other sources of enthalpy data specific heats tabulated (see appendix of thermodynamic textbook) and...

Other Sources of Enthalpy Data

Specific heats

tabulated (see Appendix of thermodynamic textbook)and graphical data

Riedel Equation

Hn/RTn = 1.092(InPc - 1,013) 0.930 - (Tn/Tc)

Watson Equation

H2 = (1 - T2/Tc)H1 (1 - T1/Tc)

0.38

Example 14b: Calculate QC using Riedel and Watson Equations.What would be the value of QC if the distillate subcools liquid to30°C?

Specific Heats of Liquids

Specific Heats of Gases

Internal Column Balances

(1)

V2 L1

V1 L0

D, xD

hD

(j)

Vj+1 Lj

V1 L0

D, xD

hD

Enriching section of the column

Example 14c: What is the composition and enthalpy of vapor entering and leaving the first tray of the distillation column shown in example 14a.

(1)

V2 L1

V1 L0

D, xD = 0.6R = 3

External Column Balances

(n)

Vn+1

B, xB

hB

Ln

(n)

(k)

Vn+1

B, xB

hB

Ln

Vk Lk-1

Stripping section of the column

Lewis Method

Lewis observed that for a distillation column:enriching sectionL1 = L2 ….. = Lj = L is constant V1 = V2 ….. = Vj = V is constantstripping sectionL1 = L2 ….. = Lk = L is constant V1 = V2 ….. = Vk = V is constantbutL L and V V

Important assumptions in distillation column calculation:(1) column is adiabatic(2) specific heat << latent heat(3) latent heat () is constant independent of concentration

this means one mole of condensed vapor willevaporate 1 mole of liquid

(4) saturated liquid and vapor lines in H-x-y diagram are parallel

Lewis Method

(i)

Li, xi

Vi, yi

Equilibrium relationy = Kx

Vi+1, yi+1

Operating equationrectifying sectionyj+1 = (L/V)xj + (1-L/V)xD

stripping sectionyk = (L/V)xj - (L/V-1)xB

Example 15: What is the composition and enthalpy of vapor entering and leaving tray 1-5 of the distillation column shown below.

(5)

V6 L5

V1 L0

D, xD = 0.6hD, R = 3

(1)

(2)

(3)

(4)

VLE Data

75

80

85

90

95

100

105

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

External Column Balances

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

Example 16: What is the composition and enthalpy of vapor entering and leaving tray 4-9 plus the reboiler for the distillation column shown below.

(9)

(4)

V10

B, xB = 0.05hB, boilup ratio = 1

L9

V4 L3

VLE Data

75

80

85

90

95

100

105

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x(ethanol mass frac.)

y(et

hano

l mas

s fr

ac.)

Example 17: A mixture of pentane and toluene was distilled in a distillation column. An analysis of the enriching section is neededto determine whether the column is performing to specification.

V4 L3

V1 L0

D, yD = 0.9hD, R = 2

(1)

(2)

(3)

Please determine the composition of liquidand vapor streams leaving each stages for(a) = 2 and 3.5 with R = 2,(b) = 3.5 with R = 1 and 4

partial condenser

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=2

=3.5

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Total and Minimum Reflux

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

Total Reflux D = 0, L0 = V1, R = L0/D = L/V = L0/V1 = 1

Minimum Reflux D = maximum, L0 = minimum allowable,

Example 18: Analysis of the stripping section of the distillation columnfor pentane-toluene separation must be conducted to determine the liquidand vapor compositions leaving each distillation trays.

(9)

(6)

V10

B, xB = 0.10hB, boilup ratio = 2

L9

V6 L5

(a) using a total reboiler,(b) using a partial reboiler.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Internal Column BalancesFeed tray

F

V

V L

L

Feed Equation:

y = -{(L - L)/(V - V)}x + Fzf/(V-V)

y = -(Lf/Vf)x + (F/Vf)zf

y = {q/(q-1)}x + zf/(1-q)

q = (L-L)/F = (H-hf)/(H-h)

Example 19: Find the value of q and draw the feed line for a feedcontaining 0.4 pentane and 0.6 toluene:

(a) the feed is a saturated liquid,(b) the feed contains 0.5 fraction of vapor,(c) the feed was superheated so that each mole of feed vaporizes 10 moles of liquid,(d) the feed was subcooled so that each mole of feed condenses 2 moles of vapor.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Example 20: The distillation column shown in the figure below was used for the separation of 0.4 mole fraction pentane in toluene. The desired distillate and bottom products are 0.1 and 0.9, respectively. The feed enters the column as a superheated vapor that vaporizes 2 moles of liquid per mole of feed.

QC

QR

F, z, hf

D, xD= 0.9, hD

B, xB= 0.1, hB

Q=0

Reflux ratio = L0/D

Boilup ratio = Vn+1/D

(n)

Reboiler

Condenser

10 Kmole/min,0.4superheated vapor

= 3 Rmin

(a) What is q-value of the feed? Plot the feed line.(b) What is the minimum reflux ratio for the separation?(c) If the column reflux was operated at 3 Rmin, where is the optimum feed-plate location?

(d) What is the boil-up ratio needed for the separation?(e) How many equilibrium stages is needed to accomplish the desired separation?(f) How much distillate and bottom are produced if the feed rate is 10 kmole/min?(g) What is the minimum number of trays needed for achieve the desired separation?

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Example 21: The distillation column shown in the figure below was used for the separation of 0.25 mole pentane from heptane. The desired distillate and bottom products are 0.05 and 0.95, respectively. The vapor flowrate in the enriching and stripping sections of the column are 2 D and 3B, respectively.

QC

QR

F, z, hf

D, yD= 0.95, hD

B, xB= 0.1, hB

Q=0

Reflux ratio = L0/D

Boilup ratio = Vn+1/D

(n)

Reboiler

Condenser

1 Kmole/min,0.25saturated liquid

(a) What are the flowrates of distillate and bottom?(b) What is the (L/V)enriching and plot the top operating line?(c) Express the the operation reflux ratio, R as n Rmin

(d) What is the boil-up ratio? Plot the bottom operating line.(e) Is the feed subcooled, saturated liquid, mixture, saturated vapor or superheated vapor? (f) How many equilibrium stages is needed to accomplish the desired separation?(g) Where is the optimum location of the feed plate?

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=2

=2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

Example 22: A stripping column shown in the figure below was used to remove oil from contaminated water. The water leaving the bottom must be at least 99.7 % pure. The VLE data is plotted in the figure below.

QR B, xB= 0.1, hB

Q=0

Boilup ratio = Vn+1/D = 4

(n)

Reboiler

F, z, hf

15 Kmole/min,0.10

(a) Derive the top and bottom operating equation for the stripping column.(b) Plot the top and bottom operating line(c) Plot the feed line and determine the q-value of the feed.

(d) What are the allowable feed in a stripping section i.e., subcooled, saturated liquid, mixture, saturated vapor and superheated vapor? and why?(e) Determine the number of stages needed for the separation.(f) What is the minimum reflux ratio for this separation column?

D, yD= 0.6, hD

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Example 23: Crude oil could be extracted from sand found in Canadian province of Saskatchewan. Steam is used in the extraction process and the oil-water mixture is send through a series of distillation column. The final column known as the dehydrating column is employed for removing the final traces of water from the crude to meet the industrial maximum tolerance level of 0.01 mole fraction water. Instead of a condenser saturated liquid water was used directly as coolant. This arrangement has the added benefit of diluting the oil that remains in the water recovered at the distillate. The water from the distillate is then sent to settling tank to remove the final traces of oil before discharge.

QR B, xB= 0.01, hB

Q=0

Boilup ratio = Vn+1/D = 3

(n)

Reboiler

C, xc, hc

(a) Derive the top operating equation for dehydration column.(b) Derive the bottom operating equation(c) Derive the feed equation(d) Plot the respective top and bottom operating line as well as the feedline

(e) Determine the number of stages needed for the separation and the optimumfeed plate location if the total tray efficiency is 0.25.

D, yD= 0.8, hD

F, z, hf

75 Kmole/min,0.20, 25 % vapor

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Example 24: The distillation column shown in the figure below was used for the separation of 0.5 mole fraction methanol-water solution. The desired distillate and bottom products are 0.10 and 0.95, respectively. The feed enters the column as a superheated vapor that vaporizes 2 moles of liquid per mole of feed.

QC

QR

F, z, hf

D, xD= 0.9, hD

B, xB= 0.1, hB

Q=0

Reflux ratio = L0/D

Boilup ratio = Vn+1/D

(n)

Reboiler

Condenser

10 Kmole/min,0.4superheated vapor

= 2 Rmin

(a) What is q-value of the feed? Plot the feed line.(b) What will happen if the feed condition changes from superheated to sat. vapor to sat. liquid and subcooled liquid.

(c) What is the minimum reflux ratio?(d) What is the minimum number of plates?

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

McCabe-Thiele Method

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. pentane)

y (m

ole

frac

. pen

tane

)

=3.5

=3.5

Column Efficiency

Overall Column Efficiency

Eo = Nequil/Nactual

Murphree Efficiency

EMV = actual change in vapor

change in vapor for equilibrium stage

= yj - yj+1

yj* - yj+1

Example 25: The distillation column shown in the figure below was used for the separation of 0.5 mole fraction methanol-water solution. The desired distillate and bottom products are 0.20 and 0.9, respectively. The feed enters the column as a subcooled liquid that condenses 2 moles of vapor per mole of feed.

QC

QR

F, z, hf

D, xD= 0.9, hD

B, xB= 0.2, hB

Q=0

Reflux ratio = L0/D

Boilup ratio = Vn+1/B

(n)

Reboiler

Condenser

10 Kmole/min,0.5Subcooled liquid

= 2 Rmin

(a) What is q-value of the feed? Plot the feed line.(b) What is the number of equilibrium stages?(c) What is the actual number of stages if the EMV = 0.5?(d) Solve the problem using Fenske, Gilliland and Underwood methods.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. methanol)

y (m

ole

frac

. met

hano

l)

McCabe-Thiele Method

=3.5

=3.5

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

x (mole frac. methanol)

y (m

ole

frac

. met

hano

l)