© 2016 Elsevier Ltd. All rights reserved. Horizontal drilling and hydraulic fracturing are two enabling technologies to create a shale gas reservoir. For the created reservoir scale, we define shale blocks between hydraulic fractures as matrixes. In the matrix scale, flow processes are defined in the components of inorganic minerals and kerogens, respectively. Under this framework, a set of partial differential equations are derived to define various flow and deformation processes: (1) mechanical equilibrium equation that defines the shale deformation; (2) gas flow in the kerogen system of matrix; (3) gas flow in the inorganic system of matrix; and (4) gas flow in the hydraulic fracture system. For each of gas flow systems, a permeability or diffusivity model is derived to define its evolution. All systems are fully coupled through these permeability models and mass exchanges between different systems. The fully couple PDE system was solved by using COMSOL, a popular PDE solver. The model was verified against gas production data from the Marcellus Shale and the Barnett Shale, respectively. The verified model was applied to investigate the impact of adsorption parameters, flow regimes (Knudsen number), initial permeability of the inorganic matrix, and the effective stress variations on the gas production. Model results show that the Langmuir parameters affect both the cumulative gas production and the gas extraction processes; that the impact of flow regimes is closely related to the initial permeability of the inorganic matrix; and that the impact of effective stress variations on the permeability of hydraulic fractures is more significant than that on the matrix system.