Mass transfer empirical correlation

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

The predictions of correlations based on the film model often are nearly identical to predictions based on the penetration and surface-renewal models. Thus, in view of its relative simphcity, the film model normally is preferred for purposes of discussion or calculation. It should be noted that none of these theoretical models has proved adequate for maldug a priori predictions of mass-transfer rates in packed towers, and therefore empirical correlations such as those outlined later in Table 5-28. must be employed. 

F = Function of the molecular volume of the solute. Correlations for this parameter are given in Figure 7 as a function of the parameter (j), which is an empirical constant that depends on the solvent characteristics. As points of reference for water, (j) = 1.0 for methanol, (j) = 0.82 and for benzene, (j) = 0.70. The two-film theory is convenient for describing gas-liquid mass transfer where the pollutant solute is considered to be continuously diffusing through the gas and liquid films. 

The above correlation is valid for a bioreactor size of less than 3000 litres and a gassed power per unit volume of 0.5-10 kW. For non-coalescing (non-sticky) air-electrolyte dispersion, the exponent of the gassed power per unit volume in the correlation of mass transfer coefficient changes slightly. The empirical correlation with defined coefficients may come from the experimental data with a well-defined bioreactor with a working volume of less than 5000 litres and a gassed power per unit volume of 0.5-10 kW. The defined correlation is ... 

Mass transfer is calculated by the empirical correlation defined for non-Newtonian filamentous fermentation ... 

Johnson et al. (J4) investigated the hydrogenation of a-methylstyrene catalyzed by a palladium-alumina catalyst suspended in a stirred reactor. The experimental data have recently been reinterpreted in a paper by Polejes and Hougen (P4), in which the original treatment is extended to take account of variations in catalyst loading, variations in impeller type, and variations of gas-phase composition. Empirical correlations for liquid-side resistance to gas-liquid and liquid-solid mass transfer are presented. 

Another approach to the design problem is to determine empirical correlations based on experimental work and to adopt these correlations for scale-up. In many of the published works the latter approach is investigated. The correlations are such that the volumetric mass-transfer coefficient is generally reported as a function of one or more of the equipment, system, or operating variables cited above. Empirical correlations can be used confidently for scale-up only for equipment that has complete geometrical similarity to the... 

Empirical Correlations of Volumetric Mass-Transfer Coefficient Ks and Specific Interfacial Area s ... 

Yoshida and Miura (Y3) reported empirical correlations for average bubble diameter, interfacial area, gas holdup, and mass-transfer coefficients. The bubble diameter was calculated as... 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

The central difficulty in applying Equations (11.42) and (11.43) is the usual one of estimating parameters. Order-of-magnitude values for the liquid holdup and kiA are given for packed beds in Table 11.3. Empirical correlations are unusually difficult for trickle beds. Vaporization of the liquid phase is common. From a formal viewpoint, this effect can be accounted for through the mass transfer term in Equation (11.42) and (11.43). In practice, results are specific to a particular chemical system and operating mode. Most models are proprietary. 

Absorption rates of carbon dioxide were measured in organic solutions of glycidyl methacrylate at 101.3 kPa to obtain the reaction kinetics between carbon dioxide and glycidyl methacrylate using tricaprylylmethylammonium chloride(Aliquat 336) as catalysts. The reaction rate constants were estimated by the mass transfer mechanism accompanied by the pseudo-first-order fast reaction. An empirical correlation between the reaction rate constants and the solubility parameters of solvents, such as toluene, A-methyl-2-pirrolidinone, and dimethyl sulfoxide was presented. 

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... 

These empirical correlations were originally based mainly on data obtained for isothermal horizontal flow at pressures close to atmospheric (to 50 psi), normal temperatures, and pipe diameters to one inch using air and eight different liquids. In order to apply these equations to singlecomponent two-phase flow with mass transfer between phases, Martinelli... 

The mass transfer between phases is, of course, the very basis for most of the diffusional operations of chemical engineering. A considerable amount of experimental and empirical work has been done in connection with interphase mass transfer because of its practical importance an excellent and complete survey of this subject may be found in the text book of Sherwood and Pigford (S9, Chap. Ill), where dimensionless correlations for mass transfer coefficients in systems of various shapes are assembled. 

Recently, a set of correlations including the effect of channel shape has been proposed by Ramanathan et al. (2003) on the basis of solution of the Navier-Stokes equations in the channel, with different solutions derived for ignited-reaction and extinct-reaction regimes. The comparison of various empirical and theoretical correlations with experimentally evaluated mass transfer coefficients is given by West et al. (2003). The correlations by Ramanathan et al. (2003) or Tronconi and Forzatti (1992) have been used in most simulations presented in this chapter. 

It can be seen that a theoretical prediction of values is not possible by any of the three above-described models, because none of the three parameters - the laminar film thickness in the film model, the contact time in the penetration model, and the fractional surface renewal rate in the surface renewal model - is predictable in general. It is for this reason that the empirical correlations must normally be used for the predictions of individual coefficients of mass transfer. Experimentally obtained values of the exponent on diffusivity are usually between 0.5 and 1.0. 

The /-factors were first used by Colburn [7] for successful empirical correlations of heat and mass transfer data. The/-factor for heat transfer, J, was defined as... 

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