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.