Fugacity parameters

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity... 

The data base contains provisions for a simple augmentation by up to eight additional compounds or substitution of other compounds for those included. Binary interaction parameters necessary for calculation of fugacities in liquid mixtures are presently available for 180 pairs. 

ASSOCIATION AND SOLVATION PARAMETERS CONSTANTS FOR ZERO PRESSURE PEFEPENCE FUGACITY EQUATION IF IVAP.EQ.I OR CONSTANTS FOR VAPOR PRESSURE EQUATION IF IVAP.GT.I... 

Fugacity is expressed as a function of the molar volume, the temperature, the parameters for pure substances Oj and h, and the binary interaction coefficients )... 

Limiting L ws. Simple laws that tend to describe a narrow range of behavior of real fluids and substances, and which contain few, if any, adjustable parameters are called limiting laws. Models of this type include the ideal gas law equation of state and the Lewis-RandaH fugacity rule (10). 

One of the most versatile and accurate generalized correlations for the prediction of the fugacity coefficient (3) involves a three-parameter generalized correlation which takes advantage of the acentric factor. The correlation breaks the fugacity coefficient into two parts (j) and ( ). ... 

When i = J, all equations reduce to the appropriate values for a pure species. When i j, these equations define a set of interaction parameters having no physical significance. For a mixture, values of By and dBjj/dT from Eqs. (4-212) and (4-213) are substituted into Eqs. (4-183) and (4-185) to provide values of the mixture second virial coefficient B and its temperature derivative. Values of and for the mixture are then given by Eqs. (4-193) and (4-194), and values of In i for the component fugacity coefficients are given by Eq. (4-196). 

The binary interaction parameters are evaluated from liqiiid-phase correlations for binaiy systems. The most satisfactoiy procedure is to apply at infinite dilution the relation between a liquid-phase activity coefficient and its underlying fugacity coefficients, Rearrangement of the logarithmic form yields... 

The estimation of the two parameters requires not only conversion and head space composition data but also physical properties of the monomers, e.g. reactivity ratios, vapor pressure equation, liquid phase activity coefficients and vapor phase fugacity coefficients. 

The expression for the fugacity of a component j in a gas or liquid mixture, fj, based on the Trebble-Bishnoi EoS is available in the literature (Trebble and Bishnoi, 1988). This expression is given in Appendix 1. In addition the partial derivative, (dlnf/dx j>P, for a binary mixture is also provided. This expression is very useful in the parameter estimation methods that will be presented in this chapter. 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

The other state variables are the fugacity of dissolved methane in the bulk of the liquid water phase (fb) and the zero, first and second moment of the particle size distribution (p0, Pi, l )- The initial value for the fugacity, fb° is equal to the three phase equilibrium fugacity feq. The initial number of particles, p , or nuclei initially formed was calculated from a mass balance of the amount of gas consumed at the turbidity point. The explanation of the other variables and parameters as well as the initial conditions are described in detail in the reference. The equations are given to illustrate the nature of this parameter estimation problem with five ODEs, one kinetic parameter (K ) and only one measured state variable. 

The fugacity coefficients fa can be calculated from the Peng-Robinson Equation of State. The values of fa are functions of temperature, pressure and composition, and the calculations are complex (see Pohling, Prausnitz and O Connell6 and Chapter 4). Interaction parameters between components are here assumed to be zero. The results showing the effect of nonideality are given in Table 6.9 ... 

The current version of CalTOX (CalTOX4) is an eight-compartment regional and dynamic multimedia fugacity model. CalTOX comprises a multimedia transport and transformation model, multi-pathway exposure scenario models, and add-ins to quantify and evaluate variability and uncertainty. To conduct the sensitivity and uncertainty analyses, all input parameter values are given as distributions, described in terms of mean values and a coefficient of variation, instead of point estimates or plausible upper values. 

The simulated C02 fugacity matches the initial reservoir C02 content and indicates that the pH is buffered by C02-calcite equilibrium. Further modelling was carried out using the Geochemists Workbench React and Tact modules with the thermodynamic database modified to reflect the elevated P conditions and kinetic rate parameters consistent with the Waarre C mineralogy. The Waarre C shows low reactivity and short-term predictive modelling of the system under elevated C02 content changes little with time (Fig. 1). 

The ideal gas model cannot be used at high pressures. Under these conditions, as pointed out in section 2.9, we have to deal with fugacities. Neglecting this and other correction parameters may lead to large errors. The point can be illustrated with results obtained by Oldani and Bor, who studied equilibrium 14.21 in hexane over the temperature range of -21.5 to 19.6°C and under a CO pressure of 198 bar [317],... 

The activity of the water is derived from this expression by use of the Gibbs-Duhem equation. To utilize this equation, the interaction parameters fif ) and BH must be estimated for moleculemolecule, molecule-ion and ion-ion interactions. Again the method of Bromley was used for this purpose. Fugacity coefficienls for the vapor phase were determined by the method of Nakamura et al. (JO). 

Eor the sake of completeness, we recall that analogies with the concept of pH do not concern solely the pe factor. In biochemistry, for instance, O2 and H2 fugacities in gaseous phases are often described by the rO and rH parameters, respectively ... 

Although steady state was not reached, at 20 days all congeners with log Kow <7 have a fugacity ratio >1. This high ratio may simply be the result of a decreasing lipid content (Table II) and a PCB depuration rate slower than that of lipids, or it could indicate an error associated with the lipid measurement. However, it brings into question the hypothesis that HOCs partition exclusively to the lipid portion of phytoplankton. These data may indicate that HOCs partition to cellular components other than lipids, and that a parameter such as the organic carbon content of the phytoplankton may be a more appropriate sorbent parameter. 

Jantunen and Bidleman [46] estimated monthly and annual fugacity ratios and fluxes of toxaphene in Lake Superior. Their calculations used monthly average air concentrations of toxaphene over the lake, estimated from their parameters of Eq. 1 (Sect. 2.2). The concentration of toxaphene in surface water was assumed constant over the year, since measurements in August 1996 and May 1997 were not statistically different. However, we now know... 

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Table B.12. Parameters for Duan et al. (1992b) gas fugacity model (Eqs. 3.37-3.48). (Numbers are in computer scientific notation where e xx stands for 10 xx)...

If the particular extracting technique applied to a solution depends on the volatility of the solute between air and water, a parameter to predict this behavior is needed to avoid trial and error in the laboratory. The volatilization or escaping tendency (fugacity) of solute chemical X can be estimated by determining the gaseous, G, to liquid, L, distribution ratio, KD, also called the nondimensional, or dimensionless, Henry s law constant, If. 

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