Numerical Approximation of a Two-Dimensional Nonlinear and Nonequilibrium Model of Reactive Chromatography

A two-dimensional nonlinear and nonequilibrium model of liquid chromatography is numerically approximated to simulate the dynamics of multicomponent mixtures in a fixed-bed isothermal liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection diffusion reaction partial differential equations, coupled with differential and algebraic equations. A semidiscrete high-resolution finite volume scheme (HV-FVS) is applied to solve the model equations. The scheme is second-order accurate in axial and radial coordinates. The resulting system of ordinary differential equations is solved by a second-order accurate Runge-Kutta method. The proposed scheme capably captures narrow peaks and sharp discontinuities in the concentration profiles. Radial gradients were not considered in the previous studies, which are particularly important in the case of nonperfect injections. Several test problems of heterogeneously catalyzed reversible reactions are performed. The considered case studies include three-and four-component elution, assuming hypothetical injections of the reactants in inner or outer sections of the column inlet cross-section. The developed numerical algorithm and results are useful tools for further improvements in reactive chromatography.