Mathematical modeling of elastic soil acid treatment

Abstract

The study is devoted to an initial boundary value problem describing the process of cleaning the bottomhole zone of an oil well with acid solution. It is assumed that the soil frame is an elastic solid body and the pore space has double porosity. The physical process is described at the microscopic level by the Stokes equations for the liquid component, the diffusion-convection equation for the concentrations of acid and chemical reaction products, and the Lame equations for the solid frame. Due to soil dissolution, the pore space has an unknown (free) boundary. The lattice Boltzmann method (LBM), the immersed boundary method (IBM) and the finite element method (FEM) are used for computer simulation. Finally, discretization of equations and results of numerical solutions are presented.