Page 163 - Separation process principles 2

128 Chapter 4 Single Equilibrium Stages and Flash Calculations

200°F (366S°K). Assuming equilibrium, what mole fraction of Bubble and Dew Points
the feed enters as liquid, and what are the liquid and vapor
compositions? Often, it is desirable to bring a mixture to the bubble point or
the dew point. At the bubble point, \I, = 0 and f (01 = 0.
Therefore, from Eq. (3), Table 4.4,
SOLUTION
f (0) = C ~i(l - Ki) = C Z; - CtiKi = 0
At flash conditions, from Figure 2.8, K3 = 4.2, K4 = 1.75, K5 =
0.74, Kg = 0.34, independent of compositions. Because some K- i
values are greater than 1 and some are less than 1, it is first neces- However, C zi = 1. Therefore, the bubble-point equation is
sary to compute values of f (0) and f {1] for Eq. (3) in Table 4.4 CZ;K;
to determine if the mixture is between the bubble point and the = 1 (4- 12)
dew point. i
At the dew point, = 1 and f (1) = 0. Therefore, from
Eq. (3), Table 4.4,

Therefore, the dew-point equation is
Since f {0} is not greater than zero, the mixture is above the bubble
point.
c$ = 1 (4- 13)
0.1(1 - 4.2) 0.2(1 - 1.75) i
'I1 = 1 + (4.2 - 1) + 1 + (1.75 - 1) For a given feed composition, zi, (4-12) or (4- 13) can be used
0.3(1 - 0.74) 0.4(1 - 0.34) to find T for a specified P or to find P for a specified T.
= 0.720
+ 1 + (0.4 - 1) + 1 + (0.34 - 1) Because of the K-values, the bubble- and dew-point equa-
tions are generally highly nonlinear in temperature, but only
Since f (11 is not less than zero, the mixture is below the dew point. moderately nonlinear in pressure, except in the region of the
Therefore, the mixture is part vapor and substitution of zi and Ki
convergence pressure, where K-values of very light or very
values in Eq. (3) of Table 4.4 gives
heavy species change radically with pressure, as in Fig-
0.1(1 - 4.2) 0.2(1 - 1.75) ure 2.10. Therefore, iterative procedures are required to
0 =
1 + Q(4.2 - 1) + 1 + Q(1.75 - 1) solve for bubble- and dew-point conditions. One exception
0.3(1 - 0.74) 0.4(1 - 0.34) is where Raoult's law K-values are applicable. Substitution
+ 1 + Q(0.74 - 1) + 1 + Q(0.34 - 1) of Ki = P//P into (4-12) leads to an equation for the direct
calculation of bubble-point pressure:
Solution of this equation by Newton's method using an initial guess c
for Q of 0.50 gives the following iteration history: Pbubble = 1 (4- 14)
P/
zi
i=l
where P/ is the temperature-dependent vapor pressure of
species i. Similarly, from (4-13), the dew-point pressure is

Another useful exception occurs for mixtures at the bub-
For this example, convergence is very rapid, giving
ble point when K-values can be expressed by the modified
Q = V/F = 0.1219. From Eq. (4) of Table 4.4, the equilibrium-
Raoult's law, Ki = yi P//P. Substituting this equation into
vapor flow rate is 0.1219(100) = 12.19 kmolih, and the
equilibrium-liquid flow rate from Eq. (7) is (100 - 12.19) = 87.81 (4-121,
kmolih. The liquid and vapor compositions computed from Eqs. (5)
and (6) are
Liquid-phase activity coefficients can be computed for a
known temperature and composition, since xi = z; at the
Propane 0.07 19 0.3021
bubble point.
n-Butane 0.1833 0.3207
n-Pentane 0.3098 0.2293 Bubble- and dew-point calculations are used to determine
n-Hexane 0.4350 0.1479 saturation conditions for liquid and vapor streams, respec-
1 .oooo 1 .oooo tively. It is important to note that when vapor-liquid equilib-
rium is established, the vapor is at its dew point and the liq-
A plot of f {q) as a function of \ZI is shown in Figure 4.11. uid is at its bubble point.