Algorithm The numerical technique embodied in the computer code.
Calibration A test of a model with known input and output information that is used to adjust or estimate factors for which data are not available.
Computer code The assembly of numerical techniques, bookkeeping, and control languages that represents the model from acceptance of input data and instruction to delivery of output.
Model An assembly of concepts in the form of a mathematical equation that portrays understanding of a natural phenomenon.
Sensitivity The degree to which the model result is affected by changes in a selected input parameter.
Validation Comparison of model results with numerical data independently derived from experiment or observation of the environment.
Verification Examination of the numerical technique in the computer code to ascertain that it truly represents the conceptual model and that there are no inherent numerical problems associated with obtaining a solution.
The expression of chemical fate can be computerized using a code to perform the computations and predict the results when inputs simulating conditions of interest are provided. Two critical aspects of the use of computer codes for predicting geochemical fate are the verification and validation of the models on which the codes are based.
In addition to the limited availability of validation, the following are some of the problems found in computer and mathematical modeling120:
1. The data on thermodynamic properties of many relevant water-miscible organic species are either incomplete or unavailable.
2. Many minerals are solid solutions (e.g., clays, amphiboles, and plagioclase feldspars). Solid-solution models are either not available or appropriate algorithms have not been incorporated into computer codes.
3. Models describing the adsorption of water-miscible organic compounds on natural materials have not been correlated with field observations under typical injection-zone conditions. Few computer codes contain algorithms for calculating the distribution of species between the adsorbed and aqueous states.
4. Calcium-sodium-chloride-type brines (which typically occur in deep-well-injection zones) require sophisticated electrolyte models to calculate their thermodynamic properties. Many parameters for characterizing the partial molal properties of the dissolved constituents in such brines have not been determined. (Molality is a measure of the relative number of solute and solvent particles in a solution and is expressed as the number of gram-molecular weights of solute in 1000 g of solvent.) Precise modeling is limited to relatively low salinities (where many parameters are unnecessary) or to chemically simple systems operating near 25°C.
5. Computer codes usually calculate only the thermodynamically most stable configuration of a system. Modifications can simulate nonequilibrium, but there are limitations on the extent to which codes can be manipulated to simulate processes that are kinetically (rate) controlled; the slow reaction rates in the deep-well environment compared with groundwater movement (i.e., failure to attain local homogeneous or heterogeneous reversibility within a meter or so of the injection site) create particular problems.
6. Little is known about the kinetics of dissolution, precipitation, and oxidation-reduction reactions in the natural environment. Consequently, simulating the kinetics of even more complicated injection- zone chemistry is very difficult.
Bergman and Meyer121 point out a particularly relevant problem with mathematical models. The relative reliability of mathematical models (compared with physical models based on empirical field or laboratory studies) decreases rapidly as the number of environmental pollutants being modeled increases (see Figure 20.8). Consequently, mathematical models tend to be less cost-effective for complex wastestreams than physical (empirical) models.
Most of the chemical processes discussed before (acid-base equilibria, precipitation-dissolution, neutralization, complexation, and oxidation-reduction) are interrelated; that is, reactions of one type may influence other types of reactions, and consequently must be integrated into aqueous- and solution-geochemistry computer codes.
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