Packed tower design transfer units

E Design of Packed Towers Using Transfer Units... 

In 1966, in a paper that now is considered a classic, Danckwerts and Gillham [Tmns. Inst. Chem. Eng., 44, T42 (1966)] showed that data taken in a small stirred-ceU laboratoiy apparatus could be used in the design of a packed-tower absorber when chemical reactions are involved. They showed that if the packed-tower mass-transfer coefficient in the absence of reaction (/cf) can be reproduced in the laboratory unit, then the rate of absorption in the l oratoiy apparatus will respond to chemical reactions in the same way as in the packed column even though the means of agitating the hquid in the two systems might be quite different. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficients. The literature on tower packings, for example, normally reports kGpa values measured at very low inlet-gas concentrations, so that yBM — 1, and at a total pressure close to 1 atmosphere. Thus, the correct rate coefficient for use in packed-tower design involving the use of the driving force (y-y /yBM is obtained by multiplying the reported kGpa values by the value of Pj employed in the actual test unit (here 1 atm = 101.3 kPa) and not the... 

To determine the required size of an absorption or stripping unit, it is necessaiy to know not only the equilibrium solubility of the solute in the solvent and the material balance around the column but also the rate at which solute is transferred from one phase to the other within the tower. This rate directly affects the volume of packing needed in a packed tower, the degree of dispersion required in a spray contactor, and (somewhat less directly) the number of trays required in a tray tower. The last effect occurs as a result of the influence of mass transfer rate on tray efficiency which is discussed in a later section. Because of its direct effect on packed tower design and the importance of this type of contactor in absorption, this discussion of mass transfer is aimed primarily at the packed tower case. A more detailed review of mass transfer theory is given in Chapter 2. 

Principles of Rigorous Absorber Design Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] have shown that when adequate data are available for the Idnetic-reaciion-rate coefficients, the mass-transfer coefficients fcc and /c , the effective interfacial area per unit volume a, the physical solubility or Henry s-law constants, and the effective diffusivities of the various reactants, then the design of a packed tower can be calculated from first principles with considerable precision. 

The height of the transfer unit has not been satisfactorily correlated for application to a wide variety of systems. If pilot plant or other acceptable data are available to represent the system, then the height of packing can be safely scaled-up to commercial units. If such data are not available, rough approximations may be made by determining Hg and Hl as for absorption and combining to obtain an Hqg (Ref. 74, pg. 330). This is only very approximate. In fact it is because of the lack of any volume of data on commercial units that many potential applications of packed towers are designed as tray towers. 

The information that is ultimately needed about a cooling tower design is the height of packing for a prescribed performance. This equals the product of the number of transfer units by the height of each one,... 

Smith (15) has presented a practical ammonia-stripping tower design based on the concept of the height of transfer unit vs the gas/liquid ratio for a given type of tower packing. He has provided a sample design problem. 

An atmospheric packed tower air stripper is used to clean contaminated groundwater with a concentration of 100 ppm trichloroethylene (TCE). The stripper was designed such that packing height is 13 ft, the diameter (D) is 5 ft, and the height of a transfer unit (HTU) is 3.25 ft. Assume Henry s law applies with a constant (N) of 324 atm at 68°F. Also, at these conditions the molar density of water is 3.47 Ibmol/ft and the air-water mole ratio (G/L) is related to the air-water volume ratio G" jL") through G" jL" = 130 G/L, where the units of G" and L" are ft /(s ft ). 

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. 

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