Application of the Correlations

The fluid properties of formation water may be looked up on correlation charts, as may most of the properties of oil and gas so far discussed. Many of these correlations are also available as computer programmes. It is always worth checking the range of applicability of the correlations, which are often based on empirical measurements and are grouped into fluid types (e.g. California light gases). 

It is noted that additional scales for the property index are shown in Figure 3.42 to correspond to liquid metals as well as water and Freon-22 at different temperatures, indicating the applicability of the correlation to other fluids. 

In the design of an industrial scale reactor for a new process, or an old one that employs a new catalyst, it is common practice to carry out both bench and pilot plant studies before finalizing the design of the commercial scale reactor. The bench scale studies yield the best information about the intrinsic chemical kinetics and the associated rate expression. However, when taken alone, they force the chemical engineer to rely on standard empirical correlations and prediction methods in order to determine the possible influence of heat and mass transfer processes on the rates that will be observed in industrial scale equipment. The pilot scale studies can provide a test of the applicability of the correlations and an indication of potential limitations that physical processes may place on conversion rates. These pilot plant studies can provide extremely useful information on the temperature distribution in the reactor and on contacting patterns when... 

The errors that result from the use of average transport coefficients are not particularly serious. The correlations that are normally employed to predict these parameters are themselves determined from experimental data on packed beds. Therefore, the applications of the correlations and the data on which they are based correspond to similar physical configurations. 

Clift and Gauvin (C7, C8) discuss application of the correlations in Table 10.1... 

Interpolating properties, a correlation is found between the desired property and another property or characteristic of related molecules in this case the desired property may be computed from within the range of application of the correlation, and the interpolated property should be accurately estimated. 

The recommended range of application of the correlation is given in Table 14-10. The clear liquid height at the froth-to-spray transition ha is calculated using the corrected Jeronimo and Sawistowski [Trans. Inst. Chem. Engnrs. 51,265 (1973)] correlation as per Eqs. (14-82) to (14-84). 

Application of the correlation rules—The Wigner-Witruer correlation rules relate the nature of molecular states to the atomic states into which they may dissociate. The quantum-mechanical selection rules determine what electronic states may be excited by radiation, and with a knowledge of them it is often possible to deduce what type an electronic state is, and from this, using the Wigner-Witmer rules, to deduce what atomic states it may dissociate into. 

The activity of naturally radioactive elements is a measure of their mass. Prerequisites of application of the correlation between mass and activity according to eq. (17.1) are that the isotopic composition of the element to be determined is constant and that interfering radioactive impurities are absent. If the daughter nuelides are also radioactive, radioactive equilibrium must be established or the daughter nuclides must be separated off quantitatively. Interference of radioactive impurities may be avoided by measuring the a or y spectrum of the radionuclide considered. 

Numerous authors have devised multiple linear regression approaches to the correlation of solvent effects, the intent being to widen the applicability of the correlation and to develop insight into the molecular factors controlling the correlated process.For example, Zilian treated polarity as a combination of effects measured by molar refraction, AN, and DN. Koppel and Palm write... 

This work results in correlations which can be used to predict parameters for the RK equation of state for hydrocarbon and other nonpolar components for which the critical pressure, critical temperature, and acentric factor are known or can be estimated. However, the applicability of the correlations to large molecules is unproven because the generalized correlations of physical and thermodynamic properties used to develop Oa and Ob are based on components no heavier than n-decane (acentric factor = 0.4885). Although the predicted parameters are based on properties for the saturated liquid phase, the parameters are applied to both vapor and liquid phases. For components above their critical temperature (a reduced temperature greater than 1.00), the values of fia and Ob determined at a reduced temperature of unity are used. 

Application of the correlations of induction time of surface nucleation and decreasing rate of the concentration of the solution to optical resolution process of DL-SCMC hy crystallization. 

Application of the correlation of the peak temperatures to the heating rates for calculation of the Arrhenius kinetic parameters and of the heat of vaporization will be considered in chapter 3.3.2. 

It should be added here that rounded or square-edged entrances can influence the values assumed by the convective heat transfer coefficient and, especially, the values assumed by the friction factor in the entrance region [1, 2]. Since the data cover only a few simple entrance geometries, the designer must exercise judgment in the application of the correlations proposed for calculating the friction factor and the convective heat transfer coefficient in the entrance region. 

Since data cover only a few simple entrance geometries, the designer must exercise judgment in the application of the correlations proposed to calculate the friction factor and the convective heat transfer coefficient in the entrance region of a microchannel. 

Owing to slight density differences between fermentation liquid and biomass the particles have the tendency to settle. Thus a biomass concentration profile along the tower may result. The pertinent model to account for biomass concentration profiles is the sedimentation-dispersion model (74,75). This model involves two parameters, neimely, the solid dispersion coefficient 3 and the mean settling velocity Us of the biomass particles in the swarm. Both parameters were determined by Kato et al. (75) in bubble columns for glass beads of 75 and 163 urn diameter. The authors presented their results by empirical correlations for both Eg and ug. Until other data for smaller density differences are available the application of the correlations of Kato and coworlcers is recommended for biological systems also. It should be pointed out that the solid phase dispersion coefficient Eg almost completely agrees with El i.e. the liquid phase dispersion coefficient. ... 

A plot of experimental kju values versus y D Mc/IucM shows a straight line for constant Ci = 4.5, which is almost the theoretical value from the model for the film contribution. The agreement between the model and the experiment is reasonably good for both circular and square capillaries. Thus the model shows a dependence of ha on capillary diameter. Furthermore, Vandu et al. [58] validated the applicability of the correlation and it was proposed that the relation performs well for a/(ug -I-Ul)/Is > 3, which corresponds to a short film contact time and a dominant film contribution. Below this range, the film contribution to mass transfer diminishes as the hquid in the film begins to approach saturation. 

Application of the correlation operator to a model function generates the projection of the exact wave function in the complementary space Q... 

Goicoechea HC, Olivieri AC, Tauler R. Application of the correlation constrained multivariate curve resolution alternating least-squares method for analyte quantitation in the presence of unexpected interferences using first-order instrumental data. Analyst 2010 135 636-42. 

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