Page 184 - Separation process principles 2

4.10 Multiphase Systems 149

Hence SOLUTION
XH~O = 51.6/(51.6 + 4.3) = 0.923 (a) Initial phase conditions are T= 136°C = 276.8"F and
P = 133.3 kPa = 19.34 psia. Vapor pressures at 276.8"F and
BY Raoult's law, p~,o = P = 4.74(0.923) = 4.38 psia
Pizo = 46.7 psia and Pic, = 19.5 psia. Because the initial
pressure is less than the vapor pressure of each component, the
initial phase condition is all vapor, with partial pressures
Approximate Method for a
Vapor-Liquid-Liquid System PH,O = YH~O P = 0.75(19.34) = 14.5 psia

Another case suitable for an approximate method is that of a PnCs = ync8P = 0.25(19.34) = 4.8 psia
mixture containing water and hydrocarbons (HCs), at condi-
(b) As the temperature is decreased, the first phase change
tions such that a vapor phase and two liquid phases, HC-rich occurs when a temperature is reached where either PAzo =
(1) and water-rich (2) coexist. Often the solubilities of water PH,O = 14.5 psia or Pic8 = pncs = 4.8 psia. The correspond-
in the liquid HC phase and HCs in the water phase are less ing temperatures where these vapor pressures occur are 21 1°F
than 0.1 mol% and may be neglected. In that case, if the liq- for H20 and 194°F for nC8. The highest temperature applies.
uid HC phase obeys Raoult's law, the total pressure of the Therefore, water condenses first when the temperature reaches
system is given by the sum of the pressures exhibited by the 211°F. This is the dew-point temperature of the initial mixture
separate phases: at the system pressure. As the temperature is further reduced,
the number of moles of water in the vapor decreases, causing
the partial pressure of water to decrease below 14.5 psia and the
partial pressure of nC8 to increase above 4.8 psia. Thus, nC8
begins to condense, forming a second liquid phase, at a tem-
For more general cases, at low pressures where the vapor perature higher than 194°F but lower than 211°F. This temper-
phase is ideal but the liquid HC phase may be nonideal, ature, referred to as the secondary dew point, must be deter-
mined iteratively. The calculation is simplified if the bubble
point of the mixture is computed first.
P = P&20 + P K~X;')
HCs From (4-34),
which can be rearranged to P = 19.34psi = Pizo + Pic, (1)

Thus, a temperature is sought, as follows, to cause Eq. (1) to be
satisfied:

psia
Equations (4-34) and (4-36) can be used directly to estimate T, OF PH~o, Ec,, psia P, psis
the pressure for a given temperature and liquid-phase com- 194 10.17 4.8 14.97
position or iteratively to estimate the temperature for a given 202 12.01 5.6 17.61
pressure. An important aspect of the calculation is the deter- 206 13.03 6.1 19.13
mination of the particular phases present from all six possi- 207 13.30 6.2 19.50
ble cases, namely, V, V-L('), v-L(')-L(~), v-L(~),
By linear interpolation, T = 206.7"F for P = 19.34 psia. Below this
L(')-L(~), and L. It is not always obvious how many and
temperature, the vapor phase disappears and only two immiscible
which phases may be present. Indeed, if a v-L(')-L(~) solu-
liquid phases are present.
tion to a problem exists, almost always V-L(') and v-L(~)
To determine the temperature at which one of the liquid phases
solutions also exist. In that case, the three-phase solution is disappears, which is the same condition as when the second liquid
the correct one. It is important, therefore, to seek the three- phase begins to appear (secondary dew point), it is noted for this
phase solution first. case, with only pure water and a pure HC present, that vaporization
starting from the bubble point is at a constant temperature until one
of the two liquid phases is completely vaporized. Thus, the sec-
EXAMPLE 4.18 ondary dew-point temperature is the same as the bubble-point
temperature or 206.7"F. At the secondary dew point, the partial
A mixture of 1,000 kmol of 75 mol% water and 25 mol% n-octane pressures are PH~O = 13.20 psia and p,~, = 6.14 psia, with all of
is cooled under equilibrium conditions at a constant pressure the nC8 in the vapor phase. Therefore, the phase amounts and com-
133.3 kPa (1,000 torr) from an initial temperature of 136°C to a positions are
final temperature of 25°C. Determine:
Vapor H20-Rich Liquid
(a) The initial phase condition
(b) The temperature, phase amounts, and compositions when each Component kmol Y kmol
phase change occurs
Assume that water and n-octane are immiscible liquids. The vapor
pressure of octane is included in Figure 2.4.