Transfer Correlations

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 are derived from models. They must be employed in a similar model. For example, if an arithmetic concentration difference was used to determine k, that k should only be used in a mass-transfer expression with an arithmetic concentration difference. 

Semiempirical correlations are often preferred to purely empirical or purely theoretical correlations. Purely empirical correlations are dangerous to use for extrapolation. Purely theoretical correlations may predict trends accurately, but they can be several orders of magnitude off in the value of k. 

Correlations with broader data bases are often preferred. 

The analogy between heat and mass transfer holds over wider ranges than the analogy between mass and momentum transfer. Good heat transfer data (without radiation) can often be used to predict mass-transfer coefficients. 

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By assuming a reasonable fluid velocity, together with fluid physical properties, standard heat transfer correlations can be used. 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

Units employed in diffusivity correlations commonly followed the cgs system. Similarly, correlations for mass transfer correlations used the cgs or Enghsh system. In both cases, only the most recent correlations employ SI units. Since most correlations involve other properties and physical parameters, often with mixed units, they are repeated here as originally stated. Common conversion factors are listed in Table 1-4. 

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

TABLE 5-21 Mass Transfer Correlations for a Single Flat Plate or Disk—Transfer to or from Plate to Fluid... 

TABLE 5-22 Mass Transfer Correlations for Falling Films with a Free between Gas and Liquid... 

TABLE 5-23 Mass-Transfer Correlations for Flow in Pipes and Duets—Transfer is from Wall to Fluid... 

TABLE 5-24 Mass Transfer Correlations for Flow Past Submerged Objects... 

TABLE 5-25 Mass-Transfer Correlations for Drops and Bubbles... 

TABLE 5-26 Mass-Transfer Correlations for Particles, Drops, and Bubbles in Agitated Systems... 

TABLE 5-27 Mass Transfer Correlations for Fixed and Fluidized Beds... 

TABLE 5-28 Mass Transfer Correlations for Packed Two-Phase Contactors—Absorption, Distillation, Cooling Towers, and Extractors (Packing Is Inert)... 

If the vapor is superheated at the inlet, the vapor may first be desuperheated by sensible heat transfer from the vapor. This occurs if the surface temperature is above the saturation temperature, and a single-phase heat-transfer correlation is used. If the surface is below the saturation temperature, condensation will occur directly from the superheated vapor, and the effective coefficient is determined from the appropriate condensation correlation, using the saturation temperature in the LMTD. To determine whether or not condensation will occur directly from the superheated vapor, calculate the surface temperature by assuming single-phase heat transfer. 

Heat Exchangers Since most cryogens, with the exception of helium 11 behave as classical fluids, weU-estabhshed principles of mechanics and thermodynamics at ambient temperature also apply for ctyogens. Thus, similar conventional heat transfer correlations have been formulated for simple low-temperature heat exchangers. These correlations are described in terms of well-known dimensionless quantities such as the Nusselt, Reynolds, Prandtl, and Grashof numbers. 

Heat Transfer Heat-transfer rates are gener ly large despite severe axial dispersion, with Ua. frequently observed in the range 18.6 to 74.5 and even to 130 kW/(m K) [1000 to 4000 and even to 7000 Btu/(h fF °F)][see Bauerle and Ahlert, Ind. Eng. Chem. Process Des. Dev., 4, 225 (1965) and Greskovich et al.. Am. Tn.st. Chem. Eng. J., 13,1160 (1967) Sideman, in Drewet al. (eds.). Advances in Chemical Engineering, vol. 6, Academic, New York, 1966, p. 207, reviewed earlier work]. In the absence of specific heat-transfer correlations, it is suggested that rates be estimated from mass-transfer correlations via the heat-mass-transfer analogy. 

The basic correlation for packed tubes is derived from those of empty tubes by properly reinterpreting some critical variables. The most important change is in the characteristic distance that is changed from the tube diameter to the particle diameter. Other corrections are also used. The transfer correlations are based on dimensional analysis, expressed as either the Nusselt-type (1930) or the Colbum-type (1933) equations. For empty tubes at high Re numbers ... 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

The mass transfer correlations are obtained by replacing Nu by Sh and Pr by Sc according to the heat and mass transfer analogy. 

HHl TABLE 4.9 Heat Transfer Correlations for Internal Flow... 

There has to be a relation between kLa with aeration rate and agitation speed, and scale-up factor has to be determined. To eliminate the effect of viscous forces, the rheology of the media and broth for a large vessel have to be similar to that of a bench-scale vessel. For scale-up based on geometric similarity, the constant values a and b are proposed for the mass-transfer correlation in Table 13.1. 

Table 13.1. Constants in mass transfer correlation for various fermenter size...

The heat transfer correlations are considered separately in the laminar and turbulent regimes in Figs. 2.21 and 2.22, respectively. The dependence of the Nusselt number on the Reynolds number is stronger in all the micro-channel predictions compared to conventional results, as indicated by the steeper slopes of the former Choi et al. (1991) predict the strongest variation of Nusselt number with Re. The predictions for all cases by Peng et al. (1996) also fall below those for a conventional channel. 

Most of heat transfer correlations are based on data obtained in flow boiling from relatively large diameter conduits and the predictions from these correlations show considerable variability. Effects of superficial liquid and gas velocity on heat transfer in gas-liquid flow and its connection to flow characteristics were studied by Hetsroni et al. (1998a,b, 2003b), Zimmerman et al. (2006), Kim et al. (1999), and Ghajaret al. (2004). However these investigation were carried out for tubes of D = 25—42 mm. These data, as well as results presented by Bao et al. (2000) in tubes of L> = 1.95 mm and results obtained by Hetsroni et al. (2001), Mosyak and Hetsroni (1999) are discussed in the next sections to clarify how gas and liquid velocities affect heat transfer. Effects of the channel size and inclination are considered. 

From the results discussed above one may conclude that due to the complex nature of two-phase gas-liquid flow there is a large variation in experimental results and heat transfer correlations presented by different investigators. For channels of... 

Kim D, Ghajar AJ, Dougherty RL, Ryali VK (1999) Comparison of 20 two-phase heat transfer correlations with seven sets of experimental data, including flow pattern and tube inclination... 

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