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 diffusion 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's isotherm and is a key production mechanism. The composition and flow properties of free and desorbed gas are the same. This model is implemented in Matlab using Marcellus shale field data.

Scaling the model shows that recovery of gas depends on two dimensionless numbers that incorporate geometry relations, time scales of flow, intrinsic variables of the porous media, non-Darcy constants, adsorption and boundary conditions. The model is initialized using laboratory and field scale measurements and investigated by sensitivity analyses. The dimensionless numbers define if the fracture or matrix control the gas production rate. When one of the media limit production, the non-Darcy flow mechanisms in the other medium have reduced importance due to lower rate in that medium. In such cases, it is less important to include non-Darcy mechanisms. It is also concluded that slippage effects impacts gas production but can be accounted for in a simpler manner in the model. By checking the magnitude of selected dimensionless numbers, the modelling approach can be determined in advance and huge 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.

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