Mass transfer outside tubes

Tjgi = saturation temperature of the vapor, °F T = wall temperature of tube, °F L = length of tube for heat transfer, ft W = vapor weight (mass) flowrate, Ib/hr Do = outside tube diameter, ft... 

Piret et al.(3> attempted to reproduce the conditions in a porous solid using banks of capillary tubes, beds of glass beads and porous spheres, and measured the rate of transfer of a salt as solute through water to the outside of the system. It was shown that the rate of mass transfer is that predicted for an unsteady transfer process and that the shape of the pores could be satisfactorily taken into account. 

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]... 

In the case where the fluid flow outside the tubes is parallel to the tubes and laminar (as in some membrane devices), the film coefficient of mass transfer on the outer tube surface can be estimated using Equation 6.26a and the equivalent diameter as calculated with Equation 5.10. 

In the case where the fluid flow outside tubes is normal or oblique to a tube bundle, approximate values of the film coefficient of mass transfer can be estimated by using Equation 6.27a [7], which is analogous to Equation 5.12a ... 

Data acquired by many investigators have shown a close analogy between the rates of heat and mass transfer, not only in the case of packed beds but also in other cases, such as flow through and outside tubes, and flow along flat plates. In such cases, plots of the /-factors for heat and mass transfer against the Reynolds number produce almost identical curves. Consider, for example, the case of turbulent flow through tubes. Since... 

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]... 

For a set diameter and tube arrangement, Eqs. (26) and (29) show that hj is fixed by the mass velocity G inside the tubes and hg is fixed by the mass velocity outside the tubes. Similarly, since the heat-transfer area A mass velocities, and flow rates determine the length of the tubes L, Eqs. (30) and (31) show that , and Eg are functions of A flow rates, and, respectively, G and Gj.t Thus, Ej and Eg are functions of hj, hg, and At,. 

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. 

When the microporous membrane is in the form of a hollow fiber (see Fig. 2.7), the interfacial areas on the two sides of the hollow fiber are different. The overall mass-transfer coefficient may be defined based on the surface area calculated using either the inside diameter (ID) or the outside diameter (OD) of the hollow fiber. For calculating an overall mass-transfer coefficient, the interfacial area should be based on the diameter where the aqueous-organic phase interface is located. Consider, for example, the aqueous feed and strip phases in hydrophobic fiber lumen (tube side) and organic LM phase on the shell side. The rate of solute extraction per unit fiber length with the aqueous-organic interface located on the fiber ID ... 

The mass transfer coefficients Kg and K/ are overall coefficients analogous to an overall heat transfer coefficient in a shell-and-tube heat exchanger. The overall coefficient in a heat exchanger has three components, an inside coefficient, a wall resistance, and an outside coefficient. Analogs exist in mass transfer. For the inside coefficient, we consider the driving force between the bulk liquid concentration and liquid concentration at the interface ... 

FLOW OUTSIDE TUBES PARALLEL TO AXIS. Some membrane separators have bundles of hollow fibers in a shell-and-tube arrangement with liquid or gas flowing parallel to the tube axis on the outside of the tubes. The external flow passages are irregular in shape and not uniform, since the fibers are not held in position as are the tubes in a heat exchanger. Empirical correlations for the external mass-transfer coefficient have been proposed using an equivalent diameter to calculate the Reynolds number. For a bundle of fibers with diameter d packed in a shell with c void fraction, the equivalent diameter is... 

Estimation of the mass-transfer coefficient in the dialysate outside the fibers is considerably more difficult because of the complex geometry. In a shell-and-tube heat exchanger, baffles are used to help direct the shell-side fluid to flow back and forth in directions largely normal to the tube length. It would... 

Considering a chromatographic process controlled by a partition equilibrium and neglecting extracolumn effects (i.e., band broadening caused by factors outside the column, e.g., tubings, detector etc.), several factors can contribute to the overall solute band broadening eddy diffusion, longitudinal diffusion, and resistance to mass transfer in mobile and stationary phase. 

A MC module contains thousands of microporous hollow fibres, which are knitted into a fabric that is wound around a distribution tube with a central baffle as shown in Figure 1.15. The baffle ensures the water is distributed across the fibres, and also results in reduced pressure drop across the contactor. The hollow fibres are packed densely in a membrane module with a surfrce area of up to 4000 n / m. The liquid flows outside (shell side) the membrane, while vacuum is appHed on the inside of the fibre (tube side) forming a film across the pores of the membrane. Mass transfer takes place through this film and the pores due to the difference in the gas partial pressure between the shell side and tube side. Since the membranes are hydrophobic, they are not wetted by water, thereby, efiectively blocking the flow of water through the membrane pores. The membrane provides no selectivity. Rather its purpose is to keep the gas phase and the Hquid phase separated. In effect, the membrane acts as an inert support that allows intimate contact between gas and liquid phases without dispersion. Vacuum on the tube side of the membrane increases the mass transfer rate as in a vacuum tower. The efficiency of the process is enhanced with the aid of nitrogen sweep gas flowing on the permeate side of the membrane. 

Film-type tube apparatus) Multitube apparatus with an absorbent falling-film on the tube insides. Cocurrent and countercurrent flow of gas phase and falling-film (both phases are coherent). Simple design with the possibility of heat removal by a cooling agent outside the tube shell. Low gas pressure drop, small interfacial area, small liquid mass transfer coefficient. 

Alternately, the cell may be designed similarly to a shell-and-tube heat exchanger, with flow inside the tubes and on the outside or shell side. The shell-side flow may be strictly parallel to the tubes or also across the tubes, or tube bundle, and directed by the use of baffles and baffle cuts. Such a layout is illustrated in Figure 6.3, with more information about the intricacies provided by Hoffman. There is an analogy with the treatment of absorbers, strippers, and distillation columns as a continuum, described in terms of the rate of mass transfer."... 

When one has decided on a well mixed reactor, possibly with one or several dispersed phases, the solution of the heat transfer problem is relatively simple. It may be merely a question of installing sufficient heat transfer area, either inside or outside the reactor. Vigorous mixing will increase the heat transfer to the wall or to submerged tube bundles. For rapid exothermic reactions, the volume of the reactor may be determined by heat transfer, not by reaction kinetics or mass transfer. The use of a boiling solvent for effective heat removal and temperature has been indicated in section 8.3.3. It can often be applied on large scales. 

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