Computation of the Longitudinal Dispersion Coecient in an Adsorbing Porous Medium Using Homogenization
Aiske Rijnks, Mohamed I. M. Darwish, Hans Bruining, Shell Exploration, Johannes M. Bruining · 2009
In a pioneering paper Bouddour, Auriault and Mhamdi-Alaoui derive upscaled expressions for the dispersion coecients for reactive ow in a porous medium using the method of homogenization. The method uses a periodic unit cell (PUC), which consists for instance of a spherical grain in a cube, but nothing prohibits dening more complex PUC's. Homogenization leads to a coupled system of equations where the ow is de- scribed by Stokes equation and the concentra- tion uctuation is described by a convection diusion source term equation. In the PUC we have semi-periodic boundary conditions (BC's). The solution of the equation is not trivial due to the source term and the BC's. The same equation arises in other upscaling techniques for upscaled dispersion coecients, such as solving equations in periodic media or REV averaging. We show that commer- cial nite element software (COMSOL) can be readily used to compute longitudinal and transversal dispersion coecients in 2-D and 3-D; this makes homogenization accessible to the engineering practice. Details of the com- plete numerical procedure are discussed in de- tail. The results are for the rst time com- pared with experimental data of the dispersion coecient versus Peclet number; there is good agreement. Adsorption enhances the longitu- dinal dispersion coecient.