Sherwood number general correlations

The designer now needs to make some estimates of mass transfer. These properties are generally well known for commercially available adsorbents, so the job is not difficult. We need to re-introduce the adsorber cross-section area and the gas velocity in order to make the required estimates of the external film contribution to the overall mass transfer. For spherical beads or pellets we can generally employ Eq. (7.12) or (7.15) of Ruthven s text to obtain the Sherwood number. That correlation is the mass transfer analog to the Nusselt number formulation in heat transfer ... 

Just as there are correlations for the Nusselt number based on the Reynolds and Prandtl numbers [Eq. (4.96)], there are empirical correlations for the Sherwood number as a function of Reynolds and Schmidt numbers, which are of the general form... 

For an isothermal situation at 600 K, develop a general correlation for the Sherwood number versus the spin Reynolds number, which should be generally in the form... 

Schmidt minimum wetting, 513, 514 Schmidt humber, 528. 531 Sherwood-Eckert generalized pressure drop correlation (GPDC), 479-481. 486. 493, 504-506 Sherwood number, 529, 531 Shiras et al. distributed component. 110... 

This relationship indicates that the Sherwood number takes the value 2 for Ap 0, as is the case in natural convection. A generalized correlation for mass and heat transfer coefficients is recommended by Calderbank and Moo-Young (1961). This correlation relates the mass-transfer coefficient to the power per unit volume and Schmidt number. The relationship is mainly applicable to low-viscosity liquids. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be very large and therefore must be carefully accounted for when using %L or Hl data. For liquids the mass-transfer coefficient kL is correlated as either the Sherwood number or the Stanton number as a function of the Reynolds and Schmidt numbers (see Table 5-24). Typically, the general form of the correlation for HL is (Table 5-24)... 

In order to characterize mass transfer in the boundary layers, it is necessary to determine the respective mass transfer coefficients. These coefficients depend on the properties of the solutions and on the hydrodynamic conditions of the system. Such coefficient can either be obtained by experiments or be estimated with the help of empirical correlations of dimensionless numbers. The majority of the correlations referred to in the literamre for various hydrodynamic conditions have the same general form. These include Sherwood number Sh), which contains the mass transfer coefficient, as a function of the Reynolds number Re) and Schmidt number (5c) [89-91]. General mass transfer correlation can be written as... 

General correlations for the Sherwood number. In [364], the following approximate equation was suggested for the mean Sherwood number ... 

The amount of additional information needed to be able directly to take into account heat and mass transfer in Model 4 is high. Using the two-film theory, information on the film thickness is needed, which is usually condensed into correlations for the Sherwood number. That information was not available for Katapak-S so that correlations for similar non-reactive packing had to be adopted for that purpose. Furthermore, information on diffusion coefficients is usually a bottleneck. Experimental data is lacking in most cases. Whereas diffusion coefficients can generally be estimated for gas phases with acceptable accuracy, this does unfortunately not hold for liquid multicomponent systems. For a discussion, see Reid et al. [8] and Taylor and Krishna [9]. These drawbacks, which are commonly encountered in applications of rate-based models to reactive separations, limit our ability to judge their value as deviations between model predictions and experimen-... 

In OMD, flux is inversely proportional to the membrane thickness, so it must be as thin as possible (O.l-l.O pm). Furthermore, in the case of OMD, a general mass transfer correlation like Equation [2.7], in which the Sherwood number is a function of the Reynolds and Schmidt numbers, can be written. 

Correlations for mass transfer are conveniently divided into those for fluid - fluid interfaces and those for fluid - solid interfaces. Many of the correlations have the same general form. That is, the Sherwood or Stanton numbers containing the mass transfer coefficient are often expressed as a power function of the Schmidt number, the Reynolds number, and the Grashof number. 

In general, values for Sh and Nu under reaction conditions are different from those observed at these limits (Hayes and Kolaczkowski [121]). Correlations which attempt to describe the variation of Sherwood (or Nusselt) numbers with the Damkohler number have been proposed. Tronconi et al. [104] and Groppi and Tronconi [122] used the result from Brauer and Petting [123] for mass/heat transfer correlations when modeling monolith reactors with circular, square, and triangular shape ... 

The design of heat and mass transfer operations in chemical engineering is based on the well-known correlations that use the dimensionless numbers Nu (Nusselt) for heat transfer and Sh (Sherwood) for mass transfer By balancing the acting forces, energies, and mass flows within the boundary layers of velocity, temperature, and concentration, the theoretical derivation of general relations for Nu and Sh is given in fundamental work [35]. 

Heat and mass transfer coefficients are usually reported as correlations in terms of dimensionless numbers. The exact definition of these dimensionless numbers implies a specific physical system. These numbers are expressed in terms of the characteristic scales. Correlations for mass transfer are conveniently divided into those for fluid-fluid interfaces and those for fluid-solid interfaces. Many of the correlations have the same general form. That is, the Sherwood or Stanton numbers containing the mass transfer coefficient are often expressed as a power function of the Schmidt number, the Reynolds number, and the Grashof number. The formulation of the correlations can be based on dimensional analysis and/or theoretical reasoning. In most cases, however, pure curve fitting of experimental data is used. The correlations are therefore usually problem dependent and can not be used for other systems than the one for which the curve fitting has been performed without validation. A large list of mass transfer correlations with references is presented by Perry [95]. 

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