherm
 parameter
 (L/L S.V.) 0.12 1.13 5.96
Mass transfer
 coefficient,
 [k.sub.m][a.sub.p]
 (1/min) 1000 2.76 4.20
Axial dispersion
 coefficient
 ([cm.sup.2]/min) Chung and Wen (1968) correlation
Total void fraction 0.70
Particle radius
 ([micro]m) 211.25
Mobile phase density
 (g/[cm.sup.3]) 0.988
Mobile phase
 viscosity (cP) 0.547

Table 2. GA parameters used in the optimization

Parameter Value

Population size 50
Number of generations 40
Length of chromosome 40 bits
Crossover probability 0.9
Mutation probability 1/(length of chromosome)

Table 3. Comparison of the optimization results for the two-zone SMB-t
and the two-zone SMB-c

The highest value achievable Purity index (PI) (%)
 Purity of B (%)

Values of decision Feed (mL/min) **
variables at optimal state Desorbent-1 (mL/min)
 Desorbent-2 (mL/min)
 Desorbent-3 (mL/min)
 Switching time (min)

 Two-zone Smb-t Two-zone Smb-c *

The highest value achievable 85.7 75.0
 82.6 88.6

Values of decision 0.5 0.5
variables at optimal state 1.26 1.30
 0.85 0.57
 2.39 1.25
 20.14 23.50

* The results for the two-zone SMB-c were taken from the literature
(Hur et al., 2006)

** The feed flow rate was fixed at 0.5 mL/min during the optimization
of each process

Table 4. Fixed parameters in the five-zone SMB and the two-zone SMB
under examination

 five zone Smb

Column configuration * 1 - 1 - 1 - 1 - 1 1 - 2 - 1 - 2 - 2
Single column length (cm) 30 30
Column diameter (cm) 1.1 1.1
Feed flow rate (mL/min) 0.625 1.0
Productivity (mL/mL-min) 4.384 x [10.sup.-3]
Maximum allowable flow
 rate in each zone (mL/min) 10 10

 Two-zone Smb

Column configuration * 1 - 1
Single column length (cm) 30
Column diameter (cm) 1.1
Feed flow rate (mL/min) 0.5
Productivity (mL/mL-min)
Maximum allowable flow
 rate in each zone (mL/min) 10

* The number of columns allocated to each zone of a given SMB process