Solution of a Cattaneo-Maxwell diffusion model using a Spectral element least-squares method

Fluidized bed reactors are widely used in gas processing facilities due to their superior heat and mass transfer characteristics. Reaction rates in these reactors depend on the diffusion of species into the catalytic particles. A more accurate description of diffusion than Fick's law provides is required for the optimization of the design of these reactors. In this work, a Least Squares Finite Element framework was implemented in order to solve the evolution of the concentration profile predicted by Cattaneo-Maxwell's law inside a catalytic pellet. Fick's and Cattaneo-Maxwell's models were compared, being the obtained predictions significantly different for time scales similar to the relaxation time but converging asymptotically for larger time scales. Time-marching and full-domain numerical approaches were compared. The convenience of the time-marching approach was verified, since this approach yields the same accuracy with less computational cost.