A Comparison of Six Transport Models of the MADE-1 Experiment Implemented With Different Types of Hydraulic Data.

Six conceptually different transport models were applied to the macrodispersion experiment (MADE)-1 field tracer experiment as a first major attempt for model comparison. The objective was to show that complex mass distributions in heterogeneous aquifers can be predicted without calibration of transport parameters, solely making use of structural and flow data. The models differ in their conceptualization of the heterogeneous aquifer structure, computational complexity, and use of conductivity data obtained from various observation methods (direct push injection logging, DPIL, grain size analysis, pumping tests and flowmeter). They share the same underlying physical transport process of advection by the velocity field solely. Predictive capability is assessed by comparing results to observed longitudinal mass distributions of the MADE-1 experiment. The decreasing mass recovery of the observed plume is attributed to sampling and no physical process like mass transfer is invoked by the models. Measures like peak location and strength are used in comparing the modeled and measured plume mass distribution. Comparison of models reveals that the predictions of the solute plume agree reasonably well with observations, if the models are underlain by a few parameters of close values: mean velocity, a parameter reflecting log-conductivity variability, and a horizontal length scale related to conductivity spatial correlation. The robustness of the results implies that conservative transport models with appropriate conductivity upscaling strategies of various observation data provide reasonable predictions of plumes longitudinal mass distribution, as long as key features are taken into account.

Evidence Based Estimation of Macrodispersivity for Groundwater Transport Applications.

The scope of this work is to discuss the proper choice of macrodispersion coefficients in modeling contaminant transport through the advection dispersion equation (ADE). It is common to model solute concentrations in transport by groundwater with the aid of the ADE. Spreading is quantified by macrodispersivity coefficients, which are much larger than the laboratory observed pore-scale dispersivities. In the frame of stochastic theory, longitudinal macrodispersivity is related to the hydraulic conductivity spatial variability via its statistical moments (mean, variance, integral scales), which are generally determined by geostatistical analysis of field measurements. In many cases, especially for preliminary assessment of contaminant spreading, these data are not available and ad hoc values are adopted by practitioners. The present study aims at recommending dispersivity values based on a thorough analysis of tens of field experiments. Aquifers are classified as of weak, medium, and high heterogeneity and for each class a range of macrodispersivity values is recommended. Much less data are available for the transverse macrodispersivities, which are significantly smaller than the longitudinal one. Nevertheless, a few realistic values based on field data, are recommended for applications. Transport models using macrodispersivities can predict mean concentrations, different from the local ones. They can be used for estimation of robust measures, like plumes spatial moments, longitudinal mass distribution and breakthrough curves at control planes.

A Critical Analysis of Transverse Dispersivity Field Data.

Transverse dispersion, or tracer spreading orthogonal to the mean flow direction, which is relevant e.g, for quantifying bio-degradation of contaminant plumes or mixing of reactive solutes, has been studied in the literature less than the longitudinal one. Inferring transverse dispersion coefficients from field experiments is a difficult and error-prone task, requiring a spatial resolution of solute plumes which is not easily achievable in applications. In absence of field data, it is a questionable common practice to set transverse dispersivities as a fraction of the longitudinal one, with the ratio 1/10 being the most prevalent. We collected estimates of field-scale transverse dispersivities from existing publications and explored possible scale relationships as guidance criteria for applications. Our investigation showed that a large number of estimates available in the literature are of low reliability and should be discarded from further analysis. The remaining reliable estimates are formation-specific, span three orders of magnitude and do not show any clear scale-dependence on the plume traveled distance. The ratios with the longitudinal dispersivity are also site specific and vary widely. The reliability of transverse dispersivities depends significantly on the type of field experiment and method of data analysis. In applications where transverse dispersion plays a significant role, inference of transverse dispersivities should be part of site characterization with the transverse dispersivity estimated as an independent parameter rather than related heuristically to longitudinal dispersivity.

Identification of heterogeneous aquifer transmissivity using an AE-based method.

Determination of hydraulic head, H, as a function of spatial coordinates and time, in ground water flow is the basis for aquifer management and for prediction of contaminant transport. Several computer codes are available for this purpose. Spatial distribution of the transmissivity, T(x,y), is a required input to these codes. In most aquifers, T varies in an erratic manner, and it can be characterized statistically in terms of a few moments: the expected value, the variance, and the variogram. Knowledge of these moments, combined with a few measurements, permits one to estimate T at any point using geostatistical methods. In a review of transmissivity data from 19 unconsolidated aquifers, Hoeksema and Kitanidis (1985) identified two types of the logtransmissivity Y= ln(T) variations: correlated variations with variance sigma2Yc and correlation scale, I(Y), on the order of kilometers, and uncorrelated variations with variance sigma2Yn. Direct identification of the logtransmissivity variogram, Gamma(Y), from measurements is difficult because T data are generally scarce. However, many head measurements are commonly available. The aim of the paper is to introduce a methodology to identify the transmissivity variogram parameters (sigma2Yc, I(Y), and sigma2Yn) using head data in formations characterized by large logtransmissivity variance. The identification methodology uses a combination of precise numerical simulations (carried out using analytic element method) and a theoretical model. The main objective is to demonstrate the application of the methodology to a regional ground water flow in Eagle Valley basin in west-central Nevada for which abundant transmissivity and head measurements are available.

Gaussian or non-Gaussian logconductivity distribution at the MADE site: What is its impact on the breakthrough curve?

The impact of the logconductivity (Y=ln K) distribution fY on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian fY characterized by heavier tails than the Gaussian. Both the logconductivity moments and fY itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y, with same variance, leads to BTCs which are more symmetrical than those for the Gaussian fY, with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals.

Effective conductivity of heterogeneous multiphase media with circular inclusions.

Determining the effective conductivity of heterogeneous media is a central problem in different fields of physics. The medium considered here contains cylinders (inclusions) of random conductivities that are distributed at random in an embedding matrix. For random systems, widely encountered in applications, we derive an approximative analytical solution that applies to significantly denser configurations than Maxwell first-order approximations. The analytic solution is tested against accurate numerical simulations. The widely used effective medium approach is shown to be exact for symmetric conductivity distributions and quite accurate for asymmetrical cases.