Particle transport method for simulation of multicomponent chromatography problems

A novel numerical technique, called the particle transport method (PTM), is applied in simulation of multicomponent chromatography problems with non-linear isotherms. The method is based on the operator-splitting approach, and combines the Lagrangian method of characteristics and the method of lines. Instead of a moving mesh, a set of numerical points (called particles) which can be interpolated to any fixed grid with a fast monotone projection procedure is used. The technique includes a special spatial adaptivity to simulate the propagation of steep fronts (shock waves) that are often encountered in non-linear chromatography. The application of PTM for solving ideal and nonideal models of chromatography is demonstrated with two-component systems following the competitive Langmuir and Fowler isotherms. The accuracy and calculation time of PTM for various cases are compared with those of classical methods such as OCFEM, MOL and the Rouchon algorithm. The numerical experiments show that the proposed approach exhibits good mass conservation while being a computationally cheap scheme.