ABSTRACT: This work investigates pore pressure and stresses around a borehole in a chemo-poroelastic shale formation subjected to the uniform pressure of a chemically active drilling fluid. Closed-form solutions of solute concentration, pore pressure, and stresses are obtained using a coupled chemo-poroelastic theory. The corresponding asymptotic (non-dimensional) short time solutions are also obtained. Comparisons between the complete and short time asymptotic solutions of pore pressure indicate that the short time solution provides accurate pore pressure (relative errors less than 5%) at non-dimensional times less than 1.0 which corresponds to real times of more than 200 hr for typical material parameters considered in previous studies. Hence, the simple short time solution may be used to predict wellbore instabilities in some combinations of drilling fluid chemistry and shale properties. Detailed numerical results of stresses are presented to illustrate the effects of ion diffusion or interaction between the drilling fluid and shale formation on the distributions of pore pressure and stresses. It is found that ion diffusion significantly influences the pore pressure and stresses around the borehole.
Wellbore instability caused by the failure of shale formations represents a major economic challenge to the oil industry. During the drilling of a borehole, the surrounding shale deforms under the action of drilling fluid pressure and tectonic stresses. Moreover, the difference between the solute concentrations of species in the drilling fluid and in the porous shale causes ion diffusion in the shale which alters the stress state in the shale and contributes to the shale failure[1, 2]. Hence, drilling fluid/shale interactions play an important role in wellbore stability and a complete understanding of shale failure and wellbore instability requires a multidisciplinary approach to take both chemical and mechanical effects into account. Sherwood[3, 4] proposed a modification of the Boit poroelasticity theory to include ionic transport effects on the pore pressure and stresses in shales. The modified theory was used by Sherwood and Bailey to study shale swelling around a wellbore. Lomba et al. [6, 7] developed a model for solute and pore pressure diffusion in shales. Their model was subsequently extended and employed to study wellbore instabilities by Yu et al.  , Chen et al.  , Yu et al.  , and Chen et al.  . Ghassemi and Diek  presented a linear chemo-poroelastic model for shale deformations. Ekbote and Abousleiman [13, 14] developed a poromechanics formulation for a chemically active, anisotropic porous medium and presented some solutions of stresses and pore pressure around a borehole. While some progress has been made in understanding chemically induced stresses in shale formations, simple closed-form solutions in the real time domain have not been available to facilitate the application of the existing theory to practical wellbore instability problems. The purposes of the present study are to develop closedform solutions of pore pressure and stresses around a borehole in a shale formation subjected to the pressure of a chemically active drilling fluid, and to examine the effects of ion diffusion in the shale on the pore pressure and stresses.