Mathematical models of a liquid filtration from reservoirs

Abstract

This article studies the filtration from reservoirs into porous media under gravity. We start with the exact mathematical model at the microscopic level, describing the joint motion of a liquid in reservoir and the same liquid and the elastic solid skeleton in the porous medium. Then using a homogenization procedure we derive the chain of macroscopic models from the poroelasticity equations up to the simplest Darcy's law in the porous medium and hydraulics in the reservoir.

Keywords

• Lame's equation
• Stokes equation
• liquid filtration
• homogenization
• poroelasticity