Macrodispersion Experiment Site Research Articles

Transport Upscaling in Highly Heterogeneous Aquifers and the Prediction of Tracer Dispersion at the MADE Site

AbstractWe present an upscaled Lagrangian approach to predict the plume evolution in highly heterogeneous aquifers. The model is parameterized by transport‐independent characteristics such as the statistics of hydraulic conductivity and the Eulerian flow speed. It can be conditioned on the tracer properties and flow data at the injection region. Thus, the model is transferable to different solutes and hydraulic conditions. It captures the large‐scale non‐Gaussian features for the evolution of the longitudinal mass distribution observed for the bromide and tritium tracer plumes at the Macrodispersion Experiment (MADE) site (Columbus, Mississippi, USA), which are characterized by a slow moving peak and pronounced forward tailing. These large‐scale features are explained by advective tracer propagation due to a broad distribution of spatially persistent Eulerian flow speeds as a result of spatial variability in hydraulic conductivity.

Hydrogeological Model Selection Among Complex Spatial Priors

AbstractHydrogeological field studies rely often on a single conceptual representation of the subsurface. This is problematic since the impact of a poorly chosen conceptual model on predictions might be significantly larger than the one caused by parameter uncertainty. Furthermore, conceptual models often need to incorporate geological concepts and patterns in order to provide meaningful uncertainty quantification and predictions. Consequently, several geologically realistic conceptual models should ideally be considered and evaluated in terms of their relative merits. Here, we propose a full Bayesian methodology based on Markov chain Monte Carlo to enable model selection among 2‐D conceptual models that are sampled using training images and concepts from multiple‐point statistics. More precisely, power posteriors for the different conceptual subsurface models are sampled using sequential geostatistical resampling and Graph Cuts. To demonstrate the methodology, we compare and rank five alternative conceptual geological models that have been proposed in the literature to describe aquifer heterogeneity at the MAcroDispersion Experiment site in Mississippi, USA. We consider a small‐scale tracer test for which the spatial distribution of hydraulic conductivity impacts multilevel solute concentration data observed along a 2‐D transect. The thermodynamic integration and the stepping‐stone sampling methods were used to compute the evidence and associated Bayes factors using the computed power posteriors. We find that both methods are compatible with multiple‐point statistics‐based inversions and provide a consistent ranking of the competing conceptual models considered.

Comparison of Multivariate Spatial Dependence Structures of DPIL and Flowmeter Hydraulic Conductivity Data Sets at the MADE Site

We analyse two datasets of hydraulic conductivity (K) from the MAcroDispersion Experiment (MADE) site, one measured by direct-push injection logging (DPIL) and the other by flowmeter profiling. The analysis is performed using copula techniques which do not rely on the assumption of multivariate Gaussianity and provide a means to characterise differing degrees of spatial dependence in different quantiles of the K distribution. This characterisation provides better insights into the similarities and differences between the two datasets. In addition to the marginal distributions and the traditional two-point geostatistical measures, copula-based bivariate rank correlation and asymmetry measures are analysed and compared. Furthermore, the parameter estimates obtained by likelihood estimation using n-point theoretical models are analysed. This analysis confirms the similarity of the spatial dependence of K between the two datasets in terms of their marginal distributions and bivariate measures, particularly in the vertical direction. We demonstrate clear indications of the existence of non-Gaussian spatial dependence structures of K at this site. We were able to improve the estimation of the K distribution by taking into account either non-Gaussianity or a censoring threshold, which are expected to lead to a more realistic description of processes that are dependent on K.

An Open, Object-Based Framework for Generating Anisotropy in Sedimentary Subsurface Models.

The spatial distribution of hydraulic properties in the subsurface controls groundwater flow and solute transport. However, many approaches to modeling these distributions do not produce geologically realistic results and/or do not model the anisotropy of hydraulic conductivity caused by bedding structures in sedimentary deposits. We have developed a flexible object-based package for simulating hydraulic properties in the subsurface-the Hydrogeological Virtual Realities (HyVR) simulation package. This implements a hierarchical modeling framework that takes into account geological rules about stratigraphic bounding surfaces and the geometry of specific sedimentary structures to generate realistic aquifer models, including full hydraulic-conductivity tensors. The HyVR simulation package can create outputs suitable for standard groundwater modeling tools (e.g., MODFLOW), is written in Python, an open-source programming language, and is openly available at an online repository. This paper presents an overview of the underlying modeling principles and computational methods, as well as an example simulation based on the Macrodispersion Experiment site in Columbus, Mississippi. Our simulation package can currently simulate porous media that mimic geological conceptual models in fluvial depositional environments, and that include fine-scale heterogeneity in distributed hydraulic parameter fields. The simulation results allow qualitative geological conceptual models to be converted into digital subsurface models that can be used in quantitative numerical flow-and-transport simulations, with the aim of improving our understanding of the influence of geological realism on groundwater flow and solute transport.

A lithofacies approach for modeling non‐Fickian solute transport in a heterogeneous alluvial aquifer

AbstractStochastic realizations of lithofacies assemblage based on lithological data from a relatively small number of boreholes were used to simulate solute transport at the well‐known Macrodispersion Experiment (MADE) site in Mississippi (USA). With sharp vertical contrasts and lateral connectivity explicitly accounted for in the corresponding hydraulic conductivity fields, experimental results from a large‐scale tracer experiment were adequately reproduced with a relatively simple model based on advection and local dispersion. The geologically based model of physical heterogeneity shows that one well‐interconnected lithofacies, with a significantly higher hydraulic conductivity and accounting for 12% of the total aquifer volume, may be responsible for the observed non‐Fickian transport behavior indicated by the asymmetric shape of the plumes and by variations of the dispersion rate in both space and time. This analysis provides a lithological basis to the hypothesis that transport at MADE site is controlled by a network of high‐conductivity sediments embedded in a less permeable matrix. It also explains the calibrated value of the ratio of mobile to total porosities used in previous modeling studies based on the dual‐domain mass transfer approach. The results of this study underscore the importance of geologically plausible conceptualizations of the subsurface for making accurate predictions of the fate and transport of contaminants in highly heterogeneous aquifers. These conceptualizations may be developed through integration of raw geological data with expert knowledge, interpretation, and appropriate geostatistical methods.

Predicting flow and transport in highly heterogeneous alluvial aquifers

AbstractSuccessful prediction of groundwater flow and solute transport through highly heterogeneous aquifers has remained elusive due to the limitations of methods to characterize hydraulic conductivity (K) and generate realistic stochastic fields from such data. As a result, many studies have suggested that the classical advective‐dispersive equation (ADE) cannot reproduce such transport behavior. Here we demonstrate that when high‐resolution K data are used with a fractal stochastic method that produces K fields with adequate connectivity, the classical ADE can accurately predict solute transport at the macrodispersion experiment site in Mississippi. This development provides great promise to accurately predict contaminant plume migration, design more effective remediation schemes, and reduce environmental risks.

Geostatistical analysis of centimeter‐scale hydraulic conductivity variations at the MADE site

Spatial variations in hydraulic conductivity (K) provide critical controls on solute transport in the subsurface. Recently, new direct‐push tools were developed for high‐resolution characterization of K variations in unconsolidated settings. These tools were applied to obtain 58 profiles (vertical resolution of 1.5 cm) from the heavily studied macrodispersion experiment (MADE) site. We compare the data from these 58 profiles with those from the 67 flowmeter profiles that have served as the primary basis for characterizing the heterogeneous aquifer at the site. Overall, the patterns of variation displayed by the two data sets are quite similar, in terms of both large‐scale structure and autocorrelation characteristics. The direct‐push K values are, on average, roughly a factor of 5 lower than the flowmeter values. This discrepancy appears to be attributable, at least in part, to opposite biases between the two methods, with the current versions of the direct‐push tools underestimating K in the highly permeable upper portions of the aquifer and the flowmeter overestimating K in the less permeable lower portions. The vertically averaged K values from a series of direct‐push profiles in the vicinity of two pumping tests at the site are consistent with the K estimates from those tests, providing evidence that the direct‐push estimates are of a reasonable magnitude. The results of this field demonstration show that direct‐push profiling has the potential to characterize highly heterogeneous aquifers with a speed and resolution that has not previously been possible.

A comparative study of three-dimensional hydraulic conductivity upscaling at the macro-dispersion experiment (MADE) site, Columbus Air Force Base, Mississippi (USA)

Simple averaging, simple-Laplacian, Laplacian-with-skin, and non-uniform coarsening are the techniques investigated in this comparative study of three-dimensional hydraulic conductivity upscaling. The reference is a fine scale conditional realization of the hydraulic conductivities at the MAcro-Dispersion Experiment site on Columbus Air Force Base in Mississippi (USA). This realization was generated using a hole-effect variogram model and it was shown that flow and transport modeling in this realization (at this scale) can reproduce the observed non-Fickian spreading of the tritium plume. The purpose of this work is twofold, first to compare the effectiveness of different upscaling techniques in yielding upscaled models able to reproduce the observed transport behavior, and second to demonstrate and analyze the conditions under which flow upscaling can provide a coarse model in which the standard advection–dispersion equation can be used to model transport in seemingly non-Fickian scenarios. Specifically, the use of Laplacian-based upscaling technique coupled with a non-uniform coarsening scheme yields the best results both in terms of flow and transport reproduction, for this case study in which the coarse blocks are smaller than the correlation ranges of the fine scale conductivities.

Geological modeling of submeter scale heterogeneity and its influence on tracer transport in a fluvial aquifer

We developed a new model of aquifer heterogeneity to analyze data from a single‐well injection‐withdrawal tracer test conducted at the Macrodispersion Experiment (MADE) site on the Columbus Air Force Base in Mississippi (USA). The physical heterogeneity model is a hybrid that combines 3‐D lithofacies to represent submeter scale, highly connected channels within a background matrix based on a correlated multivariate Gaussian hydraulic conductivity field. The modeled aquifer architecture is informed by a variety of field data, including geologic core sampling. Geostatistical properties of this hybrid heterogeneity model are consistent with the statistics of the hydraulic conductivity data set based on extensive borehole flowmeter testing at the MADE site. The representation of detailed, small‐scale geologic heterogeneity allows for explicit simulation of local preferential flow and slow advection, processes that explain the complex tracer response from the injection‐withdrawal test. Based on the new heterogeneity model, advective‐dispersive transport reproduces key characteristics of the observed tracer recovery curve, including a delayed concentration peak and a low‐concentration tail. Importantly, our results suggest that intrafacies heterogeneity is responsible for local‐scale mass transfer.

Lessons Learned from 25 Years of Research at the MADE Site

Field studies at well-instrumented research sites have provided extensive data sets and important insights essential for development and testing of transport theories and mathematical models. This paper provides an overview of over 25 years of research and lessons learned at one of such field research sites on the Columbus Air Force Base in Mississippi, commonly known as the Macrodispersion Experiment (MADE) site. Since the mid-1980s, field data from the MADE site have been used extensively by researchers around the world to explore complex contaminant transport phenomena in highly heterogeneous porous media. Results from field investigations and modeling analyses suggested that connected networks of small-scale preferential flow paths and relative flow barriers exert dominant control on solute transport processes. The classical advection-dispersion model was shown to inadequately represent plume-scale transport, while the dual-domain mass transfer model was found to reproduce the primary observed plume characteristics. The MADE site has served as a valuable natural observatory for contaminant transport studies where new observations have led to better understanding and improved models have sprung out analysis of new data.

Investigation of flow and transport processes at the MADE site using ensemble Kalman filter

In this work the ensemble Kalman filter (EnKF) is applied to investigate the flow and transport processes at the macro-dispersion experiment (MADE) site in Columbus, MS. The EnKF is a sequential data assimilation approach that adjusts the unknown model parameter values based on the observed data with time. The classic advection–dispersion (AD) and the dual-domain mass transfer (DDMT) models are employed to analyze the tritium plume during the second MADE tracer experiment. The hydraulic conductivity ( K), longitudinal dispersivity in the AD model, and mass transfer rate coefficient and mobile porosity ratio in the DDMT model, are estimated in this investigation. Because of its sequential feature, the EnKF allows for the temporal scaling of transport parameters during the tritium concentration analysis. Inverse simulation results indicate that for the AD model to reproduce the extensive spatial spreading of the tritium observed in the field, the K in the downgradient area needs to be increased significantly. The estimated K in the AD model becomes an order of magnitude higher than the in situ flowmeter measurements over a large portion of media. On the other hand, the DDMT model gives an estimation of K that is much more comparable with the flowmeter values. In addition, the simulated concentrations by the DDMT model show a better agreement with the observed values. The root mean square (RMS) between the observed and simulated tritium plumes is 0.77 for the AD model and 0.45 for the DDMT model at 328 days. Unlike the AD model, which gives inconsistent K estimates at different times, the DDMT model is able to invert the K values that consistently reproduce the observed tritium concentrations through all times.

Modeling tracer transport at the MADE site: The importance of heterogeneity

We examine three stochastic transport models of the Macrodispersion Experiment (MADE) site using high‐resolution conductivity fields derived from a new geostatistical interpretation of the flowmeter data. Evaluation of the spatial continuity of the hydraulic conductivity data revealed a hole effect structure indicating the occurrence of periodic structures, i.e., clustered lenses or facies. Alternatively, we examine geostatistical models based on indicator variables and found a similarity to bivariate Gaussian properties. Tritium transport was simulated in kriged fields and in random fields generated using different geostatistical models, at a grid spacing equal to the vertical support scale of the flowmeter measurements to explicitly represent small‐scale heterogeneity. Only those simulations obtained using the hole effect model resulted in a subset of realizations which reproduced the strong anomalous tracer spreading. Neglecting the hole effect structure of the spatial model in the Gaussian simulations resulted in a reduced tailing of the tracer, illustrating the importance of preferential flow on anomalous solute transport at the Columbus aquifer. Furthermore, we found that a multivariate Gaussian random function is adequate to model the spatial distribution of hydraulic conductivity at the MADE site, based on the results of the indicator transport simulations and the univariate and bivariate normality detected in the analysis of the flowmeter data. We conclude that, when small‐scale variability of hydraulic conductivity is correctly modeled at the flowmeter measurement support scale, the ADE is capable of reproducing the tracer spreading. Results suggest that the main contributor to the operational “memory function” used in previous successful mass transfer models is mostly a reflection of the suppressed spatial variation of hydraulic conductivity at the model scale.

Reply to comment by F. Molz et al. on “Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three‐dimensional inverse flow and transport model”

Reply to comment by F. Molz et al. on “Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three‐dimensional inverse flow and transport model”

Geophysical constraints on contaminant transport modeling in a heterogeneous fluvial aquifer

Approximately 3000 measurements of hydraulic conductivity in over 50 flowmeter boreholes were available at the Macro-Dispersion Experiment (MADE) site in Columbus, Mississippi, USA to quantify the heterogeneity in hydraulic conductivity at the site scale. This high-density measurement approach is perhaps infeasible for time and expense in typical groundwater remediation sites. A natural-gradient tracer experiment from the MADE site was simulated by a groundwater flow and solute transport model incorporating direct-current (DC) resistivity data collected over the observed plume location. Hydraulic conductivity from one borehole collected during the original site characterization was used to calibrate the electrical resistivity data to hydraulic conductivity using a previously derived log–log relationship. Application of this relationship, using site-specific empirical constants determined from the data, transforms the 3D electrical resistivity data into a 3D description of hydraulic conductivity that can be used in groundwater models. The validity of this approach was tested by using the geophysically derived hydraulic conductivity representation in numerical simulations of the natural-gradient tracer experiment. The agreement between the simulated and observed tracer plumes was quantified to gauge the effectiveness of geophysically derived and flowmeter based representations of the hydraulic conductivity field. This study demonstrates that a highly heterogeneous aquifer can be modeled with minimal hydrological data supplemented with geophysical data at least as well as previous models of the site using purely hydrologic data.