2-d mathematical and numerical modeling of fluid flow inside and outside packing in catalytic packed bed reactor

Abstract

Generally, the momentum equation of fluid flow in porous media was solved by neglecting the terms of diffusion and convection such as Ergun, Darcy, Brinkman and Forchheimer models. Their model primarily applied for laminar flow. It is true that these model are limited to condition whether the models can be applied. Analytical solution for the model type above is available only for simple one-dimensional cases. For two or three-dimentional problem, numerical solution is the only solution. This work advances the flow model in porous media and provide two-dimentional flow field solution in porous media, which includes the diffusion and convection terms. The momentum lost due to flow and porous material interaction is modeled using the available  Brinkman-Forchheimer equation. The numerical method to be used is finite volume method. This method is suitable for the characteristic of fluid  flow in porous media which is averaged by a volume base. The effect of the solid and fluid interaction in porous  media is the basic principle of the flow model in morous media. The Brinkman-Forchheimer consider the momentum lost term to be determined by a quadratic function of the velocity component. The momentum and the continuity equation are solved for two-dimentional cylindrical coordinat . the result were validated with the experimental data. The velocity of the porous media was treated to be radially oscillated. The result of velocity profile inside packing show a good agreement in their trend with the Stephenson and Steward experimental data. The local superficial  velocity attains its global maximum and minimum at distances near 0.201 and 0.57 particle diameter, d_p. velocity profile below packing was simulated. The result were validated with Schwartz and Smith experimental data. The result also show an excellent agreement with those experimental data.

Keywords : finite volume method, porous media, flow distribution, velocity profile