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Home , Equilibrium chemistry, Geochemical modeling

5.02 Modeling Low- Geochemical Processes D. K. Nordstrom US Geological Survey, Boulder, CO, USA

5.02.1 INTRODUCTION 1 5.02.1.1 What Is a Model? 2 5.02.2 MODELING CONCEPTS AND DEFINITIONS 3 5.02.2.1 Modeling Concepts 3 5.02.2.2 Modeling Definitions 3 5.02.2.3 Inverse Modeling, Mass Balancing, and Mole Balancing 4 5.02.3 SOLVING THE PROBLEM 6 5.02.4 HISTORICAL BACKGROUND TO GEOCHEMICAL MODELING 7 5.02.5 THE PROBLEM OF ACTIVITY COEFFICIENTS 8 5.02.5.1 Activity Coefficients 8 5.02.5.2 Saturation Indices 10 5.02.6 GEOCHEMICAL DATABASES 10 5.02.6.1 Thermodynamic Databases 11 5.02.6.2 Electrolyte Databases 11 5.02.7 GEOCHEMICAL CODES 11 5.02.7.1 USGS Codes 12 5.02.7.2 LLNL Codes 13 5.02.7.3 Miami Codes 13 5.02.7.4 The Geochemist’s Workbencht 13 5.02.7.5 REDEQL-MINTEQ Codes 13 5.02.7.6 Waterloo Codes 15 5.02.7.7 Harvie–Møller–Weare Code 15 5.02.7.8 Windemere Humic Aqueous Models 15 5.02.7.9 Additional Codes 16 5.02.8 WATER–ROCK INTERACTIONS 17 5.02.8.1 Aqueous Speciation 17 5.02.8.2 Modeling Sorption Reactions 18 5.02.8.3 Model Simulations of Reactions 18 5.02.8.4 Reactive-Transport Modeling in Streams 25 5.02.8.5 Geochemical Modeling of Catchments 25 5.02.8.6 Reliability of Geochemical Model Simulations 27 5.02.9 FINAL COMMENTS 29 ACKNOWLEDGMENTS 30 REFERENCES 31

A model takes on the quality of theory when it ab- 5.02.1 INTRODUCTION stracts from raw data the facts that its inventor per- ceives to be fundamental and controlling, and puts Geochemical modeling has become a popular these into relation to each other in ways that were and useful tool for a wide number of appli- not understood before—thereby generating predic- tions of surprising new facts. cations from research on the fundamental proc- H. F. Judson (1980), The Search for esses of water–rock interactions to regulatory requirements and decisions regarding permits

1 2 Modeling Low-Temperature Geochemical Processes for industrial and hazardous wastes. In low- This chapter outlines the main concepts and temperature environments, generally thought of key developments in the field of geochemical as those in the temperature range of 0–100 1C modeling for low-temperature environments and close to atmospheric (1 atm ¼ and illustrates their use with examples. It pro- 1.01325 bar ¼ 101,325 Pa), complex hydrobio- ceeds with a short discussion of what modeling geochemical reactions participate in an array is, continues with concepts and definitions of interconnected processes that affect us, and commonly used, and follows with a short his- that, in turn, we affect. Understanding these tory of geochemical models, a discussion of complex processes often requires tools that databases, the codes that embody models, and are sufficiently sophisticated to portray multi- recent examples of how these codes have been component, multiphase chemical reactions used in water–rock interactions. An important yet transparent enough to reveal the main new stage of development has been reached in driving forces. Geochemical models are such this field with questions of reliability and val- tools. The major processes that are required idity of models. Future work will be obligated to model include mineral dissolution and pre- to document ranges of certainty and sources of cipitation; aqueous inorganic speciation and uncertainty, sensitivity of models and codes to complexation; solute and desorpt- parameter errors and assumptions, propagat- ; ion exchange; oxidation–reduction, or ion of errors, and delineation of the range of transformations; gas uptake or pro- applicability. duction; organic matter speciation and com- plexation; evaporation; dilution; water mixing; reaction during fluid flow; reaction involving 5.02.1.1 What Is a Model? biotic interactions; and photoreaction. These processes occur in rain, snow, fog, dry atmos- A ‘‘model’’ has a relation to ‘‘reality,’’ but phere, interactions with flora and fauna, vege- reality is experiential, and the moment we at- tative decay, soils, bedrock , streams, tempt to convey the experience we are seriously rivers, lakes, , estuaries, brines, constrained by three limitations: our own abil- and diagenetic environments. Geochemical ity to communicate, the capability of the com- modeling attempts to understand the redistri- munication medium to portray the experience, bution of elements and compounds, through and the ability of the person receiving the com- anthropogenic and natural means, for a large munication to understand it. Communication range of scale from nanometer to global. requires the use of language and the use of ‘‘Aqueous ’’ and ‘‘environmental percepts and concepts, and the process of per- geochemistry’’ are often used interchange- ceiving, conceiving, and communicating is an ably with ‘‘low-temperature geochemistry’’ abstracting process that removes us from the to emphasize hydrologic or environmental immediate experience. Any attempt to trans- objectives. form an experience into language suffers from Recognition of the strategy or philosophy this abstraction process so that we lose the im- behind geochemical modeling is not often dis- mediate experience to gain some understanding cussed or explicitly described. Plummer (1984, of it. The problem is to transform existential 1992) and Parkhurst and Plummer (1993) com- knowledge to communicated or processed know- pare and contrast two approaches for modeling ledge and to eliminate unnecessary subjectivity : (1) ‘‘forward model- from objective knowledge. To communicate ing,’’ which predicts water compositions from knowledge, we must use a simplified and ab- hypothesized reactions and user assumptions stract symbolism (words, mathematics, pictures, and (2) ‘‘inverse modeling,’’ which uses specific diagrams, analogs, allegories, three-dimen- water, mineral, and isotopic compositions to sional physical constructs, etc.) to describe a constrain hypothesized reactions. These ap- material object or phenomenon, that is, a proaches simply reflect the amount of field in- model. Models take on many forms but they formation available. With minimal information are all characterized by being a simplification on a site, a modeler is forced to rely on forward or idealization of reality. ‘‘y models include modeling. Optimal information would include only properties and relationships that are needed detailed mineralogy on drill cores or well cut- to understand those aspects of the real system tings combined with detailed water analyses at that we are interested in y’’ (Derry, 1999). varying depths and sufficient spatial distribu- Assumptions, both explicit and implicit, are tion to follow geochemical reactions and mix- made in model construction, because either we ing of waters along defined flow paths. With do not know all the necessary properties or we do optimal information, a modeler will depend on not need to know them. Hopefully, models have inverse modeling. caught the essential properties of that which Modeling Concepts and Definitions 3 they are attempting to portray so that they are when these are not models but computer codes. useful and lead to new insights and to better Some of the models used by these codes are the answers for existing questions and problems. same so that a different code name does not Science and scientific models begin as ideas necessarily mean a different model is being used. and opinions that are formalized into a language, often, but not necessarily, mathe- matical language. Prior to the late nineteenth 5.02.2 MODELING CONCEPTS AND century, models (not usually called as such) DEFINITIONS were developed to explain and generalize 5.02.2.1 Modeling Concepts observations of phenomena. Beginning in the late nineteenth century, a new perspective Many different forms of models are utilized, developed in science that became known as usually dictated by the objectives of research. logical positivism. This perspective emphasized ‘‘Conceptual models’’ are the most fundamen- the predictive capability of science through hy- tal. All of us have some kind of concept of pothesis testing, or the hypothetico-deductive water–rock interactions. For a groundwater description of science and modeling. Useful interacting with aquifer , one might and rigorous science (and models) should have conceive that most minerals would be undersat- testable consequences. The emphasis on testa- urated in the area of recharge but that some bility, or falsifiability, is considered a funda- minerals (those that dissolve fastest) would be- mental attribute (Popper, 1934). Greenwood come saturated at some point down gradient, (1989) stated that the word model should be having reached their equilibrium (a reserved ‘‘y for well-constrained logical prop- state of ‘‘partial equilibrium’’). The conceptual ositions, not necessarily mathematical, that model can be formalized into a set of mathe- have necessary and testable consequences, and matical equations using chemical principles, the avoid the use of the word if we are merely ‘‘mathematical model,’’ entered into a computer constructing a scenario of possibilities.’’ Hence, program, the ‘‘code,’’ and predictions made to a scientific model is a testable idea, hypothesis, test the assumptions (and the databases) against theory, or combination of theories that pro- the results from real-field data. This exercise vides new insight or a new interpretation of an helps to quantify and constrain the possible re- existing problem. An additional quality often actions that might occur on the subsurface. attributed to a model or theory is its ability to Mathematical equations for complex interacting explain a large number of observations while variables are not always solved exactly and, maintaining simplicity (Occam’s razor). The therefore, systems of numerical approximations, simplest model that explains most of the or ‘‘numerical models,’’ have been developed. observations is the one that will have the most Alternatively, an experiment could be set up in appeal and applicability. the laboratory with columns made of aquifer Models are applied to a ‘‘system,’’ or a por- material with groundwater flowing through to tion of the observable universe separated by simulate the reactions, the ‘‘experimental mod- well-defined boundaries for the purpose of el’’ or ‘‘scale model.’’ Having obtained results investigation. A chemical model is a theoreti- from a mathematical or scale model, some un- cal construct that permits the calculation of expected results often occur which force us to chemical properties and processes, such as the change our original conceptual model. This ex- thermodynamic, kinetic, or quantum mechan- ample demonstrates how science works; it is an ical properties of a system. A geochemical ongoing process of approximation that iterates model is a chemical model developed for between idea, theory, observational testing of geologic systems. Geochemical models often theory, and back to modifications of theory or incorporate chemical models such as ion asso- development of new theories. ciation (IA) and aqueous speciation together with mineralogical data and assumptions about mass transfer to study water–rock interactions. 5.02.2.2 Modeling Definitions A computer code is obviously not a model. A In low-temperature geochemistry and geo- computer code that incorporates a geochemical chemical modeling, it is helpful to define several model is one of several possible tools for inter- words and phrases in common use. preting water–rock interactions in low-temper- Aqueous speciation. The distribution of dis- ature geochemistry. The computer codes in solved components among free , ion pairs, common use and examples of their application and complexes. For example, dissolved iron will be the main focus of this chapter. It is in mine drainage (AMD) can be present unfortunate that one commonly finds, in the as Fe2þ (free ferrous iron), FeSO0 (ion literature, reference to the MINTEQ model or ðaq:Þ 4ðaq:Þ 3þ 2þ the PHREEQE model or the EQ3/6 model pair), Feðaq:Þ (free ferric iron), FeðOHÞðaq:Þ, and 4 Modeling Low-Temperature Geochemical Processes þ FeSO4ðaq:Þ species. These species are present modeling is based on mass or mole balancing, in a single-phase, aqueous . Aqueous and thermodynamic and kinetic data are not speciation is not uniquely defined but depends necessary although saturation indices provide on the theoretical formulation of mass-action useful constraints. Relativistic kinetics (i.e., re- equilibria and activity coefficients, that is, it is lative mineral reaction rates) are deduced as model dependent. Some aqueous speciation can part of the results. be determined analytically but operational def- initions and assumptions are still unavoidable. Phase. Commonly defined as a uniform, 5.02.2.3 Inverse Modeling, Mass Balancing, homogeneous, physically distinct, and mechan- and Mole Balancing ically separable part of a system. Unfortunately, mineral phases are often not uniform, homo- A key concept to interpreting water–rock in- geneous, or mechanically separable except in teractions is mass balancing between water theory. Sophisticated microscopic and spec- chemistry data, mineral/gas transformations, troscopic techniques and operational definitions and biological uptake or release. The mass- are needed to define some mineral phases. balance concept is a means of keeping track of Likewise, the phase can have reacting phases that transfer mass during fluid gradients based on density gra- flow. It is an integral part of the continuity dients that may be caused by temperature and equation for steady-state and transient-state compositional differences. flow conditions. Formalizing mass balances Phase speciation. The distribution of compo- for solutes during fluid flow is simple if the nents among two or more phases. For example, solutes are conservative but more complex in a wet soil, iron can be present in at least when reactions take place. For applications three phases: as the X-ray amorphous oxyhy- to the environment, different types of mass droxide, ferrihydrite; as goethite; and as dis- balances have been used and these require some solved aqueous iron. explanation. Mass transfer. The transfer of mass between Three types of mass-balance approaches will two or more phases as in the precipitation and be discussed. In its simplest form, mass ba- dissolution of minerals in a groundwater. lancing is utilizing the law of conservation of Reaction-path calculation. A sequence of mass that reflects that any partitioning of mass mass-transfer calculations that follows defined through a system must sum to the total. The phase (or reaction) boundaries during incre- first type of mass-balance approach, catchment mental steps of reaction progress. mass balances (or mass fluxes), uses ‘‘input– Mass transport. Solute movement by mass output’’ accounting methods to identify overall flow of a fluid (could be liquid, gas, or mixture gains and losses of solutes during the flow of of solid and liquid and/or gas). water from meteoric inputs to stream outflow Reactive transport. Mass transfer combined at a specified point (Bormann and Likens, with mass transport; commonly refers to geo- 1967; Likens et al., 1977). Pacˇes (1983, 1984) chemical reactions during stream flow or called this the integral mass-balance approach: groundwater flow.

Forward geochemical modeling. Given an in- ½Mass ratein mass rateout7mass rateinternal itial water of known composition and a rock of known mineralogy and composition, the rock ¼ rate of accumulation=depletion ð1Þ and water are computationally reacted under a given set of conditions (constant or variable In difference form temperature, pressure, and water composition) to produce rock and water (or set of rocks and Dm Dm Dm waters). In forward modeling, the products are trans þ int ¼ tot ð2Þ inferred from an assumed set of conditions Dt Dt Dt (equilibrium or not, phases allowed to precip- itate or not, etc.) and thermodynamic and/or where Dmtrans/Dt is the difference in rate of kinetic data are necessary. mass (of some component) transported into Inverse geochemical modeling. Given a set of and out of the system via fluid flow, Dmint/Dt two or more actual water analyses along a flow the rate of mass produced or removed from path that have already reacted with a rock of the fluid by internal , and known mineralogy, the reactions are inferred. Dmtot/Dt the total rate of change in mass for a In inverse modeling the reactions are computed component in the fluid. Steady-state conditions from the known field conditions (known are often assumed so that the accumulation/ water chemistry evolution and known miner- depletion rate becomes 0 and the difference alogy) and assumed mineral reactivity. Inverse between input and output for a component Modeling Concepts and Definitions 5 becomes equal to the internal processes that bp the mass-transfer coefficient of the pth produce or remove that component. These phase, and j the number of phases (Plummer mass rates of change are usually obtained as et al., 1983). Because groundwaters are fre- integral mass fluxes (computed as discharge quently mixtures of different water quality times concentration). types, mixing fractions can also be employed For catchments in which input from precip- in the matrix array. Redox chemistry can be itation and dry deposition can be measured and included through conservation of electrons and the output through a weir or similar confining water balance can be used to simulate evap- outflow can be measured, the difference in oration. Plummer (1984) has called this type of solute flow averaged over an appropriate pe- modeling the inverse method, because it pro- riod of time provides an accounting of solutes ceeds in a reverse manner to that of forward gained or lost. Overviews and summaries of modeling, that is, it backs out the probable re- essential concepts of catchment mass balances actions from known data on water chemistry, have been presented by Drever (1997a, b), Bas- isotopes, and mineralogy. Parkhurst (1997) sett (1997), and Bricker et al. (Chapter 5.04). simply refers to it as mole balancing. Seman- The input–output mass balance treats the tics aside, this model is developed for water– catchment as a black box, but knowledge of rock interactions from ‘‘a set of mixing biogeochemical processes, use of lab experi- fractions of initial aqueous solutions and mole ments, additional field data, and well-control- transfers of minerals and gases that quanti- led small-scale field-plot studies can help to tatively account for the chemical composition identify the dominant processes causing the of the final solution’’ (Parkhurst, 1997). gain or loss of a particular solute. Load (or Two papers point out the fundamental na- mass flux) calculations for a river or stream use ture of mole balancing for interpreting ground- the same type of accounting procedure. water chemistry. Plummer (1984) describes A second type of mass-balance approach is the attempts to model the Madison Limestone quantitative incorporation of mass balances aquifer by both forward and inverse methods. within a reactive-transport model and could Two valuable conclusions from this paper were be applied to groundwaters, surface waters, that information gained from mole balancing and surface water–groundwater interactions. was needed to provide relativistic reaction Pacˇes (1983, 1984) calls this the local mass-bal- rates for forward modeling and that even with ance approach. There are numerous examples these rates, the well water compositions could and explanations of this approach (e.g., Freeze not be closely matched, whereas they can be and Cherry, 1979; Domenico and Schwartz, exactly matched with inverse modeling. Fur- 1990). thermore, forward modeling required much A third type of mass-balance approach is to more effort and contained more uncertainty. leave the physical flow conditions implicit, as- Similar conclusions were reached by Glynn and sume steady-state flow along a flow line in an Brown (1996) in their detailed study of aquifer, and account for observed chemical the acidic plume moving in the Pinal Creek changes that occur as the groundwater flows Basin. They found that the best approach was from recharge to discharge (Plummer and to pursue a series of mole-balance calculations, Back, 1980). This approach was introduced improving their modeling with each re-exami- formally by the classic paper of Garrels and nation of the phases and reactions considered. Mackenzie (1967), who calculated mass bal- Then they took their refined mole-balance re- ances derived from springwater data in the Si- sults and made further improvements by for- erra Nevada Mountains of California. The ward modeling. Inverse modeling, however, modeler begins with aqueous chemical data was a key to their successful interpretation. The along a flow path in an aquifer (or catchment) complex nature of interpreting a dispersed con- of known mineralogy and accounts for changes taminant plume and the associated mineral in solute by specified reaction dissolution front required the use of reactive- sources and sinks. The analytical solution is transport modeling. The reactive-transport achieved by solving a set of simultaneous linear modeling, however, would have been much equations known as mole balancing: more uncertain without the inverse modeling at the front end. Xj i It has been pointed out that inverse model- bpap ¼ Dmi ¼ miðfinalÞ miðinitialÞ ð3Þ ing assumes advective, steady-state flow and j¼1 that ‘‘reaction inversion’’ does not occur (Steefel and Van Cappellen, 1998). Although in which mi is the number of moles of element/ these are important issues, they are often j component i per kilogram of water, ap the sto- not serious limitations. These assumptions ichiometric coefficient of element i in phase p, are not a firm requirement for the system 6 Modeling Low-Temperature Geochemical Processes being studied; it is only essential that the con- 5.02.3 SOLVING THE CHEMICAL sequences of assuming them for non-steady- EQUILIBRIUM PROBLEM state flow (with or without dispersion) do not have a significant effect on the results of the Although both kinetic and equilibrium ex- calculation. For example, it can be argued that pressions can be used in geochemical modeling over a long enough period of time or for a computations, the ‘‘equilibrium problem’’ is large enough aquifer, steady-state conditions the foundation of most calculations of this never truly apply. Indeed, steady state is an type. Simply stated, the chemical equilibrium approximation of the physical and chemical problem is the determination of the most stable state of an aquifer system that works well for state of a system for a given set of pressure P, many, if not most, aquifers. As Zhu and And- temperature T, and compositional constraints erson (2002) pointed out, the most important Xi. These variables, P, T,andXi, need not be criterion is that the same parcel of water has fixed, but they must be defined for the given traveled from point A to point B. They also system. The chemical state of a system is given state that chemical steady state is sufficient but by the total , G, and its not necessary ‘‘because the underlying mathe- differential change with the progress variable, matical equations to be solved y are the x, denotes the state of the system in mathe- integrated forms of mass conservation (Licht- matical terms. For a system at equilibrium ner, 1996).’’ At the Iron Mountain mines (Al- @G pers et al., 1992), high concentrations of sulfate ¼ 0 ð4Þ (tens of grams per liter) and metals (grams per @x P;T liter) discharge from two major portals. The groundwater has advective and nonadvective and any perturbation from equilibrium will (dispersive and convective) properties, and the cause this differential to be other than 0. The variable effluent flows would indicate transient progress variable is a singular quantity that state. The chemistry, however, is still domi- expresses the extent to which a reaction has nated by oxidation of sulfide minerals and acid taken place. It is equal to the change in the dissolution of aluminosilicate minerals, and a number of moles, ni, of a reactant (or product) mass-balance calculation will still reflect these normalized to the stoichiometric coefficient, ni, geochemical processes. A mass balance going for that component, element, or species. In dif- from rainwater to portal effluent will delineate ferential form, the key minerals that dissolve and precipitate @n along the flow path. Steefel and Van Cappellen @x ¼ i ð5Þ (1998) correctly state that inverse modeling vi cannot be applied to contaminant plumes or reaction fronts unless the spatial delineation of Solving the equilibrium problem means fin- the reaction front is clearly defined. ‘‘Reaction ding the minimum in the free-energy curve for inversion,’’ such as the dissolution of a partic- the defined system. Two general approaches ular mineral changing to precipitation between have been used: the ap- two points along a flow path such that no proach and the free-energy minimization ap- overall reaction appears to have taken place, is proach. As the names suggest they primarily an interesting problem. Without additional in- use equilibrium constants to solve the problem formation it would not be possible to dis- or they use free energies. Of course, the ap- tinguish between no reaction and reaction proaches are considered the same because they inversion. In such instances, it makes no dif- are related by DrG1 ¼ RT ln K, where R is the ference to the modeling or the conclusions, universal , T the absolute temper- because the net result is the same. It is as if the ature in kelvin, and K the equilibrium constant, element of concern was conserved in the solid but the logarithmic conversion leads to differ- phase during that increment of fluid flow, a ent numerical techniques. Both approaches safe assumption for silica in quartz but not have to employ mass-balance and mass-action for silica from weathering feldspars. It might equations. Upon substitution of mass-action only matter if these small-scale processes into mass-balance expressions (or vice versa), a affect other processes such as the unidirec- set of nonlinear equations is derived that are tional release or attenuation of trace elements readily solved by a numerical method coded (released upon mineral dissolution but not for a computer. The mathematical formulation coprecipitated or adsorbed upon mineral pre- of the chemical equilibrium problem is ex- cipitation or vice versa) or similar irreversible plained in Zeleznik and Gordon (1968), Van processes involving nutrients. Further discus- Zeggeren and Storey (1970), Wolery (1979),and sion of inverse modeling is found in Sections Smith and Missen (1982). Harvie and Weare 5.02.7.1 and 5.02.8.3). (1980) and Harvie et al. (1987) have improved Historical Background to Geochemical Modeling 7 the free-energy minimization algorithm for as either a cation or neutral species form solving the general chemical equilibrium prob- (copper-chloride complexes). This calculation, lem and applied it to finding parameters for the however, did not take into account simultane- Pitzer method. Rubin (1983, 1990) provides ous competitive complexing from all the other more formalism for dealing with reactive trans- ions in seawater. Speciation was central to port and nonequilibrium conditions. Further Krauskopf’s (1951) study on gold solubility, discussion of the numerical techniques can be his discussion of trace-metal enrichment in sedi- found in the books by Smith and Missen mentary deposits (Krauskopf, 1955), and his (1982), Nordstrom and Munoz (1994), and examination of the factors controlling trace- many other textbooks and papers. A simple metal concentrations in seawater (Krauskopf, problem involving speciation of an aqueous 1956). In the US Geological Survey (USGS), solution at equilibrium with gypsum is solved Hem and Cropper (1959) and Hem (1961) were by both the Newton–Raphson method and the estimating distribution of ionic species and ‘‘continued fraction’’ method in Nordstrom activities of ions at chemical equilibrium in nat- and Munoz (1994). ural waters. Sille´ n’s (1961) first paper on sea- water considered and complex formation. At this time he and his colleagues 5.02.4 HISTORICAL BACKGROUND TO were pioneering the application of computers to GEOCHEMICAL MODELING solve complex aqueous solution equilibria (Sille´ n, 1962; Ingri and Sille´ n, 1962; Ingri The founders of geochemistry, F. W. Clarke, et al., 1967; Dyrssen et al., 1968). A classic pa- G. M. Goldschmidt, V. I. Vernadsky, and A. E. per that applied aqueous speciation to natural Fersman, clearly made major contributions to water was that of Garrels and Thompson (1962) our ‘‘models’’ of geochemical processes. Today, in their ‘‘Chemical Model of Seawater,’’ which however, we think of geochemical models in contained unique features such as the mean-salt terms of high-speed quantitative computations method for estimating activity coefficients. of water–rock interactions made possible The adaptation of water–rock geochemical with fast processors and disks with large mem- modeling to computers was pioneered by ories. This direction of research began with the Helgeson and his colleagues, who focused principles of adapted for on ore deposits and high-temperature, high- solving aqueous low-temperature geochemical pressure reactions (Helgeson, 1964, 1967, 1969) problems by Hem (1959), Garrels (1960), Sille´ n but also considered low-temperature processes (1961), Garrels and Christ (1965), and Kraus- (Helgeson et al., 1969, 1970). Helgeson’s (1971) kopf (1967). The scholarly structures that these research continued with the application of authors built would not have been possible computers to the calculation of geochemical without the foundations laid by those who kinetics. Theoretical approaches were devel- came before and developed the science of phys- oped for geochemical kinetics (Aagard and ical chemistry: Wilhelm Ostwald, Jacobius Helgeson, 1982; Helgeson and Murphy, 1983) Henricus van’t Hoff, and Svante Arrhenius and computations compared with measured (Servos, 1990). These , along with reaction rates (Helgeson et al., 1984; Murphy numerous others they influenced, established and Helgeson, 1987) and coupled with diffu- the principles upon which aqueous low-tem- sion (Murphy et al., 1989). These approaches perature geochemistry and geochemical model- provide an insight to the mechanisms of con- ing is based. Van’t Hoff himself was an early trolled laboratory studies on mineral dissolu- developer of geochemical models in his efforts tion rates, but difficulties are encountered when to apply physical chemistry to the interpreta- applications are made to the complex condi- tion of the equilibrium factors determining tions of the natural environment. Experimental the stability of gypsum and anhydrite (van’t and theoretical approaches to mineral dissolu- Hoff et al., 1903) and the equilibrium interpre- tion fail to predict the actual dissolution rates tation of the Permian Zechstein evaporite de- in catchments, because experiments do not re- posits (van’t Hoff 1905, 1909, 1912; Eugster, produce the composition and structure of nat- 1971). ural mineral surfaces, they do not account for Probably the earliest paper to apply a adsorbed inhibitors, they do not consider the speciation calculation to natural water was effect of variable climate and hydrologic flow Goldberg’s (1954) estimate of the different rates, and they do not account for biological forms of dissolved copper in seawater based activity. These factors may have taken any- on Niels Bjerrum’s theory of ion-pair forma- where from decades to millenia to develop and tion and Jannik Bjerrum’s data (see Bjerrum, they can change over short periods of time. 1950). He found that 65% was in the free Computer codes that incorporate reaction ion (Cu2 þ ) form and another 33% was present kinetics into groundwater or catchment codes 8 Modeling Low-Temperature Geochemical Processes usually do so with some type of general- relating concentration to is ized first-order rate law. the activity coefficient, gi: Beginning in the 1960s and expanding con- siderably during the 1970s, a series of computer a ¼ g m ð6Þ codes were developed that could perform a i i i wide variety of aqueous geochemical calcula- tions (Bassett and Melchior, 1990; Mangold With the accumulation of activity coefficient and Tsang, 1991) and these evolved consider- measurements and the search for a theoretical ably during the 1980s and 1990s to include expression ensued, it was discovered that in simulation of more processes, coupling of dilute solutions the logarithm of the activity processes (especially reaction with transport), coefficient was an approximate function of the and the availability of more options (Alpers square root of the molality: and Nordstrom, 1999). The advances in geochemical modeling are apparent in the 1=2 ln gi ¼aimi ð7Þ evolution of Barnes’ Geochemistry of Hydro- thermal Ore Deposits from first edition (Barnes, where ai was simply a constant. Brønsted 1967) to third edition (Barnes, 1997), in the (1922) introduced a linear term to Equation American Chemical Society (ACS) books (7) in which the coefficient, b, is a ‘‘specific-ion Chemical Modeling in Aqueous Systems that interaction parameter,’’ have shown significant advances from the first (Jenne, 1979) to the second (Melchior 1=2 and Bassett, 1990), and in the plethora of pa- ln gi ¼aimi bmi ð8Þ pers on this subject since the 1980s. Neverthe- less, advanced sophistication for geochemical Later modifications of this general approach codes does not imply a parallel advance in our became known as the specific-ion interaction understanding of geochemical processes. The theory (SIT) because of the explicit dependence sophistication of software has outdistanced on the solute or ions being considered. our capacity to evaluate the software over a An important concept that aided in the range of conditions and it has outdistanced our development of electrolyte theory was the ionic ability to obtain the field data to constrain and strength, I, introduced by Lewis and Randall test the software. (1921): X 1 2 I ¼ mizi ð9Þ 5.02.5 THE PROBLEM OF ACTIVITY 2 COEFFICIENTS where zi is the ionic charge. Thereafter, the 5.02.5.1 Activity Coefficients was used as a parameter in activity coefficient equations. Debye and Huck- Aqueous electrolytes and the equilibrium ¨ el (1923) derived an equation from electrostatic constants that define various reactions in low- theory which, in the limit of infinite dilution temperature geochemistry are inexorably (hence, the Debye–Huckel limiting law), linked with the problem of activity coefficients, ¨ becomes or the problem of nonideality for aqueous elec- trolyte solutions. Thermodynamic equilibrium 2 1=2 constants, defined by an extrapolation to infi- log gi ¼Azi I ð10Þ nite dilution for the condition (not the only standard state), require the use of where A is a Debye–Hu¨ ckel parameter activity coefficients. Unfortunately, there is (dependent on the properties of the solvent). neither a simple nor universal nonideality The extended Debye–Hu¨ ckel equation is method that works for all electrolytes under all conditions. This section provides a brief Az2I 1=2 overview of a major subject still undergoing log g i 11 i ¼ 1=2 ð Þ research and development but for which several 1 þ BaiI satisfactory approaches are available. If the activity of a solute or ion were ideal, it where B is another Debye–Hu¨ ckel solvent pa- could be taken as equivalent to the molal con- rameter and ai is an ion-size diameter derived centration, mi, of the i ion or solute. However, by empirical fit but approximates the hydrated interactions with other ions and with the ion diameter. solvent water are strong enough to cause non- The use of the extended Debye–Hu¨ ckel equa- ideal behavior, and the characteristic property tion with the appropriate equilibrium constants The Problem of Activity Coefficients 9 for mass-action expressions to solve a complex equation is chemical equilibrium problem is known as the IA method. A 2uþu ln g7 ¼ jz z jf ðIÞþ BðIÞm Several modifications of these equations 3 þ u were tried over the next several decades. Con- 2ðu u Þ3=2 tributions by Guggenheim (1935) and Scat- þ þ Cm2 ð14Þ chard (1936) and the KTH or Swedish group u (Grenthe et al., 1992, 1997) became the Brønsted–Guggenheim–Scatchard or SIT where method: I 1=2 f ðIÞ¼ þ 1:67 lnð1 þ 1:2I 1=2Þ 1 þ 1:2I 1=2 Az2I 1=2 X log g ¼ i þ eði; k; IÞm ð12Þ i 1 1:5I 1=2 k þ k and

BðIÞ¼2b1 Here the linear term is a function of molality 0 2b 1=2 1 2 aI 1=2 summed for all the other ions in solutions, þ 2 1 1 þ aI a I e k, and e(i, k,I) tends to be constant at higher a I 2 molalities but solute or ion specific. The last term in Equation (12) represents the deviat- in which b1 and b0 are specific-ion parameters, a ion of the experimentally measured activity is a constant for a similarly charged class coefficient from the prediction of the Debye– of electrolytes, and C a specific-ion parameter Hu¨ ckel equation. Other groups, such as independent of ionic strength. The B and C Truesdell and Jones (1974), kept the ionic parameters are second and third virial coeffi- strength dependence throughout the equation, cients. The parameter v ¼ v þ þ v–, is the sum of and the coefficient, b, became the difference the stoichiometric coefficients for the cation, factor but still a constant for a given solute v þ , and the anion, v–, of the solute. The Pitzer or ion: parameters have been fitted for a wide range of solutes and have been used for mixed electrolyte solutions to model the mineral solubility Az2I 1=2 log g i b I 13 behavior in brines (Harvie and Weare, 1980; i ¼ 1=2 þ i ð Þ 1 þ BaiI Harvie et al., 1980). Grenthe et al. (1997) com- pared the SIT method and the Pitzer method in detail and came to the following conclusions: The IA method using Equation (13) for ma- (1) the more extensively parametrized Pitzer jor ions in natural water compares well with model allows the most precise modeling of other more precise methods (see below) up to activity coefficients and equilibrium constants an ionic strength of seawater (0.7) but not provided that all the interaction coefficients are much higher. known; (2) when Pitzer parameters are missing The next better approximation is to allow (not available from experimental data), they the linear coefficient to be a function of the ionic must be estimated and the precision and accu- strength (Pitzer and Brewer, 1961) and it was racy of the activity coefficients can be signi- utilized by Helgeson and Kirkham (1974a, b, ficantly compromised; (3) the parameters in the 1976), Helgeson et al. (1981),andTanger and SIT model can be related to those in the Pitzer Helgeson (1988) in the development of the model and provide another means of estimating Helgeson–Kirkham–Flowers (HKF) equations, Pitzer parameters; (4) the SIT model is in good which include consideration of the Born func- agreement with the Pitzer model for the range tion and ion hydration. m ¼ 0.1–4 mol kg–1; and (5) the Pitzer model is Pitzer (1973) reexamined the statistical the preferred formalism for solutions or brines mechanics of aqueous electrolytes in water of high ionic strength. An extensive discussion and derived a different but semiempirical of the development of the Pitzer model and method for activity coefficients, commonly several hybrid approaches can be found in Pit- termed the Pitzer specific-ion interaction zer (1991a) and Millero (2001). It appears that model. He fitted a slightly different function hybrid approaches provide the best promise in for behavior at low concentrations and used a the future, because they combine the extensive virial coefficient formulation for high concen- data available on equilibrium constants with a trations. The results have proved extremely better formulation of activity coefficients. fruitful for modeling activity coefficients over The difference between the extended Debye– a very large range of molality. The general Hu¨ ckel equation and the 10 Modeling Low-Temperature Geochemical Processes concerns with how much of the nonideality of These computations describe the ‘‘tendency’’ electrostatic interactions is incorporated into of a water sample to be saturated, but they do mass-action expressions and how much into the not necessarily demonstrate whether mineral activity coefficient expression. It is important dissolution or precipitation actually happens. to remember that the expression for activity For dissolution to occur, the mineral must be coefficients is inexorably bound up with equi- present and it must dissolve at a rate that is fast librium constants and they must be consistent enough relative to the flow rate of the water to with each other in a chemical model. Ion-pair affect the water chemistry (Berner, 1978). Like- interactions can be quantified in two ways, ex- wise for a mineral to precipitate, it must precip- plicitly through stability constants (IA method) itate at a rate fast enough to affect the water or implicitly through empirical fits with activity chemistry. The kinetics of precipitation and dis- coefficient parameters (Pitzer method). Both solution reactions must be applied to get a re- approaches can be successful with enough alistic interpretation of water–rock interactions. effort to achieve consistency. At present, the Pitzer method works much better for brines, and the IA method works better for dilute wa- 5.02.6 GEOCHEMICAL DATABASES ters because of the greater number of compo- nents and species for which basic data exist. Input for aqueous geochemical codes con- When the effort is made to compare both ap- sists of field data (, petrology, miner- proaches for the same set of high-quality data, alogy, and water analyses), thermodynamic they appear to be comparable (Felmy et al., and aqueous electrolyte data, and possibly 1990). The primary challenge for the future will kinetic and sorption data. Thermodynamic be to insure that consistency is maintained be- data are fundamental to most geochemical tween the thermodynamic data, the expressions computations and several major compilations for nonideality, and the mass-action expres- are available. Although the guidelines and nec- sions in geochemical modeling codes, and to essary relations for thermodynamic consistency incorporate trace elements and redox species are well established (Rossini et al., 1952; within the same formulation. Helgeson, 1968, 1969; Haas and Fisher, 1976; Nordstrom et al., 1990; Nordstrom and Munoz, 1994), it has been difficult to employ 5.02.5.2 Saturation Indices them in the development of databases. Two general approaches have been recognized, serial After speciation and activities have been cal- networks and simultaneous regression. With culated for all the free ions, ion pairs, triplets, serial networks, an evaluator begins with a etc., a mineral saturation index can be com- single starting point, such as the standard state puted. The saturation index (SI) is defined as properties for an element (or all elements) the logarithm of the ratio of the ion-activity and gradually builds in the properties of product (IAP) to the solubility product con- compounds through the appropriate reaction stant, Ksp, combinations. Serial networks, such as that IAP developed by the National Bureau of Standards SI ¼ log ð15Þ (formerly NBS, now NIST, National Institute K sp of Standards and Technology) database (Wag- man et al., 1982), achieve continuity for a large If the solution is at equilibrium, the data set but lose thermodynamic constraints, IAP ¼ Ksp and the SI ¼ 0. If the SI40, then whereas simultaneous regression, which pre- the solution is supersaturated and the mineral serves thermodynamic relationships, can only would tend to precipitate; if the SIo0, the so- be done on a limited subset of data, and lution is undersaturated and the mineral would the weighting of the regression fit depends tend to dissolve, if present. Because the SI is on the judgment of the evaluator (Archer affected by the of the mineral and Nordstrom, 2003). Computer codes formula, it is best to normalize the SI to the have been developed for the purpose of corre- total mineral stoichiometry as pointed out by lating and evaluating a diversity of thermody- Zhang and Nancollas (1990): namic data (Haas, 1974; Ball et al., 1988), but they have not been widely used. Serious IAP 1=u SI ¼ log ð16Þ discrepancies in thermodynamic properties do Ksp appear among these compilations and some of these discrepancies have been incorporated where v ¼ v þ þ v–, is the sum of the stoic- into the databases of geochemical codes. Many hiometries of the positive and negative compo- users of these codes are not familiar with nents in the mineral formula. these databases and the possible uncertainties Geochemical Codes 11 propagated through the computations from relations to see if the properties for individual thermodynamic errors. Such error propagation species are consistent with tabulated reaction may or may not be important, depending on equilibria. Only values that agreed within a the specific objectives of the geochemical prob- close range of the stated uncertainties were lem being addressed. included in the tables. These tabulations represent a portion of the data needed for geochemical model com- 5.02.6.1 Thermodynamic Databases putations and there have been some obvious inconsistencies. By the mid-1990s, critical eval- Since the early compilations of thermo- uations of thermodynamic data were tapering dynamic data (e.g., Lewis and Randall, 1923), off and many errors and inconsistencies had numerous measurements were made during the not been resolved. Even as of 1994, serious in- twentieth century leading to the well-known consistencies still existed between calorimetric- compilations of Latimer (1952) and Rossini ally derived and solubility-derived properties et al. (1952). Measurements and compilations for such common minerals as celestine and ba- continued to expand through the later part rite, and a less common but important phase of the twentieth century, and comprehensive such as radium sulfate (Nordstrom and Mu- inventories such as Sille´ n and Martell (1964), noz, 1994). This set of discrepancies has been Martell and Smith (1974–76), Wagman et al. resolved for celestine (SrSO4) and barite (1982), Chase (1998), Robie and Hemingway (BaSO4) by new measurements using high-tem- (1995), and Gurvich et al. (1993) summarized perature oxide-melt and differential-scanning and organized a considerable amount of data. (Majzlan et al., 2002). Listing of Unfortunately, the methods used to evaluate sources of thermodynamic data compilations the data are not always transparent and occa- can be found in Nordstrom and Munoz (1994) sionally the source references are not known. and in Grenthe and Puigdomenech (1997). Notable exceptions were the publication of the CODATA tables (Garvin et al., 1987; Cox et al., 1989), the Organization Economic Co- 5.02.6.2 Electrolyte Databases operation and Development/Nuclear Energy Agency Thermochemical Data (OECD/ The classic books by Harned and Owen NEA TDB) publications (Grenthe et al., 1992; (1958) and Robinson and Stokes (1959) put Silva et al., 1995; Rard et al., 1999; Lemire electrolyte theory on a firm basis and provided et al., 2001; Guillaumont et al., 2003), and the important tabulations of electrolyte data for International Union of Pure and Applied calculations of activity coefficients and related Chemistry (IUPAC) compilations (e.g., Lam- properties. Advances in electrolyte theory, bert and Clever, 1992; Scharlin, 1996). The especially the use of the Pitzer method (Pitzer, OECD/NEA TDB, although focusing on ra- 1973, 1979), led to alternate methods of calcu- dionuclides of most concern to safe disposal of lating activities and speciation. The books ed- high-level radioactive wastes and military ited first by Pytkowicz (1979) and later by wastes, contains a considerable amount of aux- Pitzer (1991b) provided a general overview of iliary data on other common aqueous and solid the different approaches and hybrid ap- species that had to be evaluated along with the proaches to these computations. A more re- actinides. For aqueous geochemical modeling, cent reference providing a thorough overview the equilibrium-constant tables of Nordstrom of the subject with tables of molal properties, et al. (1990) have proved to be useful and activity coefficients and parameters, and disso- are found in USGS and US Environmental ciation/association constants is Millero (2001). Protection Agency (USEPA) codes described These references explain the general use of the below and in popular water-chemistry/aqueous- IA method with extended forms of Debye– geochemistry textbooks (Appelo and Postma, Hu¨ ckel equations, the Pitzer specific-ion inter- 1993; Stumm and Morgan, 1996; Langmuir, action method, and hybrid approaches that 1997; Drever, 1997a). These tables have been take advantage of the best aspects of both recompiled, expanded, and tabulated in terms approaches. of thermodynamic properties (G, H, S, CP, and log K for reaction and individual species (Nor- 5.02.7 GEOCHEMICAL CODES dstrom and Munoz, 1994)). The tabulation of Nordstrom and Munoz (1994) was organi- This listing and description of geochemical zed in such a way that individual species can be codes is not meant to be either exhaustive compared with reactions involving those spe- or complete. It is meant to be a brief overview cies that were measured independently. Conse- of several codes in current and common quently, it is easy to check thermodynamic use. Reviews by Yeh and Tripathi (1989a), 12 Modeling Low-Temperature Geochemical Processes Mangold and Tsang (1991), Parkhurst and paths. A separate but similar code, PHRQ- Plummer (1993), and Alpers and Nordstrom PITZ, uses the Pitzer method for brine calcu- (1999) provide information on more codes, lations (Plummer et al., 1988; Plummer and their evolution, and references to earlier re- Parkhurst, 1990). The PHREEQE code has views on codes and geochemical modeling. been regularly enhanced and the recent version, Loeppert et al. (1995) also contain useful in- PHREEQC v. 2, includes ion exchange, evap- formation on geochemical codes and modeling, oration, fluid mixing, sorption, solid-solution especially for soil interactions. It is important equilibria, kinetics, one-dimensional transport to remember that most codes in active use often (advection, dispersion, and diffusion into stag- undergo enhancements, database updates, and nant zones or dual porosity), and inverse mod- other improvements. The descriptions given in eling (Parkhurst and Appelo, 1999). An this section may not apply to some of these interface (PHREEQCI) was developed for in- same codes 5 years from now. teractive modification of the input files by Charlton et al. (1997). The latest development is PHAST, which includes three-dimensional 5.02.7.1 USGS Codes transport (Parkhurst et al., 2004). The program PHAST uses the solute-transport simulator The USGS has developed several codes that HST3D (Kipp, 1987, 1998) and iterates at are useful for the interpretation of water–chem- every time step with PHREEQC. Thorstenson istry data and for simulating water–rock inter- and Parkhurst (2002) have developed the the- actions. Two similar aqueous-speciation codes ory needed to calculate individual isotope equi- were developed in parallel, WATEQ (Truesdell librium constants for use in geochemical and Jones, 1974) and SOLMNEQ (Kharaka models and utilized them in PHREEQC to cal- and Barnes, 1973). The primary aim of these culate carbon-isotope compositions in unsatu- programs was to aid in the interpretation of rated zone with seasonally varying CO2 water-quality data. SOLMNEQ, however, had production (Parkhurst et al., 2001). a different subroutine for calculating tempera- Geochemical modeling of reactants in flow- ture and pressure dependence and could calcu- ing mountainous stream systems can be done late reaction equilibria above 100 1C. WATEQ with the USGS codes OTIS (Runkel, 1998) and was intended for of 0–100 1C. OTEQ (Runkel et al., 1996, 1999) that model Both of these programs have been updated. solute transport and reactive transport, re- WATEQ4F v.2 (Ball and Nordstrom, 1991, spectively. OTIS, or one-dimensional transport with database updates to 2002) uses the IA with inflow and storage, is based on the earlier method with an expanded form of the extended work of Bencala (1983) and Bencala and Wal- Debye–Hu¨ ckel equation for major ions (the ters (1983). The OTEQ code combines the Truesdell–Jones formulation or hybrid-activity OTIS code with MINTEQA2 for chemical re- coefficient; Truesdell and Jones (1974) and action at each incremental step of transport. Nordstrom and Munoz (1994), includes inde- These codes are calibrated with constant-flow pendent redox speciation computations that tracer injection studies and testable assump- assume redox disequilibrium, and has database tions regarding the solubility product constant updates for uranium (Grenthe et al.,1992), of the precipitating phases (Kimball et al., chromium (Ball and Nordstrom, 1998), and 2003). They have been tested in numerous arsenic redox species (Archer and Nordstrom, settings, primarily with the objective of quan- 2003; Nordstrom and Archer, 2003). SOL- tifying and predicting the sources, transport, MINEQ. 88 (Kharaka et al., 1988; Perkins and fate of acid drainage from mined environ- et al., 1990) covers the temperature range of ments in the western United States. 0–350 1C and 1–1,000 bar pressure, includes Codes for inverse modeling began with both the IA method and the Pitzer method, the program BALANCE (Parkhurst et al., and has mass-transfer options such as boiling, 1982) from which the interactive code NET- fluid mixing, gas partitioning, mineral precip- PATH (Plummer et al., 1991) evolved. NET- itation, mineral dissolution, ion exchange, and PATH, in addition to mass balances, does sorption. It has been found to be particularly database management for a suite of wells and applicable to deep sedimentary basins, espe- can compute speciation and saturation indices cially those containing oil and gas deposits. The with WATEQ. NETPATH has now been in- latest version, SOLMINEQ.GW is explained in corporated into PHREEQC along with uncer- an introductory text on groundwater geochem- tainty propagation (Parkhurst, 1997). Bowser istry (Hitchon et al., 1996). and Jones (1990, 2002) have incorporated Parkhurst et al. (1980) developed the the mass-balance approach into a spreadsheet PHREEQE code to compute, in addition to format that allows graphical output and a aqueous speciation, mass transfer, and reaction quick reconnaissance of ranges of mineral Geochemical Codes 13 compositions that are permissible models for and trace elements in seawater. The activity silicate solid-solution series (see Chapter 5.04). coefficient models have been influenced USGS codes and manuals can be download- strongly by the Pitzer method but are best de- ed free of charge at Water Resources Applica- scribed as hybrid because of the need to use tions Software (2006). The more current ion-pair formation constants (Millero and version and additional bibliographic and infor- Schreiber, 1982). The current model uses QBA- mation files for PHREEQC are available at SIC; computes activity coefficients for 12 major Reaction-Transport Modeling in Ground- cations and anions, 7 neutral solutes, and more Water Systems (2006). Updates on WATEQ4F than 36 minor or trace ions. At 25 1C, the ionic and revised thermodynamic data can be found strength range is 0–6 m. For major compo- at Chemical Modeling of Acid Waters (2006). nents, the temperature range has been extended The OTIS code can be accessed at OTIS (2006). to 0–50 1C, and in many cases the temperature dependence is reasonably estimated to 75 1C. Details of the model and the parameters and 5.02.7.2 LLNL Codes their sources can be found in Millero and Roy (1997) and Millero and Pierrot (1998). Com- A set of computer codes known as EQ3/6 parison of some individual ion activity coeffi- was originally developed by Wolery (1979) to cients and some speciation for seawater model rock–water interactions in hydrothermal computed with the Miami model is shown in 1 systems for the temperature range 0–300 C. Section 5.02.8.6 on model reliability. Software development was later sponsored by the US Department of Energy at Lawrence Livermore National Laboratories (LLNL) to model geochemical processes anticipated in 5.02.7.4 The Geochemist’s Workbencht high-level nuclear waste repositories. This geo- chemical code has become one of the most so- A set of five programs known as The Geo- phisticated and most applicable for a wide ’s Workbencht or GWB was developed range of conditions and processes. In addition by Bethke (1994) with a wide range of capabil- to speciation and mass-transfer computations, ities similar to EQ3/6 and PHREEQC v.2. it allows for equilibrium and nonequilibrium GWB performs speciation, mass transfer, reac- reactions, solid-solution reactions, kinetics, IA, tion-path calculations, isotopic calculations, and Pitzer methods, and both inorganic and temperature dependence for 0–300 1C, inde- organic species. The program has been used for pendent redox calculations, and sorption cal- several municipal and industrial waste situa- culations. Several electrolyte databases are tions and has been used to assess natural and available including IA with Debye–Hu¨ ckel engineered remediation processes. It has five activity coefficients, the Pitzer formulation, supporting thermodynamic data files and the the Harvie–Møller–Weare formulation, and thermodynamic data are evaluated and up- a PHRQPITZ-compatible formulation. The dated with the SUPCRT92 software (Johnson program X2t allows the coupling of two-di- et al., 1992), based on Helgeson’s formulation mensional transport with geochemical reaction. for activity coefficients and aqueous thermo- Basin3 is a basin-modeling program that can be dynamic properties over a wide range of tem- linked to GWB. Another advantageous feature perature and pressure (Helgeson and Kirkham, is the plotting capability that can produce pe– 1974a, b, 1976; Helgeson et al., 1981) and solid- pH or activity–activity or –fugacity phase thermodynamic properties (Helgeson diagrams from GWB output. Bethke (1996) et al., 1978). Thermodynamic data are updated has published a textbook on Geochemical with the availability of published research (e.g., Reaction Modeling that guides the reader Shock and Helgeson, 1988, 1990; Shock et al., through a variety of geochemical computations 1989). Several manuals for operation using GWB and provides the basis for a and general information are available at IPAC course in modeling. The GWB is a registered (2006). code and can be obtained from RockWare, Inc (RockWare, Inc. Earth Science & GIS Software (2006)). 5.02.7.3 Miami Codes It would be difficult to find more compre- hensive or more detailed studies on the physical 5.02.7.5 REDEQL-MINTEQ Codes chemistry of seawater than those done at the University of Miami (Millero, 2001). Several One of the first speciation programs that codes were developed for calculation of activity included mass-transfer reactions at equilibrium coefficients and speciation of both major ions was REDEQL (Morel and Morgan, 1972). The 14 Modeling Low-Temperature Geochemical Processes primary aim of this set of codes was to compute compared with those done by MINTEQA2. the equilibrium chemistry of dilute aqueous MODELm predicted greater amounts of solutions in the laboratory and was among the metal–organic complexing than MINTEQA2, first to include sorption. It also has been widely but no conclusions were drawn as to the cause used to interpret water quality in environmen- of this difference. MODELm can be used in tal systems. This FORTRAN code has evolved MINTEQA2 instead of the Gaussian distribu- through several versions, parallel with advan- tion model. Although cation-organic binding in ces in computer hardware and software. Incor- natural waters is a highly complex and challen- poration of the WATEQ3 database (Ball et al., ging subject to quantify for modeling purposes, 1981) with the MINEQL program (Westall advances since the early 1990s are leading us et al., 1976) produced MINTEQ (Felmy et al., much closer to practical approaches that can be 1984) which became the USEPA-supported incorporated into computerized equilibrium code, MINTEQA2 (Allison et al., 1991). The and nonequilibrium chemical codes. Geochem- more recent upgrade is MINTEQA2/PROD- istry will benefit from continued research in EFA2 v. 4 (USEPA, 1998, 1999 (revised)), and this area because organic matter exerts such contains code revisions, updates in thermody- a strong control on the behavior of trace namic data, and modifications to minimize elements in most aquatic systems. More testing nonconvergence problems, to improve and evaluation of a range of natural waters modeling, to minimize phase-rule violations, to with different trace-element concentration and enhance execution speed, and to allow output organic matter types is needed in the future. of selected results to spreadsheets. PROD- Evaluation should be accomplished by com- EFA2 is an ancillary program that produces paring analytical speciation with computed MINTEQA2 input files using an interactive speciation. preprocessor. Thermodynamic data and com- A Windows version of MINTEQA2 v. 4.0, putational abilities for Be, Co(ii/iii), Mo(iv), known as Visual MINTEQ, is available at no and Sn (ii, iv) species have been added to the cost from Visual MINTEQ ver 2.50 (2006) at program. Unfortunately, the numerous incon- The Royal Institute of Technology, Sweden sistencies, lack of regular upgrades, and ten- (last accessed June 1, 2006). It is supported by dency for numerous independent researchers to two Swedish research councils, VR and MIST- make their own modifications to the program RA. The code includes the NIST database, ad- have led to several versions that differ in reli- sorption with five surface-complexation ability. Examples of test cases to demonstrate models, ion exchange, and metal-humate com- the input setup, capabilities of the code, and plexation with either the Gaussian DOM comparisons of standard test cases have not model or the Stockholm Humic model. Input been included in the documentation as has data are accepted from Excel spreadsheets and been done for other programs. MINTEQA2 output is exported to Excel. A major update release notes on upgrades and corrections can was completed in January 2003. The Royal be obtained at USEPA. Exposure Assessment Institute of Technology also has produced Models (2006) and the manual is found HYDRA and MEDUSA for creating a data- at MINTEQA2/PRODEFA2, A Geochemical base for a given system and creating activity– Assessment Model for Enviornmental Systems activity and pe–pH diagrams. Links to other (2006). similar programs can be found online. Perhaps the most noteworthy aspect of the A Windows version of MINTEQA2, known upgraded MINTEQA2 code is the Gaussian as MINEQL þ v. 4.5, has several enhancements model for interactions of dissolved organic that make it an attractive alternative to other matter with cations. The model formulation is versions. The user interface with a relational based on the statistical treatment of proton database technique for scanning thermody- binding (Posner, 1964) that was developed by namic data, a utility for creating a personal Perdue and Lytle (1983), Perdue et al. (1984), database, a relational spreadsheet editor for and Dobbs et al. (1989). This approach uses a modifying chemical species, a multirun man- continuous distribution of sites as opposed ager, special reports for convenient data extrac- to discrete site binding. It is equivalent to a tion or additional calculations, and a tutorial collection of monoprotic , each able to with several examples provide a much more bind protons and metal cations, with the variat- flexible and practical code for modelers. It ions in log K described by a single Gaussian also provides graphic output for log C–pH distribution for each class of sites. Another plots, ion-fraction diagrams, solubility plots, code, MODELm (Huber et al., 2002), uses titration curves, and sensitivity plots. It is lim- a linear differential equilibrium function to ited in temperature to 0–50 1C and ionic account for trace-metal complexation with strength o0.5 M. The program is available natural organic matter. Computations were through Environmental Research Software, Geochemical Codes 15 Makers of MINEQL þ MINEQL þ The First complex electrolyte mixtures and their salts Choice in Chemical Equilibrium Modeling for seawater evaporation (Harvie et al., 1982). (2006). Later, the number of components was ex- panded to include H, OH, HCO3,CO3, and CO2 (Harvie et al., 1984). Incorporating the 5.02.7.6 Waterloo Codes temperature dependence to allow calculations from 25 to 250 1C was achieved by Møller A considerable history of hydrogeochemical (1988) and for lower temperatures (0–250 1C) modeling and its application has evolved at the by Greenberg and Møller (1989) and Spencer University of Waterloo, ON, Canada, and a et al. (1990). Marion and Farren (1999) ex- series of reactive-transport codes have evolved tended the model of Spencer et al. (1990) for with it. These codes have been primarily more sulfate minerals during evaporation and applied to mine tailings piles. A finite element freezing of seawater down to temperatures of transport module, PLUME2D, was utilized –37 1C. Pressure dependence for aqueous sol- with the MINTEQA2 module in an efficient utes and minerals in the Na–Ca–Cl–SO –H O two-step sequential solution algorithm to pro- 4 2 system to 200 1C and 1 kbar was obtained by duce MINTRAN (Walter et al., 1994). Leac- Monnin (1990) and applied to deep Red Sea hates from heterogeneous mine overburden brines and sediment pore waters (Monnin and spoil piles that made a contaminant front were Ramboz, 1996). Møller et al. (1998) developed modeled with MINTRAN and other codes at the TEQUIL code for geothermal brines. open-pit lignite mines in Germany (Gerke Ptacek and Blowes (2000) have reviewed the et al., 1998). When a numerical model that status of the Pitzer method applications for coupled diffusion and sulfide-mineral sulfate mineral and demonstrated oxidation, PYROX, was added to MINTRAN, the applicability of a modified Harvie–Møller– it became MINTOX (Wunderly et al.,1996). Weare (HMW) to mineral solubilities in mine MINTOX proved to be capable of simulating tailings piles. Pitzer calculations of carbonate 35 years of contaminant transport at the Nickel mineral solubility at low temperatures can be Rim mine tailings impoundment (Bain et al., made with the FREZCHEM code (Marion, 2000). The more recent version is MIN3P 2001), the behavior of strong can be (Mayer et al., 1999), which is a general reactive modeled at low temperature (Marion, 2002), transport code for variably saturated media. It and ferrous iron geochemistry can be modeled has been applied to the Nickel Rim impound- for interpreting the geochemistry of the Mars ment and to the contaminated groundwater surface. downgradient of the Ko¨ nigstein uranium mine in Saxony, Germany (Bain et al., 2001). At Ko¨ nigstein, reactions involving iron, uranium, sulfate, cadmium, chromium, nickel, lead, and 5.02.7.8 Windemere Humic Aqueous Models zinc were all modeled. A short review of similar Tipping (1994) has proposed an alternative codes and an update on those codes can be and practical model for humic acid–metal bin- found in Mayer et al. (2003). ding embodied in the speciation code Winde- mere Humic Aqueous Model (WHAM) that 5.02.7.7 Harvie–Møller–Weare Code has two versions, one for water and one for soils (Tipping, 1998). This aqueous metal– With the arrival of the Pitzer method for ca- organic model is based on the concept of elec- lculating activity coefficients at high ionic trostatic interactions at discrete sites. Hence, it strengths (X1 m), research by Harvie and We- is readily amenable to use with inorganic chem- are (1980) led to computations of equilibrium ical speciation programs for aqueous solutions mineral solubilities for brines. They could cal- and includes ionic strength and temperature culate solubility data from gypsum (Io0.06 m) effects. Tipping et al. (2002) provide a thor- to bischofite saturation (420 m). This capabil- ough evaluation of humic substance binding ity made it possible to more accurately calcu- with aluminum and iron in freshwaters. late the mineral sequences during seawater They demonstrate that 60–70% of the dis- evaporation and quantitatively solve a prob- solved organic carbon (DOC) in their samples lem that had puzzled van’t Hoff (Harvie et al., was humic substances involved in metal 1980). The original model included the compo- complexation: after accounting for organic nents Na, K, Mg, Ca, Cl, SO4,andH2O and complexing, the inorganic speciation is consist- was applied to the simpler salt systems and to ent with control of dissolved aluminum and mineral equilibria in seawater (Eugster et al., iron concentration by their hydrous oxides. A 1980). With further revision of the parameters, full explanation of the developments that led to the model was expanded to include more the WHAM model and descriptions of many 16 Modeling Low-Temperature Geochemical Processes other models (multiple versus single discrete redox species, has been introduced by Hunter models, continuous models, competitive versus et al. (1998). noncompetitive models, empirical models, Lichtner (2001) developed the computer code site heterogeneity/polyelectrolyte models, and FLOTRAN, with coupled thermal–hydro- Gaussian distribution models) can be found in logic–chemical (THC) processes in variably Tipping (2002). The latest WHAM code, saturated, nonisothermal, porous media in 1, version 6, is available at Windermere Humic 2, or 3 spatial dimensions. Chemical reactions Aqueous Model (2006). An example of a con- included in FLOTRAN consist of homoge- tinuous distribution for binding sites can be neous gaseous reactions, mineral precipitation/ found in the development of the Natural dissolution, ion exchange, and adsorption. Organic Anion Equilibrium Model, or NO- Kinetic rate laws and redox disequilibrium are AEM (Gryzb, 1995) which can also be used in allowed with this code. Debye–Hu¨ ckel and Pit- conjunction with ionic components and zer options are both available for computing electrostatic theory. activity coefficients, and thermodynamic data are based on the EQ3/6 database or user-de- fined databases. 5.02.7.9 Additional Codes Several options are available in FLOTRAN for representing fractured media. The equiva- The coupled code developed by Steefel and lent continuum model (ECM) formulation rep- Lasaga (1994) for multicomponent reactive resents fracture and matrix continua as an transport with kinetics of precipitation and equivalent single continuum. Two distinct dissolution of minerals has been developed fur- forms of dual continuum models also are avail- ther into the OS3D/GIMRT code (Steefel and able, defined in terms of connectivity of the Yabusaki, 1996). This model has been applied matrix. These models are the dual continuum to reaction fronts in fracture-dominated flow connected matrix (DCCM) and the dual con- systems (Steefel and Lichtner, 1998). Further tinuum disconnected matrix (DCDM) options. developments for nonuniform velocity fields A parallel version of the code, PFLOTRAN, by Yabusaki et al. (1998) required the use has been developed based on the PETSC par- of massively parallel processing computers, allel library at Argonne National Laboratory. although ‘‘y the accuracy of the numerical Park and Ortoleva (2003) have developed formulation coupling the nonlinear processes WRIS.TEQ, a comprehensive reaction-trans- becomes difficult to verify.’’ port-mechanical simulator that includes kinetic The model BIOKEMOD has been developed and thermodynamic properties with mass to simulate geochemical and microbiological transport (advection and diffusion). A unique reactions in batch aqueous solutions (Salvage property of this code is a dynamic compositio- and Yeh, 1998). It has been tested and nal and textural model specifically designed for found to simulate a range of processes that in- sediment alteration during . clude complexation, adsorption, ion exchange, The RATAP program was developed by precipitation/dissolution, biomass growth, Scharer et al. (1994) to predict acid generation degradation of chemicals by metabolism of in sulfide tailings piles. It includes sulfide-min- substrates, metabolism of nutrients, and eral oxidation kinetics, oxygen diffusion, tem- redox. The code has been coupled to HYDRO- perature effects, and fluid transport. It was GEOCHEM (Yeh and Tripathi, 1989b; reviewed as part of the MEND program (Mine Yeh and Cheng, 1999) for simulation of re- Environment Neutral Drainage) in a 1990 re- active transport modeling with biogeochemical port. Another program that serves a similar transformation of pollutants in groundwaters. purpose is SULFIDOX (Pantelis et al., 2002; HYDROGEOCHEM simulates transient and Ritchie, 2003). The geochemistry module in steady-state density-dependent conditions with SULFIDOX is based on PHREEQE and the transient or steady-state distribution of reactive program has been developed from considera- species for saturated or unsaturated media. tions of oxygen transport and temperature gra- Recent versions of HYDROGEOCHEM (1 dients developed within waste rock piles. and 2) can be obtained from Scientific Software Two other programs designed to simulate Group (HYDROGEOCHEM, 2006). reactive transport include CHEMFRONTS FEREACT was developed for two-dimen- (Ba¨ verman et al., 1999) and RETRASO sional steady-state flow with equilibrium and (Saaltink et al., 2004). kinetically controlled reactions (Tebes-Stevens Further research on reactive transport the- et al., 1998). Another code, which was ory, modeling, and codes can be found in developed for biogeochemical transport and the Reviews in Mineralogy volume edited by interactions of oxidative decay of organics Lichtner et al. (1996) and the special issue of with oxygen, iron, manganese, and sulfur Journal of Hydrology, vol. 209 (1998). Water–Rock Interactions 17 5.02.8 WATER–ROCK INTERACTIONS the effects of speciation for copper, sulfate, al- uminum, and iron using the WATEQ4F code. About a dozen major hydrogeochemical Table 1 shows the total dissolved concentra- processes dominate the compositions of most tions and the main species for aluminum and surface and groundwaters. These processes in- sulfate. Several conclusions are readily appar- clude calcite dissolution and precipitation, gyp- ent. First, to approximate the free ion concen- sum dissolution and precipitation, pyrite trations by the total dissolved concentrations is oxidation and formation of hydrous ferric fair as for sulfate in AMD-A (83%) and poor oxide, silicate mineral dissolution (feldspars, as for aluminum in AMD-D (4.1%). Further- micas, chlorites, amphiboles, olivines, and more, for a wide range of total dissolved sulfate pyroxenes) and clay mineral formation (kao- þ concentration, the AlSO4 ion pair is always linitization, laterization, and illitization), dolo- important (50–70% of the dissolved aluminum) mite dissolution and calcite precipitation but with increasing sulfate concentration and (dedolomitization), dolomite formation (do- decreasing pH, the Al(SO4)2 ion triplet be- lomitization), sulfate reduction and pyrite for- comes increasingly important. This ion triplet mation, silica precipitation, evaporation, and has an association constant that is not well es- cation exchange. They are explained in several tablished and some codes might not include it available textbooks (e.g., Appelo and Postma, in their database. 1993; Langmuir, 1997; Drever, 1997a), and Another example of aqueous speciation that only a few examples are given here to demon- includes redox can be shown with the arsenic strate how complex geochemistry can be easily pe–pH diagram shown in Figure 1. Arsenic computed with available codes. Aqueous can exist in several oxidation states including speciation is discussed first, because it is re- As(-iii) as in arsine gas (AsH3), As(0) as in quired for more complex computations. For elemental arsenic, As(ii) as in realgar (AsS), geochemical modeling, aqueous speciation oc- As(iii) as in orpiment (As2S3) and dissolved curs so quickly that it can safely be assumed to arsenite, and As(v) as in dissolved arsenate. be at equilibrium. This assumption is valid for Figure 1 shows the dominant dissolved species, the vast majority of aqueous reactions but not arsenate and arsenite, and their hydrolysis for redox reactions. products as a function of redox potential and pH based on the thermodynamic evaluation of 5.02.8.1 Aqueous Speciation Nordstrom and Archer (2003). These results show the dominance of hydrolysis for arsenate Some brief examples of aqueous speciation species, but it is of minor consequence for the are given here to demonstrate the large de- arsenite species. Hydrolysis is of major impor- creases in free ion concentration or activity that tance in understanding mineral reactions, occur as a result of ion-pair formation or com- kinetics of reactions, and sorption behavior. plexing. Polyvalent ions have a greater ten- At neutral to high pH, the adsorption of arse- dency to associate with other ions of opposite nate onto hydrous ferric oxides is weaker, and charge and among polyvalent cations that are the high anionic charge on the dissolved arse- found commonly in waters, iron, and alumi- nate developed through hydrolysis combined num are prime examples. Alpers and Nordst- with negatively charged surfaces helps to ac- rom (1999) tabulate analyses of four acid mine count for this lack of adsorption. The lack of waters with pH in the range 4.9–0.48 and show significant arsenite hydrolysis helps explain the

Table 1 Example of aqueous aluminum and sulfate speciation for acid mine waters covering a range of pH and composition. Sample AMD-A AMD-B AMD-C AMD-D Temperature (1C) 16.0 19.5 24.0 34.8 pH 4.9 3.25 1.10 0.48 Total dissolved Al (mg l–1) 5.06 19.8 1,410 2,210 %AsAl3 þ 29 26 10 4.1 þ % As AlSO4 51 66 57 61 % As Al(SO4)2 2 4.5 32 32 –1 Total dissolved SO4 (mg l ) 206 483 50,000 118,000 2 %AsSO4 83 71 18 8 % As HSO4 0 2 32 53 þ % As AlSO4 and AlSO4 4.5 11 12 8 % As Fe(ii/iii)–SO4 ions 0 2 29 26 18 Modeling Low-Temperature Geochemical Processes

24

20

1.0 16

0 H3AsO4 12 − H2AsO4 8 0.5

2−  HAsO p 4 4 Eh (V)

0 3− 0 H3AsO3 AsO4 0

–4

–8 – H2AsO3 –0.5

–12

–16 0268 4 10 12 14 pH Figure 1 Species predominance diagram for dissolved arsenic at 25 1C and 1 bar. Source: Nordstrom and Archer (2003).

more competitive adsorption of arsenate re- were dissolved in water at fixed lative to arsenite. until was reached. The solid line represents the equilibrium solubility of calcite for this range of carbon dioxide 5.02.8.2 Modeling Sorption Reactions partial pressure and the equilibrium pH values at each P from 8.3 to 6.7 are shown Although sorption modeling should be in- CO2 in parentheses. cluded in our discussion, this extensively re- Many shallow groundwaters reflect calcite searched area warrants an entirely separate dissolution as the dominant control on water chapter. Several books cover the subject well, quality. Groundwaters incorporate higher P including Dzombak and Morel (1990), Davis CO2 than that of the atmosphere because of carbon and Hayes (1986), Stumm (1987), and Hochella dioxide production in the soil zone and organic and White (1990). matter decomposition in the groundwater. A –2 –1 range of PCO2 from 10 to 10 and pH values 5.02.8.3 Model Simulations of Mineral from 7 to 8 are common for most groundwa- Reactions ters. Water analyses in a carbonate terrain of Pennsylvania (Langmuir, 1971) are compared One of the most ubiquitous geochemical in Figure 2b to the predictions in Figure 2a. processes is the dissolution of calcite. Dissolu- Although this plot simplifies the water chemis- tion of calcite in the environment can be the try and does not take into account dissolution dominant source of dissolved calcium in many of other minerals, it does show the dominant waters, but dissolved inorganic carbon (DIC) control by a relatively simple reaction. The can have at least two sources: calcite and CO2 PCO2 values fall within the expected range and produced from organic decay. Calcite dissolu- calcite solubility equilibrium provides an upper tion has been modeled with PHREEQCI for a boundary. The saturation index plot in Figure range of carbon dioxide partial pressure, PCO2 : 3 for the same samples takes into account tem- Figure 2a is a plot of calcite dissolution in perature and ionic strength effects on the terms of calcium and DIC concentrations at activities and also shows that saturation with –3.5 PCO2 values ranging from atmospheric (10 ) respect to calcite is reached and provides an to 10–1. Computationally, increments of calcite upper limit to calcium and DIC concentrations. Water–Rock Interactions 19

5

4 (6.7)

3 Solubility

3.5 − (6.9) −1.0 = = Equilibrium Ca (mm) 2 2 2 CO CO P (7.3) P log log −1.5 1 (8.3)

–2.0 0 (a) 0 2.5 5.0 7.5 10.0 12.5 15.0

5

4

3

Ca (mm) 2

1

0 0 2.5 5.0 7.5 10.0 12.5 15.0 (b) DIC (mm)

Figure 2 (a) Calcium and DIC concentrations plotted for calcite dissolution at log PCO2 ¼3.5, 2, 1.5, and 1 (dotted lines) up to equilibrium calcite solubility (solid line). The pH values for each equilibrium 1 solubility at the specified log PCO2 are shown in parentheses. Plot was computed with PHREEQCI for 25 C and 1 bar. (b) Calcium and DIC concentrations plotted from data of Langmuir (1971) for groundwaters taken from a limestone aquifer in Pennsylvania. Dotted and dashed lines are the same as those in (a).

2

1

0

Saturation index, calcite −1

−2 7.00 7.25 7.50 7.75 8.00 8.25 pH Figure 3 Saturation indices for calcite from the same groundwaters as in Figure 2, plotted as a function of pH. Reproduced by permission of Blackburn Press. 20 Modeling Low-Temperature Geochemical Processes As the pH increases, there is a greater propor- without forming a precipitate, shown by the tion of carbonate ions relative to bicarbonate dashed line with a crossover pH of 3.26. Third, that increases the saturation with respect a precipitate such as ferrihydrite is allowed to to calcite. At pH values t7, waters are nearly form, which lowers the crossover pH to 2.39. If always undersaturated with respect to calcite the Ksp of the precipitating phase is lower, such (and most other carbonate minerals). as that for crystalline goethite, the crossover Pyrite oxidation is a complex hydrobiogeo- pH is much lower as shown by the dotted line. chemical processes that accounts for about However, crystalline goethite is not stable at 11% of the sulfate found in river drainages pH values o2 and jarosite would precipitate (Berner and Berner, 1996; although these esti- instead. The reason for showing the goethite mates do not include large flows of acid mine curve is to demonstrate the effect of lowering drainage from Rio Tinto and Odiel Basins to the Ksp for a precipitating phase of the same the ocean, Nieto et al., 2007). Mining activities stoichiometry. The dashed lines cross over the have increased the rate of pyrite oxidation and original line, because the oxidation of ferrous caused severe contamination of many water- iron involves both proton-consuming and pro- ways with acid and metals. When pyrite oxi- ton-producing reactions. The oxidation of dizes, the sulfur rapidly converts into sulfate Fe2 þ –Fe3 þ consumes protons: but the oxidation of the iron proceeds more slowly, depending on pH. Simulating the oxi- 2þ1 þ- 3þ 1 Fe 4O2 þ H Fe þ2H2O ð17Þ dation of pyrite is instructive in summarizing the chemistry of this complex process (Nordst- which happens at all pH values. The hydrolysis rom, 2000). In Figure 4, PHREEQCI was used and precipitation of a ferric phase to simulate pyrite oxidation by adding incre- produces protons: ments of oxygen to pyrite in water. The reac- tion also could be simulated by adding Fe3þ þ H O-FeðOHÞ2þ þ Hþ ð18Þ increments of pyrite to an excess of oxygen. 2 The results vary with the amount of oxidation allowed and are represented in the figure by a 3þ - þ solution pH as a function of the amount of Fe þ3H2O FeðOHÞ3þ3H ð19Þ pyrite oxidized. First, pyrite oxidation to an acid ferrous sulfate solution only, is shown by which only happens if the pH has reached the the solid line. Second, the same reaction occurs point of hydrolysis, i.e., near or above a 3þ but the ferrous iron is allowed to oxidize pH ¼ pK1 ¼ 2.2 for Fe hydrolysis. Consequently,

Pyrite oxidized, no Fe(II) oxidized 4 Pyrite oxidized, Fe(II) oxidized no precipitation

3 Crossover pH = 3.26

pH Crossover pH = 2.39 Pyrite oxidized, 2 Fe(II) oxidized, and ferrihydrite precipitated

1 Goethite precipitation

10−2 10−1 1101 102 103 Pyrite oxidized (mmol kg−1 ) H2O Figure 4 Change in pH as a function of the amount of pyrite oxidized under four scenarios: (1) pyrite oxidizes to an acid ferrous sulfate solution without any further oxidation (solid line); (2) pyrite oxidizes and the resultant ferrous sulfate solution is allowed to oxidize, but no precipitation is allowed (upper dashed line); (3) pyrite oxidizes, the ferrous sulfate solution oxidizes and precipitates ferrihydrite (pKsp ¼ 4.89, lower dashed line); and (4) pyrite oxidizes, ferrous sulfate solution oxidizes, and goethite precipitates (dotted line). Com- puted with PHREEQCI at 25 1C and 1 bar; thermodynamic data from Nordstrom et al. (1990). Water–Rock Interactions 21

Initial pH 4 Final pH

3 pH

2

1

10−2 10–1 110102 103 Pyrite oxidized (mmol kg–1 ) H2O Figure 5 Change in pH as a function of the amount of pyrite oxidized under scenarios (1) and (3) from Figure 4. Points are actual values measured from acid mine waters. Initial pH is based on field measurements taken on site and the amount of pyrite oxidized is derived from stoichiometry assuming that all the dissolved sulfate is from pyrite oxidation. Final pH was measured after the sample had been allowed to oxidize for at least two weeks in an unfiltered, unpreserved bottle. at lower pH values there is no hydrolysis and In this comparison of a simulation with actual the pH can only increase on oxidation. The field data, two aspects are noteworthy. First crossover pH reflects the balance between the is the good agreement but since this simulation proton-consuming and the proton-producing is sensitive to the chosen Ksp of the precipita- reactions, a small buffering process repre- ting phase, the agreement indicates that the sented by the small plateau in the curves. This solubility product constant for freshly precipita- diagram, although explaining some of the ting hydrous ferric oxide is a reasonable model complexities of the chemistry of acid rock choice. drainage, does not include the consequences of Waters not only undergo geochemical reac- acid dissolution involving calcite and alumino- tions but they commonly mix. One of the clas- silicate minerals. Nevertheless, some water sic examples of mixing is seawater intrusion analyses are available from mine sites that into coastal aquifers, often enhanced because are predominantly affected by pyrite oxidation of groundwater withdrawal. When seawater andlittleelse.Thesesamples, collected from and fresh groundwater mix, both at saturation the Leviathan mine area, California, and Iron with respect to calcite, the result can lead to Mountain, California (Ball and Nordstrom, undersaturation with respect to calcite, i.e., 1989; Nordstrom, 1977), include a pH meas- calcite dissolution. The possibility of this sce- ured in situ and a pH measured some weeks nario and other combinations (some leading to later after the ferrous iron had oxidized and mineral precipitation from the mixing of waters precipitated. Figure 4 reproduces Figure 5 that are both initially undersaturated) was out- with only the two lines shown for pyrite lined by Runnells (1969). Computations made oxidation but no ferrous iron oxidation (solid by Plummer (1975) showed the proportion of line) and pyrite oxidation with precipitation mixing over which the undersaturation effect, of ferrihydrite (or the most soluble hydrous and consequent dissolution of coastal lime- ferric oxide, as a dashed line). Because there stone, was operative. Figures 6a–6d are exam- are low concentrations of cations in these ples from Plummer (1975) and demonstrate samples, the initial pH values (open circles) that for a large range of seawater in the mix- can be assumed to be caused by pyrite oxida- ture, calcite undersaturation can occur, depen- tion. The final pH after oxidation and precip- ding on carbon dioxide partial pressure and itation is shown by the closed circles. The final temperature. These calculations were done over pH can be seen to closely approximate the a range of temperatures, partial , and dashed line in agreement with the simulation. pH values. They also were conducted with 22 Modeling Low-Temperature Geochemical Processes

1.0 1.0

0.8 0.8

0.6 0.6 Supersaturation 0.4 Supersaturation 0.4 −4.0 atm −4.0 atm 10 atm 0.2 10 0.2 −3.0 −3.0 atm 10 0.0 10 0.0 atm 2.0 atm −0.2 −2.0 −0.2 − 10 10 −0.4 −0.4 − −0.6 −0.6 10 1.0 atm −1.0

10 atm index Calcite saturation Calcite saturation index Calcite saturation − −0.8 0.8 Undersaturation Undersaturation 1 atm −1.0 1 atm −1.0

−1.2 −1.2 5 °C 15 °C −1.4 −1.4 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 (a) Percent seawater in mixture (b) Percent seawater in mixture

1.0 1.0

0.8 0.8

0.6 0.6

0.4 −4.0 atm 0.4 atm atm −4.0 10 −2.0 atm −3.0 −3.0 10 2.0 10 0.2 −3.0 − 0.2 10 10 10 10 Supersaturation Supersaturation 0.0 0.0 Undersaturation 10−4.0 Undersaturation − −0.2 0.2 − −0.4 0.4 −1.0 −1.0 atm 10 10 −1.0 atm − atm −0.6 10 0.6 Calcite saturation index Calcite saturation Calcite saturation index Calcite saturation − −0.8 0.8 1 atm − 1 atm −1.0 1.0 − −1.2 1.2 25 °C − 35 °C −1.4 1.4 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 (c) Percent seawater in mixture (d) Percent seawater in mixture Figure 6 Calcite saturation indices plotted as a function of percent seawater mixing with a carbonate aquifer

water with contours representing different levels of PCO2 . Source: Plummer (1975).

actual carbonate groundwater compositions balances for catchments and groundwaters and coastal seawater for several locations along dominated by silicate hydrolysis. They investi- the Florida coast. gated nine drainages in six areas of widely The inverse or mass-balance modeling ap- varying lithology and climatic settings in the proach provides additional constraints on re- United States. One of these is shown in Figure 7 actant and product mineral phases when the for the Wyman Creek drainage in the Inyo mineral mass transfers are plotted as a function Mountains, California. Mineral mass transfers of the range of solid solution compositions. for dissolution (positive values in mol kg–1)and Bowser and Jones (2002) (Chapter 5.04) precipitation (negative values in mol kg–1)are discovered this application when investigating plotted as a function of the percent montmo- the effect of compositional ranges of feld- rillonite solid solution. The gray band shows the spars, phyllosilicates, and amphiboles on mass restricted range of solid solution composition Water–Rock Interactions 23

1,500

Calcite

1,000 Dolomite

Plagioclase )

1 500 − mol kg µ

0 MTC ( Biotite K-feldspar

−500 Smectite_ss

Goethite

−1,000 0 10203040506070 Percent montmorillonite Figure 7 Mineral mass-transfer coefficients versus smectite solid solution composition for Wyman Creek mass balances, Inyo Mountains (Bowser and Jones, 2002). Upper and lower bounds on possible smectite compositions are where goethite and K-feldspar mass transfers are equal to 0. Reproduced by permission of American Journal of Science from Bowser and Jones (2002).

(27–45%) determined by the crossover points distillations (see Chapter 5.11). Corroboration of for K-feldspar and goethite, respectively. These the isotopic modeling was achieved by predicting restrictions apply, because K-feldspar cannot the isotopic compositions of the dolomite and precipitate in these dilute waters and goethite is the anhydrite. Actual d34S values for anhydrite a weathering product being formed, not dis- fit the values assumed in the model calcula- solved. Similar arguments show that there are tions. Further consistency was found when the restrictions on the range of plagioclase subject adjusted 14C ages combined with Darcy’s law to weathering. Indeed, it is surprising to find resulted in groundwater flow velocities that how closely tied the fluid compositions for ma- agreed within a factor of 5 of those calculated jor cations are to the Na/Ca ratios of plagio- by a digital flow model. Figure 8 portrays the clase, the Ca/Mg ratio of ferromagnesian saturation indices of calcite, dolomite, and silicates, and to the Fe/Mg ratio of ferromagne- gypsum (surrogate for anhydrite) for waters sian silicates. from the Madison aquifer. Calcite reaches sat- The final example in this set is from the uration quickly and tends to be supersaturated. Madison regional aquifer study by Plummer This supersaturation may reflect the pressure et al. (1990). The Madison Limestone aquifer effect on the ion activities and the solubility occurs in Wyoming, Montana, and South Da- product constant (pressure corrections were kota. Plummer et al. (1990) utilized a combi- not modeled), it may be caused by pH changes nation of saturation index constraints, inverse on pumping pressurized water to the surface, it modeling, and carbon and sulfur isotopes to may result from calcite that has some substi- delineate geochemical reaction models for the tuted elements displacing the SI values, it may flow paths. The models indicated that the ma- be caused by an inhibition on calcite precipi- jor reaction is dedolomitization, i.e., dolomite tation kinetics by magnesium, or it may be dissolution and calcite precipitation driven caused by gypsum dissolving faster than calcite by anhydrite dissolution, sulfate reduction, can precipitate. [Ca2 þ þ Mg2 þ ]/Naþ cation exchange, with A subset of the mass-balance results for the some local halite dissolution. Sulfur isotopes Madison aquifer study is shown in Table 2 were treated as an isotope dilution problem covering the range of parameters encountered and carbon isotopes were treated as Rayleigh from recharge to discharge although these 24 Modeling Low-Temperature Geochemical Processes

1.0

0.5

0

−0.5 Calcite saturation index

−1.0 0 5 10 15 20 25

1.0

0.5

0

−0.5

−1.0

−1.5 Dolomite saturation index

−2.0 0 5 10 15 20 25

0

−1

−2

Gypsum saturation index −3

0 5 10 15 20 25 Sulfate concentration (mmol kg−1 ) H2O Figure 8 Saturation indices for calcite, dolomite, and gypsum for groundwaters from the Madison limestone aquifer. Source: Plummer et al. (1990).

selected samples are not along the same flow being formed. Cation exhange in Table 2 refers path. The general trend in chemistry is indicated to (Ca þ Mg)/Na, i.e., exchange of calcium and here. Samples near recharge are low in sulfate magnesium for sodium. The measured sulfur and the amount of mass transfer is low. As the isotopic compositions of the H2S and of the water moves down gradient and evolves chem- anhydrite match nicely with the model simula- ically, it increases in sulfate from anhydrite dis- tion and the stable carbon isotopes. solution. Increased anhydrite dissolution leads Mazor et al. (1993) pointed out that some of to increased dissolution of dolomite and in- the samples from the Madison aquifer had high creased calcite precipitation. With increasing tritium contents when the 14C results indicated age there is more organic matter (represented by dates too old for tritium and suggested that CH2OinTable 2) available for decomposition, significant mixing of younger and older waters which results in greater amounts of hydrous may have occurred. Mixing and dilution trends ferric oxides dissolving (reducing) and pyrite can have similar chemical appearances to Water–Rock Interactions 25 Table 2 Selected mass transfer (in mmol kg1 water) results from Plummer et al. (1990) for the Madison Limestone aquifer. Well no. F6-19 F6-17 F6-13 F7-10 F8-25 F8-21 F3-20

SO4 0.18 0.52 2.19 5.73 8.97 13.56 19.86 Dolomite 0.14 0.14 0.60 0.74 1.87 2.90 3.54 Calcite 0.18 0.41 1.62 2.64 4.70 7.15 5.33 Anhydrite 0.15 0.51 2.27 5.93 9.19 13.56 20.15 CH2O 0.01 0.02 0.20 0.44 0.71 0.30 0.87 FeOOH 0.00 0.01 0.05 0.12 0.21 0.11 0.09 Pyrite 0.00 0.01 0.05 0.12 0.19 0.06 0.09 Ion exch. 0.01 0.03 0.04 0.44 0.19 0.14 8.28 NaCl 0.01 0.02 0.03 2.83 1.38 0.97 15.31 KCl 0.01 0.02 0.02 0.27 0.28 0.33 2.52 CO2 0.07 0.17 –0.21 0.42 1.18 0.40 0.04 d13C(%) calculated 8.86 9.33 7.79 9.67 5.52 3.59 2.21 D13C(%) measured 7.82 10.0 6.80 9.70 5.50 3.50 2.34 Apparent age (years) Modern Modern Modern 2,386 14,461 13,310 22,588

Note: Positive values signify dissolution and negative values precipitation. Samples, although not along the same flow path, are in the general direction of recharge to discharge from left to right. hydrochemical evolution, and caution must be An example of modeling reactive transport used to distinguish evolutionary trends from of acid mine waters with OTEQ is shown in mixing trends by age-dating techniques. Figure 9 (Ball et al., 2003) for the drainage released from the Summitville mine in the San Juan Mountains of southwestern Colorado 5.02.8.4 Reactive-Transport Modeling in into the Alamosa River. The model was cali- Streams brated with tracer injection and synoptic sa- mpling techniques including measurements of Although biological reactions, mostly dis- Fe(II/III) that helped constrain precipitation of solved oxygen degradation or nutrient uptake, hydrous ferric oxides in the model. Sodium have been modeled in flowing streams and chloride was used as the tracer. Figure 9a rivers for a long time, trace-metal reactions shows measured pH and simulated pH with have not been modeled until relatively recently. reaction. The main in-stream reactive chemistry Bencala (1983) considered solute transport in in this system is the oxidation of iron, the pre- pool-and-riffle streams using a kinetic term for cipitation of hydrous ferric oxides, the precip- sorption; and Bencala and Walters (1983) in- itation of hydrous aluminum oxides, the troduced transient storage into their modeling adsorption of trace metals, and pH changes of trace-metal transport. One of the most (controlled by the oxidation, hydrolysis, and obvious inputs of trace metals to surface wa- precipitation reactions and by the neutraliza- ters is from mining and mineral-processing tion of inflows). Simulated and measured wastes. Techniques for modeling these acid dissolved and total aluminum and iron mine water reactions continued to develop concentrations are shown in Figures 9b and during the 1990s from empirical rate constants 9c, respectively. Iron and aluminum concentra- and partition coefficients to mechanistic sorpt- tions decrease rapidly because of precipitation ion models such as surface complexation and during downstream transport. Figure 9d shows equilibrium precipitation of mineral phases the copper concentrations; when adsorption is (Brown and Hosseinipour, 1991; Kimball invoked in the model the agreement between et al., 1994, 1995; Runkel et al., 1996, 1999). measured and simulated copper concentrations Reaction-transport models such as these re- is within analytical error. quire more accurate stream-discharge measure- ments than can be obtained from current-meter measurements. These are obtained from con- 5.02.8.5 Geochemical Modeling of Catchments stant-flow tracer injection studies along with synoptic sampling, including all possible in- Attempts to model chemical weathering of flows, so that the transport model can be re- catchments have used a variety of approaches liably calibrated. Not only has this approach and were originally designed to understand been used to define sources and sinks of trace acidification processes. The BIRKENES code metals in mountainous streams but it also has (Christophersen et al., 1982) was one of the first been helpful in predicting remediation scenar- developed to model catchment stream chemis- ios for mine sites (Runkel and Kimball, 2002). try. It used cation–anion charge balance, a 26 Modeling Low-Temperature Geochemical Processes

8

7

6 Alamosa River Terrace Reservoir 5 Wightman Fork at mouth

pH (standard units) 4

3 0 5 1015202530 (a)

300

250

200 Wightman Fork

m) at mouth

µ 150 Al ( 100 Terrace Alamosa River Reservoir 50

0 0 5 10 15 20 25 30 (b)

250

200

150 Wightman Fork at mouth m) µ 100 Fe ( Terrace Alamosa River 50 Reservoir

0 0 5 10 15 20 25 30 (c)

25

Dissolved Total 20 Simulated Wightman Fork Measured 15 at mouth m) µ

Cu ( 10 Terrace Reservoir 5 Alamosa River

0 0 5 10 15 20 25 30 (d) Distance (km) Figure 9 Downstream profiles in the Wightman Fork/Alamosa River system of: (a) pH measured and simulated; (b) dissolved aluminum concentrations measured and simulated; (c) dissolved iron concentrations measured and simulated; and (d) copper concentrations measured and simulated. Simulations were obtained with the OTEQ code after calibration on tracer-injection data and Fe(II/III) determinations. Water–Rock Interactions 27 gibbsite equilibrium solubility control for al- Codes that contain more detailed considera- uminum concentrations, a Gapon ion exchange tion of chemistry, especially reaction kinetics, for metals sorption, and rates for sulfate ad- include PROFILE (Sverdrup, 1990; Warfvinge sorption/desorption in a two-reservoir model. and Sverdrup, 1992) and UNSATCHEM (for The model was calibrated by input mass fluxes the unsaturated zone, Suarez and Simunek, and output mass fluxes for the Birkenes catch- 1996). ment in Norway to provide the water flux in- The main problem with any of these models formation and to fit empirical parameters. is that they are calibrated with data that are too The ILWAS code (Integrated Lake-Water- short-term for the long-term processes they are shed Acidification Study; Chen et al., 1983; trying to predict on the catchment scale Gherini et al., 1985) also contains a semi- (Drever, 1997b; Hornberger, 2002). empirical model but is much more detailed than the BIRKENES code with respect to its hydrologic and geochemical compartments. 5.02.8.6 Reliability of Geochemical Model Alkalinity was one of the key chemical com- Simulations ponents in the model. Because the code was originally calibrated on three watersheds re- One approach to determine the reliability of ceiving acid rain in upstate New York, it was geochemical codes is to take well-defined input programmed with mineral rate dissolution data and compare the output from several dif- data, gibbsite solubility equilibrium, and other ferent codes. For comparison of speciation re- parameters pertinent to those environments. sults, Nordstrom et al. (1979) compiled a The considerable quantity of detailed data seawater and a river water test case, that is, needed to calibrate the ILWAS code limits its seawater and river water analyses that were general usefulness. used as input to 14 different codes. The results The MAGIC code (Model of Acidification of were compared and contrasted, demonstrating Groundwater In Catchments; Cosby et al., that the thermodynamic databases, the number 1985a, b) is similar in many respects of ion pairs and complexes, the form of the to the BIRKENES code, but parameters for activity coefficients, the assumptions made for soil–water and stream–water chemistry are redox species, and the assumptions made for ‘‘lumped’’ or averaged over the spatial scale equilibrium solubilities of mineral phases were that can include many heterogeneities. MAGIC prominent factors in the results. Additional ar- was designed to simulate long-term (annual) senic, selenium, and uranium redox test cases averages, whereas BIRKENES was designed to were designed for testing of the WATEQ4F simulate short-term (hours to days) responses. code (Ball and Nordstrom, 1991). Broyd et al. Equilibrium reactions include soil cation- (1985) used a groundwater test case and com- exchange reactions, solubility control by pared the results from 10 different codes. Such gibbsite, CO2–H2O hydrolysis reactions, aque- test cases could be expanded to include exam- ous speciation of aluminum among sulfate ples of heterogeneous reactions, mixing with and fluoride complexes, water dissociation, reaction, sorption, temperture dependence, re- ion balance, and temperature dependence. active transport, and inverse modeling. The Activity coefficients appear not to have been current version of PHREEQC includes 18 ex- used and the sensitivity of the model to this amples of code testing. Some of these are true factor has not been addressed. Wright and ‘‘tests’’ in that they can be compared with Cosby (1987) found good agreement between measurements or independent computations, simulated and measured alkalinities for two while others are just examples of the code ca- manipulated catchments in Norway using the pability. The EQ3/6 code also shows several MAGIC code. Organic acids have been in- examples of code capability in addition to cluded with the code and the simulations of the comparative tests. A comparison of PHREEQC Norway catchments revisited with improved and HYDROGEOCHEM codes to simulate results (Cosby et al., 1995). An alternative to transport and reaction of acidic fluids in ILWAS and MAGIC is the code Enhanced alluvial material was obtained by Brown et al. Trickle Down (ETD; Nikolaidis et al., 1989, (2000). This comparison gave similar results 1991). Geochemical processes include cation and differences were attributed to different exchange, chemical weathering, sulfate adsorp- units in model output, different activity coef- tion, and sulfate reduction. Comparisons of the ficient expressions, and different ionic-strength three codes, ILWAS, MAGIC, and ETD, were calculations. The equilibrium assumptions used made by Rose et al. (1991a, b). The codes were by the codes did not appear to hold for column found to provide similar forecasts on a relative leaching studies. scale but substantial differences with respect In another example, five test cases were com- to specific concentrations (absolute scale). puted by PHREEQE and EQ3/6 and the same 28 Modeling Low-Temperature Geochemical Processes thermodynamic database was run for each recomputed the speciation assuming reasonable program (INTERA, 1983) to test for any code errors in the input analytical data and in the differences. The five examples were speciation of thermodynamic data. The conclusion was that seawater with major ions, speciation of seawater supersaturation for these minerals could not be with complete analysis, dissolution of microcline accounted for by errors in the water analyses in dilute HCl, reduction of hematite and calcite nor in the thermodynamic data. For ferric oxy- by titration with methane, and dedolomitization hydroxide, iron colloids were probably getting with gypsum dissolution and increasing temper- through the filter and contributing to the ap- ature. The results were nearly identical for each parent dissolved Fe(iii) concentrations and the test case. Test cases need to become standard supersaturation effect. For aluminum hydrox- practice when using geochemical codes so that ide, the saturation indices did not indicate the results will have better credibility. A com- supersaturation with respect to amorphous parison of code computations with experimental aluminum hydroxide and hence they were prob- data on activity coefficients and mineral sol- ably reasonable. For the remaining minerals it ubilities over a range of conditions will also im- was concluded that the supersaturation may prove credibility (Nordstrom, 1994). have been realistic, because it could not be ac- Bruno et al. (2002) compared the results of counted for by propagation of these errors. blind-prediction modeling for geochemical Other causes of supersaturation include impure modeling of several trace elements of concern mineral phases (solid substitution or defects), to radioactive waste disposal for six natural disordered or fine-grained nature, inhibition of analog sites. Blind-prediction modeling was an precipitation rates, and possible unaccounted exercise developed in radioactive research on for pressure effects on equilibria. repository analog sites whereby actual water Criscenti et al. (1996) determined overall un- analyses for major ions were given to different certainty from geochemical computations by a groups of geochemical modelers who were combination of propagating Monte-Carlo- asked to simulate dissolved trace-element con- generated analytical and thermodynamic un- centrations based on assumed solubility equili- certainties through a geochemical code and bria; the results were compared with actual applying the ‘‘generalized sensitivity analysis’’ trace-element concentrations determined on the (Spear and Hornberger, 1980) to the output. groundwaters but kept secret from the model- One of the results of this study is that the ers until the modeling was completed. They aqueous speciation scheme used in many geo- found that thorium and uranium seem to be chemical codes is not necessarily consistent controlled by mineral solubilities, whereas with the speciation scheme used to define strontium, zinc, and rare earth element (REE) standard pH buffers by the National Bureau mobilities seem to be related to the major ions of Standards. This conclusion raises the possi- and complex formation. Other elements such as bility that geochemical computations introduce nickel suffer from insufficient thermodynamic an error when speciating natural water based data. Sorption reactions were not examined in on a field pH measurement calibrated with one sufficient detail to draw conclusions. of these buffers. Cabaniss (1999) investigated Another approach to determining model re- methods of uncertainty propagation, com- liability is to perform sensitivity or uncertainty paring the derivative-based method (assumes analyses. One of the first examples is the exam- a linear approximation) with the Monte Carlo ination of equilibrium aluminum computations technique for solubility equilibria computa- for surface waters using the Monte Carlo tions of gibbsite, calcite, and jarosite. He found method of randomizing sources of error in the that derivative methods and the assumption of water analysis and thermodynamic data (Schec- Gaussian uncertainty can misrepresent the her and Driscoll, 1987, 1988). The results propagated uncertainty. showed that uncertainties in the input data did Computational speciation can be compared not contribute significantly to computational with analytical speciation for some species. speciation errors. Nordstrom and Ball (1989) There is always the problem that analytical used two different sets of water analyses, methods also suffer from operational defini- groundwater analyses from a granite in Swe- tions, interferences, limits of detection, and as- den, and surface water analyses from a creek sociated assumptions. Nevertheless, there is no receiving AMD in California, to evaluate un- better method of determining accuracy of certainties in the water analyses and uncertain- speciation than by comparing analytical results ties in the thermodynamic data as possible with computational results (Nordstrom, 1996). sources of consistent supersaturation effects for In the few instances where this has been done, calcite, fluorite, barite, ferric oxyhydroxide, and the comparison ranges from excellent to poor. aluminum hydroxide. Instead of Monte Carlo Examples of studies of this type can be found in methods, they used a brute force approach and Leppard (1983), Batley (1989), and Nordstrom Final Comments 29 (1996, 2001). Sometimes, comparison of two concentrations determined analytically with Eh analytical methods for the same speciation can values measured electrometrically with a plat- give spurious results. In Table 3, measured and inum electrode. An example of this comparison calculated ionic activity coefficients for seawa- is shown in Figure 10 (Nordstrom, 2000). For ter at 25 1Cand35% salinity are compared, iron concentrations greater than 10–6 m, the after adjusting to a reference value of comparison is generally excellent (usually gCl ¼ 0.666 (Millero, 2001). These values would within 30 mV), indicating that the analytical indicate that for a complex saline solution such data, speciation calculations, and redox meas- as seawater, the activity coefficients can be cal- urements are all consistent with equilibrium culated with a high degree of confidence. Much as predicted by the . This com- more effort along these lines is needed to better parison is one of two redox speciation compu- determine the errors and uncertainties for tations that can be tested electrometrically. speciation calculations and to identify reaction Deviations from equilibrium are apparent at equilibria and species for which thermo low iron concentrations, because the electro- dynamic data need to be measured. activity of iron is low enough that other elec- Iron redox speciation was evaluated by tron acceptors, such as dissolved oxygen, begin comparing the Eh values computed from a to interfere. The other redox condition that speciation code that accepts Fe(ii) and Fe(iii) permits testing with the Nernst equation is sulfide. Berner (1963) showed that the platinum electrode gives Nernstian behavior in anoxic marine sediments in response to dissolved Table 3 Comparison of measured and calculated sulfide activities. All other redox species in nat- ion activity coefficients in seawater at 25 1C and 35% ural waters are not sufficiently electroactive to salinity, referenced to gCl ¼ 0.666 (Millero, 2001). establish Nernstian equilibrium. Ion Measured Calculated Nordstrom (2001) demonstrated that if one compares computed free-fluoride ion activities Hþ 0.590 0.592 þ or concentrations (in this example, with WA- Na 0.6680.6700.678 0.674 TEQ4F) with measured values obtained with a Kþ 0.625 0.619 þ fluoride ion-selective electrode, the results are NH4 0.6160.592 0.624 B –6 Mg2 þ 0.2420.22 0.211 in good agreement down to 10 m. This Ca2 þ 0.2030.180 0.205 agreement between measurement and calcula- F– 0.296 0.297 tion corroborates the fluoride speciation by the Cl– 0.666 0.666 IA method. OH– 0.2420.2540.254 0.263 HS– 0.6810.6730.550 0.688 HCO3 0.5760.5920.528 0.574 5.02.9 FINAL COMMENTS B(OH)4 0.4190.3980.351 0.384 2 SO4 0.1040.1120.1210.121 0.110 Numerous models and codes have been CO2 0.0400.0410.0350.035 0.041 3 developed over the last century for interpreting

1.0

Leviathan samples 0.8 Iron Mountain samples Summitville samples 0.6

0.4

0.2 Eh (meas. Pt electrode) (V)

0 0 0.2 0.4 0.6 0.8 1.0 Eh calculated from Fe (II/III) (v)

Figure 10 Eh measured with a Pt electrode on site compared with Eh calculated from Fe(II/III) determi- nations and speciated with WATEQ4F. Source: Nordstrom (2000). 30 Modeling Low-Temperature Geochemical Processes and portraying low-temperature geochemical than what is sought in science. Evaluation of processes. They have been applied to a great model capabilities makes scientific sense but variety of conditions and processes and have not validation. The question has also been enhanced our ability to understand how low- raised as to whether it is really necessary to temperature earth systems work. However, ‘‘predict’’ in a temporal sense. Scientific pre- many of these models have a dangerous sophis- diction is better described as ‘‘logical’’ predic- tication for computing almost any type of pos- tion not temporal prediction and hanging sibility without adequately constraining what is regulatory decisions solely on the basis of probable. Perhaps this affair is little different model predictions may not be wise or neces- from many centuries ago when we had fewer sary (Oreskes, 2000b). scientific tools and more imagination to play Science progresses by testing hypotheses and with. The danger in greater model sophistication by its explanatory success. Success is measured is the difficulty in testing and refuting it. If we by consistency between observations and calcu- cannot test a model, then we have no means of lations (which is not proof of validity), logical determining its reliability. And yet if we do not structure, simplicity combined with wide appli- strive for greater sophistication, then the model cability, and consensus through independent lacks representativeness (Oreskes, 2000a). peer review (also not proof of validity). Oreskes What we must remember is that modeling (2000a) quotes Richard Feynman, ‘‘Doubt is the is a tool—a useful tool to be sure, but not essence of understanding.’’ Yet doubt is exactly something that can ever replace the experience what regulatory agencies are trying to minimize gained from directly working on a hydrogeo- or eliminate. Oreskes (2000a) offers a solution chemical problem for several years. Expert that seems obvious to Earth scientists: our com- judgment, developed over long time periods putational process has far exceeded our and involving many mistakes, along with care- observational data on natural systems. More fully acquired empirical observations in the field data and related empirical observations are field and in the laboratory, will ultimately guide needed. Field data will provide the necessary our models from possibility to probability. constraints to achieve the legitimacy that is ‘‘y even the most mathematically and compu- being sought by the public. Sophisticated com- tationallly sophisticated model will not absolve putations, especially in the hands of the un- us of the need for judgment, nor of the need skilled, have the possibility of achieving any to justify our judgment in human terms’’ preconceived result unless adequately con- (Oreskes, 2000a). Expert judgment is particu- strained by empirical data. larly important in identifying the appropriate- Future efforts should be directed toward ness of assumptions in applying a model and developing standardized test cases for a wide constitutes a bigger problem than that of model variety of processes against which code per- formulation. formance can be compared and tested, incorpo- Model reliability is a very important aspect ration of reliable methods of accounting for of communicating computational results to metal–organic complexing involving humic sub- managers, risk assessors, stakeholders, politi- stances, recognition of artifacts of sample col- cians, and the public. Unfortunately, sophisti- lection in the determination of trace elements in cated model computations are not easy to natural waters, more comparisons of analytical interpret, model results are often nonunique, versus computed speciation to obtain accuracy and modeling is often state-of-the-art science estimates of aqueous speciation, development of whose reliability has not been adequately routine techniques for estimating uncertainties tested. Because reliability has often been in model calculations, and more detailed studies couched in terms of ‘‘verification’’ and ‘‘val- of fine-grained mineralogy that are reactive idation’’ for the convenience of regulatory re- phases in geochemical systems. quirements (Jenne and Krupka, 1984; Jackson, 1988; Mattigod, 1995; OECD/NEA, 1994; Kirchner et al., 1996; Huguet, 2001; Freedman and Ibaraki, 2003; Celia et al., 1992), confusion ACKNOWLEDGMENTS about the limitations of models and even misunderstandings about how science works This chapter was accomplished through the have been propagated. Words such as verifi- support of the National Research Program and cation and validation might make sense in it has benefited substantially from the hosts of a regulatory or legal setting but are inappro- geochemical modelers who have brought the priate and even incompatible with scientific state of the art to its present status. 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