GOALI: Numerical Methods for Multiphase Flows in Porous Media

这一与石油和天然气行业合作的项目旨在改进从储油层开采石油的模式。虽然学术界已经在地下流体流动建模方面做了大量的工作，但许多方法在真实储层上的准确性和稳健性方面存在不足。事实上，储集层数据存在行业限制，该项目将通过大学和行业合作伙伴的密切合作来解决这一问题。该项目专注于两相流动，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。该项目的一个预期结果是加快了技术从学术界向行业的转移。另一个影响是对学生进行工业问题方面的培训。由教师和学生开发的最先进的算法将被应用于解决与该行业相关的具有挑战性的问题。这可能会改变工业合作伙伴和其他行业伙伴目前使用的计算工具。这个项目有两个主要目标。首先，将开发一种多数值方法，以产生快速而准确的复杂油藏中两相流动的数值模拟。该数值模型在非重叠区域上耦合有限体积方法和间断Galerkin方法，并利用子域之间的最佳耦合条件。有限体积方法的普及性和间断Galerkin方法的精度和灵活性是耦合方法的主要优点。该项目的第二个目标是一种使用物理未知数的新有限元方案，如相压力和相饱和度。利用紧致性论证，即使在相对渗透率系数退化的情况下，相压力和饱和度的数值近似也强收敛于弱解。收敛分析的基础是利用全球压力等中间变量推导出相压力梯度的界限。这一新计划的动机是在油藏模拟中使用物理基本未知数的行业限制。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.