Other Sources of Enthalpy Data Specific heats tabulated (see Appendix of thermodynamic textbook) and graphical data Riedel Equation  H n /RT n = 1.092(InP c - 1,013) (T n /T c ) Watson Equation  H 2 = (1 - T 2 /T c )  H 1 (1 - T 1 /T c ) 0.38

Example 14b: Calculate Q C using Riedel and Watson Equations. What would be the value of Q C if the distillate subcools liquid to 30°C?

Specific Heats of Liquids

Specific Heats of Gases

Internal Column Balances (1) V2V2 L1L1 V1V1 L0L0 D, x D h D (j) V j+1 LjLj V1V1 L0L0 D, x D h D 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) V2V2 L1L1 V1V1 L0L0 D, x D = 0.6 R = 3

External Column Balances (n) V n+1 B, x B h B LnLn (n) (k) V n+1 B, x B h B LnLn VkVk L k-1 Stripping section of the column

Lewis Method Lewis observed that for a distillation column: enriching section L 1 = L 2 ….. = L j = L is constant V 1 = V 2 ….. = V j = V is constant stripping section L 1 = L 2 ….. = L k = L is constant V 1 = V 2 ….. = V k = V is constant but L  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 will evaporate 1 mole of liquid (4) saturated liquid and vapor lines in H-x-y diagram are parallel 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 will evaporate 1 mole of liquid (4) saturated liquid and vapor lines in H-x-y diagram are parallel

Lewis Method (i) L i, x i V i, y i Equilibrium relation y = Kx V i+1, y i+1 Operating equation rectifying section y j+1 = (L/V)x j + (1-L/V)x D stripping section y k = (L/V)x j - (L/V-1)x B

Example 15: What is the composition and enthalpy of vapor entering and leaving tray 1-5 of the distillation column shown below. (5)(5) V6V6 L5L5 V1V1 L0L0 D, x D = 0.6 h D, R = 3 (1) (2) (3) (4)

VLE Data

External Column Balances

McCabe-Thiele Method

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) V 10 B, x B = 0.05 h B, boilup ratio = 1 L9L9 V4V4 L3L3

VLE Data

McCabe-Thiele Method

Example 17: A mixture of pentane and toluene was distilled in a distillation column. An analysis of the enriching section is needed to determine whether the column is performing to specification. V4V4 L3L3 V1V1 L0L0 D, y D = 0.9 h D, R = 2 (1) (2) (3) Please determine the composition of liquid and 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  =2  =3.5

McCabe-Thiele Method  =3.5

Total and Minimum Reflux  =3.5 Total Reflux D = 0, L 0 = V 1, R = L 0 /D =  L/V = L 0 /V 1 = 1 Minimum Reflux D = maximum, L 0 = minimum allowable,

Example 18: Analysis of the stripping section of the distillation column for pentane-toluene separation must be conducted to determine the liquid and vapor compositions leaving each distillation trays. (9) (6) V 10 B, x B = 0.10 h B, boilup ratio = 2 L9L9 V6V6 L5L5 (a) using a total reboiler, (b) using a partial reboiler.

McCabe-Thiele Method  =3.5

Internal Column Balances Feed tray F V V L L Feed Equation: y = -{(L - L)/(V - V)}x + Fz f /(V-V) y = -(L f /V f )x + (F/V f )z f y = {q/(q-1)}x + z f /(1-q) q = (L-L)/F = (H-h f )/(H-h)

Example 19: Find the value of q and draw the feed line for a feed containing 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.

McCabe-Thiele Method  =3.5

McCabe-Thiele Method  =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. QCQC QRQR F, z, h f D, x D = 0.9, h D B, x B = 0.1, h B Q=0 Reflux ratio = L 0 /D Boilup ratio = V n+1 /D (n) Reboiler Condenser 10 Kmole/min, 0.4 superheated 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?

McCabe-Thiele Method  =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. QCQC QRQR F, z, h f D, y D = 0.95, h D B, x B = 0.1, h B Q=0 Reflux ratio = L 0 /D Boilup ratio = V n+1 /D (n) Reboiler Condenser 1 Kmole/min, 0.25 saturated 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  =2

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. QRQR B, x B = 0.1, h B Q=0 Boilup ratio = V n+1 /D = 4 (n) Reboiler F, z, h f 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, y D = 0.6, h D

McCabe-Thiele Method  =3.5

McCabe-Thiele Method  =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. QRQR B, x B = 0.01, h B Q=0 Boilup ratio = V n+1 /D = 3 (n) Reboiler C, x c, h c (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 optimum feed plate location if the total tray efficiency is D, y D = 0.8, h D F, z, h f 75 Kmole/min, 0.20, 25 % vapor

McCabe-Thiele Method  =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. QCQC QRQR F, z, h f D, x D = 0.9, h D B, x B = 0.1, h B Q=0 Reflux ratio = L 0 /D Boilup ratio = V n+1 /D (n) Reboiler Condenser 10 Kmole/min, 0.4 superheated 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?

McCabe-Thiele Method  =3.5

Column Efficiency Overall Column Efficiency E o = N equil /N actual Murphree Efficiency E MV = actual change in vapor change in vapor for equilibrium stage = y j - y j+1 y j * - y j+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. QCQC QRQR F, z, h f D, x D = 0.9, h D B, x B = 0.2, h B Q=0 Reflux ratio = L 0 /D Boilup ratio = V n+1 /B (n) Reboiler Condenser 10 Kmole/min, 0.5 Subcooled 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 E MV = 0.5? (d) Solve the problem using Fenske, Gilliland and Underwood methods.

McCabe-Thiele Method  =3.5