Fracture spacing during hydro-fracturing of cap-rocks

Layered low permeability rock units, like shales, represent seals or ‘cap-rocks’ in a variety of geological settings. A continuous increase in the fluid pressure gradients across a virtually impermeable rock layer will ultimately lead to hydro-fracturing. Depending on the boundary conditions, such fracturing may lead to the formation of a set of sub-parallel cracks oriented more or less perpendicular to the cap-rock layer. In this article, we propose a new numerical model that describes interactions between multiple cross-cutting fractures in an elastic low permeability rock layer. The width of each fracture and the spacing between them are modeled as a force balance between the fluid pressure and the elastic forces in the cap-rock and between each fracture. The model indicates that the system of fractures evolves toward a spatially periodic steady-state distribution with a fixed fracture spacing and aperture. The results are similar for incompressible and compressible fluids. The steady-state conditions depend on only two dimensionless parameters, and the fracture spacing is only weakly dependent on the cap-rock thickness. This is in contrast to fracturing produced by simple extension of an elastic rock layer beyond the fracture strength, in which case fracture spacing is proportional to layer thickness.