Semi-empirical correlations

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. 

While virial coefficients can be calculated from statistical-mechanical formulas, for practical work it is usually more convenient to employ semi-empirical correlations. Most of these correlations are based on the principle of corresponding states and as a result their applicability is limited to normal... 

Plate design, like most engineering design, is a combination theory and practice. The design methods use semi-empirical correlations derived from fundamental research work combined with practical experience obtained from the operation of commercial columns. Proven layouts are used, and the plate dimensions are kept within the range of values known to give satisfactory performance. 

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

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

Recently, Knoll and Sojka[263] developed a semi-empirical correlation for the calculation of the Sauter mean diameter of the droplets after primary breakup of flat-sheets in twin-fluid atomization of high-viscosity liquids ... 

Schmitt [489] Semi-empirical correlation for a ringlike atomizer ... 

On the basis of a force balance model, Tomberg 486 derived a semi-empirical correlation for free-fall type of atomizers ... 

This approximate relationship is similar to those for centrifugal atomization of normal liquids in both Direct Droplet and Ligament regimes. However, it is uncertain how accurately the model for K developed for normal liquid atomization could be applied to the estimation of droplet sizes of liquid metals Tombergl486 derived a semi-empirical correlation for rotating disk atomization or REP of liquid metals with the proportionality between the mean droplet size, rotational speed, and electrode or disk diameter similar to the above equation. Tornberg also presented the values of the constants in the correlation for some given operation conditions and material properties. 

Due to computer storage and run time limitations, it is not yet possible to accurately model the details of flows around each individual droplet in a spray. Thus, empirical or semi-empirical correlations are typically used to model the exchange processes between droplets and gas. Correlations for drag coefficients have been suggested by many researchers.[45l[559h568Fl571l For thin sprays, the drag... 

In the SF models, all of the terms in the droplet and gas conservation equations are retained. Therefore, the SF models are the more general models for spray calculations. The models account for mass, momentum and energy exchanges between droplets and gas. To formulate the exchange terms, the nature of the conditions at droplet-gas interface is of importance. The exchange processes are typically modeled by means of semi-empirical correlations. 

A general presentation and discussion of the origin of structure of crystalline solids and of the structural stability of compounds and solid solutions was given by Villars (1995) and Pettifor (1995). For an introduction to the electronic structure of extended systems, see Hoffmann (1987, 1988). In this chapter a brief sampling of some useful semi-empirical correlations and, respectively, of methods of classifying (predicting) phase and structure formation will be summarized. 

For flow through ring packings which as described later are often used in industrial packed columns, Ergun(10) obtained a good semi-empirical correlation for pressure drop as follows ... 

The thickness of the interphase must depend on the strength of the interaction. As was pointed out previously, interaction is created by secondary, van der Waals forces. Although the range of these forces is small, the volume affected by the decreased mobility of the chains attached to the surface is much larger when the material is deformed, shown also by the larger interphase thicknesses determined by indirect, mechanical measurements (see Table 3). This volume and the thickness of the interphase can be estimated by a semi-empirical correlation de-... 

For practical purposes, heat-transfer engineers often use empirical or semi-empirical correlations to predict h values. These formulations are usually based on the dimensionless numbers described before. In this case, the appropriate formulation should be used to prevent significant errors. If dimensionless correlations are applicable under conditions of gas extraction, then heat-transfer coefficients can be determined from these correlations and the influence of parameter variations may be derived also from them. 

The intensities of the infrared absorptions and of the inelastic scattered light (Raman) are determined by such electrical factors as dipole moments and polarizabilities. At the time of the pioneering studies on the infrared spectra of carbohydrates by the Birmingham school,7"11 calculations of the vibrational frequencies had been performed only for simple molecules of fewer than ten atoms.27,34,35 However, many tables of group frequencies, based on empirical or semi-empirical correlations between spectra and molecular structure, are available.32,34"37... 

A similar problem exists in determining the diffusivity of a gas in a liquid with which it reacts. Diffusivities are not easy to measure accurately, even under the best experimental circumstances. As in the case of solubility, the diffusivity DAB needed in the basic equations can be estimated from a semi-empirical correlation, and... 

Due to the fact that protein adsorption in fluidized beds is accomplished by binding of macromolecules to the internal surface of porous particles, the primary mass transport limitations found in packed beds of porous matrices remain valid. Protein transport takes place from the bulk fluid to the outer adsorbent surface commonly described by a film diffusion model, and within the pores to the internal surface known as pore diffusion. The diffusion coefficient D of proteins may be estimated by the semi-empirical correlation of Poison [65] from the absolute temperature T, the solution viscosity rj, and the molecular weight of the protein MA as denoted in Eq. (16). 

Fluorides of N, P, S, Se, and As. Extended-basis-set near-HF calculations on the. Y3E- a1 A, and 61E+ states of NF and the 2I1 states of NF+ and NF- were reported by O Hare and Wahl in 1971.350 NF is isoelectronic with O2 and has similar low-lying excited states. The calculations were carried out at R xp for the neutral molecules. Values of De derived with the use of semi-empirical correlation energies were in excellent agreement with experiment. The dipole moments of the low-lying states are different, unlike the case of NH, because of variations in bond length. The NF bond is slightly more ionic than the NH bond. Results for PF and its ions were also discussed.380 Little is known about this species experimentally. 

In general, procedures for estimating physical and thermodynamic properties and functions can be divided into two categories, namely, group contribution methods and semi-empirical correlations. It is usually difficult, if not impossible, to employ a semi-empirical correlation for predicting the properties of a new material or those of an existing material at a condition different from that under which the available data were obtained. In contrast, the group contribution method, which is based on the assumption that the property of a material is contributed from... 

Celardin, F. (1999). Semi-empirical correlations between so-called mobilizable and mobile concentrations of heavy metals in soils. Commun. Soil Sd. Plant Anal. 30(5-6), 843—854. 

In the present state of the art of polymer physics, an exhaustive solution of the first of these two problems has not been found so far, although some attempts in this direction have been undertaken. At the same time, an intensive development of production of polymers puts forward demands of the prediction of their properties. To cope with this task chemical engineers generally use in practice some simple semi-empirical correlations. In doing so, they resort to certain qualitative theoretical approaches to treat the available experimental data. According to the most reputable adherent of this method, van Krevelen, such semi-empiri-cal correlations are highly effective and provide rather reliable results in most practically important cases (van Krevelen and te Nijenhuis, 2009). However, even in the framework of the above approach, considerable difficulties are encountered, because often there is no clear idea about which specific statistical characteristics of a polymer are responsible for a particular mechanical and physicochemical property. It especially concerns copolymers because the number of their characteristics of such a kind is larger than that for homopolymers. 

Benson [15] has created and developed a general method of calculation of the values of thermochemical and kinetic parameters based on a systematic use of the additivity of group properties on the one hand and the activated complex theory on the other. Other methods for estimating a priori kinetic parameters have recourse to structural analogies or semi-empirical correlations. 

Partly empirical but based on theoretical models or concepts these "semi-empirical" correlations are the most useful and reliable for practical purposes. 

This information may be provided by various semi-empirical correlations that have been developed over the years from the equations of Girifalco and Good, and Eowkes. Eor example, such a correlation can be... 

This universal film thickness equation immediately unifies all prior apparently conflicting film thickness data correlations. For example, one of the recurring sources of controversy and confusion in the literature is the observed variability of the exponent p in empirical and semi-empirical correlations of the form h 1/to. Some have generally assumed that p = 1/2 while others argue that p 2/3 (11,17). On the contrary, the observed values of the exponent p is in the range of 0.40-0.82 for various photoresists, electron beam resists, polyimide coatings, etc. 

A major factor in fluidized bed behavior is the interaction between the gas flow from individual orifices and the particle and gas mixture within the bed. The jet penetration and the subsequent bubble formation have an important influence upon solids and gas mixing and, ultimately, upon the usefulness of the bed for reactor purposes. While flow visualization data are available at ambient pressures and temperatures, the natures of jet penetration and bubble development at high pressures and temperatures are not easily measured. Typical data on bubble size and bubble velocity at ambient conditions are shown, represented by the small size symbols, in Figure 2. It is well known that bubble volume can be correlated as a function of gas volumetric flow rate ( ) and that bubble velocity is related to the size of the bubble radius ( ). Such semi-empirical correlations are indicated as solid lines in that figure. 

Most flows encountered in engineering practice are turbulent, and thus it is important to understand how turbulence affects wall shear stress and heat transfer. However, turbulent flow is a complex mechanism douiinaled by fluc-ttmiions, and despite tremendous amounts of work done in this area by researchers, the theory of turbulent flow remains largely undeveloped. Therefore, we must rely on experiiiierits and the empirical or semi empirical correlations developed for various situations. 

The water flux, J, which is normally expressed as kg (or L) m h is proportional to the water vapor pressure gradient, Apm, between the feed-membrane and strip-membrane interfaces, and the membrane mass transfer co-efficient K, [Eq. (3)]. The vapor pressure gradient between the two interfaces depends on the water activity, a, in the bulk feed and strip streams, and the extent to which concentration polarization reduces that activity at each interface. Whilst can be estimated using established diffusional transport equations, it is more difficult to estimate values for the water vapor pressure at the membrane wall for use in Eq. (3). However, an overall approach using the vapor pressures of the bulk solutions and semi-empirical correlations that take account of the different conditions near the membrane wall can be used to estimate J. 

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