Combination of space–time conservation element/solution element method and continuous prediction technique for accelerated simulation of simulated moving bed chromatography

•We developed a space–time CE/SE method for solving model equation of SMB.•CE/SE method is combined with continuous prediction method for fast simulation of SMB.•The calculation time is saved by 77% and 96% by CE/SE+CPM in the two case studies.•The technique for ensuring CE/SE method to be convergent is developed.

The model equation of simulated moving bed (SMB) process is solved by a space–time conservation element and solution element (CE/SE) method, which is found to be more efficient than other methods in the two case studies. Furthermore, this CE/SE method was combined with continuous prediction technique (CPM) to further accelerate determination of the cyclic steady state in SMB operation. Comparing with conventional method of lines at the same required precisions, CE/SE with CPM was proved to save the CPU time by 77% for the pseudo-linear system of glucose–fructose separation and 96% for nonlinear enantioseparation. Finally, the combination of CE/SE and CPM was applied to the optimization study to determine the optimum switching time and flow rate. To ensure the method be convergent, the four Courant numbers in four zones need to fall between 0.1 and 1. The method for fulfill this constraint is also developed.