A fast and accurate numerical method for solving simulated moving bed (SMB) chromatographic separation problems

Abstract Solving simulated moving bed (SMB) chromatography models requires fast and accurate numerical techniques, since their system size computed is large due to multi-columns and multi-components, in addition the axial solution profiles contain steep moving fronts. The space-time conservation element/solution element (CE/SE) method addressed in this study enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level) on staggered space–time grids. Thus, accurate and computationally efficient numerical solutions are obtained. Stable solutions are guaranteed if the Courant–Friedrichs–Lewy (CFL) condition is satisfied. The boundary condition and recycle flow treatments are much simpler than for the time integrator in the framework of the method of lines. Applying the CE/SE method for SMB chromatographic problems, non-dissipative and accurate solutions are obtained and fast calculation is achieved in this study. The effects of two-computational parameters (CFL number and mesh stepsize) on the numerical solution are examined, illustrating two SMB processes whose Peclet and Stanton numbers are different. It is shown that the CFL number affects little the numerical solution under the relatively high Peclet number and low Stanton number but a small mesh stepsize is required to enhance accuracy. As the Peclet number decreases and the Stanton number increases, a lower CFL number is preferable and larger mesh stepsize is permitted. In the case study of the SMB adsorption problems, a large CFL number and sufficient number of mesh points (or small mesh stepsize) are desirable to reduce the calculation time and increase accuracy.