ON THE VELOCITY COVARIANCE AND TRANSPORT MODELING IN HETEROGENEOUS ANISOTROPIC POROUS FORMATIONS .2. UNSATURATED FLOW

Velocity covariances, and the resultant macrodispersion coefficient te nser, derived by Russo (this issue) for saturated flow conditions, are applied for unsaturated flow conditions, employing the assumption tha t for a given mean capillary pressure head, water saturation is a dete rministic constant and log conductivity is a multivariate normal, stat ionary random space function. The applicability of the approach for mo deling flow and transport in the vadose zone was evaluated by the use of the stochastic theory of Yeh et al. (1985a, b) for steady, unsatura ted flow. Results of the analyses suggest that the approach may be app licable to vadose zone flow and transport, as long as the scale of het erogeneity in the direction of the mean flow is smaller than approxima tely one tenth of the characteristic length of unsaturated flow. For p orous formation of given statistics, the magnitude of macrodispersion in unsaturated flow is larger than that in saturated flow, and increas es as water saturation decreases. For a given water saturation, transp ort in unsaturated flow may approach asymptotic Fickian behavior more slowly than in saturated flow, when the two formation properties log K -s and ct are positively cross-correlated and when the correlation sca le of ct is relatively large as compared with the correlation scale of log K-s.