We construct a three-dimensional pore-network model with mixed wettability to study the two-phase flow mechanisms in dry gas producing shales. Previous pore-scale modeling studies on shale have been focused on single-phase gas flow through the nano-pores. However, at most field sites, the majority of the injected fracking fluid does not return to the surface during the flow-back period. It is believed that a large portion of the fracking fluid imbibes into the shale matrix during the fracking process, and thus two-phase flow occurs. In addition, while the inorganic shale matrix is generally water-wet, the organic material embedded within the matrix is hydrophobic. As such, the system displays spatial heterogeneity of wettability. Other important physics are also coupled in the model. Pressure-dependent gas sorption effects are included in the organic pores, with pore size reduction accounted for in those pores. Compressibility and slip flow effects of the gas phase are included throughout the pore-network, with the latter underscoring the fact that the sizes of the nano-pores are comparable to the mean free path of the methane molecule. The coupled effects of these various physical processes are studied to determine the importance of each effect. Continuum-scale properties are computed, including relative permeability curves, as a function of fraction and structure of organic regions and type and magnitude of boundary conditions.