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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Panel Report
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE This page in the original is blank.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE 1 Conceptual Models of Flow and Transport in the Fractured Vadose Zone INTRODUCTION A significant number of subsurface environmental problems involve fluid flow and solute transport in the fractured vadose zone. In this report, the vadose zone refers to that part of the subsurface from land surface to the lowest seasonal water table elevation. The vadose zone may be composed of consolidated rock and/or unconsolidated granular material, including soils. Contamination of the vadose zone can result from many sources, including chemical spills, leaky underground storage tanks, leachate from waste disposal sites and mine tailings, and application of agricultural chemicals. Another major environmental concern is the potential for long-term migration of radionuclides from low- and high-level nuclear waste disposal facilities. The presence of fractures and other channel-like openings in the vadose zone poses a particularly significant problem, because such features are potential avenues for rapid transport of chemicals from contamination sources to the water table. A key component in assessing contamination hazards and designing remedial actions is the development of flow and transport models to approximately represent real systems. Present-day models often use computer programs to simulate flow and transport processes, and such models are applied throughout the scientific, engineering, and regulatory arena. When carefully developed and supported by field data, models can be effective tools for understanding complex phenomena and for making informed predictions for a variety of assumed future scenarios. However, model results are always subject to some degree of uncertainty due to limitations in field data and incomplete knowledge of natural processes.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Thus, when models form the basis for decision-making, uncertainty will be an inescapable component of environmental management and regulation. A key consideration in the modeling process is whether or not the model has undergone sufficient development and testing to address the problem being analyzed in a sufficiently meaningful manner. The underpinning of any vadose zone fluid transport model is the conceptualization of (1) the relevant processes, (2) the structure of the subsurface, and (3) the potential events or scenarios that impact the behavior of the modeled system. These conceptualizations together form a “conceptual model,” and it is such conceptual models that are the focus of this Panel's study. The evolution of a conceptual model, from the initial formulation through the subsequent revisions and refinements, is the crux of the model development process. Conceptual models of fully saturated flow in granular aquifers have progressed to a relatively mature state due to a long history of model development and application. By contrast, conceptual models of partially saturated flow and transport in fractured vadose zone environments are poorly developed and largely untested. In cases where multiple competing conceptual models could lead to drastically different conclusions, strategies for evaluating these models must be based on sound technical criteria. The need to develop such strategies and criteria was a key reason for the appointment of this Panel. The purpose of this study is to investigate the processes through which conceptual models of flow and transport in the fractured vadose zone are developed, tested, refined, and reviewed. The Panel convened a two-day workshop in March 1999, during which a large group of specialists (see Appendix A) from the hydrogeologic, geochemical, soil science, and related fields discussed the current state of knowledge, lessons learned from field investigations, and needs for future research. A series of invited presentations provided a basis for much of the discussion at the workshop. Individually authored papers based on these presentations are presented as Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10 and Chapter 11. The Panel was charged with preparing a consensus report on the development and testing of conceptual models for fluid flow and transport in the fractured vadose zone. The Panel's conclusions and recommendations were based in large part on the workshop presentations and discussions. The report is intended to: provide information on contemporary philosophies, approaches, and techniques for conceptual model building; provide guidance to regulatory agencies on the review process for conceptual models developed for site licensing; bring together knowledge and experiences from related disciplines so that technical communities can benefit from advances in related fields; and identify future research needed to further the technical basis for developing and evaluating conceptual models of flow and transport in the fractured vadose zone.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE The Panel devoted a major portion of its study to an analysis of fluid flow models in the fractured vadose zone because (1) understanding flow is a prerequisite for understanding transport, (2) questions regarding the nature of fast pathways are a major concern, and (3) recent studies, especially investigations at the potential site for a nuclear waste repository at Yucca Mountain, have accumulated a significant body of knowledge applicable to fractured vadose zone models. In its consideration of transport in the vadose zone, the Panel focused on the application of environmental tracers (such as tritium and chlorine-36) because they provide integrated responses that are difficult to determine by point measurements of fluid potential or moisture content. The Panel briefly reviewed approaches for modeling transport of conservative solutes, but the scope of the study did not include reactive solutes or water-rock interactions. The Panel report is composed of three main sections. First, we discuss general considerations applicable to the development and testing of conceptual models. Second, we summarize the current state of knowledge of flow and transport processes in the fractured vadose zone. Third, we present our conclusions and recommendations. Appended to the Panel report are the invited papers based on presentations at the workshop. These papers served as the starting point for workshop discussions, and form much of the background material used in preparation of this report. Although the papers have undergone peer review, their inclusion in this report does not constitute any specific endorsement of their contents, either by the Panel or by the National Research Council. DEVELOPMENT AND TESTING OF CONCEPTUAL MODELS Definition of Conceptual Model Models representing natural systems are often viewed as composed of two components, a conceptual model and a mathematical model. In general terms, a conceptual model is qualitative and expressed by ideas, words, and figures. A mathematical model is quantitative and expressed as mathematical equations. The two are closely related. In essence, the mathematical model results from translating the conceptual model into a well-posed mathematical problem that can be solved. Various definitions of conceptual models can be found in the scientific and technical literature. These definitions are generally consistent in their fundamental meaning, and differ mainly in scope, detail, and context. The statement of the conceptual model often reflects the key questions and unknowns to be investigated. For example, Anderson and Woessner (1992) give the following definition for the purpose of modeling groundwater flow in aquifers: A conceptual model is a pictorial representation of the groundwater flow system, frequently in the form of a block diagram or a cross section.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE This relatively brief statement is suitable for modeling groundwater flow because the process is well understood, and the principal concern is the delineation of subsurface structure, such as stratigraphy, and the spatial distribution of hydraulic properties, such as hydraulic conductivity. By contrast, Tsang (1991) gives the following definition in the context of modeling a broad range of coupled physical-chemical processes: A site-specific conceptual model consists of three main components: structure, processes, and boundary and “initial” conditions. “Structure” refers to the geometric structure of the system, such as stratigraphy, faults, heterogeneity, fracture density and lengths, and other geometric and geologic characteristics. “Processes” are physical and chemical phenomena such as buoyancy flow, colloidal transport, matrix diffusion, and dissolution and precipitation. “Boundary conditions” are constant or time-dependent conditions imposed on the boundaries of the model domain. “Initial conditions” are the physical and chemical conditions over the model domain at a particular instant of time. This is usually taken at the initial instant of time, though in general it can be any specified point in time. The more detailed statement reflects the complexity of the modeled processes, some of which may be poorly understood. In the present study, we define a conceptual model as follows: A conceptual model is an evolving hypothesis identifying the important features, processes, and events controlling fluid flow and contaminant transport of consequence at a specific field site in the context of a recognized problem. This definition stresses several ideas. A conceptual model is a hypothesis because it must be tested for internal consistency and for its ability to represent the real system in a meaningful way. The hypothesis evolves (is revised and refined) during testing and as new information is gathered. Although a conceptual model is by necessity a simplification of the real system, the degree of simplification (or conversely, the amount of complexity retained in the model) should be commensurate with the problem being addressed. In order to present a clear and easily understandable definition, we have used the term ‘events' rather than the mathematically explicit terms ‘initial conditions' and ‘boundary conditions' that have been used in earlier definitions. The context in which the model is developed constrains the range of applicability of the model. The Modeling Process We refer to the modeling process as an iterative sequence of actions that includes (1) identifying a site-specific problem; (2) conceptualizing important features, processes, and events; (3) implementing a quantitative description; (4) collecting and assimilating field data that are used to calibrate the model and evaluate its predictive capabilities; and (5) developing predictions that are used to resolve the identified problem. This process is illustrated by the flow chart in Figure 1-1.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE FIGURE 1-1 Flow chart illustrating the elements of the modeling process.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE The modeling process usually begins with some initial perception of a field problem, expressed as questions to be answered or decisions to be made (as indicated in the upper left of Figure 1-1). Available site-specific data, related experience, and generic scientific knowledge are then combined to identify the factors (features, processes, and events) that are important for the identified problem. This typically involves preliminary calculations using generic parameters to understand the relative importance of various aspects of the problem. The result of this assessment is the initial conceptual model. The formulation of this initial conceptual model is arguably the most important step in the modeling process. The conceptual model is the foundation of the mathematical model, and strongly influences the type of computer code to be used and the design and priority of site characterization activities. Philips (this report, Chapter 9) describes a case study where processes that were neglected in the initial conceptual model were later found to be of fundamental importance, leading to a substantial revision of the conceptual model. Such revisions, possibly with additional iterations, may be expected in complex environments where often poorly understood physical, chemical, and biological processes interact. Therefore, the conceptual modeling process should consider a broad range of reasonable alternative hypotheses. It is also important to employ a variety of different types of data. For example, an initial conceptual model that is based on regional water budgets, general hydraulic properties, and sparse environmental tracer data is more likely to include relevant and significant processes than if only general hydraulic properties were considered. The conceptual model is the foundation upon which all aspects of the modeling process are constructed, and this should be clearly understood by all members of a project team, from data gatherers to modelers to managers. In any situation where a particular field problem requires a linkage between site characterization and performance assessment, the development of a conceptual model and the continued testing and assessment of the model should be an explicitly required component of efforts to address the problem. The next step in the modeling process is the development of a quantitative description of the conceptual model in terms of mathematical equations to be solved—the mathematical model. Except for simple problems, mathematical equations are usually solved by use of a computer code, also called a numerical model. A newly developed computer code must be tested to assure that it correctly solves the equations of the mathematical model. This “verification” process typically involves comparisons of the numerical results with known solutions for related simple configurations. Because the verification process of a complex code usually involves piecemeal testing of the individual transport processes represented by the model, without simultaneous testing of all or most features of a code, it is rarely possible to be assured that a code is fully verified. In addition, even a well-established computer code should be used carefully by knowledgeable analysts to avoid potential problems such as numerical instability.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE A mathematical model always includes a number of parameters, such as the distribution of hydraulic properties within the modeled region. At the early stages of the modeling process, the values of some of these parameters are unknown. The process of estimating these parameters is known as model calibration or parameter estimation. The calibration process will typically include sensitivity analyses, designed to elucidate how changes in parameters can influence the simulation results. Calibration procedures based on statistical/stochastic formulations can also provide quantitative measures of uncertainty in the parameter estimates. Such information is extremely valuable for guiding the collection of additional field data to refine the model. As shown in Figure 1-1, the calibration step can involve significant feedback to the conceptual model. Model calibration is often achieved by adjusting model parameters, either manually or by automated methods, until the model simulated results agree with field data to an acceptable level. As the model is a simplification of the real system, a perfect fit between the simulated results and field data is unlikely to be achieved. A serious lack of fit indicates that the conceptual model should be reexamined. On the other hand, a good fit does not necessarily prove that the conceptual model is adequate to address the issues in question. Another complicating factor may be that a measured parameter may not be the same as a modeled parameter, e.g., it is difficult to determine what the measured moisture tension at a porous tip actually represents for a situation where the moisture originates as film-flow in a fracture. Additional model testing, which creates another feedback loop to the conceptual model element in Figure 1-1, is essential to gain confidence that the model provides meaningful results that can be used for decision-making and problem resolution. Model testing is discussed in further detail in the next section. It is important to recognize that model predictions require assumptions about future events or scenarios. The importance of this “event” component of the conceptual model is made clear by postaudit studies of groundwater models (e.g., Anderson and Woessner, 1992, p. 288-293). These studies suggest that, when model predictions were compared to actual outcomes, a major reason for inaccurate prediction was that the assumed future scenarios (e.g., future stresses on the system) did not occur. This finding points to the need for developing model predictions for many different possible future scenarios. Another important aspect of model prediction is uncertainty, which arises from many factors, such as simplification of the real system, limited field data, measurement errors, and multiple conceptualizations or interpretations that cannot be resolved by existing data. Even if the modeling process has undergone several cycles of revision, testing, and gathering of additional field data, prediction uncertainty is reduced but not entirely eliminated. Decisions based on model predictions must take this into account by approaches such as analysis of risks, worst-case scenario, or incorporation of safety margins. If the conceptual model
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE uncertainty is too great, the project goals may not be achievable within a reasonable time or at acceptable cost. Alternatively, it may be necessary to redefine the original problem to be resolved. Model Testing The formulation of a conceptual model is inherently subjective in that it relies on limited available site-specific observations and data, as well as experience and insights developed through work on similar sites and/or related problems. A conceptualization is susceptible to biases arising from the disciplinary background and experience of the analyst, and/or by differing perceptions of the problem as influenced by external social and political forces. Although model calibration represents one level of testing by requiring the model to reproduce one set of field data, the model may be applied to field conditions that are significantly different than the conditions under which calibration data were collected. For these reasons, it is important to test the predictive capabilities of a model. Due to the large variability in the objectives of modeling projects, it is not possible to provide a prescriptive step-by-step procedure for model testing. The amount of effort devoted to model testing will strongly depend on the question to be resolved, the scope of the investigation, available resources, and the consequence of an inadequate or inappropriate model. In this section, we discuss some general issues that should be considered in conceptual model testing. We assume at the outset that the computer code used for simulation is already verified, in other words, that the program logic and numerical algorithm are correctly implemented, and the results are free of computational errors. A traditional procedure of model testing is to use the calibrated model to simulate a set of field data that was not used during the calibration process. For example, if historical data exist for the site, a portion of the data may be used for calibration and the remaining data used for testing. Alternatively, the model is used to predict the result of a field experiment, and the experiment is then carried out as a check against model predictions. The test is successful if the model simulation agrees with the test data, within reasonable limits, without the need to further adjust the model parameters. A model that passes one or a series of such tests would have demonstrated a certain level of predictive capability. If the model fails the test, then the test data are used to further calibrate the model and additional field data are needed for a new round of testing. Although the above test procedure is conceptually appearing, it may not always be feasible. In most cases, field data are limited and all the data must be used for calibration, leaving none for testing. Therefore, a broader view of model testing is often necessary. One approach is to evaluate how well the conceptual model represents the real system in terms of features, processes, and events. This
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE involves both examining the model assumptions and evaluating alternative hypotheses. The underlying rationale is that a model that has undergone such evaluations can be used with an increased degree of confidence. As an example of evaluating a “feature” component of the conceptual model, consider the question of whether a geologic stratum that is represented in the model as a continuous layer underlying the entire model region may in fact be discontinuous and absent at certain locations. The first step in evaluating this alternative hypothesis is to consider its consequence. This can be done by modifying the model according to the alternative hypothesis (discontinuous layer), recalibrating the model, and developing new predictions. If the modified model with changed parameters cannot match the data, this is an indication that the alternative hypothesis is inconsistent with available field data. If recalibration is successful but the new predictions are similar to the old predictions, this is an indication that the alternative hypothesis is of little consequence (within the context of the question to be resolved). In both cases, the alternative hypothesis may not warrant additional consideration. However, if the recalibrated model leads to new predictions that are significantly different from the old predictions, then further investigations are needed. The continuity of the layer in question may be evaluated by geophysical methods to image the subsurface, by test borings at strategic locations, or by using an understanding of the depositional environment to infer the likelihood that the layer may be continuous or discontinuous. Whether or not a model can be “validated” is a topic that has seen substantial debate in recent years. Certain authors (e.g., Konikow and Bredehoeft, 1992; Oreskes et al., 1994) have presented the opinion that models cannot be validated, because the truth of scientific theory can never be proven. Describing a model as “validated” implies, especially to a nontechnical audience, a level of correctness and certainty that is unattainable. Other authors (e.g., see discussion by Jarvis and Larsson, this report, Chapter 6)argue that a “validated model” can be taken to mean that a model is acceptable for its intended use. Currently, there is a lack of consensus on the definition of “validation.” From an operational point of view, model testing and evaluation can be viewed as activities designed to establish the credibility of a model. In this regard, peer review is an important part of the modeling process. Review by a group of objective, independent, and respected experts can utilize knowledge and opinions beyond those of the study team. Maintaining a free flow of information (e.g., field data, model results) can also add a significant measure of credibility, because the model is open to scrutiny by concerned parties (e.g., regulators, license applicants, government agencies, public citizen groups, and the general scientific community). In the final analysis, whether or not a model is acceptable to concerned parties depends on whether or not these parties have confidence that the model predictions provide meaningful input for decisionmaking and problem resolution.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE which is one of two transport mechanisms recognized in classical transport theory. The second transport mechanism is hydrodynamic dispersion, which describes the spreading and mixing of solute due to (1) microscopic and local-scale variations in velocity that are not explicitly described by the above velocity field, and (2) molecular diffusion. In the classical approach, hydrodynamic dispersion is represented as a Fickian (diffusion-like) process. The resulting equation governing solute transport is known as the advection-dispersion equation. For modeling solute transport in saturated fractured rocks, a simple extension to the classical model is applied to incorporate the effects of solute diffusion between mobile and immobile fluids. In a number of tracer experiments in saturated fractured rocks, the breakthrough curve (plot of concentration versus time) exhibits a long tail, or skewness towards later times (e.g., Novakowski et al., 1995). This feature is commonly interpreted to result from the solute moving through the fracture network while diffusing into the immobile fluid within the matrix. The conceptual flow model is that of the dual-porosity model illustrated by Figure 1-7c. The long tail in the breakthrough curve is explained by the later diffusion of solute from the matrix back into the fractures. This “matrix diffusion” can be considered as one example of solute exchange between mobile and immobile fluids. In addition to the matrix, regions of immobile fluid may exist within an individual fracture (if flow through the fracture is channeled) and in “dead-end” fractures of a network. Solute exchange between mobile and immobile fluid is commonly represented by a diffusion equation (e.g., Tang et al., 1981). Models of this type typically assume steady-state flow. For the fractured vadose zone, solute transport models typically assume that fluid flow occurs in the matrix blocks and in the fractures. The conceptual flow model is that of the dual permeability model illustrated by Figure 1-7d. Gerke and van Genuchten (1993a) use two advection-dispersion equations, coupled by a solute transfer term, to describe solute transport in the fracture and in the matrix. Solute transfer between the two domains can occur both by fluid flow (advection) and by diffusion. The latter is often approximated as a first-order process; that is, the diffusive flux is proportional to the difference between solute concentration in the fracture and in the matrix. For certain field settings, the advective mass transfer can act in a direction opposite to the diffusive mass transfer. For example, Gerke and van Genuchten (1993a) simulated the infiltration of solute-free water into a fractured vadose zone that contained initial solute in the matrix blocks. As the solute-free water infiltrated down the fractures, a portion was imbibed into the matrix by capillary forces. At the same time, the solute in the matrix tended to diffuse back into the fractures because of the concentration difference between the two domains. The result was a highly complex response in the fracture-matrix system. Further refinements of solute transport modeling have led to the development of multiregion models (e.g., Gwo et al., 1995; Hutson and Wagenet, 1995). In these models, the fractured rock or macroporous soil is represented by more
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE than two domains (or regions). These domains may be delineated in a somewhat arbitrary manner, or may be associated with geological features such as different types of fractures and matrix blocks. For example, Gwo et al. (1995) used a three-region model, composed of macropores, mesopores, and micropores, to simulate flow and transport through a laboratory column of soil from a forested watershed. In Chapter 3, Jardine et al. conceptualize the fractured weathered shale at the Oak Ridge National Laboratory to be composed of primary fractures, secondary fractures, and soil matrix. They also describe various experiments to examine the interaction and mass transfer between the different domains. In general, multiregion models are more flexible than dual- or single-domain models. However, this flexibility comes at the cost of additional model parameters. Calibration of multiregion models requires a significant amount of field data. Solute transport can also be simulated in a discrete fracture model as shown in Figure 1-7f. Substantial insight can be gained by using such a model for examining the complex interactions between solutes in fractures and in the matrix. For example, Therrien and Sudicky (1996) simulated three-dimensional transport from a hypothetical waste facility in a fractured, low-permeability stratum overlying an aquifer. Their results show that where vertical fractures are sparse, the contaminant plume can become discontinuous, making it difficult to interpret the data from a field-monitoring program. Another value of discrete fracture models is for assessing the adequacy of continuum models such as dual-permeability or multidomain models. For a realistic field application, however, a discrete-fracture model may be problematic due to the large data requirement. Use of Environmental Tracers As noted by Phillips (this report, Chapter 9), environmental tracers have not been widely applied in hydrologic investigations of fractured rocks, even though they offer a powerful and direct method for assessing solute transport effects. Often, the approach to subsurface investigation is first to characterize fluid flow processes, and then to evaluate the additional processes that affect solute transport. While this approach can lead to a detailed understanding of flow processes, key solute transport mechanisms can be overlooked. In some cases, interpretation of environmental tracers has lead to drastic revisions of a conceptual model based initially solely on hydrodynamic analysis. For example, Phillips (this report, Chapter 9) points out that measurements of tritium in the fractured chalk of southern England (see Foster, 1975, and Foster and Smith-Carrington, 1980) revealed that the process of matrix diffusion was active, and this in turn explained an apparent contradiction between the rapid hydraulic response of the aquifer to recharge versus the highly attenuated movement of dissolved pollutants. Environmental tracers consist of solutes that have a widespread or global occurrence from both natural and anthropogenic sources in precipitation, and have been entering the subsurface over large spatial and typically long temporal
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE scales (tens to millions of years). The large space and time scales associated with these tracers result in a signal that is naturally integrated. When samples for environmental tracer analyses are collected from a point in the subsurface, the results represent an integration of upstream transport mechanisms. This is in contrast to most hydraulic measurements where point sampling yields a point measurement. While numerous environmental tracers have been used in subsurface hydrology, the existence of both air and water phases in the vadose zone is likely to complicate the use of some tracers, especially those that utilize dissolved gases. Environmental tracers that are likely to be useful for directly investigating fluid flow in fractured vadose zones include tritium, stable isotopes of oxygen and hydrogen in the water molecule, halides, and chlorine-36; see Phillips (this report, Chapter 9) for a brief discussion of these tracers. Other tracers that may be useful for indirectly examining fluid flow include carbon-14, uranium-series nuclides, strontium isotopes, boron-11, silicon-32, and iodine-129; see Cook and Herczeg (2000) for a discussion of these tracers. In addition, dissolved gas tracers such as helium-3, chlorofluorocarbons (CFCs, synthetic gases that were released into the atmosphere beginning in the early 1940s), and krypton-85 can provide a measure of groundwater age in the saturated zone. These age estimates may also be useful for indirectly characterizing fractured vadose zones. Characterizing the fractured vadose zone can be accomplished by measuring the distribution of environmental tracers in the subsurface. In the absence of preferential flow, or in stratigraphic intervals of fractured rocks where matrix flow dominates, the vertical profile of tritium in the vadose zone can be used to estimate infiltration rates by identifying the depths of tritium peaks corresponding to atmospheric testing of nuclear weapons. However, if the majority of recharge at a site occurs via fracture flow, a detailed investigation of matrix processes in the vadose zone may be misleading. Furthermore, if the infiltration is localized by a few high porosity features or faults or other heterogeneities, an investigation at a random point in the map may miss the dominant vertical flow paths. In these cases, the vadose zone can be evaluated by sampling at the water table, that is, where the infiltrating fluid and solute enter into the underlying saturated zone. While the details of flow and transport processes will tend to be less well resolved by this approach, the integration (averaging) of processes may be enhanced. The following three examples illustrate the importance of sampling from both the vadose and the saturated zones. In the first example, Wood and Sanford (1995) found significant differences in the chloride concentrations in pore waters in the unsaturated zone, compared with mean chloride concentrations in underlying groundwater in Texas. These differences were interpreted to mean that the majority of recharge occurred along preferential (macropore) pathways, which were not detected by sampling in the vadose zone. In the second example, Solomon et al. (1995) obtained groundwater ages as a function of depth below the
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE water table, and then calculated vertical fluid velocities and recharge rates through the vadose zone on Cape Cod, Massachusetts. Groundwater ages were zero at the water table because the dating method (tritium/helium-3) utilized a dissolved gas, which exchanged into pore air in the vadose zone. Solomon et al. (1995) also delineated the depth of the tritium bomb peak that occurred in 1963. The difference between the total travel time of water as delineated by the tritium bomb peak (30 years), and the tritium/helium-3 age of the water since it was at the water table (16 years), provided a measure of the travel time in the vadose zone (14 years). In the third example, Busenberg et al. (1993) found that concentrations of CFCs dissolved in groundwater near the water table were much larger than expected based on measurements of the CFC content of pore air immediately above the water table. They concluded that preferential flow was not equilibrating with the vadose zone atmosphere and was responsible for significant recharge to the Snake River Plain aquifer. A mass balance of environmental tracers within the vadose zone can be useful for evaluating regional-scale solute and fluid fluxes, without necessarily understanding the details of fracture flow, fracture-matrix interaction, etc. (e.g., Cook et al., 1994). This approach assumes that a mass balance can be adequately formulated using subsurface measurements (i.e., that spatial variations in the tracer distribution can be adequately sampled), and the tracer input is sufficiently well known. It can be argued that over long time scales, diffusion processes tend to reduce small-scale spatial variation in tracer concentrations, making a mass balance feasible. However, this approach has not been extensively tested in fractured vadose zones. Environmental tracers may also be useful for evaluating and testing specific processes that are included in a conceptual model. For example, Desaulniers et al. (1981) evaluated the influence of fractures on solute transport in a clay-rich till in Southern Ontario. They found that profiles of oxygen isotopes and chloride were best explained by molecular diffusion, with minimal advective transport in fractures. Because of their usefulness, environmental tracers should be considered a primary method for investigating fractured vadose zones and for formulating and testing conceptual models, and they should be included in the field investigation strategy from the very beginning of site characterization. CONCLUSIONS AND RECOMMENDATIONS This report discusses the process through which conceptual models of flow and transport in the fractured vadose zone are developed, tested, refined, and reviewed. A conceptual model is defined as an evolving hypothesis identifying the important features, processes, and events controlling fluid flow and contaminant transport of consequence at a specific field site in the context of a recognized problem. The conclusions presented below are grouped according to the two major topics addressed in this report: (1) general considerations during
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE the development and testing of conceptual models, and (2) flow and transport in the fractured vadose zone. These conclusions are followed by the Panel's suggestions for research activities that will contribute to the conceptual modeling process. Conclusions on Development and Testing of Conceptual Models Development of the conceptual model is the most important part of the modeling process. The conceptual model is the foundation of the quantitative, mathematical representation of the field site (i.e., the mathematical model), which in turn is the basis for the computer code used for simulation. Given a sufficiently robust conceptual model, different mathematical formulations will probably produce similar results. By contrast, an inappropriate conceptual model can easily lead to predictions that are orders of magnitude in error. The context in which a conceptual model is developed constrains the range of its applicability. A conceptual model is by necessity a simplification of the real system, but the degree of simplification must be commensurate with the problem being addressed. Thus, a conceptual model developed for addressing one type of problem may not be adequate for another type of problem. For example, a conceptual model developed for estimating recharge flux may not be adequate for estimating contaminant travel time from land surface to the water table. It is important to recognize that model predictions require assumptions about future events or scenarios, and are subject to uncertainty. Quantitative assessment of prediction uncertainty should be an essential part of model prediction. A suite of predictions for a range of different assumptions and future scenarios is more useful than a single prediction. Uncertainty in model predictions can be partially quantified by sensitivity analysis (how uncertainties in estimated model parameters affect model predictions), by using a statistical-or stochastic-based calibration procedure, or by formulating the mathematical model in a probabilistic framework. However, it is difficult to quantitatively assess the possibility that the conceptual model might not adequately represent the major features and processes in the real system. Testing and refinement of the conceptual model are critical parts of the modeling process. The initial conceptual model is developed based upon limited field data and is susceptible to biases reflected by the disciplinary background and experience of the analyst. Therefore, site investigation should not be designed solely to support the initial conceptual model. Reasonable alternative conceptualizations and hypotheses should be developed and evaluated. In some cases, the early part of a study might involve multiple conceptual models until alternatives are eliminated by field results. Although model calibration does provide a certain level of model testing, a good fit to the calibration data does not necessarily prove that the
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE model is adequate to address the issues in question. The significance of a good fit to calibration data generally depends on the nature of the data. A model that matches different types of calibration data (e.g., heads and fluxes) collected under different field conditions (e.g., at different water contents) is likely to be more robust than a model that matches a limited range of calibration data. However, if the model cannot be calibrated to match the calibration data, this is an indication that the conceptualization should be re-examined. Checking model simulation results against field data (that were not used for calibration) is one, but not the exclusive, approach to model testing. In some cases, all field data are needed for calibration, and none are left for further testing. However, this does not mean that the model cannot be used for prediction. A broader view of model testing is to develop greater confidence that the model provides a good representation of the real system. This can be achieved by strengthening the justifications for model assumptions, and by evaluating alternative hypotheses. From an operational perspective, the goal of model testing is to establish the credibility of the model. A credible model is essential if it is to gain acceptance by parties involved in decision-making or problem resolution. In addition to testing and evaluation, the credibility of a model can be enhanced by peer review undertaken by an independent panel of experts, and by maintaining an open flow of information so that the model is available for scrutiny by concerned parties. Conclusions on Flow and Transport in the Fractured Vadose Zone There exists a body of field evidence indicating that infiltration through fractured rocks and structured soils does not always occur as a wetting front advancing at a uniform rate. Large variations in fluid velocity (i.e., preferential flow) may be caused by (a) the presence of macropores and fractures, (b) flow instability, or (c) funneling effects. Thus, model simulation based upon a uniform wetting front advancing down a homogeneous medium may provide erroneous estimates of flux and travel times through the vadose zone. Sophisticated characterization of geological inhomogeneity within the vadose zone increases the likelihood that non-uniform flow can be appropriately modeled. The current state of knowledge is not adequate to determine which processes are likely to control unsaturated flow and transport at a given field site. Laboratory and theoretical analyses demonstrate that film flow in fractures can transport fluid and solute at rates substantially higher than transport by capillary flow. However, at the field scale, the significance of film flow and the modeling approach are topics of controversy. The field environments in which film flow plays a significant role during infiltration are poorly understood. In addition, it is unclear whether film flow can be incorporated into traditional
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE models of capillary flow by defining effective curves for hydraulic conductivity and retention, or whether it requires a fundamentally different set of governing equations to describe the dynamics of a water film. Although not identical, structured soils and fractured rocks exhibit many similarities in flow and transport processes. Macropores and aggregates in structured soils are respectively analogous to fractures and matrix blocks in rock. However, soil studies are typically conducted in the shallow subsurface, where macropores may be dynamically altered to a greater degree than rock fractures at greater depths. Nonetheless, knowledge gained from study of one medium may be useful for the other. Communication between workers in the soil science field and in the fractured rock field will be of benefit to both groups. Models of varying complexity have been developed for preferential flow, but their adequacy for field-scale application requires further testing. The approach in many current models is to avoid explicitly simulating the mechanisms that cause preferential flow. Instead, the model is implemented to simulate fast and slow flow, by use of a composite hydraulic conductivity curve or by dual-permeability domains. Such approaches have been successfully applied to laboratory and small-scale experiments. However, further testing is needed to examine whether these models are adequate for field-scale application over a broad range of field conditions. This issue is of particular concern in the fractured vadose zone because of the inherently nonlinear nature of processes involved. As flow conditions change, different flow and transport mechanisms, not represented in the model, may become important, leading to large errors in predictions. The interaction between fracture and matrix exerts a strong control on fluid and solute movement. However, the strength of this interaction in the field is not well known. The simplified representation of this interaction in current models also requires further evaluation. Factors controlling fracture-matrix interaction include the density of water-transmitting fractures, the amount of wetted area on the fracture surface, the hydraulic conductivity of the matrix, and hydraulic conductivity at the fracture-matrix interface. Current models lump these factors into a transfer coefficient that is determined by model calibration rather than by direct measurements. Whether or not this approach can adequately simulate flow under a range of field conditions requires further evaluation. Solute transport in the fractured vadose zone can exhibit complex behavior due to the large variations in fluid velocity, and the interplay of advective and diffusive transport between fractures and matrix. Better understanding of such systems is required in order to effectively analyze complex responses. Solute transport models are more complex than flow models, and can involve multiple regions to represent the diversity of macropore and micropore sizes. To apply these models, greater guidance is needed on how to delineate different pore regions, and how to determine the parameters that characterize solute exchange between pore regions.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Environmental tracers should be included in field investigation strategies from the very beginning of a site characterization program. In a number of studies, geochemistry and environmental tracer data have led to substantial revisions of the conceptual models initially developed based upon hydrodynamic analysis. These experiences emphasize the need for better integration of geochemistry and environmental tracers early in the model development process. Recommended Research Flow and transport in the fractured vadose zone have been and will continue to be an active area of research in both the soil science and subsurface hydrology disciplines. The research recommended in this report is not meant to be inclusive. Instead, the list below reflects topics that deserve greater attention so that conceptual models of flow and transport can be improved, and to address the issues identified in this report. Fundamental research to understand flow and transport processes in unsaturated fractures should continue. Better understanding of fundamental processes will improve the model representation of the real system. Particular emphasis should be placed on understanding mechanisms that cause non-uniform (preferential) flow, film flow, and intermittent behavior. Research is needed to understand the spatial variability in vadose zone properties, and to develop upscaling methods. Spatial variability is a key cause of model uncertainty, because the subsurface cannot be exhaustively sampled. Furthermore, vadose zone properties are typically determined by small-scale laboratory measurements. To use these small-scale measurements, upscaling methods are needed to derive field-scale flow and transport properties needed in models. Such upscaling methods should be based on a thorough understanding of small-scale processes, together with an understanding of how these interact and contribute to large-scale phenomena. There is a need for comprehensive field experiments in several fractured vadose zone geologic environments. These experiments should be designed to understand the controlling processes (capillary flow, film flow, and intermittent behavior) for a broad range of field conditions, to evaluate methods of parameter upscaling, and to test alternative conceptual models. Current models should be evaluated for their adequacy for simulating flow and transport in the presence of fingering, flow instability, and funneling. One approach is to construct a model with detailed representation of small-scale heterogeneities based on high-resolution field or synthetic data, so that the processes causing preferential flow are explicitly simulated. The model results can then be compared to results from simpler models that do not explicitly simulate preferential flow. Of particular importance is the evaluation of transfer coefficients to represent fluid and solute exchange between fracture and matrix.
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CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE There is a need to develop quantitative assessment of prediction uncertainty for models of flow and transport in the fractured vadose zone. Meaningful quantification of uncertainty should be considered an integral part of any modeling endeavor, as it establishes confidence bands on predictions given the current state of knowledge about the system. If prediction uncertainties are realistically quantified, postaudit studies can be carried out in a systematic hypothesis-testing framework, which can provide a great deal of insight about the predictive capabilities of the model. Research should be undertaken to develop improved techniques for geochemical sampling from the fractured vadose zone. Current sampling technology is very limited, especially for sampling at depth. Destructive core sampling followed by fluid extraction is a viable approach for sampling matrix water in the unsaturated zone. Sampling fluids directly from fractures remains problematic. Improved sampling techniques will facilitate the use of environmental tracers and geochemical data for conceptual model building. REFERENCES Altman, S. J., B. W. Arnold, R. W. Barnard, G. E. Barr, C. K. Ho, S. A. McKenna, and R. R. Eaton, 1996. Flow Calculations for Yucca Mountain Groundwater Travel Time (GWTT-95) . Report SAND96-0819. Albuquerque, N. Mex.: Sandia National Laboratories. 170 pp. Anderson, M. P., and W. W. Woessner, 1992. Applied Groundwater Modeling. New York: Academic Press. 381 pp. Busenberg, E., E. P. Weeks, L. N. Plummer, and R. C. Bartholemay, 1993. Age Dating Ground Water by Use of Chlorofluorocarbons (CCl3F and CCl2F2), and Distribution of Chlorofluorocarbons in the Unsaturated Zone, Snake River Plain Aquifer, Idaho National Engineering Laboratory, Idaho. U.S. Geological Survey Water-Resources Investigations Report 93-4054 . Reston, Va.: U.S. Geological Survey. 47 pp. Chen, C., and R. J. Wagenet, 1992. Simulation of water and chemicals in macropore soils. I. Representation of the equivalent macropore influence and its effect on soil-water flow. Journal of Hydrology 130: 105-126. Cook, P., and A. L. Herczeg, 2000. Environmental Tracers in Subsurface Hydrology. Boston: Kluwer Academic Publishers. 529 pp. Cook, P. G., Jolly, I. D., Leaney, F. W., Walker, G. R., Allan, G. L., Fifield, L. K., and Allison, G. B., 1994. Unsaturated zone tritium and chlorine-36 profiles from southern Australia: their use as tracers of soil water movement. Water Resources Research 30(6): 1709-1719. Desaulniers, D.E., J.A. Cherry, and P. Fritz, 1981. Origin, age and movement of pore water in argillaceous quaternary deposits at four sites in southwestern Ontario. Journal of Hydrology 50: 231-257. Fabryka-Martin, J. T., A. V. Wolfsberg, S. S. Levy, J. L. Roach, S. T. Winters, L. E. Wolfsberg, D. Elmore, and P. Sharma, 1998. Distribution of Fast Hydrologic Paths in the Unsaturated Zone at Yucca Mountain. Paper presented at 8th Annual International High-Level Radioactive Waste Management Conference, Las Vegas, Nev. American Nuclear Society, La Grange Park, Ill. p. 264-268. Foster, S. S. D., 1975. The chalk groundwater tritium anomaly, a possible explanation. Journal of Hydrology 25: 159-165. Foster, S. S. D., and A. Smith-Carrington, 1980. The interpretation of tritium in the chalk unsaturated zone. Journal of Hydrology 46: 343-364.
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Representative terms from entire chapter: