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Title: Correspondence of the Gardner and van Genuchten/Mualem relativepermeability function parameters

Abstract

The Gardner and van Genuchten models of relativepermeability are widely used in analytical and numerical solutions toflow problems. However, the applicab ility of the Gardner model to realproblems is usually limited, because empirical relative permeability datato calibrate the model are not routinely available. In contrast, vanGenuchten parameters can be estimated using more routinely availablematric potential and saturation data. However, the van Genuchten model isnot amenable to analytical solutions. In this paper, we introducegeneralized conversion formulae that reconcile these two models. Ingeneral, we find that the Gardner parameter alpha G is related to the vanGenuchten parameters alpha vG and n by alpha G=alpha vG ~; 1:3 n. Thisconversion rule will allow direct recasting of Gardner-based analyticalsolutions in the van Genuchten parameter space. The validity of theproposed formulae was tested by comparing the predicted relativepermeability of various porous media with measured values.

Authors:
; ;
Publication Date:
Research Org.:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org.:
USDOE. Office of Civilian Radioactive Waste Management.Waste Management System
OSTI Identifier:
927378
Report Number(s):
LBNL-62433
Journal ID: ISSN 0043-1397; WRERAQ; R&D Project: G60651; BnR: DF0961000; TRN: US200811%%127
DOE Contract Number:
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: Water Resources Research; Journal Volume: 43; Related Information: Journal Publication Date: 2007
Country of Publication:
United States
Language:
English
Subject:
54; ANALYTICAL SOLUTION; DATA; NUMERICAL SOLUTION; PERMEABILITY; SATURATION

Citation Formats

Ghezzehei, Teamrat A., Kneafsey, Timothy J., and Su, Grace W. Correspondence of the Gardner and van Genuchten/Mualem relativepermeability function parameters. United States: N. p., 2007. Web. doi:10.1029/2006WR005339.
Ghezzehei, Teamrat A., Kneafsey, Timothy J., & Su, Grace W. Correspondence of the Gardner and van Genuchten/Mualem relativepermeability function parameters. United States. doi:10.1029/2006WR005339.
Ghezzehei, Teamrat A., Kneafsey, Timothy J., and Su, Grace W. Wed . "Correspondence of the Gardner and van Genuchten/Mualem relativepermeability function parameters". United States. doi:10.1029/2006WR005339. https://www.osti.gov/servlets/purl/927378.
@article{osti_927378,
title = {Correspondence of the Gardner and van Genuchten/Mualem relativepermeability function parameters},
author = {Ghezzehei, Teamrat A. and Kneafsey, Timothy J. and Su, Grace W.},
abstractNote = {The Gardner and van Genuchten models of relativepermeability are widely used in analytical and numerical solutions toflow problems. However, the applicab ility of the Gardner model to realproblems is usually limited, because empirical relative permeability datato calibrate the model are not routinely available. In contrast, vanGenuchten parameters can be estimated using more routinely availablematric potential and saturation data. However, the van Genuchten model isnot amenable to analytical solutions. In this paper, we introducegeneralized conversion formulae that reconcile these two models. Ingeneral, we find that the Gardner parameter alpha G is related to the vanGenuchten parameters alpha vG and n by alpha G=alpha vG ~; 1:3 n. Thisconversion rule will allow direct recasting of Gardner-based analyticalsolutions in the van Genuchten parameter space. The validity of theproposed formulae was tested by comparing the predicted relativepermeability of various porous media with measured values.},
doi = {10.1029/2006WR005339},
journal = {Water Resources Research},
number = ,
volume = 43,
place = {United States},
year = {Wed Jan 03 00:00:00 EST 2007},
month = {Wed Jan 03 00:00:00 EST 2007}
}
  • The Gardner and van Genuchten models of relativepermeability are widely used in analytical and numerical solutions toflow problems. However, the applicability of the Gardner model to realproblems is usually limited, because empirical relative permeability datato calibrate the model are not routinely available. In contrast, vanGenuchten parameters can be estimated using more routinely availablematric potential and saturation data. However, the van Genuchten model isnot amenable to analytical solutions. In this paper, we introducegeneralized conversion formulae that reconcile these two models. Ingeneral, we find that the Gardner parameter alpha G is related to the vanGenuchten parameters alpha vG and n by alphamore » G/alpha vG ~; 1.3 n. Thisconversion rule will allow direct recasting of Gardner-based analyticalsolutions in the van Genuchten parameter space. The validity of theproposed formulae was tested by comparing the predicted relativepermeability of various porous media with measured values.« less
  • Predicting contaminant migration within the vadose zone, for performance or risk assessment, requires estimates of unsaturated hydraulic conductivity for field soils. Hydraulic conductivities, K, were experimentally determined as a function of volumetric moisture content, {theta}, for Hanford sediments. The steady state head control method and an ultracentrifuge method were used to measure K{theta} in the laboratory for 22 soil samples. The van Genuchten model was used to fit mathematical functions to the laboratory-measured moisture retention data. Unsaturated conductivities estimated by the van Genuchten-Mualem predictive model, using the fitted moisture retention curve and measured saturated hydraulic conductivity, K{sub 2}, were comparedmore » to those obtained by a scaled-predictive method that uses a single K{theta} measurement as a match point near the dry regime. In general, the measured K values and those predicted form van Genuchten-Mualem relationships showed considerable disagreement. This suggests that the use of laboratory-measured K{sub s} results in an inadequate characterization of K{theta} for the desired range of moisture content. Deviations between the measured and predicted K were particularly severe at relatively low moisture contents; for some samples, there were differences in excess of 2 orders of magnitude at low {theta}. However, use of the same moisture retention curve-fitting parameters and a single steady state head control-based K{theta} measurement near the dry regime resulted in considerable improvement. In fact, for the coarse-textured soils considered in this study, results indicate that a K{theta} measurement near the dry regime must be used to obtain reliable estimates of unsaturated K at low {theta}. The study provided important insight on application of two different experimental techniques of measuring unsaturated conductivities. 27 refs., 11 figs., 3 tabs.« less
  • A new numerical scheme is proposed for generating an orthogonal grid in a simply-connected 2D domain. The scheme is based on the idea of decomposition of a global orthogonal transform into consecutive mappings of a conformal mapping and an auxiliary orthogonal mapping which was suggested by Kang and Leal (J. Comput. Phys. 102, 78 (1992)). The method is non-iterative and flexible in the adjustment of grid spacing. The grid spacing can be controlled mainly by specification of the boundary correspondence up to three sides of the boundary. The method is also equipped with a control function that provides further degreesmore » of freedom in the grid spacing adjustment. From a mathematical viewpoint, the proposed scheme can also be regarded as a numerical implementation of the constructive proof for the existence of a solution of the orthogonal mapping problem in an arbitrary simply-connected domain under the condition that the boundary correspondence is specified on three sides.« less