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26 GasPuriication

The preceding discussion is based on using the concepts of “thmretical trays” and “tray
efficiencies” to estimate the total number of actual trays required for a given absorption task.
An alternative approach is to consider the mass transfer rate on each actual tray by modeling
material and energy transfer through the interface between gas and liquid on the tray. Seader
(1989) presents an historical perspective and generalized description of the rate-based
approach for modeling staged separations and suggests that “the advantages of this approach
can usher in a new era for modeling.”
A detailed description of the “Mass Transfer Rate” model is given by Krishnamurthy and
Taylor (1985A) who list the equations describing the model as follows:

1. Material balance equations
2. Energy balance equations
3. Rate equations
4. Equilibrium relations

Since the mass transfer occurring on an actual tray depends on the tray design, the model
uses detailed information about column and tray configurations, as well as fluid composi-
tions, flow rates, diffusivities, and physical properties. Mass and energy balances are per-
formed around each phase on every actual tray. Krishnamurthy and Taylor (1985B) also pro-
pose a rate-based model for simulation and design of packed distillation and absorption
columns. The packed tower model is based on simply dividing the packing zone into a num-
ber of sections (e.g., 10 for a typical absorber) around which the mass and energy balances
are performed.
The rates of mass and energy transfer between phases are calculated based on gas and liq-
uid film coefficients and concentration and temperature driving forces. Both thermal and
chemical equilibria are assumed to exist only at the gas-liquid interface. The liquid film mass
transfer coefficient is adjusted, if necessary, for chemical reactions occurring in the liquid
phase by use of an enhancement factor (as defined in the next section). An absorption col-
umn simulator, which uses the rate-based approach, is described by Sardar et al. (1985).
They demonstrate its predictive capabilities against operating data from a number of com-
mercial plants employing various amines to remove H2S and C02 in both tray and packed
towers. The use of the ratebased design method to evaluate the performance of two amine
plants is described by Vickery et al. (1992).

Effect of Chemical Reactions
A chemical reaction of the solute with a component in the liquid phase has the effect of
increasing the liquid-film absorption coefficient over what would be observed with simple
physical absorption. This results in an increase in the overall absorption coefficient in packed
towers or an increase in tray efficiency in tray towers.
With very slow reactions (such as between carbon dioxide and water) the dissolved mole
cules migrate well into the body of the liquid before reaction occurs so that the overall
absorption rate is not appreciably increased by the Occurrence of the chemical reaction. In
this case, the liquid film resistance is the controlling factor, the liquid at the interface can be
assumed to be in equilibrium with the gas, and the rate of mass transfer is governed by the
molecular C02 concentration-gradient between the interface and the body of the liquid. At
the other extreme are very rapid reactions (such as those of ammonia with strong acids)
where the dissolved molecules migrate only a very short distance before reaction occurs. The