Transient Dispersion in Porous Media: A Comparison between Exact and Approximate Solutions in a Case Study

Three methods are proposed for studying solute dispersion over short periods of time in the case study of a one-dimensional flow: the non-local method, the spatial moments method, and the volume averaging method distinguishing two zones using both rigorous closure and classical closure. The non-local method (exact) uses the Green function. Its application in calculating the generalized dispersion tensor and solving the macroscopic problem, is a cumbersome task. The methods of moments and volume averaging distinguishing two zones using rigorous closure can be used to find a correct description in terms of the spatial moments of the solute concentration distribution up to the second order. Nevertheless, the rigorous closure cannot, in general, be applied to periodic media. Volume averaging with classical closure gives coefficients which are different from those obtained by the method of moments. Surprisingly, the macroscopic solution is very similar to the exact one, in some of the tested cases.