Nonlinear and non-local analytical solution for Darcy–Forchheimer flow through a deformable porous inclusion within a semi-infinite elastic medium

Permeability is a nonlinear and non-local function of the intimate coupling between pore fluid flow solid deformation in porous media. A class related problems involves effect injection or withdrawal on transport properties geomaterials. This paper presents an analytical solution for problem through disk-shaped elastic inclusion below free surface half-space. The accounts following mechanisms: (i) variations permeability coefficient due to flow-induced inclusion; (ii) inertial losses flow. former latter mechanisms are formulated using Green's dilatation centre half-space Darcy–Forchheimer equation media, respectively. An perturbation considered developed validated against numerical finite element same problem. described represented by two dimensionless parameter groups. extreme values these groups govern asymptotic behaviours mimicking special-case solutions which either mechanism forced vanish. applied aspects demonstrated wellbore performance index that quantifies subsurface rock ability deliver toward away from reservoir. Unlike linear models, presented captures observed dependence rate.