CBE 417“Unit Operations”

Lecture: 8

20 Sep 2010

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Overview• Flash Unit OperationFlash Unit Operation• Staged systems• McCabe-Thiele

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Cascade Flash Summary:• Additional “flash” stages improve purity but recovery is poorAdditional flash stages improve purity, but recovery is poor• Recycle of intermediate streams allows better recovery while

preserving good purity• Intermediate stages operated adiabatically – minimizing the

need for intermediate HX equipment, pumps, or valvesH t id d i b tt t id “b il ”• Heat provided in bottom stage provides vapor “boilup”

• Heat removed from top stage provides liquid “reflux”• This allows for a cascade separation to be done in one piece ofThis allows for a cascade separation to be done in one piece of

equipment – called a distillation column

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Add 3rd stage w/recycle &Middle stage adiabatic & dd e s age ad aba c &Higher “reflux” & With stage below and recycle:

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Top of “Column”

Rectifying (enriching) ti f di till tisection of distillation

column

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Equilibrium “Stage”Liquid and vapor leaving a stageLiquid and vapor leaving a stage

(tray) are assumed to be in equilibrium

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Bottom of “Column”Stripping section of distillation column

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Distillation Column

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Distillation ColumnColumn

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Distillation ColumnP Column

Design (binary)•Specify Z X X (more volatile)

XD Za, XD, XB (more volatile) Reflux Ratio (Lo/D) Optimum feed Stage location P column (condenser) F (feed flowrate) F (feed flowrate) Feed condition

•Find N (number of stages) N (feed stage)

Za

Nfeed (feed stage) D, and B (flowrates) Heat duties Diameter, height

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

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XB

Any needed modifications?

Distillation ColumnP

QC

ColumnOverall Column Balances (SS)

XD hD Material Balance (MB):

BDF BxDyFz aaa

Za hF Energy Balance (EB):

BhDhQQFh BhDhQQFh BDRCF

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

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XB hBQR

McCabe-Thiele Graphical Method (binary)

Used to simplify analysis of binary distillation (ease of understanding)Used o s p y a a ys s o b a y d s a o (ease o u de s a d g)Assumptions:• Pure components a, b have equal latent heats of vaporization / mole ( ) and they

stay constant.i

y• are much larger than

• Sensible heat changes• Heats of mixing

• Column is adiabatic (well insulated)

i

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

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

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McCabe-Thiele is done with MB and Thermodynamic information.

MB on Rectifying SectionAt Steady State (SS) for light material y ( ) g(LK) MB: Moles In = Moles Out

DxLxVy DNNNN 11

DN

NN

NN x

VDx

VLy

111

For CMO

VVLL NN 1;LL

RRatioReflux

General Operating

LineDNN x

VDx

VLy 1

DL

DLR o

LineVV

1

RR

VL

111 R

xxR

Ry DNN

1311

RV

D 11 RR

Rectifying SectionGeneral Operating Line: Rectifying Section

xR D General Operating Line: Rectifying Section

111 R

xxR

Ry DNN

?:: 1 NDN ythensoxxLet

Equilibrium 0.8

0.9

1

(xD, y1)yN

xN-1

Stage

0.5

0.6

0.7

Ya

Y=X i i i i

xN yN+1

0.2

0.3

0.4

1RxD

Equilibrium Line:• Relates composition of liquid leaving

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

Operating Line:• Relates composition of liquid leaving

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

0

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Xa

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vapor entering stage N (yN+1)Xa

Tie Together Equilibrium & Operating Lines

0.9

1

D

y1 V1

L(x1, y1)

0.6

0.7

0.8

Ya

(xD, y1) D

y1xDxD

LO

(x2, y3)(x1, y2)(x3, y3)

(x2, y2)

1

0.3

0.4

0.5 Y=X

1RxD

x1 y2

2

0

0.1

0.2 y3

x2

3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Xa

x3 y4

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MB on Stripping SectionAt SS and CMO still assumed, so: constantVL &

BL,

Bmm BxyVxL 1

constantVL &

Operating Line Stripping Section

Bmm x

VBx

VLy 1

0.8

0.9

1

0.5

0.6

0.7

Ya

Y=X

VVRatioBoilup B

0.2

0.3

0.4

(xB, yB)

(xN, yN)

(x y )

(xN-1, yN)

BVVB

0

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

X

(xB)

(xN, yB)

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Xa

Feed StageL V

D di F d “ di i ” illF

FV

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

L V

FL

L V

Suppose:

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

Suppose:• q = 1

• q = 0F

LLq

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• q = 0

Questions?

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