[1] 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), (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 ( 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.

We examine the prediction capability of two approximate models (Multi‐Rate Mass Transfer (MRMT) and Continuous Time Random Walk (CTRW)) of non‐Fickian transport, by comparison with accurate 2‐D and 3‐D numerical simulations. Both nonlocal in time approaches circumvent the need to solve the flow and transport equations by using proxy models to advection, providing the breakthrough curves (BTC) at control planes at anyx, depending on a vector of five unknown parameters. Although underlain by different mechanisms, the two models have an identical structure in the Laplace Transform domain and have the Markovian property of independent transitions. We show that also the numerical BTCs enjoy the Markovian property. Following the procedure recommended in the literature, along a practitioner perspective, we first calibrate the parameters values by a best fit with the numerical BTC at a control plane atx₁, close to the injection plane, and subsequently use it for prediction at further control planes for a few values of. Due to a similar structure and Markovian property, the two methods perform equally well in matching the numerical BTC. The identified parameters are generally not unique, making their identification somewhat arbitrary. The inverse Gaussian model and the recently developed Multi‐Indicator Model (MIM), which does not require any fitting as it relates the BTC to the permeability structure, are also discussed. The application of the proxy models for prediction requires carrying out transport field tests of large plumes for a long duration.