Mass transfer inside tubes

Single-Phase Mass Transfer Inside or Outside Tubes... 

Film coefficients of mass transfer inside or outside tubes are important in membrane processes using tube-type or the so-called hollow fiber membranes. In the case where flow inside the tubes is turbulent, the dimensionless Equation 6.25a, b (analogous to Equation 5.8a, b for heat transfer) provide the film coefficients of mass transfer k [7]... 

No good methods are available for calculating heat-transfer coefficients when appreciable subcooling of the condensate is required. A conservative approach is to calculate a superficial mass velocity assuming the condensate fills the entire tube and use the equations presented above for single-phase heat transfer inside tubes. This method is less conservative for higher condensate loads. 

W. L. Friend, and A. B. Metzner, Turbulent Heat Transfer inside Tubes and the Analogy among Heat, Mass, and Momentum Transfer, AlChE J., (4) 393-402,1958. 

Friend WL, Metzner AB. (1958) Turbulent heat transfer inside tubes and analogy among heat, mass and momentum transfer. AICHEJ, 4 393-402. 

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. 

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.)...

An air stream at approximately atmospheric temperature and pressure and containing a low concentration of carbon disulphide vapour is flowing at 38 m/s through a series of 50 mm diameter tubes. The inside of the tubes is covered with a thin film of liquid and both heat and mass transfer are taking place between the gas stream and the liquid film. The film heat transfer coefficient is found to be 100 W/mzK. Using a pipe friction chan and assuming the tubes to behave as smooth surfaces, calculate ... 

Modules Every module design used in other membrane operations has been tried in pervaporation. One unique requirement is for low hydraulic resistance on the permeate side, since permeate pressure is very low (0.1-1 Pa). The rule for near-vacuum operation is the bigger the channel, the better the transport. Another unique need is for heat input. The heat of evaporation comes from the liquid, and intermediate heating is usually necessary. Of course economy is always a factor. Plate-and-frame construction was the first to be used in large installations, and it continues to be quite important. Some smaller plants use spiral-wound modules, and some membranes can be made as capillary bundles. The capillary device with the feed on the inside of the tube has many advantages in principle, such as good vapor-side mass transfer and economical construction, but it is still limited by the availability of membrane in capillary form. 

It has been suggested, however, that for mass transfer, the transfer in the liquid phase is from a vapour-liquid interface where the liquid velocity is a maximum to the wall where it is zero. With a liquid flowing inside the tube the heat transfer is from a layer of zero velocity at the wall to the fluid all the way to the centre of the tube where it is moving with a maximum velocity. Hatta 79-1 based his analysis on the more closely related process of diffusion of a gas into a liquid, and obtained the expression ... 

Konobeev et al. (K21), 1961 Experimental study of C02 absorption by water film, with upward and downward cocurrent gas/film flow, inside tubes 1.05-1.66 cm. i.d., 20-87 cm. long. Gas velocities 6-86 m./sec. IVko = 5-105. Length and amplitude of surface ripples and local film thicknesses measured. Rate of mass transfer stated to be function of wave characteristics only. 

Finally, the question rises whether an accurate simulation of the reformer tubes does not have to include consideration of radial gradients. The two dimensional model developed for this purpose in this work neglects interfacial gradients, for reasons explained already above, but maintains the mass transfer limitations inside the catalyst, of course. 

O. Shell side of microporous hollow fiber module for solvent extraction Na, = V[dha-)/L]N%N°s M Nsh- D Nlt = K = overall mass-transfer coefficient (3 = 5.8 for hydrophobic membrane. (3 = 6.1 for hydrophilic membrane. [E] Use with logarithmic mean concentration difference. dh = hydraulic diameter 4 x cross-sectional area of flow wetted perimeter (p = packing fraction of shell side. L = module length. Based on area of contact according to inside or outside diameter of tubes depending on location of interface between aqueous and organic phases. Can also be applied to gas-liquid systems with liquid on shell side. [118]... 

The rate of mass transfer, R, for each species from shell side to tube side at any point inside the contactor is given as... 

Heat transfer between a solid wall and a fluid, e.g. in a heated tube with a cold gas flowing inside it, is of special technical interest. The fluid layer close to the wall has the greatest effect on the amount of heat transferred. It is known as the boundary layer and boundary layer theory founded by L. Prandtl2 in 1904 is the area of fluid dynamics that is most important for heat and mass transfer. In the boundary layer the velocity component parallel to the wall changes, over a small distance, from zero at the wall to almost the maximum value occurring in the core fluid, Fig. 1.6. The temperature in the boundary layer also changes from that at the wall w to at some distance from the wall. 

Endothermic reactions, such as steam reforming, are usually carried out in long narrow tubes filled with catalysts and externally heated by flames. The heat could be provided more uniformly and more accurately at the necessary level by a combustion catalyst coated on the outside of the tubes, and heat transfer rates could be further improved by coating the endothermic reaction catalyst on the inner wall of the tube. In this way, the heat of combustion is transferred to the heat sink (the endothermic reaction) through the solid wall, avoiding solid-gas heat transfer resistances. However, the tubular geometry is not most efficient for this application because of the difficulty to coat the inside of the tubes and the need to include static mixers to facilitate mass transfer to the catalytic surfaces. 

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