Groundwater contaminant transport: Prediction under uncertainty, with application to the MADE transport experiment

Transport of solutes in porous media at the laboratory scale is governed by an Advection Dispersion Equation (ADE). The advection is by the fluid velocity U and dispersion by DdL = U αdL, where the longitudinal dispersivity αdL is of the order of the pore size. Numerous data revealed that the longitudinal spreading of plumes at field scale is characterized by macrodispersivity αL, larger than αdL by orders of magnitude. This effect is attributed to heterogeneity of aquifers manifesting in the spatial variability of the logconductivity Y. Modeling Y as a stationary random field and for mean uniform flow (natural gradient), αL could be determined in an analytical form by a first order approximation in σY2 (variance of Y) of the flow and transport equations. Recently, models and numerical simulations for solving transport in highly heterogeneous aquifers (σY2 > 1), primarily in terms of the mass arrival (the breakthrough curve BTC), were advanced. In all cases ergodicity, which allows to exchange the unknown BTC with the ensemble mean, was assumed to prevail for large plumes, compared to the logconductivity integral scale. Besides, the various statistical parameters characterizing the logconductivity structure as well as the mean flow were assumed to be known deterministically. The present paper investigates the uncertainty of the non-ergodic BTC due to the finiteness of the plume size as well as due to the uncertainty of the various parameters on which the BTC depends. By the use of a simplified transport model we developed in the past (which led to accurate results for ergodic plumes), we were able to get simple results for the variance of the BTC. It depends in an analytical manner on the flow parameters as well as on the dimension of the initial plume relative to the integral scale of logconductivity covariance. The results were applied to the analysis of the uncertainty of the plume spatial distribution of the MADE transport experiment. This was achieved by using the latest, recent, analysis of the MADE aquifer conductivity data.