On a compressible miscible displacement in naturally fractured reservoirs
Catherine Choquet · 2020
We derive a double porosity model for a displacement of one compressible miscible fluid by another in a naturally fractured reservoir. In the microscopic model, the displacement is described by a set of nonlinear coupled partial differential equations, given by the conservation of mass and the Darcy law. The porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter ε representing the size of the matrix blocks. Using homogenization theory and in particular two-scale convergence, we derive rigorously the corresponding double porosity model. The scaling preserves the physics of the flow in the matrix, which then contributes in the macroscopic model as memory terms. We specify them in spite of the strong nonlinearities and of the coupling using some appropriate dilation operator.