Analysis of a finite element numerical solution for a nonlinear seepage flow model in a deformable dual media fractal reservoir

In this paper, an unsteady state flow mathematical model for a deformable dual media fractal gas reservoir in a second kind of boundary conditions is developed, with the consideration of dynamic changes in porosity and permeability as a result of pressure depletion in the system. Existence and convergence from this mathematical model are proven for a finite element discrete numerical solution in the framework of a fractal geometry theory. Then, a concise numerical solution, in the one variable linear interpolation function space, is achieved by adopting the Galerkin finite element method.