Modeling and Numerical Simulation of Fracture Closure within An Explicit Algorithm Framework

ABSTRACT: Hydraulic fracturing simulation not only includes the fracture propagation but also the fracture closure during the shut-in phase. Compared to fracture propagation, fracture closure adds a local nonlinear contact mechanism to the extended strong stiff fluid-solid coupling equations, making the modeling and solution more challenging, and current research is severely lacking. Studying three-dimensional fracture propagation and closure models and efficient solving methods is crucial for enhancing the performance of three-dimensional fracture propagation simulators. In this paper, we propose a simple explicit algorithm-based method for the non-uniform closure of hydraulic fractures within shut-in period. The fluid-solid coupling equations for the flow of fracturing fluid and rock deformation are solved using the Runge-Kutta-Legendre (RKL) method (Int J Solids Struct 191-192: 370-389); the nonlinear contact of the fracture is described by the Bandis contact stress model (Int J Rock Mech Min Sci & Geomech Abstr. 20(6): 249-268). We simplified the contact elements, that is, there is no flow and no leak-off within the contacting elements. By this way, to a certain extent, the strong nonlinear characteristics of the coupling between contact stress and fluid pressure are avoided. In the actual solution process, the width of the contacting elements is iteratively corrected until convergence is achieved, then continue the calculations for the next time step. Through our test cases, this method is efficient and can also describe the process of fracture closure after stimulation.