Flow in unsaturated random porous media, nonlinear numerical analysis and comparison to analytical stochastic models

This work presents a rigorous numerical validation of analytical stochastic models of steady state unsaturated flow in heterogeneous porous media. It also provides a crucial link between stochastic theory based on simplifying assumptions and empirical field and simulation evidence of variably satura ted flow in actual or realistic hypothetical heterogeneous porous media. St atistical properties of unsaturated hydraulic conductivity, soil water tens ion, and soil water flux in heterogeneous soils are investigated through hi gh resolution Monte Carlo simulations of a wide range of steady state flow problems in a quasi-unbounded domain. In agreement with assumptions in anal ytical stochastic models of unsaturated flow, hydraulic conductivity and so il water tension are found to be lognormally and normally distributed, resp ectively. In contrast, simulations indicate that in moderate to strong vari able conductivity fields, longitudinal flux is highly skewed. Transverse fl ux distributions are leptokurtic. the moments of the probability distributi ons obtained from Monte Carlo simulations are compared to modified first-or der analytical models. Under moderate to strong heterogeneous soil flux con ditions (sigma(y)(2)greater than or equal to 1), analytical solutions overe stimate variability in soil water tension by up to 40% as soil heterogeneit y increases, and underestimate variability of both flux components by up to a factor 5. Theoretically predicted model (cross-)covariance agree well wi th the numerical sample (cross-)covarianaces. Statistical moments are shown to be consistent with observed physical characteristics of unsaturated flo w in heterogeneous soils. (C) 1998 Elsevier Science Limited. All rights res erved.