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.

准确的数学分析和高效的数值方法在石油工业偏微分方程模型的研究中发挥着越来越重要的作用。该项目的目标是对改进的Buckley-Leverett（MBL）模型（水驱地下二次采油偏微分方程模型）进行数学分析和高阶精度数值方法设计研究。当地下油源被开采时，由于压力差，一定量的石油会自行流出。停止流动后，地下通常仍残留有大量石油。 “二次采收”的一种标准方法是通过注入井将水泵入油田，通过生产井将石油压出。在此过程中将产生水和油的混合物。 MBL 方程模拟了整个油藏（特别是生产井）含油饱和度的演变。该研究项目结合了数学分析、数值方案设计和计算技术。数学分析基于偏微分方程理论，正在开发的数值方法基于最先进的不连续伽辽金（DG）方案。结果将使用实验室实验的数据进行交叉验证。研究者计划开展以下具体研究任务：（1）将成熟的一维MBL模型扩展到2D和3D全非线性和线性化MBL模型； (2)确定在小于整个水库的空间域上采用MBL模型引起的近似误差； (3)设计高阶精度间断伽辽金(DG)方法对MBL模型进行数值求解； (4)研究MBL模型行波解的非线性渐近稳定性； (5)利用实验数据交叉验证分析和计算结论。该项目涉及一名博士后和一名研究生参与研究。研究人员还计划开发一门新的研究生课程，介绍水驱采油模型的数值解决方案。