Biot poroelasticity of a chemically active shale

The Biot theory of poroelasticity relates the strain $\varepsilon $ of a porous material to changes of the applied stress $\sigma $ and of the pore pressure p. Additional osmotic effects are present in some rocks, such as shales. This paper modifies the thermodynamic arguments used by Biot in order to include the chemical potentials $\mu ^{r}$ of all the chemical species within the pore fluid. In the limit in which salt is unable to move into or out of the shale, the deformation depends only on the chemical potential $\mu ^{w}$ of the water and the applied stress. In the limit of a chemically inert rock, the standard Biot analysis is obtained, and the pore pressure p is again the important variable. Real shales lie somewhere between these two limits.