The influence of the log-conductivity autocovariance structure on macrodispersion coefficients

Macrodispersion coefficients are derived for heterogeneous porous media under ergodic and nonergodic conditions. Influences of the log-conductivity autocovariance function on macrodispersion are investigated through six commonly used isotropic log-conductivity autocorrelation models. They are the exponential, Gaussian, spherical, linear, Whittle and Mizell A-type models. Analytical expressions for ergodic macrodispersion coefficients for each of these models are presented. The results for nonergodic macrodispersion coefficients are calculated numerically. The results show that the various autocovariance functions, which display slight differences in the preasympototic region, have little effect on the ultimate macrodispersion coefficient. The effect of nonergodicity is more significant than the log-conductivity autocovariance function for the aquifers exhibiting unimodal log-conductivity distribution.