MARIO´ ABELGON ¸CALVES Faculdade de Ciˆencias da Universidade de Lisoba Lisbon, Portugal
INTRODUCTION
A geochemical model, like any other model, is an abstract representation of a given reality, normally reduced to a set of master variables and described by mathematical equations, which aim at representing natural processes that occur in a system. The output data of these models are a quantitative representation of an outcome that can be observable in the natural system or subject to experimental validation. This operational definition of a geochemical model suggests that a model is nothing more than a set of mathematical equations, which is not strictly true. Any set of equations representing a process must be bounded within limits imposed by nature; otherwise the outcome of these models may be totally unrealistic. Thus, the modeler is called to
GEOCHEMICAL MODELS 139 set proper initial and boundary conditions such that
the natural system is correctly represented, and to feed the model with the correct parameters, most of them previously determined experimentally. The quality and self-consistency of the thermodynamic data used, as well as other parameters, such as kinetic ones, are of fundamental importance for the outcome of geochemical models. This issue is considered one of the most critical in any geochemical model. When using any of the available computer programs for geochemical modeling, the choice of the thermodynamic database is left to the modeler. Several compiled thermodynamic databases are available, but this does not mean that all data is internally self-consistent. It is, however, possible to find some databases that are self-consistent relative to some set of chemical species.
Geochemical models have been extensively reviewed in the literature, such as Yeh and Tripathi (1), Mangold and Tsang (2), Appelo and Postma (3), Nordstrom and Munoz (4), and Nordstrom (5). Some textbooks on aqueous geochemistry or geochemical modeling also discuss and include several examples and case studies where specific geochemical computer models have been used (6–8). Of relevance is also the book of Albar`ede (9), which provides a wealth of mathematical methods and extensive examples on how to build and develop geochemical models in a truly wide range of applications.
COMPONENTS OF GEOCHEMICAL MODELS
Geochemical models may have several components that can be combined in different configurations. These components may be coupled within the model or may imply certain feedback loops.
An essential component of these models is chemical reactions, and these determine, for example, the chemical speciation in solution or the saturation states relative to solid phases. Within these reactions, biological processes may be involved, which take active part in certain reactions, boosting their kinetics (catalysts), hindering the formation of certain compounds (inhibitors), or just transforming chemical compounds (such as the biodegradation of organic pollutants).
Chemical species and compounds in solution are carried away with the water by advection and disperse through the medium by molecular diffusion. These are the components of transport of chemical elements in solution, which determine their spreading in the system.
Transport of chemical elements are thus a function of water velocity and, consequently, of fluid flow in the sys- tem. Physical parameters of the system, such as porosity and permeability, determine the patterns of fluid flow and velocity variations in space and time. In the coupled reac- tive transport models, precipitation/dissolution of mineral phases can reduce/increase the porosity and permeability of the medium and change fluid flow patterns.
In certain systems, such as large-scale sedimentary basins, it is necessary to consider heat transport. Heat can increase the kinetics of several chemical reactions and induce fluid flow along thermal gradients.
TYPES OF GEOCHEMICAL MODELS
The description of the different types of geochemical models is not extensive and outlines only their main characteristics, as presented by Zhu and Anderson (8). Geochemical models are generally grouped according to their level of complexity. The simplest ones are the speciation-solubility models. These models are meant to compute the thermodynamic equilibrium of species in a system at a given temperature and pressure. Therefore, the output comprises the concentration and activity of the various ionic and molecular species in a solution. It also includes the saturation state of the solution relative to several minerals and the distribution of stable species on surfaces or ion-exchange sites in equilibrium with the aqueous solution.
Reaction-path models calculate the sequence of equi- librium states of a system in response to incremental additions (or subtractions) of mass to the system, change in temperature and/or pressure, and mass transfer between phases in the system. The configuration of these models can be diverse and includes the addition of a reactant (such as a titration), fixation of the activity of a chemical species modeling a buffered system, incremental feeding of a reactant solution (as in a continuous stirred tank reactor), and kinetic controls of heterogeneous reactions.
Another group of models corresponds to inverse mass balance models. These specialized models derive the initial composition of a water solution from its actual final composition, which takes into account the reactions and mass transfer between water and solid and/or gas phases, in agreement with the available data of a system. Thus, the initial composition of the water is determined by subtracting the amount of dissolved species caused by reaction with minerals and other phases in the system from its final composition. Inverse mass balance calculations may also involve the determination of the fractions of different waters that have, at some given time, mixed completely.
Finally, coupled reaction-transport models are the most complex. In these models, both the partial differential equations describing the advection-dispersion transport and the set of algebraic equations describing the chemical equilibrium are solved. These models can also include heat transfer and fluid flow, thus increasing the number of equations to be solved. The level of complexity depends also on the details of chemical reactions considered. These details can include multicomponent reactive transport, which accounts for the kinetics of mineral dissolution and precipitation; adsorption onto mineral surfaces; and radioactive decay, to name but a few.
FINAL REMARKS: MODEL VALIDATION AND USEFULNESS The outcome of geochemical models can be either observable in nature or subject to experimental testing. Both processes are fundamental for model validation, and they are surely the ultimate test that a model must face. However, the process is not as simple as it may seem. Usually, geochemical models may adequately describe several processes and mechanisms in nature, but nature’s
140 GEOCHEMICAL MODELING-COMPUTER CODES inherent complexity puts a limit to model precision and accuracy, which limits considerably its proper validation. Normally, the number of variables assumed within a model is limited and corresponds to a fraction of the ones found in nature. In such complex models, slight variations in parameters may induce diverse outcomes, such as in climate modeling. Thus, models are not only helpful tools to gain insight into the workings of nature, but they also must have some sort of predictive power. A model outcome may not be accurate enough to make a prediction relative to contaminant dispersion in a groundwater system, for example. However, it may give enough confidence to help make decisions on regulatory issues.
BIBLIOGRAPHY
1. Yeh, G.T. and Tripathi, V.S. (1989). A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components. Water Resour. Res. 25: 93–108.
2. Mangold, D.C. and Tsang, C.-F. (1991). A summary of subsurface hydrological and hydrochemical models. Rev. Geophys. 29: 51–79.
3. Appelo, C.A.J. and Postma, D. (1993). Geochemistry, Ground- water and Pollution. A.A. Balkema, Rotterdam.
4. Nordstrom, D.K. and Munoz, J.L. (1994). Geochemical Ther- modynamics, 2nd Edn. Blackwell, Boston, MA.
5. Nordstrom, D.K. (2004). Modeling low-temperature geochem- ical processes. In: Treatise on Geochemistry—Surface and Ground Water, Weathering, and Soils. J.I. Drever (Ed.). Vol. 5, pp. 37–72.
6. Langmuir, D. (1996). Aqueous Environmental Geochemistry. Prentice-Hall, Upper Saddle River, NJ.
7. Drever, J.I. (1997). The Geochemistry of Natural Waters, 3rd Edn. Prentice-Hall, Upper Saddle River, NJ.
8. Zhu, C. and Anderson, G. (2002). Environmental Applications of Geochemical Modeling. Cambridge University Press, Cambridge, UK.
9. Albar`ede, F. (1996). Introduction to Geochemical Modeling. Cambridge University Press, Cambridge, UK.