HR: 0800h
AN: H31D-0435    [Abstracts]
TI: Hydraulic functions of variably saturated porous media: Upscaling from single-pore to sample-scale model
AU: Gogolashvili, B E
EM: Bulat.Gogolashvili@ksu.ru
AF: Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya Street, Kazan, 420008 Russian Federation
AU: Egorov, A G
EM: Andrey.Egorov@ksu.ru
AF: Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya Street, Kazan, 420008 Russian Federation
AU: * Nieber, J L
EM: nieber@umn.edu
AF: Department of Biosystems and Agricultural Engineering, University of Minnesota, 1390 Eckles Ave., St. Paul, MN 55108 United States
AB: Extrapolation of hydraulic functions ($P_c(S) and K(S)$) to oven dry conditions is of interest for many practical problems such as for example modeling of fingering in porous media. Experimental soil water-retention data are normally obtained for high and moderate values of the saturation and lacking at saturations below or close to residual. We develop a model which predicts hydraulic functions down to oven dryness by using pore-scale modeling. Following the approach by Tuller and Or [1, 2], the pore space is represented by an array of connected polygonal unit cells. Three steady-state and laminar flow regimes in the unit cell are considered to derive the hydraulic functions: 1) flow in completely filled pores, 2) corner flow in partially filled pores, and 3) film flow on solid surfaces. Unlike the Tuller and Or model we take into account an influence of the adjacent cells. The state of the unit cell (either filled with liquid or yielding corner and film flow) depends on the pressure in that cell and is affected by the state of the adjacent cells as well. Thus, this model may be treated as a combination of the Mualem model [3] and the the Tuller and Or model. This general model allows us to take into account hysteretic properties of the $P_c-S$ relation and calculate the main drainage curve, the main wetting curve, and scanning curves for all ranges of saturation even below residual. We fit our model with available experimental data, obtained with typical laboratory silica sand in the high to moderate saturation range for the drainage cycle. All calculated hydraulic functions (hydraulic conductivity, main wetting curve, and scanning drainage curves) match experimental data without any additional assumptions. We regard this fact as a validation of the proposed model. \begin{enumerate} \item Tuller, M., Or D, Dudley LM. Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores. Water Resour. Res., 1999, 35:1949-1964. \item Tuller, M., Or D. Unsaturated hydraulic conductivity of structured porous media: A review of liquid configuration-based models. Vadose Zone J., 2002, 1:14-37. \item Mualem Y. A conceptual model of hysteresis. Water Resour. Res., 1974, 10:514-520. \end{enumerate}
DE: 1866 Soil moisture
DE: 1875 Unsaturated zone
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting