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Ch E 441: Chemical Kineticsand Reaction Engineering
Reaction Conversion
David A. Rockstraw, Ph.D., P.E.New Mexico State UniversityChemical Engineering
Reaction Conversion• Consider the general reaction;
• on a “per mole of A basis”…
dDcCbBaA
Da
dC
a
cB
a
bA
Reaction Conversion• The conversion of A (XA) is defined as:
fedA moles
reactedA molesXA
Da
dC
a
cB
a
bA
Conversion (Batch System)• Consider the batch reactor mole balance:
reaction
consumed
A of moles
0at t
fedinitially
A of
at t
reactorin
A of moles
by
moles
XNNN AoAoA
Ao
AAo
N
NNX
X1NN AoA
Batch Reactor Design Equation• Recall the batch reactor design equation
Vrdt
dNA
A X1NN AoA
Vrdt
dXN AAo
tX
0A
Ao Vr
dXNt
differential form integral form
Conversion (Flow System)• Consider the flow reactor mole balance:
system thewithin
consumed isA
at which ratemolar
system from
A of rate
flowmolar
system into
A of rate
flowmolar
XFFF AoAoA
Ao
AAo
F
FFX
X1FF AoA
CSTR Design Equations• Recall the CSTR Design Equation:
X1FF AoA A
AAo
r
FFV
exitA
Ao
r
XFV
PFR Design Equations• Recall the PFR Design Equation:
X1FF AoA
AAo rdV
dXF
AA r
dV
Fd
X
0A
Ao r
dXFV
differential form integral form
Application of Design Equations• Consider a single reaction system with functional
dependence as;
X1kCr AoA
X1
1
kC
1
r
1
AoA
Application of Design Equations• For the CSTR;
X vs r
1
AVoF
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.82
3
4
5
6
7
8
1r x( )
x
AAo r
X
F
V
Application of Design Equations• For the PFR;
X vs r
1
AVoF
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.82
3
4
5
6
7
8
1r x( )
x
X
0AAo r
X
F
V
Comparison• PFR always requires less volume than a
CSTR to achieve a given conversion.VoF
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.82
3
4
5
6
7
8
1r x( )
x
Reactors in Series
FA,1
X1
FA,2
X2
FA,3
X3
V3V1
FA,0
30,A0,A3,A
20,A0,A2,A
10,A0,A1,A
XFFF
XFFF
XFFF
reactorfirst tofeedin A of moles
2point toup reactedA molesX2
Where the conversion for successive reactors is defined as:
V 2
Reactors in Series
1,A
10,A1 r
X0FV
FA,1
X1
FA,2
X2
FA,3
X3
V3V1
FA,0
V 2
Reactors in Series
1,A
10,A1 r
X0FV
FA,1
X1
FA,2
X2
FA,3
X3
V3V1
FA,0
V 2
2
1
X
XA
0,A2 r
dXFV
Reactors in Series
1,A
10,A1 r
X0FV
FA,1
X1
FA,2
X2
FA,3
X3
V3V1
FA,0
V 2
2
1
X
XA
0,A2 r
dXFV
3,A
230,A3 r
XXFV
Reactors in Series
1,A
10,A1 r
0XFV
FA,1
X1
FA,2
X2
FA,3
X3
V3V1
FA,0
V 2
2
1
X
XA
0,A2 rdX
FV
3,A
230,A3 r
XXFV
V3
V1
Ar
1
X1 X2 X3
V2
Relative Reaction Rates• Relative reaction rates of the species involved in a
reaction can be obtained from the stoichiometric coefficients:
dDcCbBaA
d
r
c
r
b
r
a
r DCBA
Space Time ()• Time necessary to process
1 reactor volume of fluid at entrance conditions– Also called residence time or holding time– 1/ is referred to as the Space Velocity– For a PFR,
o
V
X
0A
Ao r
dXC
X
0A
Ao r
dXFV
Example CD P2-DB
A 400 L CSTR and a 100 L PFR are available to process 1.0 L/s of feed. Feed contains: 41% A, 41% B, 18% inerts. Consider the irreversible, gas-phase reaction A + B C to be carried out at 10 atm, 227°C.
a. Estimate the volume of a PFR required to achieve 30% conversion of A for an entering volumetric flow rate of 2 m3/min.
b. Estimate the volume of a CSTR required to take the effluent from the PFR above and achieve 50% total conversion (based on species A fed to the PFR).
c. What is the total volume of the two reactors?
d. What volume of a single PFR is necessary to achieve 60 & 80% conversion?
e. What is the volume of a single CSTR necessary to achieve 50% conversion?
f. What volume of a 2nd CSTR is needed to raise conversion from 50 to 60%?
g. Plot the rate of reaction and conversion as a function of PFR volume
h. Give a critique of the answers to this problem.
-rA 0.2 0.0167 0.00488 0.00286 0.00204
X 0.0 0.1 0.4 0.7 0.9
