Analytic solutions with ionic flow for a pressure transmission test on shale

Ion/water transport between drilling fluid and shale formations can result in altered pore pressure in the shale. This chemically induced pore pressure plays an important role in controlling shale stability during drilling operations. In this paper analytic solutions are derived for a transient pressure transmission test on shale by solving the previously derived partially-coupled diffusivity equations taking into account chemical ionic flow effects. The diffusivity equations were solved under a no-flow boundary condition which is prescribed in a particular kind of transient pressure transmission test. By determining the three chemo-poroelastic coefficients KI (permeability coefficient), KII (membrane efficiency coefficient), and Deff (ion diffusivity) experimentally, the analytic solutions are compared with the actual experimental data. In general, a good agreement between the analytic solutions and the actual pressure measurements in the time-dependent pressure transmission tests has been found and is presented. The analytic solutions are provided for both the linear and cylindrical pressure transmission geometries. The pressure transmission experimental data discussed in this paper are from linear-geometry tests. Results presented in this paper can be used to study the transient pore pressure and stresses in the near-wellbore region, and to optimize the drilling fluid design (e.g., optimized salt type, salt concentration, optimized membrane efficiency, fluid pressure etc.).