engleski

On the influence of higher moments for tracer transport in heterogeneous porous media

Flow and transport processes are mainly characterized by multi-scale physical interpretation, variability and heterogeneity of all variables, such as hydraulic conductivity or sorption. The only rational way for describing uncertainties is by using stochastic modeling. Heterogeneity is usually described by variogram or multi-Gaussian (MG) field which is not able to reproduce curvilinear high or low connected lnK zones. Moreover, many analytical first-order solutions have been obtained, but they are limited by uniform and steady mean flow, low heterogeneity and also rely only on two first statistical moments. On the other side, field observations show that describing solute and flow variables with only two moments, mean and variance, insufficiently describes specified physical processes implying predefined Gaussianity. Using Adaptive Fup Monte-Carlo Method (AFMCM), we analyze travel time statistics for different lnK variability, MG and non-Gaussian heterogeneity fields, in uniform and radial convergent computational setup. Higher moments are needed for accurate description of early and late arrivals, as well as travel time peak, in case of highly heterogeneous MG fields and especially non-Gaussian fields with connected highly permeable lnK zones. Involving local diffusion and using Random Walk Particle Tracking Method over continuous velocity field, normalized concentration pdf is obtained with respect to Maximum Entropy (MaxEnt) and beta pdf. Even in mild heterogeneous aquifers, concentration pdf is not completely described by first two moments. MaxEnt pdf requires more than four moments for accurate description, however beta pdf presents relatively well matching with simulated Monte-Carlo pdf.

tracer transport; travel time; concentration; porous media; higher moments

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