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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
1
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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
12
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( )
18
. . . .
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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
=
24