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The Stoichiometric Table aA + bB cC + dD rewrite in terms of limiting specie A + (b/a)B (c/a)C + (d/a)D = -1, -b/a, c/a, d/a
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CHE 354CHE 354Chemical Reactor Chemical Reactor
DesignDesignStoichiometryStoichiometry
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?
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
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
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) )
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)
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
SpeciesSpecies jj jj
COCO
HH22
CHCH44
HH22OO
NN22
SpeciesSpecies jj jj
COCO 11 -1-1
HH22 22 -3-3
CHCH44 00 11
HH22OO 0.50.5 11
NN22 1.51.5 00
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)
-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!
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
Methane Synthesis Methane Synthesis Stoichiometric TableStoichiometric Table
SpeciSpecieses
Feed Feed RateRate
ChangeChange Effluent RateEffluent Rate
HH22 FFA0A0
COCOCHCH44
HH22OONN22
TotalTotal
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)
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
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.
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