Tower Height

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, 

Fan power consumption is the major operating cost and can be counterbalanced in part by greater investment in natural draft construction. In the majority of process applications, fen-operated towers are preferred. Very large installations such as those in power plants employ chimney assisted natural draft installations. A limited use of atmospheric towers is made in areas where power costs are especially high. 

Sizing of a Cooling Tower Number of Transfer Units and Height of Tacking 

The maximum allowable L/G corresponds to equilibrium between exit air and entering water at 110. The saturation enthalpy at 110°F is 92, so that Eq. (9.30) becomes 

The applicable equations with numerical substitutions are listed here and incorporated in the computer program for solution of this problem [Eqs. (9.30)-(9.33)]  

The HETP of a packed-tower section, valid for either distillation or dilute-gas absorption and stripping systems in which constant molal overflow can be assumed and in which no chemical reactions occur, is related to the height of one overall gas-phase mass-transfer unit H0G by the equation 

For gas absorption systems in which the inlet gas is concentrated, the corrected equation is 

The design of a tray tower for gas absorption and gas-stripping operations involves many of the same principles employed in distillation calculations, such as the determination of the number of theoretical trays needed to achieve a specified composition change (see Sec. 13). Distillation differs from absorption because it involves the separation of components based upon tne distribution of the various substances between a vapor phase and a liquid phase when all components are present in both phases. In distillation, the new phase is generated from the original phase by the vaporization or condensation of the volatile components, and the separation is achieved by introducing reflux to the top of the tower. 

In gas absorption, the new phase consists of a relatively nonvolatile solvent (absorption) or a relatively insoluble gas (stripping), and normally no reflux is involved. This section discusses some of the considerations peculiar to gas absorption calculations for tray towers and some of the approximate design methods that can be applied (when simplifying assumptions are valid). 

Substitution of Eq. (9.33) into (9.36) will result in an equation that has as the only unknown. This is solved for with the Newton-Raphson method. 

Substitution of this value of T, back into Eq. (9.31) will evaluate h.  

The integrand l/(/ij -h) now may be evaluated at each temperature and the integration performed with Eq. (9.35). 

Example 9.11 employs this method for finding the number of transfer units as a function of liquid to gas ratio, both with finite and infinite values of k jk. The computer programs for the solution of this example are short but highly desirable. Graphical methods have been widely used and are described for example by Foust et al. (1980). 

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The required tower height may thus be easily calculated usiag equation 47, where Hqq is given by equation 54 and Nqq by equation 56. 

In many situations, however, especially when m > 1, the results using the simpler equation 54 are virtually the same. The required tower height is finally calculated by means of equation 47. 

Xm are not. For unimolecular diffusion through stagnant gas = 1), and reduce to T and X and and reduce to and equation 64 then becomes equation 34. For equimolar counterdiffusion = 0, and the variables reduce tojy, x, G, and F, respectively, and equation 64 becomes equation 35. Using the film factor concept and rate equation 28, the tower height may be computed by... 

The principles outlined so far may be used to calculate the tower height as long as it is possible to estimate the temperature as a function of Hquid concentration. The classical basis for such an estimate is the assumption that the heat of solution manifests itself entirely in the Hquid stream. It is possible to relate the temperature increase experienced by the Hquid flowing down through the tower to the concentration increase through a simple enthalpy balance, equation 68, and thus correct the equiHbrium line in ajy—a diagram for the heat of solution as shown in Figure 9. 

Equation 74 is shown graphically ia Figure 19a for a given set of conditions. Curves such as these cannot be directly used for design, however, because the Peclet number contains the tower height as a characteristic dimension. Therefore, new Peclet numbers are defined containing as the characteristic length. These relate to the conventional Pe as... 

Computation of Tower Height The required height of a gas-absorption or stripping tower depends on (1) the phase equilibria involved, (2) the specified degree of removal of the solute from the gas, and (3) the mass-transfer efficiency of the apparatus. These same considerations apply both to plate towers and to packed towers. Items 1 and 2 dictate the required number of theoretic stages (plate tower) or transfer units (packed tower). Item 3 is derived from the tray efficiency and spacing (plate tower) or from the height of one transfer unit (packed tower). Solute-removal specifications normally are derived from economic considerations. 

Substitution and rearrangement leads to the equation for the tower height,... 

Note that the tower height is inversely proportional to the enhanced mass-transfer coefficient, or to the enhancement factor itself. 

Some performance data of plants with DEA are shown in Table 23-11. Both the absorbers and strippers have trays or packing. Vessel diameters and allowable gas and liquid flow rates are estabhshed by the same correlations as for physical absorptions. The calciilation of tower heights utilizes data of equilibria and enhanced mass-transfer coeffi-... 

Many operating data for carbonate plants are cited by Kohl and Riesenfeld (Gn.s Purification, Gulf, 1985) but not including tower heights. Pilot plant tests, however, are reported on 0.10- and 0.15-m (4- and 6-in) columns packed to depths of 9.14 m (30 ft) of Raschig rings hy Benson et al. (Chem. Eng. Prog., 50, 356 [1954]). 

A. Total Tower Height. This is an assumed maximum. 

Alternately, a separate scrubber vessel can be provided so that the tower height can be decreased. This vessel should be designed in accordance with the procedures in Volume 1 for design of two-phase separators. 

L = liquid flow rate, lb/hr-fl of cros,s-sectional area m = constant, allowing for vertical tower height consumed by distribution/redistribution equipment S = tray spacing, in. 

Determine the number of transfer units, and the packed tower height. 

The transfer unit concept is also applicable to distillation in packed towers. Height of the packing required is ... 

The hydrolysis is performed as a continuous countercurrent reaction in tall reaction towers (height 15-20 m, diameter 0.7 m). The reaction time amounts to 60-90 min. Reaction products are as well obtained an aqueous glycerin solution (about 15%) as on a mixture of raw fatty acids [50]. The free fatty acids are carefully distilled with the aid of a thin film evaporator (2-10 mbar, 260°C maximum) [51]. Crystallization and transwetting are additional methods for fractionation of fatty acid mixtures. 

Taking ah 5 0 and assuming as a first estimate a tower height of 100 in. then in equation 13.31 ... 

Limit the tower height to about 175 ft max because of wind load and foundation considerations. An additional criterion is that L/D be less than 30. 

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