SOLUTE TRANSPORT IN 3-DIMENSIONAL HETEROGENEOUS MEDIA WITH A GAUSSIANCOVARIANCE OF LOG HYDRAULIC CONDUCTIVITY

The analytical solutions for the velocity covariance, u(ij), one parti cle displacement covariance X-ij, and the macrodispersivity tensor alp ha(ij) defined as (0.5/mu)(dX(ij)/dt), were derived in three-dimension al heterogeneous media. A Gaussian covariance function (GCF) of logari thmic hydraulic conductivity, log K, Was used, assuming uniform mean f low and first-order approximation in log-conductivity variance, where mu is the magnitude of the mean flow velocity mu. Based on these solut ions, the time-dependent ensemble averages of the second spatial momen ts, Z(ij) = [A(ij)] - A(ij) (0) = X-ij - R-ij and the effective disper sivity tensor gamma(ij), defined as (0.5/mu)(d[A(ij)]/dt), were evalua ted for a finite line source either normal or parallel to mu, where A( ij)(0) is the initial value of the second spatial moment of a plume, A (ij), and R-ij is the plume centroid covariance. The results obtained in this study were compared with previous results for an exponential c ovariance function (ECF). It was found that in a stationary log K fiel d the spreading of a solute plume depends not only on the variance and integral scale of the log K field but also on the shape of its covari ance function. The more strongly correlated the hydraulic conductiviti es at short separation distances are, the faster Z(ii) and gamma(ii) g row at early time. Also, the earlier that y(ii) approaches its asympto te or peak, and the higher the peak is, the larger the negative transv erse dispersivity. More importantly, the ergodic limits for GCF are re ached faster than those for ECF, as the initial size of a plume increa ses. The ergodic limit X-11 for GCF is slightly larger than that for E CF, but X-22 and X-33 are significantly smaller than those for ECF eve n though the asymptotic alpha(ii) for GCF is the same with that for EC F.