CAREER: Mathematical Analysis and Numerical Methods for the Underground Oil Recovery Models

该职业奖支持一系列协调的研究和教育活动，其目标是阐明地下石油开采的建模和计算，并刺激俄克拉荷马州大学应用分析和计算的研究和学习环境。该项目涉及俄克拉荷马州应用分析计算小组，该小组由本科生和研究生、博士后研究人员、俄克拉荷马州大学教师以及来自俄克拉荷马州大学和学院网络的教师组成。精确的数学分析和高效的数值方法在研究石油工业中的偏微分方程（PDE）模型中发挥着越来越重要的作用。本课题的主要目的是研究水驱地下二次采油偏微分方程模型的数学分析和高精度数值方法设计。PI将结合联合收割机的数学分析，数值方案设计和计算技术，在我们提出的研究。数学分析是基于偏微分方程理论，提出的数值方法是基于国家的最先进的间断伽辽金（DG）计划。此外，将使用PI的学术合作者提供的实验室实验数据和PI的行业合作者提供的油藏模拟数据对所获得的结果进行交叉验证。该项目的跨学科性质将提供一个沟通和协作的环境，该奖项反映了NSF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进行评估，被认为值得支持的搜索.

This CAREER award supports a coordinated set of research and educational activities with the goals of elucidating the modeling and computation of underground oil recovery and stimulating the environment for research and study in applied analysis and computation at the University of Oklahoma. The project involves the Oklahoma Applied Analysis & Computing Group, a team consisting of undergraduate and graduate students, postdoc researchers, University of Oklahoma faculty, and faculty from Oklahoma's network of universities and colleges.Accurate mathematical analysis and efficient numerical methods play a more and more important role in studying partial differential equation (PDE) models in the petroleum industry. The goal of this project is to perform research in the mathematical analysis and high order accuracy numerical methods design for the PDE models describing the water-drive secondary underground oil recovery. The PI will combine mathematical analysis, numerical scheme design and computational techniques in our proposed research. The mathematical analysis is based on PDE theory, and the numerical methods proposed are based on state-of-the-art discontinuous Galerkin (DG) schemes. Furthermore, the obtained results will be cross-validated using data from laboratory experiments provided by the PI's academic collaborator, and oil reservoir simulation provided by the PI's industry collaborator. The interdisciplinary nature of this project will provide an environment of communication and collaboration, as well as provide an opportunity for students at different levels and with diverse background to apply mathematical and computational tools to investigate the underground oil recovery models.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.