Discrete Fracture Modeling of Shale Plays with Multi-stage Hydraulic Fracturing Using Centroidal Voronoi Mesh

摘要

While application of PEBI grids for Discrete Fracture Models has been suggested in the past, little has been done to ensure and improve the quality of the grids for simulation of unconventional shale plays. Compared with ordinary PEBI grids, Centroidal Voronoi tessellation has superior properties in generating high quality mesh, especially combined with finite volume method, in which all the physical properties are evaluated at the nodes of the corresponding grids. In this paper, a novel approach for discrete fracture modeling of shale gas reservoirs using Centroidal Voronoi grids is introduced. Our proposed mesh generation algorithm is based on the equilibrium state of forces in a truss. Specifically, we construct the analogues truss system and then we apply a dynamical model to the Delaunay triangulation giving rise to the equilibrium position of nodes. Moreover, we perform grid optimization based on an iterative strategy to ensure that the grid nodes land on the centroids of their corresponding control volumes. Thus, all the values evaluated at each node represent the properties of its control volume more accurately. To reduce the error in capturing the near fracture transients, we use a grid refinement strategy that allows for smooth variation of grid size. Geometrical adaptivity for the level of refinement around fractures is achieved by applying a proper distance function, enabling the user to change the grid refinement more readily depending on the near fracture physics. We employ the proposed mesh generation strategy for simulation of horizontal wells with multi-stage hydraulic fracturing in shale gas reservoirs with up to two phases (water and gas). Coupled with the formulation is different physical phenomena including gas desorption/ adsorption. non-Darcy flow and Klinkenberg effect. We show that the proposed high quality mesh generation algorithm enables capturing some of the most important features of shale gas plays with multiple transverse fractures.