Stochastic analysis of macrodispersion in a stratified aquifer

Abstract

The longitudinal dispersion produced as a result of vertical variations of hydraulic conductivity in a stratified aquifer is analyzed by treating the variability of conductivity and concentration as homogeneous stochastic processes. The mass transport process is described using a first‐order approximation which is analogous to that of G. I. Taylor for flow in tubes. The resulting stochastic differential equation describing the concentration field is solved using spectral representations. The results of the analysis demonstrate that for large time the longitudinal dispersivity approaches a constant value which is dependent on statistical properties of the medium. The analysis also describes the transient development of the dispersive process and some non‐Fickian effects which occur early in the displacement process.

Tracer transport in fractured crystalline rock: Evidence of nondiffusive breakthrough tailing

“…This relationship implies that the observed breakthrough tailing is an expression of hydrodynamic transport, and the extending tailing implies that this hydrodynamic transport is non-Fickian in nature. Such a hypothesis seems justifiable, in light of theoretical investigations that predict Fickian transport will occur only after the tracer traveled a sufficient distance to encounter a statistically significant hydraulic conductivity distribution [Gelhar et al, 1979]. This sufficient distance is expected to be large or even infinite in highly heterogeneous media such as fractured rock [Matheron and de Marsily, 1980;Neretnieks, 1983].…”

Channel model of flow through fractured media

“…In fact, there is much field evidence that the dispersivity is not a constant due to medium heterogeneities, but depends on the travel distance and/or scale of the system. Several workers have taken different approaches to incorporate the scale dependent dispersion in modeling studies (e.g., Sauty et al,1979;Gelhar et al,1979;Pickens and Grisak, 1981).…”

Propagation de pollution dans un aquifère alluvial. L'effet de parcours

“…Cette formulation rejoint des études théoriques récentes ( (7], [8]) qui montrent, pour un milieu poreux fortement hétérogène, que le mouvement d'un traceur ne suit pas l'équation classique de la dispersion et que les propriétés dispersives du milieu peuvent être caractérisées par des fonctions du temps. On doit alors s'interroger sur la signification physique de cette dépendance temporelle.…”