UO Lecture 7 Final Lecture - South Dakota School of Mines...

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Unit Operations Lecture 7 26 May 2010 1

Transcript of UO Lecture 7 Final Lecture - South Dakota School of Mines...

Unit OperationsLecture 7

26 May 2010

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Overview• Questions on homework??Questions on homework??•AspenPlus:

o Shortcut methods: DSTWURi th d RADFRACo Rigorous method: RADFRAC

• Efficiencies•Introduction to multicomponent distillation

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AspenPlus: DSTWU / RADFRAC

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EfficienciesAssumed equilibriumAssumed equilibrium stages, but may not reach equilibrium on a stage; why?

Flooding!

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EfficienciesO ll l ffi i ilNOverall column efficiency:

actual

equilO N

NE

Murphree efficiency:..

.* equilatchangeconcvapor

changeconcvaporactualyyyyE

inout

inoutMV

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EfficienciesTypically yp ca ycolumns operated at 50% - 85% of flooding.

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Seader & Henley, 2006

Efficiencies

MVE

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Efficiencies

Seader & Henley, 2006

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Overview• Questions on homework??Questions on homework??• McCabe-Thiele graphical technique (binary systems)

•CondensersR b il•Reboilers

• Binary Shortcut Methods• AspenPlus:

o Shortcut methods: DSTWUo Rigorous method: RADFRAC

• EfficienciesEfficiencies•Introduction to multicomponent distillation (read Ch 5 Wankat)

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Multicomponent Distillation (Introduction)

• In binary distillation we could specify xD and xB ….b a y d s a o we cou d spec y D a d B ….• Now: define “Key Components”

Decreasing Decreasing Relative Volatility Keys

112 Light3 Heavy

Most of LK obtained in distillate productMost of HK obtained in bottoms product

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Today, most multicomponent systems are solved rigorous simulation.

But need to do shortcut methods to get good starting point (FUG-Kirkbride).

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Multicomponent Shortcut MethodsMinimum number of stages: Fenske Equation

BotLK

HK

DistHK

LK

xx

xx

N

ln

HKLK

BotLKDistHKN

lnmin

FRFR

ln11

ln

min

BotHK

HK

DistLK

LK

FRFR

FRFR

Nln

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BotFeedDistBotDist or

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Multicomponent Shortcut MethodsMinimum reflux ratio: Underwood Equationu e u a o: U de wood qu o

,,

FHK

DHKHKLK

FLK

DLK

FzDx

FzDx

L

Case A:NKs don’tdistribute D

LR minmin

1,,min

HKLK

FHKFLK FzFz

FL

D

di ib h i d i h kCase B & C: NKs distribute, or there is a “sandwich” NK: see Wankat; numerical iterative procedures can be involved.

R = factor * Rmin

Approximate number of equilibrium stages (N): Gilliland correlation

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Multicomponent Shortcut MethodsOptimum feed stage location (NF): Kirkbride EquationOp u eed s age oca o ( F): b de qu o

206.02

,

BxxN BLKHKR

,

DxxN DHKFeedLKS

DSTWU (AspenPlus)DSTWU (AspenPlus)• Uses Winn, Underwood, and Gilliland methods to find Nmin, Rmin, & N.• Specify LK and HK recoveries in the distillate product stream

If i 1 2 f fl i i fi d N R 1 2 * R• If input -1.2 for reflux ratio; it finds N at R = 1.2 * Rmin.• N given by DSTWU is number of equilibrium stages (includes partial

condensers and/or partial reboilers)

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Multicomponent Rigorous MethodsMaterial balance on each stage:

j

jjj

lx

xKy

jjjj zFlKV

lKV

l

11 **1*1

jj L

x

jjjj

jj

j zFlL

lL

l

1

11 11

DlClBlA *** )1(2 Nj

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jjjjjjj DlClBlA 11 )1(2 Nj

Multicomponent Rigorous MethodsMaterial balance on each stage:

DlClBlA *** )1(2 Nj

12111 ** DlClB 1j

jjjjjjj DlClBlA 11 *** )1(2 Nj

NNNNN DlBlA ** 1 Nj

DlCoeff Tri-diagonal matrix: write for each component….

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Multicomponent Rigorous MethodsRigorous Methods

CiFz

i

ldisti

boti

ispec

DxBxFzD

1 ,1 calcdisti ,

cordisti lDx

l ,

corboti

uncorjicalcdisti

corcorji

lBx

l

lDx

l

,

,,

,

corji

uncorjicalcboti

corcorji

lx

lBx

l

,

,,

,

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C

i corji

corji

lx

1 ,,

Multicomponent Rigorous MethodsEnergy balance on each stage:

jFjjjjjjjjjj QhFHVhLHVhL 1111

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1

j

j

kkjj

FDVL

FDVL

***0 VHhVhHV

1

1k

kjj FDVL

1111 ***0 jjjjjjj VHhVhHV

1

1

1

j

j

kj

j

kjjjFjj hFhFhhDQhF

DVCVBVA *** )1(2 Nj

111

1

jk

kjk

kjjjFjj Q

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EjjEjjEjjEj DVCVBVA 11 )1(2 Nj

Multicomponent Rigorous MethodsMaterial balance on each stage:

DVCVBVA *** )1(2 Nj

12111 ** DVCVB EE 1j

EjjEjjEjjEj DVCVBVA 11 *** )1(2 Nj

ENNENNEN DVBVA ** 1 Nj

EDVCoeff Tri-diagonal matrix:

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Multicomponent Rigorous MethodsRigorous Methods

LL

calcj

oldjcalcj

LLL

,

,,

calcj

oldjcalcj

VVV

,

,,

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Questions?

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