Reaction processes can be driven by the transfer of mass into or out of a multicomponent chemical system held at equilibrium. Complex reactions, for example, can occur when a solid phase dissolves into or precipitates from a fluid held in equilibrium. This chapter discusses how such processes might be simulated and interpreted using computer modeling techniques.

Chemists commonly find need to trace the rates at which aqueous species form complexes with other species in solution, or with reactive sites on mineral surfaces, and conversely how rapidly such complexes break apart. This chapter shows how kinetic rate laws applied to association and dissociation reactions can be incorporated into multicomponent chemical reaction models and provides a fully worked calculation, using aluminum fluoride complexing as an example.

Many minerals in the geochemical environment do not react rapidly enough with coexisting fluids to maintain thermodynamic equilibrium. Kinetic laws for this reason are required to predict the rates at which such minerals dissolve and precipitate. This chapter shows how rate laws of this class can be incorporated in multicomponent chemical reaction models, illustrates how such models behave, and provides advice on how the models might be best applied to advantage by scientists and engineers.

Stable isotopes serve as naturally occurring tracers that can provide much information about how chemical reactions proceed in nature, such as which reactants are consumed and at what temperature reactions occur. This chapter shows how multicomponent chemical reaction models can be adapted to account for the stable isotope fractionation of hydrogen, carbon, oxygen, and sulfur. In the modeling approach, solid mineral phases can be held in isotopic equilibrium with the aqueous fluid or be segregated from isotope exchange. In the latter case, the isotopic composition of minerals varies only in response to precipitation and dissolution reactions. A fully worked example calculation traces the dolomitization reaction of a limestone, computed assuming the minerals are segregated from isotope exchange.

The distribution of chemical mass in a multicomponent system held at equilibrium changes when the system’s temperature varies, or when chemical potentials in a phase in contact with the system shift. This chapter discusses how to construct numerical simulations of reaction processes driven by polythermal conditions, or by changing chemical boundary conditions.

Natural waters near Earth’s surface commonly exist far from redox equilibrium and hence hold a thermodynamic drive for the oxidation of some aqueous species at the expense of others, which are reduced. The rates at which such oxidation and reduction reactions occur in the natural environment are described by kinetic laws, which may account for heterogeneous catalysis or promotion by enzymes. This chapter shows how to incorporate redox kinetics into multicomponent chemical reaction models and gives a fully worked example of how such models can be applied.

The kinetics of microbially catalyzed reactions are of special interest because of the control the reactions exert of the redox state of laboratory experiments and the natural environment. A general description of microbial kinetics must address the requirement of thermodynamic consistency, so the kinetic laws apply equally well far from chemical equilibrium, and close to it. This chapter shows how to formulate thermodynamically consistent rate laws for microbial respiration and fermentation, the process of incorporating such laws into multicomponent chemical reaction models, and a fully worked example demonstrating how such models behave.

The movement of gas species across the air–water interface is a central aspect of biogeochemical cycling and plays a critical role in controlling not only the composition of the atmosphere, but the chemistry of aquatic and marine systems. This chapter shows how kinetic rate laws describing the transfer of gas species into and out of aqueous solution can be integrated into multicomponent chemical reaction models and shows a fully worked calculation, using carbon dioxide efflux from a biologically active lake as an example.

Valid solutions to the multicomponent equilibrium problem are commonly but not invariably unique roots of the governing equations. Modelers for this reason need to consider the possibility of the existence of more than one mathematically correct root to the equations describing chemical equilibrium in multicomponent systems. This chapter demonstrates the origin of nonunique roots to the equilibrium problem, provides several worked examples of how such roots may arise, and gives advice about coping with the possibility of nonuniqueness.

Chemical buffers, reactions that resist change in a system’s chemical state, exert strong controls on the chemistry of the natural environment. Important buffers in nature include heterogeneous buffers arising from reactions among aqueous species, as well as heterogeneous buffers caused by reactions of a fluid with an external solid or gas phase.

Any consideration of reaction processes in multicomponent chemical systems begins with a conceptual model of the setting of interest. This chapter describes how to develop a conceptual basis for constructing a geochemical reaction model and discusses the uncertainties inherent in evaluating such a model.

Using a historical sketch, this chapter traces the development and application of numerical methods for predicting speciation in multicomponent chemical systems. Discussion begins with attempts to predict the thrust provided by rocket fuels and continues through the application of advanced algorithms today to solve problems of scientific, practical, and societal importance in geochemistry and related fields.