Enhanced Separation Performance of a Five-Zone Simulated Moving

9258

Ind. Eng. Chem. Res. 2010, 49, 9258–9270

Enhanced Separation Performance of a Five-Zone Simulated Moving Bed Process by Using Partial Collection Strategy Based on Alternate Opening and Closing of a Product Port Sungyong Mun* Department of Chemical Engineering, Hanyang UniVersity, Seoul 133-791, Korea

A five-zone simulated moving bed (SMB) process for ternary separation has been developed previously and applied to the purification of biochemicals in the literature. Although this process was effective to some degree in many of previous research studies, its separation performance was always limited by the presence of overlap between the highest-affinity and the intermediate-affinity solutes. Since a proper control of the overlap was almost impossible under the current configuration and operation method, the application scope of a conventional five-zone SMB was restricted within the separation tasks that permitted either relatively medium purities or low throughput. To overcome such a limitation, an efficient operation strategy for improving the five-zone SMB performance was proposed in this study. The core of the proposed strategy is to partially collect the product stream by alternate opening and closing of the extract-2 port, which is in charge of recovering the intermediate-affinity solute molecules. Simultaneously, the zone II flow rate during the port-opening state is adjusted properly for complete desorption of the intermediate-affinity solute in zone II. The application of such a strategy was found to improve the five-zone SMB performance dramatically. One of the noteworthy improvements was that all three products could be recovered with extremely high purities at the same time. Furthermore, a marked increase in the throughput could also be obtained under the given purity requirements. Therefore, the strategy proposed in this study is expected to substantially upgrade the five-zone SMB performance, allowing its application to the separation tasks that demand either high purities or high throughput. 1. Introduction Simulated moving bed (SMB) is one of the most attractive processes for a large-scale separation of bioproduct with high purity and high throughput.1 The first commercial SMB was introduced in 1961 for the separation of paraffins from branchedchain and cyclic hydrocarbons.2 Its application scope was then extended to the separation of high fructose corn syrup (HFCS), chiral drugs, and biochemical products.1,3,4 Most of such SMB applications have been focused on a binary separation. For a ternary separation that is often demanded in bioproduct purification processes, two SMB units should be connected in series and operated simultaneously.4-7 However, the use of two SMB units in series leads to much higher operation and maintenance costs, compared to the use of a single SMB unit.5-7 Certainly, the application of a single SMB unit is more economical if it can be effective in separating a ternary mixture with desired purities. Until now, intensive efforts have been made to develop a single SMB unit that can perform a ternary separation. The examples of such developments included the JO SMB process,8 a two-zone SMB,9 a five-zone SMB,5-7,10,11 an eight-zone SMB,12 a nine-zone SMB,13 a three-fraction SMB (3F-SMB),14 and a pseudo-SMB process.15 Recently, a multicolumn countercurrent solvent gradient purification (MCSGP) process16 has been developed for ternary separation, and it has been successfully applied to valuable separation tasks. Among the aforementioned single-cascade SMB processes for ternary separation, a five-zone SMB was chosen as the * Correspondence concerning this article should be addressed to Prof. Sungyong Mun, Department of Chemical Engineering, Hanyang University, Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea. E-mail: [email protected]. Tel.: +82-2-2220-0483. Fax: +82-2-2298-4101.

subject of further investigation in this study. This process was devised to handle a ternary separation using five chromatographic zones, two inlet ports, and three outlet ports as shown Figure 1. The details for this process and its separation principle will be summarized in the following section. Although the five-zone SMB has been studied extensively in many of the previous research studies,5-7,10,11 it was known to have an unresolved problem that virtually limited its ternary separation performance. The unresolved limitation was that a proper control of the overlapping region between the highestaffinity and the intermediate-affinity components was almost impossible under the current configuration and operation method of the five-zone SMB. Because of such an inevitable limitation, the application scope of the five-zone SMB has been restricted within the ternary separation tasks that permitted either relatively medium purities or low throughput.5-7,10,11 The goal of this study is to propose an efficient operation strategy for overcoming the aforementioned limitation in the current five-zone SMB process for ternary separation. The key concept of the proposed strategy is based on the alternate opening and closing of the product port that is directly subject to the aforementioned limitation. Also, the operating parameters are to be adjusted accordingly at every moment of opening or closing the product port. It should be mentioned that there are some analogies between the strategy proposed in the present study and the strategies employed in some of previous processes in the literature. First, the proposed strategy is similar to the PowerFeed,17 Modicon,17 MCSGP,16 and intermittent SMB18 processes in that the operating parameters undergo a change within every switching period. Second, the proposed strategy is similar to the Varicol process19 in that the product port subject to the aforementioned limitation behaves differently from the other ports in every switching period. In addition, the proposed strategy and the previous strategies of partial feeding,20 partial

10.1021/ie100366g  2010 American Chemical Society Published on Web 08/20/2010

Ind. Eng. Chem. Res., Vol. 49, No. 19, 2010

9259

Figure 1. Schematic diagram of the standard five-zone SMB for ternary separation, where the desired direction of solute migration (relative to the ports) for successful ternary separation is indicated by arrows. A, lowest-affinity component; B, intermediate-affinity component; C, highest-affinity component.

withdrawal,21 partial discard,22 and fractionation and feedback23 are somewhat analogous in the aspect of introducing a partial implementation into SMB operation. Among these previous strategies, the partial feeding20 was reported to improve SMB separation efficiency by adjusting feed length and feed time. The partial withdrawal (or partial collection)21 was also known to increase the separation efficiency of a three-zone SMB by reusing some portion of the raffinate stream as a makeup desorbent. The first part of this paper will be devoted to investigating how much the application of the proposed strategy improves a ternary separation performance or throughput in a five-zone SMB process. The physical basis for such an improvement in the five-zone SMB performance will also be explained using equilibrium theory and detailed simulations. In the second part, it will be studied how a change in the level of purity requirement or a change in the selectivity affects the performance of a conventional five-zone SMB and the five-zone SMB based on the proposed strategy. 2. Basics and Limitations of the Standard Five-Zone SMB for Ternary Separation The first half of this section will be devoted to a brief introduction regarding basic principles of the five-zone SMB that has been developed and studied intensively in previous research studies.5-7,10,11 The five-zone SMB process consists of multiple chromatographic columns that are connected in series, creating a circular flow path as shown in Figure 1. The circle is partitioned into five zones of constant flow rates by two inlet ports (feed and desorbent) and three outlet ports (extract-1, extract-2, and raffinate). These five ports are moved periodically in the direction of the liquid-phase flow, leading to “simulated” countercurrent movement of the adsorbent (solid phase) relative to the liquid phase. Under this condition, the solute molecules in each zone can migrate downstream or upstream relative to the ports. Such a migration direction relative to the ports is virtually determined by the combined effects of port movement velocity, zone flow rates, and adsorption affinities of solute molecules. The desired direction of solute migration (relative to the ports) for successful ternary separation is illustrated by arrows in Figure 1, where components A, B, and C stand for the lowest-affinity, intermediate-affinity, and highest-affinity solutes, respectively. As long as the migration patterns of the three components in each zone are maintained as in Figure 1 and simultaneously the component C molecules do not reach the extract-2 port at every end of a switching period, the low-affinity solute molecules (A) can be recovered from the raffinate port while the intermediate-affinity (B) and high-affinity solute molecules (C) can be collected from the extract-2 and extract-1 ports, respectively.5-7,10,11 For a five-zone SMB with one column per zone, the design criteria to be satisfied for maintaining the aforementioned

conditions of ternary separation can be expressed by the following constraints, which were derived based on equilibrium theory (or band movement theory) in a previous publication.14 zone I:

m1 > KC

zone II:

K B < m2 < KC -

zone III:

KA < m3 < KB

(1c)

zone IV:

KA < m4 < KB

(1d)

zone V:

m5 < KA

(1e)

(1a) 2ε - m 3 - m4 1-ε

(1b)

where mj is the flow rate ratio in zone j and it can be expressed by the following equation:24,25 mj )

Qjtsw - Vcε Vc(1 - ε)

(1f)

where Qj is the volumetric flow rate in zone j; tsw is the switching time; Vc is the column volume; and ε is the total void fraction. Using the constraints on m2, m3, and m4 (eqs 1b-1d), a graphical representation of the complete ternary separation region in the plane of (m3, m4) was established in the literature.14 In such a graphical representation, eqs 1c and 1d define the region of a classical right triangle while eq 1b generates the following linear inequality. m4 < KC - KB -

2ε - m3 1-ε

(1g)

which results from the fact that the upper bound in eq 1b should be larger than the lower bound. Thus, in the (m3, m4) plane, complete ternary separation is achieved only in the region inside the triangle (eqs 1c and 1d) and below the critical line (eq 1g). The above five constraints for the five respective zones (eqs 1a-1e) and the additional linear-inequality (eq 1g) are the only necessary conditions for complete ternary separation. The remaining issue to be addressed further is a proper control of the overlap between different product components, which is usually aggravated by the presence of dispersion and masstransfer resistances. Unless such an overlapping region is well controlled between their corresponding product ports, it may pass through either of the product ports and lead to a decrease in product purities. In the five-zone SMB, three different types of overlapping regions can happen, which include A-B, A-C, and B-C overlapping regions. Among them, the A-B and the A-C overlapping regions can be well handled under the current fivezone SMB configuration on the premise that the zone flow rates and switching time are properly designed. By contrast, the presence of the B-C overlapping region can be a serious limitation in the five-zone SMB separation, because its confinement within zone II (between the product ports for

9260


Figure 2. Uncontrollable behavior of the B-C overlapping region in the standard five-zone SMB. (a) End of the Nth step; (b) middle of the (N + 1)th step; (c) middle of the (N + 2)th step; (d) end of the (N + 2)th step; (e) beginning of the (N + 3)th step. The shaded area indicates the B-C overlapping region.

B and C) is virtually impossible.5-7,10,11 To explain this point, a general behavior of the B-C overlapping region along the five-zone SMB bed is illustrated in Figure 2. Note that the B-C overlapping region is created first in zone IV and is then shifted to zone III and zone II with a series of port switchings. Obviously, such a shift of the overlapping region upstream from the feed port is due to lower migration velocities of the solute molecules than the ports (Figure 2). Once the B-C overlapping region enters zone II, its contamination of the extract-2 product (B) and/or the extract-1 product (C) is inevitable, as can be seen in Figure 2. To make matters worse, the occurrence of violating the constraints of eq 1g can happen with high possibility. If such a case occurs, the degree of the B-C overlap will become more serious. One of the ways to reduce the degree of such a product contamination is to use such a low feed flow rate that the region of B-C overlap can be minimized. However, this causes a significant decrease in the throughput of the five-zone SMB. Because of the aforementioned limitations, the five-zone SMB developed in previous studies has been regarded as suitable for only the separation tasks that permit either relatively medium purities under a fixed throughput or low throughput under given

purity requirements. Such a conventional five-zone SMB with the unavoidable limitations will be called “standard five-zone SMB” or “standard process” hereafter. 3. Proposed Operation Strategy for Improving the FiveZone SMB Performance 3.1. Principle. In this section, an efficient operation strategy is proposed to overcome the aforementioned limitations in the standard five-zone SMB that has been established previously for ternary separation. The core of this strategy is that the product port is not kept open all the time throughout the SMB operation but is open during only a part of the switching time in each step. During the rest of the time, the product port is closed. Accordingly, the product is partially collected during only the period that the product port is open in each step. During the other period of the port closing, the product stream is not exiting through the corresponding port but totally recycled to the adjacent zone for further separation. Although this strategy can be applied to all three product ports, its application is attempted to only the extract-2 port in this study. This is because the extract-2 port is the most affected


Figure 3. Control of the B-C overlapping region in the modified fivezone SMB based on the proposed strategy. (a) Between Ntsw and (N + TE-2)tsw; (b) at (N + TE-2)tsw; (c) between (N + TE-2)tsw and the end of the Nth step; (d) at the end of the Nth step. TE-2 is the period of opening the extract-2 port (expressed as a fraction of the switching time, tsw).

by the B-C overlapping region, which places a virtual limitation on the five-zone SMB performance as stated in the previous section. The detailed operation scheme for performing the aforementioned strategy is illustrated in Figure 3. Note that the extract-2 port is kept open for collecting the product B until the B-C overlapping region reaches the zone II outlet (Figure 3a). After then, the extract-2 port is immediately closed (Figure 3b) and the overlapping region is made to migrate into zone III without passing by the extract-2 port (parts c and d of Figure 3). The opening and closing of the extract-2 port are implemented in series within a switching period, and this operation is repeated in every moment of port switching. Such a five-zone SMB based on the proposed strategy will be called “modified five-zone SMB” or “modified process” hereafter. One of the noteworthy features in the modified five-zone SMB proposed above is that the zone configuration and the operating parameters undergo a regular change in every switching period. During the period of the port opening, the zone configuration is exactly the same as that in the standard fivezone SMB process (Figure 3a). The operating parameters such as zone flow rates and switching time are also maintained the same as in the standard process. By contrast, when the extract-2 port is closed, zones II and III become merged into one zone, where the flow rate should be uniform as a whole (parts b-d of Figure 3). For a comparative study between the two processes on an equal basis of feed flow rate (i.e., throughput), the flow rate in such a merged zone was kept the same as the zone III flow rate of the standard process, which also corresponds to the zone III flow rate of the modified process during the period of opening the extract-2 port. To sum up, the zone III flow rate of the modified process remains unchanged regardless of the port opening or closing. By contrast, the zone II flow rate of the modified process

9261

undergoes a stepwise decrease to the zone III flow rate at the moment of the port closing, which is done by increasing stepwise the extract-1 flow rate. Such a modified five-zone SMB operation, namely, the partial product collection by alternate opening and closing of the extract-2 port, introduces one additional degree of freedom. It is the period of opening the extract-2 port (TE-2), which corresponds to the length of the first operation stage in each switching period. In this study, the port-opening period (TE-2) is expressed as a fraction or a percentage of the switching time, and it can serve as one of the variables to be optimized for improving the five-zone SMB performance. The details of the other variables associated with the modified and standard fivezone SMB operations are summarized in Table 1, including their notations to be used in the following text. As indicated by Table 1, the port-opening period (TE-2) and M M T Q2-b ) in the alternate change of the zone II flow rate (Q2-a the modified process have no effect on the flow rates of the feed and the desorbent. Thus, the separation performance of the modified process, which was proposed in this article, can be compared with that of the standard process on an equal basis. 3.2. Design Criteria in Accordance with Equilibrium Theory. It is obviously a worthwhile task to derive the design criteria of the modified process in terms of the flow rate ratios (mj) and to further develop a graphical illustration of the complete ternary separation region. To facilitate such derivation work, the concept of the flow rate ratio based on average flow rate18 was introduced and was used in expressing the m2 value as follows. m2 )

M M {TE-2Q2-a + (1 - TE-2)Q2-b tsw} - Vcε Vc(1 - ε)

(2)

M ) Q3M as a result of the closing of the extract-2 port. where Q2-b On the basis of this concept, the complete separation constraints for the modified process with one column per zone were derived in a similar manner to that in the literature.14 Since the derivation procedure is simple and easy, only the final results are presented here.

zone I:

m1 > KC

zone II:

K B < m2 < KC -

(3a)

( 1 -ε ε )(1 + T

E-2)

-

TE-2m3 - m4

(3b)

zone III:

KA < m3 < KB

(3c)

zone IV:

KA < m4 < KB

(3d)

zone V:

m5 < KA

(3e)

additional constraint: m4 < KC - KB -

( 1 -ε ε )(1 + T

E-2)

-

TE-2m3

(3f)

Note that the above design criteria of the modified process are highly dependent on the TE-2 value, and they are reduced to the design criteria of the standard process (eq 1) if the TE-2 value is set to unity. To clarify the advantage of the modified process over the standard process, the region of complete ternary separation can be compared between the two processes in the (m3, m4) plane. Such a comparison is illustrated in Figure 4, where the triangular region is common to the two processes. The

9262


Table 1. Operation Variables Associated with the Standard and Modified Five-Zone SMB Operations standard five-zone SMB zone I flow rate zone II flow rate

QS1 QS2

zone III flow rate zone IV flow rate zone V flow rate switching time raffinate flow rate extract-1 flow rate

QS3 QS4 QS5 S tsw S QRaf ) QS4 - QS5 S QExt-1 ) QS1 - QS2

extract-2 flow rate

S QExt-2 ) QS2 - QS3

feed flow rate desorbent flow rate period of opening the extract-2 port

S QFeed ) QS3 - QS4 S QDes ) QS1 - QS5

only difference occurs in the region defined by the critical line (eqs 1g and 3f). As shown in Figure 4, the y-intercept of the critical line of the modified process is always larger than that of the standard process. Simultaneously, the absolute value of the slope of the former is always smaller than that of the latter. Such behaviors in the critical line of the modified process lead to a marked expansion of the complete separation region, compared to the standard process. Note also in Figure 4 and eq 3f that the complete separation region of the modified process is larger as the TE-2 value is set at a smaller value. It can thus be inferred that the modified process will outperform the standard process at least under the equilibrium condition. This will be verified again using the space-time diagram based on equilibrium theory in the following sections. Along with such an equilibrium analysis, the analysis based on detailed simulations will also be performed in the following sections to confirm the superiority of the modified process over the standard process under the case where mass-transfer resistances and axial dispersion take place. 4. Mathematical Model 4.1. Simulation of Five-Zone SMB Processes. The mathematical model used for simulation of a five-zone SMB is based on differential mass balance equations for both liquid

modified five-zone SMB based on the proposed strategy QM 1 M Q2-a (during the period of opening the extract-2 port) M Q2-b ) QM 3 (during the period of closing the extract-2 port) QM 3 M Q4 QM 5 M tsw M M QRaf ) QM 4 - Q5 M M QExt-1-a ) QM 1 - Q2-a (during the period of opening the extract-2 port) M M QExt-1-b ) QM Q 1 2-b (during the period of closing the extract-2 port) M M QExt-2-a ) Q2-a - QM 3 (during the period of opening the extract-2 port) M M QExt-2-b ) Q2-b - QM 3 (during the period of closing the extract-2 port) M M QFeed ) QM 3 - Q4 M M QDes ) QM 1 - Q5 TE-2 (expressed as a fraction or a percentage of the switching time)

and solid phases. The model equations consider convection, axial dispersion, and film mass transfer, as shown below:5-7,10,11 j ∂Cji ∂2Cji ∂Cji (1 - ε) ∂qi + ) Ejb,i 2 - uj0 ∂t ε ∂t ∂z ∂z

(4a)

∂qji j ) km,i ap(q*i ,j - qji) ∂t

(4b)

where the subscript i stands for different solutes; the superscript j is the zone number (I, II, III, IV, or V); C and q are the solute concentrations in liquid and solid phases, respectively; Eb is the axial dispersion coefficient; q* is the solid-phase concentration in equilibrium with the liquid-phase concentration (C); u0 is the liquid-phase interstitial velocity; km is the mass-transfer coefficient; ap ) 3/Rp for spherical particles; and Rp is the radius of solid particle. The equilibrium relationship between qi*and Ci is usually expressed by an adsorption isotherm model, which is given below in the case of a linear adsorption relationship. q*i ) KiCi

where Ki is the linear isotherm parameter of component i. To solve the aforementioned model equations, a biased upwind differencing scheme (BUDS) was used in conjunction with Gear integration having a step size of 0.1. The number of nodes in each column was set at 40. All of these numerical computations were carried out in Aspen Chromatography simulator. 4.2. Performance Parameters of Five-Zone SMB Processes. One of the prevalent criteria for evaluating the fivezone SMB performance is the purity index (PI),7,9,11 which is defined as the average of the purities of three product components as follows: PI )

Figure 4. Illustration of the critical lines (eqs 2f and 3f) in the (m3, m4) diagram. Only the operating points located in the overlapping region between the region inside the triangle and the region below the critical line allow the separation of the feed mixture into three pure fractions.

(5)

(PurA) + (PurB) + (PurC) 3

(6)

where PurA, PurB, and PurC are the purities of A, B, and C in the raffinate, extract-2, and extract-1 streams, respectively. As a matter of course, high value of PI is the important requirement to be satisfied in the operation of a five-zone SMB. But the maximization of only a PI value may not always ensure complete separation of all three products.7,11 The reason is that one of the products sometimes tends to have too high purity at the expense of the other, resulting in an unbalanced distribution of product purities. To take into account such an issue in the


9263

Table 2. System Parameters and the Other Details of the Model System Used for Simulation and Optimization of the Standard and Modified Five-Zone SMBs in This Study component A component B component C linear isotherm parameter, K (L/L S.V.) mass-transfer coefficient, kmap (1/s) axial dispersion coefficient, Eb (cm2/min) column diameter, dc (cm) column length, Lc (cm) adsorbent particle size, dp (µm) total void fraction, ε feed concentration, Cfeed (g/L)

3.0

6.0

20.0

0.3

0.3

0.3

Chung and Wen correlation26 1.0 25.0 20.0 0.8 1.0 (for each component)

evaluation of the five-zone SMB performance, an additional criterion is introduced. It is the minimum purity (MP), namely, the lowest purity among the three product purities as follows: MP ) Min(PurA, PurB, PurC)

(7)

Obviously, the MP value should also be maintained high like the PI value for desirable ternary separation. Hence, both the PI and MP values must be checked in order to confirm that a ternary separation in a five-zone SMB is well performed. When the aforementioned performance parameters (PI and MP) are compared between different processes or operations, it is customary to keep throughput and desorbent consumption (i.e., feed and desorbent flow rates) the same between them for a fair comparison. On the other hand, the throughout can be compared under the same desorbent consumption and the same constraints on product purities. The throughput, which is also one of the important performance parameters in separation processes, is defined as follows: Throughput )

QFeed BV

(8)

where QFeed and BV are the feed flow rate and the total bed volume, respectively. 5. Results and Discussion 5.1. Simulation Results for the Standard Five-Zone SMB Process. In this study, a typical model system that can be representative of a ternary mixture to be separated into three pure fractions was chosen as the target of process design and simulation. The system parameters of the model system are listed in Table 2, where the adsorption isotherm and mass-transfer parameters of three components are presented together with column dimension, adsorbent particle size, and feed concentration. Prior to the simulation for the standard five-zone SMB with the aforementioned system parameters, its operating parameters such as five-zone flow rates and switching time are to be determined in advance. This task was carried out using the design criteria for the standard five-zone SMB (eq 1), which were explained in the frame of equilibrium theory in the theory section (section 3.2). First, the complete separation region based on the design criteria was examined in the (m3, m4) plane of Figure 5a, where the triangle (eqs 1c and 1d) related to the A-B separation was drawn together with the critical line (eq 1g) related to the B-C separation. It is evident from Figure 5a that

Figure 5. Region of complete ternary separation in the (m3, m4) plane for the model system. The region inside the triangle and below the critical line allows for complete ternary separation. (a) Standard five-zone SMB (TE-2 ) 1) and (b) modified five-zone SMB based on strategy I (TE-2 < 1).

the region of complete ternary separation (i.e., the overlap between the region inside the triangle and the region below the critical line) does not exist for the model system. Therefore, a set of operating points (a-d) were chosen in several subregions of the (m3, m4) plane without regard to the possibility of ternary separation, while varying the switching time under the fixed feed flow rate of 0.7 mL/min. The four operating points chosen (a-d) are marked in Figure 4. Among them, only point c (m3 ) 3.75, m4 ) 4.80, and tsw ) 5.8905 min) was selected as the operating point of the standard fivezone SMB. This is because the other three points (a, b, and d) could have no room for fulfilling ternary separation, even if the proposed strategy (i.e., the modified five-zone SMB operation) would be applied. On the other hand, point c could have a sufficient possibility of fulfilling ternary separation by moving up the critical line with the help of the proposed strategy, which will be discussed in detail in the next section. Table 3 lists the finalized mj values of the standard five-zone SMB. Among the listed values, the m3 and m4 values came from those of point c in the aforementioned operating diagram (Figure 5a). In addition, the m1 and m5 values were chosen to fulfill the constraints of eqs 1a and 1e with a sufficient margin. By contrast, the m2 value could not be obtained from the constraint of eq 1b because the upper bound in eq 1b is smaller than the lower bound. Thus, as an alternative, the desired direction of solute migration in zone II (relative to the ports) in Figure 1 was used as a guideline for selecting the m2 value. In other words, the m2 value was chosen in such a way that component

9264


Table 3. Flow Rate Ratios (mj) and the Product Purities of the Standard and Modified Five-Zone SMBs Based on Operating Point c in Figure 5 (Feed Flow Rate ) 0.7 mL/min)

standard process modified process (strategy I) modified process (strategy II)

TE-2

m1

m2

m3

m4

m5

PurA (%)

PurA (%)

PurA (%)

1.0 0.8 0.62 0.3 0.19

25.00 25.00 25.00 25.00 25.00

7.50 6.75 6.08 4.88 6.46

3.75 3.75 3.75 3.75 3.75

4.80 4.80 4.80 4.80 4.80

2.40 2.40 2.40 2.40 2.40

99.69 99.64 99.54 99.54 99.49

88.95 92.25 96.72 99.07 98.48

99.89 99.68 96.85 67.43 99.51

Table 4. Operating Parameters of the Standard Five-Zone SMB and the Modified Five-Zone SMBs That Were Designed to Improve the Ternary Separation Performance under a Fixed Feed Flow Rate of 0.7 mL/min modified five-zone SMB standard five-zone SMB QS1 QS2

(mL/min) (mL/min)

19.3333 7.6667

QS3 (mL/min) QS4 (mL/min) QS5 (mL/min) S tsw (min) S QRaf (mL/min) S QExt-1 (mL/min)

5.1667 5.8667 4.2667 5.8905 1.6000 11.6666

S QExt-2 (mL/min)

2.5000

S QFeed (mL/min) S QDes (mL/min)

0.7000 15.0666

QM 1 (mL/min) M Q2-a (mL/min) M Q2-b (mL/min) QM 3 (mL/min) QM 4 (mL/min) QM 5 (mL/min) M tsw (min) M QRaf (mL/min) M QExt-1-a (mL/min) M QExt-1-b (mL/min) M QExt-2-a (mL/min) M QExt-2-b (mL/min) M QFeed (mL/min) M QDes (mL/min) TE-2 (%)

Table 5. Simulation Results for the Product Purities, the Purity Index (PI), the Minimum Purity (MP), and the Yields of the Standard Five-Zone SMB and the Modified Five-Zone SMBs That Were Designed to Improve the Ternary Separation Performance under a Fixed Feed Flow Rate of 0.7 mL/min modified five-zone SMB standard strategy I strategy I five-zone SMB (optimal PI) (optimal MP) strategy II PurA (%) PurB (%) PurC (%) PI (%) MP (%) Yield_A (%) Yield_B (%) Yield_C (%)

99.69 88.95 99.89 95.18 85.95 99.65 98.85 84.14

99.61 95.54 98.79 97.98 95.54 99.55 98.32 95.72

99.54 96.72 96.85 97.70 96.72 99.41 96.33 97.02

99.49 98.48 99.51 99.16 98.48 99.09 97.80 99.39

B migrates faster than the ports while component C migrates slower than the ports. On the basis of the above-determined mj values and switching time, the five-zone flow rates were calculated on the basis of eq 1f and the resultant operating parameters are given in Table 4. Using these operating parameters, detailed rate-model simulation was carried out for the standard five-zone SMB, and the simulation results are presented in Table 5. Note that the purities of A and C products are sufficiently high whereas the purity of B product is so low, resulting in a relatively medium PI and such a low MP. To elucidate this phenomenon, the column profiles of the standard five-zone SMB at cyclic steady state were obtained from the simulation. It is clearly seen from the column profiles (Figure 6) that the extract-2 port is kept contaminated with the B-C overlapping region and the following solute band of C throughout the second half of a switching period, resulting in a severe drop in the B purity of the extract-2 stream. This also causes a large decrease in the yield of C in the extract-1 stream (Table 5). Obviously, these undesirable phenomena should be prevented if the five-zone SMB performance is to be improved substantially, i.e., both PI and MP are to be enhanced simultaneously. However, such a task is almost impossible under the current process configuration

strategy I (optimal PI)

strategy I (optimal MP)

strategy II

19.3333 7.6667 5.1667 5.1667 5.8667 4.2667 5.8905 1.6000 11.6666 14.1666 2.5000 0 0.7000 15.0666 68

19.3333 7.6667 5.1667 5.1667 5.8667 4.2667 5.8905 1.6000 11.6666 14.1666 2.5000 0 0.7000 15.0666 62

19.3333 14.6667 5.1667 5.1667 5.8667 4.2667 5.8905 1.6000 4.6666 14.1666 9.5000 0 0.7000 15.0666 19

and operation method. Some modifications are to be made in the standard five-zone SMB, as will be explained below. 5.2. Strategy I: Partial Collection of the Extract-2 Stream by Alternate Opening and Closing of the Extract-2 Port. To make a simultaneous improvement in both PI and MP by overcoming the aforementioned limitation, one can use the modified five-zone SMB based on the strategy proposed in the section 3, which is to collect partially the extract-2 stream by alternate opening and closing of the extract-2 port in each switching period (strategy I). 5.2.1. Use of Equilibrium Theory for Analysis of Strategy I. The (m3, m4) diagram for the modified five-zone SMB based on strategy I (TE-2 < 1) was prepared using the relevant design equations (eq 3) that were presented in the theory section (section 3.2). The resulting diagram is shown in Figure 5b, where the three critical lines based on high, medium, and low TE-2 values were drawn. Note that the position of the critical line relative to operating point c is largely affected by the TE-2 value. As shown in Figure 5b, a decrease in the TE-2 value causes the critical line to move upward in the (m3, m4) plane. As a consequence, operating point c, which had been ineffective in ternary separation by the standard five-zone SMB (Figure 5a), could belong to the complete separation region by virtue of strategy I application based on a proper value of TE-2 (Figure 2). The flow rate ratios and the product purities of the modified five-zone SMB corresponding to each critical line in Figure 5b are summarized in Table 3, where the reported purities were obtained from simulations for analysis purpose. Note that strategy I based on TE-2 ) 0.8 seems to fall short of a satisfactory ternary separation whereas strategy I based on TE-2 ) 0.62 seems to allow a satisfactory ternary separation. These phenomena can be well understood in the (m3, m4) plane of Figure 5b, which shows that the critical line is located below operating point c in the former case (TE-2 ) 0.8) and above operating point c in the latter case (TE-2 ) 0.62). However, a failure in ternary separation that was observed for strategy I based on TE-2 ) 0.3 cannot be explained only by


Figure 6. Column profiles of the standard five-zone SMB (Table 3) at cyclic steady state: (a) at the beginning of a switching period, (b) at the middle of a switching period, (c) at the end of a switching period. Thick line, A; thin line, B; gray line, C.

the (m3, m4) diagram of Figure 5b, because the corresponding critical line is located far above operating point c. The direct reason for such a failure lies in the m2 value (Table 3), which is too low to fulfill the constraint on m2 of eq 3b. The occurrence of such an undesirable phenomenon is entirely due to the fact that a lower TE-2 leads to a direct reduction in the m2 value under the strategy I scheme (eq 2). A few remarks are necessary at this point. The feasible range of m2 (i.e., the interval between the upper bound and the lower bound) becomes rather larger as the TE-2 value decreases (see eq 3b). Therefore, the aforementioned problem can be easily overcome by increasing the m2 value, which can be implemented M M as a free variable (i.e., increasing Q2-a simply by setting Q2-a beyond Q2S). This method will be discussed later in detail. 5.2.2. Use of Space-Time Diagram for Analysis of Strategy I. The advantage of strategy I can also be confirmed by a space-time diagram18 based on equilibrium theory. This diagram is known to be highly efficient in representing the SMB cyclic steady-state behavior under the equilibrium (or ideal) condition for better understanding of solute migration path in each switching period.18 Thus, the space-time diagram is usually regarded as an essential means of validating the effectiveness of a certain operation strategy. Parts a-d of Figure 7 show the space-time diagrams for the standard five-zone SMB (TE-2 ) 1) and the modified fivezone SMBs based on strategy I (TE-2 ) 0.8, 0.62, 0.3), which were prepared on the basis of the operating parameters in Table 3. Since the B-C separation dominates the five-zone SMB performance, only the solute bands (fronts and tails) related to

9265

Figure 7. Space-time diagram based on equilibrium theory: (a) standard process, (b) modified process based on strategy I (TE-2 ) 0.62), (c) modified process based on strategy I (TE-2 ) 0.30), (d) modified process based on strategy I (TE-2 ) 0.80), (e) modified process based on strategy II (TE-2 ) 0.19). B-f, front of B band; B-t, tail of B band; C-f-i, front of the ith C band; C-t-i, tail of the ith C band.

the B-C separation were demonstrated in the relevant zones instead of displaying all three solutes in five zones. In the case of solute C in zone II, only a part of the solute C bands affecting the B-C separation were demonstrated while the other solute C bands located upstream from the C tail-3 were omitted to avoid the visual complexity in the diagrams. Note first in Figure 7 that component B forms a single band (front and tail) whereas component C forms multiple bands (fronts and tails). Each corresponding front and tail delimits the area where the relevant component is present.18 In light of such a principle of the space-time diagram, one can easily find that the B-C separation is virtually dependent on the behaviors of the B tail and the C front-3 (see Figure 7). In the case of the standard process (Figure 7a, TE-2 ) 1), it is clearly seen that the C front-3 passes through the extract-2 port to a large degree, resulting in a significant contamination of the B product. Such a separation problem seems to be solved in the modified process, if the period of opening the extract-2 port (TE-2) is chosen properly. As shown in Figure 7b (TE-2 ) 0.62), the extract-2 port is closed before the C front-3 reaches the extract-2 port, which will be obviously of advantage to the attainment of a high purity of B. On the other hand, it is observed that the modified process cannot fulfill satisfactory B-C separation if TE-2 is chosen to be too much smaller or too much larger than that in Figure 7b. First, in the former case (Figure 7c, TE-2 ) 0.3), the problem happens not in the C front-3 but in the B tail. As shown in Figure 7c, the B tail does not leave completely zone II at the end of a switching period, which

9266


Figure 9. Column profiles of the modified five-zone SMB based on strategy I at cyclic steady state: (a) TE-2 ) 68% and (b) TE-2 ) 62%. The column profiles in (a) were obtained at the last moment of the port-opening period while those in (b) were obtained at the end of a switching period. Thick line, A; thin line, B; gray line, C. Figure 8. Effect of TE-2 on the ternary separation performance of the modified five-zone SMB based on strategy I: (a) product purities and (b) purity index and minimum purity.

can lead to a severe contamination of the C product in the subsequent switching period. Second, in the latter case (Figure 7d, TE-2 ) 0.8), the extract-2 port is closed too late to prevent the C front-3 from contaminating the B product. The results of this section that were obtained from the space-time diagram are consistent with the results of the previous section that were derived from the design criteria and the relevant flow-rate-ratio diagram. Both results indicate that the selection of a proper TE-2 is of critical importance in maximizing the separation performance of the modified process. 5.2.3. Use of Detailed Simulation for Analysis of Strategy I. In the previous section, the equilibrium analysis was used for verifying the advantage of the modified process and enlightening the importance of the TE-2 selection. To investigate these two issues under more realistic conditions where masstransfer effects are present, a series of detailed simulations were conducted for the modified process while varying the value of TE-2. Even though such an operation was performed, the throughput and desorbent consumption remained constant at those of the standard process regardless of the value of TE-2, because the feed and the desorbent flow rates in all these cases remained unchanged. The resulting product purities from the application of the modified process are presented as a function of TE-2 in Figure 8a. Note that, in the range of TE-2 from 40% to 100%, the purity of B dramatically improves with decreasing TE-2. This result could be easily understood by the space-time diagrams in parts b-d of Figure 7. However, such a decrease in TE-2 causes a reduction in the averaged zone II flow rate per each switching M M period (Q2M ) Q2-a TE-2 + Q2-b (1 - TE-2)), which eventually becomes much lower than the zone II flow rate of the standard process (Q2S). Obviously, this will make it more difficult to remove (or desorb) component B from zone II within a switching period. In this case, the B molecules remaining in

zone II at the end of a switching period can be shifted to zone I at the instant of the next port switching, thereby contaminating product C in the extract-1 stream. This is why the purity of C keeps decreasing with decreasing TE-2, as shown in Figure 8a. On the basis of the product purities in Figure 8a, the performance parameters such as purity index (PI) and minimum purity (MP) were calculated. Figure 8b shows the plot of the resulting PI and MP as a function of TE-2. Notice that the optimal PI and MP occur at TE-2 ) 68% and TE-2 ) 62%, respectively. The corresponding product purities at these two TE-2 values are listed in Table 5 along with the PI and MP values. It is clearly seen that the modified process based on strategy I gives higher PI and MP values than the standard process. In spite of this advantage, the purities of B and C from the application of strategy I may be sometimes insufficient for separation processes in the pharmaceutical industry, where an extremely high purity is demanded. To find out the reason for the occurrence of such purities of B and C, the column profiles of the modified process with the optimal PI (TE-2 ) 68%) were obtained at the last moment of the port-opening period (Figure 9a), and those with the optimal MP (TE-2 ) 62%) were obtained at the end of a switching period (Figure 9b). It is worth noting that, in the former case (Figure 9a), a little contamination of the extract-2 port with component C is the major reason for the failure of achieving a high purity of B. In the latter case (Figure 9b), a little amount of the remaining component B in zone II is the major reason for the failure of achieving a high purity of C. Such behaviors of components B and C also affect the yields of B and C in the two cases. First, in the former case (TE-2 ) 68%), some amount of component C is lost through the extract-2 port. This is why the yield of C is lower in the former case than in the latter case (Table 5). Second, in the latter case (TE-2 ) 62%), some amount of component B is lost through the extract-1 port, resulting in a lower yield of B than in the former case (Table 5).


All the above results indicate that the adjustment of only the port-opening period (TE-2) is not enough for separating a ternary mixture with sufficiently high purities. An additional factor is to be taken into account. From the above analyses, it is easily inferred that the zone II flow rate (Q2M) can be well suited for the additional factor. Since the zone II flow rate in the second stage (during the port-closing state), QM 2-b, should be maintained the same as the zone III flow rate, only the zone II flow rate M , can serve in the first stage (during the port-opening state), Q2-a as the additional factor. Certainly, the adjustments of both TE-2 M (port-opening period) and Q2-a (zone II flow rate in the first stage), which will be called strategy II in the following sections, are expected to guarantee more complete ternary separation, namely, both higher PI and higher MP. 5.3. Strategy II: Partial Collection of the Extract-2 Stream by Alternate Opening and Closing of the Extract-2 Port + Adjustment of the Zone II Flow Rate in the Stage of the Port-Opening State. The equilibrium analysis based on the space-time diagram was carried out first for verifying the potential advantage of strategy II over strategy I. In strategy II, TE-2 (port-opening period) and QM 2-a (zone II flow rate in the first stage) should be adjusted in such a way that the following two changes can occur simultaneously in the corresponding space-time diagram: (1) the C front-3 should be farther away from the extract-2 port at the last moment of the port-opening period and (2) the B tail should be farther away from the zone II outlet at the end of a switching period, compared to the space-time diagram of strategy I (Figure 7b). Examining the space-time diagram (Figure 7b) closely, one can easily find that the first and second conditions can be fulfilled at the same time by decreasing TE-2 (i.e., closing the extract-2 port earlier) M ). These two measures and increasing the m2 value (i.e., Q2-a were made and the resultant space-time diagram, i.e., that of strategy II, is presented in Figure 7e. Note that the desired changes on the C front-3 and the B-tail, which were mentioned above, occurred simultaneously. For this reason, the use of strategy II could enhance the purities of B and C further, compared to strategy I (Table 3). The above-reported results, which were verified within the scope of equilibrium theory, need to be proved again under the circumstances where mass-transfer resistance and axial dispersion are present. For this study, the simulation works in the previous section, which were conducted by varying the TE-2 value, were repeated again while varying the QM 2-a value. During M M occurs when Q2-a ) Q2S such a variation, the minimum of Q2-a M S M and QExt-1-a ) QExt-1, and its maximum occurs when Q2-a ) Q1M M () Q1S) and QExt-1-a ) 0. M M Since Q2-a ) Q1M - QExt-1-a and Q1M remains fixed at Q1S, the M change in Q2-a can be expressed as a change in QMExt-1-a that ranges S (maximum) to 0 (minimum). Recall that the from QExt-1 simulation of the modified process in the previous section was M S ) QExt-1 . In this section, three based on the condition of QExt-1-a more simulations were performed under the conditions of M S M S M ) 0.8QExt-1 , QExt-1-a ) 0.4QExt-1 , and QExt-1-a ) 0, QExt-1-a M decreases in this manner, the zone respectively. When QExt-1-a II flow rate increases accordingly due to the aforementioned M M ) Q1M - QExt-1-a ). mass balance (Q2-a M The resulting PI and MP values for each condition of QExt-1-a are demonstrated in Figure 10. As expected from the previous results based on equilibrium theory (Figure 7e), the decrease M M (or increase in Q2-a ) caused the optimal PI and MP in QExt-1-a values to be obtained at a shorter TE-2 (Figure 10). It was also found that the optimal PI and MP values from such a S simultaneous adjustment of TE-2 and QM j ) Qj (strategy II) were

9267

M M Figure 10. Effects of TE-2 and Q2-a (i.e., QExt-1-a ) on the purity index and the minimum purity of the modified five-zone SMB based on strategy II: M S M S M (a) QExt-1-a ) 0.8QExt-1 , (b) QExt-1-a ) 0.4QExt-1 , (c) QExt-1-a ) 0.

higher than those from the adjustment of only the TE-2 value (strategy I), which can be confirmed by comparing Figures 8b and 10. The advantage of the modified process based on strategy II becomes much more pronounced if it is compared with the standard process. As shown in Table 5, an extreme improvement in both PI and MP, especially in the purity of B, occurs in the case where the standard process is replaced by the modified process based on strategy II. This phenomenon can be well understood by the column profiles of the modified process based M S ) 0.4QExt-1 ), which were on strategy II (TE-2 ) 0.19 and QExt-1-a obtained during one of the switching periods at cyclic steady state (Figure 11). Note that the front of the B-C overlapping region in zone II does not reach the extract-2 port until 60.19 steps, i.e., until the extract-2 port is closed (Figure 11a and b). This implies that the TE-2 value was properly chosen for the attainment of high purity of B. In addition, the column profiles in Figure 11c show that zone II is almost free of component B at the end of a switching period, which means that the QM 2-a value was well selected for the achievement of high purity of C.

9268


practically representative of feed flow rate because the adsorbent volumes of the two processes are the same. During the optimization, the purities of all three products were constrained to be >95%. The other details in such an optimization task are presented below. First, those for the standard process are as follows: S S Max J ) ThroughputS[QS1 , QS2 , QS3 , QFeed , tsw ]

Subject to PurA g 95%, PurB g 95%, PurC g 95%

(9a) (9b)

S QFeed g 0.01 mL/min

(9c)

S fixed variables QDes ) 15.0666 mL/min

(9d)

Second, the optimization details for the modified process are as follows: M M M M Max J ) ThroughputM[QM 1 , Q2 , Q3 , QFeed, tsw, TE-2]

(10a) Subject to PurA g 95%, PurB g 95%, PurC g 95% (10b) M QFeed g 0.01 mL/min

(10c)

M S fixed variables QDes ) QDes ) 15.0666 mL/min

(10d) M QExt-2-b )0

Figure 11. Column profiles of the modified five-zone SMB based on strategy M S II (TE-2 ) 0.19 and QExt-1-a ) 0.4QExt-1 ) at cyclic steady state: (a) at the beginning of a switching period, (b) at the moment of closing the extract-2 port, (c) at the end of a switching period. Thick line, A; thin line, B; gray line, C.

Simultaneously, the front and the tail of the solute band of A are well confined within zones V and III, respectively, during the entire switching period (Figure 11). The front of the solute band of B is also well confined within zone IV while the tail of the solute band of C is within zone I during the entire switching period (Figure 11). All of these behaviors make it possible for the modified process to achieve almost complete ternary separation, which is mostly due to the well-designed values of M . TE-2 and Q2-a 5.4. Comparison of the Standard and Modified Five-Zone SMBs in Terms of the Optimized Throughput under the Same Purity Constraints. In the design stage of separation processes, increasing the feed flow rate (or throughput) under given purity requirements is often regarded as more important than increasing product purities under a fixed feed flow rate (or throughput). Hence, it is of course a worthwhile task to make a comparative study between the standard process and the modified process based on strategy II in terms of throughput. For such a task, the standard and the modified processes were optimized, each for maximizing the throughput while the constraints on product purities were kept the same between the two processes. For the purpose of facilitating a comprehensive optimization of both the processes, the optimization tool of the NSGA-II-JG27-29 coupled with Aspen Chromatography simulator was used. In this optimization, the objective function was the throughput, which is

(10e)

Note in the above optimization frames that the desorbent flow rate was kept the same between the two processes to be compared. This is because the desorbent flow rate, like the purity constraints, can affect the maximum feed flow rate attainable. The optimization results for the two processes are summarized in Table 6. It is clearly seen that the modified process has an overwhelming superiority over the standard process. As listed in Table 6, the throughput of the modified process is about 10 times higher than that of the standard process. In the above optimization tasks, the product purities were constrained to be >95% each. Such a purity constraint may sometimes be tightened according to the market demands. It is thus necessary to investigate how a change in the purity constraint affects the above optimization results. For such an investigation, the above optimizations were performed again under the constraint that each of the product purities must be >98%. One of the noteworthy results is that the standard process failed in meeting the purity constraint (g98%) even when its feed flow rate was reduced to the lower bound, 0.01 mL/min. By contrast, Table 6 shows that the modified process readily succeeded in meeting the purity constraint (g98%) even though its feed flow rate was ∼112 times higher than the lower bound. This implies that the modified process has at least 112 times the throughput, compared to the standard process. The amount of such an improvement in throughput is extremely larger than the previous case where the modified and the standard processes were compared under the less strict purity constraint (g95%). Taking into account everything in this section, it can be concluded that strategy II proposed in this article is highly effective in increasing throughput as well as improving product purities. Furthermore, the advantage of strategy II over the standard operation in the aspect of throughput becomes greater as the level of product purity constraint is higher.


9269

Table 6. Operating Parameters and Simulations Results for the Standard Five-Zone SMB and the Modified Five-Zone SMBs That Were Designed to Maximize the Throughput under the Same Constraints on Product Purities standard five-zone SMBa purity constraint throughput (L/L-h) product purities optimal values of decision variables

a

g95% 0.1145 PurA ) 95.29% PurB ) 95.01% PurC ) 95.14% QS1 ) 18.0940 QS2 ) 4.9359 QS3 ) 4.5032 S QFeed ) 0.1873 S tsw ) 8.0644

optimal values of dependent variables

QS4 ) 4.6905 QS5 ) 3.0274 S QRaf ) 1.6631 S QExt-1 ) 13.1581 S QExt-2 ) 0.4327

values of fixed variables

S QDes ) 15.0666

modified five-zone SMBa g95% 1.1719 PurA ) 95.10% PurB ) 95.02% PurC ) 95.01% QM 1 ) 20.0197 M Q2-a ) 14.0510 QM 3 ) 5.6748 M QFeed ) 1.9175 M tsw ) 4.9630 TE-2 ) 25.46 M Q2-b ) 5.6748 QM 4 ) 7.5923 QM 5 ) 4.9531 M QRaf ) 2.6392 M QExt-1-a ) 5.9687 M QExt-1-b ) 14.3449 M QExt-2-a ) 8.3762 M QExt-2-b ) 0 M QDes ) 15.0666

g98% 0.6883 PurA ) 98.03% PurB ) 98.07% PurC ) 98.14% QM 1 ) 18.4972 M Q2-a ) 8.0869 QM 3 ) 4.0703 M QFeed ) 1.1262 M tsw ) 7.1409 TE-2 ) 35.85 M Q2-b ) 4.0703 QM 4 ) 5.1965 QM 5 ) 3.4306 M QRaf ) 1.7659 M QExt-1-a ) 10.4103 M QExt-1-b ) 14.4269 M QExt-2-a ) 4.0166 M QExt-2-b ) 0 M QDes ) 15.0666

The units of Qj, Qinlet, and Qoutlet are in mL/min, and the units of tsw and TE-2 are in min and %, respectively.

region of the B-C selectivity that is lower than the A-B selectivity. Such a further improvement research study is now in progress. The results will be reported in a subsequent paper. 6. Conclusions

Figure 12. Effect of the B-C selectivity on the optimized throughputs of the standard process and the modified process based on strategy II. The dotted line indicates the throughput value corresponding to the feed flow rate of 0.1 mL/min.

5.5. Effect of the Selectivity between B and C on the Throughput of the Five-Zone SMB. In all the previous sections, the selectivity between B and C was fixed at 3.3, which was far higher than the selectivity between A and B. It is interesting to examine how the selectivity between B and C affects the performances of the standard process and the modified process. For such an examination, a series of throughput optimizations were carried out for the two processes under the purity constraint (g95%), and in each optimization, the B-C selectivity was made to be reduced gradually, which was implemented by varying only the linear isotherm parameter of C (KC) from 20 to lower values. The optimization results are presented in Figure 12, where the dotted line indicates the throughput value corresponding to the feed flow rate of 0.1 mL/min, which is assumed to be the criterion for a meaningful separation. It is worth noting that the modified process can perform a meaningful separation until the B-C selectivity is reduced to 2.5. By contrast, a meaningful separation is no longer practicable in the standard process if the B-C selectivity is reduced to

Enhanced Separation Performance of a Five-Zone Simulated Moving

Recommend Documents