AN ASSESSMENT OF FIRST-ORDER STOCHASTIC DISPERSION THEORIES IN POROUS-MEDIA

Random realizations of three-dimensional exponentially correlated hydr aulic conductivity fields are used in a finite-difference numerical fl ow model to calculate the mean and covariance of the corresponding Lag rangian-velocity fields. The dispersivity of the porous medium is then determined from the Lagrangian-velocity statistics using the Taylor d efinition. This estimation procedure is exact, except for numerical er rors, and the results are used to assess the accuracy of various first -order dispersion theories in both isotropic and anisotropic porous me dia. The results show that the Dagan theory is by far the most robust in both isotropic and anisotropic media, producing accurate values of the principal dispersivity components for sigma gamma as high as 1.0. In the case of anisotropic media where the flow is at an angle to the principal axis of hydraulic conductivity, it is shown that the dispers ivity tensor is rotated away from the how direction in the non-Fickian phase, but eventually coincides with the flow direction in the Fickia n phase.