Transient and steady-state models for simulated moving bed processes: numerical solutions

Abstract

The objective of this work is to compare different strategies for the numerical solution of mathematical models of simulated moving bed (SMB) processes to predict the transient and steady-state behaviour. The mathematical model is based on the true moving bed (TMB) description of SMB processes. The model assumes axial dispersion flow for the liquid phase and plug flow for the solid phase. Intraparticle mass transfer was described in terms of a simple linear driving force (LDF) approximation. The mathematical models for transient situations (TM_1 and TM_2) can be written in terms of system of partial differential-algebraic equations (PDAEs) or partial differential equations (PDEs), respectively, when the algebraic equation representing the adsorption equilibrium isotherm is inserted into the mass conservation/mass transfer kinetics equations or written as separate equation. Similarly, for steady-state the mathematical models (SSM_3 and SSM_4) are represented by a system of differential-algebraic equations (DAEs) or ordinary differential equations (ODEs). Different public domain solvers were used to numerically solve the four mathematical models described above. For the transient model TM_1 the DASSL solver was used to solve the system of PDAEs and for TM_2 the PDECOL package was used to solve the system of PDEs. For the steady-state model, the solvers COLDAE and COLNEW were used to solve the DAEs and ODEs systems, corresponding to the models SSM_3 and SSM_4, respectively. The glucose/fructose separation was used as a test case in a SMB with a 12 column configuration considering both linear and non-linear isotherms. The study of the effect of the operating conditions on the TMB performance and separation regions was also analysed. For the calculation of steady-state concentration profiles and process performance COLDAE solver is recommended because it requires less computing time and allows working with the adsorption equilibrium isotherm separately permitting easy changes on the algebraic relationship.