The plume spreading in the MADE transport experiment: Could it be predicted by stochastic models?

Key Points A semi-analytical transport model is applied to the MADE experiment The parameters are derived from literature, and no fitting was required Results suggest that advection may explain the MADE plume behavior The transport experiment at the MADE site (a highly heterogeneous aquifer) was investigated extensively in the last 25 years. The longitudinal mass distribution m(x,t) of the observed solute plume differed from the Gaussian shape and displayed strong asymmetry. This is in variance with the prediction of stochastic models of flow and transport in weakly heterogeneous aquifers. In the last decade, we have forwarded a model coined as MIM (multi-indicator), in which the heterogeneous structure consists of blocks of different of different and independent random lognormal K. Thus, the structure is completely characterized by K_G (the geometric mean), σY2 (the logconducitvity variance) and the integral scale I. Flow (uniform in the mean) and advective transport were solved by the semianalytical SCA (self-consistent approximation). The SCA models the travel time of a solute parcel from an injection to a control plane as a sequence of independent time steps, each resulting from the simple solution for isolated blocks surrounded by a uniform matrix. The aim of the article is to determine whether the model could predict the observed mass distribution of MADE (σY2≃7 based on the most recent direct-push injection logger data), by using the recently collected detailed K data and the observed mean head gradient. It was found that the agreement with the measured plume is quite satisfactory, differences related to incomplete mass recovery, injection condition and ergodicity notwithstanding. It is concluded that the physical mechanism of advection, modeled by the local ADE, and the heterogeneity of K, are able to explain the MADE plume behavior and the stochastic model could predict it.