Two-Zone SMB Process for Binary Separation - ACS Publications

In this research, we design a new two-zone SMB system for binary separation. The basic proposed two-zone SMBs are shown in Figure 2. The 2-zone SMB us...
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Ind. Eng. Chem. Res. 2005, 44, 1565-1575

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Two-Zone SMB Process for Binary Separation Weihua Jin and Phillip C. Wankat* Purdue University, School of Chemical Engineering, Forney Hall of Chemical Engineering (FRNY), 480 Stadium Mall Drive, West Lafayette, Indiana 47907-2100

Two-zone simulated moving bed (SMB) systems with a storage tank were developed for binary separation. Simulations were done with Aspen Chromatography for the linear dextran T6raffinose mixture and the nonlinear binaphthol enantiomers mixture. The results for these linear isotherms show that two-zone SMBs give purities comparable to those obtained for a four-zone SMB with the same productivity and desorbent-to-feed ratio (D/F). At D/F ) 2.794, the purities obtained in a two-zone decoupled SMB for dextran T6 and raffinose are 94.5% and 97.6%, respectively, whereas in a two-zone coupled SMB, the purities are 95.0% and 97.5%, respectively, compared to a four-zone SMB’s purities of 96.1% and 96.6%, respectively. The results for the nonlinear isotherms show that these two-zone SMB systems can obtain good separation but with more desorbent than required for a four-zone SMB. Simulations for two-zone SMBs with one column per zone show that partial feed can improve the product purities and recoveries considerably, particularly at the optimum feed length. Early feed introduction increases the raffinose purity, whereas late feed introduction increases the dextran T6 purity. Partial-feed operation shows very modest improvement in raffinate purity for the binaphthol enantiomers system. The results for two-zone SMBs with multiple columns per zone show that adding more columns per zone is not always beneficial for separation in two-zone SMBs for both linear and nonlinear isotherms. Introduction Simulated moving bed (SMB) technology can be used to do large-scale continuous chromatographic separation of fine chemicals and enantiomers. Compared to batch chromatography, SMBs have high productivity and low eluent consumption, particularly for high-purity products. SMB systems have been used commercially for the separation of liquid mixtures since their commercialization by UOP (Universal Oil Products) in the 1960s demonstrated that they were an efficient means for doing large-scale chromatographic separation, particularly of binary mixtures.1-4 In the past decade, attention has increased, and SMBs are now extensively used for large-scale fractionation or purification of numerous mixtures of importance ranging from petrochemicals2-4 to pharmaceuticals.5-7 The basis for a simulated moving bed is the continuous countercurrent true moving bed (TMB). In the true moving bed, the liquid moves up the column while the solid moves down. Unfortunately, it is very difficult to avoid axial mixing of the solid particles. To avoid mixing, the simulated moving bed (SMB) was developed. The simulated moving bed preserves most of the TMB’s benefits but without the problems associated with moving the solid adsorbent by using a fixed-bed system with multiple columns or multiple sections. To simulate the countercurrent movement of the solid and fluid achieved in the TMB, the inlet and outlet ports of the SMB are switched from one position to the next at the end of each switch period, as illustrated in Figure 1 for a four-zone SMB. In this paper, the Arabic numerals inside the columns indicate columns, and the Roman numerals outside the columns indicate zones. The columns are fixed. At the end of each switch period, the * To whom correspondence should be addressed. Tel.: 765494-7422. Fax: 765-494-0805. E-mail: [email protected].

Figure 1. Complete cycle for a four-zone SMB with one column per zone. A is the less-retained component, and B is most-retained, KA < KB. A, raffinate; B, extract; F, feed; D, desorbent.

inlet and outlet ports are moved up one column, and when a port reaches the top of the columns, it is recycled back down to the bottom. The more columns there are per zone, the closer the SMB is to a TMB. Although the most widely used scheme among simulated moving bed separation processes is the four-zone SMB, usually with multiple columns per zone, there are alternative schemes that might be more suited to various particular cases. The three-zone SMB has been widely studied.8,16 In the classical operation of the threezone SMB, the desorbent stream is not recycled;8,16 therefore, the solution exiting zone I is the raffinate product. Compared to a four-zone SMB, the classic three-zone system has insufficient use of the desorbent, and significant dilution of the raffinate stream occurs. The performance of a three-zone SMB can be improved significantly by using partial feed and selective withdrawal.8

10.1021/ie040132r CCC: $30.25 © 2005 American Chemical Society Published on Web 01/28/2005

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listed in Tables 1 and 2, respectively. A lumped parameter linear driving force model was used for mass transfer11,12

∂q ) kmap(c - c*) ∂t

Figure 2. System configuration for a two-zone SMB with one column per zone. Decoupled is without the dotted-line connection; coupled is with the dotted-line connection. D1 ) 0 for coupled. D1, Dopt are desorbent inputs.

A one-zone analogue to the SMB was developed by Abunasser et al.9 The analogue system is a single adsorption column with an appropriate number of tanks, and it uses fluid recycling to mimic an SMB. The simulation results show that the one-zone analogue to the four-zone SMB gives lower purities but is more flexible than the SMB. A two-zone SMB different from the one proposed here was developed and tested by Lee.10 From the experimental results, he concluded that a two-section SMB with six columns per zone can reach the same fractionation efficiency as a classical three-zone SMB. Lee’s system had only two sections with different flow rates: prefeed and postfeed. The products come out in the order of slow- and fast-moving components because of the difference of exit time of each component. In this research, we design a new two-zone SMB system for binary separation. The basic proposed twozone SMBs are shown in Figure 2. The 2-zone SMB uses a two-step process. First, feed is introduced between zones I and II while some desorbent is recycled from zone I to zone II and the remaining desorbent exiting zone I is sent to the tank. In the second step (without feed) fresh desorbent and desorbent from the tank is used to produce products. The raffinate product is withdrawn from zone I and the extract product from zone II. At the end of the second step, the ports are switched and process repeats. The system in Figure 2 without the dotted lines during step b is a “decoupled” SMB because of the decoupled B (extract) product, whereas the system with dotted lines and without desorbent D1 input is a “coupled” SMB. In these twozone SMBs, zone I does the separations done in zones I and II of the four-zone SMB (Figure 1), and zone II does the separations done in zones III and IV of the fourzone SMB. The tank holds desorbent temporarily for later use. The performance of the decoupled and coupled two-zone SMBs is studied for both linear and nonlinear isotherm systems. Partial-feed operation8,12 is also applied to these systems while keeping the productivity constant. Simulations The processes were modeled and simulated using Aspen Chromatography v11.1. System and operating parameters used for the linear dextran T6-raffinose and the nonlinear binaphthol enantiomers systems are

(1)

The local equilibrium theory was used to estimate initial values for the flow rates. This theory assumes that the mass-transfer rates in the system are very high, so that the fluid and solid can be considered to be in equilibrium locally.1 The equilibrium solution has been extensively applied to analyze SMB systems with both linear and nonlinear isotherms. To simplify the explanation, the analyses shown below are restricted to linear isotherms; however, the new SMB processes are also applicable to nonlinear isotherms. For linear isotherms, the velocity is given by1

usolute i,zone j )

vj

) 1 - p (1 - e)(1 - p) 1+ K + Fs K i e p Di e (C′i)vj ) (Ci)vsuper,j (2)

where ui is the velocity of the solute, vj is the interstitial velocity of the fluid; vsuper,j is the superficial velocity; e is the external void fraction; p is the internal void fraction; KDi is the fraction of the interparticle volume that species can penetrate; Ki is the equilibrium parameter, where Ki ) q/c; C′i is the solute movement constant associated with the interstitial velocity; and Ci is the solute movement constant associated with the superficial velocity, Ci ) C′i/e. The equilibrium analysis can be applied to the twozone SMBs in Figure 2 to determine the appropriate flow rates in each zone. The superficial velocities in each section and each step must satisfy the following set of equations for a two-zone decoupled SMB

v1aCAta ) MaL

(A not at breakthrough, Ma e1) (3)

v1aCBta + v1bCBtb ) MbL (B not at breakthrough, Mb e1) (4) v1bCAtb + v2aCAta ) McL (trailing edge of A exits column, Mc g 1) (6) v1bCBtb + v2aCBta + v2bCBtb ) MdL (trailing edge of B exits column, Md g 1) (6) where v1a, v2a, v1b, and v2b are superficial velocities and ta and tb are the operation times of steps a and b, respectively. A is the less-retained component, and B is the more-retained component. In the two-zone coupled SMB, only the last equation is different

v2aCBta + v2bCBtb ) MdL (trailing edge of B exits column, Md g 1) (7)

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005 1567 Table 1. System and Operating Parameters for the Dextran T6-Raffinose System12,16 System Parameters column length column diameter external void fraction internal void fraction adsorbent particle radius liquid density mass-transfer coefficient (dextran T6) mass-transfer coefficient (raffinose) initial liquid height of tank tank diameter initial concentration for both solutes in the tank feed concentrations for all configurations feed flow rate for all configurations

L Dcol e p Rp F kmap (dextran T6) kmap (raffinose) H dtank cT

35.625 cm 1.4 cm 0.45 0 0.0011 cm 1.0 g/mL 0.0469 1/s 0.0570 1/s 1.0 cm 1.0 cm 0 g/L

Operating Parameters cF,i, i ) D, R feed flow rate

50.0 g/L 1.0 cm3/min

Table 2. System and Operating Parameters for the Binaphthol Enantiomers System6,18 System Parameters column length column diameter external void fraction internal void fraction adsorbent particle radius liquid density liquid viscosity mass-transfer coefficient (A) mass-transfer coefficient (B) initial liquid height of tank tank diameter initial concentration for both solutes in the tank feed concentrations for all configurations feed flow rate for all configurations

feed volume/time total adsorbent volume

(8)

This condition can be relaxed. For a two-zone decoupled SMB, the mass balance equations for step a are (assuming constant densities)

vD,to_tank ) vF

(9a)

vF ) v1a - v2a

(9b)

The mass balance equations for step b are

vD1 ) v1b

(9c)

vD,opt + vD,from_tank ) v2b

(9d)

The tank filled in step a will be emptied in step b, the mass balance equation is (assuming ta ) tb)

vD,to_tank ) vD,from_tank

21.0 cm 2.4 cm 0.40 0 0.0016 cm 0.6 g/mL 0.876 cP 0.5 1/s 0.5 1/s 1.0 cm 1.0 cm 0 g/L

Operating Parameters cF,i, i ) D, R feed flow rate

We arbitrarily kept ta ) tb ) tsw/2 so that Figures 1 and 2 have the same productivities, which are defined as

productivity )

L Dcol e p Rp F µ kmap (A) kmap (B) H dtank cT

(9e)

where vF is the feed velocity, vD,to_tank is the fluid velocity into the tank, vD,from_tank is the fluid velocity out of the tank, and vD1 and vD,opt are the desorbent input velocities. For the two-zone coupled SMB, eq 9c is not needed. Equations 2-7 and 9 are the design equations for the linear two-zone SMB. The Mi values are multipliers or safety factors. These equations were used to calculate the flow rates needed for the simulations with different values of the multipliers. Alternative approaches are

10.0 g/L 3.64 cm3/min

“triangle theory”13 and “standing wave theory”,14,15 which were developed from the equivalent TMB model. Results for Linear Isotherms The adsorbent used in the dextran T6-raffinose system is silica gel, and the operation temperature is 25 °C. The isotherms are linear at low concentrations.12,16

dextran T6:

qD ) 0.23cD

(10a)

raffinose:

qR ) 0.56cR

(10b)

A four-zone SMB with one column per zone and both the decoupled and coupled two-zone SMBs with one column per zone were simulated. The simulations were run with a feed composition of cF ) 50.0 g/L for each component. The desorbent used was pure water. The values of multipliers were changed to achieve, first, maximum average purity of these two components and, second, an extract purity of 99.9% and the best raffinate purity with fixed D/F values. To find the optimal purities, one of the multipliers was changed with the others fixed. By this trial-and-error method, the nearoptimal superficial flow rates in each zone and each step were determined (Table 3). Flow rate set 1 is for the maximum average purity, and flow rate set 2 is for an extract purity of 99.9%. Although we selected two value functions (maximum average purity and extract purity ) 99.9%) as examples, the optimization procedure can be done for any value function. Notice that the productivities of the four-zone and two-zone SMBs are equal to allow comparison of the systems at the same efficiency. The use of identical column dimensions is also appropriate for the use of off-

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Table 3. Near-Optimal Superficial Flow Rates of Four-Zone and Two-Zone SMBs for Linear Isotherms at D/F ) 2.794 two-zone SMB flow rate (cm3/s)

four-zone SMB

decoupled

coupled

zone I step a zone II step a zone I step b zone II step b Dto_tank Dfrom_tank D1 Dopt

Set 1 0.0787 (zone I) 0.1057 (zone II) 0.0891 (zone III) 0.1251 (zone IV) -

0.0682 0.0516 0.0264 0.0365 0.0166 0.0166 0.0264 0.0200

0.0682 0.0516 0.0264 0.0630 0.0166 0.0166 0.0464

zone I step a zone II step a zone I step b zone II step b Dto_tank Dfrom_tank D1 Dopt

Set 2 0.0649 (zone I) 0.0983 (zone II) 0.0817 (zone III) 0.1112 (zone IV) -

0.0351 0.0185 0.0382 0.0248 0.0166 0.0166 0.0382 0.0082

0.0351 0.0185 0.0382 0.0630 0.0166 0.0166 0.0464

Table 4. Purity Comparisons of Four-Zone and Two-Zone SMBs for Linear Isothermsa two-zone SMB four-zone SMB

decoupled

coupled

dextran T6 purity (%) raffinose purity (%) average purity (%) dextran T6 recovery (%) raffinose recovery (%) average recovery (%)

Set 1 96.1 96.6 96.4 96.9 95.9 96.4

94.5 97.6 96.1 97.6 94.3 96.0

95.0 97.5 96.3 97.6 94.9 96.3

dextran T6 purity (%) raffinose purity (%) average purity (%) dextran T6 recovery (%) raffinose recovery (%) average recovery (%)

Set 2 74.1 99.9 87.0 99.8 65.0 82.4

73.0 99.9 86.5 99.9 63.3 81.6

73.4 99.9 86.7 99.9 64.0 82.0

a In all cases, D/F ) 2.794 and productivity ) 0.004 56 (cm3 of feed/min)/(cm3 of adsorbent).

Figure 3. Partial-feed operation for step a in two-zone SMBs. tF, feed length; tft, feed time (refer to step a in Figure 2).

linear and the two components are relatively easy to separate, the purities are very close to each other. The effect of mixing in the tank can be studied by dividing the tank into smaller tanks.9 The original tank was split into two tanks with volumes equal to one-half that of the original tank. The tanks were emptied in the order in which they were filled. The simulation results for a two-zone coupled SMB gave a raffinate purity of 95.1% and an extract purity of 97.6% with two tanks, whereas with one tank (Table 4, set 1), the raffinate purity was 95.0%, and the extract purity was 97.6%. Unlike the one-column analogue,9 the improvement is very modest, probably because component concentrations in the tank are low. Thus, in this example, adding more tanks does not improve product purities significantly. In the rest of this paper, the systems will be optimized only for maximum average purity with constant productivity. Partial-Feed Results for Linear Isotherms

the-shelf systems or for retrofitting, which have fixed column dimensions. In the optimization procedure, the flow rates are changed rather than the length and diameter of the columns. The simulation results are reported in Table 4 for both optimization cases, which show that, for linear isotherms, two-zone SMBs give average purities (for both sets 1 and 2) that are slightly lower than but comparable to those of a four-zone SMB with the same productivity. Decoupled and coupled two-zone SMBs have similar separation behaviors, although the two-zone coupled SMB is typically slightly better. The recoveries of dextran T6 in the two-zone SMBs are slightly better than that in the four-zone SMB; however, the recoveries of raffinose in the two-zone SMBs are worse than that in the four-zone SMB, which makes the average recoveries of two-zone SMBs slightly worse than that for the four-zone SMB. In general, the average recovery of the coupled two-zone SMB is slightly better than that of the decoupled two-zone SMB. The results also show that the comparison is consistent for different value functions. The lower purities and recoveries of the two-zone SMBs are probably due to the mixing in the tanks, whereas the four-zone SMB retains concentration profiles in the columns. This effect also occurs with the one-zone analogue to the SMB.9 Because these isotherms are

In partial-feed operation,8,12 the feed flow rate changes from a continuous constant flow (total feed) to a discontinuous pulse flow (Figure 3). Only the flow rates in the two zones change during step a according to the change in feed flow rate, whereas the flow rates of the desorbent, extract, and raffinate are maintained constant. Although the feed flow rate is changed, the feed amount for each switching period is kept the same as in total-feed operation

[(feed flow rate)ta]total feed ) [(feed flow rate)tF]partial feed

tF e ta (12)

which keeps the productivity, eq 8, constant. Partial-feed operation introduces two additional degrees of freedom: the “feed length” and the “feed time”. Feed length (tF) refers to how long the feed lasts, which is the length of the second interval in Figure 3. Feed time (tft) defines the time when the center of the feed pulse enters the column. The operation does not have to be symmetric. The separation efficiency of a partialfeed SMB will depend on the choice of these two parameters. Partial feed has been shown to be effective in improving the separation both for four-zone SMBs12 with one column per zone and for three-zone SMBs.8

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005 1569 Table 5. Superficial Flow Rates (cm3/s) of Two-Zone SMBs for Partial-Feed Operationa at D/F ) 2.794: Linear Isotherms zone I step a without feed zone II step a without feed zone I step a with feed zone II step a with feed zone I step b zone II step b Dto_tank without feed Dto_tank with feed Dfrom_tank D1 Dopt a

decoupled

coupled

0.0516 0.0516 0.1346 0.0516 0.0264 0.0365 0 0.0830 0.0166 0.0264 0.0200

0.0516 0.0516 0.1346 0.0516 0.0264 0.0630 0 0.0830 0.0166 0.0464

tF/tsw ) 0.1.

The system and operating parameters for the simulations are listed in Table 1. The multipliers are the nearoptimal values for total-feed operation at D/F ) 2.794. The flow rates are listed in Table 5. For the same average feed rate under total-feed and partial-feed operations, the latter shows significant improvement in product purities and recoveries compared with the former (Table 6). The recovery of one component is controlled by the purity of the other component with constant product flow rates. Higher dextran T6 purity gives a higher raffinose recovery, and vice versa. The influences of feed length and feed time are shown in Figure 4. The points at tF/ta ) 1.0 in Figure 4a and b represent total-feed operation. If the feed length is shortened, the leading edge of the raffinose further departs from the raffinate product, as does the trailing edge of the dextran T6 from the extract product. Thus, the products are initially purer. On the other hand, shortening the feed length increases the velocity, which reduces the retention time and limits the extent to which feed length can be shortened (Figure 4a and b). Figure 4c and d shows the influence of feed time. Early feed introduction increases raffinose purity, whereas late feed introduction increases dextran T6 purity. An early feed pulse moves the dextran T6 characteristics further from the raffinose product and reduces the dextran T6 impurity in the extract product. However, the early feed moves the raffinose characteristics toward the dextran T6 product and makes the raffinose spend a longer time in the SMB columns, thereby increasing dispersion compared to late feed. Thus, the dextran T6 product purity is reduced. As expected, a late feed time increases the dextran T6 purity and decreases the raffinose purity. A compromise is to input the feed near the center of the step. These results are qualitatively similar to the results obtained for four-zone SMBs with partial feed.12 The purities and recoveries of four-zone and two-zone SMBs for total and partial feed are listed in Table 6. The results show that the dextran T6 purity of partialfeed operation has 3.4% and 3.5% improvements and the dextran T6 recovery of partial-feed operation has 1.4% and 1.3% improvements for decoupled and coupled two-zone SMBs, respectively, compared to total feed. The raffinose purity has 2.0% and 1.2% improvements, and raffinose recovery has 3.1% and 3.5% improvements for decoupled and coupled two-zone systems, respectively. The two-zone SMB systems with partial feed produce higher-purity products than the four-zone totalfeed SMB. Because partial-feed operation also improves the four-zone SMB, the highest purities are obtained with the four-zone SMB with partial feed. An alterna-

tive use of partial feed is to reduce desorbent consumption with constant productivity and product purities. Results for Nonlinear Isotherms The adsorbent used in the binaphthol enantiomers system is 3,5-dinitrobenzoyl phenylglycine bonded silica gel, and the operation temperature is 25 °C. This system is modeled with a variable dispersion coefficient that was estimated using the Chung and Wen correlation for each component.17 The isotherms for this adsorption system are correlated by bi-Langmuir-type isotherms6,18

q/A )

2.69cA 0.10cA + (12a) 1 + 0.0336cA + 0.0466cB 1 + cA + 3cB

q/B )

3.73cB 0.30cB + (12b) 1 + 0.0336cA + 0.0466cB 1 + cA + cB

A is the less strongly adsorbed component, and B is the more strongly adsorbed component. The system was simulated in the nonlinear (cA,F ) 10.0 g/L, cB,F ) 10.0 g/L) region. The system and operating parameters are listed in Table 2. The values of multipliers were changed to achieve the maximum average purity of these two components at the same D/F. The near-optimal flow rates are listed in Table 7. The results for both the four-zone SMB with one column per zone and the two-zone coupled SMB with one column per zone are shown in Figure 5. The purities increased with increasing D/F for both systems. The corresponding purities achieved with the two-zone coupled SMB were lower than those obtained with the four-zone SMB in all cases. The differences between the extract and raffinate purities decrease as D/F increases. From Figure 5, the increase in D/F needed in the twozone coupled SMB to achieve the same purity as obtained in the four-zone SMB can be determined. For example, in Figure 5, the horizontal line shows that D/F ) 2.2 is needed for a two-zone coupled SMB to achieve the same extract purity as a standard four-zone SMB at D/F ) 1.0 with the same productivity. The results for the two-zone decoupled SMB are shown in Figure 6. Comparison with Figure 5 shows that the trends are different than for the two-zone coupled SMB. The raffinate purity in the two-zone decoupled SMB does not increase as much as that in the two-zone coupled SMB with increasing D/F. This difference is probably due to the diffuse wave of B formed in the nonlinear decoupled system when desorbent D1 is added (Figure 2). This results in the zone spreading of zone II of step b and contamination of the raffinate product by component B. The use of pure desorbent for D1 has a much larger impact for nonlinear than for linear isotherms. Partial-Feed Results for Nonlinear Isotherms The simulations for two-zone SMBs with partial-feed operation had feed concentrations of 10 g/L for each component and D/F ) 4.0. The system and operating parameters are listed in Table 2, and the superficial flow rates are listed in Table 7. For the same average feed rate under total-feed and partial-feed operations, the latter shows improvement in product purities compared with the former. The influences of feed length and feed time are shown in Figure 7. The points at tF/ta ) 1.0 in

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Table 6. Purity Comparisons between Total-Feed Operation and Near-Optimal Partial-Feed Operation at D/F ) 2.794 for Linear Isotherms two-zone SMB four-zone SMB dextran T6 purity (%) raffinose purity (%) average purity (%) dextran T6 recovery (%) raffinose recovery (%) a

decoupled

coupled

total

partiala

totalb

partiala

totalb

partiala

96.1 96.6 96.4 96.9 95.9

98.4 98.9 98.7 99.6 99.1

94.2 97.0 95.6 97.6 94.3

97.4 98.9 98.2 99.0 97.3

95.1 97.5 96.3 97.6 94.9

98.4 98.7 98.6 98.9 98.2

tF/tsw ) 0.1. b tF/ta ) 1.

Figure 4. Partial-feed results for a two-zone SMB for separation of dextran T6 and raffinose (linear) at D/F ) 2.794. Influence of feed length (feeds are introduced in the middle of the switch time) for (a) decoupled and (b) coupled SMBs. Influence of feed time (feed lengths are 0.2tsw) for (c) decoupled and (d) coupled SMBs. Table 7. Near-Optimal Superficial Flow Rates (cm3/min) for Two-Zone SMBs for Total and Partial Feeds at D/F ) 4.0: Nonlinear Isotherms decoupled zone I step a without feed zone II step a without feed zone I step a with feed zone II step a with feed zone I step b zone II step b Dto_tank without feed Dto_tank with feed Dfrom_tank D1 Dopt a

coupled

totala

partialb

totala

partialb

14.40 10.76 9.25 8.95 3.64 3.64 9.25 5.31

10.76 10.76 28.96 10.76 9.25 8.95 0 18.20 3.64 9.25 5.31

15.78 12.14 7.40 18.20 3.64 3.64 14.56

12.14 12.14 30.34 12.14 7.40 18.20 0 18.20 3.64 14.56

tF/ta ) 1. b tF/tsw ) 0.1.

Figure 7a and b represent total feed. The conclusions are similar to those for the partial-feed operation for the linear system. Initially, shortening the feed length increases all product purities, but there is limit to the

Figure 5. Product purities for a four-zone SMB with one column per zone and for a two-zone coupled SMB for the separation of binaphthol isomers (nonlinear).

amount the feed length can be shortened because of mass-transfer limitations. Early feed introduction in-

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about tft/ta ) 0.9. The different partial-feed behavior for nonlinear as compared to linear isotherms is probably caused by the concentration dependence of the solute velocity with nonlinear isotherms. Results for Multiple Columns per Zone for Two-Zone SMBs: Linear and Nonlinear Isotherms

Figure 6. Product purities for a two-zone decoupled SMB and average purities for two-zone coupled and decoupled SMBs for the separation of binaphthol isomers (nonlinear).

creases extract purity, whereas late feed introduction increases raffinate purity. The results show that, for the set of flow rates in Table 7, partial-feed operation has less impact on raffinate purity than on extract purity. In the two-zone decoupled SMB, the raffinate purity is 67.5% at tF/ta ) 1.0, and in the two-zone coupled SMB, it is 77.7%. Compared to the maximum value (67.9%) for the twozone decoupled SMB and 77.8% for the two-zone coupled SMB, both at tF/ta ) 0.6, the increase in raffinate purity is small. The extract purity increases considerably as the feed length is shortened. Comparing parts c and d of Figure 7 shows that the optimal average purity for the two-zone decoupled SMB occurs at about tft/ta ) 0.3, whereas that for the two-zone coupled SMB occurs at

In the four-zone SMB, separation efficiency can be improved with more columns per zone at the same productivity and a shorter switching period because of a closer approach to true countercurrent operation.1 Hence, the raffinate and extract purities are higher with more columns per zone. A four-zone SMB with one column in each zone I and zone IV (Figure 1) and two columns in each zone II and zone III is described as a (1,2,2,1) SMB. A two-zone SMB with one column in each zone is defined as a (1,1) system; a two-zone SMB with two columns in zone I and one column in zone II is defined as a (2,1) system; and so forth. The (2,1) twozone coupled SMB is shown in Figure 8 for all three steps of a complete cycle. We compared these systems with constant productivities. The system and operating parameters are listed in Table 1 for linear isotherms and in Table 2 for nonlinear isotherms, except that the column length and switching time were changed corresponding to the different systems to keep the same productivities. These column lengths and flow rates are listed in Table 8 for linear isotherms and Table 9 for nonlinear isotherms. The simulation results with D/F ) 1.16 for linear isotherms and D/F ) 4.0 for nonlinear isotherms are reported in Table 10. These

Figure 7. Partial-feed results for a two-zone SMB for the separation of binaphthol isomers (nonlinear) at D/F ) 4.0. Influence of feed length (feeds are introduced in the middle of the switch time) for (a) decoupled and (b) coupled SMBs. Influence of feed time (feed lengths are 0.1tsw) for (c) decoupled and (d) coupled SMBs.

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Table 8. Column Lengths, Switching Times, and Superficial Flow Rates for Two-Zone SMBs with One and Multiple Columns per Zone at D/F ) 1.16 for Linear Isothermsa column length (cm) switching time (min)

(1,1)

(2,1)

(1,2)

(2,2)

(3,1)

(3,3)

35.625 18.52

23.75 12.35

23.75 12.35

17.8125 9.26

17.8125 9.26

11.875 6.17

Flow Rates (cm3/s) feed rate zone I step a zone II step a zone I step b zone II step b D1 Dopt a

decoupled

coupled

0.0166 0.0564 0.0398 0.0177 0.0181 0.0177 0.0015

0.0166 0.0564 0.0398 0.0177 0.0358 0.0192

Productivity (all systems) ) 0.004 56 (cm3 of feed/min)/(cm3 of adsorbent). Table 10. Purity Comparisons for Two-Zone SMBs with One and Multiple Columns per Zone for Linear (D/F ) 1.16) and Nonlinear (D/F ) 4.0) Isotherms (1,1)

Figure 8. Complete cycle for a (2,1) two-zone coupled SMB. The columns inside the dotted lines are in the same zone. Table 9. Column Lengths, Switching Times, and Superficial Flow Rates for Two-Zone SMBs with One and Multiple Columns per Zone at D/F ) 4.0 for Nonlinear Isothermsa column length (cm) switching time (min)

(1,1)

(2,1)

(1,2)

(2,2)

(3,1)

(3,3)

21.0 18.51

14.0 12.34

14.0 12.34

10.5 9.26

10.5 9.26

7.0 6.17

Flow Rates (cm3/s)

feed rate zone I step a zone II step a zone I step b zone II step b D1 Dopt

decoupled

coupled

3.64 14.40 10.76 9.25 8.95 9.25 5.31

3.64 15.78 12.14 7.40 18.2 14.56

a Productivity (all systems) ) 0.009 58 (cm3 of feed/min)/(cm3 of adsorbent).

results are qualitatively different from the typical results for four-zone SMBs with multiple columns per zone. Adding more columns to either zone I or zone II or both zones has a negative effect on the extract purity and a positive effect on the raffinate purity for two-zone coupled SMBs with linear isotherms. The recovery of one component decreases with decreases of purity of the other component, as mentioned previously. The improvement depends on how the columns are added. For example, the dextran T6 purity is 87.7% in a (1,1) twozone coupled SMB. When an additional column is added to zone I to form a (2,1) SMB, the dextran T6 purity rises to 92.9%. When yet another column is added to zone I to form a (3,1) SMB, the dextran T6 purity rises further to 94.1%. If the first additional column is added

(1,2)

(2,2)

(3,1)

(3,3)

Linear Isotherms Coupled dextran T6 purity (%) 87.7 92.9 88.9 raffinose purity (%) 90.3 89.3 88.8 average purity (%) 89.0 91.1 88.9 dextran T6 recovery (%) 90.8 89.0 88.9 raffinose recovery (%) 87.3 93.1 89.0

97.9 88.4 93.2 87.5 97.8

94.1 87.9 91.0 87.2 94.6

98.4 86.6 92.5 84.9 98.3

80.8 94.7 87.8 93.3 77.8

84.7 94.7 89.7 94.0 81.8

86.9 90.7 88.8 90.9 85.6

82.0 92.7 87.4 92.0 78.8

Nonlinear Isotherms Coupled 77.7 73.5 73.9 82.3 83.1 82.2 80.0 78.3 78.1 83.7 85.9 83.6 75.9 69.1 70.1

71.9 82.1 77.0 83.5 66.6

72.2 84.0 78.1 86.7 67.8

68.5 78.8 73.7 83.4 61.7

64.2 80.7 72.5 87.1 51.0

64.6 82.0 73.3 87.6 53.7

62.6 79.9 71.3 86.5 47.3

dextran T6 purity (%) raffinose purity (%) average purity (%) dextran T6 recovery (%) raffinose recovery (%)

A purity (%) B purity (%) average purity (%) A recovery (%) B recovery (%) A purity (%) B purity (%) average purity (%) A recovery (%) B recovery (%)

(2,1)

Decoupled 83.7 86.6 93.5 92.2 88.6 89.4 92.9 91.9 81.9 84.7

Decoupled 67.5 65.9 77.8 80.8 72.7 73.4 82.8 86.9 60.1 55.1

64.5 79.1 71.8 86.1 52.7

to zone II instead to form a (1,2) SMB, the dextran T6 purity increases only slightly to 88.9%. A synergistic effect occurs if additional columns are added to both zones 1 and 2 to form a (2,2) SMB. The dextran T6 purity increases significantly to 97.8%. The raffinose purity decreases slightly with more columns per zone. These results can be partially explained from the concentration profiles in the columns. Figure 9 shows steady-state axial concentration profiles at the beginning of step b for two-zone coupled SMBs with one and two columns per zone according to Aspen Chromatography simulations. The profiles for dextran T6 and raffinose in the different configurations are similar in zone II at the beginning of step b, particularly for the dextran T6 profiles. During step b, the profiles exit from zone II, and part of the fluid is collected as extract product. Hence, the extract purities are close to each other for the different configurations. The slight difference might be due to concentration changes in the tank. The results are more complicated for the raffinate product. Comparing the profiles of zone I in Figure 9a and the first column of zone I in Figure 9b, we see that the concentration of raffinose is lower in Figure 9a than

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005 1573

Figure 9. Steady-state axial concentration profiles at the beginning of step b for two-zone coupled SMBs with one and two columns per zone for the dextran T6-raffinose system. Arrows show the direction of solute movement. (a) (1,1) system, (b) (2,1) system, (c) (1,2) system, (d) (2,2) system.

that in 9b. Thus, we obtain a purer raffinate product (less raffinose) with the (2,1) two-zone coupled SMB. Comparison of the profiles of zone I in parts a and c of Figure 9 shows that they are similar. Thus, these raffinate purities are similar. When an additional column is added to each zone, we can achieve much better raffinate purities compared to those of the (1,1) two-zone coupled SMB. Comparing the raffinose profiles in zone I in parts b and d of Figure 9, one can see that the raffinose concentration rises more quickly in the (2,2) than in the (2,1) two-zone coupled SMB when they exit from zone I. At the outlet of zone I, however, the raffinose concentration in the (2,2) two-zone coupled SMB is lower than that in the (2,1) two-zone coupled SMB, whereas the dextran T6 concentrations are at the same level. Thus, at the beginning of step b, we can achieve a purer raffinate product. Figure 10 shows the profiles of zone I of the (2,1) and the (2,2) two-zone coupled SMB at the end of step b. The raffinose concentration in the (2,2) two-zone coupled SMB is still lower than that in the (2,1) two-zone coupled SMB. This explains why a purer raffinate product is obtained in (2,2) than in (2,1) two-zone coupled SMBs. As expected, when an additional column is added to each zone of the (2,2) arrangement to make it a (3,3) two-zone coupled SMB, the raffinate purity increases, and the extract purity decreases further. The average purity decreases because the increase in raffinate purity must become small as it approaches 100%. The results for two-zone decoupled SMBs with multiple columns per zone are different from those for twozone coupled SMBs for linear isotherms (Table 10). When an additional column is added to zone I, the raffinate purity increases, and the extract purity decreases. On the other hand, if the additional column is

Figure 10. Steady-state axial concentration profiles in zone I at the end of step b for the (2,1) and (2,2) two-zone coupled SMBs for the dextran T6-raffinose system. Arrows show the direction of solute movement.

added to zone II, the extract purity increases, and the raffinate purity decreases. Adding a column to each zone increases both the raffinate and extract purities compared to those in the (1,1) two-zone decoupled SMB. When an additional column is added to each zone of a (2,2) two-zone decoupled SMB, both purities decrease, as shown for the (3,3) two-zone decoupled SMB. Note that the average purities of the two-zone coupled SMB are always higher than those of the two-zone decoupled SMB. The difference in results for two-zone SMBs and typical four-zone SMBs with multiple columns per zone probably occurs because the functions of the zones in the four-zone SMB are combined in the two-zone SMBs. For the two-zone SMBs with these nonlinear isotherms, the simulation results at D/F ) 4.0 show that adding more columns in zone I, zone II, or both zones

1574

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005

Table 11. Purity Comparison with Different Isotherm Constants for Linear Systems at D/F ) 1.0

CA CB Ma Mb Mc Md D/F A purity (%) B purity (%)

hypothetical system

dextran T6-raffinose system

1.98 0.90 1.07 0.93 0.98 0.97 1.00 88.4 89.3

1.73 1.32 1.00 1.00 1.00 1.00 1.00 80.3 89.6

Conclusions

never has a positive effect on raffinate purity. Moreover, for the extract purities, adding more columns has less impact than with linear isotherms. The purities increase or decrease slightly in the (2,1), (3,1), (1,2), and (2,2) coupled and decoupled two-zone SMBs. When an additional column is added to each zone of the (2,2) twozone SMB, both the raffinate and extract purities decrease when it becomes a (3,3) two-zone SMB (Table 10). This is due to the profile shifting when more columns are added to either or both zones. Unlike the four-zone SMB, adding more columns in the different zones in two-zone SMBs does not always have advantages, especially for nonlinear isotherms. Discussion The two-zone SMBs proposed here have a relatively simple design and use less equipment than four-zone SMBs. The partial-feed results for two-zone SMBs show that partial feed is an effective operating strategy for improving the product purities. There is a limitation on the application of two-zone SMBs. When all multipliers are set to 1.0 to obtain D/F ) 1.0, we can determine the superficial velocities from eqs 5 and 6 for a two-zone decoupled SMB

v1a )

(

L CAta

v1b )

(13)

)

CB L CA CBtb

1-

(14)

Substituting eqs 13 and 14 into eq 5 gives

v2a )

(2CB - CA)L CAta

(15)

Because A is the less-retained component (CA > CB), CA and CB must satisfy the following inequality to guarantee a positive value of superficial velocity in column 2 of step a

R′ )

CA e 2.0, CB

CB ) 0.9, where CA/CB ) 2.2 > 2.0, which violates eq 16. The system and operating parameters are listed in Table 1, and the Mi values are adjusted to make D/F ) 1.0. Product purities are reported in Table 11. As expected, because R′ is larger for the hypothetical system, the separation is better for this system than for the dextran T6-raffinose system. Thus, the constraint in eq 16 can easily be bypassed by varying the multipliers.

Ma ) Mb ) Mc ) Md ) 1.0 (16)

Although this derivation is for two-zone decoupled SMBs, it is also valid for two-zone coupled SMBs. This is an ideal constraint, and it applies to the base case only when all multipliers are 1.0 and D/F ) 1.0. The multipliers can be adjusted to obtain a positive velocity in every column regardless of the constraint in eq 16 for Mi values at D/F ) 1.0. For example, consider the hypothetical case with D/F ) 1.0, CA ) 1.98, and

Two-zone SMBs, a simple alternative to the four-zone SMB, have been developed in this paper. The conclusions of this work are as follows: (i) For the linear system studied, the two-zone SMBs provide comparable purities and use less complex equipment than a normal four-zone SMB. The purities and recoveries achieved with the two-zone SMBs were slightly lower than those achieved with a four-zone SMB. (ii) The partial-feed operation strategy, operating the feed flow rate in three distinct subintervals within each switching step, increases both two-zone and four-zone SMBs separation efficiency with one column per zone. Under such operation, product purities and recoveries are enhanced when the productivity is constant. The productivity will be improved if the purity is unchanged.8 Two parameters in partial-feed operation can be adjusted to achieve the desired separation. Shortening the feed length can increase the quality of both products. Adjusting the feed time can be used to optimize the SMB for a given product. (iii) The results for the nonlinear system studied here indicate that, for these two-zone SMBs to obtain high purities, D/F is significantly larger than for a four-zone SMB. Partial-feed operation gives a very modest improvement in raffinate purity for the binaphthol enantiomers system; however, the improvement in extract purity is considerable. The two-zone coupled SMB is significantly better than the two-zone decoupled SMB for nonlinear isotherms. (iv) The results for the two-zone SMBs with multiple columns per zone show that adding more columns per zone does not always increase the product purities in two-zone SMBs. The improvement depends on how the columns are added. Adding more columns to either or both zones has less impact in nonlinear systems than in linear systems. (v) There are similarities and differences between four-zone and two-zone SMBs. The similarities are that (a) the minimum amount of desorbent under ideal linear conditions is 1.0 for both four-zone and two-zone SMBs, (b) partial-feed operation can improve the product purities significantly for both four-zone and two-zone SMBs, and (c) increasing D/F can increase product purities for both four-zone and two-zone SMBs. The differences are that (a) the multipliers obtained for the optimal average purities are different for four-zone and two-zone SMBs and (b) the separation behaviors are different for four-zone and two-zone SMBs with multiple columns per zone. Acknowledgment This research was partially supported by NSF Grant CTS-0211208. The assistance of Dr. Yifei Zang, Nadia

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005 1575

Abunasser, Dr. Jeung Kun Kim, and Jin Seok Hur is gratefully acknowledged.

recovery ) (amount of desired component in its product)/ (amount of this component in the feed)

Notation

Literature Cited

c ) solute concentration, g/L c* ) solute equilibrium liquid concentration corresponding to the solid concentration, g/cm3 cF ) feed concentration, g/L cT ) initial concentration in the tank, g/L CA, CB ) solute movement constants associated with superficial velocity C′A, C′B ) solute movement constants associated with interstitial velocity dtank ) tank diameter, cm Dcol ) column diameter, cm D1, Dopt ) desorbent flow rate, cm3/min Dto_tank ) input flow rate to the tank, cm3/min Dfrom_tank ) output flow rate from the tank, cm3/min D/F ) desorbent-to-feed ratio F ) feed flow rate, cm3/min H ) initial liquid height in the tank, cm kmap ) mass-transfer resistance, 1/s K ) linear equilibrium parameter, L/(g of solute) L ) column length, cm Mi (i ) a, b, c, d) ) multiplier for linear system analysis q ) solute concentration on the solid phase, g/(cm3 of adsorbent) Rp ) partical radius, cm t ) time, s ta, tb ) operation times of steps a and b, respectively, s tF ) feed length, s tft ) feed time, s tsw ) switch time, s u ) solute velocity, cm/s vcolumn i,step j (i ) 1, 2; j ) a, b) ) superficial velocity, cm/s vF ) feed velocity ) F/4πDcol2, cm/s vD,from_tank ) fluid velocity out of the tank, cm/s vD,to_tank ) fluid velocity into the tank, cm/s vD1, vD,opt ) desorbent input velocities, cm/s vj ) interstitial velocity, cm/s vsuper,j ) superficial velocity, cm/s

(1) Wankat, P. C. Rate-Controlled Separations; Kluwer Academic Publishers: Amsterdam, 1990. (2) Broughton, D. B.; Carson, D. B. The Molex Process. Pet. Refin. 1959, 38, 130. (3) Broughton, D. B.; Neuzil, R. W.; Pharis, J. M.; Brearley, C. S. The Parex Process for Recovering Paraxylene. Chem. Eng. Prog. 1970, 66, 70. (4) Broughton, D. B. Production-Scale Adsorptive Separations of Liquid Mixture by Simulated Moving Bed Technology. Sep. Technol. 1984, 19, 723. (5) Wu, D.; Xie, Y.; Ma, Z.; Wang, N.-H. L. Design of Simulated Moving Bed Chromatography for Amino Acid Separation. Ind. Eng. Chem. Res. 1998, 37, 4023. (6) Pais, L.; Loureiro, J. M.; Rodrigues, A. Modeling Strategies for Enantiomers Separation by SMB Chromatography. AIChE J. 1998, 44, 561. (7) Mun, S.; Xie, Y.; Kim, J. M.; Wang, N.-H. L. Optimal Design of a Size-Exclusion Tandem Simulated Moving Bed for Insulin Purification. Ind. Eng. Chem. Res. 2003, 42, 1977. (8) Zang, Y.; Wankat, P. C. Three-Zone SMB with Partial Feed and Selective Withdrawal. Ind. Eng. Chem. Res. 2002, 41, 5283. (9) Abunasser, N.; Wankat, P. C.; Kim, Y.-S.; Koo, Y. M. OneColumn Chromatograph with Recycle Analogous to a Four-Zone Simulated Moving Bed. Ind. Eng. Chem. Res. 2003, 42, 5268. (10) Lee, K. Two-Section Simulated Moving-Bed Process. Sep. Sci. Technol. 2000, 35, 519. (11) Dunnebier, G.; Weirich I.; Klatt, K. U. Computationally Efficient Dynamic Modeling and Simulation of Simulated Moving Bed Chromatographic Processes with Linear Isotherms. Chem. Eng. Sci. 1998, 53, 2537. (12) Zang, Y.; Wankat, P. C. SMB Operation StrategysPartial Feed. Ind. Eng. Chem. Res. 2002, 41, 2504. (13) Storti, G..; Mazzotti, M.; Morbidelli, M.; Carra, S. Robust Design of Binary Countercurrent Adsorption Separation Processes. AIChE J. 1993, 39, 471. (14) Ma, Z.; Wang, N.-H. L. Standing Wave Analysis of SMB Chromatography: Linear Systems. AIChE J. 1997, 43, 2488. (15) Mallmann, T.; Burris, B. D.; Ma, Z.; Wang, N.-H. L. Standing Wave Design of Nonlinear Simulated Moving-Bed (SMB) Systems for Fructose Purification. AIChE J. 1998, 44, 2628. (16) Ching, C. B.; Chu, K. H.; Hidajat, K.; Uddin, M. S. Comparative Study of Flow Schemes for a Simulated Countercurrent Adsorption Separation Process. AIChE J. 1992, 38, 1744. (17) Chung, S. F.; Wen, C. Y. Longitudinal Dispersion of Liquid Flowing through Fixed and Fluidized Beds. AIChE J. 1968, 14, 867. (18) Kim, J. K.; Wankat, P. C. Scaling and Intensification Procedures for Simulated Moving-Bed Systems. AIChE J. 2003, 49, 2810.

Greek Letters R′AB ) separation factor ) uA/uB ) CA/CB e ) external void fraction p ) internal void fraction µ ) liquid viscosity, cP F ) liquid density, g/mL Fs ) solid density, g/mL Definitions productivity ) (feed volume/time)/(total adsorbent volume) purity ) (amount of desired component)/(sum of all feed components in the product)

Received for review April 26, 2004 Revised manuscript received September 22, 2004 Accepted November 29, 2004 IE040132R