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This work developed a numerical mathematical model based on mass conservation. This developed model was designed by incorporating and investigating the impact of the governing parameter - apparent gas permeability, Knudsen diffusion, Forchheimer factor and Langmuir's isotherm to define pressure-dependent gas adsorption necessary for the flow transition from the matrix to fracture-matrix inflow, and then fracture to the wellbore. The model developed was also used to look at the effect of non-Darcy flow mechanism contribution of the matrix in shale gas production. The developed model is a sensitive tool that describes the complexity of the shale gas reservoirs production and identifies flow regimes for various production conditions. The dimensionless variables or their product defines the shale gas production, and the contributing dominance of either the matrix or the fracture.