## M FIG. 14-7 Number of overall gas-phase mass-transfer units in a packed absorption tower for constant mGM/LM; solution of Eq. (14-23). (From Sherwood and Pigford, Absorption and Extraction, McGraw-Hill, New York, 1952. )

Another approach is to divide the tower arbitrarily into a lean section (near the top) where approximate methods are valid, and to deal with the rich section separately. If the heat effects in the rich section are appreciable, consideration should be given to installing cooling units near the bottom of the tower. In any event, a design diagram showing the operating and equilibrium curves should be prepared to check the applicability of any simplified procedure. Figure 14-10, presented in Example 6, is one such diagram for an adiabatic absorption tower.

Stripping Equations Stripping or desorption involves the removal of a volatile component from the liquid stream by contact with an inert gas such as nitrogen or steam or the application of heat. Here the change in concentration of the liquid stream is of prime importance, and it is more convenient to formulate the rate equation analogous to Eq. (14-6) in terms of the liquid composition x. This leads to the following equations defining the number of transfer units and height of transfer units based on liquid-phase resistance:

Xbm^X

XjiM^X

- HOLNOL

where, as before, subscripts 1 and 2 refer to the bottom and top of the tower, respectively (see Fig. 14-5).

In situations where one cannot assume that HL and HOL are constant, these terms need to be incorporated inside the integrals in Eqs. (14-24) and (14-25), and the integrals must be evaluated numerically (using Simpson's rule, for example). In the normal case involving stripping without chemical reactions, the liquid-phase resistance will dominate, making it preferable to use Eq. (14-25) together with the approximation HL ~ HOL.

The Weigand approximations of the above integrals, in which arithmetic means are substituted for the logarithmic means (xbm and xBm), are

In these equations, the first term is a correction for finite liquidphase concentrations, and the integral term represents the numbers of transfer units required for dilute solutions. In most practical stripper applications, the first (logarithmic) term is relatively small.

For dilute solutions in which both the operating and the equilibrium lines are straight and in which heat effects can be neglected, the integral term in Eq. (14-27) is

This equation is analogous to Eq. (14-23). Thus, Fig. 14-7 is applicable if the concentration ratio (x2 — y1/m)/(x1 — yj/m) is substituted for the abscissa and the parameter on the curves is identified as LM/mGM.

Example 3: Air Stripping of VOCs from Water A 0.45-m diameter packed column was used by Dvorack et al. [Environ. Sci. Tech. 20, 945 (1996)] for removing trichloroethylene (TCE) from wastewater by stripping with atmospheric air. The column was packed with 25-mm Pall rings, fabricated from polypropylene, to a height of 3.0 m. The TCE concentration in the entering water was 38 parts per million by weight (ppmw). A molar ratio of entering water to entering air was kept at 23.7. What degree of removal was to be expected? The temperatures of water and air were 20°C. Pressure was atmospheric.

Solution. For TCE in water, the Henry's law coefficient may be taken as 417 atm/mf at 20°C. In this low-concentration region, the coefficient is constant and equal to the slope of the equilibrium line m. The solubility of TCE in water, based on H = 417 atm, is 2390 ppm. Because of this low solubility, the entire resistance to mass transfer resides in the liquid phase. Thus, Eq. (14-25) may be used to obtain NOL, the number of overall liquid phase transfer units.

In the equation, the ratio xBM'/(1 — x) is unity because of the very dilute solution. It is necessary to have a value of HL for the packing used, at given flow rates of liquid and gas. Methods for estimating HL may be found in Sec. 5. Dvorack et al. found HOL = 0.8 m. Then, for hT = 3.0 m, NL = NOL = 3.0/0.8 = 3.75 transfer units.

Transfer units may be calculated from Eq. 14-25, replacing mole fractions with ppm concentrations, and since the operating and equilibrium lines are straight,

ln 38/(ppm)exit

Solving, (ppm)exit = 0.00151. Thus, the stripped water would contain 1.51 parts per billion of TCE.

Use of HTU and KGa Data In estimating the size of a commercial gas absorber or liquid stripper it is desirable to have data on the overall mass-transfer coefficients (or heights of transfer units) for the system of interest, and at the desired conditions of temperature, pressure, solute concentration, and fluid velocities. Such data should best be obtained in an apparatus of pilot-plant or semiworks size to avoid the abnormalities of scale-up. Within the packing category, there are both random and ordered (structured) packing elements. Physical characteristics of these devices will be described later.

When no KGa or HTU data are available, their values may be estimated by means of a generalized model. A summary of useful models is given in Sec. 5. The values obtained may then be combined by use of Eq. (14-19) to obtain values of HoG and HoL. This simple procedure is not valid when the rate of absorption is limited by chemical reaction.

Use of HETP Data for Absorber Design Distillation design methods (see Sec. 13) normally involve determination of the number of theoretical equilibrium stages N. Thus, when packed towers are employed in distillation applications, it is common practice to rate the efficiency of tower packings in terms of the height of packing equivalent to one theoretical stage (HETP).

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 HOG by the equation ln (toGm/Lm)

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

, ,„„, , ln (toGm/Lm) HETP = -- | Hog — „-" (14-30)

where the correction term y%M /(1 — y) is averaged over each individual theoretical stage. The equilibrium compositions corresponding to each theoretical stage may be estimated by the methods described in the next subsection, 'Tray-Tower Design." These compositions are used in conjunction with the local values of the gas and liquid flow rates and the equilibrium slope m to obtain values for HG, HL, and HOG corresponding to the conditions on each theoretical stage, and the local values ofthe HETP are then computed by Eq. (14-30). The total height of packing required for the separation is the summation of the individual HETps computed for each theoretical stage.