The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics

This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The consists two governing partial differential equations (PDEs) written terms effective diffusivities for free sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution Laplace equation PDEs Green’s second identity. domain integrals arising due time-dependent function nonlinear transformed into employing dual-reciprocity method. transformation retains domain-integral-free, boundary-integral-only character standard BEM approaches. In proposed solution, free- sorbed-gas flow matrix is solved simultaneously after coupling fracture gas. Well production performance under effect relaxation phenomenon delayed responses nonequilibrium condition rigorously captured by imposing zero-flux at fracture–matrix interface equation. validity verified several case studies through comparison against commercial finite-element numerical simulator.