In this work, the problem of structural deformation with two-phase flow of carbon sequestration is presented. A model to simulate miscible CO2 injection with structural deformation in the aqueous phase is established. In the first part of this paper, we developed analytical solution for the problem under consideration with certain types of boundary conditions, namely, Dirichlet and Neumann boundary conditions. The second part concerns to numerical simulation using IMPDES scheme. A simulator based on cell-centered finite difference method is used to solve this equations system. Distributions of CO2 saturation, and horizontal and vertical displacements have been introduced.

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