On the Velocity Covariance and Transport Modeling in Heterogeneous Anisotropic Porous Formations: 2. Unsaturated Flow

Abstract

Velocity covariances, and the resultant macrodispersion coefficient tensor, derived by Russo (this issue) for saturated flow conditions, are applied for unsaturated flow conditions, employing the assumption that for a given mean capillary pressure head, water saturation is a deterministic constant and log conductivity is a multivariate normal, stationary random space function. The applicability of the approach for modeling flow and transport in the vadose zone was evaluated by the use of the stochastic theory of Yeh et al. (1985a, b) for steady, unsaturated flow. Results of the analyses suggest that the approach may be applicable to vadose zone flow and transport, as long as the scale of heterogeneity in the direction of the mean flow is smaller than approximately one tenth of the characteristic length of unsaturated flow. For porous formation of given statistics, the magnitude of macrodispersion in unsaturated flow is larger than that in saturated flow, and increases as water saturation decreases. For a given water saturation, transport in unsaturated flow may approach asymptotic Fickian behavior more slowly than in saturated flow, when the two formation properties log Ks and α are positively cross‐correlated and when the correlation scale of α is relatively large as compared with the correlation scale of log Ks.