Arrival times and temporal moments of breakthrough curves for an imperfectly stratified aquifer

Using concepts developed in an earlier study, a solution in Laplace transform space is obtained for transport of resident concentration in an imperfectly but yet highly stratified porous medium. The flow field, into which an instantaneous pulse of tracer is injected, is taken to be steady and mean uniform parallel to the direction of stratification. From this transform-space solution either temporal moments can be derived by taking derivatives with respect to the Laplace parameter, or the transform-space solution can be inverted numerically to obtain breakthrough curves for the mean concentration. When compared to an equivalent solution with a Fickian dispersive flux, these temporal moments indicate the extent to which transport in heterogeneous porous media deviates from classical Fickian behavior. The numerical inversion of the Laplace transform solution gives partial breakthrough curves for the mean concentration which have the appearance of conflicting with the derived moment information. A hypothesis is put forth which resolves this apparent conflict; this hypothesis is verified by adding a component of local dispersion to the governing transport equation. On the basis of the flux-averaged concentration a form for the expected probability density function for the arrival time of a tracer particle is derived; arrival time moments and an arrival time cumulative distribution function are available as a consequence. Arrival time moments, as derived from the flux-averaged concentration, do not differ significantly from the resident moments, as derived from the resident concentration.