A model for the flow of water and oil in granular porous media treated with polymer and gels is presented. The pore geometry is represented by a triangular duct with a periodically varying section while the topological features are modeled by a statistical network. The mathematical treatment consists of the solution of the hydrodynamic equations in the duct and the up-scaling by a percolation type of approach.
The relative permeabilities of a wetting (water) and non-wetting phases (water and oil or gas respectively) are derived both (a) in the absence and (b) in the presence of the an adsorbed polymer or gels. The preliminary results show that both the flow restrictions at the pore level and the topological changes resulting from polymer adsorption or gel retention contribute to the disproportionate permeability reduction (DPR) for water and oil.
A more systematic study of the effects of the parameters and the comparison of the model with the experiments are required for a full validation of the model.