Upscaling and Inverse Modeling of Groundwater Flow and Mass ...

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6 CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . 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 the 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. 2.1 Introduction In the last decades, two large-scale natural-gradient tracer tests were conducted to enhance the understanding of solute transport in highly heterogenous aquifers. These experiments were conducted at the Columbus Air Force Base in Mississippi, where the hydraulic conductivity variability is very high, with σ 2 lnK ≈ 4.5 (Rehfeldt et al., 1992). The site and the experiments performed are commonly referred to as MADE (MAcro-Dispersion Experiment). The present analysis focuses on the second experiment, which was performed between June 1990 and September 1991 using tritium as a non-reactive tracer. The aim of the experiment was to develop an extensive field database for validating the type of geochemical models used to predict the transport and fate of groundwater contaminants (Boggs et al., 1993). The observed tritium plume exhibits a strongly non-Fickian, highly asymmetric spreading (at the formation scale) with high concentrations maintained near the source injection area and extensive low concentrations downstream. Although there exists abundant literature on the modeling of the (so termed) anomalous spreading at the MADE site, only a few works related with this paper will be referred to in this introduction. These works can be classified into two groups according to the approach used for transport modeling. In a first group, a number of authors have employed the classical advectiondispersion equation (ADE) to describe the strongly non-Fickian transport behavior (e.g., Adams and Gelhar, 1992; Eggleston and Rojstaczer, 1998; Barlebo et al., 2004; Salamon et al., 2007). Of these works, Salamon et al. (2007) showed that, with proper modeling of the fine-scale variability, it is possible to generate realizations of the hydraulic conductivity capable to reproduce the observed tracer movement, simply using the ADE. They used a hole-effect variogram model to characterize the flowmeter-derived conductivities. The final realizations displayed the apparent periodicity of the observed conductivities,
CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . . 7 which was enough to induce the type of spreading observed in the experiment. However, in practice, it is difficult to work with this type of high-resolution models, involving millions of nodes, particularly if multiple realizations are to be analyzed. This difficulty is what motivates our paper. In a second group, researchers have used models that go beyond the advectiondispersion model (e.g., Berkowitz and Scher, 1998; Feehley et al., 2000; Harvey and Gorelick, 2000; Benson et al., 2001; Baeumer et al., 2001; Schumer et al., 2003; Guan et al., 2008; Liu et al., 2008; Llopis-Albert and Capilla, 2009). These authors use dual-domain mass transfer models, continuous time random walk or other alternative models capable of accounting for the strongly delayed solute transport as an alternative to the classical ADE. However, these approaches are able to provide a good match to the observed field data only a posteriori; that is, they need to calibrate their model parameters once the concentration data are collected, and then, they can reproduce, almost perfectly, any departure from Fickian transport. These works prove that there are alternative transport models able to explain the MADE data; however, at this point, they lack predictive capabilities since their parameters can only be determined after the experiment is done. All of these studies had varying degrees of success in reproducing the spreading of the tracer plume. For instance, Barlebo et al. (2004) obtained a good reproduction of the irregular plume using the ADE after calibrating the concentration measurements and head data. However, calibrated hydraulic conductivities resulted a factor of five larger than the flowmeter-derived measurements. The authors attributed this discrepancy to a systematical measurement error. The accuracy of the flowmeter-derived conductivities and of the measured concentrations have raised further discussions (see Molz et al., 2006; Hill et al., 2006). Our work builds on the study by Salamon et al. (2007) with the purpose to show that the observed transport spreading at the MADE site can also be reproduced on a coarse model by the ADE. A high-resolution hydraulic conductivity realization is selected from the study by Salamon et al. (2007) and it is upscaled onto a coarser model with several orders of magnitude less elements. This upscaling approach, if successful, would permit multiple realization analyses since it would reduce significantly the computational effort needed to obtain the solute evolution at the site. Unlike previous studies of upscaling focusing on two-dimensional examples or synthetic experiments (e.g., Warren and Price, 1961; Gómez-Hernández, 1991; Durlofsky et al., 1997; Chen et al., 2003), we analyze, with real data, a variety of three-dimensional (3D) hydraulic conductivity upscaling techniques ranging from simple averaging over a uniform grid to sophisticated Laplacian-based upscaling approaches on non-uniform grids. To the best of our knowledge, this is the first time that an analysis of this type has been performed in a real 3D case. Since we will be
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70 BIBLIOGRAPHY Dagan, G., 1994. Up
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72 BIBLIOGRAPHY Lawrence, A. E., Sa
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74 BIBLIOGRAPHY Zhang, Y., 2004. Up
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102 BIBLIOGRAPHY Durlofsky, L. J.,
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104 BIBLIOGRAPHY Tran, T., 1996. Th
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136 BIBLIOGRAPHY Chen, Y., Zhang, D
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138 BIBLIOGRAPHY Journel, A., 1974.
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140 BIBLIOGRAPHY Wen, X., Deutsch,
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142 CHAPTER 6. GROUNDWATER FLOW INV
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170 BIBLIOGRAPHY Deutsch, C. V., Jo
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172 BIBLIOGRAPHY Lee, S., Carle, S.
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174 BIBLIOGRAPHY Yeh, W., 1986. Rev
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176 CHAPTER 7. CONCLUSIONS travels
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178 CHAPTER 7. CONCLUSIONS predicti
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