This paper presents some closed-form solutions of the coupled thermo-chemo-hydraulic problem of pressure diffusion through shales. The solution is based on the Biot’s poroelasticity theory that has been extended to incorporate temperature and solute diffusion and chemical osmosis into the constitutive equations. Explicit equations in the time domain were derived for appropriate boundary conditions of specialized laboratory equipment that allows one-dimensional diffusion of temperature, salt ions and water throughout a shale sample. The results showed that the proposed closed-form solution can represent fairly well the laboratory results and it can be used as a tool for quality control assurance of tests to determine the input parameters for advanced coupled modeling of shale behavior under pressure, thermal and chemical gradients like the drilling of oil and gas wells in high pressure and high temperature environments.
Shales and mudstones are the most abundant sedimentary rocks worldwide. In the last decade these rocks have received attention of different engineering areas such as nuclear waste isolation [1, 2] and mainly petroleum geomechanics [3, 4]. It has been extensively reported that 90% of wellbore instability problems occur when drilling shales, generating costs of US$ 1-6 billion per year. The poromechanical behavior of shales while drilling wellbores is a very complex process and results from a coupling between hydraulic, mechanical, chemical and thermal forces, which impact the pore pressure and stress distribution around the borehole. In order to predict the behavior of shales under the in-situ or down hole conditions, several models have been developed based on the extension of poroelasticity theory to include the chemical and thermal effects between the drilling fluid and rock [6, 7, 8], which show that a better prediction of the rock failure can be obtained by such models.
