Analytical model of vertical oil-water displacement with the account of viscous, capillary and gravity forces

A mathematical model of water displacement in vertical porous media is presented. The mathematical formulation takes the form of a nonlinear convection-diffusion equation. Its contribution comes from consideration of the three chief forces: viscous, capillary and gravity in oil recovery processes. A numerical model was based on the simulator Schlumberger ECLIPSE ver. 2004a_1. Finally, analytical and numerical results are compared.