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.

A new model for predicting the hydraulic conductivity of unsaturated porous media

A theory of moisture movement in porous, materials under temperature gradients is developed which explains apparently discordant experimental information, including (a) the large value of the apparent vapor transfer, (b) effect of moisture content on net moisture transfer, and (c) the transfer of latent heat by distillation.

The previous simple theory of water vapor diffusion in porous media under temperature gradients neglected the interaction of vapor, liquid and solid phases, and the difference between average temperature gradient in the air-filled pores and in the soil as a whole. With these factors taken into account, an (admittedly approximate) analysis is developed which predicts orders of magnitude and general behavior in satisfactory agreement with the experimental facts.

An important implication of the present approach is that experimental methods used to distinguish between liquid and vapor transfer have not done so, since what has been supposed to be vapor transfer has actually been series-parallel flow through liquid ‘islands’ located in a vapor continuum.

Equations describing moisture and heat transfer in porous materials under combined moisture and temperature gradients are developed. Four moisture-dependent diffusivities arising in this connection are discussed briefly.

Moisture movement in porous materials under temperature gradients

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.

/pdf/the-retc-code-for-quantifying-the-hydraulic-functions-of-30xerlmq7o.pdf

The RETC code for quantifying the hydraulic functions of unsaturated soils

Theory of Infiltration

The flow of homogeneous fluids through porous media: analogies with other physical problems

The permeability of a porous material to water is a function of the geometry of the boundary between the solid component and the pore space. Expressions of the Kozeny type purporting to represent this function are based upon the particle size or specific surface of the solids, and whilst, for engineering practice, they have given satisfaction for saturated sands, they may fail badly in other cases. By developing a Kozeny type of expression for the particular structure of a bundle of capillary tubes of assorted radii, we demonstrate the cause of the failure. Such failure may be avoided by relating permeability to pore-size distribution, which is the factor of prime concern and which may be measured directly by even simpler means than are used to determine particle-size distribution. The pore-size distribution is arrived at by an interpretation of the moisture characteristic of the material, i.e. of the curve of moisture content plotted against pressure deficiency. A simple statistical theory, based upon the calculation of the probability of occurrence of sequences of pairs of pores of all the possible sizes, and of the contribution to the permeability made by each such pair, leads to an expression of the permeability as the sum of a series of terms. By stopping the summation at a selected upper limit of pore size one may calculate the permeability at any chosen moisture content and plot it as a function of that content. An example is presented, using a coarse graded sand specified by its moisture characteristic. To check these calculations, experimental determinations of the permeabilities of unsaturated materials are presented, using two different grades of sand and a sample of slate dust, the results being compared with computed values. The agreement seems good, and is certainly better than that provided by the Kozeny formula as developed, with difficulty, for the purpose. The limitations and possible improvements of our concept are very briefly discussed, and finally it is shown how a combined use of the moisture characteristic and the permeability (which is itself derivable from the moisture characteristic) leads to an expression for the coefficient of diffusion of water in the material as a function of moisture content. From this it should be possible, in principle, to calculate in suitable cases the course of water movement down a gradient of moisture content. Such a calculation awaits a satisfactory solution of the problem of non-linear diffusion.

/pdf/the-permeability-of-porous-materials-lx3bgthtrr.pdf

N. Collis-George

Papers

The permeability of porous materials