Correlation coefficients

It is important to be consistent in the use of fugacity coefficients. When reducing experimental data to obtain activity coefficients, a particular method for calculating fugacity coefficients must be adopted. That same method must be employed when activity-coefficient correlations are used to generate vapor-liquid equilibria. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Discharge coefficients for critical flow nozzles are, in general, the same as those for subsonic nozzles. See Grace and Lapple, Trans. Am. Soc. Mech. Fug., 73, 639-647 (1951) and Szaniszlo, ]. Eug. Power, 97, 521-526 (1975). Arnberg, Britton, and Seidl [J. Fluids Eug., 96, 111-123 (1974)] present discharge-coefficient correlations for circular-arc venturi meters at critical flow. For the calciilation of the flow of natural gas through nozzles under critical-flow conditions, see Johnson,/. Ba.sic Eng., 92, 580-589 (1970). 

FIG. 16 11 Axial dispersion coefficient correlations for well-packed beds for e = 0.4. 

The rate coefficients tor detritiation of some 3-substituted-l-tritiated azulenes were also measured in a range of aqueous perchloric acid media at 25 °C (Table 136). The log rate coefficients correlated with — HQ with slopes of 1.05, 1.08,... 

The differential equation describing the temperature distribution as a function of time and space is subject to several constraints that control the final temperature function. Heat loss from the exterior of the barrel was by natural convection, so a heat transfer coefficient correlation (2) was used for convection from horizontal cylinders. The ends of the cylinder were assumed to be insulated. The equations describing these conditions are ... 

Although the methods developed here can be used to predict liquid-liquid equilibrium, the predictions will only be as good as the coefficients used in the activity coefficient model. Such predictions can be critical when designing liquid-liquid separation systems. When predicting liquid-liquid equilibrium, it is always better to use coefficients correlated from liquid-liquid equilibrium data, rather than coefficients based on the correlation of vapor-liquid equilibrium data. Equally well, when predicting vapor-liquid equilibrium, it is always better to use coefficients correlated to vapor-liquid equilibrium data, rather than coefficients based on the correlation of liquid-liquid equilibrium data. Also, when calculating liquid-liquid equilibrium with multicomponent systems, it is better to use multicomponent experimental data, rather than binary data. 

A second generalized form for the heat-transfer coefficient correlations is... 

The dimensionless group hD/k is called the Nusselt number, /VNu, and the group Cp i/k is the Prandtl number, NPl. The group DVp/p is the familiar Reynolds number, NEe, encountered in fluid-friction problems. These three dimensionless groups are frequently used in heat-transfer-film-coefficient correlations. Functionally, their relation may be expressed as... 

Mackay D, Yeun ATK (1983) Mass transfer coefficients correlations for volatilisation of organic solutes from water. Environ Sci Technol 17 211-233 Maier-Reimer E, Kriest I, Segschneider J, Wetzel P (2005) The UAMburg Ocean Carbon Cycle Model HAMOCC5.1 - Technical Description Release 1.1 -. MPI Reports on Earth System Science No. 14 1-57... 

Baneijee, S., Yalkowsky, S. H., Valvani, S. C. (1980) Water solubility and octanol/water partition coefficients of organics. Limitations of the solubility-partition coefficient correlation. Environ. Sci. Technol. 14, 1227-1229. 

Isnard, P., Lambert, S. (1989) Aqueous solubility/w-octanol-water partition coefficient correlations. Chemosphere 18, 1837-1853. 

Figure 8-14 Drag coefficient correlation. Data from API RP 521, Guide for Pressure-Relieving and Depressurizing Systems, 2d ed. (Washington, DC American Petroleum Institute, 1982).

Note the similarity between Equations (c) and (a), where x = ht and y = U. From a standard heat transfer coefficient correlation (Gebhart, 1971), you can find that ht also varies according to Ktwt°, where Kt is a coefficient that depends on the fluid physical properties and the exchanger geometry. If we lump 1 /hs and 1 /hf together into one constant l/hsf, the semiempirical model becomes... 

Airlift reactors, 15 703-709, 726-727 gas-liquid volumetric mass transfer coefficient correlations for,... 

Gas-liquid volumetric mass transfer coefficient correlations, for airlift reactors, 15 704-705t Gas lubrication, 15 252 Gas mantles cerium in, 5 689 thorium in, 24 757 Gas masks, 5 832-835 Gas meter provers, liquid displacement, 11 652... 

Vowles and Mantoura [38] determined sediment-water partition coefficients and the high-performance liquid chromatography capacity factors for 14 alkylbenzene and polyaromatic hydrocarbons. The partition coefficients correlated well with the alkyl-cyano capacity factors, and it was concluded that this phase gave a better indication of sorption on sediment than either the octanol or octadecylsilane phases. 

Tsonopoulous, C. "Second Virial Cross Coefficients Correlation and Prediction of k..," Adv. in Chem., in press(1979). 

An alternative approach to the calculation of accurate thermochemical data is to scale the computed correlation energy with multiplicative parameters determined by fitting to the experimental data. Pioneering methods using such an approach include the scaling all correlation (SAC) method of Gordon and Truhlar [32], the parameterized correlation (PCI-X) method of Siegbahn et al. [33], and the multi-coefficient correlation methods (MCCM) of Truhlar et al. [34-36]. Such methods can be used... 

The results for the heat transfer coefficient were satisfactorily correlated by equation 6.68 as shown in Figure 6.30. Since the resistance to heat transfer in the solid could be neglected compared with that in the gas, the coefficients which were calculated were gas-film coefficients, correlated by ... 

Mackay, D. and Yeun, A.T.K. Mass transfer coefficient correlations for volatilization of organic solutes from water. Environ. Sci Technol, 17(4) 211-217, 1983. 

CORRELATION COEFFICIENT CORRELATION DIAGRAM CORRELATION FUNCTION... 

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