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

University Of Arizona, Tucson AZ

Investigators

Abstract

0110289 Neuman To 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.