kkek2158 flash distillation 2

8/2/2019 KKEK2158 Flash Distillation 2

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Flash Distilla tion

1. Know how to spec ify the numb er of

system.

2. n erstan t e eta o asdistillation

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n t 1 : as st a t on

Gibbs Phase Rule for Flowing Systems as s a on

Isothermal Flash

Deriva tion of Rac hford Ric e equa tion DePriester Chart

Example on Isotherma l Flash d istilla tion

Ad a iba tic flash

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Gibbs Phase Rule for a Flowing SystemThenumberofthermodynamicconditionsthatcanbespecifiedforasystemwith3components

with2phasesin equilibrium.

Variables: Equations:

T,P,

X1,X2,

X3...

Xi

i

= 1

Yi = 1 Pinal

1, 2, 3...

Z1,Z2,Z3...i

Zii

= 1C

ki, =

Xi ( )1C P

Ori

F,Zi,TF,PFV L ... P

Ci

Fzi = Vyi +Lxi + ... Citional

Q

2CP+ Original

Fhf + Q = Vhv + Lhl + ... 1

CP C P + 2F C P= +

Ad

4C P+ + Additional C+ 1 3F P = +

F= C+ 5For a flow system:

3

F= C+ 5Foraflowsystem:


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Determina tion of Unspec ified

Variables

F,T,P,TF,PF,ZiF= C+ 5If variablesareusedtospecify

Thenremaining ( )1 1C P+ + variablesmustbefoundfrom

B) K-Value rela tionships ( )1P CC) Ma ss ba lanc es

C

4

nergy a ance


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- Given tempera ture, the overa ll c omposition (feed ), find the

- Given the overa ll c omposition (feed ) and the

find the tempera ture o f the p roc ess and the c ompositionsof the phases

Isotherma l, ad iabatic c ond itions

- If you know the a mount o f liquid phase, you c an selec t an appropria teflash tank from sta ndard sizes

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flash Distilla tion

, ,i vV y h

FFF

F

iTPhzF ,,,,

TP

T

Tb(B)

V

11,TP

Tb(A)

L

, ,i LL x hxAy*x*

- ,

the va lve, the liquid mixture is pa rtia lly va porized

in a boiler or va our c ondensed in a c oo ler

1 FP P=isotherma l p roc ess

1 F

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Considerthefollowingoperationwhichproducesaliquidvaporequilibriumfroma

liquidfeed:

Flash

Drum

VaporoutV,yi,TV,PV,hv

LiquidFeed

F,zi,TF,PF,hF

L,xi,TL,PL,hL

qu ouQ

Foreachstream:

n:molarflowrate:F,L,V

zi

:compositionvariables:x,y,z

P:pressure

h:enthalpy

Q:heattransfer

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Isotherma l Flash Va riab les

LiquidFeed VaporoutV,yi,TV,PV,hv

FlashDrum

, i, F, F, F

L,xi,

TL,

PL,

hL

LiquidoutQ

We showed that there are C+5 de rees of

Forthissystemthereare3C+10variables: F,V,L,TF,PF, TV,PV,TL,PL,Q,{xi ,yi ,zi}C

freedom.If

we

specify

F,

zi,

TF,

PF we

have

specified(C+3)variablesand

wecanspecifytwoadditionalvariables.

CommonSpecifications:

TV,PV IsothermalFlash

V/F=0,PL BubblePointTemperature

V/F=1,PV DewPointTemperature

V/F=0,TL BubblePointPressure

V/F=1,

TV Dew

Point

Pressure, V

Q,PV Nonadiabaticflash

V/F,PV PercentVaporizationFlash

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Isotherma l Flash Equa tions

variables F,Tv,Pv,TF,PF,ZiF= C+ 5Ifwespecifythe

Thenremaining variablesmustbefoundfrom:1 3 2 5C P C+ + = +

NotethatifTandPof

eachproduct

stream

Equations

A)mole

fraction

summations

P

arenotconsideredas

variables,thenwe

wouldnthave

B)KValuerelationships

C Mass balances

( )1P CC

equationsforthermal

andmechanical

equilibriumintheD)Energybalance

drum.E T erma an mec anica equi i rium

Total

2C+ 5

IflessthanC+5variablesarespecified,thenthesystemisundetermined(underspecified).

IfmorethanC+5variablesarespecified,thenthesystemisoverdetermined

overs ecified .

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Isotherma l Flash Equa tions

Wehave2C+5 variablestodeterminefrom2C+5 equations.Theexpression

=givesthetotalnumberofequationsforthissystemof2C+3(thesystemcreatesatwo

phaseequilibrium).Thetwoadditionalequationsweneedcomefromourassumption

ofthermalandmechanicalequilibrium inthedrum.

Wehavetotalmaterialbalance: F= V+ L

TL = TV PL = PV

FZi = VYi + LXi

Wehave

component

material

balances,

one

for

each

component:

Wehavethemolefractionsummations foreachphase(orstream):

Xi = 1 Yi = 1 Zi = 1

Inequilibrium,wehaveaKvaluerelationship foreachcomponent:V

10ki

L,V

=

i

XiL


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ac or c e er va t onItisconvenienttodefinetheVaporFraction asfollows: =

V

Substitutingintoourtotalmaterialbalance:

L F F= Forthecomponentmaterialbalances:

FZi = VYi + LXi

Zi = VFYi + FFF Xi Zi = Yi + Xi Xi

Zi = Yi + Xi XiXi =

Zi

Zi = KiXi + Xi Xi

WeusetheKValue toget:

i +

K Z

Yi = KiXi

1/29/200911

i =Ki + 1

13/01/10


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R hf r Ri E i n

Weusethemolefractionsummations: Xi = 1 Yi = 1 Yi Xi( ) = 0

Substitutinginourexpressionsforthemolefractions:

i

GivesustheRachfordRice Equation:

Xi =Ki + 1

Yi =Ki + 1

KiZi

Ki + 1 Zi

Ki + 1

i

= 0 f() = Zi Ki 1( )Ki + 1i

= 0

Therootsofthisequationgiveusthecompositions,andvaporfraction ofthe

IsothermalFlash

o eration.

Tosolvethisequation,weneedtousesomeprocedureforfindingtheroots:

Iterative

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Graphical


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Newtons Iterative MethodTosolvetheRachfordRiceequationwecanuseNewtonsmethodtofind:

k+1 = k f

f' k

ew on sme o es ma esa e er

rootusingthelastguessandtheratio

ofthefunctiontoitsderivativeatthat

uess:

k+1 = k +

Zi Ki 1( )k K

i 1( )+ 1

i

FortheRachfordRiceEquation

Zi Ki 1

k Ki 1( )+ 1( )2i

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Rachford-Rice Procedure

TheRachfordRiceprocedureusingNewtonsmethodisthen:

Step1: TL = TV Thermalequilibrium

Ste 2: =

Step3: SolveRachfordRiceforV/F wheretheKvaluesaredeterminedby

L, L

Zi Ki 1( )Ki + 1i

= 0 CanuseNewtonsmethodhere.

Step4: V = F

Zi KiZi

DetermineV

Step7:

iKi + 1

i =Ki + 1

L = FF DetermineL

14 Step8: Q = Vhv + Lhl Fhf DetermineQ


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e r ester

In order to c a rry out a n ana lysis of a separa tion whic h uses d ifferenc es in

K-va lues betw een two phases to c ause a sep ara tion, we need a source of-va ues.

A lot o f eq uilib rium (K-Va lue) information for binary systems isoften conta ined in vapor-liquid phase d iagrams.

For h d roc a rb on s stems interac tions between molecules a re ver similarand c onseq uent ly, the K-Va lues will not be a func tion of composition. K-Valuesa t d ifferent p ressures and temperatures for hydroc arbons c an thus be g raphed

for multic omponent systems.

One type of these g raphs is c a lled DePriester c ha rts.

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DePriester Cha rts: Low T

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High T

17

13/01/10


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Example

Aflashchamberoperatingat50Cand200kPaisseparating1000kgmoles/hrofa

feedthatis30mole%propane,10%nbutane,15%npentane,and45%nhexane.

Whataretheproductcompositionsandflowrates?

1)Using

the

Depriester

Chart we

determine

that:

K1 (propane)=7.0

K2 (nbutane)=2.4

3 .

K4 (nhexane)

=0.30

2)WefirstwritetheRachfordRiceEquationandsubstituteinthecompositionandKvalues:

f

V

=

Zi Ki 1( )

fV

=

0.3 7.0 1( )+

0.1 2.4 1( )+

0.15 0.8 1( )+

0.45 0.3 1( )

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. . . .


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Wecan

either

plot

the

Rachford

Rice

Equation

as

afunction

of

V/F

or

use

Newtons

method:

fV

=

Zi Ki 1( )

fV

=0.3 7.0 1( )

+0.1 2.4 1( )

+0.15 0.8 1( )

+0.45 0.3 1( )

. . . .

GuessV/F=0.1

0.3 7.0 1 0.1 2.4 1 0.15 0.8 1 0.45 0.3 1. =

0.1 7 1( ) + 1+

0.1 2.4 1( ) + 1+

0.1 0.8 1( ) + 1+

0.1 0.3 1( )+ 1= .

ToobtainanewguessweneedthederivativeoftheRRequation:

f'V

F

=

0.3 7.0 1( )2

7 1( ) + 1[ ]

2+

0.1 2.4 1( )2

2.4 1( )+ 1[ ]

2+

0.15 0.8 1( )2

0.8 1( ) + 1[ ]

2+

0.45 0.3 1( )2

0.3 1( ) + 1[ ]

2

' 0.1 =0.3 7.0 1( )2

+0.1 2.4 1( )2

+0.15 0.8 1( )2

+0.45 0.3 1( )2

= 4.6310.1 7 1( )+ 1[ ] 0.1 2.4 1( )+ 1[ ] 0.1 0.8 1( )+ 1[ ] 0.1 0.3 1( )+ 1[ ]

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Soour

next

guess

is

2 0.879.

4.631.

= 0.3 7.0 1( ) 0.1 2.4 1( ) 0.15 0.8 1( ) 0.45 0.3 1( ) =.0.29 7 1( )+ 1 0.29 2.4 1( )+ 1 0.29 0.8 1( )+ 1 0.29 0.3 1( )+ 1

.

ToobtainanewguessweneedthederivativeoftheRRequation:

f' 0.29( ) = 0.3 7.0 1( )2

0.29 7 1( )+ 1[ ]2+ 0.1 2.4 1( )

2

0.29 2.4 1( )+ 1[ ]2+ 0.15 0.8 1( )

2

0.29 0.8 1( )+ 1[ ]2+ 0.45 0.3 1( )

2

0.29 0.3 1( )+ 1[ ]2= 1.891

3 = 0.29 +

0.329

1.891= 0.46

f 0.46( ) = 0.066 f' 0.46( )= 1.32

4

0.46+0.066

= 0.51.

f 0.51( )= 0.0017320


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So:V/F= 0.51 V= 510k /hr

Xi =Zi

Ki + 1 Yi =

KiZi

Ki + 1

Using:

X1 (propane)=0.0739 Y1 (propane)=0.5172

2 .

X3 (npentane)=0.1670

X4 (nhexane)=0.6998

2 .

Y3 (npentane)=0.1336

Y4 (nhexane)=0.2099

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, ,i VV y h

FFF

F

i TPhzF ,,,,TP

, ,i LL x h

- Li uid feed is heated under ressure and then ad iab atic all flashed throu hthe p ressure red uc ing va lve

PP F

Lx Vy Fz + =FTT 1 L V F+ =

= (1 ) 0L V Fh h h + =L V F (1 ) 0L V Fh h h +22


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Ob ective : find V L andtheir c ompositions

roc e ure: 1) Guess T1

2) Isothermal flash procedure

(1 )( ) 0

Fi iz Kf = =

3) Validate

i

(1 ) 0L V Fh h h + = not

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Objective: find V, L, and

their compositions

Procedure: 1 Guess

2) Isothermal flash procedure

/L F =

find temperature of the flash drum

so that:

(1 )( ) 0

1 ( 1)

F

i ii

i i

z Kf K

K

= =

+

1Ta ate

(1 ) 0L V Fh h h + =not F L

V L

h h

h h

=

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kkek2158 flash distillation 2

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