An appropriate description of gas transfer from shale matrices to fracture networks is one of the most fundamental issues in shale gas extraction modeling. Existing gas transfer functions can be classified into the following categories: (1) direct single-continuum matrix to fracture transfer; (2) kerogen, inorganic matrix, and fracture series gas transfer; and (3) kerogen to fracture and inorganic matrix to fracture parallel gas transfer. The scanning electron microscope (SEM) images of shale samples reveal the heterogeneous distribution of pure inorganic regions, kerogen and inorganic-matrix interwoven regions, and pure kerogen regions. As fracture networks can penetrate different matrix regions at different locations, the mass transfer between matrices and fractures cannot be comprehensively simulated by any of the above methods. This paper presents a new matrix-fracture transfer function considering type 1: the direct inorganic matrix to fracture network inflow for pure inorganic regions; type 2: the kerogen, inorganic matrix, and fracture series flow for kerogen and inorganic-matrix interwoven regions; type 3: the direct kerogen to fracture network inflow for kerogen-rich regions. The contribution of each type in the transfer function is weighted through the volume percentage of each matrix-region type. Different multi-scale and multi-physics gas flow processes are included in kerogen and inorganic matter respectively. Finally, fluid transfer from fracture networks to hydraulic fractures is coupled through a linear flow system with stimulated reservoir volumes (SRVs). This model has been validated against field data with an excellent agreement. And the degraded model's calculation matches well with that of a published composite linear flow model. Sensitivity analyses indicate that matrix-fracture gas transfer patterns affect certain flow regimes from the matrix-fracture transient regime to the transient regime before the boundary dominant regime. Types 1 and 2 gas transfer mechanisms with direct inorganic matter and secondary fracture connection exhibit lower dimensionless pressure and higher dimensionless rate values. The effects of the organic matter volume fraction and organic-rich reservoir block allocations on well production are also documented. This approach is a general tool for characterizing the gas transfer from shale matrices to fracture networks.