Mass film coefficients

The relationship of the overall gas-phase mass transfer coefficient to the individual film coefficients maybe found from equations 4 and 5, assuming a straight equiHbrium line ... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

This leads to rate equations with constant mass transfer coefficients, whereas the effect of net transport through the film is reflected separately in thej/gj and Y factors. For unidirectional mass transfer through a stagnant gas the rate equation becomes... 

Equation 28 and its liquid-phase equivalent are very general and valid in all situations. Similarly, the overall mass transfer coefficients may be made independent of the effect of bulk fiux through the films and thus nearly concentration independent for straight equilibrium lines ... 

Neither the penetration nor the surface renewal theory can be used to predict mass transfer coefficients directiy because T and s are not normally known. Each suggests, however, that mass transfer coefficients should vary as the square root of the molecular diffusivity, as opposed to the first power suggested by the film theory. 

The rate of mass transfer,/, is then assumed to be proportional to the concentration differences existing within each phase, the surface area between the phases,, and a coefficient (the gas or Hquid film mass transfer coefficient, k or respectively) which relates the three. Thus... 

Mass-Transfer Coefficients with Chemical Reaction. Chemical reaction can occur ia any of the five regions shown ia Figure 3, ie, the bulk of each phase, the film ia each phase adjacent to the iaterface, and at the iaterface itself. Irreversible homogeneous reaction between the consolute component C and a reactant D ia phase B can be described as... 

Overall Coefficients. Often overall coefficients of heat and mass transfer are available, rather than the film coefficients used eadier. In that case equation 35 can be rewritten as... 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Simplified Mass-Transfer Theories In certain simple situations, tne mass-transfer coefficients can be calculated from first principles. The film, penetration, and surface-renewal theories are attempts to extend tnese theoretical calculations to more complex sit-... 

The Shei wood-number relation for gas-phase mass-transfer coefficients as represented by the film diffusion model in Eq. (5-286) can be rearrangecTas follows ... 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

Design of inorganic absorbers quite often involves a system whose major parameters are well defined such as system film control, mass transfer coefficient equations, etc. Ludwig gives design data for certain well-known systems sueh as NH3-Air-H20, CI2-H2O, COi in alkaline solutions, etc. Likewise, data for commercially available packings is well documented such as packing factors, HETP, HTU, etc. 

Kqa = Gas film overall mass transfer coefficient, lb mols/hr (fP) (ATM)... 

Hog, Hql = Height of transfer unit based on overall gas or liquid film coefficients, ft Gm, Ljn = Gas or liquid mass velocity, lb mols/(hr) (ft ) Kga, Kla = Gas or liquid mass transfer coefficients, consistent units... 

In heat transfer applications, this jacket is considered a helical coil if certain factors are used for calculating outside film coefficients. The equivalent heat transfer diameter, D, for a rectangular cross-section is equal to 4 w (w being the width of the annular space). Velocities are calculated from the actual cross-section of the flow area, pw (p being die pitch of die spiral baffle), and die effective mass flowrate W dirough die passage. The effective mass flowrate is approximately 60% of die total mass flowrate of die jacket. 

WTien heat transfer occurs in the presence of suspended solid particles, the chemical reacdon may require mass transfer, etc. However, the mixing part of the operation must be designed to accomplish the process results, which may be those named above (and others) plus the required heat transfer affecting the outside film coefficient, hg, across/around any coils, flat surfaces, or wall jackets. 

Liquid film mass transfer coefficient ( b moles) (cu ft)/(sec) (sq ft) (lb mole)... 

Overall mass transfer coefficient based on liquid phase, lb mol/ (hr) (ft ) (lb mol/ft ) Overall mass transfer coefficient based on liquid film controlling, lb mol (hr) (ft ) (lb mol/ft3)... 

Figure 10-50C. Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm . A fluid inside pipes/tubes, turbulent flow only. Note h= average film coefficient, Btu/hr-ft -°F d = inside tube diameter, in. G = mass velocity, Ib/sec/ft v = fluid velocity, ft/sec k = thermal conductivity, Btu/hr (ft )(°F/ft) n, = viscosity, lb/(hr)(ft) Cp = specific heat, Btu/(lb)(°F). (Used by permission Engineering Manual for Dowtherm Heat Transfer Fluids, 1991. The Dow Chemical Co.)...

Figure 10-71. Condensing steam film coefficients for vertical surfaces or horizontal tubes. G 7n,/ restricted to < 1,090. For theoretical h , for horizontal tubes, use and multiply results by 0.8. G = condensate mass flow per unit tube outside circumference, vertical tubes, lb/(hr) (ft). (Used by permission Devore, A. Petroleum Refiner, V. 38, No. 6, 1959. Gulf Publishing Company, Houston, Texas. All rights reserved.)...

Calculate the shell-side dry-gas film coefficient, hg or h, for outside tube conditions. Assume a baffle spacing or about equal to one shell diameter. Use the shell-side method described in Equation 10-48 and Figure 10-54. This is necessary for inlet conditions and then must be checked and recalculated if sufficient change occurs in the mass flow rate, G, to yield a change in hg. 

The thesis of Steward indicates that the overall liquid film and mass transfer coefficients were functions of the gas flow rate and the column pressure and are independent of the liquid flow rate and inlet air temperature. The gas film heat transfer coefficient was found to be a function only of the air flow rate. 

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