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WWRC 92-09
Modeling Groundwater Flow and Contaminant Transport in Heterogeneous Aquifers: Final Project Report

Technical Synopsis

1.1 Objectives

The main aim of the research was to develop methodologies for modeling simultaneous groundwater flow and contaminant transport in highly heterogeneous aquifers. Most previously existing flow and transport models are based on techniques that, while adequate for nearly homogeneous aquifers, are inappropriate in the presence of significant, fine-scale heterogeneities. The inappropriateness stems from two facts. First, the numerical methods used are inefficient or inaccurate in heterogeneous problems, so that modelers typically sacrifice accuracy in favor of affordability when running the codes. Second, the relationships between actual, fine-scale variations in the media and the parameter values that one should use to represent the media in affordable, coarse-scale models remain poorly understood.

The proposed project had two objectives. The immediate objective was to incorporate recent improvements in numerics to assemble a computer code that is computationally efficient even when the aquifer being modeled is highly heterogeneous. The long-range objective was to use the code to investigate methods for scaling from individual realizations of heterogeneity to ensembles of realizations that are consistent with measured data and, more specifically, to investigate scaling of such parameters as hydraulic conductivity and hydrodynamic dispersion for use in standard flow and transport codes.

1.2 Utility of the research.

The research has utility to groundwater hydrologists who use models to understand the complex flow a.nd transport phenomena affecting groundwater contamination. Natural aquifers can have permeabilities and porosities that exhibit large spatial variations as a consequence of variable depositional environments, diagenesis, and structural events. Among the problems that heterogeneities pose are the following:

• It is extremely difficult to measure heterogeneous aquifer parameters, so the data used in mathematical models often fail to characterize aquifers realistically.
• Even when heterogeneities are known, resolving them numerically often requires the modeler to discretize the aquifer into a large number of very small grid cells. This not only makes the equation sets to be solved large, hence expensive; it also makes them poorly conditioned, hence prone to slow convergence and accumulation of roundoff errors.
• Beyond the effect of small grid cells, heterogeneity itself leads to poor conditioning arising from the fact that important coefficients, such as hydraulic conductivity, can range in value over several orders of magnitude.
• Heterogeneity often occurs at scales that simply cannot be resolved in affordable models. In these cases, there arises the issue of how to scale aquifer parameters to arrive at values that adequately represent the physics in "megascopic" models. Research into this question is in its infancy, since the computational horsepower needed to explore relationships between fine- and coarse-scale models has evolved only recently.

As a consequence of these facts, heterogeneity has been a source of tremendous difficulties in the transfer of modeling technologies from theoretical settings to field applications, where there is an increasing need for reliable predictive tools. The development of robust and efficient numerical techniques is a necessary step, not only for the direct application of models to field studies but also to the more fundamental task of understanding how to incorporate uncertain and sparsely measured geologic data into deterministic computer codes.

The research also has implications for other areas of technology involving underground flow. For example, advances in numerical techniques for flows in heterogeneous porous media simultaneously improve the state of the art in the design of enhanced oil recovery technologies and the simulation of in-situ mining.

1.3 Summary of accomplishments

The project's accomplishments fall into four categories. First, Some effort focused on enhancing the capabilities of a two-dimensional groundwater transport simulator developed in previous work for the Wyoming Water Research Center. This work led to the effective incorporation of a timestepping algorithm based on contaminant paths ( "modified method of characteristics" ) into an existing transport code based on alternating-direction collocation (Allen and Khosravani, 1992) and an adaptive local grid refinement algorithm for this code that allows for fine-scale spatial resolution in regions where contaminant concentrations vary rapidly in space (Curran, submitted).

A second focus for the research was the implementation of an efficient, well-conditioned algorithm for solving the groundwater flow equation using the mixed finite-element method. Proper formulation of the mixed method allows one to solve for groundwater velocities whose accuracies are comparable to those of the computed heads. The method differs from standard finite-element approaches, in that it does not require one to differentiate heads numerically to compute velocities — a common procedure that introduces inherent inaccuracies. The new algorithm avoids the poor conditioning (and associated inefficiency) associated with fine-scale, heterogeneous simulations by using an iterative solver based on a multigrid approach (Allen, Ewing, and Lu, 1992). The algorithm has the additional feature that it is readily amenable to parallel processing (Allen and Curran, 1992).

Summaries and overviews of these methodologies for groundwater flow and transport appear in Allen and Ewing (1991) and Allen and Curran (to appear).

A third approach, tailored to a more specialized form of heterogeneity, incorporates a finite-layer technique into models of groundwater flow in highly stratified aquifers. This approach takes advantage of certain simplifying assumptions about the geometry of the heterogeneity to develop a discrete formulation that is suitable for large-scale computing (because of its inherent parallelism) and for microcomputing (because of its ability to decompose large problems into small subproblems). The project addressed both the practical implementation of the method (Smith, Allen, Puckett, and Edgar, 1991; Smith, Allen, Puckett, and Edgar, 1992) and its theoretical basis (Smith, 1992; Smith and Allen, in preparation).

Finally, some effort was devoted to an analysis of standard finite-element techniques for modeling contaminant transport in aquifers characterized by highly heterogeneous adsorption. This analysis was mainly theoretical, although the work generated a computer code that proved useful in testing error estimates derived using abstract methods (Chunyu, 1990).

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