Development of an embedded discrete fracture model for 2D and 3D unstructured grids using an element-based finite volume method

Abstract

Recently, the unstructured gridding technique has been extensively used in reservoir simulation because of the high flexibility it provides to represent geologically realistic reservoirs. The embedded discrete fracture model (EDFM) has also attracted attention in recent years for the simulation of complex fractures in various types of computational grids. In this work, we develop a methodology to apply the EDFM in 2D and 3D unstructured grids using an element-based finite volume method (EbFVM). In this method, triangular and quadrilateral elements are used in 2D grids, and tetrahedron, prism, hexahedron, and pyramid elements are used in 3D grids. New approaches to addressing matrix-fracture connectivity and reducing the number of fracture unknowns in this type of grid are presented. The methodology is implemented in an EDFM preprocessing code.A series of case studies are presented to demonstrate the methodology in 2D and 3D simulations using an in-house compositional reservoir simulator. Different types of elements are used in the simulations to represent the reservoir geometries. Both primary and secondary recovery processes are simulated. The results show that when the number of control volumes is similar, the proposed method can obtain similar results on different grids with various types of elements, which confirms the effectiveness of the approach. Case studies with complex reservoir geometries are also presented to demonstrate the applicability of the model.This work demonstrates the extensiveness of the EDFM to unstructured matrix grids. It also shows the compatibility of the EDFM with various numerical approximation schemes. The use of unstructured gridding with mixed types of elements facilitates the representation of complex reservoir geometries, and through the combination with the EDFM, complicated gridding around fractures is avoided. Therefore, the approach in this work has high flexibility for simulating densely fractured media with complex geometries.