A Genetic Algorithm for Predicting Pore Geometry Based on Air Permeability Measurements

curves need to be interpreted to calculate pore sizes using the Young and Laplace equation Pore size distributions of porous media are of interest to soil scientists, geologists, and engineers with a variety of backgrounds. If known, Pc 2 cos r [1] pore size distributions can be used to determine fluid retention and permeability relationships. In this study, we propose a methodology to predict pore size distributions from air permeability measurements where Pc (Pa) is the capillary pressure, (N m 1) is the combined with a numerical model representing a porous medium. liquid surface tension, is the liquid–material contact The model is an extension of the capillary model, which was modified angle, and r (m) is the pore radius. This method is elaboso that the capillaries are composed of sections with different diamerate and time-consuming. In fact, it is not uncommon ters. An optimization scheme that makes use of the measured air permefor this test to last 3 to 4 wk. ability values was developed to predict the best possible pore size In the impregnation method, molten paraffin or epdistribution and pore arrangement. A genetic algorithm, a popular oxy is applied to the undisturbed soil sample, which is evolutionary computational methodology, was chosen for the optimiplaced in a sampling tin with both ends open. Once zation process. During our numerical study, we observed that it is not only the pore size distribution that is important, but also how the impregnated, the sample is cooled to room temperature, pores are distributed, in other words, the pore geometry. the core is then sawed and sections are photographed. The calculations are based on two-dimensional slices, thus limiting the representativeness. In the Hg injection T of fluids through porous media, with method, Hg is forced under pressure into a previously applications in soils, subsurface hydrology, geology, oven-dried and air-evacuated sample (Nagpal et al., oil and gas fields, and the medical industry, is of interest 1972). The applied pressure is increased in discrete to scientists and engineers. Before predicting transport steps, and the volume of pores that is intruded between phenomena in a porous medium, its hydraulic properties steps is obtained. The equivalent pore size correspond(i.e., the water retention and hydraulic conductivity relaing to the applied pressure can be calculated with Eq. tionships) must be determined. This is often time-con[1], with being the contact angle between the Hg suming and expensive if done by currently available methand soil and being the surface tension of Hg. The ods. For a given porous medium, the values obtained for advantage of the Hg intrusion method is that it is much water retention and hydraulic conductivity at different faster than the other two techniques previously exwater content values depend on an intricate system of plained. However, the disadvantage is that pore sizes pores with different size, shape, orientation, and conneccan change during the injection. It should be mentioned tivity. This intricate system makes it difficult to express that Hg is a nonwetting fluid in regard to hydrophilic the pore size distribution in a quantitative manner. If porous media, such as soils and rocks. Pore sizes of a porous medium have a direct effect known, however, pore size distributions can be used on the permeability values; larger pores have a higher to calculate water retention and hydraulic conductivity permeability. Pore size is of direct importance in underrelationships. Because of the high degree of complexity standing transport of volatile organic compounds in the of the pore structure, simplifying assumptions need to subsurface (Moldrup et al., 1998; Poulsen et al., 1999) be made. or soil–atmosphere gas exchange (Hutchinson and LivSeveral methods, such as the water-desorption method, ingston, 2002), a subject of interest to agriculture and visualization method using impregnation, and the Hg the turf grass industry. Pore size values can also be used injection method, are available for the determination as indicators of hydraulic conductivity because pore size of pore size distributions (Flint and Flint, 2002). Each affects water run-off (Römkens et al., 2002). The objecof these methods, however, has its own disadvantage(s). tives of this study were to (i) determine the air permeThe water-desorption method is based on calculations ability of a consolidated rock sample (experimental study), of pressures at which water is displaced by air in pores of and (ii) optimize the pore size distribution of the sample different radii. Therefore, the obtained water retention by reproducing the air permeability–water content relationship curve that was experimentally determined. The E. Unsal and J.H. Dane, Dep. of Agronomy and Soils, 202 Funchess advantage of using air permeability is that it is easy to Hall, Auburn Univ., Auburn, AL 36849; G.V. Dozier, Dep. of Commeasure. Because, pore size distributions may have more puter Science and Software Eng., 107 Dunstan Hall, Auburn Univ., than one modal pore size, as a result of aggregation (Kutı́Auburn, AL 36849. Received 5 Aug. 2004. Original Research Paper. lek and Nielsen, 1994), we used two distribution func*Corresponding author ([email protected]). tions to determine pore sizes: (i) a lognormal distribution Published in Vadose Zone Journal 4:389–397 (2005). and (ii) a bimodal lognormal distribution. If successful doi:10.2136/vzj2004.0116 © Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA Abbreviations: GA, genetic algorithm. 389 Published online May 13, 2005