Non-Local Continuum Damage and Transport Modeling Framework for Hydraulic Fracturing

ABSTRACT: Recent experiments and field observations show that fractured geomaterials exhibit hierarchal crack networks and fluid-flow capillary networks at multiple scales. Fracturing is often associated with non-linear material response such as plasticity and softening. We present a novel non-local continuum damage model for hydraulic fracturing. The model accounts for the crack networks by the introduction of non-local damage, and the presence of long-range sub-scale capillary networks is represented using non-local transport. Cracks are modeled as regions of the continuum featuring degraded stiffness as well as elevated permeability; which allows the model to represent the key characteristics of hydraulic fracturing. The model is implemented in a non-linear mixed finite element framework and used to solve benchmark hydraulic fracturing and shear loading problems. It is shown that the model adequately represents elevated fluid velocity inside the fluid-driven crack and is able to successfully represents changes to pore pressure at damaged material points, including pressure rise until breakdown point as well as stagnating open-fracture pressure. The analysis shows the influence of the variation of the non-local length scale parameters for the damage and transport. The results indicate that porous media featuring more widespread sub-scale networks exhibit shorter and wider fluid-driven fractures. The presented model provides a tool for the calculation and prediction of fracking fluid leak-off from the major crack to the surrounding porous media.