Incorporating electrokinetic effects in the porochemoelastic inclined wellbore formulation and solution

Abstract

The porochemoelectroelastic analytical models and solutions have been used to describe the response of chemically active and electrically charged saturated porous media such as clays, shales, and biological tissues. However, these attempts have been restricted to one-dimensional consolidation problems, which are very limited in practice and not general enough to serve as benchmark solutions for numerical validation. This work summarizes the general linear porochemoelectroelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active and ionized formation, such as shale, and subjected to a three-dimensional in-situ state of stress. The analytical solution to this geometry incorporates the coupled solid deformation and simultaneous fluid/ion flows induced by the combined influences of pore pressure, chemical potential, and electrical potential gradients under isothermal conditions. The formation pore fluid is modeled as an electrolyte solution comprised of a solvent and one type of dissolved cation and anion. The analytical approach also integrates into the solution the quantitative use of the cation exchange capacity (CEC) commonly obtained from laboratory measurements on shale samples. The results for stresses and pore pressure distributions due to the coupled electrochemical effects are illustrated and plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic solutions.