Fixed fugacity path

The results of fixed-fugacity paths can differ considerably from those of simple titration models. Consider, for example, the oxidation of pyrite to goethite,... 

In a fixed activity path, the activity of an aqueous species (or those of several species) maintains a constant value over the course of the reaction path. A fixed fugacity path is similar, except that the model holds constant a gas fugacity instead of a species activity. Fixed activity paths are useful in modeling laboratory experiments in which an aspect of a fluid s chemistry is maintained mechanically. In studying reaction kinetics, for example, it is common practice to hold constant the pH of... 

In an example of a fixed fugacity path we model the dissolution of pyrite (FeS2) at 25 °C. We start in REACT with a hypothetical water in equilibrium with hematite (Fe203) and oxygen in the atmosphere... 

Fig. 14.4. Mineralogical results (top) of a fixed fugacity path in which pyrite dissolves at 25 °C into water held in equilibrium with 02 in the atmosphere, and the variation in pH (bottom) over the path.

The fixed fugacity path (Fig. 14.4) differs from the previous calculation (in... 

Fig. 14.5. Concentrations of species involved in the dissolution of pyrite, for the fixed fugacity path shown in Figure 14.4.

Sliding activity and sliding fugacity paths are similar to fixed activity and fixed fugacity paths, except that the model varies the buffered activity or fugacity over the reaction path rather than holding it constant. Once the equilibrium state of the initial system is known, the model stores the initial activity a° or initial fugacity / / of the buffered species or gas. (The modeler could set this value as a constraint on the initial system, but this is not necessary.)... 

The fixed fugacity path (Fig. 12.4) differs from the previous calculation (in which the fluid was closed to the addition of oxygen) in that pyrite dissolution continues indefinitely, since there is an unlimited supply of oxygen gas. Initially, the reaction proceeds as... 

Fixed-activity and sliding-activity paths (Sections 14.2-14.3) are analogous to their counterparts in fugacity, except that they apply to aqueous species instead of gases. Fixed-activity paths are useful for simulating, for example, a laboratory experiment controlled by a pH-stat, a device that holds pH constant. Sliding-... 

To calculate a fixed activity path, the model maintains within the basis each species At whose activity at is to be held constant. For each such species, the corresponding mass balance equation (Eqn. 4.4) is reserved from the reduced basis, as described in Chapter 4, and the known value of a, is used in evaluating the mass action equation (Eqn. 4.7). Similarly, the model retains within the basis each gas Am whose fugacity is to be fixed. We reserve the corresponding mass balance equation (Eqn. 4.6) from the reduced basis and use the corresponding fugacity fm in evaluating the mass action equation. 

In fixed and sliding fugacity paths, the model transfers gas into and out of an external buffer to obtain the fugacity desired at each step along the path (see Chapter 14). The increment Anr is the change in the total mole number Mm of the gas component as it passes to and from the buffer (see Chapter 3). When... 

Delany, J. M. and T. J. Wolery, 1984, Fixed-fugacity option for the eq<5 geochemical reaction path code. Lawrence Livermore National Laboratory Report UCRL-53598. 

The latter path differs from the closed system calculation because of the effect of C02(g) dissolving into the fluid. In the initial part of the calculation, the C02(aq) in solution reacts to form HCOJ in response to the changing pH. Since the fluid is in equilibrium with C02(g) at a constant fugacity, however, the activity of C02(aq) is fixed. To maintain this activity, the model transfers C02... 

Here, the symbol q characterizes the kind of statistics Bose (q = +1) or Fermi (q = —1). Let us set z = , + ( and consider the action f on a transit path that passes through the saddle point at a fixed imaginable variable Imz = Co- In this case, 91 may be regarded as the functional that depends on the two field variables [Pg.516]

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