A non-local plasticity model of stimulated volume evolution during hydraulic fracturing

Abstract

Hydraulic fracturing in naturally fractured rocks often leads to the creation of a stimulated zone in which the target rock formation is deformed and fractured by the reactivation and shear dilation of natural fractures and the plastic deformation, damaging, and fracturing of the bulk. In this paper, we present a novel mathematical model with the goal of simulating the evolution of the stimulated volume during hydraulic fracturing. This was achieved by introducing an equivalent continuum non-local poro-elastic-plastic zone of enhanced permeability for the stimulated region, characterized by an internal length scale. The non-local plastic constitutive behavior of the rock, combined with the classical Biot�s poroelastic theory, was implemented using a new implicit C0 non-local finite element method. A predictor-corrector return algorithm for the non-local plasticity model was formulated as an extension of the classical plasticity algorithm. To improve the performance of the iterative solution scheme, a consistent algorithmic stiffness tangent modulus was developed. First, the elastic-plastic constitutive behavior of the proposed methodology is verified using the standard non-porous biaxial compression test with strain softening behavior. Next, it is verified that the poro-elastic-plastic model correctly simulates the evolution of the stimulated zone and the subsequent change in the flow and fluid pressure for several hydraulic fracturing examples under various far-field in-situ stress conditions. Lastly, the non-local poro-elastic-plastic model is shown to be mesh-independent and capable of capturing a wide range of complex fracturing behavior.