Practice Problems

Separation Processes (CHE311)

Instructor: Professor Farnood

Single Equilibrium Stages and Flash Calculations

1. Problem # 4.10. (Ans: xA = 0.4575 for bottoms, yA = 0.6275, for distillate)

2. In a chemical plant, a mixture of propane (C3) and normal butane (nC4) is to be

separated in an isothermal flash drum operating at 200 oF and 200 psia. The flow

rate of C3 and nC4 are 20 and 180 kmol/h, respectively. The K-values for C3 and

nC4 at the above temperature and pressure are 2.056 and 0.925, respectively.

a) Determine the flow rate and composition of the liquid stream leaving the flash drum.

b) Due to a plant upset, the flow rate of C3 in the feed stream entering the flash drum is increased to 30 kmol/h while the flow rate of nC4 remains unchanged at 180 kmol/h. Assuming that the temperature and pressure stays at 200 oF and 200 psia, does any separation occur in the flash drum under these conditions? why?

F

C3nC4

V, y

L, x

200 psia200 oF

F

C3nC4

V, y

L, x

200 psia200 oF

Single stage Absorption:

3. Problem# 4.63 (#4.62 in 2nd Edition) (Ans: XA,out = 0.0051)

Multi-stage Absorption:

4. Problem # 6.7. (Ans : a) 1.74, b) Y1 = 0.024)

5. Problem #6.10. (Ans : a) about 3 stages, b) X1 = 0.0217, c) between 5 & 6 stages)

6. Problem #6.8 (Ans: a. minimum L’/V’=1.06, b.N=9, c. x=0.113)

7. Problem #6.11 (Ans: DCA = 0.005 ppm)

8. Air stripping is a cost effective technology for removing volatile organic

compounds (VOCs) from contaminated ground water. In a pilot set up, ground

water contaminated with TCE is introduced to a square Plexiglas column

measuring 0.41 cm 0.41 cm in cross section and packed with 1.52 m of a

commercial random packing (LANPAC® with nominal size of 5.8 cm). TCE

concentrations in the inlet and outlet water streams are 11.910-9 and 5.710-9 (in

mole fraction), respectively. The molar flow rates of air and water are G = 1.94

kmol/h and L = 435 kmol/h, respectively, and inlet air has no TCE. The stripper

operates at 20 oC and atmospheric pressure (P =1 atm). Using Henry’s law under

the above operating conditions, the equilibrium relationship for TCE is given by:

yTCE

= 1100 xTCE

, where yTCE

and xTCE

are the mole fractions of TCE in air and

water, respectively.

a) Determine the number of transfer units based on the liquid phase (NOL)? b) Determine the number of theoretical stages and HETP? c) To further reduce the concentration of TCE in the treated water, it has

been suggested to increase the air flow rate by orders of magnitude. However, concern has been raised that a drastic increase in air flow rate may result in flooding. Using the generalized pressure drop chart (below), determine the maximum air flow rate before flooding could occur. The packing factor for this random packing is Fp= 69 m2/m3 and

.1}{}ρ{ LL ff Data: Average densities and molecular weights of liquid and gas streams are:

kg/kmol18M ,kg/m1000ρ L3 L & kg/kmol92M ,kg/m2.1ρ G

3 G

g = 9.8 m/ s2

Mass Transfer

9. Problem # 3.35 (Ans: kc = 0.315 cm/s)

10. Problem # 3.38 (Ans: a. nwater=5.5 x 10-4 mol/s, b. KG= 1.24 x 10-4 mol/s.cm2.atm)

11. Problem # 3.39 (Ans: a. kp = 0.893 lbmol/h-ft2-atm )

Distillation

12. We wish to separate ethanol from water in a distillation column with a total

condenser and a kettle reboiler. Feed is 1000 kmol/h with a composition of 25

mol% ethanol, and is saturated liquid. We desire a distillate product with 80 mol%

ethanol. The recovery of ethanol is 96% (i.e.96% of ethanol in feed will end up in

the distillate) . External reflux is saturated liquid. Column pressure is 1 atm and it

is well insulated. The feed is to be introduced at its optimum location. Assuming

constant molar overflow (CMO):

a. Find the minimum reflux ratio and explain briefly how you calculated it. b. Calculate the flow rate and composition of bottom product. c. If bottom product contains 1.4% ethanol and the external reflux ratio is 2

calculate:

L, xin

G, yin =0

Air

Contaminated Groundwater

L, xout

G, yout

20oC1 atm

L, xin

G, yin =0

Air

Contaminated Groundwater

L, xout

G, yout

20oC1 atm

i. Slope of q-line. ii. Slopes of operating lines for rectifying and stripping sections.

iii. Number of theoretical stages using McCabe-Thiele graphical method.

iv. Estimate the actual number of trays using O’Connell correlation: 226.0)μα(3.50 oE where μ&α are relative volatility and liquid viscosity (in

cP), respectively. Assume average liquid viscosity is 0.36 cP and use the geometric average relative volatility of top and bottom of the column:

bottomtopavg

 Ethanol-Water Equilibrium @ 1 atm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x (Ethanol)

y (E

than

ol)

13. (Chap. 7, Exercise 7.9) Liquid air is fed to the top of a perforated-tray reboiler stripper operated at 1 atm. 60% of the oxygen in the feed is to be drawn off in the bottoms vapor product, which is to contain 0.2 mol% nitrogen. Based on the assumptions and equilibrium data below, calculate : (a) the mole % nitrogen in the vapor from the top plate, (b) the vapor generated in the still per 1`00 moles of feed, and (c) the number of stages required. Assume constant molar overflow equal to

the moles of feed. Liquid air contains 20.9 mol% oxygen and 79.1 mol% nitrogen. The equilibrium data in 1 atm are:

Temp, K mol% N2 in liquid

mol% N2 in vapor

77.35 100 100 77.98 90 97.17 78.73 79 93.62 79.44 70 90.31 80.33 60 85.91 81.35 50 80.46 82.54 40 73.50 83.94 30 64.05 85.62 20 50.81 87.67 10 31.00 90.17 0 0

14. (Chap. 7, Exercise 7.15) A continouous distillation with a refulux ration of 3.5

yields a distillate containing 97 wt% B (benzene) and a bottoms of 98 wt% T (toluene). Due to weld failures, the 10 stirpping plates in the bottom section of the column are ruined, but the 14 upper rectifying plates are intact. It is suggested that the column still be used, with the feed as saturated vapor at the dew point, with F = 13,600 kg/h containing 40 wt% B and 60 wt% T. Assuming that the plate efficiency remains unchanged at 50%: (a) can this column still yield a distillate containing 97 wt% B? (b) how much distillate is there? (c) what is the residue compostion in mole %? Equilibrium data in mole-fraction benzene, 101 kPa y 0.21 0.37 0.51 0.64 0.72 0.79 0.86 0.91 0.96 0.98x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95

Extraction 15. A solution containing 10 g/L of a valuable protein and 1 g/L of a protein impurity

is extracted in a stirred vessel using an organic solvent. Distribution coefficient K = 8 for the valuable protein and 0.5 for the impurity. The initial volume is 500 L, and 400 L of solvent are used for the extraction. What are the final concentrations in the two phases, and what fraction of each protein is recovered in the solvent phase?

16. An organic solute is to be extracted from a dilute aqueous solution using a solvent with a distribution coefficient of 6.8. For a continuous counterflow extractor, how many ideal stages are needed if the solvent flow is 0.35 times the solution flow and 99 percent recovery of the solute is required.

17. In a continuous countercurrent train of mixer-settlers, 100 kg/h of a 40:60 acetone-water solution is to be reduced to 10 percent acetone by extraction with pure 1,1,2-trichloroethylene at 25°C. (a) Find the minimum solvent rate. (b) At 1.8 times the

minimum (solvent rate)/(feed rate), find the minimum number of stages required. (c) For conditions of part (b) find the mass flow rates of all streams. Use the McCabe-Thiele method (see below for the x,y diagram)

0.2 0.4 0.6 0.80.

0.2

0.4

0.6

0.8

0.

x (acetone in raffinate)

y (a

ceto

ne in

ext

ract

)

0.2 0.4 0.6 0.80.

0.2

0.4

0.6

0.8

0.

x (acetone in raffinate)

y (a

ceto

ne in

ext

ract

)

18. Problem # 8.28,

19. Problem # 8.30,

20. Problem # 8.31

21. Problem # 8.32

22. A multistage RDC extraction column uses water as solvent (continuous phase) to separate acetone from an organic mixture (dispersed phase). Flow rates of the solvent and the organic solution streams are 000,12cm and 000,15Dm kg/h,

respectively. Densities of the dispersed and continuous phases ae 750 and 1000 kg/m3.

a. Find the hold up at the flooding point , fD )(

b. Assuming that the design value of hold up for the normal operation of the column to be D =20%, estimate the tower diameter. The characteristic

rise velocity of dispersed phase droplets is 05.0ou m/s.

Leaching

23. Problem # 16.3

24. Problem # 16.4

25. Problem # 16.5

Membranes

26. A new asymmetric polyimide polymer membrane has been developed for the

separation of nitrogen (N2) from methane (CH4). At 30 oC, the permeance values

(i.e. mMP / ) for nitrogen and methane are 6.03× 10-6 and 1.21× 10-6

kmol/(m2.h.kPa), respectively. This new membrane is used to perform the

separation shown in the figure below. Feed flow rate is 1000 kmol/h and it

contains 20% nitrogen and the rest is methane. Cut is 0.46. Using the arithmetic

average of the partial pressure of the entering feed and the exiting retentate for

calculating the driving force for diffusion through the membrane, determine:

a) Concentration of nitrogen in the permeate (yp).

b) Permeate flow rate and the membrane surface area required.

27. We desire to reduce the concentration of CO2 in a mixture of carbon dioxide (CO2)

and methane (CH4) using a membrane process. Feed has 95 mol % methane and

5mol% carbon dioxide and the target purity for methane in the retentate is 99

mol%. The gas is perfectly mixed on both sides of the membrane. The feed flow

rate is Fin = 1000 mol/min and feed temperature and pressure are 35oC and pH = 20

atm. The permeate pressure is pL =1 atm. The cut is = 0.4 and the permeability of

membrane for CO2 is PCO2 = 2 10 -11mol/(m.s.atm). The thickness of the active

layer of membrane is tm = 1 micrometer. Determine:

Feed= 1000 kmol/h5,500 kPa, 30oCN2 & CH4

N2 mole fraction:xf = 0.20

Retentate5,450 kPa30oC

N2 & CH4

Permeate100 kPa30oCN2 & CH4

Feed= 1000 kmol/h5,500 kPa, 30oCN2 & CH4

N2 mole fraction:xf = 0.20

Retentate5,450 kPa30oC

N2 & CH4

Permeate100 kPa30oCN2 & CH4

a. The flow rate of permeate (Fp) and its composition ( yp ).

b. The membrane selectivity ().

c. The surface area of membrane.

)(:i""component for flux transferMass

:,:

,,

4

2

LipHioutm

ii

CH

CO

in

p

pypyt

PJ

P

PySelectivit

F

FCut

28. A tubular membrane with a water permeability of Pwater = 2.5 10-4 L/m.h.atm is

used for ultrafiltration of cheese whey. The concentration of protein in the feed

solution is 10 g/L and the thickness of the active layer of membrane is 1 micron.

The osmotic pressure for whey protein solution is given by: c3104.4 .

where “c” is the concentration of protein in g/L, and is in atmospheres. Assume

an ideal membrane (i.e. the rejection coefficient R=1).

a) Ignoring the effects of concentration polarization and gel formation, calculate the flux of water if the feed and permeate pressures are 1.3 and 1.0 atm, respectively.

b) Ignoring gel formation (concentration polarization is no longer negligible), calculate the flux of water if the pressure gradient across membrane is p = 0.3 atm and the mass transfer coefficient for protein inside the tubes is: kc = 7.8 10-6 m/s.

c) Now, assume a layer of gel is formed on the membrane surface. The thickness of this layer is 2 microns and the water permeability in the gel is half of the water permeability in the membrane. The concentration of protein in the gel is 400 g/L and the mass transfer coefficient inside the tube remains at kc = 7.8 10-6 m/s. Calculate: 1- Flux of permeate through the membrane. 2- Pressure gradient (p) across the membrane.

Data: 1000 L = 1 m3 29. An experimental RO membrane is evaluated by passing pure water through it. At

p= 40 atm, the flux of water is measured to be 1000 L/(m2.day). In a second

experiment, this membrane is used to remove solute “A” from an aqueous solution.

Both feed and permeate side of the membrane are assumed to be fully mixed, and the

solute concentration in the feed side of the membrane is 10 wt%. The pressure

gradient across the membrane remains at 40 atm. The rejection coefficient in the

absence of concentration polarization for this membrane is R o = 0.90. Assuming the

thickness of the active layer of membrane is 0.8 microns, and the osmotic pressure for

compound “A” is given by C60 where C is the concentration of A in weight

fractions and is the osmotic pressure in atmospheres.

1- Calculate the water permeability (Pwater). 2- Estimate the flux of water in the second experiment, if the concentration

polarization is neglected (M=1). 3- In reality, the concentration polarization in the second experiment cannot be

ignored, and measurement shows that the actual flux of water is 800 L/(m2.day). Calculate the modulus of polarization and the apparent rejection coefficient ( R ) in this case.

)(:solventfor flux transferMass

1&)1(M

pt

PJ

C

CRRCC

m

solventsolvent

b

pobp