Slightly compressible gas slip flow in a fracture: macroscopic model and simulations

Gas flow in fractures is of interest in many fields ranging from hydrocarbon gas recovery from fractured reservoirs (Berkowitz, 2002) to sealing between clamped rough surfaces (Vallet et al., 2009). The present work is focused on gas flow in a single fracture in the creeping, slightly compressible and slip regime. An equivalent of the Reynolds equation is first derived from the complete 3D Stokes problem governing the flow in the fracture. In a second step, a macroscopic model, describing the flow at the scale of a Representative Elementary Surface (RES), is derived by upscaling the Reynolds equation. Numerical solutions for the prediction of the fracture transmissivity appearing in the macroscopic model are illustrated on model fractures. Finally, the determination of the global transmissivity of a heterogeneous fracture characterized by a field of local anisotropic transmissivities is presented.