Analytical solution of a circular opening in an axisymmetric elastic-brittle-plastic swelling rock

Unconventional gas reservoirs such as coal and shale have been increasingly considered for methane production and CO2 sequestration, over the last decades. In these reservoirs, methane and/or CO2 are usually in an adsorbed state which is associated with swelling and/or shrinkage. There exist a number of experimental and theoretical studies on the effect of swelling and/or shrinkage in prediction of permeability, stress, and displacement distribution. However, most of these studies have only considered the elastic deformation of the reservoir. The plastic deformations within brittle reservoir rock can have significant implications for production, injectivity and stability and the wellbore and the reservoir. Therefore, development of improved models to estimate the distribution of stress and deformation around the wellbore is of great importance. A large number of analytical solutions for axisymmetric opening problem have been presented in the literature where different models are used for material behaviour. This paper aims to include the effect of swelling/shrinkage in the elasto-plastic formulations around the wellbore. The reservoir is assumed to behave as a linear elastic material up to the yield point, which is identified by the Mohr-Coulomb failure criterion. The post-failure brittle behaviour of the rock is modelled by defining the residual strength parameters and employing a non-associated flow rule. Strains are decomposed into mechanical elastic, elastic swelling/shrinkage, and mechanical plastic parts. Although the swelling/shrinkage strains are considered to be elastic, their distributions are closely linked with distributions of plastic strains through sophisticated integral and differential relationships. The swelling/shrinkage is defined using a Langmuir-like curve, which is directly related to the pore pressure distribution within the reservoir. The model is then used to study the distributions of stress and strain around the wellbore, in both elastic and plastic zones and verified against a numerical solution. A parametric study is also conducted by defining different values for swelling parameters, and pre-failure and residual strength parameters. The provided model can be useful to estimate the failed zone around the wellbore, where the formation is irreversibly damaged. On the other hand, the estimated distributions and radial and tangential stress from this model can help develop new permeability models for unconventional reservoirs. (C) 2016 Elsevier B.V. All rights reserved.