Case study of using boundary integration technique in reservoir modeling of single- and two-phase immiscible fluid flow

Petroleum reservoir simulation is a process of modeling the complex physical phenomena inside a reservoir. The goal is to determine how hydrocarbons and water behave and how local reservoir characteristics affect the oil and gas recovery in the reservoir. This study presents an application of two rigorous analytical based numerical schemes in petroleum engineering, so called the Boundary Element Method (BEM) and its hybrid form, the Dual Reciprocity Boundary Element Method (DRBEM). They are proven to be able to provide a computationally efficient means of handling single- and multi-phase flow in a homogeneous medium through the comparison with results obtained by COMSOL. The accuracy can be further enhanced by incorporating singularity programming and Laplace transformation techniques; hence an alleviation of numerical errors caused by singularities and a time derivative is achieved. It is observed that these two methods can be an alternative tool to analyze pressure transient performance in both single- and multi-phase flow, and estimate the saturation change during an immiscible displacement process. In addition, it has been shown that there are numerous potential areas of oil recovery where COMSOL can be a useful and successful means of research and design advancement.