An indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity

Solute transport takes place in heterogeneous porous formations, with the log conductivity, Y = ln K, modeled as a stationary random space function of given univariate normal probability density function (pdf) with mean < Y >, variance sigma(2)(Y), and integral scale I-Y. For weak heterogeneity, the above mentioned quantities completely define the first-order approximation of the longitudinal macrodispersivity sigma(L) = sigma I-2(Y)Y. However, in highly heterogeneous formations, nonlinear effects which depend on the multipoint joint pdf of Y, impact alpha(L). Most of the past numerical simulations assumed a multivariate normal distribution (MVN) of Y values. The main aim of this study is to investigate the impact of deviations from the MVN structure upon alpha(L). This is achieved by using the concept of spatial correlations of different Y classes, the latter being defined as the space domain where Y falls in the generic interval [Y,Y + Delta Y]. The latter is characterized by a length scale lambda(Y), reflecting the degree of connectivity of the domain (the concept is similar to the indicator variograms). We consider both "symmetrical" and "non-symmetrical" structures, for which lambda(Y') = lambda(-Y') (similar to the MVN), and lambda(Y') not equal lambda(-Y'), respectively, where Y' = Y - < Y >. For example, large Y zones may have high spatial correlation, while low Y zones are poorly correlated, or vice versa. The impact of lambda(Y) on alpha(L) is investigated by adopting a structure model which has been used in the past in order to investigate flow and transport in highly heterogeneous media. It is found that the increased correlation in the low conductive zones with respect to the high ones generally leads to a significant increase in alpha(L), for the same global I-Y. The finding is explained by the solute retention occurring in low Y zones, which has a larger effect on solute spreading than high Y zones. Conversely, alpha(L) decreases when the high conductivity zones are more correlated than the low Y ones. Dispersivity is less affected by the shape of lambda(Y) for symmetrical distributions. It is found that the range of validity of the first-order dispersivity, i.e., alpha(L) = I-Y sigma(2)(Y), narrows down for non-symmetrical structures.