Mesh Adaptation in Fractured Reservoir Simulation

Abstract

Natural fractures exist in many oil and gas reservoirs. On the other hand, hydraulic fracturing (fracking) is needed to create fractures in some reservoirs to improve the production rate. For example, shale gas reservoirs typically have extremely low permeability but have become an attractive source for natural gas production largely due to the advancement of horizontal drilling and hydraulic fracturing techniques. The permeability in fractures are much higher than that in other parts of the reservoir but the sizes of the fractures are much smaller. Thus, it is desirable to place more mesh elements around the fractures during the simulation and computations. Mesh adaptation is a very useful technique to help improving the accuracy and efficiency of the computation, and can be applied in computations for many problems such as plasma physics, image processing, and reservoir simulation in petroleum engineering. This study will focus on mesh adaptation in fractured reservoir simulation. The mesh will be adapted automatically so that more elements are concentrated around the fractures and less elements are distributed in other places. By this way, the reservoir simulation can be more accurate and efficient which is critical in helping control the production rate, optimize hydraulic fracturing design, and evaluate enhanced oil recovery processes. The goal of this study is to evaluate the effects of different mesh adaptation methods when solving a partial differential equation called porous media equation (PME). The porous media equation is solved using Finite Element Method with the software FreeFem++ that has built-in mesh adaptation functionality. The mesh is adapted based on a metric tensor that determines the shape, size and orientation of the mesh elements. The results are compared with uniform meshes and meshes created based on log-spacing. The numerical results show that adaptive meshes based on metric tensor provide the best results.