Groundwater flow velocity and dispersivity might be temporally or spatially variable rather than constant. In this paper, linearly-asymptotically or exponentially distance-dependent dispersivities and temporally exponential flow velocity were coupled to the conventional advection-dispersion equation. The mathematical models were established by considering the case of a coupled time-dependent velocity and scale-dependent dispersivities where one-dimensional (1D) semi-analytical solutions were obtained using the Laplace transform in a finite domain. The solution was verified by comparing it with a numerical solution, based on finite-element COMSOL Multiphysics. The impacts of different parameters of time-dependent flow velocity and scale-dependent dispersivities on breakthrough curves (BTCs) were thoroughly analyzed. The results show that a slight change of time-dependent flow velocity will lead to considerable change of BTCs, meaning that solute transport is sensitive to the temporally variable flow velocity. Secondly, a larger growth rate of the dispersivity in linear-asymptotically distance-dispersivity function can lead to a faster solute transport at early stage, but a lower concentration at late stage; as for the exponentially distance-dependent function, the growth rate of the dispersivity has the same effects on BTCs. Thirdly, it was observed that an increase in final steady velocity (or asymptotic velocity) will amplify the impacts on solute transport due to advection; as for the asymptotic dispersivity, it has similar impacts on the solute transport due to dispersion. Overall, our results show that the effects of time-dependent flow velocity and distance-dependent dispersivities are not negligible when describing solute transport process in subsurface hydrology.
Keywords: Distance-dependent dispersivity; Finite domain; Semi-analytical solutions; Time-dependent velocity.