Bromley estimation

The equation given by Bromley (1950) can be used to estimate the heat-transfer coefficient for film boiling on tubes. Heat transfer in the film-boiling region will be controlled by conduction through the film of vapour, and Bromley s equation is similar to the Nusselt equation for condensation, where conduction is occurring through the film of condensate. 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

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). 

For ionic species i and j with charges of different signs 0 9--numbers were estimated from Pitzer s results forJstrong electrolytes using a method proposed by Bromley (2) 0 ) -numbers were determined from an... 

The ion-ion electrostatic interaction contribution is kept as proposed by PITZER. BEUTIER estimates the ion - undissociated molecules interactions from BORN - DEBYE - MAC. AULAY electric work contribution, he correlates 8 and 8 parameters in PITZER S treatment with ionic standard entropies following BROMLEY S (9) approach and finally he fits a very limited (one or two) number of ternary parameters on ternary vapor-liquid equilibrium data. 

Wilcox, D.E., and Bromley, R.A., Computer estimation of heat and free energy of formation for simple inorganic compounds, Ind. Eng. Chem., 32-39 (1963). 

The thermal conductivities of the pure components are estimated by Bromley s method. 

To estimate the factors A,j, the Lindsay-Bromley equation is appropriate and... 

As explained in section 3.6.1, many modifications have been proposed for the Debye-Hiickel relationship for estimating the mean ionic activity coefficient 7 of an electrolyte in solution and the Davies equation (equation 3.35) was identified as one of the most reliable for concentrations up to about 0.2 molar. More complex modifications of the Debye-Huckel equation (Robinson and Stokes, 1970) can greatly extend the range of 7 estimation, and the Bromley (1973) equation appears to be effective up to about 6 molar. The difficulty with all these extended equations, however, is the need for a large number of interacting parameters to be taken into account for which reliable data are not always available. 

Based on Bromley s (S3) assumption that activity coefficient interaction parameters for individual ions could be added to estimate the value for a salt ... 

As in Pawlikowski and Prausnitz s (S24) paper on Setschenow constants, Edwards et al. (PS, P6) used Bromley s theory of the additivity of single ion Interactions to estimate ion-ion and ion-mdecule interactions ... 

As mentioned earlier, the "excess enthalpy term is small and difficult to obtain. For purposes of illustration only, we can estimate the Yi(T) for the Na and Cl ions based upon binary correlation parameters published by Rastogi and Tassios (14). The Bromley formulation for calculating activity coefficients, simplified for a 1 1 salt, is ... 

The similar behavior of the Bromley equation B parameters allows for the estimation of the parameter for untabulated species. VIhen Bromley presented his equations in 1973, along with the B values for many species, he presented tabulated values based upon an expanded estimation equation ... 

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