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where subscripts 1 and 2 refer to the bottom and top of the tower, respectively, and the absorption factors are defined by the equations

This procedure has been applied to the absorption of C5 and lighter hydrocarbon vapors into a lean oil, for example.

Stripping Equations When the liquid feed is dilute and the operating and equilibrium curves are straight lines, the stripping equations analogous to Eqs. (14-31) and (14-33) are

(X2 — X1)/(X2 — x1) = (SN+1 — S)/(SN+1 — 1) (14-39)

where x1 = yi/m; S = mGM/LM = A 1 and ln [(i - A)(x2 - xi)/(xi - x0) + A]

For systems in which the concentrations are large and the stripping factor S may vary along the tower, the following Edmister equations [Ind. Eng. Chem., 35, 837 (1943)] are applicable:

and the subscripts 1 and 2 refer to the bottom and top of the tower respectively.

Equations (14-37) and (14-42) represent two different ways of obtaining an effective factor, and a value of Ae obtained by taking the reciprocal of Se from Eq. (14-42) will not check exactly with a value of Ae derived by substituting Ai = 1/Si and A2 = 1/S2 into Eq. (14-37). Regardless of this fact, the equations generally give reasonable results for approximate design calculations.

It should be noted that throughout this section the subscripts 1 and 2 refer to the bottom and to the top of the apparatus respectively regardless of whether it is an absorber or a stripper. This has been done to maintain internal consistency among all the equations and to prevent the confusion created in some derivations in which the numbering system for an absorber is different from the numbering system for a stripper.

Tray Efficiencies in Tray Absorbers and Strippers Computations of the theoretical trays N assume that the liquid on each tray is completely mixed and that the vapor leaving the tray is in equilibrium with the liquid. In practice, complete equilibrium cannot exist since interphase mass transfer requires a finite driving force. This leads to the definition of an overall tray efficiency

E Ntheoretical/Nactual

which can be correlated with the system design variables.

Mass-transfer theory indicates that for trays of a given design, the factors that have the biggest influence on E in absorption and stripping towers are the physical properties of the fluids and the dimensionless ratio mGM/LM. Systems in which mass transfer is gas-film-controlled may be expected to have efficiencies as high as 50 to 100 percent, whereas tray efficiencies as low as 1 percent have been reported for the absorption of low-solubility (large-m) gases into solvents of high viscosity.

The fluid properties of interest are represented by the Schmidt numbers of the gas and liquid phases. For gases, the Schmidt numbers are normally close to unity and independent of temperature and pressure. Thus, gas-phase mass-transfer coefficients are relatively independent of the system.

By contrast, the liquid-phase Schmidt numbers range from about 102 to 104 and depend strongly on temperature. The temperature dependence of the liquid-phase Schmidt number derives primarily from the strong dependence of the liquid viscosity on temperature.

Consideration of the preceding discussion in connection with the relationship between mass-transfer coefficients (see Sec. 5)

indicates that the variations in the overall resistance to mass transfer in absorbers and strippers are related primarily to variations in the liquidphase viscosity | and the slope m. O'Connell [Trans. Am. Inst. Chem. Eng., 42,741 (1946)] used the above findings and correlated the tray efficiency in terms of the liquid viscosity and the gas solubility. The O'Con-nell correlation for absorbers (Fig. 14-9) has Henry's law constant in lbmol/(atmft3), the pressure in atmospheres, and the liquid viscosity in centipoise.

The best procedure for making tray efficiency corrections (which can be quite significant, as seen in Fig. 14-9) is to use experimental FIG. 14-9 O'Connell correlation for overall column efficiency Eoc for absorption. H is in lb'mol/(atm'ft3), P is in atm, and ^ is in cP. To convert HPin pound-moles per cubic foot-centipoise to kilogram-moles per cubic meter-pascal-second, multiply by 1.60 x 104. [O'Connell, Trans. Am. Inst. Chem. Eng., 42, 741 (1946).]

FIG. 14-9 O'Connell correlation for overall column efficiency Eoc for absorption. H is in lb'mol/(atm'ft3), P is in atm, and ^ is in cP. To convert HPin pound-moles per cubic foot-centipoise to kilogram-moles per cubic meter-pascal-second, multiply by 1.60 x 104. [O'Connell, Trans. Am. Inst. Chem. Eng., 42, 741 (1946).]

data from a prototype system that is large enough to be representative of the actual commercial tower.

Example 4: Actual Trays for Steam Stripping The number of actual trays required for steam-stripping an acetone-rich liquor containing 0.573 mole percent acetone in water is to be estimated. The design overhead recovery of acetone is 99.9 percent, leaving 18.5 ppm weight of acetone in the stripper bottoms. The design operating temperature and pressure are 101.3 kPa and 94°C respectively, the average liquid-phase viscosity is 0.30 cP, and the average value of K = y°/x for these conditions is 33.

By choosing a value of mGM /LM = S = A-1 = 1.4 and noting that the stripping medium is pure steam (i.e., x°= 0), the number of theoretical trays according to Eq. (14-40) is

The O'Connell parameter for gas absorbers is pL/KM|L, where pL is the liquid density, lb/ft3; |L is the liquid viscosity, cP; M is the molecular weight of the liquid; and K = y°/x. For the present design pL/KM|L = 60.1/(33 x 18 x 0.30) = 0.337

and according to the O'Connell graph for absorbers (Fig. 14-7) the overall tray efficiency for this case is estimated to be 30 percent. Thus, the required number of actual trays is 16.8/0.3 = 56 trays.