Mass transfer empirical coefficient correlations

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. 

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 ... 

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 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. 

EMPIRICAL CORRELATION FOR PREDICTING THE SOLUTE MASS TRANSFER COEFFICIENT (km) IN ED CELLS WITH EDDY PROMOTERS... 

The heat and mass transfer properties can be represented by heat and mass transfer coefficients, which are commonly given in empirical or semiempirical correlation form. The transfer coefficient is defined in terms of flow models under specific flow conditions and geometric arrangements of the flow system. Thus, when applying the correlations, it is necessary to employ the same flow model to describe the heat and mass transfer coefficients for conditions comparable to those where the correlations were obtained. An accurate characterization of the heat and mass transfer can be made only when the hydrodynamics and underlying mechanism of the transport processes are well understood. 

Equation (12.71) provides a means to quantify kf on the basis of experimentally measured inlet and outlet concentrations of species A in the bed under low gas velocity conditions. Wen and Fane (1982) proposed the following empirical correlations for overall mass transfer coefficients in gas-solid fluidized beds, using the experimental data of Kato et al. (1970) based on Eq. (12.71) ... 

Film theory predicts that the mass transfer coefficient for a phase (or the overall mass transfer coefficient) is proportional to the diffusion coefficient and inversely proportional to the thickness of the stagnant zone. The diffusion coefficient can be calculated from either the Wilke-Chang or the FSG equations. However, 6 is difficult (if not impossible) to determine. Hence, mass transfer coefficients are often determined from empirical correlations. Also, Film theory is based on the assumption that the bulk fluid phases are perfectly mixed. While this might approach reality for well-mixed turbulent systems, this is certainly not the case for laminar systems. 

Numerous empirical correlations for the prediction of residual NAPL dissolution have been presented in the literature and have been compiled by Khachikian and Harmon [68]. On the other hand, just a few correlations for the rate of interface mass transfer from single-component NAPL pools in saturated, homogeneous porous media have been established, and they are based on numerically determined mass transfer coefficients [69, 70]. These correlations relate a dimensionless mass transfer coefficient, i.e., Sherwood number, to appropriate Peclet numbers, as dictated by dimensional analysis with application of the Buckingham Pi theorem [71,72], and they have been developed under the assumption that the thickness of the concentration boundary layer originating from a dissolving NAPL pool is mainly controlled by the contact time of groundwater with the NAPL-water interface that is directly affected by the interstitial groundwater velocity, hydrodynamic dispersion, and pool size. For uniform... 

Yi, y2, and y3 are empirical coefficients that were determined by fitting the nonlinear power law correlation Eq. (91) to 484 average Sherwood numbers computed for 121 different pool dimensions and four different sets of hydro-dynamic conditions. The resulting time invariant, average mass transfer correlation for elliptic pools is given by... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

The similarities between the governing equations for heat, mass, and momentum transfer suggest that empirical correlations for the mass-transfer coefficient would be similar to those for the heat-transfer coefficient. This turns out to be the case, and some of the empirical relations for mass-transfer coefficients are presented below. Gilliland 14] presented the equation... 

Mass-Transfer Correlations Because of the tremendous im-ortance of mass transfer in chemical engineering, a veiy large num-er of studies have determined mass-transfer coefficients both empirically and theoretically. Some of these studies are summarized in Tables 5-17 to 5-24. Each table is for a specific geometry or type of contactor, starting with flat plates, which have the simplest geometry (Table 5-17) then wetted wall columns (Table 5-18) flow in pipes and ducts (Table 5-19) submerged objects (Table 5-20) drops and... 

Mass-Transfer Coefficients Mass-transfer coefficients (and the equally important interfacial area, a parameter with which they frequently are combined) may be computed from empirical correlations or theoretical models. 

A paper by McCabe and Stevens (M4) illustrates an empirical approach to the correlation of growth rate coefficients. These authors reasoned that mass transfer to the interface consists of two parallel processes, a diffusion effect independent of velocity and a flow effect linear in velocity. They expressed this by a rate term (r + /Jit). This was related to rg, the over-all growth rate coefficient, by the conventional expression for rate processes in series,... 

It seems clear that a two phase model will be able to predict low values of the heat and mass transfer coefficients as Kunii has done O). The trouble with this approach will be an accurate estimate of the equivalent bubble bed diameter. Thus, improved empirical correlations are still useful for design purposes, when one looks for estimates of gas-solid heat and mass transfer coefficients. 

In case of complex membrane morphology such as asymmetric or composite membranes, or when Fickian diffusion is not valid, evaluating will be more complex. Individual mass transfer coefficients in Equation 2.2 depend on multiple factors such as temperarnre, pressure, flow rates, and diffusion coefficients and could often be estimated from empirical correlations available in literature [1,2,6]. 

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