Numerical and analytical analysis of flow in stratified heterogeneous porous media.

Abstract

The groundwater flow through a porous media is well-researched to extend the basic knowledge in both academia and industry, specially the oil industry. The Boussinesq equation represents a water height of fluid spreads into the semi-infinite medium for unsteady flow. Property of this flow represents a groundwater flow after a high water period or after a breakthrough of a dam around a reservoir. The fluid is drained out as an intense pulse at the boundary and ow through the porous medium by gravity-driven motion. In this studying, the Boussinesq equation is re-produced from Barenblatt et al. (1999) [1]. The analytical and numerical analysis is used to solve this equation for a homogeneous porous medium. In the real life, we do not always have the homogeneous porous medium. A system fissures is counted into the Boussinesq equation and applies a basic of a "double-porosity" model for a stratified heterogeneous porous medium. The model is a system of two equations: one for water level in fissurized porous blocks and one for water level in system cracks. These equations are only solved with numerically because they are very complicated when we solve with analytically. For comparison, a purely porous blocks is obtained under same conditions with fissurized porous blocks. This demonstrates how the fissures influence on the groundwater flow in stratified heterogeneous porous media, increasing of the speed and the penetration of the fluid into the medium. At first stage, the groundwater flow is rapid breakthrough at the boundary into the porous media via a system cracks; and at later stage, the fissures is supported by the fluid in fissurized porous blocks.