New Multi-Dimensional Solutions for Water Flow Through Heterogeneous and Unsaturated Media

University Of Arizona, Tucson AZ

Investigators

Abstract

Warrick 0309515 We propose new multi-dimensional solutions for water flow through heterogeneous and unsaturated porous media. Geometrical discontinuities and inclusions will be taken within an otherwise homogeneous system. The approach combines two successful lines of pursuit: 1. use of the analytic element method, which has recently found numerous applications for steady-state flow through saturated media containing heterogeneities; and 2. solution of the Helmholtz equation, which has been applied to flow around a single obstruction in an unsaturated medium. Inspired by the simpler saturated flow case, the proposed work extends the analytic element method to include numerous, even hundreds of inclusions for unsaturated soil. This allows flexibility to describe complex realizations of heterogeneous flow fields. A limitation of the method is an assumption of a "Gardner" soil for which the unsaturated hydraulic conductivity of material is exponentially related to the pressure head. Thus, a critical component of the study is a comparison of results using the Gardner soil to solutions based on other hydraulic functions. This will identify which results are generic and which are dependent on the exact form of the hydraulic functions chosen. In addition to the analysis of flow through heterogeneous soils, an important application of the new solutions regards flow around measurement devices, such as tensiometers, TDR probes and collection devices. DIFFERENCES BETWEEN FULL PROPOSAL AND SCALED-DOWN PROJECT The primary differences between the revised and original project are that the new plan eliminates all lab work (under the old Objective I) and the development of particle tracking schemes (planned under the original Objective 4). The new emphasis will be on completion of Objective 2 and the first three bullets of Objective 3. Thus, the all important comparisons of how well the Gardner soils can be used to identify universal results common to other unsaturated hydraulic functions (e.g., "van Genuchten" and "Brooks and Corey") would be complete. Also, the revised project still includes development of new analytical solutions a,.,; related to measurement devices and source/sinks as included in Objective 3.