Page 28 - Gas Purification 5E

18 Gas Punifictrtion

In equations 1-9 and 1-10, y and x refer to the mole fractions of solute in the gas and liq-
uid streams, respectively, and LM and pM represent the molar values of liquid flow rate and
density, Le., lb moles/(hr)(sq ft) and lb moledcu ft. The subscript 1 refers to the bottom of
the column, subscript 2 to the top of the column, and subscript e to the equilibrium composi-
tion with respect to the main body of the other phase. The other symbols have the same sig-
nificance as in the previous equations. h general, it is preferable to employ the overall gas-
film coefficient when the gas-film resistance is predominant, and the overall liquid
coefficient when the principal resistance to absorption is in the liquid phase.
Equations 1-9 and 1-10 may be solved by relatively simple graphical integration. Howev-
er, a further simplification, which can fiequently be employed, is the use of a logarithmic
mean driving force in the rate equation rather than graphical integration. This can be shown
to be theoretically correct where the equilibrium curve and operating line are. linear over the
composition range of the column. The equations then reduce to

(1-11)

or

where (y - y h and (x, - xh~ equal to the logarithmic mean of the driving forces at the
are.
top and bottom of the column. Although not thmticdy correct, the logarithmic mean driving
force is often used to correlate values for systems where the equilibrium curve is not a
straight line and even for cases of absorption with chemical reaction. This greatly simplifies
data reduction but can lead to Serious errors. In general, the procedure is useful for comparing
similar systems within narrow ranges of liquid composition and gas partial pressure.
A considerable amount of data on absorption-column performance is presented in terms of
the “height of the transfer unit” (HTU), and design procedures based on this concept are pre-
ferred by many because of their simplicity and similarity to plate-column calculation meth-
ods. The basic concept which was originally introduced by Chilton and Colburn (1935) is
that the calculation of column height invariably requires the integration of a relationship
such as (from equation 1-9)

The dimensionless value obtained from the integration is a measure of the difficulty of the
gas-absorption operation. In the above case, it is called the number of transfer units based on
an overall gas driving force, NOG, and equation 1-9 can be reduced to

(1-13)