بهینه سازی تصادفی از حرکت شبیه سازی شده فرآیند بستر: تجزیه و تحلیل حساسیت برای عملیات isocratic و شیب

A random search strategy has been used for designing and optimization of simulated moving bed process (SMB) under isocratic as well as under solvent gradient conditions. The effectiveness of both the process modes has been compared. For predictions of the objective functions, i.e., the minimum of eluent consumption and/or the maximum of the process productivity a mathematical model of the process dynamics has been employed and implemented in the optimization procedure. Four-dimensional space of decision variables corresponding to the flowrates in the SMB zones has been searched in order to find the optimal set of the process parameters. The optimization was constrained to the purity demand in the outlet streams withdrawn in the raffinate and the extract port. The obtained set of random decision variables fulfilling purity constraints was used to construct the operating window of parameters guaranteeing successful separation. For feasible operating points the sensitivity of the purity constraints with respect to the operating parameters has been calculated. The results of calculations indicated that operating conditions, which ensure similar process efficiency, could correspond to different sensitivity of the process constraints. Such an analysis was found to be useful for the selection of process conditions, for which the best trade-off between the process efficiency and its robustness can be achieved. This appears to be particularly important for designing the gradient SMB process, for which robustness of the operating conditions is a factor of a major importance.

In the last decade the simulated moving bed (SMB) process has been successfully implemented as a separation technique in the petrochemical, biochemical and fine chemical industries. The SMB is a well-established separation technology basing on continuous chromatography process. The SMB unit was designed as a practical realization of a true moving bed (TMB) where the solid and fluid phases move countercurrently. The general concept of a classical four-zone SMB unit is illustrated schematically in Fig. 1. There are two incoming streams: the feed mixture to be separated (View the MathML sourceV˙F) and desorbent or eluent (View the MathML sourceV˙D). Two streams leave the unit, one enriched with the less adsorbable raffinate (View the MathML sourceV˙R), and one enriched with the more adsorbable extract (View the MathML sourceV˙E). The four streams divide the unit into four zones (I–IV). Each of these zones contains at least one fixed bed (column) and has to fulfill distinct tasks, i.e., in the zones II and III separations takes place, while in zones I and IV the solid and the fluid phases are regenerated, respectively. The movement of the solid bed is simulated by switching of ports or columns in certain time intervals (Ruthven & Ching, 1989). Full-size image (20 K) Fig. 1. Scheme of a four-zone SMB unit allowing the implementation of a gradient operation. Figure options The SMB technique is implemented in an industrial scale using the same solvent to prepare the feed and to perform the adsorbent regeneration. This so-called isocratic process is presently well understood (Mazzotti et al., 1994, Mazzotti et al., 1996 and Mazzotti et al., 1997; Migliorini et al., 1998 and Migliorini et al., 1999; Storti, Masi, Carra, Mazzotti, & Morbidelli, 1989). Recently, the idea of modulating of solvent strength in order to increase productivity was introduced to the liquid SMB separation (Abel et al., 2002 and Abel et al., 2004; Antos and Seidel-Morgenstern, 2001 and Antos and Seidel-Morgenstern, 2002a; Houwig, van Hateren, Billiet, & van der Wielen, 2002; Jensen, Reijns, Billiet, & van der Wielen, 2000). The solvent strength can be modulated in two steps using different solvents at the two inlet ports. The feed is dosed continuously in a relatively weak solvent, whereas as the desorbent a stronger solvent is used (see Fig. 1). Thus, in the classical four zones closed-loop SMB process two distinct levels of internal solvent composition exist which are separated by the two inlet positions. These two characteristic levels of solvent strength can be adjusted by using different amounts of a suitable modifier in the two feed streams. As a result, the components to be separated are more retained in the solvent regeneration zone of the SMB process (zone IV) and more easily eluted in the sorbent regeneration zone (zone I). Recent results of studying this type of two-step gradient SMB process in the closed-loop arrangement demonstrated its potential to reduce significantly the solvent consumption and, thus, to increase product concentrations (Abel et al., 2002 and Abel et al., 2004; Antos and Seidel-Morgenstern, 2001 and Antos and Seidel-Morgenstern, 2002a; Ziomek, Kaspereit, Jeżowski, & Seidel-Morgenstern, 2005). Design and optimization of such a complex process in an industrial scale can be done by the use of an optimization procedure coupled with an adequate mathematical model of process dynamics. Recently, stochastic optimization algorithms have been successfully applied for the optimization of isocratic SMB process, e.g., a genetic algorithm was implemented in the multiobjective optimization of a reactive SMB process (Subramani, Hidajat, & Ray, 2003; Zhang, Hidajat, & Ray, 2002a), SMB and the Varicol process (Zhang et al., 2002b and Zhang et al., 2003), a random search algorithm of Luus and Jaakola (1973) was used for the optimization of mobile phase composition in the isocratic and gradient SMB process (Ziomek et al., 2005). In this work the multi-pass Luus and Jaakola (1973), Luus (2001) MPLJ algorithm was modified and utilized to construct the window of the operating parameters for isocratic as well as for gradient SMB process. The effectiveness of both the process modes has been compared. Since the application of the solvent gradient was found to be very promising with respect to the productivity and the eluent consumption, main efforts have been focused on the developing of a reliable numerical tool for the designing of the gradient SMB operation, i.e., selecting conditions favorable for both the process effectiveness and its robustness. The optimization involved four decision variables corresponding to the flowrates in the SMB zones and it was constrained to the purity demand in the outlet streams withdrawn in the raffinate and the extract port. For the operating points generated during the calculations sensitivity functions of the purity with respect to the operating parameters have been calculated. The sensitivity analysis indicated that operating conditions, which guarantee similar process effectiveness can correspond to different values of the sensitivity functions. Low absolute values of sensitivity are related to high robustness, i.e., ability of the unit to be retained in the state, in which it can perform purity demand required. Hence, for the process realization a set of the operating parameters favorable for both effectiveness and robustness should be selected. This appears to be particularly important for the designing of the solvent gradient SMB process, for which small deviations from the operating conditions can results in failure of the separation.

In this work an efficient numerical tools has been proposed for optimization of SMB process. The main efforts have been focused on the designing of the solvent gradient SMB operation, which was proved to outperform isocratic mode with respect to the eluent consumption and the process productivity. The multi-pass Luus–Jaakola algorithm has been modified and used for the optimization of the separation process. For predictions of the objective functions, i.e., the minimum of eluent consumption the equilibrium stage model accounting for real system efficiency was employed and implemented in the optimization procedure. Such an optimization tool allowed the construction of the operating window of parameters guaranteeing successful separation. For feasible operating points generated during the random search calculations several performance indexes were simultaneously observed: eluent consumption (the goal function), extract and raffinate port purities (constraints), productivity, and sensitivity of the purity with respect to such operating parameters as the flowrates and the modifier concentration. The results of calculations indicated that a number of operating parameters correspond to the similar process efficiency but different maintainability of the purity at the desired level. The sensitivity analysis was found to be helpful for balancing high efficiency of the process with its high robustness. The results of the sensitivity analysis revealed that in the gradient operation, which performance is superior compared to the isocratic mode, maintaining of the modifier concentration at the level predicted is a factor of major importance.