An Analysis of Dispersion in a Stratified Aquifer
Article first published online: 9 JUL 2010
Copyright 1984 by the American Geophysical Union.
Water Resources Research
Volume 20, Issue 10, pages 1337–1354, October 1984
How to Cite
1984), An Analysis of Dispersion in a Stratified Aquifer, Water Resour. Res., 20(10), 1337–1354, doi:10.1029/WR020i010p01337., , and (
- Issue published online: 9 JUL 2010
- Article first published online: 9 JUL 2010
- Manuscript Accepted: 21 MAY 1984
- Manuscript Received: 9 APR 1984
The dispersion of a conservative solute produced as a result of vertical variations of hydraulic conductivity in a horizontal stratified aquifer of finite thickness is analyzed by applying the moment method of Aris to solve the governing advection-dispersion equation describing mass transport. In the analysis it is assumed that the aquifer is of constant thickness and of infinite lateral extent, the hydraulic conductivity is a known function of the vertical coordinate only, and the flow is unidirectional, parallel to the stratification. The applicable Aris moment equations are developed in a suitable nondimensional form. Analytical solutions are obtained for the zeroth and first moments and for the time derivative of the second moment of the longitudinal concentration distribution for the case of an instantaneous plane source for several idealized hydraulic conductivity profiles (parabolic, linear, step function, and cosine profiles and their even periodic extensions). The analysis gives the time-dependent variation of the longitudinal macrodispersivity for these idealized cases throughout the transient development of the dispersion process. The results of the analysis are applied to a field-measured hydraulic conductivity profile, and predicted values of the longitudinal macrodispersivity are compared with field results. An important conclusion from the analyses is that nonuniformities in the hydraulic conductivity profile which persist over long distances may produce rather large values of longitudinal macrodispersivity which are comparable to those observed in some aquifers and which are much larger than those predicted by some previous stochastic analyses. Implications of the analytical results for field dispersion problems are discussed.