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

为了有效地利用和保护地下水供应，必须对复杂水文地质环境中的流体流动和溶质运移进行量化。这种环境在多种尺度上表现出水力和传输特性的随机空间变化。目前的趋势是描述这种地质统计学的变异性，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法，它允许人们直接基于分布自由的非局部(积分-微分)方程来计算地下水流动和运移的领先的多尺度条件集合矩。这种方法依赖于过去几年由PI、他的学生和同事出版的一系列工作。它提供了流量而不是输送的正向预测，条件是测量水力传导性，但不是水头或浓度。我们建议在我们最近提出的多尺度框架内，通过开发用于传输的正向计算算法和对流和传输的逆算法来填补这些空白。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突破。具体地说，我们的目标是在多尺度随机框架内发展(1)允许稳态地下水流动的矩方程根据测量的水力水头和导流来调节的逆算法；(2)高精度的正向条件矩算法来预测随机稳态速度场中的平流溶质运移，并评估预测误差；以及(3)允许平流溶质运移的矩方程根据测量的浓度、水头和导流来调节的反算法。

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.