HR: 09:15h
AN: H21A-06    [PDF]
TI: Instrument Spatial Weighting Functions and the Meaning of Measurements in Heterogeneous Porous Media
AU: * Molz, F J
EM: fredi@clemson.edu
AF: Environmental Engrg. and Sci. Dept., Clemson University, 342 Computer Court, Anderson, SC 29625 United States
AU: Guan, J Y
EM: jguan@clemson.edu
AF: Environmental Engrg. and Sci. Dept., Clemson University, 342 Computer Court, Anderson, SC 29625 United States
AU: Wang, J
EM: jinjunw@clemson.edu
AF: Environmental Engrg. and Sci. Dept., Clemson University, 342 Computer Court, Anderson, SC 29625 United States
AB: Instruments that are designed to measure hydraulic conductivity (K) based on multi-dimensional flow fields, such as the gas mini-permeameter, weight various portions of the flow domain differently when determining a single K value, even under homogeneous and isotropic conditions. For natural heterogeneous materials, virtually all flow fields are 3-D, even those set up using standard permeameters and small cores. Thus the question of how a given instrument weights different portions of a domain is fundamental to understanding the meaning of a measurement. Recently, the instrument spatial weighting function (ISWF) has been derived for steady-state measurement procedures using compressible or incompressible fluids and identified physically as the ratio of the hydraulic energy dissipation rate at each point of a homogeneous domain to the total energy dissipation rate throughout the flow domain [Molz et al., WRR, 39(4), DAN-1, 2003]. Such an ISWF identifies the points of a domain that most influence a measurement and has units of erg/cc.sec/erg/sec or 1/cc (inverse volume); the concept generalizes to other types of geophysical measurements. The present work shows that the existing ISWF development extends naturally to transient K measurements, such as those made using a slug test or pumping test. When measurements are made in heterogeneous domains, the "measured" K value results from a complex interaction between the ISWF and the heterogeneity. Given known K distributions, ISWFs are calculated for K measurements made on cores. A rather general dilemma appears to arise in that one is led to conclude that in order to calculate the ISWF, and hence have a well-defined measurement, one must know the K distribution before the measurement is made. Implications for the well-known up-scaling problem in porous media are discussed.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1878 Water/energy interactions
DE: 1894 Instruments and techniques
SC: Hydrology [H]
MN: 2003 Fall Meeting