Time-dependent horizontal cracking in shales subject to steam injection

Steam stimulation has been used to extract viscous heavy oil and bitumen in oil sand in Canada. Overlain the oil sand formation are low-permeability clay shales forming an impermeable barrier to migration of fluid, and natural horizontal fissures or fractures are commonly found in these shale formations. One of the geomechanics-related problems is whether these pre-existing fractures would propagate under steam injection. In this paper, a simple analytical crack model of interfacial crack in viscoelastic bimaterial is used to investigate this problem. The introduction of steam to the oil sand formation is modelled by imposing a center of dilatation in a two-dimensional viscoelastic bimaterial. The stress intensity factor of a twodimensional bimaterial crack induced by a center of dilatation is formulated in Laplace transformed space using the correspondence principle for viscoelastic solids. Principle of superposition is used to solve the corresponding elastic problem. The final solutions for the stress intensity factor are written in terms of the transformed moduli, and inverse Laplace transform is taken using Schapery's approximate method.