in which subscripts 1 and 2 refer to the bottom and top of the absorption tower respectively, y = mole-fraction solute in the gas phase, and y° = gas-phase solute mole fraction in equilibrium with bulk-liquid-phase solute concentration x. When the equilibrium line is straight, y° = mx.
The traditional design method normally makes use of overall KGa values even when resistance to transfer lies predominantly in the liquid phase. For example, the CO2-NaOH system which is most commonly used for comparing KGa values of various tower packings is a liquid-phase-controlled system. When the liquid phase is controlling, extrapolation to different concentration ranges or operating conditions is not recommended since changes in the reaction mechanism can cause kL to vary unexpectedly and the overall KGa do not capture such effects.
Overall KGa data may be obtained from tower-packing vendors for many of the established commercial gas absorption processes. Such data often are based either upon tests in large-diameter test units or upon actual commercial operating data. Since application to untried operating conditions is not recommended, the preferred procedure for applying the traditional design method is equivalent to duplicating a previously successful commercial installation. When this is not possible, a commercial demonstration at the new operating conditions may be required, or else one could consider using some of the more rigorous methods described later.
While the traditional design method is reported here because it has been used extensively in the past, it should be used with extreme
caution. In addition to the lack of an explicit liquid-phase resistance term, the method has other limitations. Equation (14-71) assumes that the system is dilute (yBM ~ 1) and that the operating and equilibrium lines are straight, which are weak assumptions for reacting systems. Also, Eq. (14-65) is strictly valid only for the temperature and solute partial pressure at which the original test was done even though the total pressure pT appears in the denominator.
In using Eq. (14-71), therefore, it should be understood that the numerical values of Kca will be a complex function of pressure, temperature, the type and size of packing employed, the liquid and gas mass flow rates, and the system composition (e.g., the degree of conversion of the liquid-phase reactant).
Figure 14-15 illustrates the influence of system composition and degree of reactant conversion upon the numerical values of KGa for the absorption of CO2 into sodium hydroxide at constant conditions of temperature, pressure, and type of packing. An excellent experimental study of the influence of operating variables upon overall K^a values is that of Field et al. (Pilot-Plant Studies of the Hot Carbonate
Process for Removing Carbon Dioxide and Hydrogen Sulfide, U.S. Bureau of Mines Bulletin 597, 1962).
Table 14-2 illustrates the observed variations in KGa values for different packing types and sizes for the CO2-NaOH system at a 25 percent reactant conversion for two different liquid flow rates. The lower rate of 2.7 kg/(s-m2) or 2000 lb/(h ft2) is equivalent to 4 U.S. gal/(min-ft2) and is typical of the liquid rates employed in fume scrubbers. The higher rate of 13.6 kg/(s m2) or 10,000 lb/fh-ft2) is equivalent to 20 U.S. gal/min-ft2) and is more typical of absorption towers such as used in CO2 removal systems, for example. We also note that two gas velocities are represented in the table, corresponding to superficial velocities of 0.59 and 1.05 m/s (1.94 and 3.44 ft/s).
Table 14-3 presents a typical range of KGa values for chemically reacting systems. The first two entries in the table represent systems that can be designed by the use of purely physical design methods, because they are completely gas-phase mass-transfer-limited. To ensure a negligible liquid-phase resistance in these two tests, the HCl was absorbed into a solution maintained at less than 8 wt % HCl, and the NH3 was absorbed into a water solution maintained below pH 7 by the addition of acid. The last two entries in Table 14-3 represent liquid-phase mass-transfer-limited systems.
Scaling Up from Laboratory Data Laboratory experimental techniques offer an efficient and cost-effective route to develop commercial absorption designs. For example, Ouwerkerk (Hydrocarbon Process., April 1978, 89-94) revealed that both laboratory and small-scale pilot plant data were employed as the basis for the design of an 8.5-m (28-ft) diameter commercial Shell Claus off-gas treating (SCOT) tray-type absorber. Ouwerkerk claimed that the cost of developing comprehensive design procedures can be minimized, especially in the development of a new process, by the use of these modern techniques.
In a 1966 paper that is considered a classic, Dankwerts and Gillham [Trans. Inst. Chem. Eng., 44, T42 (1966)] showed that data taken in a small stirred-cell laboratory 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(kL) can be reproduced in the laboratory unit, then the rate of absorption in the laboratory apparatus will respond to chemical reactions in the same way as in the packed column, even though the means of agitating the liquid in the two systems may be quite different.
According to this method, it is not necessary to investigate the kinetics of the chemical reactions in detail; nor is it necessary to determine the solubilities or diffusivities of the various reactants in their unreacted forms. To use the method for scaling up, it is necessary to independently obtain data on the values of the interfacial area per unit volume a and the physical mass-transfer coefficient k0L for the commercial packed tower. Once these data have been measured and tabulated, they can be used directly for scaling up the experimental laboratory data for any new chemically reacting system.
Dankwerts and Gillham did not investigate the influence of the gasphase resistance in their study (for some processes, gas-phase resistance
Packing size, mm
L = 2.7 kg/(s'm2)
L = 13.6 kg/(s'm2)
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