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.