Download - CHE 354 Chemical Reactor Design Stoichiometry. PFR Design Equations But r A = f(C i or P i ) so how…
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CHE 354CHE 354Chemical Reactor Chemical Reactor
DesignDesignStoichiometryStoichiometry
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PFR Design EquationsPFR Design Equations
AA r
dVdF
0A
A
Fr
dVd
But rA = f(Ci or Pi) so how do we find one common independent variable?
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The Stoichiometric TableThe Stoichiometric Table
aA + bB cC + dDrewrite in terms of limiting
specieA + (b/a)B (c/a)C + (d/a)D
= -1, -b/a, c/a, d/a
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Stoichiometric TableStoichiometric TableSpeciSpeci
esesFeed Feed RateRate
ChangeChange Effluent RateEffluent Rate
AA FFA0A0 -1 F-1 FA0A0 X X FFA0A0 (1-X) (1-X)BB FFB0B0 BB F FA0A0 X X FFB0B0 + + BB F FA0A0 X XCC FFC0C0 CC F FA0A0 X X FFC0C0 + + CC F FA0A0 X XDD FFD0D0 DD F FA0A0 X X FFD0D0 + + DD F FA0A0 X XII FFI0I0 ------ FFI0I0
TotalTotal FFT0T0 jj F FA0A0 X X FFT0T0 + + jj F FA0A0 X X
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Let’s simplify a bit:Let’s simplify a bit:Define Define j ≡ Fj ≡ Fj0j0/F/FA0A0
≡ ≡ jj = -1 - b/a + c/a + d/a = -1 - b/a + c/a + d/a
≡ ≡ yyA0A0 = (F = (FA0A0/F/FT0T0) )
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Stoichiometric TableStoichiometric TableSpeciSpeci
esesFeed Feed RateRate
ChangeChange Effluent RateEffluent Rate
AA FFA0A0 - F- FA0A0 X X FFA0A0 (1 - X) (1 - X)BB FFA0A0 BB BB F FA0A0 X X FFA0 A0 ((BB + + BB X) X)CC FFA0A0 CC CC F FA0A0 X X FFA0 A0 ((CC + + CC X) X)DD FFA0A0 DD DD F FA0A0 X X FFA0 A0 ((DD + + DD X) X)II FFA0A0 II ------ FFA0A0 II
TotalTotal FFT0T0 jj F FA0A0 X X FFT0T0 (1 + (1 + X) X)
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Comparing Moles Comparing Moles ReactedReacted
Let’s use a real reaction: CO + 3H2 CH4 + H2O
A + 3B C + D
10 mol CO/min20 mol H2/min5 mol H2O/min15 mol N2/min
T = 200oCP = 2 atm
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SpeciesSpecies jj jj
COCO
HH22
CHCH44
HH22OO
NN22
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SpeciesSpecies jj jj
COCO 11 -1-1
HH22 22 -3-3
CHCH44 00 11
HH22OO 0.50.5 11
NN22 1.51.5 00
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Methane Synthesis Methane Synthesis Stoichiometric TableStoichiometric Table
SpeciSpecieses
Feed Feed RateRate
ChangeChange Effluent RateEffluent Rate
COCO FFA0A0 - F- FA0A0 X X FFA0A0 (1 - X) (1 - X)HH22 2 F2 FA0A0 FFA0A0 X X FFA0 A0 (( - 3 X) - 3 X)
CHCH44 00 FFA0A0 X X FFA0 A0 XXHH22OO 0.5 F0.5 FA0A0 FFA0A0 X X FFA0 A0 (( + X) + X)NN22 1.5 F1.5 FA0A0 ------ FFA0A0
TotalTotal FFT0T0 FFA0A0 X X FFT0T0 (1 - 0.4 X) (1 - 0.4 X)
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-15
-10
-5
0
5
10
15
20
25
0.0 0.2 0.4 0.6 0.8 1.0Conversion
Mol
ar F
low
Rat
e (m
ol/m
in)
CO
H2
CH4
H2O
N2
Uh, oh – negative flow rate!
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H2 + 1/3 CO 1/3 CH4 + 1/3 H2O
A + 1/3 B 1/3 C + 1/3 D
10 mol CO/min20 mol H2/min5 mol H2O/min15 mol N2/min
T = 200oCP = 2 atm
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Methane Synthesis Methane Synthesis Stoichiometric TableStoichiometric Table
SpeciSpecieses
Feed Feed RateRate
ChangeChange Effluent RateEffluent Rate
HH22 FFA0A0
COCOCHCH44
HH22OONN22
TotalTotal
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Methane Synthesis Methane Synthesis Stoichiometric TableStoichiometric Table
SpeciSpecieses
Feed Feed RateRate
ChangeChange Effluent RateEffluent Rate
HH22 FFA0A0 - F- FA0A0 X X FFA0A0 (1 - X) (1 - X)COCO 0.5 F0.5 FA0A0 FFA0A0 X X FFA0 A0 (( – 1/3 X) – 1/3 X)CHCH44 00 1/3 F1/3 FA0A0 X X 1/3 F1/3 FA0 A0 XXHH22OO 0.25 F0.25 FA0A0 1/3 F1/3 FA0A0 X X FFA0 A0 (( + 1/3 X) + 1/3 X)NN22 0.75 F0.75 FA0A0 ------ FFA0A0 0.75 0.75
TotalTotal FFT0T0 FFA0A0 X X FFT0T0 (1 - 0.267 X) (1 - 0.267 X)
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How About CHow About Cjj??CCjj = F = Fjj/v = F/v = FA0A0 ( (jj + + jj X)/v X)/v
if v not constant (as in this case)if v not constant (as in this case)v = vv = v00 (F (FTT/F/FT0T0) (P) (P00/P) (T/T/P) (T/T00))
FFTT/F/FT0T0 = (1 + = (1 + X) X)
CCjj = F = FA0A0 ( (jj + + jj X)/[v X)/[v00 (1 + (1 + X)] X)]isothermal, isobaricisothermal, isobaric
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Would you like to bypass Would you like to bypass X?X?
...
///
00
BAT
ABBB
TT
BB
AA
BAAA
FFF
rrdVdF
FFvvvFCvFC
CkCrdVdF
Look at a 2nd order reaction that is isothermal and isobaric.
Need a balance for every chemical specie.