Page 164 - Separation process principles 2

4.4 Multicomponent Flash; Bubble-Point, and Dew-Point Calculations 129

SOLUTZON

In Figure 1.9, the nC4-rich bottoms product from column C3 has Because the bubble-point pressure is likely to be below ambi-
the composition given in Table 1.5. If the pressure at the bottom of ent pressure, the modified Raoult's law in the form of (4-16)
the distillation column is 100 psia (689 Ha), estimate the tempera- applies for either liquid phase. If the methanol-rich layer data are
ture of the mixture. used:

Pbubble = 1.118(0.7615)(2.45) $4.773(0.1499)(1.89)
SOLUTZON + 3.467(0.0886)(6.14)
= 5.32 psia (36.7 Ha)
The bottoms product will be a liquid at its bubble point with the
following composition:
A similar calculation based on the cyclohexane-rich layer gives an
identical result because the data are consistent with phase equilib-
Component kmol/h zi = xi
rium theory such that y/L)x/l) = y/Z)~/2). A pressure higher than
i-Butane 8.60 0.03 19 5.32 psia will prevent formation of vapor at this location in the ex-
n-Butane 215.80 0.7992 traction process. Thus, operation at atmospheric pressure is a good
i-Pentane 28.10 0.1041 choice.
n-Pentane 17.50 0.0648
270.00 1 .OOOO

The bubble-point temperature can be estimated by finding the tem- EXAMPLE 4.4
perature that will satisfy (4-12), using K-values from Figure 2.8.
Propylene (P) is to be separated from 1-butene (B) by distillation
Because the bottoms product is rich in nC4, assume that the K-value
into a vapor distillate containing 90 mol% propylene. Calculate
of nC4 is 1. From Figure 2.8, for 100 psia, T = 150°F. For this
the column operating pressure assuming the exit temperature from
temperature, using Figure 2.8 to obtain the K-values of the other
the partial condenser is 100°F (37.S°C), the minimum attainable
three hydrocarbons and substituting these values and the z-values
temperature with cooling water. Determine the composition of the
into (4-12),
liquid reflux. In Figure 4.12, K-values estimated from Eq. (3,
Table 2.3, using the Redlich-Kwong equation of state for the vapor
xzi Ki = 0.0319(1.3) + 0.7992(1.0) + 0.1041(0.47) fugacity, are plotted and compared to experimental data [7] and
+ 0.0648(0.38) Raoult's law K-values.
= 0.042 + 0.799 + 0.049 + 0.025 = 0.915
Because the sum is not 1 .O, another temperature must be assumed
and the summation repeated. To increase the sum, the K-values 10
must be greater and, thus, the temperature must be higher. Because
the sum is dominated by nC4, assume that its K-value must be
1.000(1.00/0.915) = 1.09. This corresponds to a temperature of Eq. (3). Table 2.3
160°F, which results in a summation of 1.01. By linear interpola- Eq. (51, Table 2.3
0 Experimental data
tion, T = 159°F.

EXAMPLE 4.3
m
3
Cyclopentane is to be separated from cyclohexane by liquid-liquid -
extraction with methanol at 25°C. In extraction it is important that 4
the liquid mixtures be maintained at pressures greater than the bub-
ble-point pressure. Calculate the bubble-point pressure using the
following equilibrium liquid-phase compositions, activity coeffi-
cients, and vapor pressures:

Methanol Cyclohexane Cyclopentane
Vapor pressure, psia 2.45 1.89 6.14
Methanol-rich layer:
x 0.7615 0.1499 0.0886
0.1
Y 1.118 4.773 3.467 60 80 100 120 140 160 180 200
Cyclohexane-rich layer: Pressure, psia
x 0.1737 0.5402 0.2861 Figure 4.12 K-values for propylenell-butene system
Y 4.901 1.324 1.074 at 100°F.