Semi-Analytical Modeling of Geological Features Based Heterogeneous Reservoirs Using the Boundary Element Method

Abstract

The objective of this work is to innovatively apply the boundary element method (BEM) as a general modeling strategy to deal with complicated reservoir modeling problems, especially those related to reservoir heterogeneity and fracture systems, which are common challenges encountered in the practice of reservoir engineering. The transient flow behaviors of reservoirs containing multi-scale heterogeneities enclosed by arbitrarily shaped boundaries are modeled by applying BEM. We demonstrate that a BEM-based simulation strategy is capable of modeling complex heterogeneous reservoirs with robust solutions. The technology is beneficial in making the best use of geological modeling information. The governing differential operator of fluid flow within any locally homogeneous domain is solved along its boundary. The discretization of a reservoir system is only made on the corresponding boundaries, which is advantageous in closely conforming to the reservoir’s geological description and in facilitating the numerical simulation and computational efforts because no gridding within the flow domain is needed. Theoretical solutions, in terms of pressure and flow rate responses, are validated and exemplified for various reservoir–well systems, including naturally fractured reservoirs with either non-crossing fractures or crossing fractures; fully compartmentalized reservoirs; and multi-stage, fractured, horizontal wells with locally stimulated reservoir volumes (SRVs) around each stage of the fracture, etc. A challenging case study for a complicated fracture network system is examined. This work demonstrates the significance of adapting the BEM strategy for reservoir simulation due to its flexibility in modeling reservoir heterogeneity, analytical solution accuracy, and high computing efficiency, in reducing the technical gap between reservoir engineering practice and simulation capacity.