Transit and Steady State Prediction by Wavelet: Application to the SMB Separation Process

摘要

The industrial applications of the simulated moving bed (SMB) technology bring in the increasing attention in the development of numerical solution tool for good design and effective control. The major problem in traditional numerical methods is on the definition of the spatial grid points where the solution has steep fronts, which is typical in chromatographic separation. In our research, we have been making effort to promote wavelet based approaches for solving SMB chromatographic models. The original function can be represented as wavelet expansion function and operations will be performed using the corresponding wavelet coefficients only. The treatment of the boundary conditions will be based on some modified interpolating functions constructed to achieve an interpolating operator at the interval of the same accuracy as the counterpart on the line. Wavelet application to the solution of single column chromatographic process represented by a Transport-Dispersive-Equilibrium linear model was firstly studied to investigate the solution power of wavelet on the prediction of transit behaviour of wave propagation. Comparisons of finite difference and wavelet methods with analytical solution were conducted on a range of Peclet numbers. Application to a dynamic SMB model was carried out for an enantiomers separation process. Using wavelet for spatial discretization combined with a 3 rd order semi-implicit integrator, it has provided encouraging results in terms of computation time, prediction accuracy on steep front, and it is faster at achieving steady state.