CE 318: Transport Process 2(Heat and Mass Transfer)

Lecture 22: Distillation and Mass Transfer(UB CBE Spiral Initiatives)

NSC 2105/5/2015

Mid-terms

2

2nd Midterm

Average: 61/100

Median: 62

SID: 20

>=81: 10

61-81: 26

41–61: 22

< 41: 14

1st Midterm

Average: 67/100

Median: 71

SID: 19

>=86: 10

67-86: 32

48–67: 17

< 48: 13

3rd Midterm (To be update)

Average: /100

Median:

SID:

>=81: 10

61-81: 26

41–61: 22

< 41: 14

Mid-terms

3

Final exam: 8am – 11am; May 12

Please let me know if you have time conflict by today.

Overview of Transport Processes

4

Momentum Heat Mass

Profile

Steady state

Non-steady state

dy

dvxyx

dx

dTkqx

dx

dCDJ AAA

2

2

y

v

t

v xx

2

2

x

T

t

T

2

2

x

CD

t

C AA

A

5

Overview of Mass Transfer

• Steady State Molecular Diffusion

Fick’s Law for Molecular Diffusion

DA: gas, liquid, solid, biological materials

calculation: • Counter-diffusion;

• Unimolecular diffusion;

• diffusion/reaction

• Convective Mass-Transfer Coefficient

• Unsteady State Diffusion

• Mass Transfer Equipment

dx

dCDJ AAA

dx

dCA

21 AAAA CCkJ )(Re,ScfkA

2

2

x

CD

t

C AA

A

Multi-componentsDiscontinuous interface

zBzAAA

ABzA NNydz

dycDN ,,,

6

Convective Mass Transfer Coefficients

ABSc DN

Schmidt number

Sherwood number

)(Re,ScfD

LkSh

ABc

21 AAcA cckN

Forced Heat Convection:Semi-Empirical Method to Estimate h

7

k

c

ckN p

pPr

Prandtl Number

Nusselt Number

Pr)(Re,fk

hDNu

TThA

qs

x

8

Industrial Separation Processes

Distillation Gas sorption

9

Separation Process: Drying

10

Separation Process: Evaporation

11

Solvent Extraction

Extraction

12

Spiral Problem: Lactic Acid Evaporation from water

Consider a film of liquid water having instantaneous thickness lwater running down the right side of a vertical solid wall (see Figure below). The wall has thickness lwall = 0.2 cm and thermal conductivity kwall = 0.5 J/(cm·s·oC). Its left side is maintained at 100oC. To the right of the film of liquid water is air at a pressure of 500 mm Hg, a bulk temperature T = 25oC and a bulk water vapor mole fraction ywater = 0 (completely dry); “bulk” means far from the wall (“at infinity”). Heat transfer through the air is characterized by a heat transfer coefficient h = 0.003 J/(cm2·s·oC). Mass transfer of water vapor through the air is characterized by a mass transfer coefficient Fwater = 0.0001 mol/(cm2·s).

lwall = 0.2 cm lwater

solid wall

  P = 500 mm HgAir T = 25 °C in bulk

ywater = 0 in bulk

T = 100 °C Ti = ?

13

Spiral Problem 2016

14

CBE Spiral Initiatives

CE408 Process Design: Lactic acid production (2016)

Cornsteep liquor

Fermentation of corn Solvent extraction of lactic

acid from H2O

Distillation of lactic acid and organic solvent

Lactic acidLactide

15

CBE Spiral Initiatives: Lactic Acid Production

Cornsteep liquor

• CE212: Liquid extraction

• CE304: VLE of lactic acid and 1-octanol

• CE317: Pumping solution

• CE318: Distillation

• CE407: Extraction

16

Spiral Problem: Distillation of Lactic Acid and 1-Octanol

1-octanol

LA

H2O

Other junk

   

H2O

1-octanolLA

LAH2O

Other junk 

1-octanol 

1-octanol

LA

H2O

Other junk  

To distillation

H2O

1-octanolLA

Cutachievedbydistillation

17

Spiral Problem: Distillation of Lactic Acid and 1-Octanol

Octanol (“OCT”) is the light component (more volatile, lower boiling); its boiling point at e.g. 14 mm Hg is 94C.

 

Lactic acid (“LA”) is the heavy component (less volatile, higher boiling); its boiling point at e.g. 14 mm Hg is 132C.

18

How does distillation work?

Vapor (condense what comes off top)More Oct, less LA

Liquid (stay behind)More LA, less OCT

19

How do you make distilltion better?

Collect only some of the condensed vapor as distillate product

Send the rest of condensed vapor back down the column as reflux

Rectifying tower contains “trays”

Reflux

20

How does reflux work?

Liquid reflux to tray below

xlactic acid = x1

 Rising vapor

ylactic acid = y2

Liquid reflux from

tray above

xlactic acid = x0

 

Rising vapor

ylactic acid = y1

L  

21

How does reflux work?

ybulk xbulk = x1

Equilibrium distribution of lactic acid at interface: y* = xbulk Psat / P (Raoult’s law modified by activity coefficient; mole fractions, activity coefficient and saturated vapor pressure refer to lactic acid)

22

Mass Transfer across the Interface

23

Murphree or Tray Efficiency

https://www.youtube.com/watch?v=rk8jpKHpD2o

where A is the interfacial area per mole of vapor on the tray. The quantity M is called the Murphree efficiency or tray efficiency.

The larger the mass transfer coefficient (ky), the larger the interfacial area (A) or the longer the residence time of the bubble spends on the tray (L / ububble), the closer M is to unity, and the more nearly equal y1 is to y*.

A tray for which the vapor leaving the tray has a lactic acid mole fraction perfectly in equilibrium with that of the liquid leaving the tray (i.e., y1 = y*(x1)) is called an ideal or theoretical tray (M = 1 = 100%).

24

Example

Suppose the volume fraction of bubbles in the froth (bubbly liquid on tray) is f = 0.4. What is A, the interfacial area per mole of vapor on the tray, for a bubble diameter of (a) 2 mm and (b) 2 cm? (The important parameter A appears in the equation for M at the top of this page.) Assume atmospheric pressure.

ybulk

xbulk = x1

25

Take Home Messages

Message #1: In distillation (and other staged operations), we are usually given a tray efficiency hM. When we work in terms of hM, mass transfer seems not to enter distillation calculations. However, the joy of mass transfer is actually embedded in hM.

 

Message #2: We learned all about distillation from Dr. Lockett in CE 407 this semester that is ending now. We will use distillation to separate lactic acid from an extraction solvent like 1-octanol in our CE 408 plant design project in spring 2016.