Simulation of non‐Gaussian space random functions for modeling transport in groundwater

The recent developments and successful applications of covariance‐related stochastic methods to groundwater field experiments suggest that further efforts in developing spatial characterization methods are warranted. One area that deserves further attention is that of characterizing multimodal distributions, such as fractured rock masses, dolomite rocks with dissolution channels, and sand‐shale formations. Traditionally used covariance functions may not be enough to fully characterize spatial continuity in applications where the pattern of spatial continuity depends on the specific magnitude level of the attribute, for example, hydraulic conductivity. Alternative models based on multiple indicator covariances or mixture of populations offer greater flexibility. Applying such models to the case of perfect stratification, a stochastic simulation is proposed which allows generating different realizations, all sharing the same vertical conductivity covariance yet differing by other spatial statistics and leading to widely different transport characteristics. A mere covariance‐based approach would have failed to distinguish between these alternatives. Investigation of tracer transport in bimodal stratified formations suggests a dependence of the mean advection velocity on the dispersion coefficients as a result of a mechanism that enhances longitudinal dispersion directly proportional to lateral pore scale dispersion and entails a diversion of a substantial portion of the plume into the low‐conductivity layers. This mechanism may not be evident when the class‐specific spatial structures of the conductivities are ignored.