Adaptive predictive collocation with a cubic spline interpolation function for convection-dominant fixed-bed processes: Application to a fixed-bed adsorption process

Interference effects and nonlinearities that are inherent in an adsorption equilibrium add challenges to the task of modeling fixed-bed adsorption processes. In particular, the interference effect tends to produce steep transient concentration fronts, which are enhanced by the high convection to dispersion ratio that is found in normal bed operation conditions. This causes spatial stiffness and renders numerical computations difficult and inaccurate. To solve this problem, we propose a novel numerical procedure using gradient-directed adaptive predictive collocation with a cubic spline interpolation function and far-side boundary conditions. The spatial domain is divided into fixed subdomains and the number of collocation points for each subdomain is adaptively adjusted according to the present location and advancement speed of the maximum gradient in each subdomain. The proposed method was applied to a fixed-bed adsorption process capturing CO₂ from a CO₂/N₂ gas mixture and its effectiveness was compared with that of cubic spline and orthogonal collocation methods with fixed interpolation points, respectively. The effects of kinetic rates on the simulation results were also investigated from the viewpoint of accuracy and CPU time.