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Solute transport in heterogeneous media: A discussion of technical issues coupling site characterization and predictive assessment
Advances in WaterResources17 (1994) 259 264 © 1994 Elsevier Science Limited Printed in Great Britain. All rights reserved 0309-1708/94/$07.00 ELSEVIER
Short Communication Solute transport in heterogeneous media: A discussion of technical issues coupling site characterization and predictive assessment Chin-Fu Tsang, a Lynn Gelhar, b Ghislain de Marsily c & Johan Andersson a aEarth Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California, USA
bDepartment of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA CDepartment ofa Applied Geology, University of Pierre and Marie Curie, Paris, France Swedish Nuclear Power Inspectorate, Stockholm, Sweden
(Received 2 February 1994; accepted 18 April 1994) Long-term predictive evaluation of solute transport and transformation in geologic media is a critical element in the performance assessment of nuclear waste geologic repositories and in the environmental restoration or control of contaminated sites that is facing many countries today. Since the geologic media are heterogeneous and their details can never be known deterministically, longterm prediction of flow and transport in such systems requires new thinking. Thus, it is no longer possible to consider site characterization and predictive modeling calculations to be separate activities; rather they are highly coupled. This paper presents a discussion of the coupling and proposes a framework of technical issues that need to be studied.
The geologic medium is not an engineering system, meaning that it is almost impossible to characterize in detail deterministically. By the time sufficient boreholes are drilled into the medium to characterize it to any degree of detail, the medium will be so full of boreholes that it is no longer the same medium as at the beginning! Thus we are forced to content ourselves with the characterization of only the major features and treating finer structures by stochastic modeling techniques, unless nondestructive geophysical techniques can be made reliable and sensitive enough to detect and to characterize hydrologically the fine structures. This immediately introduces a certain degree of uncertainty in predicting solute transport and geochemical transformations in the geologic medium. For example a major uncertainty is in the identification of 'significant' major features to be characterized. It is not at all clear if one can know a priori which are the significant features. Also, often the significance level depends on the particular bottom line question to be answered, i.e. on the performance measure or predictive quantities required in the predictive assessment.
1 INTRODUCTION Geologic media are heterogeneous, i.e. they contain fractures and faults, layering and lateral features as well as finer spatial variations in its permeability and chemical properties. Until recent years, interest in hydrogeology has been much in water resources with additional concerns on heat transfer (geothermal energy, heat storage) and pressure fields (construction, stability, mechanical effects). The pressure and temperature fields are not much affected by fine structures, while the effects of major features can be estimated based on site studies that characterize these features, if they have been identified. On the other hand, solute transport and geochemical reactions along the solute paths are highly sensitive not only to the large features, but also to finer structures that are much harder to characterize. For example, these fine heterogeneities may give rise to channeling effects, which can be the cause of the surprisingly fast solute transport observed in a number of field observations. 259
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Many advances have been made in recent years in site characterization methods, modeling techniques of fractured and heterogeneous rocks, and simulation methods of flow and transport in these systems. However, these advances have been made mostly in each of these areas separately. The coupling of these areas to address the need of predicting long-term solute transport and fate in the geologic medium is still in an early stage of development. Such long-term predictive evaluation of solute transport and transformation in the subsurface is a critical element in the performance assessment of nuclear waste geologic repository and in the environmental control and restoration of contaminated sites that are faced by many countries today. Thus there is an urgency in carefully thinking through the process coupling site characterization and predictive assessment, and in developing the necessary techniques and strategies needed for the coupling. This can most effectively be carried out through international cooperation. 9 The present short article attempts to provide a framework and definitions of technical issues for a study of this coupling.
2 REMARKS ON CONCEPTUAL MODELS A few preliminary remarks on conceptual models may be helpful before we discuss a proposed framework of technical issues. Since it is impossible to deterministically characterize the details of the geologic medium at a given site, it is necessary to develop a simplified conceptual model of the medium. The structures of the medium that are ignored or smoothed out in some fashion, in the simplified conceptual model, can have a major effect on the validity of this model. In some cases, these fine structures can be aggregated into an equivalent 'macroscopic' coefficient; this is sometimes the case for transport, where a macrodispersivity, valid at a large scale, can be defined. 7 To define such effective properties, some statistical properties of the fine structure must be known, but this change of scale has two consequences: (i) the governing equations of the conceptual model may change compared to the microscopic ones; and (ii) even if the required statistical properties are reasonably determined, this change of scale introduces an irreducible uncertainty. In some cases, however these simplified or smoothed fine structures may not be amenable to the definition of an effective property, and then the simplified conceptual model becomes even more uncertain. In any case, the simplification of the conceptual model introduces uncertainties in the prediction; consequently, a prediction which is not accompanied by uncertainty estimates is probably meaningless. The uncertainty that is discussed here is not the same as uncertainty due to
error ranges in input parameter values. Rather it is the uncertainty due to simplifications associated with the conceptual model of the geologic medium at the site. Such uncertainties can cause orders of magnitude errors in predictions of solute transport travel times. In the design of conceptual models it is important to recognize that the particular design depends on the predictive quantities required by the problem at hand. In nuclear waste geologic repository programs, these are called performance measures. In environmental restoration, these may be the criteria that determine the best clean-up or control strategies. With certain predictive quantities, uncertainties due to errors in conceptual models may be very large, while with other predictive quantities, such uncertainties may be much smaller. Hence, the particular design of conceptual models should be specified in relevance to predictive quantities required. In the context of this article, we will enlarge the conventional definition of conceptual model of the medium to include not only the structural features but also events and processes, the so-called FEP. 1'2'16 Thus the conceptual model has the following three elements: (1) Features. Geometric structure of the medium, spatial variations of property parameters, discontinuities (fractures and faults), boundary conditions (recharge boundaries, rainfall, sources and sinks), and also temporal variations of the above, except those accounted for in (2) below. (2) Events. Temporal changes, including those due to drastic events, such as earthquakes, glacial movements, and climatic changes, and alternative scenarios. Of particular concern is the current state of the geologic system which forms the 'initial conditions' for model simulation. In certain sites, the current conditions are not in steady state, which means that the system is still transient due to past events. These transients may have time scales of thousands of years, and are not important fo," shorter term predictions. However, for long-term predictions of thousands of years, they can play a significant role, and these past events must be identified and evaluated. (3) Processes. Physical, chemical, and biological processes that may occur in the medium such as density-driven flow and chemical sorption and matrix diffusion; coupled processes - - those involving jointly fluid flow, fracture aperture deformations and chemical reactivity. One must pay attention to slow processes that may show up in long-term predictions. These are often identified through studies of natural analog systems or in very accurate laboratory experiments. In numerical simulations, the features (1) are usually incorporated in the mesh design, the events (2) are in the input data, and the processes (3) are described in the
Solute transport in heterogeneous media governing equations. One can easily see that any errors in the conceptual model may cause drastic errors in the predictive results. The design of a conceptual model depends on site information and characterization experiments. It is, in general, an iterative process. 3'18 Ideally, one studies all site information available initially and considers the required predictive quantities. On the basis of such considerations, a conceptual model is proposed. From the proposed conceptual model, site characterization experiments will be designed and carried out. 15 These experiments should be of two types. The first is to determine the values of parameters that describe the conceptual model, and the second is to test its validity, i.e. to look for information and data that may invalidate the model for the particular required predictive quantity. With new information, the conceptual model may be substantiated or modified. With the modified conceptual model, further site characterization experiments will need to be made. Thus, this is an iterative procedure. The procedure does not necessarily produce a unique conceptual model. 4 Often alternative models may fit all the available data, which often are quite scanty (from prediction assessment point of view). Thus, two research groups that have slightly different strengths of expertise may choose to start with different conceptual models and obtain different modified or improved models by the iterative procedure. Then the question is how to discriminate among the alternative conceptual models, and if such discrimination is not possible, how should the results of these alternatives be combined. If the results of long-term predictions are similar, the alternative conceptual models need not to be discriminated against. Actually, they may even increase our confidence that the predictions may be physically correct, since the results are not sensitive to alternative conceptual models (all of which are consistent with available data). On the other hand, if the results are strongly divergent, the divergence is a measure of the uncertainties of prediction. If the uncertainty level is unacceptable, we may have to admit that we cannot do better and have to abandon the site, or look for other approaches. Or, we may review whether the predictive quantities required are too stringent and unnecessary for the overall problem at hand. Perhaps the required predictive quantities can be modified and still satisfy the problem needs. The iteration between site characterization and conceptual model development should be concluded based on predictive assessment. For example, the process can stop if the long-term predictions have an acceptable level of uncertainty within the model or if the uncertainty level cannot be reduced by further iterations. In this view, it is important to note that site characterization and predictive assessment are not a successive process where one continues from the point at which the other has ended. Rather, both should be
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performed simultaneously from beginning to conclusion. Finally the results based on a conceptual model with the associated uncertainties should be compared with those from alternative models, and together they form inputs for decision making. The plausible notion that a phased site characterization program will tend to reduce the uncertainty and converges towards reality is by no means established scientifically. The following example illustrates this point. In the UK, Mackay 1° developed an exercise where a 'true' conceptual model was made available to one team (using very sophisticated simulation techniques to generate lithofacies in a sedimentary basin, and parameter values at a very fine scale of 15 × 15 × 0.1 m). This team calculated the transport of radionuclides to the environment, for a given release scenario, on the 'exact' model. Another team, which was not shown the 'true' model, was asked to perform a three-staged site characterization program, and was given all the information that was asked for, essentially from a large series of boreholes and well tests, at the location and elevation that the team required. These data were extracted from the 'exact' model. At each phase of the site characterization, a predictive assessment was made, very much along the line of the above suggestions. To make a long story short, to the despair of the whole project, the more the site characterization program developed, the worse the predictive assessment became (compared to the 'exact' release), and furthermore, the predicted uncertainty given by the assessment team (which was using a probabilistic approach) was shown to decrease after each phase, but was completely out of range; the prediction and uncertainty underestimated the risk by about 4 orders of magnitude. Mackay and coworkers are studying the reasons for such a poor behavior. One of the present explanations is that the second team erroneously assumed that a confining clay layer was continuous, when in fact it was not. Its permeability was also underestimated, and transverse dispersivity was neglected. This example illustrates that it is not appropriate to presume that a phased site characterization program will always converge and provide a reasonable range of the uncertainty. A careful scientific evaluation at every step of the process is needed.
3 A FRAMEWORK OF TECHNICAL ISSUES TO BE STUDIED The discussions in the last section indicate that the areas of predictive assessment, site characterization and conceptual models are highly coupled and interwoven. To address the question of long-term predictions of solute transport and transformation in heterogeneous geologic media, one needs to consider all these together as a whole entity. We believe that the coupling of these
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areas is still in an early stage of development. Below we attempt to present a framework of technical issues that need to be studied. These technical issues are presented as separate items though we should keep in mind their iterative and coupled nature as emphasized above.
will influence the revision of the conceptual models, with the iteration terminated when predictive assessment is concluded. Planning for successive stages of site characterization should also be included in this site characterization program.
3.1 Initial screening methodology
3.4 Parameter determination
For a given problem at a new site, there is the question of what is the best approach for the initial screening. The strategy for studying the initial available information in the context of required predictive quantities (performance measures) needs to be developed. Associated with this is an evaluation of the reconnaissance information (regional geological, geophysical, geochemical and hydrological). Based on the information, possible initial conceptual models should be suggested.
For each alternative model, the effective, lumped, or representative (stochastic) parameters need to be defined as well as their space and time dependencies. We also need to understand whether these parameters are local property parameters or whether they are dependent on potential (pressure) fields. Associated with this is the need of studying the possibility of using spatial averaging or approximate representations which incorporate such dependencies. 6'13'17 After adequate theoretical understanding, a strategy needs to be developed to measure these parameters and their dependencies in the field or in a laboratory, and to determine as to what degree calibrations can be done. This includes determination of the parameters characterizing heterogeneity using, where possible, statistical techniques which also provide estimates of the uncertainty of the model parameters. Formal parameter estimation (inverse) methods may be useful here to identify large scale features and possibly model structure. It is important to realize that the calibration of parameters from the data collected in the site characterization program must proceed in parallel with the validation/improvement of the conceptual models. L~
3.2 Conceptual model development After the initial stage, the conceptualization of the site should cover all three parts of the conceptual model, FEP, as discussed in the previous section. The concern, here, is on: (i) the methods of identifying relevant features and structures; (ii) the methods of evaluating relevant events and scenarios; and (iii) the methods of determining relevant processes. With the identification of FEP, one will need to consider how to develop a conceptual model for heterogeneous systems, in terms of both porous and fractured rocks. Various models, such as geostatistical, fractal, Boolean random set of features, etc. have been used. 5'8'12'14 Then the question is whether it is possible to use one model as preferred over the others or whether one needs to study several models simultaneously as equally likely. In some cases the question of the appropriateness of a certain type of model of heterogeneity can be evaluated via established statistical inference techniques, whereas for other types of models appropriateness will be addressed more subjectively.
3.3 Design of site characterization program Based on the conceptual models proposed, the next issue is the strategy for designing a characterization program to carry out various field tests. The purpose of these field tests is to investigate and confirm all three parts of the proposed conceptual models (FEP). While some parts of the FEP may be obviously important, the others (especially slow processes and boundary conditions) need to be subjected to careful evaluation, so that their relevance and importance to the entire problem can be thoroughly understood. Data collection programs should be systematically designed to permit evaluation of alternative models, recognizing that different conceptual models of heterogeneity may have conflicting data requirements. The results of site characterization
3.5 Simulation techniques To perform calculations on the heterogeneous models includes not only the generation of heterogeneous fields, but also the solution of flow and transport through such systems. These calculations should also be concerned with the sensitivities of various parameters, or in other words, with the uncertainties due to parameter error ranges. Thus the desired accuracy of these input parameters can be estimated. This will be considered in the context of the parameter measurement program discussed in Section 3.4. The simulation should strive to improve computational efficiencies to enable multiple realization studies. The question of non-uniqueness and how to handle results from multiple realizations should be addressed. Techniques also need to be developed on performing conditioning with various field data (both hard and soft data), taking into account the measurement scales of such data.
3.6 Field test methodology Under this issue, one must consider how to use results from pressure and tracer tests to better define the heterogeneous model, including the anisotropy effect
Solute transport in heterogeneous media which is likely to be present in the field. One needs to determine measurement scales for a heterogeneous system for single well tests, interference tests, and tracer transport tests. In many cases multiple experiments at multiple locations may be necessary. Then the question is how to integrate and use these multiple results. Because tracer tests are usually localized within 10 to 103m range, the use of such results to make predictions over a scale of several kilometers can introduce large errors. On the other hand, if a multiple tracer experiment is performed at several locations, the integration of the results may be useful to reduce such errors. We need to develop approaches to do this integration and estimate the improved confidence level. In low permeability media, such as clay, one must remember that both pressure tests and tracer tests (even under extreme conditions) can at best provide information on the scale of a few meters. There is little hope of performing tests over the entire potential migration distance, even in small steps, and the integration can be very uncertain. 3.7 Predictive assessment
To arrive at successful predictive assessment, we need to know how to combine the results from alternative conceptual models, all of which satisfy the main information and data from the site. Uncertainties due to alternative models, parameters ranges and other sources should be evaluated together to define the overall uncertainty or confidence level. The question is then whether the overall uncertainty in the required predictive quantities is acceptable for decision making. If not, either further site measurement and modeling studies should be made, or a revision of the required predictive quantities (while still satisfying the needs of decision-makers on the problem at hand) may be necessary for the success of the whole assessment. 3
4 CONCLUDING REMARKS
The above seven major scientific issues are defined to stimulate the kind of integrated research on long-term prediction of transport and transformation in the subsurface that is required to address critical problems of national and international importance. In current national efforts, while many of the above items are explicitly or implicitly addressed, often one or more of the above items are ignored or treated superficially, thereby reducing significantly the credibility of the scientific results needed for decision making. We believe these are important questions that should be investigated in programs of coupled site characterization and predictive assessment. The costs of these investigations will turn out to be negligible as compared to the societal
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consequences of erroneous scientific inputs to the decision-makers.
ACKNOWLEDGMENTS We appreciate the discussions over the years with members of the international I N T R A V A L 9 project, which have helped to shape many of the ideas in this paper. The paper was prepared during the sabbatical year of the second author (L.G.) at the Lawrence Berkeley Laboratory whose support is gratefully acknowledged. The work is jointly supported by grants from the Swedish Nuclear Power Inspectorate, Stockholm, Power Reactor and Nuclear Fuel Development Corporation, Japan and by the Office of Basic Energy Sciences, Engineering and Geosciences Division, Office of Energy Research of the US Department of Energy, under Contract DE-AC03-76SF00098.
REFERENCES
1. Andersson, J., Carlsson, T., Eng, T., Kautsky, F., Soderman, E. & Wingefors, S., The Joint SKI/SKB Scenario Development Project, SKI TR 89:14, Swedish Nuclear Power Inspectorate, Stockholm, 1989. 2. Cranwell, R. M., Guzowski, R. V., Campbell, J. E. & Oritz, N. R., Risk Methodology for Geologic Disposal of Radioactive Waste: Scenario Selection Procedure. SAND80-1429, NUREG/CR-1667, Sandia National Laboratories, Albuquerque, USA, 1990. 3. Cook, N. G. W. & Tsang, C. F., Dynamic use of geoscience information to develop scientific understanding for a nuclear waste repository. In International High Level Radioactive Waste Management Conf., LBL-28329, Las Vegas, Nevada, 8-12 April 1990. 4. Doughty, C. & Tsang, C. F., A comparative study of a heat and fluid flow problem using three models of different levels of sophistication. J. Math. Modelling, 8 (1987) 412-8. 5. Fayers, F. J. & Hewett, T. A., A review of current trends in petroleum reservoir description and assessing the impacts on oil recovery. Adv. Water Resour., 15(6) (1992) 341-65. 6. Gelhar, L. W., Stochastic Subsurface Hydrology, Prentice Hall, Englewood Cliffs, USA, 1993. 7. Gelhar, L. W. & Axness, C. L., Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res., 19(1) (1983) 161-80. 8. Haldorsen, H. H. & Damsleth, E., Stochastic modelling, aT. Pet. Tech., 42 (1990) 404-12 (and discussion, pp. 929-30). 9. INTRAVAL, The INTRAVAL Phase-1 Summary Report, the International INTRAVAL Project. OECD/NEA, Paris, and the Swedish Nuclear Power Inspectorate, Stockholm, 1993. 10. Mackay, R., A study of the effect of the extent of site investigation on the estimation of radiological performance. Vol. 3: Overview report to HMIP. UK Department of the Environment, Ref. DOE/HMIP/RR/93053, 1993. 11. de Marsily, G., Validation of conceptual models of flow and transport in porous or fractured media, Geoval 90. In Int. Workshop, SKI-OECD/NEA, Stockholm, Sweden, 14 17 May 1990. 12. de Marsily, G., Quelques methodes d'approche de la
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variabilite spatiale des reservoirs souterrains. Hydrogeologie. BRGM Orleans, 4 (1993) 10. 13. Mantoglou, A. & Gelhar, L. W., Stochastic modeling of large-scale transient unsaturated flow systems. Water Resour. Res., 23(1) (1987) 37-46. 14. Matheron, G., Beucher, H., de Fouquet, C., Galli, A., Guerillot, D. & Ravenne, C., Conditional simulation of the geometry of fluvio-deltaic reservoirs. Soc. of Petrol. Engineers, SPE 16753, 1987. 15. Nir, A., Doughy, C. & Tsang, C. F., Validation of design procedure and performance modeling of a heat and fluid
transport field experiment in the unsaturated zone. Adv. Water Resour., 15(3)(1992) 153-66. 16. OECD/NEA, Systematic approaches to scenario development. A report of the NEA working group on the identification and selection of scenarios for performance assessment of nuclear waste disposal, OECD, Paris, 1991. 17. Tsang, C. F., Tracer travel time and model validation. Int. J. Radioactive Waste Management & Nuclear Fuel Cycle, 13(I-4) (1989) 311-23. 18. Tsang, C. F., The modeling process and model validation. LBL-30293. J. Ground Water, 29(6) (1991) 825-31.
Short Communication Solute transport in heterogeneous media: A discussion of technical issues coupling site characterization and predictive assessment Chin-Fu Tsang, a Lynn Gelhar, b Ghislain de Marsily c & Johan Andersson a aEarth Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California, USA
bDepartment of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA CDepartment ofa Applied Geology, University of Pierre and Marie Curie, Paris, France Swedish Nuclear Power Inspectorate, Stockholm, Sweden
(Received 2 February 1994; accepted 18 April 1994) Long-term predictive evaluation of solute transport and transformation in geologic media is a critical element in the performance assessment of nuclear waste geologic repositories and in the environmental restoration or control of contaminated sites that is facing many countries today. Since the geologic media are heterogeneous and their details can never be known deterministically, longterm prediction of flow and transport in such systems requires new thinking. Thus, it is no longer possible to consider site characterization and predictive modeling calculations to be separate activities; rather they are highly coupled. This paper presents a discussion of the coupling and proposes a framework of technical issues that need to be studied.
The geologic medium is not an engineering system, meaning that it is almost impossible to characterize in detail deterministically. By the time sufficient boreholes are drilled into the medium to characterize it to any degree of detail, the medium will be so full of boreholes that it is no longer the same medium as at the beginning! Thus we are forced to content ourselves with the characterization of only the major features and treating finer structures by stochastic modeling techniques, unless nondestructive geophysical techniques can be made reliable and sensitive enough to detect and to characterize hydrologically the fine structures. This immediately introduces a certain degree of uncertainty in predicting solute transport and geochemical transformations in the geologic medium. For example a major uncertainty is in the identification of 'significant' major features to be characterized. It is not at all clear if one can know a priori which are the significant features. Also, often the significance level depends on the particular bottom line question to be answered, i.e. on the performance measure or predictive quantities required in the predictive assessment.
1 INTRODUCTION Geologic media are heterogeneous, i.e. they contain fractures and faults, layering and lateral features as well as finer spatial variations in its permeability and chemical properties. Until recent years, interest in hydrogeology has been much in water resources with additional concerns on heat transfer (geothermal energy, heat storage) and pressure fields (construction, stability, mechanical effects). The pressure and temperature fields are not much affected by fine structures, while the effects of major features can be estimated based on site studies that characterize these features, if they have been identified. On the other hand, solute transport and geochemical reactions along the solute paths are highly sensitive not only to the large features, but also to finer structures that are much harder to characterize. For example, these fine heterogeneities may give rise to channeling effects, which can be the cause of the surprisingly fast solute transport observed in a number of field observations. 259
260
Chin-Fu Tsang et al.
Many advances have been made in recent years in site characterization methods, modeling techniques of fractured and heterogeneous rocks, and simulation methods of flow and transport in these systems. However, these advances have been made mostly in each of these areas separately. The coupling of these areas to address the need of predicting long-term solute transport and fate in the geologic medium is still in an early stage of development. Such long-term predictive evaluation of solute transport and transformation in the subsurface is a critical element in the performance assessment of nuclear waste geologic repository and in the environmental control and restoration of contaminated sites that are faced by many countries today. Thus there is an urgency in carefully thinking through the process coupling site characterization and predictive assessment, and in developing the necessary techniques and strategies needed for the coupling. This can most effectively be carried out through international cooperation. 9 The present short article attempts to provide a framework and definitions of technical issues for a study of this coupling.
2 REMARKS ON CONCEPTUAL MODELS A few preliminary remarks on conceptual models may be helpful before we discuss a proposed framework of technical issues. Since it is impossible to deterministically characterize the details of the geologic medium at a given site, it is necessary to develop a simplified conceptual model of the medium. The structures of the medium that are ignored or smoothed out in some fashion, in the simplified conceptual model, can have a major effect on the validity of this model. In some cases, these fine structures can be aggregated into an equivalent 'macroscopic' coefficient; this is sometimes the case for transport, where a macrodispersivity, valid at a large scale, can be defined. 7 To define such effective properties, some statistical properties of the fine structure must be known, but this change of scale has two consequences: (i) the governing equations of the conceptual model may change compared to the microscopic ones; and (ii) even if the required statistical properties are reasonably determined, this change of scale introduces an irreducible uncertainty. In some cases, however these simplified or smoothed fine structures may not be amenable to the definition of an effective property, and then the simplified conceptual model becomes even more uncertain. In any case, the simplification of the conceptual model introduces uncertainties in the prediction; consequently, a prediction which is not accompanied by uncertainty estimates is probably meaningless. The uncertainty that is discussed here is not the same as uncertainty due to
error ranges in input parameter values. Rather it is the uncertainty due to simplifications associated with the conceptual model of the geologic medium at the site. Such uncertainties can cause orders of magnitude errors in predictions of solute transport travel times. In the design of conceptual models it is important to recognize that the particular design depends on the predictive quantities required by the problem at hand. In nuclear waste geologic repository programs, these are called performance measures. In environmental restoration, these may be the criteria that determine the best clean-up or control strategies. With certain predictive quantities, uncertainties due to errors in conceptual models may be very large, while with other predictive quantities, such uncertainties may be much smaller. Hence, the particular design of conceptual models should be specified in relevance to predictive quantities required. In the context of this article, we will enlarge the conventional definition of conceptual model of the medium to include not only the structural features but also events and processes, the so-called FEP. 1'2'16 Thus the conceptual model has the following three elements: (1) Features. Geometric structure of the medium, spatial variations of property parameters, discontinuities (fractures and faults), boundary conditions (recharge boundaries, rainfall, sources and sinks), and also temporal variations of the above, except those accounted for in (2) below. (2) Events. Temporal changes, including those due to drastic events, such as earthquakes, glacial movements, and climatic changes, and alternative scenarios. Of particular concern is the current state of the geologic system which forms the 'initial conditions' for model simulation. In certain sites, the current conditions are not in steady state, which means that the system is still transient due to past events. These transients may have time scales of thousands of years, and are not important fo," shorter term predictions. However, for long-term predictions of thousands of years, they can play a significant role, and these past events must be identified and evaluated. (3) Processes. Physical, chemical, and biological processes that may occur in the medium such as density-driven flow and chemical sorption and matrix diffusion; coupled processes - - those involving jointly fluid flow, fracture aperture deformations and chemical reactivity. One must pay attention to slow processes that may show up in long-term predictions. These are often identified through studies of natural analog systems or in very accurate laboratory experiments. In numerical simulations, the features (1) are usually incorporated in the mesh design, the events (2) are in the input data, and the processes (3) are described in the
Solute transport in heterogeneous media governing equations. One can easily see that any errors in the conceptual model may cause drastic errors in the predictive results. The design of a conceptual model depends on site information and characterization experiments. It is, in general, an iterative process. 3'18 Ideally, one studies all site information available initially and considers the required predictive quantities. On the basis of such considerations, a conceptual model is proposed. From the proposed conceptual model, site characterization experiments will be designed and carried out. 15 These experiments should be of two types. The first is to determine the values of parameters that describe the conceptual model, and the second is to test its validity, i.e. to look for information and data that may invalidate the model for the particular required predictive quantity. With new information, the conceptual model may be substantiated or modified. With the modified conceptual model, further site characterization experiments will need to be made. Thus, this is an iterative procedure. The procedure does not necessarily produce a unique conceptual model. 4 Often alternative models may fit all the available data, which often are quite scanty (from prediction assessment point of view). Thus, two research groups that have slightly different strengths of expertise may choose to start with different conceptual models and obtain different modified or improved models by the iterative procedure. Then the question is how to discriminate among the alternative conceptual models, and if such discrimination is not possible, how should the results of these alternatives be combined. If the results of long-term predictions are similar, the alternative conceptual models need not to be discriminated against. Actually, they may even increase our confidence that the predictions may be physically correct, since the results are not sensitive to alternative conceptual models (all of which are consistent with available data). On the other hand, if the results are strongly divergent, the divergence is a measure of the uncertainties of prediction. If the uncertainty level is unacceptable, we may have to admit that we cannot do better and have to abandon the site, or look for other approaches. Or, we may review whether the predictive quantities required are too stringent and unnecessary for the overall problem at hand. Perhaps the required predictive quantities can be modified and still satisfy the problem needs. The iteration between site characterization and conceptual model development should be concluded based on predictive assessment. For example, the process can stop if the long-term predictions have an acceptable level of uncertainty within the model or if the uncertainty level cannot be reduced by further iterations. In this view, it is important to note that site characterization and predictive assessment are not a successive process where one continues from the point at which the other has ended. Rather, both should be
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performed simultaneously from beginning to conclusion. Finally the results based on a conceptual model with the associated uncertainties should be compared with those from alternative models, and together they form inputs for decision making. The plausible notion that a phased site characterization program will tend to reduce the uncertainty and converges towards reality is by no means established scientifically. The following example illustrates this point. In the UK, Mackay 1° developed an exercise where a 'true' conceptual model was made available to one team (using very sophisticated simulation techniques to generate lithofacies in a sedimentary basin, and parameter values at a very fine scale of 15 × 15 × 0.1 m). This team calculated the transport of radionuclides to the environment, for a given release scenario, on the 'exact' model. Another team, which was not shown the 'true' model, was asked to perform a three-staged site characterization program, and was given all the information that was asked for, essentially from a large series of boreholes and well tests, at the location and elevation that the team required. These data were extracted from the 'exact' model. At each phase of the site characterization, a predictive assessment was made, very much along the line of the above suggestions. To make a long story short, to the despair of the whole project, the more the site characterization program developed, the worse the predictive assessment became (compared to the 'exact' release), and furthermore, the predicted uncertainty given by the assessment team (which was using a probabilistic approach) was shown to decrease after each phase, but was completely out of range; the prediction and uncertainty underestimated the risk by about 4 orders of magnitude. Mackay and coworkers are studying the reasons for such a poor behavior. One of the present explanations is that the second team erroneously assumed that a confining clay layer was continuous, when in fact it was not. Its permeability was also underestimated, and transverse dispersivity was neglected. This example illustrates that it is not appropriate to presume that a phased site characterization program will always converge and provide a reasonable range of the uncertainty. A careful scientific evaluation at every step of the process is needed.
3 A FRAMEWORK OF TECHNICAL ISSUES TO BE STUDIED The discussions in the last section indicate that the areas of predictive assessment, site characterization and conceptual models are highly coupled and interwoven. To address the question of long-term predictions of solute transport and transformation in heterogeneous geologic media, one needs to consider all these together as a whole entity. We believe that the coupling of these
262
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areas is still in an early stage of development. Below we attempt to present a framework of technical issues that need to be studied. These technical issues are presented as separate items though we should keep in mind their iterative and coupled nature as emphasized above.
will influence the revision of the conceptual models, with the iteration terminated when predictive assessment is concluded. Planning for successive stages of site characterization should also be included in this site characterization program.
3.1 Initial screening methodology
3.4 Parameter determination
For a given problem at a new site, there is the question of what is the best approach for the initial screening. The strategy for studying the initial available information in the context of required predictive quantities (performance measures) needs to be developed. Associated with this is an evaluation of the reconnaissance information (regional geological, geophysical, geochemical and hydrological). Based on the information, possible initial conceptual models should be suggested.
For each alternative model, the effective, lumped, or representative (stochastic) parameters need to be defined as well as their space and time dependencies. We also need to understand whether these parameters are local property parameters or whether they are dependent on potential (pressure) fields. Associated with this is the need of studying the possibility of using spatial averaging or approximate representations which incorporate such dependencies. 6'13'17 After adequate theoretical understanding, a strategy needs to be developed to measure these parameters and their dependencies in the field or in a laboratory, and to determine as to what degree calibrations can be done. This includes determination of the parameters characterizing heterogeneity using, where possible, statistical techniques which also provide estimates of the uncertainty of the model parameters. Formal parameter estimation (inverse) methods may be useful here to identify large scale features and possibly model structure. It is important to realize that the calibration of parameters from the data collected in the site characterization program must proceed in parallel with the validation/improvement of the conceptual models. L~
3.2 Conceptual model development After the initial stage, the conceptualization of the site should cover all three parts of the conceptual model, FEP, as discussed in the previous section. The concern, here, is on: (i) the methods of identifying relevant features and structures; (ii) the methods of evaluating relevant events and scenarios; and (iii) the methods of determining relevant processes. With the identification of FEP, one will need to consider how to develop a conceptual model for heterogeneous systems, in terms of both porous and fractured rocks. Various models, such as geostatistical, fractal, Boolean random set of features, etc. have been used. 5'8'12'14 Then the question is whether it is possible to use one model as preferred over the others or whether one needs to study several models simultaneously as equally likely. In some cases the question of the appropriateness of a certain type of model of heterogeneity can be evaluated via established statistical inference techniques, whereas for other types of models appropriateness will be addressed more subjectively.
3.3 Design of site characterization program Based on the conceptual models proposed, the next issue is the strategy for designing a characterization program to carry out various field tests. The purpose of these field tests is to investigate and confirm all three parts of the proposed conceptual models (FEP). While some parts of the FEP may be obviously important, the others (especially slow processes and boundary conditions) need to be subjected to careful evaluation, so that their relevance and importance to the entire problem can be thoroughly understood. Data collection programs should be systematically designed to permit evaluation of alternative models, recognizing that different conceptual models of heterogeneity may have conflicting data requirements. The results of site characterization
3.5 Simulation techniques To perform calculations on the heterogeneous models includes not only the generation of heterogeneous fields, but also the solution of flow and transport through such systems. These calculations should also be concerned with the sensitivities of various parameters, or in other words, with the uncertainties due to parameter error ranges. Thus the desired accuracy of these input parameters can be estimated. This will be considered in the context of the parameter measurement program discussed in Section 3.4. The simulation should strive to improve computational efficiencies to enable multiple realization studies. The question of non-uniqueness and how to handle results from multiple realizations should be addressed. Techniques also need to be developed on performing conditioning with various field data (both hard and soft data), taking into account the measurement scales of such data.
3.6 Field test methodology Under this issue, one must consider how to use results from pressure and tracer tests to better define the heterogeneous model, including the anisotropy effect
Solute transport in heterogeneous media which is likely to be present in the field. One needs to determine measurement scales for a heterogeneous system for single well tests, interference tests, and tracer transport tests. In many cases multiple experiments at multiple locations may be necessary. Then the question is how to integrate and use these multiple results. Because tracer tests are usually localized within 10 to 103m range, the use of such results to make predictions over a scale of several kilometers can introduce large errors. On the other hand, if a multiple tracer experiment is performed at several locations, the integration of the results may be useful to reduce such errors. We need to develop approaches to do this integration and estimate the improved confidence level. In low permeability media, such as clay, one must remember that both pressure tests and tracer tests (even under extreme conditions) can at best provide information on the scale of a few meters. There is little hope of performing tests over the entire potential migration distance, even in small steps, and the integration can be very uncertain. 3.7 Predictive assessment
To arrive at successful predictive assessment, we need to know how to combine the results from alternative conceptual models, all of which satisfy the main information and data from the site. Uncertainties due to alternative models, parameters ranges and other sources should be evaluated together to define the overall uncertainty or confidence level. The question is then whether the overall uncertainty in the required predictive quantities is acceptable for decision making. If not, either further site measurement and modeling studies should be made, or a revision of the required predictive quantities (while still satisfying the needs of decision-makers on the problem at hand) may be necessary for the success of the whole assessment. 3
4 CONCLUDING REMARKS
The above seven major scientific issues are defined to stimulate the kind of integrated research on long-term prediction of transport and transformation in the subsurface that is required to address critical problems of national and international importance. In current national efforts, while many of the above items are explicitly or implicitly addressed, often one or more of the above items are ignored or treated superficially, thereby reducing significantly the credibility of the scientific results needed for decision making. We believe these are important questions that should be investigated in programs of coupled site characterization and predictive assessment. The costs of these investigations will turn out to be negligible as compared to the societal
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consequences of erroneous scientific inputs to the decision-makers.
ACKNOWLEDGMENTS We appreciate the discussions over the years with members of the international I N T R A V A L 9 project, which have helped to shape many of the ideas in this paper. The paper was prepared during the sabbatical year of the second author (L.G.) at the Lawrence Berkeley Laboratory whose support is gratefully acknowledged. The work is jointly supported by grants from the Swedish Nuclear Power Inspectorate, Stockholm, Power Reactor and Nuclear Fuel Development Corporation, Japan and by the Office of Basic Energy Sciences, Engineering and Geosciences Division, Office of Energy Research of the US Department of Energy, under Contract DE-AC03-76SF00098.
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