CPE624_WEEK5
14
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING The reaction occurs only on the external surface of a pellet - only the external surface is reactive (e.g: non porous pellets) ASSUMPTION AND CONSIDERATION. Steady state assumption: there is no accumulation on the surface: [rate of transport to surface] = [rate of reaction at surface] As As Ab mA C k R r R C C k R " 4 " 4 ) ( 4 2 2 2 For a first-order irreversible reaction on a single spherical pellet of radius R, the total rate of reaction on the external surface of the pellet is:
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Transcript of CPE624_WEEK5
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
The reaction occurs only on the external surface of a pellet - only the external surface is reactive (e.g: non porous pellets)
ASSUMPTION AND CONSIDERATION.
Steady state assumption: there is no accumulation on the surface:
[rate of transport to surface] = [rate of reaction at surface]
AsAsAbmA CkRrRCCkR "4"4)(4 222
For a first-order irreversible reaction on a single spherical pellet of radius R, the total rate of reaction on the external surface of the pellet is:
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
AsAsAbmA CkRrRCCkR "4"4)(4 222
Transport
The rate of reaction on the pellet with surface area is equal to the rate of mass transfer from the bulk fluid to the surface
24 R
AbmAAsmAAs
AsAsmAAbmA
AsAsAbmA
AsAsAbmA
CkCkCk
CkCkCk
CkCCk
CkRCCkR
"
"
")(
"4)(4 22
mA
AbAs
mA
AbmAAs
AbmAmAAs
k
k
CC
kk
CkC
CkkkC
"1
"
"
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
Eliminate from the rate expression and solve for the rate to yield
AsC
Abeff
mA
Ab
As
Ck
k
k
Ckr
Ckr
''
"1
""
""
The reaction rate has an effective rate constant:
mA
eff
k
k
kk
"1
"''
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
If k” << kmA, then.....
mA
eff
k
k
kk
"1
"''LIMITING CASES:
AbAb Ck
Ckr "
01
""
Reaction limited
If kmA << k” then.....
AbmACkr "
Mass transfer limited
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
Consider the effect of pore diffusion on the overall rate
AsCkr ""
Diffusion effects are handled through an effectiveness factor of η, which is a function of rate coefficients and geometry of the catalyst
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
PORE DIFFUSION
SINGLE PORE
HONEYCOMB CATALYST
POROUS SPHERES AND
CYLINDERS
POROUS CATALYST
SLAB
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
A shell balance between x and x+dx:
[Net flux in at x] – [net flux out at x+dx] = [rate of reaction on wall between x and x+dx]
Consider a single pore of length l and diameter dP. The walls are uniformly reactive with r’’=k’’CA(x). The concentration at the pore mouth (x = l) is CAS and the end of the pore is assumed to be unreactive so that dCA/dx = 0 at x = 0.
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
Rate in the pore if the concentration remained at CAs:
Average rate within the pore:
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
Effectiveness factor – fraction which the rate is reduced by pore diffusion limitations
rate ideal
rate actual
Thus:
tanh1
ee
eel
Dd
kl
Ap
21
"4
AsCkr ""
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
The limits of η:
Φ « 1, η = 1 no pore diffusion limitation Φ = 1 η = 0.762 some limitation Φ » 1 η = 1/ϕ strong pore diffusion limitation
Where Φ is Thiele Modulus
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
Consider slab with average diameter dp and length, l with irregular pores
tanh
lD
kS
A
cg2
1
"
CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
Shell balance:
AbgA
A CkSdR
dCDR
dR
d
R"
1 2
2
1coth3
00
21
"RR
D
kS
A
cg
η = 1, ϕ « 1 η = 0.8, ϕ = 1 η = 1/ϕ ϕ » 1
CHE594: CHEMICAL REACTION ENGINEERING
