Uncertainty in geochemical modeling

Calculating a geochemical model provides not only results, but uncertainty about the accuracy of the results. Uncertainty, in fact, is an integral part of modeling that deserves as much attention as any other aspect of a study. To evaluate the sources of error in a study, a modeler should consider a number of questions  

As Hem (1985) notes, a chemical analysis with concentrations reported to two or three, and sometimes four or five, significant figures can be misleadingly authoritative. Analytical accuracy and precision are generally in the range of 2 to 10%, but depend on the technique used, the skill of the analyst, and on whether or not the constituent was present near the detection limit of the analytical method. The third digit in a reported concentration is seldom meaningful, and confidence should not necessarily be placed on the second. 

Care should be taken in interpreting reported pH values, which may have been determined in the field or in the laboratory after the sample had been stored for an unknown period of time. Only the field measurement of pH is meaningful and, in the case of a groundwater, even the field measurement is reliable only if it is made immediately after sampling, before the water can exchange CO2 with the atmosphere. 

The following example shows why this is important. The calculations in this book make use of the dataset compiled by Thomas Wolery, Ken Jackson, and numerous co-workers at Lawrence Livermore National Laboratory (the LLNL dataset Delany and Lundeen, 1989), which is based in part on a dataset developed by Helgeson et al. (1978). The dataset includes a number of Cu-bearing species and minerals, including the cupric species Cu++ and Cu(OH)+ that are dominant at room temperature under oxidized conditions in acidic and neutral solutions. 

At pH values greater than about 9.5, the species Cu(OH)2, Cu(OH)J, and CufOH) — dominate the solubility of cupric copper by some orders of magnitude (Baes and Mesmer, 1976) these species, however, are not included in the database version used in this book. To construct a valid model of copper chemistry in an oxidizing, alkaline solution, the modeler would need to extend the database to include these species. 

10 Use of the dump option to simulate scaling. The pore fluid is initially in equilibrium with minerals in the formation. As the fluid enters the well bore, the minerals are isolated (dumped) from the system. The fluid then follows a polythermal, sliding fugacity path as it ascends the wellbore toward lower temperatures and pressures, depositing scale. 

Care should be taken in interpreting reported pH values, which may have been determined in the field or in the laboratory after the sample had been stored 

11 Configuration of a continuum model of water-rock interaction in a system open to groundwater flow, showing positions of reaction fronts as they migrate through the system. 

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Caveat Emptor Modelers should realize that activity coefficients are affected by all solution components, and that simple, all-inclusive equations such as those above, which rely on the ionic strength (/) to work equally well for all compositions, cannot be expected to be very accurate. Moreover, the degree to which they are inaccurate in specific cases is usually not known. Undoubtedly, the situation is helped considerably by the fact that in equilibrium calculations the errors in calculated activity coefficients of products and reactants cancel one another to a large extent. Nevertheless, uncertainties in activity coefficients in geochemical models are always a major concern. 

Certain geochemical processes can both retard the transport of radionuclides, delaying arrival times at the receptor location(s), and reduce radionuclide concentrations at the point of exposure. An understanding of geochemical processes that influence radionuclide transport may be used to compensate for uncertainties in hydrologic models of the Yucca Mountain system (Simmons et al., 1995). 

While over the past ten years, our ability to measure U-series disequilibria and interpret this data has improved significantly it is important to note that many questions still remain. In particular, because of uncertainties in the partition coefficients, fully quantitative constraints can only be obtained when more experimental data, as a function of P and T as well as source composition, become available. Furthermore, the robustness of the various melting models that are used to interpret the data needs to be established and 2D and 3D models need to be developed. However, full testing of these models will only be possible when more comprehensive data sets including all the geochemical parameters are available for more locations and settings. 

Given this array of error sources, how can a geochemical modeler cope with the uncertainties implicit in his calculations The best answer is probably that the modeler should begin work by integrating experimental results and field observations into the study. Having successfully explained the experimental or field data, the modeler can extrapolate to make predictions with greater confidence. 

The fact that basic thermodynamic data are imprecisely known means that model results such as p values, SI values, and so on, will all be to some extent imprecise as well. The imprecision of the input data is propagated through the calculation procedure and appears in the results. The nature of this propagation has not been extensively investigated, but it depends not only on uncertainties in the thermodynamic and analytical data, but also on the nature of the geochemical system involved. See Anderson (1976, 1977) and Criscenti el al. (1996) for discussions. 

System Condition Redox and Metastabilitv. Two major sources of uncertainty in modeling aqueous systems are the redox potential and metastability these are frequently acknowledged as conceptual problems, but discussion of the error which results from improper assumptions and calculations is generally avoided. The Eh or electrochemical potential which is computed from a potential measured with a platinum electrode, is used in almost all geochemical models as a system parameter. 

A clear understanding of the limits of applicability of geochemical models and of the uncertainties and potential errors in the analytical and thermodynamic data is essential to the correct use of SOLMINEQ.88 and the interpretation of the results. These limits can be primarily divided into four different groups, which are errors and uncertainties in the physical parameters the chemical analysis and in the thermodynamic data and extrapolation of the equations and formulas beyond their range of applicability. 

The problem of activity coefficient scale is more important when the measured pH is introduced in geochemical calculations. The measured pH is not likely to be on the same activity coefficient scale as the aqueous model because the buffers used to define pH are conventional (28). Even if the pH is on the same scale as the aqueous model, uncertainties in its measurement in brines, such as due to liquid-junction potentials (28.38). will always introduce inconsistencies. Consequently, it is unlikely that the measured pH will be consistent with the particular scale used for the individual ions. 

The e(Ni, X ) values are unlikely to be identical, and estimated uncertainties have been increased for values obtained from experiments in which a considerable part of the background electrolyte was replaced by the complex-fonning anion. In some cases it has been necessary to make very arbitrary assumptions in generation of association constants for weak complexes. If used consistently, these should have little or no impact on geochemical modelling using the TDB database, or on regeneration of the experimental values. 

Ekberg, C. (2002) Uncertainties connected with geochemical modelling of waste disposal in mines. Mine Water Environ., 21, 45-51. 

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