ITR/AP: Forward and Inverse Conditional Moment Algorithms for Flow and Transport in Multiscale, Randomly Heterogeneous Hydrogeologic Environments Under Uncertainty

ITR/AP：不确定性下多尺度、随机异质水文地质环境中流动和输运的正向和逆向条件矩算法

• 批准号: 0110289
• 负责人: Shlomo Neuman
• 金额: $ 40万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0110289&HistoricalAwards=false
• 关键词: ITR; AP; Forward; Inverse; Conditional

0110289NeumanTo efficiently utilize and protect subsurface water supplies, one must quantify fluid flow and solute transport in complex hydrogeologic environments. Such environments exhibit random spatial variations in hydraulic and transport properties on a multiplicity of scales. The trend has been to describe this variability geostatistically and to analyze subsurface fluid flow and solute transport stochastically. The common method of stochastic analysis is computational Monte Carlo simulation. We propose an alternative, which allows one to compute leading multiscale conditional ensemble moments of groundwater flow and transport directly on the basis of nonlocal (integro-differential) equations that are distribution free. The approach rests on a body of work published by the PI, his students and coworkers over the last few years. It provides forward predictions of flow but not transport, conditioned on measurements of hydraulic conductivity but not head or concentration. We propose to fill these gaps by developing a forward computational algorithm for transport and inverse algorithms for both flow and transport, within a multiscale framework proposed by us recently. No such inverse or multiscale algorithms presently exist, and their development would constitute an important conceptual and algorithmic breakthrough. In particular, our objectives are to develop, within a multiscale stochastic framework, (1) an inverse algorithm that allows conditioning moments equations of steady state groundwater flow on measured hydraulic head and conductivity; (2) a high-accuracy forward conditional moment algorithm to predict advective solute transport in random steady state velocity fields, and to assess prediction errors; and (3) an inverse algorithm that allows conditioning moments equations of advective solute transport on measured concentration, hydraulic head and conductivity.

为了有效地利用和保护地下水供应，必须量化复杂水文地质环境中的流体流动和溶质运移。此类环境在多种尺度上表现出水力和运输特性的随机空间变化。目前的趋势是用地质统计学的方法来描述这种变化，并随机分析地下流体流动和溶质运移。随机分析的常用方法是计算蒙特卡罗模拟。我们提出了一种替代方案，它允许一个计算领先的多尺度条件集合矩的地下水流量和运输的基础上直接的非局部（积分微分）方程是分布自由。这种方法依赖于PI，他的学生和同事在过去几年中发表的一系列工作。它提供了向前预测的流量，但没有运输，条件是测量的水力传导率，但没有头或浓度。我们建议填补这些空白，通过开发一个正向计算算法的运输和逆向算法的流量和运输，我们最近提出的多尺度框架内。目前还不存在这样的逆或多尺度算法，它们的发展将构成一个重要的概念和算法的突破。特别是，我们的目标是发展，在多尺度随机框架内，（1）一个逆算法，允许条件的时刻方程的稳态地下水流的实测水头和电导率;（2）一个高精度的正向条件矩算法预测平流溶质运移在随机稳态速度场，并评估预测误差;以及（3）允许对流溶质运移的矩方程对测量的浓度、水头和电导率进行调节的逆算法。