Macro-scale and micro-scale natural fractures are widely observed in shale. Their deformation during reservoir pressure depletion changes the major flow channel aperture for oil and gas flow, dominates permeability evolution, and hence controls gas production. A significant portion of fracture deformation comes from gas desorption-induced matrix shrinkage. Due to the matrix-fracture permeability difference, pressure changes faster in fractures. There is a matrix-fracture pressure equilibrium time lag. As matrix gas is released from matrices and enters fractures, matrix shrinkage may occur. During this period, the drained matrix shrinkage area propagates from the fracture wall into the inner matrix, leading to the transition from localized shrinkage near the fracture wall to bulk rock shrinkage. During this transition process, matrix shrinkage can be divided into two parts: one opens fractures (localized shrinkage), while the other determines bulk rock shrinkage. Currently, how the shrinkage transition induced by the equilibrium time lag influences gas production and fracture permeability evolution across the reservoir is not clear.

In this paper, we define a splitting function as a dynamic drained matrix volume ratio based on the gradual drained matrix area propagation to quantify matrix shrinkage's contribution to local and bulk shrinkage. Initially, the drained matrix volume ratio is close to zero. Matrix shrinkage occurs at the fracture surface with its maximum contribution to local shrinkage. Then, its contribution to local shrinkage drops with drained shrinkage area propagation, while the contribution to bulk shrinkage increases. When the final matrix-fracture pressure equilibrium is reached, the whole matrix is drained with a unit drained matrix volume ratio. Matrix shrinkage completely contributes to bulk shrinkage without any local effect. Based on this conceptual understanding, we develop a generic natural fracture permeability model that incorporates shrinkage transition and flow regime's effect. The proposed permeability model is then implemented into a multiphysics model for shale gas reservoirs. In this model, multiple physical processes are defined by a group of Partial Differential Equations (PDEs) fully-coupled through permeability and porosity models. These PDEs are numerically solved by a commercial PDE solver.

We verify the fracture permeability model against experimental data and validate this numerical reservoir model by comparing with analytical model's results and the production data of two field cases. The existence of shrinkage transition generates time-dependent multi-stage permeability evolution. Initially, the natural fracture permeability is relatively stable. Then the permeability declines due to pressure depletion. Later on, localized shrinkage opens the fracture aperture, leading to a permeability enhancement. After a peak value, permeability drops again and finally becomes stable. If shrinkage transition is ignored, the 30-year cumulative gas production of the given case will be underestimated by up to 22.2%. Parametric investigations are performed to examine the influences of different reservoir and hydraulic fracture properties on cumulative gas production.

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