A homogenization approach for modeling a propagating hydraulic fracture in a layered material

Abstract

Shales are known to have a finely layered structure, which greatly influences the overall material’s response. Incorporating the effect of all these layers explicitly in a hydraulic fracture simulator would require a prohibitively fine mesh. To avoid such a scenario, a suitable homogenization, which would represent the effect of multiple layers in an average sense, should be performed. We consider a sample variation of elastic properties and minimum horizontal stress versus depth that has more than a hundred layers. We evaluate methodologies to homogenize the stress and the elastic properties. The elastic response of a layered material is found to be equivalent to that of a transversely isotropic material, and the explicit relations for the effective parameters are obtained. To illustrate the relevance of the homogenization procedure for hydraulic fracturing, the propagation of a plane strain hydraulic fracture in a finely layered shale is studied. To reduce the complexity of the numerical model, elastic layering is neglected and only the effect of the stress layers is analyzed. The results demonstrate the ability of the homogenized stress model to accurately capture the hydraulic fracture behavior using a relatively coarse mesh. This result is obtained by using a special asymptotic solution at the tip element that accounts for the local stress variation near the tip, which effectively treats the material at the tip element as nonhomogenized.