10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 18: External Mass-transfer Resistance
This lecture covers: Gas-liquid reactions in multiphase systems
fluid
mass
transfer
coefficient
reactants
products
external
transport
rate law
observed rxn rate
=f(reactant concentration
and product)
intraparticle
diffusion
adsorption desorption
solid
sites
rxn
Figure 1. Schematic of surface reaction kinetics.
Analogies:
noncovalent
biomolecular
interactions
↔
Michaelis↔
Menton
enzyme kinetics
(Briggs-Haldane, Henri)
Langmuir
adsorption
isotherms
Langmuir-Hinshelwood
Haugen-Watson
kinetics
Logic:
•
•
•
•
list rxns
hypothesize rate-limiting step
derive rate law
check for consistency w/ rate data
Single site, unimolecular decomposition
kA
kS
kD
k− A
k− S
k− D
A R AS R BS + C R S + B + C
S ≡ site on catalyst
product
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
rAd ≡ rate of A adsorption
rs ≡ rate of rxn on surface
rD ≡ rate of desorption
rAd = k A PACS − k− AC AS
* units
partial
reactive
pressureA sites
1
sites
time
mass catalyst
often CS is given as fractional occupancy
KA =
θ
kA
k− A
⎛
C ⎞
rAd = k A ⎜ PACS − AS ⎟
KA ⎠
⎝
⎛
PC ⎞
Similarly, rS = k S ⎜ C AS − C BS ⎟
KS ⎠
⎝
⎛
PC ⎞
1
Æ
rD = k D ⎜ CBS − B S ⎟ Æ K B =
KD
KD ⎠
⎝
At steady-state,
rD = k D ( CBS − K B PB CS )
rAd = rS = rD (or else you would accumulate molecules)
For a rate-limiting step
i,
r r
ri
j, l
ki
k j kl
Hypothesize, that adsorption is rate-limiting:
r
rA
r
S , D ≈0
kA
kS k D
rS
PC
C P
≈ 0 ⇒ C AS − C BS ⇒ C AS ≈ BS C
KS
kS
KS
rD
≈ 0 ⇒ CBS − K B PB CS ⇒ CBS ≈ K B PB CS
kD
K PC P
Æ C AS ≈ B B S C
KS
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 18
Page 2 of 4
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
⎛
C ⎞
rAd = k A ⎜ PACS − AS ⎟
KA ⎠
⎝
⎛
⎞
KB
= k A ⎜ PACS −
PB PC CS ⎟
KS K A
⎝
⎠
⎛
⎞
KB
PB PC ⎟
= k ACS ⎜ PA −
KS K A
⎝
⎠
Material balance on CS (available sites):
C S0 = C S +
CS0 = CS + C AS + CBS
KB
PB PC CS + K B PB CS
KS
⎛ K
⎞
= CS ⎜1 + B PB PC + K B PB ⎟
⎝ KS
⎠
Adsorption as rate-limiting step:
eq. driving force
⎞
⎛
⎜
⎟
KB
k ACS0 ⎜ PA −
PB PC ⎟
KS K A
⎜
⎟
⎝
⎠
− rA =
KB
PB PC + K B PB
1+
KS
equilibrium driving force is 0 at equilibrium!
Surface reaction is rate-limiting:
⎛
PP ⎞
k S CS0 K A ⎜ PA − B C ⎟
KC ⎠
⎝
− rA =
1 + PB K B + PA K A
Desorption is rate-limiting:
⎛
PP ⎞
k D CS0 K S K A ⎜ PA − B C ⎟
KC ⎠
⎝
− rA =
PC + PA K A K S + K A PC PA
Initial rate expirements, approximate − rA = f ( PA ) , PB ≈ PC ≈ 0 , K C =
K AKS
.
KB
Adsorption limit:
− rA = k ACS0 PAo
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 18
Page 3 of 4
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
− rA
PAo
Figure 2. Reaction rate vs. initial partial pressure of A for the absorption limiting
case.
Surface reaction limit:
− rA =
kS CS0 K A PAo
1 + K A PAo
− rA
PAo
Figure 3. Reaction rate vs. initial partial pressure of A for the surface reaction
limiting case.
Desorption limit:
− rA = k D CS0
− rA
PAo
Figure 4. Reaction rate vs. initial partial pressure of A for the desorption limiting
case.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 18
Page 4 of 4
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].