Naturally fractured shale reservoirs with multiple hydraulic fractures have been repeatedly described by dual porosity models. In these models the reservoir volume is divided into extremely low permeable shale matrix blocks surrounded by a fracture network. The low permeability of the matrix blocks limits the gas flow from matrix to the fracture. However, in many shale reservoirs unexpected high gas production has been observed which cannot be justified with the conventional dual porosity models.
Recent discoveries reveal that natural and induced micro fractures, may serve as hidden pathways for the communication between matrix and fracture network. Hence, one idea to more reliably model the gas production in shale reservoirs is incorporating micro fractures in the Dual porosity models.
In this paper, we hypothesis that the matrix blocks considered in the dual porosity model can themselves be considered a dual porosity media. We assume that the overall matrix system is composed of sub-matrices with nano Darcy permeability and micro fractures with milli to micro Darcy permeability. We assume that viscous Darcy flow is dominant in macro and micro fracture networks, and diffusion and desorption mechanisms are dominant in sub-matrices. Furthermore, we extend the existing transient and pseudo-steady-state dual porosity formulations, and develop a triple porosity model for the inner shale reservoir. We perform sensitivity analysis to the non-dimensional parameters including inter-porosity transmissivity ratios and storativity of each medium on the pressure transient behavior. We observe that the proposed model can be appropriately used to see the effect of the properties of each medium on the pressure response.