Numerical Calculation Method of Multi-Scale Seepage Equation Considering Langmuir Desorption of Shale Gas

Abstract

Utilizing Besok-Karniadakist's motion equations for ultra-low permeability shale gas reservoirs, which accommodate four flow modes, and incorporating the Langmuir adsorption, transportdiffrential equations are derived. A pseudo-pressure formulation adhering to Darcy's law and a pseudo-time are introduced. By applying the mass conservation, a correspondence between nonlinear and linear equation parameters is established, merging both types of equations. Through examples, the production dynamics of nonlinear seepage, including fixed well-bottom pressure and production rates, and parameter sensitivity are analyzed, offering insights for enhancing shale gas productivity.