A model for elastic fracture closure on heterogeneous distribution of compressible solids and etched walls

Abstract

Fracture elasticity problems become far nontrivial with complex fracture geometries or heterogeneity of surrounding medium. For closing fractures, which can be partly open, partly closed, and partly clamping the filling solids, the elasticity problem is even more complicated due to mixed boundary conditions and nonlinear stress-strain relationship of filling. Accurate modeling of fracture closure in such conditions requires development of a stable and computationally effective numerical model. It is important, for instance, in oilfield industry, to correctly evaluate conductivity of hydraulic fractures either heterogeneously filled by injected proppants or having residual apertures of walls etched by acidizing.In this work, we develop a computationally efficient numerical solver for such sorts of problems. Given the spatial distribution of filling solids, or fracture wall etching, we employ the iterative Displacement Discontinuity Method to solve for the opening shape of a 3D planar fracture. In addition to the applied stresses and inner fluid pressure, the fracture opening is shown to be sensitive to the elastic properties of filling solids, which may exhibit a nonlinear dependency between stress and strain. The model allows to deal with multiple solids of different elastic properties. Knowing the fact that computational time increases with increase of spatial fracture filling resolution, we employ the Fast Multipole Method to gain computational time in case of large number of grid cells. We verify the model correctness against exact analytical solutions of selected fracture problems.The developed model is shown to be practically useful for simulations of hydraulic fracture closure on heterogeneously distributed proppants or acid-etched fracture walls after the end of fracturing treatment, as well as for valid estimations of fractured well productivity sensitive to pressure drawdown.