Abstract
For a dilute feed, a four-zone SMB with temperature gradient (4-zone TSMB-FC) can fractionate and simultaneously concentrate two solutes. Optimization of the operating parameters for this system, which include four zone flow rates and port switching time, is a major challenge because of the five variables. Initial choice of the variables using the triangle theory followed by a systematic search using rate model simulations is time-consuming. In this study, the SWD developed previously for isothermal systems is modified for the first time for a 4-zone TSMB-FC. The optimum operating parameters are determined with the new method. Only linear isotherm systems with significant mass transfer resistances are considered. For a dilute feed, a 4-zone SMB-FC can produce pure desorbent, in addition to extract and raffinate products with high purities. For the separation of p-xylene and toluene with silica gel in the temperature range from 0 to 80 °C, the enrichment factor in the linear region can be as high as 80 fold for an extract purity of 99.99 % and tenfold for raffinate purity of 99.8 %, while withdrawing the desorbent at a desorbent to feed flow rate ratio of 0.53 and 0.78, respectively.
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Abbreviations
- A i :
-
Pre-exponential factor of the Arrhenius equation (L g−1)
- c :
-
Concentration of solute in the liquid phase (g L−1)
- c * i :
-
Concentration of solute i in the pore phase (g L−1)
- c D, i :
-
Concentration of solute i in the desorbent stream (g L−1)
- c F, i :
-
Concentration of solute i in the feed (g L−1)
- c Fb, i :
-
Concentration of solute i before the feed port (g L−1)
- c FP, i :
-
Concentration of solute i after the feed port (g L−1)
- c R, i :
-
Concentration of solute i in the raffinate stream (g L−1)
- c E, i :
-
Concentration of solute i in the extract stream (g L−1)
- C pL :
-
Heat capacity of the liquid phase (J g−1 K−1)
- C pS :
-
Heat capacity of the solid phase (J g−1 K−1)
- D :
-
Desorbent flow rate (mL min−1)
- D ax,i,j :
-
Axial dispersion coefficient of solute i in zone j (cm2 min−1)
- D ax,E :
-
Thermal axial dispersion coefficient (cm2 min−1)
- EF :
-
Enrichment factor
- K di :
-
Size exclusion factor
- k f,i,j :
-
Mass transfer coefficient of solute i in zone j (LDF) (min−1)
- k f,i a p :
-
Effective mass transfer coefficient (min−1)
- K(T) :
-
Temperature dependent equilibrium constant (L g−1)
- L :
-
Column length (cm)
- P :
-
Bed phase ratio
- PI :
-
Purity index (average purity of the raffinate and extract stream)
- P R, i :
-
Purity of solute i in the raffinate stream (%)
- P E, i :
-
Purity of solute i in the extract stream (%)
- q :
-
Concentration of solute in the solid phase (g L−1)
- \(\overline{q}\) :
-
Average concentration of solute in the solid phase (g L−1)
- F :
-
Volumetric flow rate of the feed (mL min−1)
- Q j :
-
Volumetric flow rate of zone j (mL min−1)
- R :
-
Ideal gas constant (J K−1 mol−1)
- S :
-
Column cross-sectional area (cm2)
- T :
-
Temperature (K)
- u i,j :
-
Solute wave velocity of solute i in zone j (cm min−1)
- u port :
-
Port velocity (cm min−1)
- ū o,j :
-
Interstitial velocity of the mobile phase in zone j (cm min−1)
- u o,j :
-
Zone linear velocity in zone j (cm min−1)
- Y i :
-
Yield of solute i
- ΔH :
-
Heat of adsorption (J mol−1)
- β i j :
-
Decay coefficient of solute i in zone j
- δ i,j :
-
Retention factor of solute i in zone j
- ε e :
-
Bed void fraction
- ε p :
-
Intra-particle void fraction
- ρ L :
-
Density of the liquid phase (g mL−1)
- ρ S :
-
Density of the solid phase (g mL−1)
References
Abunasser, N., Wankat, P.C.: Improving the performance of one column analogs to SMBs. AIChE J. 52(7), 2461–2472 (2006)
Abunasser, N., Wankat, P.C., Kim, Y.S., Koo, Y.M.: One-column chromatograph with recycle analogous to a four-zone simulated moving bed. Ind. Eng. Chem. Res. 42(21), 5268–5279 (2003)
Azevedo, D.C.S., Rodrigues, A.E.: Fructose–glucose separation in a SMB pilot unit: modeling, simulation, design, and operation. AIChE J. 47(9), 2042–2051 (2001)
Beste, Y.A., Lisso, M., Wozny, G., Arlt, W.: Optimization of simulated moving bed plants with low efficient stationary phases: separation of fructose and glucose. J. Chromatogr. A868(2), 169–188 (2000)
Broughton, D.B., Carson, D.B.: The molex process. Pet. Refin. 38(4), 130–134 (1959)
Broughton, D.B., Neuzil, R.W., Pharis, J.M., Brearley, C.S.: The Parex process for recovering paraxylene. Chem. Eng. Prog. 66(9), 70–75 (1970)
Ching, C.B., Ruthven, D.M.: Experimental study of a simulated counter-current adsorption system—IV. Non-isothermal operation. Chem. Eng. Sci. 41(12), 3063–3071 (1986)
Chung, S.F., Wen, C.Y.: Longitudinal, dispersion of liquid flowing through fixed and fluidized beds. AIChE J. 14(6), 857–866 (1968)
Francotte, E.R., Richert, P.: Applications of simulated moving-bed chromatography to the separation of the enantiomers of chiral drugs. J. Chromatogr. A769(1), 101–107 (1997)
Guest, D.W.: Evaluation of simulated moving bed chromatography for pharmaceutical process development. J. Chromatogr. A760(1), 159–162 (1997)
Hritzko, B.J., Xie, Y., Wooley, R.J., Wang, N.H.L.: Standing wave design of tandem SMB for linear multicomponent systems. AIChE J. 48(12), 2769–2787 (2002)
Jin, W., Wankat, P.C.: Thermal operation of four-zone simulated moving beds. Ind. Eng. Chem. Res. 46(22), 7208–7220 (2007)
Jin, W., Wankat, P.C.: Two-zone SMB process for binary separation. Ind. Eng. Chem. Res. 44(5), 1565–1575 (2005)
Keßler, L.C., Seidel-Morgenstern, A.: Improving performance of simulated moving bed chromatography by fractionation and feed-back of outlet streams. J. Chromatogr. A1207(1–2), 55–71 (2008)
Kim, J.K., Abunasser, N., Wankat, P.C.: Thermally assisted simulated moving bed systems. Adsorption 11(1), 579–584 (2005)
Kim, J.K., Zang, Y., Wankat, P.C.: Single-cascade simulated moving bed systems for the separation of ternary mixtures. Ind. Eng. Chem. Res. 42(20), 4849–4860 (2004)
Lee, J.W., Wankat, P.C.: Thermal simulated moving bed concentrator. Chem. Eng. J. 166(2), 511–522 (2011)
Lee, K.N.: Two-section simulated moving bed process. Sep. Sci. Technol. 35(4), 519–534 (2000)
Ludemann-Hombourger, O., Nicoud, M., Bailly, M.: The “VARICOL” process: a new multicolumn continuous chromatographic process. Sep. Sci. Technol. 35(12), 1829–1862 (2000)
Ma, Z., Wang, N.H.L.: Standing wave analysis of SMB chromatography: linear Systems. AIChE J. 43(10), 2488–2508 (1997)
Matz, M.J., Knaebel, K.S.: Recycled thermal swing adsorption: applied to separation of binary and ternary mixtures. Ind. Eng. Chem. Res. 30(5), 1046–1054 (1991)
Mazzotti, M., Storti, G., Morbidelli, M.: Optimal operation of simulated moving bed units for nonlinear chromatographic separations. J. Chromatogr. A769(1), 3–24 (1997)
Migliorini, C., Mazzotti, M., Morbidelli, M.: Continuous chromatographic separation through simulated moving bed under linear and nonlinear conditions. J. Chromatogr. A827(2), 161–173 (1998)
Migliorini, C., Wendlinger, M., Mazzotti, M.: Temperature gradient operation of a simulated moving bed unit. Ind. Eng. Chem. Res. 40(12), 2606–2617 (2001)
Murthy, D.S., Sivakumar, S.V., Kant, K., Rao, D.P.: Process intensification in a “simulated moving-bed” heat regenerator. J. Heat Transf. 130(9), 1–091801 (2008)
Negawa, M., Shoji, F.: Optical resolution by simulated moving-bed adsorption technology. J. Chromatogr. A590(1), 113–117 (1992)
Nicolaos, A., Muhr, L., Gotteland, P., Nicoud, R.M., Bailly, M.: Application of equilibrium theory to ternary moving bed configurations (four + four, five + four, eight and nine zones): i. Linear case. J. Chromatogr. A908(1–2), 71–86 (2001)
Pais, L., Loureiro, J.M., Rodrigues, A.E.: Modeling strategies for enantiomers separation by SMB chromatography. AIChE J. 44(3), 561–569 (1998)
Paredes, G., Rhee, H.K., Mazzotti, M.: Design of simulated-moving-bed chromatography with enriched extract operation (EE-SMB): Langmuir isotherms. Ind. Eng. Chem. Res. 45(18), 6289–6301 (2006)
Schramm, H., Kaspereit, M., Kienle, A., Seiderl-Morgenstern, A.: Simulated moving bed process with cyclic modulation of the feed concentration. J. Chromatogr. A1006(1–2), 77–86 (2003)
Sivakumar, S.V., Rao, D.P.: Adsorptive separation of gas mixtures: mechanistic view, sharp separation, and process intensification. Chem. Eng. Proc. 53, 31–52 (2012)
Storti, G., Mazzotti, M., Morbidelli, M., Carra, S.: Robust design of binary countercurrent adsorption separation process. AIChE J. 39(3), 471–492 (1993)
Wankat, P.C.: Rate-Controlled Separations, Chapt. 6. Chapman & Hall, Glasgow (1994)
Wankat, P.C.: Separation Process Engineering: Includes Mass Transfer Analysis, 3rd edn., Chapt. 18. Pearson Education Inc., Upper Saddle River (2012)
Wooley, R., Ma, Z., Wang, N.H.L.: A nine-zone simulating moving bed for the recovery of glucose and xylose from biomass hydrolyzate. Ind. Eng. Chem. Res. 37(9), 3699–3709 (1998)
Xie, Y., Chin, C.Y., Phelps, D.S.C., Lee, C.H., Lee, K.B., Mun, S., Wang, N.H.L.: A five-zone simulated moving bed for the isolation of six sugars from biomass hydrolyzate. Ind. Eng. Chem. Res. 44(26), 9904–9920 (2005)
Xie, Y., Mun, S., Kim, J., Wang, N.H.L.: Standing wave design and experimental validation of a tandem simulated moving bed process for insulin purification. Biotechnol. Prog. 18(6), 1332–1344 (2002)
Zang, Y., Wankat, P.C.: Three-zone SMB with partial feed and selective withdrawal. Ind. Eng. Chem. Res. 41(21), 5283–5289 (2002)
Zhang, Z., Mazzotti, M., Morbidelli, M.: PowerFeed operation of simulated moving bed units: changing flow-rates during the switching interval. J. Chromatogr. A1006(1–2), 87–99 (2003)
Acknowledgments
Support from Purdue University is gratefully acknowledged. The authors are thankful to Dr. Anand Venkatesan and Mr. George Weeden from Purdue University for their helpful discussions and suggestions.
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Appendices
Appendix 1: Derivation of SWD equation
The mass balance equations for solutes in the mobile phase and pore phase within zone i shown in the equations below are used in deriving the mathematical model for the Linear, Non-Ideal SWD method (Ma and Wang 1997).
where c bi and \(c_{i}^{*}\) are the concentration of solute i in the mobile and pore phase, respectively; D ax,i,j is the axial dispersion coefficient of solute i in zone j; \(\overline{u}_{o,j}\) is the interstitial velocity of the mobile phase in the axial direction; u o,j is the linear velocity in zone j that controls the propagation of the concentration waves relative to the solid phase; P is the bed phase ratio defined by \(\frac{{\left( {1 - \varepsilon_{e} } \right)}}{{\varepsilon_{e} }}\); k f,i,j is the mass transfer coefficient of solute i in zone j; u port is the port velocity; and ε p is the intra-particle void fraction.
The steady state solution to (13) and (14) in each zone must satisfy:
where δ i is the retention factor of solute i defined by δ i = ε p + (1 − ε p )K i ; and K i is the linear isotherm equilibrium constant. Remember that zones 1 and 2 desorbs solute B and A, respectively, while zones 3 and 4 adsorbs solute B and A, respectively. Using the feed port (x = 0) as the reference point, the steady-state equation for solute A in zone 2 can be solved by rearranging (15) with the following boundary conditions:
The solution to (16) is shown in (3b).
In addition, the steady-state equation for solute B in zone 3 can also be solved using the following boundary conditions:
The solution to (17) is shown in (3c). The velocities of zones 1 and 4 can also be derived using a similar approach where zones 1 and 4 will be solved using solute B and A, respectively. The overall zone velocity equation results are shown in (3).
Appendix 2: Derivation of decay coefficients of the SWD equation
The decay coefficients, \(\beta_{j}^{i}\), for the SWD equations (3) is defined by the natural log of the ratio of the highest and lowest concentration of solute i in zone j. However, since the concentrations of the solutes inside the columns in each zone is unknown a priori, it is necessary to estimate the decay coefficients for the standing wave concentrations in each zone. One approach to do this is to link the concentration wave to the yield of each component through a simple mass balance of the inlet and outlet ports. The decay coefficient equations for each zone based on the concentration waves are as follows;
where c k,i is the concentration of solute i in the k port where the subscripts F, E, R, and D represents the feed, extract, raffinate, and desorbent ports while c FP,i is the concentration of solute i after the feed port.
The yield of each component is defined by the ratio of the amount product produced in the outlet port and the amount of feed entering the system.
where Q R = Q 3 − Q 4 and Q E = Q 1 − Q 2 . By substituting Q R and Q E , and rearranging (B2) and solving for c E,B and c R,A , the following equations are obtained.
Next, the mass balance needed for solute A and B around both the raffinate and extract port are:
Solute A:
Solute B:
The four equations are used to express the four unknown concentrations, c Fb,A , c FP,B , c D,A , and c D,B . Rearrangement of (B4) and (B5), and substituting these equations along with (B3) into (B1), the overall decay coefficient expression in terms of yield and zone flow rates are obtained and shown in (4).
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Soepriatna, N., Wang, N.H.L. & Wankat, P.C. Standing wave design of a four-zone thermal SMB fractionator and concentrator (4-zone TSMB-FC) for linear systems. Adsorption 20, 37–52 (2014). https://doi.org/10.1007/s10450-013-9547-y
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DOI: https://doi.org/10.1007/s10450-013-9547-y