Numerical Investigation of Non-Darcy Flow Regime Transitions in Shale Gas Production

Abstract

Shale gas reservoirs are organic rich formations with often ultra-low permeability. Gas is stored in free and adsorbed form. Conventional Darcy flow cannot fully describe the gas transport in such porous media. It is thus crucial to study the shale gas production considering different flow regimes and time dependent permeability, which can improve well-induced fracture design and ultimate gas recovery. In particular, this paper will focus on the transition in non-Darcy flow regimes near fracture-matrix interfaces using mathematical modelling. Especially, we investigate conditions at which these effects vanish, and Darcy flow assumptions become reasonable. The model describes a representative well-induced high permeability fracture surrounded by shale matrix. Investigated Non-Darcy mechanisms include apparent permeability, Knudsen diffusion, gas desorption and Forchheimer flow. Pressure depletion is the main driving force for single phase gas flow from the matrix to the fracture and from the fracture to the well. Pressure dependent gas desorption is defined by Langmuir isotherm and is a key production mechanism. This model is implemented in Matlab using Marcellus shale data. Scaling the model shows that recovery of gas depends on two dimensionless number that incorporates geometry relations, time scales of flow, intrinsic parameters of the porous media, non-Darcy constants, adsorption and boundary conditions. The dimensionless numbers define respectively if 1) the fracture or matrix limit the gas production rate 2) if non-Darcy flow is significant in the fracture or matrix. When one of the media limit production, the non-Darcy flow in the other medium has reduced importance and can be excluded from the model. Non-Darcy flow is important if it limits flow in the medium limiting the production. By checking the magnitude of the selected dimensionless numbers, the modelling approach can be determined in advance and significant computational time can be saved. The proposed model provides a tool for interpretation of complex shale gas production systems. It can be used for screening of flow regimes at different operational configurations and hence appropriate modelling approaches. The model can be used to optimise fracture network design and potentially in identifying stimulation operations that may significantly improve production rates and ultimate recovery from unconventional gas reservoirs.