Uncertainty propagation of hydrodispersive transfer in an aquifer: an illustration of one-dimensional contaminant transport with slug injection

It is evident that the hydrodynamic dispersion coefficient and linear flow velocity dominate solute transport in aquifers. Both of them play important roles characterizing contaminant transport. However, by definition, the parameter of contaminant transport cannot be measured directly. For most problems of contaminant transport, a conceptual model for solute transport generally is established to fit the breakthrough curve obtained from field testing, and then suitable curve matching or the inverse solution of a theoretical model is used to determine the parameter. This study presents a one-dimensional solute transport problem for slug injection. Differential analysis is used to analyze uncertainty propagation, which is described by the variance and mean. The uncertainties of linear velocity and hydrodynamic dispersion coefficient are, respectively, characterized by the second-power and fourth-power of the length scale multiplied by a lumped relationship of variance and covariance of system parameters, i.e. the Peclet number and arrival time of maximum concentration. To validate the applicability for evaluating variance propagation in one-dimensional solute transport, two cases using field data are presented to demonstrate how parametric uncertainty can be caught depending on the manner of sampling.