GOALI: Numerical Methods for Multiphase Flows in Porous Media

这项与油气行业的合作项目旨在改进油藏的产油量模型。虽然学术界在模拟地下流体流动方面做了大量的工作，但许多方法在真实储层的准确性和鲁棒性方面都存在不足。事实上，油藏数据存在行业限制，该项目将通过大学和行业合作伙伴之间的密切合作来解决这一问题。该项目侧重于两相流，例如油和水的流动。许多正在开发的技术可以应用于黑油（三相流）或成分模型。该项目的一个预期成果是加速技术从学术界向工业界的转移。另一个影响是培训学生解决工业问题。由教师和学生开发的最先进的算法将用于解决与该行业相关的具有挑战性的问题。这有可能改变目前工业合作伙伴使用的计算工具。这个项目有两个主要目标。首先，将开发一种多重数值方法，以产生快速和准确的复杂油藏两相流数值模拟。该数值模型将有限体积法与不连续伽辽金法耦合在非重叠区域上，并利用子区域之间的最优耦合条件。有限体积法的流行与不连续伽辽金法的准确性和灵活性相结合是该耦合方法的主要优点。该项目的第二个目标是采用一种新的有限元方案，该方案采用了物理未知数，如相压力和相饱和度。利用紧性论证，表明相压力和饱和度的数值近似强收敛于弱解，即使在相对渗透率系数退化的情况下也是如此。收敛分析的基础是利用全局压力等中间变量，推导相压力梯度的边界。这个新方案是由在油藏模拟中使用物理主要未知数的行业限制所驱动的。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.