Effective solute transport in temporally fluctuating flow through heterogeneous media

Abstract

We investigate the effective spreading of a passive solute evolving from a finite source in temporally fluctuating flow through a heterogeneous porous medium. To this end, we distinguish between two stochastic processes: one to represent the spatial variability of hydraulic conductivity (K) and one to model the temporal fluctuations of the hydraulic gradient (J). In a second‐order perturbation approach we systematically investigate the time evolution of “effective” dispersion coefficients, which quantify solute spreading in response to longitudinal and transverse fluctuations of the hydraulic gradient, spatial heterogeneity, and local dispersion. The effective dispersion coefficients consist of three contributions that reflect (1) local dispersion, (2) the interaction between local dispersion and spatial heterogeneity, and (3) the interaction of local dispersion, spatial heterogeneity, and temporal fluctuations (i.e., time fluctuations enhance spreading only as a consequence of the interplay with spatial heterogeneity). Furthermore, longitudinal and transverse temporal fluctuations of the hydraulic gradient induce macroscopic contributions to the longitudinal as well as the transverse effective dispersion coefficients, which can both be comparable to the contributions to longitudinal dispersion due to steady flow, i.e., large. An application to a field‐scale tracer experiment gives evidence that temporal fluctuations help in explaining observed macroscopic transverse solute spreading. Furthermore, aquifer remediation techniques that rely on the mixing of injected reactants with resident contaminants, or simply on dissolving these, can benefit from forcing velocity fluctuations. The presented results provide a quantitative basis for the design of such hydraulic manipulation techniques.