AN INVESTIGATION OF THE VALIDITY OF 1ST-ORDER STOCHASTIC DISPERSION THEORIES IN ISOTROPIC POROUS-MEDIA

Monte Carlo simulations are used to (1) investigate the accuracy of approximations that are implicit in first-order stochastic dispersion theories and (2) identify the accuracy limits of first-order dispersion theories in isotropic porous media. The Fickian theory of Gelhar and Axness (1983), as well as the Fickian and non-Fickian theories of Dagan (1984) and Neuman and Zhang (1990) are investigated. All Monte Carlo simulations are in three dimensions. Confidence limits of ensemble-averaged Monte Carlo results in isotropic porous media are established for 0.1 less-than-or-equal-to sigma(Y) less-than-or-equal-to 1.5. These results showed that first-order theoretical estimates of the Eulerian velocity covariance function are quite accurate for sigma(Y) < 1; theoretical estimates of the non-Fickian longitudinal dispersivity do not deviate significantly from theory for at least sigma(Y) less-than-or-equal-to 1.5; theoretical estimation of the transverse dispersivity is limited to sigma(Y) < 1; and, the Fickian longitudinal dispersivity is overestimated by the theory of Gelhar and Axness (1983). Of all first-order dispersion theories, the theory of Dagan (1984) is most robust in estimating the dispersivity tensor.