Page 181 - Separation process principles 2

146 Chapter 4 Single Equilibrium Stages and Flash Calculations

the system temperature. When the partial pressure of the
solute in the gas phase exceeds the vapor pressure of the
solid, desublimation occurs. At equilibrium, the vapor pres-
sure of the species as a solid is equal to the partial pressure
of the species as a solute in the gas phase. This is illustrated
in the following example.

Ortho-xylene is partially oxidized in the vapor phase with air to
produce phthalic anhydride, PA, in a catalytic reactor (fixed bed or
fluidized bed) operating at about 370°C and 780 torr. However, a
very large excess of air must be used to keep the xylene content of
the reactor feed below 1 mol% to avoid an explosive mixture. In
X mol NH3/mol H20
a typical plant, 8,000 lbmolh of reactor effluent gas, containing
Figure 4.29 Equilibrium for air-NH3-H20 at 20°C, 1 atm, in 67 lbmollh of PA and other amounts of N2, 02, CO, C02, and water
Example 4.14.
vapor are cooled to separate the PA by desublimation to a solid at a
total pressure of 770 torr. If the gas is cooled to 206"F, where the
A molar material balance for ammonia about the equilibrium vapor pressure of solid PA is 1 ton; calculate the number of pounds
stage is of PA condensed per hour as a solid, and the percent recovery of PA
from the gas if equilibrium is achieved. Assume that the xylene is
converted completely to PA.
where G = moles of air and L = moles of HzO. Then G = 10 -
2.3 = 7.7 mol and L = 10 - 0.91 = 9.09 mol. Solving for Yl from SOLUTION
Eq. (I),
At these conditions, only the PA condenses. At equilibrium, the
partial pressure of PA is equal to the vapor pressure of solid PA, or
1 torr. Thus, the amount of PA in the cooled gas is given by Dalton's
This material-balance relationship is an equation of a straight law of partial pressures:
line of slope (LIG) = -9.0917.7 = -1.19, with an intercept of PPA
(~PA)G -nG (1)
=
(L/G)(Xo) + Yo = 0.42. P
The intersection of this material-balance line with the equilib- where
rium curve, as shown in Figure 4.29, gives the ammonia composi-
tion of the gas and liquid phases leaving the stage as Yl = 0.195 and
X1 = 0.19. This result can be checked by an NH3 balance, since the and n = lbmollh. Combining Eqs. (1) and (2),
amount of NH3 leaving is (0.195)(7.70) + (0.19)(9.09) = 3.21,
which equals the total moles of NH3 entering.
It is of importance to recognize that Eq. (2), the material balance
line, called an operating line and discussed in great detail in
Chapters 5 to 8, is the locus of all passing stream pairs; thus, Xo, Yo
Solving this linear equation gives
(point F) also lies on this operating line.

The amount of PA desublimed is 67 - 10.3 = 56.7 lbmolih. The
4.9 GAS-SOLID SYSTEMS percent recovery of PA is 56.7167 = 0.846 or 84.6%. The amount
Systems consisting of gas and solid phases that tend to of PA remaining in the gas is a very large quantity. In a typical
plant, the gas is cooled to a much lower temperature, perhaps
equilibrium are involved in sublimation, desublimation, and
140°F, where the vapor pressure of PA is less than 0.1 ton; bringing
adsorption separation operations.
the recovery of PA to almost 99%.
Sublimation and Desublimation
Gas Adsorption
In sublimation, a solid vaporizes into a gas phase without
passing through a liquid state. In desublimation, one or more As with liquid mixtures, one or more components of a gas
components (solutes) in the gas phase are condensed to a mixture can be adsorbed on the surface of a solid adsorbent.
solid phase without passing through a liquid state. At low Data for a single solute can be represented by an adsorption
pressure both sublimation and desublimation are governed isotherm of the type shown in Figure 4.25, or in similar dia-
by the solid vapor pressure of the solute. Sublimation of the grams, where the partial pressure of the solute in the gas
solid takes place when the partial pressure of the solute in is used.in place of the concentration. However, when two
the gas phase is less than the vapor pressure of the solid at components of a gas mixture are adsorbed and the purpose