Other Empirical Correlations

Several other half-empirical scales of surfactant emulsifying action have been proposed. Beerbower and Hill introduced the Cohesive Energy Ratio (CER), defined as the ratio of the surfactant adhesion energy to the oil phase to the surfactant adhesion to the water phase. The calculation of adhesion energies is done in terms of the Hildebrand solubility parameters. Kruglyakov et alP proposed the Hydrophile-Lipophile Ratio (HLR), which is the ratio of the energy of adsorption of the surfactant molecule from the water phase to its energy of 

The Equivalent Alkane Carbon Number (EACN) is an empirical correlation which helps to evaluate the location of a balanced point for different emulsified oils and oil mixtures. The Calculation of Phase Inversion in Concentrates (CAPICO) method is similar to the EACN. 

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Robinson and Lurie (1962) reported several other empirical correlations for CHF in organic coolants. These correlations are... 

There are numerous other empirical correlation for the droplet sizes generated by impinging jets. Ingebo [40] provided a correlation for the impingement of heptane jets collided at 90 with 9-30 m/s velocities and diameters in the range of 0.1-22 mm. His correlation for volume mean diameter is ... 

The minimum fluidization velocity, u f, can be determined directly from experimental data (3), as shown in Figure 22.6. And, similarly, one can determine the terminal velocity, Ut, or drag velocity, Ut (7). There are other empirical correlations for these velocities (Kunii and Levenspiel, 1991). 

For several batches of the same catalyst material with quite different mass median diameters, Gwyn found the exponent b to be constant, whereas the attrition constant was found to decrease with mean particle size. Equation (1) is therefore valid for a particular size distribution only. Other empirical correlations for the time dependence of the mass ratio Q have been... 

Fig. 3-20 compares the flexural modulus versus temperatures for four 30% GRTP s. Because modulus is a frequently appearing property in mechanical design equations, creep data often are plotted as apparent or creep modulus. These data are shown in Table 3-6 for GRTP s. As can be seen, the apparent creep modulus improves with glass reinforcement. Generally, the creep modulus of the reinforced thermoplastics decreases as stress and temperature are increased. However, the creep modulus data for reinforced nylon, acetal, polyester, polysulfone, and polyvinyl chloride appear to be less dependent on stress under the conditions of this particular test. When creep modulus data at different stresses coincide—a phenomenon known as the Boltzman superposition—there is an obvious reduction in the amount of testing required. However, such a relationship is both temperature and stress dependent and must be confirmed at the conditions of interest for the specific material involved. Other techniques, such as time-temperature superposition and other empirical correlations, also have been devised to simplify the time-dependent response of plastics ... 

After many years of emulsion research, several reliable empirical trends in macroemulsion stability to coalescence have been established. The most powerful rules of thumb are (i) the correlation between the surfactant spontaneous curvature and the macroemulsion stability and (ii) the tight monolayer packing concept. Other empirical correlations, HLB scale and Bancroft s rule, can be substantially reduced to these two. In rare cases when the oriented wedge trend and the HLB scale, or Bancroft s rule, disagree, nature usually follows the oriented wedge trend. Thus, Bancroft s rule often fails for nonionic surfactants of the ethylene oxide type below the balanced point, while the oriented wedge trend does not. 

Other empirical correlations suggest a dependence of P shifts to bond angles although in the case of phosphine oxides (Hays and Peterson, 1972), phosphine sulfides (Maier, 1972), and cyclophosphines (Smith and Mills, 1976 Mills, 1977) as with phosphines (Mann, 1972 Tolman, 1977) a... 

Theoretically based correlations (or semitheoretical extensions of them), rooted in thermodynamics or other fundamentals are ordinarily preferred. However, rigorous theoretical understanding of real systems is far from complete, and purely empirical correlations typically have strict limits on apphcabihty. Many correlations result from curve-fitting the desired parameter to an appropriate independent variable. Some fitting exercises are rooted in theory, eg, Antoine s equation for vapor pressure others can be described as being semitheoretical. These distinctions usually do not refer to adherence to the observations of natural systems, but rather to the agreement in form to mathematical models of idealized systems. The advent of readily available computers has revolutionized the development and use of correlation techniques (see Chemometrics Computer technology Dimensional analysis). 

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). 

Because of the time and expense involved in conducting laboratoiy distillation tests of all three basic types, it has become increasingly common to use empirical correlations to estimate the other two distillation curves when either the ASTM, TBP, or EFN- curve is available. Preferred correlations given in the API Technical Data Book—Petroleum Refining (op. dt.) are based on the work of Edmister and Pollock [Chem. Eng. Prog., 44, 905 (1948)], Edmister and Okamoto [Pet. Refiner, 38(8), 117 (1959) 38(9), 271 (1959)], Maxwell Data Book on... 

There are two other useful empirical correlations as follows ... 

The many empirical correlations advanced to represent the frictional resistance to flow vary from exact results because of the specific simplifying assumptions incorporated in each. Some relations agree in one region of flow and diverge in others. 

This method for vertical thermosiphon reboilers is based on semi-empirical correlations of experimental data and is stated to predict heat transfer coefficients 30 percent, which is about the same range of accuracy for most boiling coefficient data. The advantage of this method is that it has had significant design experience in the industry to support it. It is also adaptable to other types of reboilers used in the industry. See Figures 10-110 and 10-111. 

On the other hand, Jens and Lottes (1951) and Thom et al. (1965) presented empirical correlations that showed another dependence of wall superheat on pressure. Dependence of the dimensionless wall superheat = AroNB/A7Qj,jg on... 

The optimization of empirical correlations developed from the ASPEN-PLUS model yielded operating conditions which reduced the steam-to-slurry ratio by 33%, increased throughput by 20% while maintaining the solvent residual at the desired level. While very successful in this industrial application the approach is not without shortcomings. The main disadvantage is the inherent assumption that the data are normally distributed, which may or may not be valid. However, previous experience had shown the efficacy of the assumption in other similar situations. 

One of the calculation results for the bulk copolyroerization of methyl methacrylate and ethylene glycol dimethacrylate at 70 C is shown in Figure 4. Parameters used for these calculations are shown in Table 1. An empirical correlation of kinetic parameters which accounts for diffusion controlled reactions was estimated from the time-conversion curve which is shown in Figure 5. This kind of correlation is necessary even when one uses statistical methods after Flory and others in order to evaluate the primary chain length drift. 

For plant cell suspensions cultivated in shake flasks, Huang et al. [45] used the energy dissipation rate as a correlating parameter for system response. Specific power input was calculated using the empirical correlation proposed by Sumino et al. [46] and subsequently employed in other applications [47,48] ... 

The choice of capacity is sometimes a problem, and may change according to the particular circumstance. Sometimes using a definition of time constant, based on the above equations, is not very helpful and other means must be employed. For example, mixing time is a very important time constant relating to liquid mixing, and this is best obtained directly from empirical correlations of experimental data. 

On the other hand, there is a blizzard of empirical and semi-empirical correlations which exist in the fluidized bed literature to predict... 

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