A fractal investigation of solute travel time in a heterogeneous aquifer: transition probability/Markov chain representation

Abstract

Solute transport behavior in heterogeneous type structures is generally assessed in terms of its basic statistical properties, such as mean, variance, and correlation. With increasing evidence that the solute transport process in subsurface aquifers exhibits some degree of order at multiple scales (i.e. fractal or scaling), it is crucial to investigate if random representations of aquifers could also explain fractal solute transport behavior. Here, we investigate transport processes that occur in first order Markov chain-type aquifer structures, defined by transition probabilities between constituent hydrofacies. Markov chain structures possess certain advantages with respect to data requirements when compared to traditional Gaussian approaches. The statistical moment scaling function method is employed to investigate solute travel times. The results indicate the potential presence of multi-fractal behavior in the solute transport process, revealing the ability of the transition probability/Markov chain (TP/MC) approach to represent aquifer structures that give rise to fractal solute transport. A sensitivity analysis of the solute transport behavior to the four principal hydrostratigraphic parameters in the TP/MC approach indicates that the degree of fractality increases with an increase in: (1) the number of facies; (2) the volume proportions of the coarse sediments; (3) the dip to vertical mean length ratio; and (4) the order of bedding sequences.