NUMERICAL MODELING OF MACRODISPERSION IN HETEROGENEOUS MEDIA - A COMPARISON OF MULTI-GAUSSIAN AND NON-MULTI-GAUSSIAN MODELS

The macrodispersion of an inert solute in a 2-D heterogeneous porous m edia is estimated numerically in a series of fields of varying heterog eneity. Four different random function (RF) models are used to model l og-transmissivity (ln T) spatial variability, and for each of these mo dels, In T variance is varied from 0.1 to 2.0. The four RF models shar e the same univariate Gaussian histogram and the same isotropic covari ance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme va lues (both high and low) are spatially uncorrelated. The other three m odels are non-multi-Gaussian: model B with high connectivity of high e xtreme values, model C with high connectivity of low extreme values, a nd model D with high connectivities of both high and low extreme value s. Residence time distributions (RTDs) and macrodispersivities (longit udinal and transverse) are computed on lnT fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RT Ds and macrodispersivities for the multi-Gaussian model are in good ag reement with analytically derived values using first-order theories fo r log-transmissivity variance up to 2.0. The results from the non-mult i-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when In T variance is small. RTDs in non-m ulti-Gaussian realizations with high connectivity at high extreme valu es display earlier breakthrough than in multi-Gaussian realizations, w hereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian rea lizations are, in general, larger than in the multi-Gaussian ones, whi le transverse macrodispersivities in the non-multi-Gaussian realizatio ns can be larger or smaller than in the multi-Gaussian ones depending on the type of connectivity at extreme values. Comparing the numerical results for different flow directions, it is confirmed that macrodisp ersivities in multi-Gaussian realizations with isotropic spatial corre lation are not flow direction-dependent. Macrodispersivities in the no nmulti-aaussian realizations, however, are flow direction-dependent al though the covariance of ln T is isotropic (the same for all four mode ls). It is important to account for high connectivities at extreme tra nsmissivity values, a likely situation in some geological formations. Some of the discrepancies between first-order-based analytical results and field-scale tracer test data may be due to the existence of highl y connected paths of extreme conductivity values. (C) 1998 Elsevier Sc ience B.V.