Improved Performance of a Simulated Moving Bed Process by a

Article pubs.acs.org/IECR

Improved Performance of a Simulated Moving Bed Process by a Recycling Method in the Partial-Discard Strategy Kyung-Min Kim, Hyeon-Hui Lee, and Chang-Ha Lee* Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul, 120-749, Korea ABSTRACT: The recycling partial-discard (RPD) strategy was developed to improve the performance of simulated moving bed (SMB) chromatography in partial-discard (PD) strategy by a simulation study. In the RPD operation, each discarded product portion of extract and raffinate is recycled as part of the feed. This strategy was applied to a binary mixture with a nonlinear isotherm in a four-zone SMB with two columns per zone. The two additional operating variables, recycle length (RL) and recycle f lowrate (RF), were suggested for the RPD strategy in order to determine the time duration and flowrate of the recycle feed. Compared to those of the PD operation, extract and raffinate with higher purities can be produced from the RPD operation. Simultaneously, the losses in the other performance parameters (recovery, productivity, and eluent consumption) stemming from the PD operation could be favorably reduced by controlling the recycle length and recycle ratio in the RPD operation. The two variables, RL and RF, in the RPD operation played key roles in the improvement and trade-off of SMB performance parameters (purity, recovery, productivity, and eluent consumption).

1. INTRODUCTION Simulated moving bed (SMB) chromatography is receiving considerable attention due to its inherent advantages in achieving higher productivity and lower solvent consumption than in batch chromatography. It has been applied in a large-scale separation of petrochemical and sugar industries and now the adoption of SMB is being extended to fine chemical applications such as the separation of natural products, pharmaceuticals, and aromas.1−5 Many of these applications deal with the resolution of racemates, which is becoming one of the major fields of SMB applications.6,7 It is currently necessary to produce pharmaceutical compounds with extremely high purity in order to develop safer and more effective drugs.8 Many researchers are inquiring about the application of SMB regarding the purification of drug chemicals and the separation of enantiomers.9 However, chiral stationary phases exhibit usually low or moderate separation factors (typically between 1.1−1.4) and low separation capacities while being relatively expensive compared to others.10 There has been a continuous effort to develop modified SMB operating strategies for high purity products while maintaining the high performances of the other parameters. One of the ways to improve the performance of an SMB is periodic modulation of certain operating parameters between two consecutive switches. Examples of such modification are the VariCol,11 PowerFeed,12 Partial-feed,13 ModiCon,14 Partial-Discard,15 and FF-SMB.16,17 In a previous study, our group suggested the partial-discard (PD) strategy, in which a small portion of product is discarded to improve purity.15 Recently, the “Outlet Streams Swing (OSS)” strategy and the “partial-feeding and partial-closing operation” were suggested to improve purity by controlling the outlet port flowrates of the high purity sector and the low purity sector in a switching period.18,19 Extract and raffinate purities can be enhanced significantly by discarding a small portion of product or closing a port temporally because most of the impurity in each product elutes at one side of a switching period. In the PD operation, however, the other performance parameters © 2012 American Chemical Society

(especially recovery) deteriorated from the discarded waste of highly concentrated product. As a result, the productivity and eluent consumption declined simultaneously. In the recently proposed fractionation and feedback approach (FF-SMB), where the product stream is fractionated for internal recycling and refeeding, both the original feed and the fractionated mixture were used alternately as feed during one cycle time.16,17 The alternative feeding concept in the FF-SMB operation was introduced to recover the loss of yield while maintaining a purity threshold. In the recycling operation, the amount of supplied original feed can be reduced because a certain amount of feed is replaced by recycling the mixture during part of the switching period. This may lead to deteriorations in productivity and eluent consumption if a higher concentration or flowrate of original feed is not applied to the system. In addition, the flowrate of each product node is generally higher than the feed flowrate in the conventional SMB because of the addition of eluent. Therefore, it was reported that the direct recycling of discarded product led to the decreases in performance parameters including purity, due to the flowrate difference between the original feed and the recycle feed and the improper recycling timing in the SMB process.20 Therefore, when the recycling strategy is applied to the PD strategy, new operating variables, such as the amount of discarded product portion recycled as feed, the flowrate of the recycle feed, and the time duration of the recycling step, will play key roles in improving the performances of overall SMB processes. In the study, a recycling method in PD operation was applied to a binary mixture with a nonlinear isotherm in a four-zone SMB with two columns per zone. And the recycling partial-discard (RPD) strategy was applied simultaneously to both raffinate and extract through a simulation study. Two additional operating Received: Revised: Accepted: Published: 9835

February 20, 2012 June 4, 2012 June 15, 2012 June 15, 2012 dx.doi.org/10.1021/ie300446x | Ind. Eng. Chem. Res. 2012, 51, 9835−9849

Industrial & Engineering Chemistry Research

Article

Figure 1. (a) Schematic illustration of a conventional SMB operation in a switching period. (b) Schematic illustration of the RPD operation in a switching period.

greater influence on the raffinate product, and the last part of the feed has a greater influence on the extract product, respectively. Therefore, it can be expected that the SMB performance is improvable via the following recycling method: the discarded product portion of the extract node (extract-rich composition) is substituted for the feed during the last part of the switching period. Meanwhile, the raffinate product discarded at the last part of the switching period is recycled as feed during the initial part of the next switching period (Figure 1b). Because the recycling concept in this study naturally leads to the time interval between product discarding and recycling, a small storage tank is needed at each product node to store each discarded product temporarily for the time interval. In this study, the recycle feed supplied from the product-storage tank and the raw feed were referred to as the recycle-feed and the original-feed, respectively. As shown in Figure 1b, each switching period in the RPD operation is partitioned into three parts: the feed and two product nodes. Compared to the conventional SMB shown in Figure 1a, the operation in the middle part of the switching period is similar to the conventional SMB operation, except for the withdrawal of the unused discarded product portion from the storage tank. Also, the operations at both the initial and last parts of the switching period differ from those of the conventional SMB operation due to the product discard and recycling. Figures 2a and b show the partitioned times and flowrates at feed and product nodes during a switching period. At the feed node in Figure 2a and b, the feed is substituted for the raffinate discarded product portion (raffinate recycle-feed), which was collected from the previous switching period, at the feed initial stage (tF‑ini). The original-feed is then injected during the feed middle stage (tF‑mid). Finally, the extract discarded product portion (extract recycle-feed) from the storage tank replaces the original-feed during the feed last stage (tF‑last). At the two product nodes, the discarded extract and raffinate products are collected into individual storage tanks during the product initial stage (tE‑ini) and product last stage (tR‑last), respectively. Because the time durations (tE‑ini, tF‑ini and tR‑last, tF‑last) of the partitioned stages do not have to be equal, the time durations of each stage act as operating variables in the RPD strategy. The discarded product portion is of lower concentration than the original-feed at high flowrates due to the addition of desorbent. Therefore, a certain amount of the discarded product

variables were suggested for the design of RPD operation and their effects on the RPD operation were evaluated. Then, four performance parameters (purity, recovery, productivity, and eluent consumption) of the RPD operation were compared to those of conventional SMB and PD operations for the same amount of feed.

2. PRINCIPLE OF A RECYCLING PARTIAL-DISCARD (RPD) STRATEGY Figure 1 shows conventional and RPD operations of four-zone SMB. In the conventional SMB, the flows of two inlet nodes (feed and desorbent node) and two outlet nodes (extract and raffinate node) were maintained during the entire switching period (Figure 1a). And, the majority of the impurity (raffinate) in the extract node appeared during the initial stage of switching, while most of the impurity (extract) in the raffinate node emerged in the last stage. Therefore, the purity could be significantly improved by withdrawing a certain amount of product into which the main impurity was present in the partialdiscard (PD) operation.15 However, in order to obtain a high purity product from the PD strategy, some amount of high concentration product will need to be discarded. As a result, the other performance parameters (recovery, productivity, and eluent consumption) are naturally deteriorated.15 The recycling concept of the discarded product portion should reduce the loss of recovery in the PD operation and at least guarantee the same product specifications. In the previous study, we directly recycled the discarded product into the feed node.20 Although this method had the advantage of simplicity, the purity and productivity deteriorated due to the high flowrate and low concentration of the recycled portion used as feed and the decreased amount of raw feed handled during the switching period. Therefore, it is important to determine when and for how long the discarded product portion should be recycled within a switching period. In a conventional SMB, the initial part of the feed in a switching period easily reaches the raffinate product node during the switching period. On the other hand, the last part of the feed moves back in the direction of the extract product node when the next switch occurs. As a result, the initial part of the feed has a 9836

dx.doi.org/10.1021/ie300446x | Ind. Eng. Chem. Res. 2012, 51, 9835−9849


Article

Figure 2. (a) Time duration and (b) flowrate of each section in feed and two product nodes during a switching period in RPD operation and feed concentrations of (c) conventional SMB and (d) RPD operation at cyclic steady-state.

portion can be supplied as a recycle-feed, but the remaining portion should be withdrawn from each storage tank in the middle stage of the switching period, as shown in Figure 1b. In addition, the flowrates of the two recycle-feeds (QF,F‑ini and QF,F‑last) are determined from additional variables (RFR and RFE) in the RPD operation, as shown in Figure 2b. The new operating variables generated in the RPD operation are discussed in a later section. Compared to a conventional SMB, the alternative feeding method in the RPD operation, using the original-feed and recycle-feed, decreases the total loading amount of raw feed during the same switching period if the concentrated originalfeed is not supplied. In this study, the criterion used for comparing the performances of conventional SMB, PD, and RPD operations was the treatment of the same amount of raw feed during the same switching period. Therefore, the concentration of original-feed during the feed middle stage (tF,mid) of the RPD operation shown in Figure 2d is higher than that of the raw feed in the conventional SMB shown in Figure 2c because the original-feed can be supplied to the system only during that period. The concentration of this feed should vary in inverse proportion to the duration of the feed middle stage (tsw/tF,mid). As a matter of course, the total amount of treated feed in the RPD operation (original-feed + recycle-feed) is greater than that in the conventional SMB, as shown in Figure 2d. Since the productivity in the SMB processes can increase with concentrated feed, it is attractive to choose the highest possible feed concentration in the operation. However, in many cases, this is not applicable to real fields due to the decrease of operational reliability with increasing feed concentration. That is, the system should be capable of maintaining an operating point in the

presence of various disturbances. In the nonlinear condition, a higher feed concentration typically requires lower feed flowrate, which might be difficult to control in real operation. Therefore, a small fluctuation of flowrate, temperature, or feed concentration may cause significant contamination of the products. As a result, a lower feed concentration is typically chosen, which is clearly below the solubility limitation.14,20 Therefore, in this study, the solubility of raw-materials and the typical feed concentration were assumed to 5 and 3 g/L, respectively. As a result, even though the developed RPD strategy simply adopts the recycling concept of the discarded product portion, as shown in Figures 1b, this strategy naturally includes the synchronous combination of various modified SMB strategies. It uses the asynchronous switch of the recycle-feed of the Varicol strategy,11 the concentration modulation of the original-feed during the switch interval of Modicon,14 the flowrate variation of the recycle-feed from Powerfeed,12 and the alternative feeding among the discard products and original-feed from the FF-SMB strategy.16,17

3. NEW OPERATING VARIABLES FOR RPD STRATEGY Two operating variables were introduced in the PD strategy: discard length (DL), the time duration of the withdrawal product, and discard time (DT), the time gap from the beginning of each switching period to the midpoint of the withdrawal period.15 As mentioned before, the recycling time duration and its flowrate play a key role in the RPD operation. Therefore, two additional variables are introduced in this study: recycle length (RL) and recycle flowrate (RF). 9837



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condition was different from the FF-SMB operated at the fixed flowrate of the feed.

RL (%) = ratio of recycling time of the discarded product portion at the feed node (tF‑ini or tF‑last) to total switching period (tSW) RLext

t t = F ‐ last × 100; RLraf = F ‐ ini × 100 tSW tSW

4. MODELING OF THE SIMULATED MOVING BED PROCESS 4.1. Mathematical Models. To study the RPD operation, the four-zone SMB with two columns per zone (2-2-2-2) was chosen because it is widely considered the standard configuration. In this study, the transport-dispersive model was used as a column model to predict the internal concentration profile and the transient variations in the extract and raffinate concentrations.22 In this model, the mass balance equation was combined with the kinetic equation. The mass transfer kinetics of the solute to the surface of the adsorbent were determined using either the liquid film linear driving force model or the solid film linear driving force model.23 Also, it was assumed that the rates of adsorption and desorption were very fast. In the transport-dispersive model, the differential mass balance is expressed as follows:

(1)

RF (%) = ratio of recycle-feed flowrate (QF,F‑ini or QF,F‑last) to original-feed flowrate during the middle stage of the switching period (tF‑mid in Figure 3) RFext =

Q F,F ‐ last Q F,F ‐ mid

× 100; RFraf =

Q F,F ‐ ini Q F,F ‐ mid

× 100 (2)

∂Ci , j ∂t

+u

∂Ci , j ∂z

+

∂ 2Ci , j 1 − ε ∂qi , j uL DL = = DL 2Np ∂t ε ∂z 2 (3)

where Ci,j and qi,j are the liquid phase and solid phase concentrations of component i (i = A, B) in column j, u is the liquid-phase interstitial velocity, ε is the total porosity, Np is the number of dispersion units, L is the column length, and DL accounts for the axial dispersion. The following linear driving force (LDF) model was used to express the overall mass transfer kinetics across the column:

Figure 3. Complete separation and regeneration region with operating point of flowrate ratio.

Therefore, the recycle length (RLR and RLE) and recycle flowrate (RFE and RFR) can be determined using the recycling time duration and flowrate (QF,F‑ini at tF‑ini and QF,F‑last at tF‑last) at the feed node, as shown in Figures 2a and b. In Figure 2b, the flowrate in the raffinate node is affected by that in the feed node, while the flowrate in the extract node is constant (QE,F‑ini = QE,F‑mid = QE,F‑last = QE). To compare the performances of different operating variables, the standard RPD operation was set under the condition that the flowrate of the recycle-feed was equal to the flowrate of the original-feed; that is, QF,F‑ini = QF,F‑last = QF,F‑mid (QF: feed flowrate in the conventional SMB). Therefore, at the standard RF (RFE = RFR = 100%), the flowrates of zone III, the raffinate node and the feed are the same as those of the conventional SMB and constant during the entire switching period in the RPD operation. In the FF-SMB, the “nonproduct” fraction was set to the part of the product which does not fulfill the purity requirement.16 As an alternative, the “nonproduct” fraction was fixed to the last and initial part of a switching period at raffinate and extract, respectively,17 which is the same as the partial-discard (PD) strategy.15 Naturally, it is also the same as the discarding period (initial stage of extract (tE‑ini) and the last stage of raffinate (tR‑last)) in the RPD operation. In addition, because the raffinate recycle-feed in the RPD operation is injected at the beginning of a switching period, followed by the original-feed and extract recycle-feed, the feeding sequence is the same as the “RFE” in the FF-SMB.17 As a result, the RPD operation at the standard RF was the same as the FF-SMB operation with the feeding sequence “RFE”. On the other hand, since the feed flowrate in the RPD operation can be changed in one switching period by controlling the recycle flowrate (RF), the RPD operation at the other RF

∂qi ∂t

= ki(qi* − qi)

(4)

where ki is the mass transfer coefficient. A nonlinear adsorption equilibrium isotherm was assumed between liquid and solid phases. The Langmuir-type isotherm was used as qi* = fi (C1 , C2) =

K iCi N

1 + ∑i =C1 biCi

(5)

The Langmuir-type isotherm parameters in eq 6 are summarized in Table 1. To solve the mass balance equations, the shift of port position was expressed by updating the initial and boundary conditions of each column at the beginning of each switching period. The initial and boundary conditions of SMB operation are at t = 0:

z = 0:

Ci , j(x , 0) = 0, qi , j(x , 0) = 0

Ci , j = Ciin, j +

DL ∂Ci , j uj ∂z

(6)

(7)

The subscript i indicates the solute, and j is the column number (j = I-1, I-2, II-1, II-2, III-1, III-2, IV-1, and IV-2). For the simulation of the RPD operation, the following relationship for each node was combined with the above column model. Desorbent node:

Q IV ‐ 2 + Q D = Q I ‐ 1 9838

(8)



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Table 1. System and Operating Parameters for Conventional SMB, PD, and RPD Operations

Ci ,F ‐ last = Ci ,E ‐ storage tank during last recycle period in RPD operation (t F ‐ last)

System Parameters

(19)

SMB configuration 2-2-2-2 (8 columns) column diameter, D [cm] 2.6 column length, L [cm] 10.5 total porosity, ε 0.4 number of plate, Np 80 mass transfer coefficient, k [s−1] 0.5 Nonlinear Isotherm Coefficient and Selectivity KA (raffinate component) (−) KB (extract component) (−) bA (raffinate component) (L/g) bB (extract component) (L/g) selectivity Operating Parameters Ci,F (feed concentration) i = A, B (g/L) QF (feed flow rate) (mL/min) QE (extract flow rate) (mL/min) QR (raffinate flow rate) (mL/min) QD (desorbent flow rate) (mL/min) QI (flow rate of zone I) (mL/min) QII (flow rate of zone II) (mL/min) QIII (flow rate of zone III) (mL/min) QIV (flow rate of zone IV) (mL/min) Tsw (switching time) (s)

Raffinate draw-off node:

(k = I, II, III, IV)

(11)

(23)

Cini,j

(12)

Major product concentration [g/L]: (extract) CA̅ ;

Q F ‐ ini = Q R ‐ mid × RR raf

(raffinate) C̅ B

during initial recycle period in RPD operation (t F ‐ ini) (13) Q F ‐ mid = Q F

(24)

CA,E ̅

Purity[%]: (extract)

during middle recycle period in RPD operation (t F ‐ mid) (14)

(raffinate)

Q F ‐ last = Q E ‐ mid × RR ext

CA,E ̅ + C̅ B,E

C̅ B,R CA,R ̅ + C̅ B,R

during last recycle period in RPD operation (t F ‐ last) Recovery[%]: (extract)

(15) in Ciout ,II ‐ 2Q II ‐ 2 + Ci ,F ‐ lQ F ‐ l = Ci ,III ‐ 1Q III ‐ 1

(l = ini, mid, last)

(22)

In these equations, and are the concentrations of component i at the outlet and inlet of column j, respectively, Qj is the flowrate of column j, Ci,F‑l is the concentration of feed component i at stage l (initial, middle, and last) of the recycle period, and Ci,F is the concentration of component i of the feed in the conventional SMB or the original-feed in the RPD operation. 4.2. SMB Performance Parameters. In the PD strategy, the purity can be significantly improved, while the other performance parameters become worse than those of a conventional SMB.15 Therefore, the goal of the RPD strategy is to improve the purity while minimizing the reductions in the other performance parameters. In this study, the performance parameters (purity, recovery, productivity, and eluent consumption) of the RPD operation were evaluated and compared to those of the conventional SMB and PD operations. However, the definitions of these parameters are different for each operation due to the withdrawal and/or recycling in the PD and RPD strategies. These performance parameters of the conventional SMB can be defined as follows:24

(10)

(l = ini, mid, last)

(k = I, II, III, IV)

Cout i,j

Extract draw-off node:

Q II ‐ 2 + Q F ‐ l = Q III ‐ 1

(21)

in Ciout , k − 1 = Ci , k − 2

(9)

in Ciout ,I ‐ 2 = Ci ,II ‐ 1 = Ci ,E Feed node:

in Ciout ,III ‐ 2 = Ci ,IV ‐ 1 = Ci ,R

Q k‐1 = Q k‐2

3 0.568 3.624 2.538 5.594 34.994 31.370 31.938 29.400 233.22

Q I ‐ 2 − Q II ‐ 1 = Q E

(20)

Midnode of zone k:

3.000 3.300 0.030 0.040 1.10

in Ciout ,IV ‐ 2Q IV ‐ 2 = Ci ,I ‐ 1Q I ‐ 1

Q III ‐ 2 − Q IV ‐ 1 = Q R

(raffinate)

(16)

Ci ,F ‐ ini = Ci ,R ‐ storage tank

Q R C̅ B,R Q FC B,F

× 100;

× 100

Q ECA,E ̅ Q FCA,F

(25)

× 100;

× 100 (26)

Productivity [g/(h L)]:

during initial recycle period in RPD operation (t F ‐ ini) (17)

(extract)

Ci ,F ‐ mid = Ci ,F during middle recycle period in RPD operation (t F ‐ mid) (18)

Q ECA,E ̅ Ncolumn(1 − ε)Vcolumn

(raffinate) 9839

;

Q R C̅ B,R Ncolumn(1 − ε)Vcolumn

(27)



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Table 2. Raffinate Product Amount Dependent on the Relationship between the Time Duration case

feed initial stage

feed middle stage

feed last stage

tF‑last > tR‑last tF‑last = tR‑last tF‑last < tR‑last

QR,F‑iniC̅ B,R,F‑initF‑ini QR,F‑iniC̅ B,R,F‑initF‑ini QR,F‑iniC̅ B,R,F‑initF‑ini

QR,F‑midC̅ B,R,F‑midtF‑mid QR,F‑midC̅ B,R,F‑midtF‑mid QR,F‑midC̅ B,R,F‑mid(tF‑mid + tF‑last − tR‑last) (partially discarded)

QR,F‑lastC̅ B,R,F‑last(tF‑lasttR‑last) (partially discarded) no product (discarded) no product (discarded)

Eluent consumption [L/g]: (extract) (raffinate)

QD + QF Q ECA,E ̅

Productivity [g/(h L)]:

;

QD + QF Q R C̅ B,R

(extract)

(28)

In this study, the PD operation was applied to the initial stage of a switching period at the extract node and to the last stage at the raffinate node. A certain amount of the discarded product portion was then recycled into the RPD operation. Therefore, the definitions of recovery and productivity should be reflected by the discard durations in the PD and RPD operations. In addition, the definition of eluent consumption should be modified for the RPD operation because the recycle-feed contains a certain amount of eluent. In the RPD operation, the recovery and productivity equations of raffinate could be expressed in three forms for the condition of discard length (DL) and recycle length (RL) because the raffinate flowrate was changed by controlling the recycle flowrate (RF) even at the fixed flowrate of zone IV. Due to the RF, the raffinate flowrate was changed during a switching period (QR,F‑ini at the feed initial stage, QR,F‑mid at the feed middle stage, and QR,F‑last at the feed last stage) as shown in Figure 2b. Therefore, in the RPD operation, the performance parameters for the raffinate should be presented with these three terms (QR,F‑ini, QR,F‑mid, and QR,F‑last). As shown in Figure 2a, the product last stage (tR‑last) was the discard duration of a raffinate node. Then, the raffinate product was discarded during the feed last stage when the raffinate discard duration is equal to or longer than the feed last stage (tF‑last = tR‑last and tF‑last < tR‑last). Meanwhile, the raffinate product at the feed last stage (QR,F‑lastC̅ B,R,F‑last) was gained from the beginning of the feed last stage to the beginning of the raffinate discard duration (tF‑last − tR‑last) when the raffinate discard duration was shorter than the feed last stage (tF‑last > tR‑last). Similarly, the raffinate product at the feed middle stage was obtained from the beginning of the feed middle stage to the beginning of raffinate discard duration (tF‑mid + (tF‑last − tR‑last)) when the raffinate discard duration was longer than feed last stage (tF‑last < tR‑last). As a result, the raffinate product amount depended on the relationship between the time duration of each feed stage was expressed in Table 2. The applied performance parameters for the PD and RPD operations are as follows:

Recovery [%]: (extract)

(raffinate)

(

(

Q R C̅ B,R 1 − Q FC B,R

Q FCA,F t R ‐ last tsw

t E ‐ ini tsw

)

t E ‐ ini tsw

Ncolumn(1 − ε)Vcolumn

(raffinate)

(

t R − last tsw

Q R C̅ B,R 1 −

;

)


(30)

Eluent consumption [L/g]: QD + QF

(extract)

(

Q ECA,E ̅ 1− (raffinate)

t E − ini tsw

)

;

QD + QF

(

Q R C̅ B,R 1 −

t R − last tsw

)

(31)

For RPD Operation. Major product concentration [g/L]: eq 24 Purity [%]: eq 25 Recovery [%]: (extract)

Q ECA,E ̅ (tsw − t E − ini) Q F,F ‐ midCA,Ft F ‐ mid

× 100 (32)

(raffinate) case I: tF‑last > tR‑last {[Q R,F ‐ iniC̅ B,R,F ‐ init F ‐ ini + Q R,F ‐ midC̅ B,R,F ‐ midt F ‐ mid + Q R,F ‐ lastC̅ B,R,F ‐ last(t F ‐ last − t R ‐ last)] /[Q F,F ‐ midC B,Ft F ‐ mid]} × 100

(33)

(raffinate) case II: tF‑last > tR‑last {[Q R,F ‐ iniC̅ B,R,F ‐ init F ‐ ini + Q R,F ‐ midC̅ B,R,F ‐ midt F ‐ mid] /[Q F,F ‐ midC B,Ft F ‐ mid]} × 100

(34)

(raffinate) case III: tF‑last < tR‑last {[Q R,F ‐ iniC̅ B,R,F ‐ init F ‐ ini + Q R,F ‐ midC̅ B,R,F ‐ mid

For PD Operation. Major product concentration [g/L]: eq 24 Purity [%]: eq 25 Q ECA,E ̅ 1−

(

Q ECA,E ̅ 1−

× (t F ‐ mid + t F ‐ last − t R ‐ last)]/[Q F,F ‐ midC B,Ft F ‐ mid]} (35)

× 100 Productivity [g/(h L)]:

) × 100;

(extract)

) (29)

(

Q ECA,E ̅ 1−

t E ‐ ini tsw

)


(36)

(raffinate) case I: tF‑last > tR‑last 9840



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Table 3. Simulated Runs for Conventional SMB, PD, and RPD Operationsa,b DL [%]

RL [%]

run

DLE

DLR

1 2-1 2-2 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-11 3-12 3-13 3-14 3-15 4-1 4-2 4-3 4-4 4-5

10 20 10 10 10 5 20 10 10 10 10 10 10 10 10 10 10 1.6 3.4 4.8 2.7 1.6

10 20 10 10 10 5 20 10 10 10 10 10 10 10 10 10 10 2.3 4.5 2.3 5.2 6.8

RLE

RF [%]

RLR

20 20 20 20 20 5 10 20 20 20 20 20 20 30 10 10 20 30 17 10

20 20 20 20 20 5 10 20 20 20 20 20 20 10 30 10 20 10 23 30

RFE

feed duration [%] RFR

100 100 100 100 100 100 100 50 150 200 100 100 100 100 100 100 100 100 100 100

100 100 100 100 100 100 100 100 50 50 50 150 200 100 100 100 100 100 100 100

recycle-feed (raf)

concentrated feed

recycle-feed (ext)

0−20 10−30 20−40 0−20 0−20 0−5 0−10 0−20 0−20 0−20 0−20 0−20 0−20 0−10 0−30 0−10 0−20 0−10 0−23 0−30

0−100 0−100 0−100 20−80 0−10, 30−70, 90−10 0−20, 40−60, 80−100 20−80 20−80 5−95 20−80 20−80 20−80 20−80 20−80 20−80 20−80 10−70 30−90 10−90 20−80 10−70 23−83 30−90

80−100 70−90 60−80 80−100 80−100 95−100 90−100 80−100 80−100 80−100 80−100 80−100 80−100 70−100 90−100 90−100 80−100 70−100 83−100 90−100

a

Original-feed concentration, CF,E = CF,R = 3.0 g/L for run 1, 2-1−2-2; CF,E = CF,R = 3.33 g/L for run 3-6; CF,E = CF,R = 3.75 g/L for run 3-7, 4-1; CF,E = CF,R = 5.0 g/L for run 3-1−3-5, 3-8−3-15, and 4-2−4-5. bDTE = DTR = 5%, DTE = DLE/2, DTR = 100 − (DLR/2) for other runs.

⎡ ⎛t ⎞ ⎢Q R,F ‐ iniC̅ B,R,F ‐ ini⎜ F ‐ ini ⎟ ⎢⎣ ⎝ tsw ⎠

(extract)

⎞ ⎛t + Q R,F ‐ midC̅ B,R,F ‐ mid⎜ F ‐ mid ⎟ ⎝ tsw ⎠

t F ‐ mid tsw

Q ECA,E ̅

[Q Dtsw + Q Ft F ‐ mid]/[Q R,F ‐ iniC̅ B,R,F ‐ init F ‐ ini + Q R,F ‐ midC̅ B,R,F ‐ midt F ‐ mid + Q R,F ‐ lastC̅ B,R,F ‐ last × (t F ‐ last − t R ‐ last)]

(37)

(raffinate) case II: tF‑last = tR‑last

(Raffinate) case II: tF‑last = tR‑last

⎡ ⎛t ⎞ ⎢Q R,F ‐ iniC̅ B,R,F ‐ ini⎜ F ‐ ini ⎟ ⎢⎣ ⎝ tsw ⎠

[Q Dtsw + Q Ft F ‐ mid]/[Q R,F ‐ iniC̅ B,R,F ‐ init F ‐ ini + Q R,F ‐ midC̅ B,R,F ‐ midt F ‐ mid]

⎛t ⎞⎤ + Q R,F ‐ midC̅ B,R,F ‐ mid⎜ F ‐ mid ⎟⎥ ⎝ tSW ⎠⎥⎦ /[Ncolumn(1 − ε)Vcolumn]

(41)

(42)

(Raffinate) case III: tF‑last < tR‑last [Q Dtsw + Q Ft F ‐ mid]/[Q R,F ‐ iniC̅ B,R,F ‐ init F ‐ ini (38)

+ Q R,F ‐ midC̅ B,R,F ‐ mid(t F ‐ mid + tF ‐ last − tR ‐ last)] (43)

(Raffinate) case III: tF‑last < tR‑last

A binary mixture with low selectivity (α = 1.1) was selected in this study. The nonlinear isotherm was chosen because the feed concentration was changed by the condition of recycle in the RPD operation.14 The mass transfer coefficient was assumed at 0.5. All of the system parameters are summarized in Table 1. The eight identical columns were designed using the above column models (eqs 3−7) and were connected to each other with global node mass balances (eqs 8−12 and 16−23 for the conventional SMB and PD operation and eqs 8−23 for the RPD operation), as shown in Figure 1a and b. In the column model,

⎡ ⎛t ⎞ ⎢Q R , F ‐ iniC̅ B,R,F ‐ ini⎜ F ‐ ini ⎟ ⎢⎣ ⎝ tsw ⎠ ⎛t + t F ‐ last − t R ‐ last ⎞⎤ + Q R,F ‐ midC̅ B,R,F ‐ mid⎜ F ‐ mid ⎟⎥ tsw ⎝ ⎠⎥⎦ /[Ncolumn(1 − ε)Vcolumn]

(40)

(Raffinate) case I: tF‑last > tR‑last

⎛t − t R ‐ last ⎞⎤ + Q R,F ‐ lastC̅ B,R,F ‐ last⎜ F ‐ last ⎟⎥ tsw ⎝ ⎠⎥⎦ /[Ncolumn(1 − ε)Vcolumn]

( )

QD + QF

(39)

Eluent consumption [L/g]: 9841



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of three runs (run 3-1−3-3) were compared with those at the standard condition (DLE = DLR = 10%, DTE = 5%, DTR = 95%, RLE = RLR = 20%, and RFE = RFR = 100%). The purity and recovery results improved slightly when the raffinate discarded portion and extract discarded portion were recycled near the beginning and the end of a switching period, respectively. The result implies that the raffinate discarded portion needs to be injected to the beginning of a switching period, but the extract discarded portion has to be recycled at the end of a switching period. The next sections discuss the RPD operational results, applied by raffinate and extract recycle-feeds (raffinate recyclefeed + original-feed + extract recycle-feed), simultaneously. 5.2. Effect of Discard Length (DL). Figure 4a−d show the effect of discard length (DL) on the PD and RPD operations (runs 2-0−2-6 in Table 3) when the other variables are fixed to the standard values (run 3-1) in the RPD operations. The RPD operation was only applied to the systems in which DLE was greater than 3.13% and DLR was greater than 4.48% because a minimum amount of recycle-feed was needed to satisfy the other standard values (RLE = RLR = 20% and RFE = RFR = 100%). Compared to the conventional SMB, the purity improved with an increase of the DL in both PD and RPD operations, while the other performance parameters deteriorated.15 In the RPD operation, the recycle-feed with high purity and low concentration is supplied to the system during the recycling stage. Therefore, the raffinate-rich recycle- and original-feeds are injected during the initial stage and the middle stage of the switching period, respectively, and the extract component hardly reaches the raffinate node, while the raffinate component moves far from the extract node along the eluent flow. Thus, Figure 4a shows that the improved level of extract purity in the RPD operation was greater than that in the PD operation. However, the raffinate purity improvement of RPD was slightly lower than that of the PD operation due to the additional feed (recycle-feed). Therefore, the increase of total feed amount by adding the recycle-feed in the RPD operation was advantageous to the extract purity but disadvantageous to the raffinate purity. In Figures 4b−d, the losses of the other performance parameters in the PD operation were also successfully reduced by use of the RPD operation. In particular, at DLE = DLR = 5%, the recovery and productivity were almost the same as those in the conventional SMB because most of the discarded product portion was reused as a recycle-feed. However, they were reduced with an increase in DL because the unused discarded product portion was wasted from the storage tank at the fixed RL and RF. In additional, the eluent consumption at DLE = DLR = 5% in the RPD operation was slightly less than that in the conventional SMB because the recycle-feed contains a certain amount of eluent. This implies that the eluent consumption may be further improved in the RPD operation through control of the recycle-feed amount. This is discussed in section 5.3. 5.3. Effect of Recycle Length (RL). Two cases of RPD operation were studied to elucidate the role of the recycle length (RL), one of the key operating parameters in the RPD operation. The RPD case I used the fixed condition of DLE = DLR = 10% (runs 3-1, 3-6, and 3-7). On the other hand, each discard length (DLE and DLR) was set to recycle more than 90% of discarded portion for desired recycle amount in the RPD case II (runs 4-1−4-3). Figure 5 shows the feed concentration variation composed of original-feed and recycle-feeds at a cyclic steady-state of each run 1, 3-1, 3-6, and 3-7. The longer RL in the initial and last stages was applied to the recycling, the more concentrated original-feed should be supplied to the middle stage in the SMB system

the axial dispersion coefficient was assumed to be the same for all of the components and was constant in all of the columns. The mass transfer coefficient was also assumed to be the same for all of the components. In the RPD operation, it is also assumed that the discard product portion was completely mixed in each storage tank, as in Figures 1b and 2a and d. Initially, the flowrate ratios mj (j = 1, 2, 3, 4) were chosen in the complete separation and regeneration regions to obtain both the extract and raffinate products with higher than 97.5% purity, as shown in Figure 3.24 The flowrate of each zone and the switching period, tsw, were calculated to maximize the feed flowrate satisfying the assumed limitation of flowrate in a column as 35 mL/min (zone I ≤ 35.0 mL/min in this study). The operating parameters in Table 1 were then applied to all the other runs. Therefore, the effects of the new operating variables (DL, RL, and RF) on the RPD operation were systematically evaluated, and the performance of the RPD operation could be compared to those of the conventional SMB and PD operations.

5. RESULTS AND DISCUSSION Two PD runs (run 2-1 and 2-2) and 20 RPD runs (run 3-1−3-15 and run 4-1−4-5) were designed to study the effect of each variable (Table 3). In this study, to compare the performance parameters among the conventional SMB, PD, and RPD operations, discard lengths (DL), recycle lengths (RL), and recycle flowrate (RF) varied for the range of 0−20%, 0−30%, and 50− 200%. The feed duration means the duration from the beginning to the end of each feed injection (extract recycle-feed, raffinate recycle-feed, and original-feed) when the switching period was set from 0 to 100%. To improve purity, the PD operation was applied to the initial stage of the switching period for the extract node and to the last stage for the raffinate node.15 Therefore, the discard times (DT) of the extract and raffinate were then determined at each discard length (DL): DTE = DLE/2, DTR = 100 − (DLR/2) In this study, the same DL values in the PD and RPD operations were applied to the extract and raffinate as a case study. In the case of RLE = RLR = 20%, the original-feed concentration in the RPD operation (which is the same amount of feed as in the conventional SMB) was almost equivalent to the limitation of solubility, and it was injected into the system during only 60% of the total switching period. In this study, since the maximum solubility of the mixture was assumed to be 5 g/L, total RL values (RLE + RLR) were limited to 40% to treat the same amount of the feed in the conventional SMB (run 1). To study the effect of each operating variable on the RPD performance, run 3-1 (DLE = DLR = 10%, DTE = 5%, DTR = 95%, RLE = RLR = 20%, and RFE = RFR = 100%) in Table 3 was selected as the standard run of the RPD strategy. These standard values of DL and RL were chosen arbitrarily, and the standard value of RF was chosen so as to make the flowrates of the recyclefeed and raffinate product node same as the corresponding flowrates in the conventional SMB. 5.1. Effective Injection Time of Recycle-Feed. In Table 4, to verify the proper injection time of each recycle-feed, the results Table 4. Purity and Recovery Results of Runs 3-1−3-3 recycle duration [%]

purity [%]

recovery [%]

run

extract

raffinate

extract

raffinate

extract

raffinate

3-1 3-2 3-3

0−20 10−30 20−40

80−100 70−90 60−80

98.9 98.8 98.7

98.6 98.5 98.5

86.7 86.6 86.6

88.1 88.0 87.9 9842



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Figure 4. Effects of discard length on PD and RPD operations at RLE = RLR = 20%, RFE = 100%, and RFR = 100%: (a) purity, (b) recovery, (c) productivity, and (d) eluent consumption. (solid symbols) RPD operation, (blank symbols) PD operation, (dotted line) raffinate of conventional SMB, (short dashed line) extract of conventional SMB.

Figure 5. Feed concentration profile at each recycle length condition in steady-state RPD operation: (a) extract and (b) raffinate. (solid line) RLE = RLR = 20%, (dashed line) RLE = RLE = 10%, (dashed−dotted line) RLE = RLR = 5%, (dotted line) conventional SMB.

RFR = 100%). And, the blank symbols (triangle for the extract and diamond for the raffinate) in Figure 6 show the results of RPD case II. The extract purity in the RPD operation (cases I and II) enhanced as the RL values increased. At RLE = RLR = 20%, the improved extract purity of RPD operation (cases I and II) was obtained compared to those in the conventional SMB and PD operations (Figure 6a). As mentioned in the principle of the RPD strategy: the extract-rich or raffinate-rich condition in the recycle-feed and the pulse injection of the original-feed

because the same amount of feed had to be treated within the fixed switching period. As a result, an exceedingly long RL leads to an excess supply of overly concentrated original-feed to the SMB in the limited period. The effect of recycle length (RL) on the RPD operation performance is shown in Figure 6. The solid symbols (circle for extract and squire for raffinate) are the results of RPD case I when the other variables were fixed to the standard conditions (DLE = DLR = 10%, DTE = 5%, DTR = 95%, and RFE = 100%, and 9843



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Figure 6. Effects of recycle length on RPD operation. (solid symbols) RPD case I operation at DLE = DLR = 10%, RFE = 100%, and RFR = 100%, (blank symbols) RPD case II operation at RFE = 100% and RFR = 100%): (a) purity, (b) recovery, (c) productivity, and (d) eluent consumption. (dotted line) Raffinate of conventional SMB, (dashed line) Extract of conventional SMB, (dashed−dotted line) Extract of PD operation at DLE = DLR = 10%, (dash− dot−dot line) raffinate of PD operation at DLE = DLR = 10%).

In the FF-SMB, most of the “nonproduct” fraction was recycled to maximize the yield while maintaining a purity threshold.17 Therefore, it becomes the same as the RPD case II operation with little waste of the discarded portion because more than 90% of the discarded portion was recycled at a fixed discard length (DL) of each run. However, it is different from the RPD case I using a part of discarded portion (e.g., 31.3% of extract discarded portion and 44.8% of raffinate discarded portion was recycled at run 3-1). In the RPD case II operation, recycling of the discarded portion was dominant for the separation performance because very small values of DLE and DLR should be applied to the product node (Table 3, run 4-1−4-5). In the RPD case I, however, large values of the DLE and DLR were used to improve the purity so that discarding a product node played one of key roles in the separation performance. Therefore, the RPD case I, called “partial-recycling operation of partial-discard”, could achieve significant improvement of purity at the relative loss of the other performance parameters (Figure 6). Figure 7 shows the column internal concentration profiles of runs 2-1 (PD operation at RLE = RLR = 0% fixed DLE = DLR = 10%), 3-1, 3-6, and 3-7 (RPD operations at RLE = RLR = 5−20%). Each product concentration around the feed node was increased with an increase in the RL due to the higher concentration of the original-feed in the RPD operation. The concentrations of both

contribute to the improvement in purity.14 However, the raffinate purity showed the same or slightly decreased result with an increase in RL as mentioned in section 5.2; the raffinate purity can be damaged from the increased average feed concentration with an increase in recycle-feed amount because the mixture can be moved rapidly to the separation section (zones II and III) by the concentrated original-feed and additional recycle-feed. This phenomenon is explained by the internal concentration profiles detailed later. In Figures 6b−d, nearly linear improvements in recovery, productivity, and eluent consumption were observed as the RL increased due to the increased amount of recycle-feed in the RPD case I operation. Since the flowrate of the extract was higher than that of the raffinate, the reused amount of the components in the extract discarded product portion was smaller than that of the raffinate, even under the same conditions for DL, RL, and the flowrate of recycle-feed (Table 3). Therefore, the improved level was much higher in the raffinate than in the extract. In the RPD case II, compared to the conventional SMB, recovery and productivity were almost the same because of little waste of discarded portion. And the eluent consumption was improved due to the recycle of eluent included in the recycle-feed. As a result, the RPD operation can produce high-purity products, just like the PD operation, and it can also improve other performance parameters much better than the PD operation. 9844



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increased while the raffinate concentration was decreased by the nonlinear effect, and the high-purity recycle-feed. Thus, the extract purity can be enhanced over the full range of RL, as shown in Figure 6a. 5.4. Effect of Recycle Flowrate (RF). The control range of RL can be limited by the solubility of the original-feed in the RPD operation even though a higher RL can significantly contribute to the performance, as shown in Figure 6. As an alternative, flowrate control of the recycle-feed (recycle flowrate, RF) functions as the other operating variable in the RPD operation. Figures 8 and 9 show the effects of RFE (runs 3-4 and 3-8−3-10) and RFR (runs 3-4 and 3-11−3-13), respectively. In both figures, the other variables were fixed at the standard values (DLE = DLR = 10% and RLE = RLR = 20%). The effect of RFE variation is shown in Figure 8 at RFR = 100%. As shown in Figure 8a, the extract purity was increased with an increase in RFE; however, the raffinate purity was significantly decreased with an increased RFE, and its purity at RFE above 150% was less than that of the conventional SMB. An increase in recycle-feed flowrate implies a rapid flowrate in zone III and a high flowrate of raffinate (QR). Therefore, a greater amount of mixture in zone III easily propagates to the raffinate node so that the raffinate purity declines. On the other hand, due to the rapid propagations of the mixture and extract-rich recycle-feed in zone III, the extract purity can be improved with an increase in the feed flowrate. In the low propagation of mixture in zone III (RFE = lower than 100%), the opposite results (a decrease in extract purity and an increase in raffinate purity) were obtained because the mixture in zone III, which contained more raffinate, moved in the direction of the extract node after the switch.

Figure 7. Internal concentration profiles at different recycle lengths: run 2-1 (PD operation: dotted line), run 3-6 (RPD operation: dashed− dotted line, RLE = RLR = 5%), run 3-7 (RPD operation: dashed line, RLE = RLR = 10%) and run 3-1 (RPD operation: solid line, RLE = RLR = 20%) with fixed DLE = DLR = 10%, RFE = 100% and RFR = 100%.

raffinate and extract were then increased between the feed and raffinate nodes because of the skewed peak due to the nonlinear effect.21,26 Therefore, the raffinate purity was slightly decreased by the increased impurity (extract concentration around the raffinate node) at an excessively long RL condition. On the other hand, the extract concentration around the extract node was

Figure 8. Effects of recycle ratio of extract on RPD operation at DLE = DLR = 10%, RLE = RLR = 20%, and RFR = 100%: (a) purity, (b) recovery, (c) productivity, and (d) eluent consumption (same condition as in Figure 7). 9845



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Figure 9. Effects of recycle ratio of raffinate on RPD operation at DLE = DLR = 10%, RLE = RLR = 20%, and RFE = 100%: (a) purity, (b) recovery, (c) productivity, and (d) eluent consumption (same condition as in Figure 7).

The rapid flowrate in zone III during the last feed stage due to the increase in the RFE leads to an increased discard flowrate in the raffinate product node during the last product stage (tR‑last), as shown in Figure 2b. In addition, the waste amount in the raffinate storage tank also increased with a fixed recycle amount of discarded raffinate. As a result, when RFE increased, the other performance parameters (recovery, productivity, and eluent consumption) of raffinate worsened, while those of the extract improved due to greater use of the discard extract and its improved purity (Figures 8b−d). Figure 9 shows the effects of RFR on the RPD operation at RFE = 100%. The variation in performance parameters was different from the results of the RFE effect in Figure 8. All the performances of the extract was hardly changed regardless of the variation in RFR, because the change in flowrate in zone III during the initial stage of the switching period had little effect on the extract product node, as shown in Figure 2b. However, because the increased flowrate in zone III leads to the fast propagation of the mixture, it can be expected to deteriorate the raffinate purity and increase the production of raffinate. In Figure 9a, the raffinate purity worsened with an increase in the RFR, similar to the results of RFE in Figure 8a. However, the variation level of raffinate purity was smaller because of the increased amount of raffinate recycle-feed with high purity. The other performance parameters of raffinate (recovery, productivity, and eluent consumption) improved up to almost the same levels of those of the conventional SMB because of

greater production of raffinate compared to the results of the PD operation. 5.5. Asymmetric Design of Recycle Length. The duration of the original-feed injection can be controlled by the asymmetric design of a recycle length (RL). Therefore, the two operations in RPD case I (runs 3-14 and 3-15) and the three operations in RPD case II (runs 4-3−4-5) were designed to apply various originalfeed durations to RPD operations. Figure 10 shows the performance results of asymmetric design, depending on the duration of the original-feed injection (runs 3−1, 3-14, 3-15, and 4-2−4-5). When the duration of the originalfeed was allocated to the latter part of the total feed duration, raffinate purity, extract recovery, productivity, and eluent consumption were improved while the other performance parameters were deteriorated in RPD case II. On the contrary, the early part of the duration of the original-feed was advantageous to the extract purity and disadvantageous to the raffinate recovery, productivity, and eluent consumption. The results are similar to the previous studies for the feed variation.12,13 In the RPD case I, all the performance parameters of raffinate were improved when the original-feed injected to the latter part of total feed duration because more discarded raffinate portion could be recycled through large RLR. However, the reduction of extract yield was caused by the reduced recycling amount of extract discarded portion. 9846



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Figure 10. Asymmetric design of recycle length. (solid symbols) RPD case I operation at DLE = DLR = 10% and RFE = RFR = 100%, (blank symbols) RPD case II operation at RFE = RFR = 100%: (a) purity, (b) recovery, (c) productivity, and (d) eluent consumption (same condition as in Figure 7).

6. CONCLUSION In this study, the recycling strategy applied to the partial-discard strategy was considered as recycling partial-discard (RPD) . The effects of each operating variable to the recycle feeds on the RPD operation were rigorously investigated. In a conventional SMB, the initial and last stages of a switching period have a significant effect on the raffinate and extract products, respectively. In addition, the flowrate of each product node is generally higher than the feed flowrate in the conventional SMB because of the addition of eluent. Therefore, the proper recycling time and amount of product to be withdrawn from the partial-discard (PD) operation within a switching period can improve all the performance parameters of the conventional SMB and PD operations. The new operating variables recycle length (RL) and recycle flowrate (RF) were suggested for use in the RPD strategy in order to determine the time duration and flowrate of the recyclefeed, respectively. Compared to the PD operation, products with higher purity could be produced by the RPD operation. Simultaneously, the reductions in the other performance parameters (recovery, productivity, and eluent consumption) that stemmed from the PD operation could be successfully lessened by controlling RL and RF in the RPD operation. The increase in RL could contribute significantly to the improvement of performance in the RPD operation. However, because a longer RL leads to injecting a higher concentration of

original-feed into the system, the control of RL is limited by the solubility of the original-feed. As an alternative, flowrate control of the recycle-feed (RF) could be applied to the RPD operation. The increase in RFE led to improvements in all of the performance parameters of the extract product; however, the opposite results were observed in the raffinate product. On the other hand, the increase in RFR enhanced the recovery, productivity, and eluent consumption of the raffinate, while it slightly worsened the raffinate purity. RFR hardly affected the extract product. In the RPD operation, the original-feed (pulse feed) can be concentrated to the solubility limit by using a short feed middle stage (tF‑mid). Since the short feed middle stage leads to the long time duration of a recycle-feed, a greater amount of the discarded portion can be recycled. Therefore, the higher solubility limit contributes to better performance in the RPD operation while lower solubility limit leads to weakening the advantages of the RPD operation. Because the raw feed in the RPD operation is supplied to the SMB unit for a limited time during the switching period, its concentration exceeds that of the conventional SMB, allowing it to handle the same amount of raw feed for the same duration. Therefore, application of the RPD operation may be limited by an upper boundary of solubility in practical applications. In addition, an optimization study of the RPD operation is needed in the future because three degrees of freedom (discard length 9847



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from PD operation and recycle length and recycle flowrate from RPD operation) were added to the conventional SMB.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-2-2123-2762. Fax: +82-2-312-6401. E-mail: leech@ yonsei.ac.kr.

DT = discard time RL = recycle length RF = recycle flowrate

REFERENCES

(1) Broughton, D. B. Molex: Case history of a process. Chem. Eng. Prog. 1968, 64, 60−65. (2) Broughton, D. B. Production-scale adsorption separation of liquid mixtures by simulated moving-bed technology. Sep. Sci. Technol. 1984, 19, 723−736. (3) Stinson, S. C. Chiral drugs. Chem. Eng. News 1995, No. October 9, 44−74. (4) Lim, Y. I.; Lee, J. S.; Bhatia, S. K.; Lim, Y. S.; Han, C. Improvement of para-Xylene SMB Process Performance on an Industrial Scale. Ind. Eng. Chem. Res. 2010, 49, 3316−3327. (5) Branch, S. K.; Subramanian, G. Chiral Separation Techniques a Practical Approach; Wiley−VCH: Weinheim, 2001; pp 317−341. (6) Kinkel, J. N.; Schulte, M.; Nicoud, R. M.; Charton, F. Proceedings of Chiral Europe ’95 Symposium; Spring Innovations: Stockport, 1995; pp 121−132. (7) Gattuso, M. J.; McCulloch, B.; House, D. W.; Baumann, W. M.; Gottschall, K. Chimica oggi. 1996, 11, 17−20. (8) FDA. Chirality 1992, 4, 338−340. (9) Rajendran, A.; Paredes, G.; Mazzotti, M. Simulated moving bed chromatography for the separation of enantiomers. J. Chromatogr. A 2009, 1216 (4), 709−738. (10) Francotte, E. Contribution of preparative chromatographic resolution to the investigation of chiral phenomena. J. Chromatogr. A 1994, 666, 565−601. (11) Ludemann-Hombourger, O.; Nicoud, R.; Bailly, M. The “VARICOL” Process: A New Multicolumn Continuous Chromatographic Process. Sep. Sci. Technol. 2000, 35, 1829−1862. (12) Zhang, Z.; Mazzotti, M.; Morbidelli, M. PowerFeed operation of simulated moving bed units: changing flow-rates during the switching interval. J. Chromatogr. A 2003, 1006, 87−99. (13) Zang, Y.; Wankat, P. C. SMB Operation Strategy−Partial Feed. Ind. Eng. Chem. Res. 2002, 41, 2504−2511. (14) Schramm, H.; Kienle, A.; Kaspereit, M.; Seidel-Morgenstern, A. Improved operation of simulated moving bed processes through cyclic modulation of feed flow and feed concentration. Chem. Eng. Sci. 2003, 58, 5217−5227. (15) Bae, Y. S.; Lee, C. H. Partial-discard strategy for obtaining high purity products using simulated moving bed chromatography. J. Chromatogr. A 2006, 1122, 161−173. (16) Keßler, L. C.; Seidel-Morgenstern, A. Improving performance of simulated miving bed chromatography by fractionation and feed-back of outlet streams. J. Chromatogr. A 2008, 1207, 55−71. (17) Li, S.; Kawajiri, Y.; Raisch, J.; Seidal-Morgenstern, A. Optimization of simulated moving bed chromathgraphy with fractionation and feedback: Part II. Fractionation of both outlets. J. Chromatogr. A 2010, 1217, 5349−5357. (18) Gomes, P. S.; Rodrigues, A. E. Outlet streams swing (OSS) and ultiFeed operation of simulated moving beds. Sep. Sci. Technol. 2007, 42, 223−252. (19) Mun, S. Improving performance of a five-zone simulated moving bed chromatography for ternary separation by simultaneous use of partial-feeding and partial-closing of the product port in charge of collecting the intermediate-affinity solute molecules. J. Chromatogr. A 2011, 1218, 8060−8074. (20) Kim, K. M.; Bae, Y. S.; Moon, J. H.; Lee, S. J.; Lee, C. H. Improved partial-discard strategy for simulated moving bed chromatography: Nonlinear condition. FOA9, Sicily, Italy, May 2007. (21) Lee, H. H.; Kim, K. M.; Lee, C. H. Improved performance of simulated moving bed process using column-modified feed. AIChE J. 2011, 57, 2036−2053. (22) Pais, L. S.; Loureiro, J. M.; Rodrigues, A. E. Modeling strategies for enantiomers separation by SMB chromatography. AIChE J. 1998, 44, 561−569.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of the Advanced Biomass R&D Center (ABC) of Korea Grant (2011−0028382) funded by the Ministry of Education, Science and Technology is gratefully acknowledged.

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NOMENCLATURE Ki = first Langmuir isotherm parameter of component i (−) bj = second Langmuir isotherm parameter of component i (L/g) qi = solid phase concentration of component i (g/L) q*i = equilibrium solid phase concentration of component i (g/L) Ci = liquid phase concentration of component i (g/L) Ci,F = concentration of feed in the SMB (g/L) u = the liquid-phase interstitial velocity (cm/s) in Cout i,j , Ci,j = concentrations of component i at the outlet and the inlet of column j (g/L) DL = the axial dispersion coefficient (m2/s) k = mass transfer coefficient (1/s) D = diameter of a column (cm) L = length of a column (cm) Np = number of dispersion units (−) Ncolumn = number of columns of the SMB system (−) Qj = flowrates of zone or column j (mL/min) QD, QE, QF, QR = desorbent, extract, feed, and raffinate flow rates (mL/min) QF,F‑l = feed flow rates at the feed l stage of a switching period (mL/min) QR,F‑l = raffinate flow rates at the feed l stage of a switching period (mL/min) t = time (s) tsw = switching period in the conventional SMB operation (s) tF‑l = l stage of a switching period in the feed node tE‑l = l stage of a switching period in the extract node tR‑l = l stage of a switching period in the raffinate node Vcolumn = volume of one column in SMB (L)

Greek Letters

α = selectivity (−) ε = total column porosity (−) Subscripts

D = desorbent E = extract F = feed R = raffinate i (A, B) = components j = column or inlet/outlet ports l = stage of a switching period k = zone Abbreviations

PD = partial-discard RPD = recycling partial-discard DL = discard length 9848



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(23) Guiochon, G.; Shirazi, S. G.; Katti, A. M. Fundamentals of Preparative and Nonlinear Chromatography; Academic Press: Boston, MA, 1994. (24) Bae, Y. S.; Kim, K. M.; Moon, J. H.; Byeon, S. H.; Ahn, I. K.; Lee, C. H. Effects of flowrate ratio on startup and cyclic steady-state behaviors of simulated moving bed under linear conditions. Sep. Purif. Technol. 2008, 62, 148−159. (25) Mazzotti, M.; Storti, G.; Morbidelli, M. Optimal operation of simulated moving bed units for nonlinear chromatographic separations. J. Chromatgr. A 1997, 769, 3−24. (26) Zhong, G.; Guiochon, G. Simulated moving bed chromatography. Effects of axial dispersion and mass transfer under linear conditions. Chem. Eng. Sci. 1997, 52, 3117−3132.

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Improved Performance of a Simulated Moving Bed Process by a

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