Tower coefficients

The Ntu corresponding to a set of hypothetical conditions is called the required coefficient. When operational tests have been performed, the Ntu represents the available coefficient and is an evaluation of the equipment involved. 

The minimum required coefficient for a given temperature occurs at an L G ratio of zero. This situation corresponds to an infinite air rate. There is 

both cross- and counterflow towers have the same minimum coefficient at an L G ratio of zero and both increase to infinity at (L G)max. A 

A low air rate requires a large tower, while a high air rate in a smaller tower requires greater fan power. Limitations in air velocities are typically 300-500 fpm in counterflow towers, and 350-650 fpm in crossflow towers. 

Higher velocities are obtainable in crossflow towers because of larger air inlet and greater eliminator area. Also, the discharging air does not pass through the water distribution system. 

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Cooling towers are capable of operating over a wide range of water rates, air rates and heat loads. Variations are reflected in the approach of the cold water to the wet-bulb temperature. The available tower coefficient is not a constant but varies with operating conditions. 

The thermal design of cooling towers follows the same general procedures already presented. Integration of equation 35 is usually done numerically using the appropriate software, mass-transfer coefficients, saturation enthalpies, etc. In mechanical-draft towers the air and water dows are both suppHed by machines, and hence dow rates are fixed. Under these conditions the design procedure is straightforward. 

When it is known that Hqg varies appreciably within the tower, this term must be placed inside the integr in Eqs. (5-277) and (5-278) for accurate calculations of hf. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows ... 

Investigators of tower packings normally report kcCi values measured at very low inlet-gas concentrations, so that yBM = 1, and at total pressures close to 100 kPa (1 atm). Thus, the correct rate coefficient For use in packed-tower designs involving the use of the driving force y — y /yBM is obtained by multiplying the reported k co values oy the value of pf employed in the actual test unit (e.g., 100 kPa) and not the total pressure of the system to be designed. 

Data for determining the size of natural-draft towers have been presented by Chilton [Proc. Inst. Elec. Eng., 99,440 (1952)] and Rish and Steel (ASCE Swuposium on Thermal Power Plants, October 19.58). Chilton showed that the duty coefficient Df of a tower is approximately constant over its normal range of operation and is related to tower size by an efficiency factor or performance coefficient as follows ... 

Example 14 Uttiy Coefficient for a Hyperbolic Tower Determine the duty coefficient for a hyperbolic tower operating with... 

To determine how a natural-draft tower of any given duty coefficient will perform under varying conditions, Rish and Steel plotted the nomograph in Fig. 12-22. The straight hne shown on the nomograph illustrates the conditions of Example 14. 

Traditional Design Method The traditionally employed conventional procedure for designing packed-tower gas-absorption systems involving chemical reactions makes use of overall volumetric mass-transfer coefficients as defined by the equation... 

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. 

According to this method, it is not necessaiy to investigate the kinetics of the chemical reactions in detail, nor is it necessary to determine the solubihties or the diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessaiy independently to obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient /c for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scahng up the experimental laboratory data for any new chemic ly reac ting system. 

Danckwerts and Gillham did not investigate the influence of the gas-phase resistance in their study (for some processes gas-phase resistance may be neglected). However, in 1975 Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] showed that by placing a stirrer in the gas space of the stirred-cell laboratoiy absorber, the gas-phase mass-transfer coefficient fcc in the laboratoiy unit could be made identical to that in a packed-tower absorber. When this was done, laboratoiy data obtained for chemically reacting systems having a significant gas-side resistance coiild successfully be sc ed up to predict the performance of a commercial packed-tower absorber. 

It would be desirable to reinterpret existing data for commercial tower packings to extract the individual values of the interfacial area a and the mass-transfer coefficients fcc and /c in order to facilitate a more general usage of methods for scaling up from laboratory experiments. Some progress in this direction has afready been made, as discussed later in this section. In the absence of such data, it is necessary to operate a pilot plant or a commercial absorber to obtain kc, /c , and a as described by Ouwerkerk (op. cit.). 

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. 

Inspection of Eqs. (14-71) and (14-78) reveals that for fast chemical reactions which are liquid-phase mass-transfer limited the only unknown quantity is the mass-transfer coefficient /cl. The problem of rigorous absorber design therefore is reduced to one of defining the influence of chemical reactions upon k. Since the physical mass-transfer coefficient /c is already known for many tower packings, it... 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

In these expressions, B = ZJd, Nps = dVp/EE, Np r = dVn/Eii, where d = some characteristic length such as dp for packed towers or T for spray towers. Ep and Er are the longitudinal dispersion coefficients, which must ultimately be deter-... 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

TABLE 23-7 Selected Absorption Coefficients for CO in Various Solvents in Towers Packed with Raschig Rings ... 

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

The other major type is gas absorption of inorganic components in aqueous solutions. For this type design one uses mass transfer coefficients. Packed towers are used so often for this type that its discussion is often included under sections on packed towers. However, in this book it is included here. 

Overall Mass Transfer Coefficient C02/Na0H System Metal Tower Packings... 

At = total tower cross-sections, area, ft-Cq = vapor discharge coefficient for dry tray g = acceleration of gratdty, 32.2 ft/sec hj, = head loss due to vapor flow through perforations, in. liquid... 

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