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Ind. Eng. Chem. Res. 2005, 44, 3268-3283
Strategies to Control Batch Integrity in Size-Exclusion Simulated Moving Bed Chromatography Sungyong Mun,† Yi Xie,‡,§ and Nien-Hwa Linda Wang*,‡ Department of Chemical Engineering, Hanyang University, Seoul 133-791, Korea, and School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
In pharmaceutical production, it is important to link each batch of product to its source materials and track each batch throughout the production process. Tracking and controlling each batch is more challenging in a simulated moving bed (SMB) process than in conventional batch chromatography. Solutes coming from a certain feed batch in an SMB can be mixed with solutes coming from adjacent feed batches. The mixing is due to the location of the product ports relative to the feed port, periodic port movement, internal recycle, and dispersion due to mass transfer resistances. The degree of mixing, or the size of the overlap region of the different batches in the product stream, largely depends on solute residence time. Decreasing the zone lengths, using partial feeding, or applying pinched wave operating conditions can effectively reduce residence time and therefore decrease the overlap region. To eliminate the overlap region completely (or achieve complete control of batch integrity), an eluent gap can be applied between two adjacent feed batch injections. The strategies for reducing residence time can minimize the eluent gap, thereby reducing eluent consumption and increasing productivity. One can further reduce the amount of eluent by closing the feed port during the gap period and opening the feed port only during the feed loading period. 1. Introduction Conventional batch chromatography is a highly selective separation technique. It has been widely used for producing high-purity pharmaceuticals. This technique, however, has a major limitation for difficult separations (selectivity < 2). To achieve high product purity and high yield, the product band must be completely separated from adjacent impurity bands. Mass transfer spreading causes solute bands to overlap, making complete separation difficult. A trade-off between purity and yield is usually needed. Simulated moving beds (SMBs) can achieve high product purity without sacrificing yield by using a continuous countercurrent process. Multiple adsorbent columns are connected to allow a circular flow path. The circle is divided into four zones of constant flow rates by four ports, one each for the feed, the desorbent, the fast-migrating product, and the slow-migrating product (Figure 1). 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” countercurrent movement of the adsorbent phase relative to the fluid phase. The average port movement velocity and the zone flow rates are designed to allow feed to be added in the mixed region (where the two bands overlap) and allow two pure products to be drawn from the pure component regions (where the two bands do not overlap). High throughput and low solvent consumption can be achieved because the two migrating bands partially overlap, thus increasing loading per unit column volume and reducing product dilution. Such processes can achieve both high yield and high product purity and use the adsorbent and * To whom correspondence should be addressed. Tel.: (765) 494-4081. Fax: (765) 494-0805. E-mail:
[email protected]. † Hanyang University. ‡ Purdue University. § Current address: Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN 46285.
Figure 1. Comparison of the port locations between batch chromatography and an SMB.
the solvent more efficiently than conventional batch chromatography. Conventional SMB systems have been developed for the separation of binary mixtures of low molecular weight compounds (MW < 1 000). They have been used successfully for the production of hydrocarbons since the 1970s,1,2 high-fructose corn syrup since the 1980s,3-5 and chiral pharmaceuticals since the late 1990s.6-9 However, SMB has rarely been attempted for protein separations at the laboratory scale and has never been used for protein production. The major barriers for the application of SMB for protein purification have been the following (Figure 2): (1) Splitting Strategies for a Multicomponent Mixture. The design method for multicomponent separation in an SMB had not been developed for systems with significant mass transfer effects (or so-called “nonideal systems”). Almost all protein feedstocks are complex multicomponent mixtures, and their purification involves low-pressure chromatography systems, which have significant mass transfer resistances (or nonideality). The design methods for multicomponent
10.1021/ie049685s CCC: $30.25 © 2005 American Chemical Society Published on Web 03/24/2005
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Figure 2. Key issues and barriers in the development of an SMB for insulin purification.
separation in the literature have been focused on systems without significant mass transfer effects (or ideal systems). Such methods are applicable to highpressure systems (>2000 psi), but they cannot guarantee high yield and purity in low-pressure systems. (2) Protein Aggregation and Denaturation. During a long chromatography process, proteins can aggregate or denature. Methods for estimating and reducing the residence times of proteins in an SMB are needed to control residence time. (3) Periodic Regeneration. The slow decrease of column capacity due to fouling or gelation in protein purification requires periodic column regeneration using a harsh chemical solution. An effective cleaning schedule is needed to maintain column capacity and product quality. (4) Batch Integrity. In pharmaceutical purification, each feed mixture comes from a specific, documented batch of fermentation broth. All purified products should be linked to their source materials in case a certain batch is defective or contaminated. This requirement is easily attained in conventional batch chromatography, which has only one product port located at a fixed position. Moreover, there is no recycle stream and all the solutes experience the same flow rate. However, in a four-zone SMB, the raffinate product port is located downstream from the feed port, whereas the extract product port is located upstream from the feed port. The ports also move periodically along the eluent flow direction (Figure 1). The four zones have different flow rates, and solutes are continuously migrating within the circular path. These properties plus dispersion cause some solutes from a certain feed batch in the SMB to be mixed with solutes from adjacent feed batches if all the batches are fed consecutively. As a result, a certain portion of the product stream may come from multiple batch sources. In addition, undesirable components in a feed batch can contaminate the product from an adjacent feed batch. Therefore, it is important to follow the different batches throughout the SMB process. Strategies to identify and control each batch in the SMB are needed in order to decrease the amount of loss if a certain feed batch is defective or contaminated. Our previous studies have addressed the first three barriers for the use of size-exclusion SMB chromatography for insulin purification.10-14 Insulin is a solute with intermediate migration velocity in size-exclusion chromatography. The insulin crude contains two other groups of impurities, pro-insulin and high molecular weight proteins (fast-moving impurities) and zinc chloride (a slow-moving impurity). Two splitting steps involving two SMBs in series (or a tandem SMB) can be used to recover insulin (Figure 3). Pro-insulin (HPI)
Figure 3. Schematic of a tandem SMB process for insulin purification.
and other high molecular weight proteins (HMWP) are removed from the raffinate port in the first SMB (ring I). The effluent from the extract port of ring I is collected and loaded into the second SMB (ring II). An efficient splitting strategy for multicomponent separation based on the concept of standing concentration waves was developed and tested experimentally.10,11 A systematic model-based design approach was used to develop the SMB with a minimal number of experiments. Both theoretical results and experimental results showed that an SMB can be used to improve recovery of insulin from a multicomponent mixture. An efficient optimization method was developed based on the standing wave analysis to find the optimal tandem SMB for insulin purification.12 Both system parameters (column length, particle size, zone configuration, and the total number of columns) and operating parameters (feed flow rate, zone flow rates, and port velocity) were optimized to achieve the lowest purification cost. In a production environment, system parameters (stationary phase properties, column packing density, and column length) and operating parameters (pump flow rates and step time) can deviate from target values. We have extended the standing wave design method to account for these variations while still ensuring high purity and high yield.15 In the size-exclusion chromatographic (SEC) process for insulin purification, the regeneration step is needed to prevent fouling and gelation. We incorporated this regeneration step into our tandem SMB and tested it experimentally. The results show that the performance of the SMB is stable within the five day testing period.14 The results to date showed that the product purity and yield of the tandem process can be quite high (99%). The throughput per bed volume can be increased 5-fold, and the eluent consumption can be reduced by 2/3 compared to the case of batch chromatography.11 The focus of this study is the fourth barrier, the issues of batch integrity. In a standard procedure, all the
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batches are fed consecutively. If the solutes from an earlier batch stay longer in the SMB, the degree of overlap with the solutes from a later batch will be greater. Therefore, solute residence time should be shortened to reduce the degree of overlap. Furthermore, long residence time of a protein can result in aggregation or denaturation. For these two reasons, the understanding of solute residence time distribution in the SMB is important for controlling both solute residence time and batch integrity. There has been a previous study on the residence time distribution of a solute in an SMB.13 The results showed that residence time in the SMB is related to the injection time, zone flow rates, zone lengths, selectivity, and dispersion due to mass transfer. For a fast-moving solute that is recovered in the raffinate, since the raffinate port is located downstream from the feed port, the molecules that are injected earlier during the injection period have a shorter residence time than those injected later during the injection period (first in and first out). For a slow-moving solute, since the extract port is located upstream from the feed port, the trend is reversed (first in and last out). For this reason, a partial feeding strategy (i.e. injection feed during only a fraction of the step time)13,17 can effectively reduce the average solute residence time. To shorten the residence time of a fast-moving solute, one can feed during the first half of the switching period, shorten the length of zone III, or increase zone II flow rate beyond the requirement of standing wave design (or so-called “pinched wave design”).13,16 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 zone II, or decrease zone III flow rate. High selectivity and small dispersion effects also result in short residence time. However, the previous study did not address the control of batch integrity in an SMB. The first goal of this study is to understand how the adjacent feed batches are mixed as a result of recycle, periodic port movement, and mass transfer effects in the SMB. The second goal is to find strategies to control batch integrity. First, the effects of residence time of the product solute on the mixing of products from adjacent batches in the product stream are studied. A general method of tracking a feed batch throughout the SMB process for a linear isotherm system (including size exclusion) is developed for this purpose. On the basis of the analysis, strategies to control batch integrity are formulated. Furthermore, strategies to shorten residence time and maintain complete batch integrity are proposed. The results of this study show that solute residence time determines the degree of mixing (or overlap) of two adjacent batches in the product stream. This overlap has more serious impact on batch integrity for a smaller batch. Strategies to reduce residence time are effective in reducing the overlap between two adjacent batches. Short zone length, partial feeding, and pinched wave operating conditions can reduce solute residence time and, thus, the degree of overlap. To completely remove the overlap region, eluent can be injected into the feed port (to replace the feed) to create a gap between the two adjacent batches and maintain complete batch integrity in the product stream. The strategies to reduce residence time can minimize the amount of eluent needed during the gap period. One can further reduce
Figure 4. (a) Definitions of breakthrough time (tb) and extinction time (te) in the effluent history resulting from the injection of one feed batch. (b) Representation of ∆S in the effluent history. Concentrations in the effluent history are averaged over one switching period.
the amount of eluent if there is no eluent flowing into the feed port during the gap period. 2. Theory This study is based on the following assumptions: (1) All the feed batches have the same volume and concentration. (2) The volume of one feed batch is sufficiently large to reach a cyclic steady state in the effluent history. (3) The system of investigation is either a sizeexclusion system or a linear isotherm system. Several terms are introduced to facilitate the analysis. First, the amount of time needed for completing the injection of each feed batch is defined as ∆feed. If tin is the starting time of the nth feed batch injection and there is no gap between each feed batch, ∆feed can be expressed as follows:
∆feed ) tin+1 - tin (n ) 1, 2, 3, ...)
(1)
where ∆feed has the unit of time and indicates the size of the feed batch at a given feed flow rate. Unless noted otherwise, the feed batch injections are continuous. The breakthrough time and the extinction time of the nth batch in a product stream are denoted as tnb and tne , respectively. As shown in Figure 4a, the breakthrough time is defined as the time when a product concentration in the advancing wave reaches a threshold concentration. Similarly, the extinction time is defined as the time when a product concentration in the trailing wave reaches a threshold concentration. Unless noted otherwise, the threshold concentration is 1% of the plateau (or steady state) concentration as shown in Figure 4a. ∆feed is also the length of time between the mass centers of the advancing wave and the trailing wave in the effluent history (Figure 4b). The time to collect a batch of product from a given batch of feed (te - tb) is greater than ∆feed (Figure 4b). The additional time required for complete collection of a batch of product is defined here as the batch spreading time, ∆S.
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∆S ≡ (te - tb) - ∆feed
(2)
∆S is related to the spreading of the two boundaries of a batch in a SMB process. The spreading results from the various dispersion mechanisms, which were explained in detail in a previous study using differential tracer pulse analysis.13 ∆S is related to the residence time and residence time distribution of the solute, as explained below. 2.1. Effect of Residence Time on Batch Spreading Time and Batch Integrity. In an ideal system (with no mass transfer resistances), as a series of feed batches are consecutively introduced into an SMB (Figure 5a), the resulting effluent history of a product component is shown in Figure 5b. Although mass transfer effects are negligible in an ideal system, the product batch corresponding to each batch of feed is spread, resulting in an overlap of two adjacent batches (Figure 5b). The spreading is due to the location of the product port relative to the feed port, periodic port movement, and internal recycle (Figure 1).13,18 The spreading of a feed batch in a nonideal system (with significant mass transfer resistances) is broader than that in an ideal system, because the spreading due to port movement/recycle is further enhanced by axial dispersion, film mass transfer, and intraparticle diffusion. As a result, the amount of time needed for collecting all the solutes from the batch is larger in a nonideal system than in an ideal system (Figure 5b). The increase in the overlapping region in the effluent history has undesirable effects on batch integrity. To further explain the meaning of ∆S, we compare Figure 5a with Figure 5b. The comparison reveals that a decrease in ∆feed may cause an overlap between solutes coming from the first batch and solutes coming from the third batch (or solutes coming from the nth batch and solutes coming from the (n + 2)th batch). This indicates the existence of a minimum ∆feed to prevent the overlap of the nth batch and the (n + 2)th batch (Figure 6). The minimum ∆feed is denoted here as ∆min feed. One can easily S. is equal to ∆ prove that ∆min feed
Figure 5. Batch integrity in the first ring of a tandem SMB for insulin purification. (a) Injections of a series of feed batches with a size of 50ts. (b) Effluent history of insulin at the extract port. Concentrations in the effluent history are averaged over one switching period.
S ∆min feed ) ∆ ≡ (te - tb) - ∆feed
(3)
∆S or ∆min feed is independent of the feed batch size as long as the feed batch size is larger than ∆S. It is fixed for a given set of zone lengths and operating conditions. As shown in Figures 5 and 6, although the feed sizes are different, the ∆S values are the same. ∆S is proportional to the solute residence time, t0.99, as shown in Figure 7 and explained later in section 2.5. ∆S also allows tracking of a given feed batch throughout the SMB process. If ∆S is known and the beginning of the feed loading time and ∆feed are specified, one can easily calculate the time period to collect the product from this given feed batch. 2.2. Batch Integrity in an SMB. To maintain batch integrity in an SMB, the product stream coming from a certain batch should be collected separately from the product streams coming from the adjacent two batches. The fraction of product in the overlapping region (FO) can be derived in terms of ∆feed and ∆S as follows:
FO ≡ amount of product in the overlapping region ) amount of product in one batch ∆S (4) ∆feed On the basis of eq 4, we define the batch integrity index (BII) as follows:
BII ≡ 1 - FO ) 1 -
∆S ∆feed
(5)
To improve batch integrity in an SMB, one can decrease ∆S or increase ∆feed. Since a shorter residence time leads to a smaller ∆S, strategies to reduce residence time in an SMB13 are also effective in improving batch integrity (or decreasing FO and increasing BII). To achieve complete batch integrity (or BII ) 1) in an SMB, one can input eluent between two adjacent batches (Figure 8). However, this method causes a significant decrease in productivity and an increase in
Figure 6. Effluent history of insulin from the injections of a series of batches with a size of ∆S in ring I. (a) Injections of a series of feed batches. (b) Effluent history of insulin at the extract port. Concentrations in the effluent history are averaged over one switching period.
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Figure 7. Correlation between t0.99 and ∆S in the second ring of a tandem SMB for insulin purification. t0.99 is the time at which 99% of the insulin has left the SMB when the feed is injected during one switching period. The y-axis is normalized by the switching time (ts ) 36.2 min).
min is constant If the operating conditions are fixed, ∆gap and independent of feed batch size. By replacing ∆gap with ∆S in eqs 6 and 7, one can obtain the highest productivity and the lowest solvent consumption under the condition of complete batch integrity. Furthermore, strategies to shorten residence time in an SMB can be min applied to reduce ∆S and ∆gap as discussed below. 2.3. Effect of Partial Feeding on Batch Integrity. Because of port location, periodic port movement, and recycle, the residence time of a solute in an SMB is a strong function of injection time within one switching period.13 To reduce ∆S, one can inject feed only during a fraction (h) of the switching period in order to shorten the residence time of the solute of interest. During the rest of the period, eluent is injected into the feed port. Such alternating injections, defined as a partial feeding strategy, are repeated every switching time. The partial feeding increases the amount of time required to complete the injection of one feed batch as follows:
∆PF feed ) (tin+1 - tin)PF )
(tin+1 - tin) h
)
∆feed h
(10)
where PF stands for a partial feeding strategy. Equations 4 and 10 are used to express the FO based on the partial feeding strategy.
FOPF )
Figure 8. Application of a minimal eluent gap between batch injections for complete batch integrity in ring I. (a) Injections of a series of feed batches. (b) Effluent history of insulin at the extract port. Concentrations in the effluent history are averaged over one switching period.
solvent consumption as follows:
prodG ∆feed ) prod ∆feed + ∆gap SCG ∆feed + ∆gap ) SC ∆feed
(6)
(7)
where prod and SC stand for productivity and solvent consumption, respectively, and the subscript G stands for the placement of an eluent gap between batch injections. ∆gap is the size of the gap in time units. To achieve complete batch integrity between the nth batch and the (n+1)th batch, tnb should be less than tn+1 b , resulting in the following condition:
∆gap g ∆S
(8)
To minimize loss in productivity and solvent consumpmin ). It is tion, one should apply the minimal gap (∆gap obvious that the minimal gap for complete batch integrity is ∆S. S ∆min gap ) ∆
(9)
( )
∆S,PF ∆S,PF )h FO PF ∆feed ∆S
(11)
where ∆S,PF ) (t1e - t1b)PF - ∆PF feed. Since h is less than unity and ∆S,PF is smaller than ∆S, the partial feeding strategy always has a lower FO, or less product in the overlapping region. As shown in the previous study, a lower h leads to a shorter residence time,13 which in turn reduces ∆S,PF and FOPF. However, a lower h results in a lower productivity and a higher solvent consumption as follows:
prodPF )h prod
(12)
SCPF 1 ) SC h
(13)
The derivations of eqs 12 and 13 are in Appendix A. The partial feeding strategy can be employed together with an eluent gap between two adjacent batches to achieve complete batch integrity. As in the previous section, we obtain the minimal gap for the partial feeding strategy as follows:
) ∆S,PF ∆PF,min gap
(14)
Since ∆S,PF is smaller than ∆S, the partial feeding strategy requires a smaller gap to achieve complete batch integrity. The smaller gap results in an increase in productivity. However, the partial feeding itself increases the time needed to process each batch (eq 10), resulting in a decrease in productivity (eq 12). The two opposing trends lead to an optimal h for productivity as explained below. The following two equations show the resulting changes in the productivity and solvent consumption when the partial feeding with a minimal eluent gap between two batches (PF-G) is used to achieve complete batch integrity.
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prodPF-G ) prod ∆
h∆feed
feed
+ h∆
S,PF
SCPF-G 1 ∆S,PF ) + SC h ∆feed
(15)
substantially reduced by decreasing f. However, a lower f decreases productivity and increases solvent consumption as follows:
(16)
prodPW )f prod
The derivations of eqs 15 and 16 are given in Appendix A. Since ∆S,PF decreases as h decreases, eqs 15 and 16 do not change proportionally with respect to h. This indicates the importance of determining the optimal h for the highest productivity or the lowest solvent consumption under the condition of complete batch integrity (FO ) 0). 2.4. Relationship Between ∆S and Residence Time. As an example, the relationship between ∆S and residence time (t0.99) is investigated for the second ring in a tandem SMB for insulin purification.11 The relationship between the two is presented in Figure 7, in which a partial feeding method with a different throughput is applied to vary the residence time of insulin.13 One can see that ∆S or ∆min feed is proportional to the residence time. 2.5. Effect of Pinched Wave Design on Batch Integrity. In the standing wave design (SWD),10,17 the flow rates in the four zones are chosen so that the four waves are standing in the appropriate zones in a timeaveraged sense. In this case, the velocities of a fastmoving solute in zone II and a slow-moving solute in zone III relative to the port velocity are minimized to achieve the maximum throughput. However, this leads to a significant increase in solute residence time. To shorten residence time, a pinched wave design (PWD) can be used. The flow rate in zone II, for example, can be increased above the value required for the standing wave condition. The concentration wave in zone II is no longer “standing” but “stuck” or “pinched” between zone II and zone III. This strategy can shorten the residence time of the fast-moving component in the SMB.13 Similarly, the zone III flow rate can be decreased such that the advancing wave of the slow-moving solute is pinched between zone II and zone III. This strategy can shorten the residence time of the slow-moving solute.13 Both strategies result in a decrease in the feed flow rate as follows:
Ffeed,PW ) fFfeed
(17)
where PW stands for a pinched wave design and f is the ratio of the feed flow rate in the PWD (Ffeed,PW) to the feed flow rate in the SWD (Ffeed). The decrease in the feed flow rate increases the time required to complete the injection of one batch (or batch size in time units) as follows:
∆PW feed )
∆feed f
(18)
The shortened residence time and the increased batch size in time units are both effective in improving batch integrity as shown in the following:
( )
∆S,PW ∆S,PW FO FOPW ) PW ) f ∆feed ∆S
(19)
where ∆S,PW ) (t1e - t1b)PW - ∆PW feed. As shown in eq 19, the amount of product in the overlapping region can be
(
(20)
)
SCPW 1 Feluent + fFfeed ) SC f Feluent + Ffeed
(21)
where Feluent is the eluent flow rate into the eluent port. See Appendix A for details on the derivations of eqs 20 and 21. Complete batch integrity (FOPW ) 0) cannot be achieved using only a PWD method. An eluent gap is needed between batch injections to achieve complete batch integrity. One can find that the minimal gap PW,min needed in the PWD method, ∆gap , is equal to ∆S,PW. S,PW Since ∆ decreases as f decreases, a lower f results PW,min , which has a desirable effect on in a smaller ∆gap productivity and solvent consumption. However, a lower f decreases the feed flow rate, resulting in a lower productivity and a higher solvent consumption. Therefore, there exists an optimal f for either the highest productivity or the lowest solvent consumption while maintaining complete batch integrity. For a PWD with a minimal eluent gap between two adjacent batches (PW-G), the productivity and solvent consumption are given by
prodPW-G ) prod ∆
f∆feed
feed
(
)(
(22)
+ f∆S,PW
)
SCPW-G 1 ∆S,PW Feluent + fFfeed ) + SC f ∆feed Feluent + Ffeed
(23)
The derivations of eqs 22 and 23 are presented in Appendix A. Compared to the calculation for SCPF-G (eq 16), that for SCPW-G (eq 23) has an additional term, which is always less than unity. This is due to the difference in the feed flow rate between the two methods. The feed flow rate of the PWD is decreased, whereas the feed flow rate of the partial feeding strategy remains unchanged. Therefore, if the difference between f and h is small, the PWD method has less solvent consumption than the partial feeding strategy. 2.6. Effect of Maximum Allowable Residence Time on Batch Integrity. There is a general concern that a protein spending a long time in the stationary phase can undergo aggregation or denaturation. Therefore, the residence time of a protein in an SMB should be maintained below a certain limit, which is defined here as a maximum allowable residence time (RTlimit). Since residence time decreases with decreasing h, in a partial feeding, or f, in a PWD, one can determine the h or f value corresponding to RTlimit as follows:
h e hlimit, f e flimit so that RT e RTlimit
(24)
As shown in eq 24, the residence time requirement reduces the region of h or f that can be used to control batch integrity. However, this has no adverse effect on batch integrity. First, if there is no eluent gap between batch injections, the amount of product in the overlapping region decreases continuously with decreasing h or f, as expected from eqs 11 and 19. Second, if there is
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Table 1. Intrinsic Parameter Values Used in the Standing Wave Design HPI Ke D∞ (cm2/min) Dp (cm2/min) kf (cm/min) Eba (cm2/min) column properties
insulin
ZnCl2
0.19 0.74 0.99 5.49 × 10-5 3.96 × 10-4 4.80 × 10-5 2.29 × 10-5 1.65 × 10-4 2.00 × 10-5 Wilson and Geankoplis correlation23 Chung and Wen correlation24 b ) 0.35, p ) 0.89
a The E value of insulin in zone III of ring I is chosen to be 40 b times as large as that estimated from the Chung and Wen correlation.24
Table 2. Operating Conditions of a Tandem SMB Used in the Analysis of Batch Integrity ring I zone
configurationa
zone linear velocitiesb (cm/min) inlet and outlet linear velocitiesb (cm/min)
zone I zone II zone III zone IV feed eluent raffinate extract
switching time (min)
ring II
2-2-4-2
2-3-3-2
2-2-2-2
1.1265 0.6608 0.9932 0.6507 0.3324 0.4758 0.3425 0.4657 30.06
1.0972 0.9299 1.0890 0.9080 0.1591 0.1892 0.1810 0.1673 36.20
1.1429 0.9734 1.1325 0.9455 0.1591 0.1974 0.1870 0.1695 34.76
a Single column length ) 15 cm. b u ) F/( S), where F and S 0 b are the flow rate and the column cross-sectional area, respectively.
an eluent gap, complete batch integrity can always be achieved by adjusting the size of the eluent gap to any value of h or f, as expected from eq 14. 3. Simulation and Parameters min In each case, ∆S is needed for calculating FO or ∆gap . Only one effluent history from a batch with an arbitrary size is required for estimating ∆S. The effluent history was generated from rate model simulations. The simulations were carried out using VERSE, which has been validated in several previous studies.11,19-22 An SMB for insulin purification11 was chosen as an example for this study. The operating conditions of the SMB were determined from the standing wave design,10,17 unless noted otherwise. The intrinsic parameters used in the standing wave design and the simulations were reported by Xie et al.,11 and they are listed in Table 1. Note that, in the standing 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.24 The large Eb was used to overcome the dispersion of insulin due to nonideal flow or other effects in zone III of ring I.11 The resulting zone linear velocities and switching times (ts) for ring I and ring II are listed in Table 2, and they were used in the batch integrity analysis. For ring II, two sets of operating conditions were determined for two different zone configurations. Unless noted otherwise, ring II had the operating conditions based on the zone configuration 2-3-3-2. The volume of each feed batch injected into ring I was fixed, and the loading time was 1503 min (or 50ts). The batch size in time units (∆feed) for ring II was determined based on the amount of output from ring I.
any eluent gap and the operating conditions are based on the standing wave design and full feeding. The strategies that can reduce residence time13 are then applied to control batch integrity. Furthermore, the methods to achieve complete batch integrity with the highest productivity or the lowest solvent consumption are developed. In all the methods, the threshold concentration is set to be 1%. The effect of the threshold is also discussed. 4.1. Batch Integrity in Ring I. Insulin is recovered from the extract port in ring I. First, VERSE simulations are used to generate the effluent history of insulin for a series of batches with a size of 50ts which are introduced consecutively into the SMB. For this batch size, no overlap is observed between insulin coming from the nth batch and insulin coming from the (n + 2)th batch (Figure 5). However, if a smaller batch size is used, overlap between the two can occur. The value of ∆S for ring I determined from the effluent history (Figure 5) is about 25ts. Effluent history resulting from a series of batches of 25ts is shown in Figure 6. The nth batch and the (n + 2)th batch are barely separated within the tolerance. Therefore, a batch size larger than 25ts should be used in ring I in order to ensure
