Page 183 - Separation process principles 2

148 Chapter 4 Single Equilibrium Stages and Flash Calculations

Approximate Method for a
Vapor-Liquid-Solid System
n-hexane-rich
liquid The simplest case of multiphase equilibrium is that encoun-
Aniline-rich tered in an evaporative crystallizer involving crystallization
of an inorganic compound, B, from its aqueous solution at its
bubble point in the presence of its vapor. Assume that only
two components are present, B and water. In that case, it is
Phosphorous
common to assume that B has no vapor pressure and water is
not present in the solid phase. Thus, the vapor is pure water
(steam), the liquid is a mixture of water and B, and the solid
Mercury phase is pure B. Then, the solubility of B in the liquid phase
is not influenced by the presence of the vapor, and the system
Figure 4.31 Seven phases in equilibrium. pressure at a given temperature can be approximated by
applying Raoult's law to the water in the liquid phase:

P = P~zO~~zO (4-33)
is a schematic diagram of a photograph of a laboratory where XH~O can be obtained from the solubility of B.
curiosity taken from Hildebrand [16], which shows seven
phases in equilibrium at near-ambient temperature. The
phase on top is air, followed by six liquid phases in order EXAMPLE 4.17
of increasing density: hexane-rich, aniline-rich, water-rich,
A 5,000-lb batch of 20 wt% aqueous MgS04 solution is fed to a
phosphorous, gallium, and mercury. Each phase contains all
vacuum, evaporative crystallizer operating at 160°F. At this tem-
components in the seven-phase mixture, but the mole frac- perature, the stable solid phase is the monohydrate, with a MgS04
tions in many cases are extremely small. For example, solubility of 36 wt%. If 75% of the water is evaporated, calculate:
the aniline-rich phase contains on the order of 10 mol%
(a) Pounds of water evaporated
n-hexane, 20 mol% water, but much less than 1 mol% each of
(b) Pounds of monohydrate crystals, MgS04 . H20
dissolved air, phosphorous, gallium, and mercury. Note that
even though the hexane-rich phase is not in direct contact (c) Crystallizer pressure
with the water-rich phase, an equilibrium amount of water
(approximately 0.06 mol%) is present in the hexane-rich SOLUTION
phase because each phase is in equilibrium with each of
(a) The feed solution is 0.20(5,000) = 1,000 1b MgS04, and
the other phases, as attested by the equality of component
5,000 - 1,000 = 4,000 lb H20. The amount of water evapo-
fugacities:
rated is 0.75(4,000) = 3,000 lb H20.
fW = f,@) = fJ3) = f(4) = fJ5) = fJ6) = fJ7) (b) Let W = amount of MgS04 remaining in solution. Then
1 1 1 1 1 1 1
MgS04 in the crystals = 1,000 - W.
More practical multiphase systems include the vapor-
MW of H20 = 18 and MW of MgS04 = 120.4.
liquid-solid systems present in evaporative crystallization
Water of crystallization for the monohydrate
and pervaporation, and the vapor-liquid-liquid systems that = (1,000 - W)(18/120.4) = 0.15(1,000 - W).
occur when distilling certain mixtures of water and hydro- Water remaining in solution
carbons or other organic chemicals having a limited solubil- = 4,000 - 3,000 - 0.15(1,000 - W) = 850 + 0.15W.
ity in water. Actually, all of the two-phase systems consid- Total amount of solution remaining
ered in the previous sections of this chapter involve a third = 850+0.15W + W = 850+ 1.15W.
phase, the containing vessel. However, the material of the From the solubility of MgS04,
container is selected on the basis of its inertness to and lack
of solubility in the phases it contains, and therefore the
material of the container does not normally enter into phase-
equilibria calculations. Solving: W = 522 pounds of dissolved MgS04.
Although calculations of multiphase equilibrium are MgS04 crystallized = 1,000 - 522 = 478 lb.
based on the same principles as for two-phase systems Water of crystallization = 0.15(1,000 - W)
(material balances, energy balances, and phase-equilibria = 0.15(1,000 - 522) = 72 lb.
criteria such as equality of fugacity), the computations can Total monohydrate crystals = 478 + 72 = 550 lb.
be quite complex unless simplifying assumptions are made, (c) Crystallizer pressure is given by (4-33). At 160°F the vapor
in which case approximate results are obtained. Rigorous pressure of H20 is 4.74 psia. Then water remaining in solution =
calculations are best made with a computer algorithm. In this (850 4- 0,15W')/18 = 51.6 lbrnol.
section both types of calculations are illustrated. MgS04 remaining in solution = 522/120.4 = 4.3 lbmol.