Pre-asymptotic dispersion revisited

Abstract

We develop a new approach to formulation and solution of mathematical models of one-dimensional advective–dispersive transport that specifies the hydrodynamic dispersion coefficient as a function of time since the solute has entered the flow field, termed ‘age.’ This approach addresses Taylor’s concern about the use of time-dependent dispersion coefficients to model pre-asymptotic dispersion by replacing time-dependence with age-dependence, where age of solute is exposure-time to the flow. We show closed form solutions obtained for transport on the −∞<x<∞ and a numerical solution for transport on the 0<x<∞ domain. We demonstrate how this works by application to an in-silico experiment recently published in a study addressing the same issue in a different manner. Our simple and intuitive approach matches the simulated pre-asymptotic data without additional terms or parameter fitting. The same principle applies to pre-asymptotic dispersion in other important upscaled one-dimensional transports e.g., in river corridor or groundwater flows.