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

Abstract

[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), 2 Y (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 ( 2 Y ' 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.Citation: Fiori, A., G. Dagan, I. Jankovic, and A. Zarlenga (2013), The plume spreading in the MADE transport experiment: Could it be predicted by stochastic models? Water Resour.

Tracer travel and residence time distributions in highly heterogeneous aquifers: Coupled effect of flow variability and mass transfer

“…The dependence on time (after the inversion of the LT) is illustrated by Fiori et al [19, Fig.6], displaying the departure from an inverse Gaussian shape (for σ 2 Y < 1) to a highly skewed one for large σ 2 Y . The BTC was calculated by numerical inversion of (22) or by an efficient 205 algorithm based on random sampling [11], with good agreement with numerical simulations [34], or the MADE field experiment [22]. We shall coin the basic result (22) as MIMSCA (multi-indicator model and self consistent approximation) based BTC.…”

“…Due to the form of (17), the structure was coined as MIM, the multiindicator model, in our publications in the past (the terminology "inclusions 170 model" was also used). The centers x (i) are located on a periodic grid with nodes at equal distances 2I in the x direction, but with random shift of the rows of blocks in the y, z directions [22]. The selected structure is completely defined by stating that Y (i) is a random normal vector and that Y (i) and Y (k) are uncorrelated for any i ̸ = k, i.e.…”

Effective retardation factor for transport of reactive solutes in highly heterogeneous porous formations

“…Following a customary approach, the log conductivity Y 5 ln K, of variance r 2 Y , is assumed to be normally distributed while anisotropy is axisymmetric. Along the lines of Fiori et al [2013], we employ for simplicity parallelepiped blocks of length L which tessellate the space Figure 1], but the developments are similar for other shapes such as spheroids, which are used in the numerical simulations described in the sequel.…”

“…This model, coined as multi-indicator, has enabled derivation of highly precise numerical and analytical approximate solutions of K eff . Similarly, the model has served for modeling transport of conservative solutes in highly heterogeneous formation [e.g., Fiori et al, 2013].…”

Mechanisms of anomalous dispersion in flow through heterogeneous porous media

“…Eames and Bush [40] studied solute dispersion in such media and derived expressions for the dispersion coefficients. Fiori et al [41,42,43] studied anomalous transport in media consisting of inclusions with lognormal distributions of hydraulic conductivity and derived semi-analytical expressions for solute travel times. These solutions have been implemented into a time-domain random walk approach, which is similar to the CTRW [44].…”