The stress and pore pressure dependence of permeability of shale gas rock is considered for the case of two-solid constituents porous medium. It is done for a generalized model of composite sphere phases each of them being gas/fluid saturated. It is shown that the total mean stress in each of the phases is different from the confining stress even for homogeneous state. This leads to a more complicated dependence of permeability rather than that of Terzaghi effective stress, i.e. confining stress minus pore pressure as in the case of one-solid constituent porous medium. Additional dependence of permeability on pore pressure is captured by taking into account Knudsen and slip flow contributions. Because depletion-induced variation of pore pressure leads to variation of eigen-strain, the resultant strain and stress exerted at the reservoir by surrounding country rock is found by using Eshelby-type inclusion model. The depletion-induced evolution of reservoir permeability is expressed as a function of pore pressure.
Finding an adequate description of permeability in shale gas is a challenging problem because of complexity of the rock which contains both organic and non-organic components. Because the shale gas rock is constituted by at least two main components: organic matter and shale, we would like to consider how this feature can affect dependence of effective medium permeability on stress and pore pressure.
As usual we assume that permeability is some function of porosity. In conventional theory of poroelasticity variation of porosity is a function of Terzaghi effective stress:
The average stress, σV, in the eq. 1 relates to the stress in the part of rock, the porosity is defined for. If the rock has only one solid porous constituent, then the average stress is unique. Situation might be different if there are two or more solid constituents in porous medium. The local variations of stress in the different solid components are the same as global one only in some special cases (Berryman et al, 1991).
Stress dependence of permeability is particularly important for the case of low porosity because stress increase may effectively close some flow paths. In that sense the system is close to percolation threshold.