Page 105 - Separation process engineering

C. Derivations

C1. Determine the effect of pressure on the temperature, separation and diameter of a flash drum.
C2. Solve the Rachford-Rice equation for V/F for a binary system.

C3. Assume that vapor pressure can be calculated from the Antoine equation and that Raoult’s law
can be used to calculate K values. For a binary flash system, solve for the drum pressure if drum
temperature and V/F are given.
C4. Derive Eq. (2-24) and show that it is correct.

C5. Choosing to use V/F to develop the Rachford-Rice equation is conventional but arbitrary. We
could also use L/F, the fraction remaining liquid, as the trial variable. Develop the Rachford-Rice
equation as f(L/F).

C6. In flash distillation a liquid mixture is partially vaporized. We could also take a vapor mixture
and partially condense it. Draw a schematic diagram of partial condensation equipment. Derive
the equations for this process. Are they different from flash distillation? If so, how?
C7. Plot Eq. (2-40) vs. V/F for Example 2-2 to illustrate that convergence is not as linear as the
Rachford-Rice equation.

C8. Show how to use a temperature composition diagram to solve a binary flash distillation problem
when the drum temperature, feed mole fraction, drum pressure, and feed rate are specified. Show
how to determine x, y, L, and V.

C9. For a vapor-liquid-liquid flash distillation, derive Eqs. (2-62) and (2-63) and the equations that
allow calculation of all the mole fractions once V/F and L /F are known.
liquid_1
D. Problems

*Answers to problems with an asterisk are at the back of the book.
D1.* We are separating a mixture of methanol and water in a flash drum at 1 atm pressure. Equilibrium
data are listed in Table 2-7.

a. Feed is 60 mol% methanol, and 40% of the feed is vaporized. What are the vapor and liquid
mole fractions and flow rates? Feed rate is 100 kmol/h.

b. Repeat part a for a feed rate of 1500 kmol/h.
c. If the feed is 30 mol% methanol and we desire a liquid product that is 20 mol% methanol, what
V/F must be used? For a feed rate of 1000 lbmol/h, find product flow rates and compositions.

d. We are operating the flash drum so that the liquid mole fraction is 45 mol% methanol. L = 1500
kmol/h, and V/F = 0.2. What must the flow rate and composition of the feed be?
e. Find the dimensions of a vertical flash drum for Problem 2.D1c.

3
3
Data: ρ = 1.00 g/cm , ρ m,L = 0.7914 g/cm , MW = 18.01, MW = 32.04. Assume vapors are
m
w
w
ideal gas.
f. If z = 0.4, p = 1 atm, and T drum = 77°C, find V/F, x , and y .
m
m
g. If F = 50 mol/h, z = 0.8, p = 1 atm, and y = 0.892 mole fraction methanol, find V, L, and x .
m
m
Table 2-7. Vapor-liquid equilibrium data for methanol water (p = 1 atm) (mol%)