GOALI: Numerical Methods for Multiphase Flows in Porous Media

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This collaborative project with the oil and gas industry aims to result in improved models of oil production from reservoirs. While there has been extensive work in academia on modeling subsurface fluid flows, many of the methods fall short in delivering accuracy and robustness on real reservoirs. Indeed, there are industrial constraints on the reservoir data, which this project will address by a close collaboration between university and industry partners. The project focuses on two-phase flow, for instance the flow of oil and water. Many of the techniques under development can be applied to black-oil (three-phase flow) or compositional models. One anticipated outcome of this project is an accelerated transfer of technology from academia to industry. Another impact is the training of students on industrial problems. State-of-the-art algorithms developed by faculty and students will be applied to solve challenging problems relevant to the industry. This could have the potential of transforming the current computational tools used by the industrial partner and beyond. This project has two main goals. First, a multi-numerics approach will be developed to produce fast and accurate numerical simulations of two-phase flow in complex reservoirs. The numerical model couples finite volume methods with discontinuous Galerkin methods on non-overlapping domains, and it utilizes optimal coupling conditions between the subdomains. The popularity of finite volume methods combined with the accuracy and flexibility of discontinuous Galerkin methods are key positive features of the coupled method. A second goal of the project is a new finite element scheme that employs physical unknowns, such as phase pressure and phase saturation. Using a compactness argument, the numerical approximations of the phase pressure and saturation are shown to converge strongly to the weak solution, even in the case of degenerate relative permeability coefficients. The convergence analysis is based on deriving bounds for the gradient of the phase pressure, using intermediate variables like global pressure. This new scheme is motivated by the industry constraints of using physical primary unknowns in reservoir simulations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.