Computer-based chemical equilibrium

Several workers have intended to estimate the chemical compositions of Kuroko ore fluids based on the chemical equilibrium model (Sato, 1973 Kajiwara, 1973 Ichikuni, 1975 Shikazono, 1976 Ohmoto et al., 1983) and computer simulation of the changes in mineralogy and chemical composition of hydrothermal solution during seawater-rock interaction. Although the calculated results (Tables 1.5 and 1.6) are different, they all show that the Kuroko ore fluids have the chemical features (1 )-(4) mentioned above. 

Crerar, D. A., 1975, A method for computing multicomponent chemical equilibria based on equilibrium constants. Geochimica et Cosmochimica Acta 39,1375-1384. 

Whatever the aim of a particular titration, the computation of the position of a chemical equilibrium for a set of initial conditions (e.g. total concentrations) and equilibrium constants, is the crucial part. The complexity ranges from simple 1 1 interactions to the analysis of solution equilibria between several components (usually Lewis acids and bases) to form any number of species (complexes). A titration is nothing but a preparation of a series of solutions with different total concentrations. This chapter covers all the requirements for the modelling of titrations of any complexity. Model-based analysis of titration curves is discussed in the next chapter. The equilibrium computations introduced here are the innermost functions required by the fitting algorithms. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

Table 8.1 describes the steps of the methodology in more detail. The procedure starts with the Problem definition production rate, chemistry, product specifications, safety, health and environmental constraints, physical properties, available technologies. Then, a first evaluation of feasibility is performed by an equilibrium design. This is based on a thermodynamic analysis that includes simultaneous chemical and physical equilibrium (CPE). The investigation can be done directly by computer simulation, or in a more systematic way by building a residue curve map (RCM), as explained in the Appendix A. This step will identify additional thermodynamic experiments necessary to consolidate the design decisions, mainly phase-equilibrium measurements. Limitations set by chemical equilibrium or by thermodynamic boundaries should be analyzed here. 

Complex Chemical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

An alternative way of relating concentrations (mass fractions) of individual species to/ is the assumption of chemical equilibrium. An algorithm based on minimization of Gibbs free energy to compute mole fractions of individual species from / has been discussed by Kuo (1986). The equilibrium model is useful for predicting the formation of intermediate species. If such knowledge of intermediate species is not needed, the much simpler approximation of mixed-is-burnt can be used to relate individual species concentrations with/. In order to calculate the time-averaged values of species concentrations the probability density function (PDF) approach is used. 

The concentration-based equilibrium constant embodied in Equation 9-7 on page 234 provides only an approximation to real laboratory measurements. In this chapter, we show how the approximate form of the equilibrium constant often leads to significant error. We explore the difference between the activity of a solute and its concentration, calculate activity coefficients, and use them to modify the approximate expression to compute species concentrations that more closely match real laboratory systems at chemical equilibrium. 

Dissolved Organic Matter-Solution Speciation Few studies report actual measurement of Cd + speciation in soil solutions. Many authors report Cd speciation based on measured total dissolved Cd concentration and computation of free Cd2+ using chemical equilibrium models. The accuracy of the... 

The first chapter introduces the reader to the software it can be speed-read or skipped by those already familiar with Windows- or Mac-based spreadsheets. The last chapter discusses macros, which can convert a spreadsheet into a powerful computing tool. Sandwiched between these are the four main parts of this book statistics and related methods, chemical equilibrium, instrumental methods, and mathematical analysis. These parts can be used independently, although some aspects introduced in chapters 2 and 3 are used in subsequent chapters, and the spreadsheet instructions tend to become somewhat less detailed as the text progresses. 

The difficulties of experimentally determining the speciation of actinides present at very low concentrations in natural waters have encouraged the use of computer simulations, based on thermodynamic data, as a means of predicting their speciation and hence their environmental behaviour. The use of modelling techniques to describe the speciation, sorption, solubility and kinetics of inorganic systems in aqueous media has been reviewed in the papers given at an international conference in 1978. Both chemical equilibrium models, exemplified by computer programs such as MINEQL and SOLMNQ, and dynamic reaction path models, exemplified by EQ6, have been developed. Application of the equilibrium models to radioactive waste disposal... 

Few studies report actual measurement of Cd + speciation in soil solutions. Many authors report Cd speciation based on the measured total dissolved Cd concentration and computation of free Cd using chemical equilibrium models. The accuracy of the speciation depends on the correctness of Cd-complex stability constants (Turner, 1995). For example, the proportion of free Cd (as Cd ) in solution varies from 16 to 82% depending on the log K values for Cd-(DOM) dissolved organic matter complexes (Table 4). The stability constants of Cd-humics are particularly uncertain. The reported high values of pCd + ranged... 

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