This paper presents a model of the stress and pore-pressure dependence of permeability in organic-rich shale rocks such as gas shales, which are porous media that consist of (at least) two constituents – kerogen (organic) and inorganic matter – with significantly different mechanical properties. The model treats these organic-rich rocks as porous media in which both organic and inorganic constituents have laminar morphology. This leads to a more complicated dependence of permeability rather than that of differential (Terzaghi) effective stress, i.e. confining stress minus pore pressure as in the case of one-solid constituent porous medium. The model provides a better description of effective stress, and better explains the dynamic impact of geomechanical stresses on key production parameters such as porosity and permeability. Comparison of this model with classical theories and limited experimental results is performed. This new model is a generalization of the earlier developed spherical composite model  for more realistic laminated texture of gas shale rock. Additional dependence of permeability on pore pressure is captured by taking into account Knudsen flow contributions. The model provides basis for estimation of maximum drawdown which still avoids collapse of porosity and permeability of softer organic constituent.
Gas shale rock has at least two distinct solid constituents, which are organic and inorganic matter. The most important mechanical difference is that the organic matter is significantly softer (approximately four times, see [1, 2]) than the inorganic matter. It may cause a noticeable difference in stress values in organic matter and inorganic matter. In turn this feature leads to different evolution of porosity and permeability in the different solid constituents.