ON THE VELOCITY COVARIANCE AND TRANSPORT MODELING IN HETEROGENEOUS ANISOTROPIC POROUS FORMATIONS .1. SATURATED FLOW

Velocity covariances for saturated heterogeneous formations with aniso tropic structures were derived for mean flow parallel and perpendicula r to the formation bedding and were employed for modeling transport in these formations by the use of a Lagrangian formulation. Relatively s imple analytical expressions, each requiring only a single numerical i ntegration, were obtained for the longitudinal and transverse componen ts of the velocity covariance, the displacement covariance, and the ma crodispersion coefficient tensors, all as functions of the anisotropy of the formation. Closed-form analytical expressions were derived for the longitudinal and transverse components of the velocity variance an d for the asymptotic values of the transverse components of the displa cement covariance. The applicability of this approach for modeling flo w and transport in the vadose zone is tested in the companion to this paper by the use of the stochastic theory of Yeh et al. (1985a, b) for unsaturated flow.