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## Brazilian Journal of Chemical Engineering

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*Print version* ISSN 0104-6632*On-line version* ISSN 1678-4383

### Braz. J. Chem. Eng. vol.20 no.2 São Paulo Apr./June 2003

#### http://dx.doi.org/10.1590/S0104-66322003000200012

**A design and study of the effects of selectivity on binary separation in a four-zone simulated moving bed for systems with linear isotherms**

**M.A.Cremasco ^{I}; N.-H.Linda Wang^{II}**

^{I}School of Chemical Engineering, State University of Campinas, PO Box 6066, 13083-970, Campinas - SP, Brazil. E-mail: cremasco@feq.unicamp.br

^{II}Chemical Engineering Department, Purdue University, 47907-1283, West Lafayette - Indiana, USA. E-mail:wangn@ecn.purdue.edu

**ABSTRACT**

The simulated moving bed (SMB) is potentially an economical method for the separation and purification of natural products because it is a continuous processes and can achieve higher productivity, higher product recovery, and higher purity than batch chromatographic processes. Despite the advantages of SMB, one of the challenges is to specify its zone flow rates and switching time. In this case it is possible to use the standing wave analysis. In this method, in a binary system, when certain concentration waves are confined to specific zones, high product purity and yield can be assured. Appropriate zone flow rates, zone lengths and step time are chosen to achieve standing waves. In this study the effects of selectivity on yield, throughput, solvent consumption, port switching time, and product purity for a binary system are analyzed. The results show that for a given selectivity the maximum throughput decreases with increasing yield, while solvent consumption and port switching time increase with increasing yield. To achieve the same purity and yield, a system with higher selectivity has a higher throughput and lower solvent consumption.

**Keywords:** simulated moving bed, standing wave, adsorption.

**INTRODUCTION**

The simulated moving bed (SMB) for hydrocarbon purification has been utilized since the 1960's (Broughton, 1968). Its application has been extended to protein desalting (Hashimoto et al., 1989), chiral separation (Pais et al*.*, 1997), and separation of paclitaxel from taxanes (Cremasco et al., 2001). The SMB is a continuous system and can obtain higher throughput, recovery, and purity than batch chromatography systems. However, in order to achieve a high purity separation, a good SMB design depends on the choice of flow rate in each zone and the simulated adsorbent velocity, which is related to port switching time and column length.

In this paper, a systematic comparison is shown for the binary separation of L-phenylalanine (Phe) from L-tyrosine (Tyr); Phe from L-tryptophan (Trp), and Tyr from Trp. These amino acids have been chosen because they represent solutes with similar affinities for a poly-4-vinylpyridine (PVP) resin (Cremasco et al., 2001). The design method utilized in this work is based on the standing wave analysis (Ma and Wang, 1997).

**THEORY**

In chromatographic separation in a simulated moving bed (SMB) system, a series of fixed beds packed with an appropriate adsorbent is connected to form a circuit. This circuit is divided into four zones with two inlet ports: a feed port and a solvent port, and two outlet ports: a raffinate port, where a low-affinity solute A is removed, and an extract port, where a high-affinity solute B is removed, as shown on Figure 1. The inlet and outlet ports are periodically moved in the solvent flow direction by multiple position valves, causing an apparent countercurrent movement between the liquid and the solid phase. As in batch chromatography, solute A migrates faster than solute B in the liquid flow direction. In a four-zone SMB, solute A adsorption occurs in zone IV, while its desorption occurs in zone II. Solute B adsorption occurs in zone III, and its desorption occurs in zone I. In this case, the standing wave method says that solute A, adsorption wave remains stationary in zone IV, while its desorption wave remains stationary in zone II. Solute B, adsorption wave remains stationary in zone III, and its desorption wave remains in zone I (Ma and Wang, 1997).

The migration velocity of solute i in zone j can be obtained from the solute movement theory if an SMB can be proximate as a batch chromatography process. If mass transfer effects are negligible, the solute migration velocity is given by (Wankat, 1994),

where

and

The net migration velocity of solute i in zone j can be related to and the adsorbent movement velocity, n ,

The net solute i migration wave velocity in zone j have be positive, negative, or null values depending on the relative movement between solute and adsorbent. Separation occurs when the following conditions are obeyed (Wankat, 1994; Ma and Wang, 1997):

To achieve standing waves, the inequalities of (3) to (6) become equalities,

or Eq. (2) becomes

If mass transfer effects are considered, Eq. (8) becomes

The B_{j} values represent the flow rate corrections needed to counter mass transfer effects. In this case, when one attempts to recover a certain product with a specified yield, the concentration waves of the products are dispersed, resulting in contamination of the products in the extract and raffinate (Fig. 2).

Because the simulated adsorbent velocity is the same in all the zones, one can substitute Eq. (1) into Eq. (9) to obtain

From inspection of Figure 1, the volumetric flow rate of the feed stream, F, at steady state is related to the interstitial liquid velocities of zones II and III by

where A_{c} is the column cross-sectional area. If an equivalent interstitial velocity is defined as uF=F/(e_{b}A_{c}) and Eqs. (11) and (12) are substituted into Eq. (14), the following is obtained:

The axial dispersion coefficient in Eqs. (10) to (13) can be estimated from experimental data (Cremasco et al., 2001) or from literature (Gunn, 1987). For linear isotherm systems, the terms associated with the corrections to the mass transfer effects can be calculated by (Ma et al., 1996),

where the film mass transfer coefficient can be estimated from the Wilson and Geankoplis (1966) correlation. The effective diffusion coefficient in Eq. (16) can be obtained from pulse experiments (Cremasco et al., 2001) or from a correlation (Mackie and Meares, 1955).

From analysis of Ma and Wang (1997), and on the left-hand side of Eqs. (10) and (12), respectively, are associated with the standing desorption and adsorption waves of solute B in zones I and III, respectively. These coefficients are defined as the natural logarithm of the ratio between the highest and the lowest concentration of B in a given zone (Figure 2).

Coefficients and in Eqs. (11) and (13) are associated with the standing desorption and adsorption waves of solute A in zones II and IV, respectively. These coefficients are defined as

The four b values can be estimated from simple material balances around zones and mixing points (Figures 1 and 2). The following assumptions are made: (i) the concentration of solute A at the outlet of zone III is equal to its concentration at the raffinate port, (ii) the concentration of solute B at the inlet of zone II is equal to its concentration at the extract port, and (iii) the ratio between the highest and the lowest concentrations for component (A or B) is the same in both adsorption and desorption zones. These assumptions lead to the following expressions:

If the yields of A and B at the outlet ports are defined as

where and are the equivalent raffinate and extract interstitial velocities, it is possible to rewrite the b values by mass balances for solutes A and B. The results are substituted into Eqs. (21) and (22) to give

The following expression is obtained from Eq. (15) and can be used to calculate the apparent adsorbent velocity:

where

Notice that the SMB operational conditions are obtained from the solution of Eqs.(10) to (13) and (15), which are restricted to the condition l_{2} __>__ 0. The port switching time, t_{p}, is calculated from

where L_{c} is the single column length.

Strategy for obtaining SMB operating parameters

The SMB operating parameters are found by the following steps:

1) Find the adsorption constants k_{p} (linear case) for both solutes and identify the less-retained solute (A) and the more-retained solute (B).

2) Find bed and particle characteristics (D, L, e_{b}, d_{p}, and e_{p}) and mass transfer parameters (D_{p}, k_{f}, and E_{p}). It should be noted that the value of D_{p} does not depend on flow rate. The values of k_{f} and E_{b} depend on flow rate and should be calculated by using known correlations.

3) Fix the feed concentrations and .

4) Fix the solute A yield at the raffinate port (Y_{A}) and the solute B yield at the extract port (Y_{B}).

5) Choose a feed flow rate F.

6) Calculate the liquid interstitial velocity in each zone and apparent adsorbent velocity using Eqs. (10) to (13) and Eq. (15), assuming B_{1} = B_{2} = B_{3} = B_{4} = 0 (equilibrium conditions).

7) Calculate the values of the flow-rate-dependent mass transfer parameters using the velocities calculated from step 6 and the correlation in step 2.

8) Calculate = and = from Eqs. (25) and (26).

9) Calculate the new liquid interstitial velocity in each zone and simulated adsorbent velocity.

10) Calculate the convergence criteria given by

where k is the iteration number and j is the zone.

11) Calculate the restriction l_{2} __>__ 0, Eq. (29). If this restriction is obeyed, then return to step 5 and increase F. When l_{2} < 0, the F value in the previous iteration is the maximum feed flow rate (F_{max}).

12) Determine zone flow rates and port switching time.

**SIMULATION**

A four-zone SMB system was simulated. Each zone consisted of a single 1.5 cm I.D. × 12.5 cm column, with a bed porosity of 0.37. The column was packed with particles with a porosity particle of 0.55 and an average diameter of 0.036 cm. Three different aqueous solutions of amino acids (Phe-Tyr, Phe-Trp, and Tyr-Trp) with = = 0.4 mg/mL are considered. This concentration was chosen in order to have linear adsorption isotherms (Cremasco et al., 2001). The mass transfer parameters and partition coefficients of the three amino acids are shown in Table 1, and the selectivity is given by (Table 2).

**RESULTS AND DISCUSSION**

For practical applications, the values of Y_{A} and Y_{B} are fixed at greater than 0.95. Since the two solutes have the same feed concentration and the same yield, the purity of the raffinate and the purity of the extract as defined in Table 3 are the same. The purity also equals the specified yield based on mass balances. The strategy developed in this paper is used to obtain the inlet and outlet zone flow rates (Fig. 3). This figure shows that in order to maintain the same purity and achieve higher yield, the maximum feed flow rate must be decreased to allow better band separation. As the feed flow rate decreases with yield, desorbent, raffinate, extract (Fig. 3) and all zone flow rates decrease accordingly and Q^{I} > Q^{II}, Q^{I} > Q^{IV} and Q^{III} > Q^{II}, Q^{III} > Q^{IV} (Fig. 4).

The trends shown in Figs. 3 and 4 also apply to the separation of Phe from Tyr and Tyr from Trp. However, these two systems have lower selectivities than the Phe and Trp system (Table 2). For a lower selectivity system, the maximum feed flow rate at a given yield is smaller (Fig. 5) because loading must be smaller in order to maintain purity and yield. As a result, throughput or productivity (Pr in Table 3) decreases with decreasing selectivity (Fig. 6). Solvent consumption (defined in Table 3) increases with decreasing selectivity (Fig. 7) because as loading decreases, product concentrations decrease, resulting in increasing solvent consumption.

Figure 8 shows a strong dependence of the simulated adsorbent velocity on selectivity and specified yield. This velocity decreases with decreasing feed flow rate and zone flow rates (Figs. 4 and 5). As shown in Figs. 3 and 4, as feed flow rate decreases, all zone flow rates decrease accordingly. From the solute movement theory, Eq. (1), wave velocities also decrease. Since the adsorbent velocity equals the wave velocities, it decreases with decreasing feed flow rate (Fig. 8). Figure 9 shows that as the adsorbent velocity decreases, the switching time increases as expected from Eq. (29).

**CONCLUSIONS**

The standing wave concept was applied to design the flow rates and switching time for a linear SMB system for the separation of two amino acids with the same feed concentration. The design of the simulated moving bed includes the specification of the following to achieve the desired product yield: (1) the maximum feed flow rate; (2) the solvent flow rate; (3) the raffinate flow rate; (4) the extract flow rate; and (5) the port switching time., As shown in this work, these parameters depend on the adsorption and mass transfer characteristics of the solutes. The results show that a small variation in specified yield can significantly alter the switching time and maximum feed flow rate. To obtain a higher yield and higher purity, it is necessary to use a lower feed flow rate and higher solvent consumption. On the other hand, this flow rate depends on pump configuration, which can strongly influence SMB performance.

**ACKNOWLEDGEMENTS**

Prof. Cremasco acknowledge the financial assistance of FAPESP (under grandt 01/08101-3) during the development of the present research.

**NOMENCLATURE**

* *

**REFERENCES**

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Received: July 29, 2001

Accepted: November 28, 2002