Critical parameters, acentric factors

At low and moderate pressures, the viscosity of a gas is nearly independent of pressure and can be correlated for engineering purposes as a function of temperatnre only. Eqnations have been proposed based on kinetic theory and on corresponding-states principles these are reviewed in The Properties of Gases and Liquids [15], which also inclndes methods for extending the calculations to higher pressures. Most methods contain molecular parameters that may be fitted to data where available. If data are not available, the parameters can be estimated from better-known quantities such as the critical parameters, acentric factor, and dipole moment. The predictive accuracy for gas viscosities is typically within 5%, at least for the sorts of small- and medinm-sized, mostly organic, molecules used to develop the correlations. 

Table 1. Critical parameters, acentric factors and binary interaction parameters used in the calculations.

The data bank on basic physical and chemical properties of individual substances stores the following data the name of the substance, molecular mass, the structural formula of the molecule and the number of carbon atoms, melting and boiling temperatures at atmospheric pressure, critical parameters, acentric factor and polarity, parameters of the Lennard-Jones and Stockmayer potentials, the coefficients of an equation for calculation of isobaric heat capacity in the ideal-gas state and some other properties. The content of the bank is enlarged continuously by input of information on new substances. 

YOU MUST SUPPLY CRITICAL TEMPERATURE, CRITICAL PRESSURE, ACENTRIC FACTOR, PRSV KAPPA-1 PARAMETER FOR EACH COMPOUND, AMD A TEMPERATURE ALONG WITH A (PAIR OF) PREVIOUSLY SELECTED MODEL PARAMETER(S). ... 

In the absence of any experimental VLE data, the program can be used to calculate VLE at a given temperature using internally generated liquid mole fractions of component 1 from 0 to 1 at intervals of 0.1. In this case the user only needs to supply the critical temperature, critical pressure, acentric factor, and PRSV ki parameter for each compound, and a temperature as input following the directions that appear on the screen. In this mode the program will return isothermal x-y-P predictions at the temperature entered in the composition range xt == 0 to 1 at intervals of 0.1. Several temperature values can be selected successively. A tutorial is provided below (see Example D.4.C). 

This example. serves to demonstrate tlie predictive mode of the program WS, which is selected with the preceding entry. This mode is used in the absence of VLE data, and therefore no data are entered to, or can be accessed from the disk in this mode. Instead, the user provides the critical temperature, critical presssure, acentric factor, and the PRSV kj parameter for each pure component, selects an excess free-energy model provides model parameters and a temperature. The program will return isothermal x-y-P predictions at the temperature entered, in the composition range X] = 0 to 1, at intervals of 0.1.)... 

Most of the values given in Table 1 are unremarkable, but the critical temperature, acentric factor and binary interaction parameter are high for the product BHP. This may be explained by the fact that BHP is a larger long molecule with an -OH group. 

With the critical data, acentric factors, and the binary parameters, the pure component and mixture parameters have to be calculated for a temperature of 723.15 K. As initial composition, the mole fractions determined assuming ideal gas behavior are used and the parameters required for the calculation of the fugacity coefficients calculated. 

The estimation of the three parameters —pseudo-critical temperature, pseudo-critical pressure, and the acentric factor— should be done using the same method because these constants should be coherent. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Critical temperature and pressure are reqmred and can be estimated from the methods of this section. Vapor pressure is predicted by the methods of the next section. Experimental values should be used if available. The acentric factor is used as a third parameter with and... 

An afternate method with approximately the same accuracy as the Rackett method is the COSTALD metnod of Hanldnson and Thomson.The critical temperature, a characteristic volume near the critical volume, and an acentric factor optimized for vapor pressure prediction by the Soave equation of state are required input parameters. The method is detailed in the Technical Data Book ... 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

Figure 13.1a shows reduced vapor pressures and Fig. 13.1b reduced liquid molar densities for the parent isotopomers of the reference compounds. Such data can be fit to acceptable precision with an extended four parameter CS model, for example using a modified Van der Waals equation. In each case the parameters are defined in terms of the three critical properties plus one system specific parameter (e.g. Pitzer acentric factor). Were simple corresponding states theory adequate, the data for all... 

The carbon di oxi de/lemon oil P-x behavior shown in Figures 4, 5, and 6 is typical of binary carbon dioxide hydrocarbon systems, such as those containing heptane (Im and Kurata, VO, decane (Kulkarni et al., 1 2), or benzene (Gupta et al., 1 3). Our lemon oil samples contained in excess of 64 mole % limonene so we modeled our data as a reduced binary of limonene and carbon dioxide. The Peng-Robinson (6) equation was used, with critical temperatures, critical pressures, and acentric factors obtained from Daubert and Danner (J 4), and Reid et al. (J 5). For carbon dioxide, u> - 0.225 for limonene, u - 0.327, Tc = 656.4 K, Pc = 2.75 MPa. It was necessary to vary the interaction parameter with temperature in order to correlate the data satisfactorily. The values of d 1 2 are 0.1135 at 303 K, 0.1129 at 308 K, and 0.1013 at 313 K. Comparisons of calculated and experimental results are given in Figures 4, 5, and 6. 

In any cases, the critical parameters Tc and Pc, and acentric factor to are unknown and should be estimated by G.C. methods. Different approaches are available in literature and have been applied for the calculation of the solubility. 

Oy (J m mof ) and b-, (m mol ) are the parameters of the Redlich-Kwong-Soave equation of state they are easily calculated from the critical temperature and pressure and the acentric factor of the adsorbate... 

Look up the critical temperature and pressure (Tc and Pc) for the species of interest in Table B.l or elsewhere. Also look up the Pitzer acentric factor, selected compounds, and a more complete list can be found in Reid et al. 

Here is the fluid s critical pressure in atm, is the fluid s critical temperature in Kelvins, and u) is the fluid s acentric factor as defined in Poling et al. (2001). With these parameters, the kinetic theory reproduces the viscosities of the 14 investigated normal fluids with a RMS deviation of 2.13 percent. 

Some corresponding-statescorrelations use the critical compressibility factor Z, ratlier tlian tile acentric factor m, as a third parameter. The two types of correlation (one based on Tc, Pc, and Zc, the other on Tc, Pc, and w) would be equivalent were tliere a one-to-one correspondence between and w. The data of App. B allow a test of tliis correspondence. Prepare a plot of Z vs. w to see how well Z correlates witli w. Develop a linear correlation (Zc = a for nonpolar substances. 

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