Generalized charts

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

An alternative to the use of generalized charts is an analytical equation of state. Equations of state which are expressed as a function of reduced properties and nondimensional variables are said to be generalized. The term generalization is in reference to the wide appHcabiHty to the estimation of fluid properties for many substances. 

Extension of Generalized Charts. In 1975, the usehilness of generalized charts was extended upon the pubtication of extensive tables of residual enthalpy, entropy, and heat capacity (82). This tabular data has also been converted into graphical form (3). The corresponding equations incorporate the acentric i2iC. or.PesiduaIenthalpy. 

Another property which can be represented by generalized charts is fugacity, ( ). The fugacity of a substance can be regarded as a corrected vapor pressure. At low pressures (below atmospheric) the use of pressure in the place of fugacity leads to tittle error in calculations. The fugacity coefficient is defined by... 

Generalized charts are available for the calculation of (j) and ( ) based on experimental data (61,65,66). A generalized chart for methane and pentane has also been made (84). 

Miscellaneous Generalized Correlations. Generalized charts and corresponding states equations have been pubhshed for many other properties in addition to those presented. Most produce accurate results over a wide range of conditions. Some of these properties include (/) transport properties (64,91) (2) second virial coefficients (80,92) (J) third virial coefficients (72) (4) Hquid mixture activity coefficients (93) (5) Henry s constant (94) and 6) diffusivity (95). 

When a Mollier chart is available for the gas involved the first method, which is illustrated by Figure 12-12A is the most convenient. On the abscissa of Figure 12-12A four enthalpy differences are illustrated. (Hg — Hj) is the enthalpy difference for the isentropic path. (Hg — Hi°) is the ideal gas state enthalpy difference for the terminal temperatures of the isentropic path. The other AH values are the isothermal pressure corrections to the enthalpy at the terminal temperatures. A generalized chart for evaluating these pressure corrections was presented previously. 

Chidambarams, S., Narsimham, G. Generalized Chart Gives Activity Coefficient Correction Factors, Chemical Engineering, Nov. 23, 1964, p. 135. 

The fugacity coefficients (f/P) for the various species may be determined from the generalized chart in Appendix B if one knows the reduced temperature and pressure corresponding to the species in question. Therefore,... 

The principle, in the form originally stated by vanderWaals ca 1881 at the time of development of his equations of state (See under Introduction to Equations of State), is based on the reduction of the variables using the critical constants (qv). This formulation is the basis of the generalized charts for the compressibility and thermody-... 

Fig. 3. Generalized chart for calculation of the coefficient of self-diffusion of gases at high densities, prepared by Slattery (S10),...

The field of diffusion in dense-gas systems is one in which much needs yet to be done. Enough experimental data should be taken so that a generalized chart based directly on diffusion data may be constructed these data are also necessary for the testing of any new theory of high-density diffusion. The theory needs to be extended to include multiple... 

Although the IR spectrum is characteristic of the entire molecule, it is true that certain groups of atoms give rise to bands at or near the same frequency regardless of the structure of the rest of the molecule. It is the persistence of these characteristic bands that permits the chemist to obtain useful structural information by simple inspection and reference to generalized charts of characteristic group frequencies. We shall rely heavily on these characteristic group frequencies. 

Figure 17.6. Generalized chart of catalyst effectiveness for reactions of order n in particles with external surface Ap and volume Vp. The upper curve applies exactly to zero-order reaction in spheres, and the lower one closely for first- and second-order reactions in spheres.

Figure 3. Generalized chart for self-difiiisivities of dense gases. Ordinate of the plot is the ratio of the pressuie-difiusivity at pressure p and temperature T to the pressure-difiiisivity product at the same temperature but low pressure. (Reprinted with permission from Ref. 12, Fig. 16.3-1, 1960, John Wiley and Sons.)...

An extension of the generalized charts that provides somewhat greater accuracy also allows for a dependence of z T, P) on the compressibility factor at the critical point, which generally varies between 0.25 and 0.29,... 

The FRI data for dualflow trays have been used to form a tentative design method (Garcia and Fair, 2002). Data for Turbogrid trays have been included in the model. A generalized chart for predicting allowable vapor velocity, similar to that for cross flow trays given in Fig. 13.32(b), is included. 

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