The main operational parameters controlling borehole stability in drilling shales are the density and the chemical composition of the drilling fluid. The density of the drilling fluid provides support of the borehole wall, while the chemical composition of the drilling fluid can be adopted to reduce the infiltration rate and to maintain hole stability for prolonged exposure time of the drilling fluid to the shale. To describe the interaction between the drilling fluid composition and the mechanical behaviour of shales, an electro-chemo-mechanical formulation of quasi-static finite deformation of swelling compressible porous media has been derived from the theory of mixtures. The model presented in this paper, which is applicable to biological tissues and synthetic hydrogels also, consits of an electrically charged porous solid, saturated with an ionic solution. The mixture as a whole is assumed electro-neutral. Four phases following different kinematic paths are defined; solid, fluid, anions and cations. Balance laws have been derived for each constituent and for the mixture as a whole. A Lagrangian form of teh second law of thermo-dynamics has been derived to formulate the constitutive relations for the swelling behaviour of shales as well as the transport equations for the fluid and the ions.
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