Generalized correlations

NOTE - r NG GIl ES THE TENPERArURE RANGE tKl OF THE EXPERIMENTAL DATA USED TO FIT THE CONSTANTS CONSTANTS FOR NCNCONDENSABLES CCOMPONENTS 1-B) MERE DETERMINED FROM A GENERALIZED CORRELATION FOR THE HYPOTHETICAL REFERENCE FUGACITY. 

The most popular of the scanning probe tecimiques are STM and atomic force microscopy (AFM). STM and AFM provide images of the outemiost layer of a surface with atomic resolution. STM measures the spatial distribution of the surface electronic density by monitoring the tiumelling of electrons either from the sample to the tip or from the tip to the sample. This provides a map of the density of filled or empty electronic states, respectively. The variations in surface electron density are generally correlated with the atomic positions. 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

The volumetric properties of fluids are represented not only by equations of state but also by generalized correlations. The most popular generalized correlations are based on a three-parameter theorem of corresponding states which asserts that the compressibiHty factor is a universal function of reduced temperature, reduced pressure, and a parameter CO, called the acentric factor ... 

According to equation 184, all fluids having the same value of CO have identical values of Z when compared at the same T and P. This principle of corresponding states is presumed vaHd for all T and P and therefore provides generalized correlations for properties derived from Z, ie, for residual properties and fugacity coefficients, which depend on T and P through Z and its derivatives. 

Although generalized correlations are based on data for pure fluids, they are frequently appHed to mixtures. The mole fraction is introduced as a variable through empirical recipes for the composition dependence of parameters upon which the correlation is based. The simplest such recipes provide pseudoparameters that are linear in mole fraction ... 

Generalized Correlations. Generalized correlations are often the only recourse when a property value cannot be determined from empirical correlations or by other means. Several powerful correlating techniques fall under this category, including the principle of corresponding states (3,17), reduced property models (1), and the Polanyi-type characteristic curve for microporous adsorbents (14). 

A generalized correlation is a functional relationship between dimensionless or reduced variables. Most generalized correlations may be expressed by the following function ... 

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 ( ). ... 

Generalized Correlations for Viscosity. Gas viscosity has also been predicted by corresponding states theory (90) using... 

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). 

Though limited to pressures where the two-term virial equation in pressure has approximate vahdity, this correlation is applicable to most chemical-processing conditions. As with all generalized correlations, it is least accurate tor polar and associating molecules. 

Supercritical Mixtures Dehenedetti-Reid showed that conven-tionaf correlations based on the Stokes-Einstein relation (for hquid phase) tend to overpredict diffusivities in the supercritical state. Nevertheless, they observed that the Stokes-Einstein group D g l/T was constant. Thus, although no general correlation ap es, only one data point is necessaiy to examine variations of fluid viscosity and/or temperature effects. They explored certain combinations of aromatic solids in SFg and COg. 

Compares different situations versus general correlation. See also 5-24-F. 

High Fins To calculate heat-transfer coefficients for cross-flow to a transversely finned surface, it is best to use a correlation based on experimental data for that surface. Such data are not often available, and a more general correlation must be used, making allowance for the possible error. Probably the best general correlation for bundles of finned tubes is given by Schmidt [Knltetechnik, 15, 98-102, 370-378 (1963)] ... 

Flooding and Loading Since flooding or phase inversion normally represents the maximum capacity condition for a packed column, it is desirable to predict its value for new designs. The first generalized correlation of packed-column flood points was developed by Sherwood, Shipley, and Holloway [Ind. Eng. Chem., 30, 768 (1938)] on the basis of laboratory measurements primarily on the air-water system. 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

Lockhart and Martinelli used pipes of one inch or less in diameter in their test work, achieving an accuracy of about -l-/-50%. Predictions are on the high side for certain two-phase flow regimes and low for others. The same -l-/-50% accuracy will hold up to about four inches in diameter. Other investigators have studied pipes to ten inches in diameter and specific systems however, no better, generalized correlation has been found.The way... 

Tandon, T., N., Varma, H., K., and Gupta, C., P., Generalized Correlation for Condensation of Binary Mixtures Inside a Horizontal Tube, Inti. J. Refrigeration, Vol. 9, ppl34-136, 1986. 

Leung, J. C., 1986, A Generalized Correlation for One-Component Homogenous Equilibrium Flashing Choked Flow, AIChE Journal U32U, 10, pp 1743-1746. 

Most new triazolopyridines reported include data on H-NMR spectra, but there are no new studies of general correlations. 

Leung, J. C. and Grolmes, M. A., A Generalized Correlation for Flashing Choked Flow of Initially Subcooled Liquid, AIChEJ, 34 (4), 688-691, April 1988. 

Leung, J. C. and Epstein, M., A Generalized Correlation for Two-Phase Nonflashing Homogeneous Choked Flow, Trans. ASME—Journal of Heal Transfer 2 (2), 528-530, May-... 

Figure 8-4B. DePriestsr Charts K-Values of light hydrocarbon syst s, generalized correlations, high-temperature range. Used by permission, The American Institute of Chemical Engineers, Chemicai Engineering Progress Ser. 49, No. 7 (1953), all rights reserved.

Figure 8-107. Trapezoidal slot generalized correlation. Used by permission, Bolles, W. L., Pet. Processing, Feb. thru May (1956).

The HETP (Height Equivalent to a Theoretical Plate (stage or plate)) is the tray spacing divided by the fractional overall tray efficiency [82]. The transfer unit concept has been useful for generalized correlations [89]. Because packed towers operate with continuously changing compositions through the packed height, the concept... 

The generalized correlations of Sakiadis and Johnson [59] are reported to satisfy a wide variety of systems. 

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