Permeability of porous solids
01 Jan 1961-Transactions of The Faraday Society (The Royal Society of Chemistry)-Vol. 57, pp 1200-1207
TL;DR: In this article, an expression was derived to describe both saturated and unsaturated permeability of porous media in terms of the pore size distribution as obtained from mercury-injection data or water-desorption isotherms.
Abstract: An expression has been derived to describe both saturated and unsaturated permeability of porous media in terms of the pore size distribution as obtained from mercury-injection data or water-desorption isotherms. An interaction model has been adopted wherein both pore radius and effective area available for flow have been considered. The permeability values obtained using this expression have been compared with water and gas permeabilities of a variety of porous media. Satisfactory agreement is found between experimental and calculated values over a wide range of permeability.
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TL;DR: Van Genuchten et al. as mentioned in this paper proposed a closed-form analytical expression for predicting the hydraulic conductivity of unsaturated soils based on the Mualem theory, which can be used to predict the unsaturated hydraulic flow and mass transport in unsaturated zone.
Abstract: A new and relatively simple equation for the soil-water content-pressure head curve, 8(h), is described in this paper. The particular form of the equation enables one to derive closedform analytical expressions for the relative hydraulic conductivity, Kr, when substituted in the predictive conductivity models of N.T. Burdine or Y. Mualem. The resulting expressions for Kr(h) contain three independent parameters which may be obtained by fitting the proposed soil-water retention model to experimental data. Results obtained with the closed-form analytical expressions based on the Mualem theory are compared with observed hydraulic conductivity data for five soils with a wide range of hydraulic properties. The unsaturated hydraulic conductivity is predicted well in four out of five cases. It is found that a reasonable description of the soil-water retention curve at low water contents is important for an accurate prediction of the unsaturated hydraulic conductivity. Additional Index Words: soil-water diffusivity, soil-water retention curve. van Genuchten, M. Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898. T USE OF NUMERICAL MODELS for simulating fluid flow and mass transport in the unsaturated zone has become increasingly popular the last few years. Recent literature indeed demonstrates that much effort is put into the development of such models (Reeves and Duguid, 1975; Segol, 1976; Vauclin et al., 1979). Unfortunately, it appears that the ability to fully characterize the simulated system has not kept pace with the numerical and modeling expertise. Probably the single most important factor limiting the successful application of unsaturated flow theory to actual field problems is the lack of information regarding the parameters entering the governing transfer equations. Reliable estimates of the unsaturated hydraulic conductivity are especially difficult to obtain, partly because of its extensive variability in the field, and partly because measuring this parameter is time-consuming and expensive. Several investigators have, for these reasons, used models for calculating the unsaturated conductivity from the more easily measured soil-water retention curve. Very popular among these models has been the Millington-Quirk method (Millington and Quirk, 1961), various forms of which have been applied with some success in a number of studies (cf. Jackson et al., 1965; Jackson, 1972; Green and Corey, 1971; Bruce, 1972). Unfortunately, this method has the disadvantage of producing tabular results which, for example when applied to nonhomogeneous soils in multidimensional unsaturated flow models, are quite tedious to use. Closed-form analytical expressions for predicting 1 Contribution from the U. S. Salinity Laboratory, AR-SEA, USDA, Riverside, CA 92501. Received 29 June 1979. Approved 19 May I960. 'Soil Scientist, Dep. of Soil and Environmental Sciences, University of California, Riverside, CA 92521. The author is located at the U. S. Salinity Lab., 4500 Glenwood Dr., Riverside, CA 92502. the unsaturated hydraulic conductivity have also been developed. For example, Brooks and Corey (1964) and Jeppson (1974) each used an analytical expression for the conductivity based on the Burdine theory (Burdine, 1953). Brooks and Corey (1964, 1966) obtained fairly accurate predictions with their equations, even though a discontinuity is present in the slope of both the soil-water retention curve and the unsaturated hydraulic conductivity curve at some negative value of the pressure head (this point is often referred to as the bubbling pressure). Such a discontinuity sometimes prevents rapid convergence in numerical saturated-unsaturated flow problems. It also appears that predictions based on the Brooks and Corey equations are somewhat less accurate than those obtained with various forms of the (modified) Millington-Quirk method. Recently Mualem (1976a) derived a new model for predicting the hydraulic conductivity from knowledge of the soil-water retention curve and the conductivity at saturation. Mualem's derivation leads to a simple integral formula for the unsaturated hydraulic conductivity which enables one to derive closed-form analytical expressions, provided suitable equations for the soil-water retention curves are available. It is the purpose of this paper to derive such expressions using an equation for the soil-water retention curve which is both continuous and has a continuous slope. The resulting conductivity models generally contain three independent parameters which may be obtained by matching the proposed soil-water retention curve to experimental data. Results obtained with the closedform equations based on the Mualem theory will be compared with observed data for a few soils having widely varying hydraulic properties. THEORETICAL Equations Based on Mualem's Model The following equation was derived by Mualem (1976a) for predicting the relative hydraulic conductivity (Kr) from knowledge of the soil-water retention curve
22,781Â citations
TL;DR: In this article, a simple analytic model is proposed which predicts the unsaturated hydraulic conductivity curves by using the moisture content-capillary head curve and the measured value of the hydraulic conductivities at saturation.
Abstract: A simple analytic model is proposed which predicts the unsaturated hydraulic conductivity curves by using the moisture content-capillary head curve and the measured value of the hydraulic conductivity at saturation. It is similar to the Childs and Collis-George (1950) model but uses a modified assumption concerning the hydraulic conductivity of the pore sequence in order to take into account the effect of the larger pore section. A computational method is derived for the determination of the residual water content and for the extrapolation of the water content-capillary head curve as measured in a limited range. The proposed model is compared with the existing practical models of Averjanov (1950), Wyllie and Gardner (1958), and Millington and Quirk (1961) on the basis of the measured data of 45 soils. It seems that the new model is in better agreement with observations.
6,529Â citations
01 Nov 1999
TL;DR: This report is a self-contained guide to application of Tough2 to subsurface flow problems, and gives a technical description of the TOUGH2 code, including a discussion of the physical processes modeled, and the mathematical and numerical methods used.
Abstract: TOUGH2 is a numerical simulator for nonisothermal flows of multicomponent, multiphase fluids in one, two, and three-dimensional porous and fractured media. The chief applications for which TOUGH2 is designed are in geothermal reservoir engineering, nuclear waste disposal, environmental assessment and remediation, and unsaturated and saturated zone hydrology. TOUGH2 was first released to the public in 1991; the 1991 code was updated in 1994 when a set of preconditioned conjugate gradient solvers was added to allow a more efficient solution of large problems. The current Version 2.0 features several new fluid property modules and offers enhanced process modeling capabilities, such as coupled reservoir-wellbore flow, precipitation and dissolution effects, and multiphase diffusion. Numerous improvements in previously released modules have been made and new user features have been added, such as enhanced linear equation solvers, and writing of graphics files. The T2VOC module for three-phase flows of water, air and a volatile organic chemical (VOC), and the T2DM module for hydrodynamic dispersion in 2-D flow systems have been integrated into the overall structure of the code and are included in the Version 2.0 package. Data inputs are upwardly compatible with the previous version. Coding changes were generally kept to a minimum, and were only made as needed to achieve the additional functionalities desired. TOUGH2 is written in standard FORTRAN77 and can be run on any platform, such as workstations, PCs, Macintosh, mainframe and supercomputers, for which appropriate FORTRAN compilers are available. This report is a self-contained guide to application of TOUGH2 to subsurface flow problems. It gives a technical description of the TOUGH2 code, including a discussion of the physical processes modeled, and the mathematical and numerical methods used. Illustrative sample problems are presented along with detailed instructions for preparing input data.
1,597Â citations
01 Jan 1992
TL;DR: The RETC computer code as mentioned in this paper uses the parametric models of Brooks-Corey and van Genuchten to represent the soil water retention curve, and the theoretical pore-size distribution models of Mualem and Burdine to predict the unsaturated hydraulic conductivity function from observed water retention data.
Abstract: This report describes the RETC computer code for analyzing the soil water retention and hydraulic conductivity functions of unsaturated soils. These hydraulic properties are key parameters in any quantitative description of water flow into and through the unsaturated zone of soils. The program uses the parametric models of Brooks-Corey and van Genuchten to represent the soil water retention curve, and the theoretical pore-size distribution models of Mualem and Burdine to predict the unsaturated hydraulic conductivity function from observed soil water retention data. The report gives a detailed discussion of the different analytical expressions used for quantifying the soil water retention and hydraulic conductivity functions. A brief review is also given of the nonlinear least-squares parameter optimization method used for estimating the unknown coefficients in the hydraulic models. Several examples are presented to illustrate a variety of program options. The program may be used to predict the hydraulic conductivity from observed soil water retention data assuming that one observed conductivity value (not necessarily at saturation) is available. The program also permits one to fit analytical functions simultaneously to observed water retention and hydraulic conductivity data. The report serves as both a user manual and reference document. Detailed information is given on the computer program along with instructions for data input preparation and sample input and output files. A listing of the source code is also provided.
1,553Â citations
Cites methods from "Permeability of porous solids"
...These include the models by Gates and Lietz [1950], Childs and Collis-George [1950], Burdine [1953], Millington and Quirk [1961], and Mualem [1976a], among others....
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...to b = (0, t3,, (I, n) when the Mualem restriction m = l-l/n is implemented and only retention data are used in the optimization. RETC uses a nonlinear least-squares optimization approach to estimate the unknown model parameters from observed retention and/or conductivity or diffusivity data. A helpful text with background information on fitting equations to experimental data using this method is given by Daniel and Wood [1971]. The approach is based on the partitioning of the total sum of squares of the observed values into a part described by the fitted equation and a residual part of observed values around those predicted with the model....
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...Tables 3 and 4 give average parameter values for soil textural groups according to the USDA classification [Soil Conservation Service, 1975] as estimated by Rawls et al. [1982] and Carsel and Parrish [1988], respectively, from analyses of a large number of soils....
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...These include the models by Gates and Lietz [1950], Childs and Collis-George [1950], Burdine [1953], Millington and Quirk [1961], and Mualem [1976a], among others. An excellent review of previously published pore-size distribution models was given recently by Mualem [1986]. Implementation of these predictive conductivity models still requires independently measured soil water retention data....
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01 Nov 1973
TL;DR: In this article, hydraulic conductivity was measured as a function of soil-water content at 30.5 cm depth intervals to a depth of 182.9 cm in twenty 6.5 meters square plots randomly established over a 150-hectare field.
Abstract: Infiltration and redistribution of water following an irrigation was studied, and
the work was replicated at 20 locations on a 150 hectare plot of land. Hydraulic conductivity
was measured as a function of soil-water content at 30.5 cm depth intervals to a depth
of 182.9 in twenty 6.5-meter-square plots randomly established over a 150-hectare
field. Tensiometers installed at 30.5, 61.0, 91.4, 121.9, 152.4, and 182.9 cm were
used to measure hydraulic gradients. Soil-water contents were ascertained from soil-water
characteristics obtained from six soil cores taken from each of the above depths for
each plot. Variations in soil-water content were found to be normally distributed
with depth and with horizontal distance throughout the field, while values of the
hydraulic conductivity were found to be log-normally distributed. The correlation
between hydraulic conductivity during steady-state infiltration and the clay fraction
was significant at the 1 per cent level. Several equations for predicting water movement
and retention under field conditions are examined.
1,051Â citations