CBE 417“Chemical Engineering Equilibrium

Separations”

1

Lecture: 8

24 Sep 2012

Overview

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• Multicomponent Flash• Flash Unit Operation (AspenPlus)• Staged systems• McCabe-Thiele

Distillation Column

3

Distillation Column

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Design (binary)• Specify Za, XD, XB (more volatile) Reflux Ratio (Lo/D) Optimum feed stage location P column (condenser) F (feed flowrate) Feed condition• Find N (number of stages) Nfeed (feed stage) D, and B (flowrates) Heat duties Diameter, height

XB

XD

Za

P

Simulation (binary)• Use existing column Simulate to see performance Any needed modifications?

Distillation Column

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Overall Column Balances (SS)

XB

XD

Za

P

hD

hF

hB

QC

QR

Material Balance (MB):

BDF BxDyFz aaa

Energy Balance (EB):

BhDhQQFh BDRCF

• heat added is (+)• heat removed (-)• adiabatic (well insulated)

McCabe-Thiele Graphical Method (binary)

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Used to simplify analysis of binary distillation (ease of understanding)

Assumptions:• Pure components a, b have equal latent heats of vaporization / mole ( ) and they

stay constant.• are much larger than

• Sensible heat changes• Heats of mixing

• Column is adiabatic (well – insulated)• Constant pressure (P) throughout the column (i.e. no P in the column)

i

i

Called Constant Molal Overflow (CMO)• Assumes for every 1 mole of light material vaporized that 1 mole of heavy material

condenses from the vapor phase• Net result:

• Total molar flowrates (i.e. L and V) remain constant within that column section (rectifying or stripping, or other)• Do not need a stage by stage energy balance

McCabe-Thiele is done with MB and thermodynamic information.

MB on Rectifying Section

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At Steady State (SS) for light material (LK) MB: Moles In = Moles Out

DxLxVy DNNNN 11

DN

NN

NN x

V

Dx

V

Ly

111

For CMO

VVLL NN 1;

General Operating

LineDNN x

V

Dx

V

Ly 1

D

L

D

LR

RRatioReflux

o

1

11

RV

DR

R

V

L

111 R

xx

R

Ry D

NN

Equilibrium Stage

Rectifying Section

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Operating Line:• Relates composition of liquid leaving

stage N (i.e. xN) to the composition of vapor entering stage N (yN+1)

General Operating Line: Rectifying Section

111 R

xx

R

Ry D

NN

?:: 1 NDN ythensoxxLet

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Xa

Ya

Y=X line

(xD, y1)

1R

xD

Equilibrium Line:• Relates composition of liquid leaving

stage N (i.e. xN) to the composition of vapor leaving stage N (yN)

yN

xN

xN-1

yN+1

Tie Together Equilibrium & Operating Lines

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Xa

Ya

Y=X line

(xD, y1)

1R

xD

D

y1

x1

xD

y2

xD

y1 V1

LO

y3

x3

x2

y4

(x2, y3)

(x1, y1)

(x1, y2)(x3, y3)

(x2, y2)

1

3

2

MB on Stripping Section

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At SS and CMO still assumed, so:

Bmm BxyVxL 1

constantVL &

Operating Line Stripping Section

B

VV

VRatioBoilup

B

B

Bmm x

V

Bx

V

Ly 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Xa

Ya

Y=X line

(xB)

(xB, yB)

(xN, yN)

(xN, yB)

(xN-1, yN)

Feed Stage

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Suppose:• q = 1

• q = 0

Depending on Feed “condition” will get changes to vapor and liquid flowrates…

F

LLq

Define q = Moles of liquid flow in Stripping section that result from one mole of feed.

F

ZF

L V

L V

FV

FL

Feed Stage Operating Line

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F

ZF

L V

L V

FV

FL

DNN x

V

Dx

V

Ly 1

Bmm x

V

Bx

V

Ly 1

rectifying section

stripping section

DNN DxLxVy 1

Bmm BxxLyV 1

BD BxDxLLxVVy Feed stage & overall column MBs:

BDF BxDxFz

VLVLF

FFzLLxFLLy

FLLVV

FzF

LLx

F

LLy

1

11 q

zx

q

qy F feed line eqn.

Plot Feed MB Line

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Xa

Ya

Y=X line

zF

Feed Condition q Slope

11 q

zx

q

qy F

sat’d liquid = 1

sat’d vapor = 0 0

sat’d liq.q = 1

mixed V & L 0 < q < 1 neg. (-)

subcooled L > 1 pos. (+)

superheated V < 0 pos. (+)sat’d vap. q = 0

0<q<1

subcooled liq.

q>1

Superhtd vapor

q<0

partial V&L

Lets put all three lines together:• rectifying section• stripping section• feed line

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

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0.8

0.9

1

X

Y

Operating Lines (McCabe-Thiele)

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zF

R incr.q is constant

Rectifying & stripping lines must intersect at the same point on the feed line.

Consider limits:• R = • R where rectifying line

intersects the equil. curve

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

Operating Lines (McCabe-Thiele)

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zF

q incr.

R is constant

Rectifying & stripping lines must intersect at the same point on the feed line.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

McCabe-Thiele Graphical Method

16

Binary Distillation

Feed stage location: point where switch from rectifying operating line to the stripping operating line.zF

“step off” equilibrium stages on the XY diagram.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

McCabe-Thiele Graphical Method

17

Binary Distillation

Feed stage location: point where switch from rectifying operating line to the stripping operating line.zF

Optimum feed stage location: switching point to obtain smallest number of stages. Switch when intersection of 3 operating lines is first crossed.

“step off” equilibrium stages on the XY diagram.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

McCabe-Thiele Graphical Method

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Binary Distillation

Total reflux; so D = ?and R = ??

zF

Minimum Number of Stages

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

McCabe-Thiele Graphical Method

19

Binary Distillation

One or both operating lines intersect the equilibrium line.

zF

Result: infinite number of stages.

Minimum Reflux Ratio

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

McCabe-Thiele Graphical Method

20

Binary Distillation

One or both operating lines intersect the equilibrium line.

zF

Result: infinite number of stages.

Minimum Reflux Ratio

McCabe-Thiele Graphical Method (binary)

21

Used to simplify analysis of binary distillation (ease of understanding)

Assumptions:• Pure components a, b have equal latent heats of vaporization / mole ( ) and they

stay constant.• are much larger than

• Sensible heat changes• Heats of mixing

• Column is adiabatic (well – insulated)• Constant pressure (P) throughout the column (i.e. no P in the column)

i

i

Called Constant Molal Overflow (CMO)• Assumes for every 1 mole of light material vaporized that 1 mole of heavy material

condenses from the vapor phase• Net result:

• Total molar flowrates (i.e. L and V) remain constant within that column section (rectifying or stripping, or other)• Do not need a stage by stage energy balance

McCabe-Thiele is done with MB and thermodynamic information.

Problem Solving Exercise

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Questions?

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