Numerical modeling of a trickle bed reactor

Trickle bed reactors are widely used in the chemical and petroleum industries to perform processes such as hydrodesulfurization and oxidation reactions. These reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass.; Our numerical method to solve these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high resolution finite difference methods to discretize the equations. Our results show that the algorithm is second-order accurate for smooth problems. Additionally, we are able to capture the effects of capillary pressure and the Ergun equation.; In addition, we utilize Adaptive Mesh Refinement (AMR) techniques developed by Berger and Oliger to concentrate computational effort where it is needed. We refine in space using a nested hierarchy of block-structured patches. We refine in time by using subcycling—we advance finer grids several times and synchronize them with the coarser grids. We introduce three new innovations in our adaptive algorithm. First of all, we utilize a volume discrepancy method to correct for freestream preservation problems at coarse/fine interfaces. We introduce a lagged correction scheme for coarse/fine boundary conditions to minimize the number of multilevel elliptic solves. Finally, we use an error estimation method based on Richardson extrapolation to determine the patches of refinement; this error estimation method is suitable for the hyperbolic-elliptic problem we are solving. Our results demonstrate that the adaptive mesh refinement algorithm is able to reproduce the results from a single-grid code with a substantial savings in memory and computational effort.