Modeling, Analysis, and Computation for Water-Drive Oil Recovery

水驱采油的建模、分析和计算

• 批准号: 1720489
• 负责人: Ying Wang
• 金额: $ 14万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-06-15 至 2021-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720489&HistoricalAwards=false
• 关键词: Modeling; Analysis; Computation; Water; Drive

Accurate mathematical analysis and efficient numerical methods play an increasingly important role in studying partial differential equation models in the petroleum industry. The goal of this project is to carry out research in mathematical analysis and design of high-order-accuracy numerical methods for the modified Buckley-Leverett (MBL) model, which is a partial differential equation model for water-drive secondary underground oil recovery. When an underground source of oil is tapped, a certain amount of oil flows out on its own due to pressure difference. After the flow stops, there is typically a significant amount of oil still left in the ground. One standard method of "secondary recovery" is to pump water into the oil field through an injection well, forcing oil out through a production well. In this process there will be a water and oil mixture created. The MBL equation models the evolution of the oil saturation in the entire oil reservoir, in particular, at the production well.This research project combines mathematical analysis, design of numerical schemes, and computational techniques. The mathematical analysis is based on partial differential equation theory, and the numerical methods under development are based on state-of-the-art discontinuous Galerkin (DG) schemes. The results will be cross-validated using data from laboratory experiments. The investigator plans to carry out the following specific research tasks: (1) extend the well-developed 1D MBL model to 2D and 3D fully nonlinear and linearized MBL models; (2) determine the approximation error induced by employing the MBL model on a spatial domain smaller than an entire reservoir; (3) design high-order-accuracy discontinuous Galerkin (DG) methods to numerically solve the MBL model; (4) study the nonlinear asymptotic stability of the traveling-wave solutions of the MBL model; (5) employ experimental data to cross-validate both the analytical and computational conclusions. The project involves a postdoctoral associated and a graduate student in the research. The investigator also plans to develop a new graduate-level course on numerical solutions to water-drive oil recovery models.

准确的数学分析和有效的数值方法在研究石油行业的部分微分方程模型中起着越来越重要的作用。该项目的目的是在修改后的Buckley-Leverett（MBL）模型的数学分析和设计方面进行数学分析和设计研究，这是水驱动次要地下油回收的部分微分方程模型。当挖掘地下石油来源时，由于压力差，一定量的油自行流出。流量停止后，通常仍有大量的油在地面上。 “次级恢复”的一种标准方法是通过注射井将水泵入油田，迫使油通过生产井出去。在此过程中，将产生水和油混合物。 MBL方程对整个储油油中油饱和度的演变进行了建模，尤其是在生产井中。该研究项目结合了数学分析，数值方案的设计和计算技术。数学分析基于部分微分方程理论，并且正在开发的数值方法基于最新的不连续Galerkin（DG）方案。结果将使用实验室实验的数据进行交叉验证。研究人员计划执行以下特定的研究任务：（1）将发达的1D MBL模型扩展到2D和3D，完全非线性和线性化MBL模型； （2）通过在小于整个储层的空间结构域上使用MBL模型来确定引起的近似误差； （3）设计高阶 - 准确性不连续的盖尔金（DG）方法，以数值求解MBL模型； （4）研究MBL模型行进波溶液的非线性渐近稳定性； （5）采用实验数据来跨验证分析和计算结论。该项目涉及博士后相关的研究和研究生。研究人员还计划开发一门新的研究生级课程，以用于水驱动石油回收模型的数值解决方案。