Aqueous fluid equilibrium

CONSTRUCTION OF THE SOLID SOLUTION - AQUEOUS FLUID EQUILIBRIUM FUNCTION ( ISOTHERM ... 

Fig. 2.1. Schematic diagram of a reaction model. The heart of the model is the equilibrium system, which contains an aqueous fluid and, optionally, one or more minerals. The system s constituents remain in chemical equilibrium throughout the calculation. Transfer of mass into or out of the system and variation in temperature drive the system to a series of new equilibria over the course of the reaction path. The system s composition may be buffered by equilibrium with an external gas reservoir, such as the atmosphere.

In Chapter 3, we developed equations that govern the equilibrium state of an aqueous fluid and coexisting minerals. The principal unknowns in these equations are the mass of water n w, the concentrations m,- of the basis species, and the mole numbers n/c of the minerals. 

Such a method has seldom been used with systems containing an aqueous fluid, probably because the complexity of the solution s free energy surface and the wide range in aqueous solubilities of the elements complicate the numerics of the calculation (e.g., Harvie el al., 1987). Instead, most models employ a procedure of elimination. If the calculation described fails to predict a system at equilibrium, the mineral assemblage is changed to swap undersaturated minerals out of the basis or supersaturated minerals into it, following the steps in the previous chapter the calculation is then repeated. 

The examples in the previous section demonstrate that nonunique solutions to the equilibrium problem can occur when the modeler constrains the calculation by assuming equilibrium between the fluid and a mineral or gas phase. In each example, the nonuniqueness arises from the nature of the multicomponent equilibrium problem and the variety of species distributions that can exist in an aqueous fluid. When more than one root exists, the iteration method and its starting point control which root the software locates. 

In a solid-fluid reaction system, the fluid phase may have a chemistry of its own, reactions that go on quite apart from the heterogeneous reaction. This is particularly true of aqueous fluid phases, which can have acid-base, complexation, oxidation-reduction and less common types of reactions. With rapid reversible reactions in the solution and an irreversible heterogeneous reaction, the whole system may be said to be in "partial equilibrium". Systems of this kind have been treated in detail in the geochemical literature (1) but to our knowledge a partial equilibrium model has not previously been applied to problems of interest in engineering or metallurgy. 

With an aqueous fluid phase of high ionic strength, the problem of obtaining activity coefficients may be circumvented simply by using apparent equilibrium constants expressed in terms of concentrations. This procedure is recommended for hydro-metallurgical systems in which complexation reactions are important, e.g., in ammonia, chloride, or sulfate solutions. 

Constraints on Li isotopic fractionation from equilibrium laboratory experiments in magmatic-hydrothermal systems have been examined in only one instance (Lynton 2003). This study examined Li in a quartz-muscovite-aqueous fluid system at conditions of formation of magmatic hydrothermal porphyry-type deposits (400-500°C, 100 MPa). In the presence of a fluid containing L-SVEC (5T i = 0), quartz showed rapid shift from 5 Li = +27 in the starting material to c. +10 at both run temperatures. Muscovite (initial 5 Li = +9), shifted more sharply at 500°C (to c. +20) than at 400°C (to c. +13). Although the results are difficult to put directly into the context of a natural mineral deposit, they do indicate that over geologically relevant time scales, minerals in magmatic-hydrothermal systems should show appreciable Li isotopic fractionation, and that this may permit the composition and/or temperature of ore... 

In the laboratory experiments of Seyfried et al. (1998), naturally altered sea floor basalt (5 Li = +7.4) was reacted with Li-free alkali-chloride aqueous fluid at 350°C for 890 hours (initial fluid/solid mass ratio 2). Samples of the fluid were taken throughout the experiment, and showed initial rapid influx of isotopically heavy-enriched Li released by early-dissolving alteration minerals. However, with progressive reaction, isotopic composition of the fluid decreased and Li concentration reaehed apparent steady state. Although an equilibrium model applies best to the synthetic results, Rayleigh distillation was considered most likely to apply in hydrothermal reactions occurring in nature. 

Since the major chemical reactions take place through the agency of an aqueous fluid, the system can be considered to be saturated with respect to water. H O is always the major component of an omnipresent fluid phase during the attainment of equilibrium and it is therefore considered a component in excess. We are left with a four component system, Na-K-Al-Si where, for unspecified P-T conditions over a short range, there will be a maximum of four phases coexisting. 

The equilibrium constant K does not change when the inhibitor is added to the aqueous fluid, but it is only a function of temperature. 

An important aspect of the design of an acid gas injection scheme is the non-aqueous phase equilibrium. Fluid phase equilibrium involving water, which is also very important, will be discussed in chapter 4 and hydrates in chapter 5. 

Metamorphism of carbonate iron-formations in the presence of aqueous fluids leads to the formation of cummingtonite. When equilibrium is reached, reactions of the type ... 

Fig. 93. Equilibrium of magnesian-iron minerals in rocks with excess silica. A. In silicate iron-formations (aqueous fluid. Cum + Px -t- OH- Q association). B. In carbonate iron-rich rocks (carbonic acid fluid. Car -(- Px -I- 01 -t- Q association). Figures indicate maximum iron content of orthopyroxene in association with quartz and olivine.

The liquid-liquid extraction process is based on the specific distribution of dissolved components between two immiscible fluids, for instance, between aqueous and organic liquids. The process refers to a mass exchange processes in which the mass transport of component (j) from phase (1) to phase (2) by means of convection or molecular diffusion acts to achieve the chemical potential (p) equilibrium (134) ... 

Luo K, Shi Z, Varesi J, Majumdar A (1997) Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy. J Vac Sci Technol B 15 349-360 Majumdar A (1999) Scanning thermal microscopy. Annu Rev Mater Sci 29 505-585 Manghk RM, Wasekar VM, Zhang J (2001) Dynamic and equilibrium surface tension of aqueous surfactant and polymeric solutions. Exp Thermal Fluid Sd 25 55-64... 

This mechanism as a main cause for epithermal-type Au deposition is supported by sulfur isotopic data on sulfides. Shikazono and Shimazaki (1985) determined sulfur isotopic compositions of sulfide minerals from the Zn-Pb and Au-Ag veins of the Yatani deposits which occur in the Green tuff region. The values for Zn-Pb veins and Au-Ag veins are ca. +0.5%o to -f4.5%o and ca. -l-3%o to - -6%c, respectively (Fig. 1.126). This difference in of Zn-Pb veins and Au-Ag veins is difficult to explain by the equilibrium isotopic fractionation between aqueous reduced sulfur species and oxidized sulfur species at the site of ore deposition. The non-equilibrium rapid mixing of H2S-rich fluid (deep fluid) with SO -rich acid fluid (shallow fluid) is the most likely process for the cause of this difference (Fig. 1.127). This fluids mixing can also explain the higher oxidation state of Au-Ag ore fluid and lower oxidation state of Zn-Pb ore fluid. Deposition of gold occurs by this mechanism but not by oxidation of H2S-rich fluid. 

Factors in controlling chemical compositions of gold in equilibrium with the ore fluids are temperature, pH, concentration of aqueous H2S and Cl in the ore fluids, concentration ratio of Au and Ag species in the ore fluids, activity coefficient of Au and Ag components in gold, and so on (Shikazono, 1981). In the Yamizo Mountains, as a result, Ag/Au ratios of gold are correlated with a kind of the host rocks and sulfur isotopic compositions of the deposits. This correlation could be used to interpret Ag/Au ratios of gold. 

Fig. 2.37. Phase diagram for Ca0-Na20 Si02-(Al203)-H20 system in equilibrium with quartz at 400°C and 400 bars. Plagioclase solid solution can be represented by the albite and anorthite fields, whereas epidote is represented by clinozoisite. Note that the clinozoisite field is adjacent to the anorthite field, suggesting that fluids with high Ca/(H+) might equilibrate with excess anorthite by replacing it with epidote. The location of the albite-anorthite-epidote equilibrium point is a function of epidote and plagioclase composition and depends on the model used for calculation of the thermodynamic properties of aqueous cations (Berndt et al., 1989).

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