Dimensioning of Mass Transfer Columns

The demands on effective mass transfer equipments can be understood from the basic eqnation of mass transfer (Taylor and Krishna 1993)  

To achieve a high mass transfer rate N each factor in (5.4-1) should be large. The driving force (y -y) is high at a conntercurrent flow of gas and liquid. A large interfacial area A is provided by colnmn internals like trays or packings. The mass transfer coefficient qg high valnes if the interfacial area is steadily renewed. All these demands are well met by tray columns and by packed columns. 

Process Washing agent Absorptive T in °C Chemical reaction Regeneration 

Cold caustic soda process 8 wt% sodium hydroxide C02, H2S 10-30 2NaOH + COj NajCOj + HjO 2NaOH + HjS NajS + 2H2O 60 kg CaO, 300 kg steam, 7 m cooling water, 15 kWlv mN.iye 

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Equation 16 shows that the peak variance or band broadening is comprised of individual contributions from different aspects of the separation process. The first term in equation 16 represents the contribution of the width of the feed band to the peak variance. The second term represents the contribution to band broadening from dispersion due to eddy diffusion. The third term represents the contribution of mass transfer effects external to the particles while the fourth term represents the contribution of diffusional resistances within the stationary phase. The significance of each term relative to the total variance depends upon the operating parameters, the column and packing dimensions and the size of the solute. 

The overall mass transfer coefficients Kg and Ky have units of (moIes)/(time-interfacial area-unit mole fraction driving force). In the case of a wetted-wall column, the interfacial area is known. However, for most types of mass transfer equipment the interfacial area cannot be determined. It is necessary therefore to define a quantity a that is the interfacial area per unit of active equipment volume. Although separate compilations of a can be found in handbooks and vendor literature, this parameter is usually combined with the mass transfer coefficients to define capacity coefficients (k a) and (K a) for the liquid phase and (K,a) or (k,a) for the vapor phase, which then have the dimensions of moles per unit time per unit driving force per unit of active equipment volume. The application of these composite coefficients to the design of packed towers is now demonstrated. 

In pulsed packed columns [6.19, 6.43], the loadability decreases with increasing pulsation frequency, but generally increases with larger dimension of the filling material and an increasing void fraction. The type of mass transfer, continuous -> disperse or disperse - continuous, generally influences the droplet motion and separation efficiency ... 

The optimum flow rate for most SEC separations using conventional PLgel column dimensions (internal diameter 7.5 mm) is 1.0 ml/min. It may be of some benefit to work with lower flow rates, particularly for the analysis of higher molecular weight polymers where the reduced flow rate improves resolution through enhanced mass transfer and further reduces the risk of shear... 

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 86). Multiple path, molecular diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral spreading. Consequently, the initially circular spots become progressively elliptical in the direction of flow. Efficiency and resolution are thus impaired. Elution must be halted before the solvent front reaches the opposite edge of the plate as the distance it has moved must be measured in order to calculate the retardation factors (Rf values) of separated components (p. 86). 

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

Wetted-wall columns have been used for many years for determining mass-transfer coefficients on the assumption that the interfacial area across which mass transfer occurs can be obtained accurately from the dimensions of the column and a knowledge of the film thickness. It is therefore of considerable practical interest to determine whether the interfacial waves lead to an appreciable increase in the interfacial area of the film, which would introduce a grave uncertainty into such methods of determining mass-transfer coefficients. 

In the course of extensive measurements on bubble columns with different dimensions [89], the gas hold-up H proved to be directly proportional to the volume-related mass transfer coefficient kLa. For this reason, H will be the target number in the following considerations. 

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 82). Multiple path, molecular,diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral... 

Reducing particle size of the SEC column packings reduces the time requirements in SEC because of the increased mass transfer and resultant separation efficiency. Hence, columns can become smaller in dimensions while maintaining resolution. This approach has been used for many years. Column bank lengths dropped from several meters to now typically 60 cm with current SEC column particle sizes of 5 pm as compared with about 100 pm in the early 1960s. During the same period, time requirements dropped from about 6 hr to less than 1 hr. 

The preceding discussion refers to mass-transfer rates based on the unit volume of dispersion. But the interfacial area per unit volume of liquid a is often required. To convert a to a , one must know the gas holdup a, with a = (1 - a) a ". A correlation covering a wide range of column dimensions, flow conditions, and system properties has been developed by Hughmark (H13) and modified by Mashelkar (M8) ... 

The values of interfacial area and of overall mass-transfer coefficient increase with decreasing distance S between the spray nozzle and gas inlet, whatever the nozzle type, column dimensions, and flow rates. Indeed the spray provides a large interfacial area in the vicinity of the nozzle, where there is intensive circulation. Then a decreases quickly away from the nozzle, as a result of both coalescence of droplets and collection of liquid on the column walls, kaa and a are approximately proportional to (P7, H12, Mil) for absorption and desorption pro-... 

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