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Mass Transfer
Chapter 10
Hererogeneous and Homogeneous
Chemical reactions
r. . c e - ec ure . .
28. November 2012
Overview: Chemical reactions
-
Reaction rateorder reaction
equilibrium constant
- Hetero eneous & Homo eneous reactions
- -
- Diffusion and 1st Order Heterogeneous Reactions
-
- Heterogeneous Reactions of Unusual Stoichiometries
Mass Transfer Chemical reactions 10-2
Introduction to chemical reactions
A chemical reaction is a conversion of one set of chemical
substances into another.
AB+CD AD +BF
The reaction rate is the decrease in reactant concentration or the
increase in product concentration with time:
(1)
Mass Transfer Chemical reactions 10-3
reactants:
With being the rate constant.
Many chemical reactions are reversible and forward and
reverse reactions finally lead to an equilibrium
We can define (1) and (2) also for the reverse reaction:
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Now, the rate of the total reaction is the difference in the rates
of the forward and reverse reactions:
If and
the reaction has reached the chemical equilibrium and the ratio
reaction:
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eac on or er Apart from temperature and pressure, the reaction rate can
depend on the concentration of the reactants.
reactant is a first order reaction, e.g.:
one depending on two concentrations is of second order:
or an rrevers e secon or er reac on
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The forward reaction
is third order, since:
Note: Reactions typically occur in a series of multiple reactions. One step
is the rate determining one. Therefore, the overall reaction would be
of second or first order. (depending also on concentration)
A reaction rate not depending on any concentration is called a
.
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Reactions and mass transfer
since the reactants have to travel to the location where the
conversion takes place (sink for the reactants) while the
products have to travel away (source for the products).
reaction allows to determine the rate-limiting step and whether
the reactions have to be accounted for:
mass transfer >> reaction rate include reactions
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When reaction rate and mass transfer are comparable then we
need to incorporate reaction into the models.
iiii
rccDt
c
02
(see: Generalized Mass Balances)
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Activation energyc va on energys requ re or e reac on o s ar an o carry
on. The activation energy is typically supplied as heat (higher
radiation, such as UV light.
the reaction at a certain temperature. The catalyst (typically a
solid but could also be a li uid is not consumed after the
reaction.
Exam les of chemical reactions
Combustion (gaseous, liquid or solid fuels)
Production of chemicals (catalysts) Fuel cells, batteries (catalysts)
Gas cleaning (e.g. removal ofSO2by CaO)
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-
Heterogeneous & Homogeneous reactions
Heterogeneous reactions take place AT an interface (e.g. solid
catalyst surface, coal combustion) and diffusion and reaction
.
in the same phase (fuel combustion in engine). Diffusion and
reaction occur by steps partially in PARALLEL.
For sim lification of mass transfer roblems some
heterogeneous reactions can be treated as homogeneousones, depending on the definition of the observation space.
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For example, in combustion of coalCO2O2
par c es n u ze e s n a y
reaction takes place AT the coal
O2
O2Coal
.
O2CO2
O2
O2O2
CO2
a er on, owever, a g y porous
inorganic structure (e.g. fly ash)
O2
O2
THROUGHOUT the particle.
CO2
Even though microscopically the reaction still is a surface reaction,
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macroscop c o serva on o e en re par c e g ves e p c ure o
reactions occurring homogeneously throughout the particle.
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Thus, this case can be described as a homogeneous reaction
and the homogeneous reaction model can be applied:
assignment of the reaction type can be
sub ective!
Combustion is an irreversible reaction, so
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In summary, coal particle combustion can be described as:
01121 ccDc
The reaction is introduced at the boundary conditions!
b) Homogeneous (homogeneous-like) reaction model and
transport:
1
0
11
21 rccDc
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Examples of reaction assignment
PbS particles porous PbOheat
emova o ammon a rom o -gas:
scrubbing
3 2 4
Adsorption of sulfur dioxide (from combustion off-gas):scrubbing
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2 2 2 4using Ca(OH)2 slurry
8.1 Diffusion-Controlled Reaction
Every diffusion-controlled process involves
multi le ste s. E. . in deh dro enation of
(a)
C2H6 on Pt crystals
(1) C2H6 diffuses to Pt surface
(2) C2H6 reacts on the surface
surface
When step 1 takes much longer than step 2 then we have adiffusion-controlled reaction.
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In a) we have a diffusion-controlled
heterogeneous reaction where the(a)
reactant diffuses to a (e.g. hot or
catalytic) surface, reacts and the.
In b) we have a porous particle and
the reactant diffuses to catalytically
active sites where it reacts and the
pro uc uses away w e reac on
continues. Very important in catalysis,
Mass Transfer Chemical reactions 10-17
(homogeneous reaction model).
In c) a slow-moving molecules
react with more mobile ones
(c)
facilitating the transport of the
former across a membraneexamp e: oxygen upta e y
hemoglobin in the lungs).
In case d), molecules are well
mixed and react u on contact. The
reaction rate depends on the
Brownian motion of the moleculesac ase reac ons, 4combustion etc.)
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(a)
(b)
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Goal: To find the overall rate of the process
. us on an r er e erogeneous
Reactions (dilute solutions)
A first-order reaction with respect
to a reactant is one where the
reac on ra e s propor ona o ereactant concentration:
i i
At the steady state the overall
reaction rate/area equals the
diffusion fluxes
2232
1111
)(
cckn
ccn
i
i
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2r
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The surface reaction is
Species 1 Species 22
-2
And the reaction rate is given by
Note that the e uilibrium constant is
2
2
2K
To find the overall reaction we must eliminate the surface (or
interfacial concentrations that are hard to measure.
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Following the analysis of the mass transfer across interfaces
2ccKnr 2
ere e overa or res s ance s:
1
2321 Kk11k1
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Similarities/differences with interfacial mass transfer:
1. The resistances 1 / k1, 1 / 2 and 1 / (k3K2) add to the total
resistance 1/K
1speciesofionconcentrat
2speciesofionconcentratbulk
ex s ngewmequ r un22c
2. Henrys law constant (partition coefficient) characterizes
2
K2 and H vary over a wide range. Here, similarly to H, the K2determines the relative impact of k1 and k3.
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Example 8.2.1: Limit ing cases of 1st order reactions
(a) Fast stirring
Determine overall rate of the process when:
k1 and k3 are large, so K 2. Then,
2122
Kcr
(b) High temperatureUsually at high Tthe reactions are fast
2c1
so 1/2 is very small and can be
neglected 2231 KKk1k1
(c) Irreversible reaction -2 = 0 so K2 1212 c
1k1
1r
Note that ONLY in this case the resistances are simplyadditive.
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Example 8.2.2: Cholesterol so lubilization in bile
Bile* is the bodys "detergent" for fat digestion through cholesterol
excretion. Failure of bile leads to cholesterol gallstones. Typically,
. ,
gallstones can be dissolved by administering certain components
of the bile.
Goal: Find dissolution (reaction) rate of gallstone
As a cholesterol gallstone is a solid, mass transfer/chemical
(spinning) disk apparatus for cholesterol dissolution rates.
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*Bile = Galle (in German)
cholesterol dissolution rate= 5.39 10-9 g/(cm2 s) = r2= -3 3 =. 1
D = 210-6 cm2/s
disk diameter, d = 1.59 cmRe = 11200
bile kinematic viscosity, = 0.036 cm2/sc o es ero so u on, ens y over e e = - g cm
If the reaction is irreversible find:
a surface reaction rate constantb) dissolution rate of a 1 cm radius cholesterol gallstone
Mass Transfer Chemical reactions 10-26
(a) For this case21 /1k1
K
9 22
2 1 3 3
1
5.39 10 g cm srr K c K
c 1.48 10 g cm
Find k1 from the appropriate mass transfer coefficient using the
dD 331212
.Dd
.1
o 2 can e o a ne rom 1 an as 2 = . - cm s
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(b) dissolution rate of a 1 cm radius cholesterol gallstone
,
density gradient between cholesterol and bile results in flow by
free convection so the mass transfer coefficient is:
1/4 1/331k d d g
2.
D D
3 5 3 21 31
6 2 3 2 2
k 1cm (1cm) 1 10 g / cm 980cm / s2 0.6 (18000)
2 10 cm / s 1g / cm (0.036cm / s)
51k 5.6 10 cm / s
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As we are still dealing with irreversible reactions:
1K
1
/1k1
65
21
s/cm104.3
..
6
In a unstirred bile, the rate is also controlled by the reaction.
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8.3 Finding the Mechanism of Irreversible Heterogeneous Reactions
Typically, the reaction mechanism is not known so it has to be
inferred.
productssolidgaseous
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spec esspec es
Physical situation Rate-controlling
step
Size
R = (time, reagent)
Size = (temperature) Size = (f low) Remarks
A Shrinking Reaction R c1t strong temperature Independant of flow Other reactionparticle variation stoichomerties can
be found easily
2 1
particle R3/2 (c1t)larger particles variation particles only with flow dependson the mass transfer
coefficient
C Shrinkin Reaction R c stron tem erature Inde endent of flow This is the same as 1 corea case A, except for
ash formation
D Shrinking External diffusion R c1t Weak Usually about square This case iscorea root of flow uncommon
E Shrinking Ash diffusion R (c1t)1/2 Weak Independant of flow This case is common,corea an interesting
contrast with the
previous one
Notes: aThis is often called the topochemical model. The size Rrefers to the cone
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Cases A and C: surface reaction controls
2122ccr
As the solid concentration (c2) is constant the reaction is 1st
order with respect to c1.
22
dr
r4rcr3dt
2122
dr
rccdt
cr
Be careful, distinguish
12dt
reaction rate r2!
If the gas phase concentration c1 is constant and the particlehas an initial radius R0
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Case B: Diffusion outside of a shrinking particle controls
Identify correlation (forced convection around solid sphere)
1/2 1/3
1 =2+0.6D D
. or very sma par c es e , sor
kD
2
Ddr
ccrkcrdt i
22
112 )(43
cDdr
r
crdt
c
12
tDc
Rr
cdt
122
2
2
Mass Transfer Chemical reactions 10-33
c 2
B.2) For large particles 3/12/1
1 vd6.0dk
2/13/22/1 rDv42.0k
DD
Similarly,
1/ 2 2 / 31/ 2
2 11/ 6
dr v Dc r -0.42 c
dt
1/ 2 2 / 33 / 2 3 / 2 1
01/ 6
c0.64 v Dr R - t
c
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Cases C, D, and E: shrinking core model:
Two diffusional resistances in seriesPhysical situation Rate-controlling step
Bulk fluid
R0 particle
ar c e sur aceUnreacted core
particle
corea
corea
E Shrinking Ash diffusiona
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Case D: Diffusion in the surrounding bulk fluid controls
Mass balance: kcr4cr3dt
12
23
kcr4dtrcr4 1222
tc
ckRr
2
10
Similar dependence ofrwith tas with cases A and C.
Dependence on flow (through k) but weak dependence on
temperature.
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Case E: Diffusion in the ash (or shell) controls
Here the thickness of the shell is important Film model:
DrR0
123 cD4d
2/1
0
cD2
rR3dt
20 c
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8.4 Heterogeneous Reactions of Unusual Stoichiometries
8.4.1 Irreversible second-order heterogeneous reaction
(additivity of resistances)
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Steady-state mass transfer to the surface:
)cc(knr i11111
Surface reaction: 2i121 cr
Find the c1iby equating the above 0ckckc 11i112i12
1k
c1
2c
1
12
2
1i1
So the overall reaction rate is: 1 2 1
1 1 1
k 4 cr k c 1 1 1
Mass Transfer Chemical reactions 10-39
ompare s w e correspon ng rs or er reac on:
1 2 11 1 1
1 2 1
k 4 cr k c 1 1 1
2c k 11 /1/1
1c
kr
first order reactionsecond order reaction
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8.4.2 Heterogeneous Reactions in Concentrated Solutions
Until now we assumed that k1 f(r2). This is good for dilute
solutions.
Cracking of hydrocarbons:
xamp e:
Reforming
1 mol of species 1 n moles of species 2,n > 1
1 mol of species 1 n moles of species 2,n < 1
Mass Transfer Chemical reactions 10-41
In both cases we must account for CONVECTION in the calculation of mass transfer.
In cracking, convection is AWAY from the surface: The
reacting species must diffuse AGAINST the current of
product species.
In reforming, convection is TOWARDS the surface as" " . .
> 1 cracking
< 1 reforming
= 1 treat as be ore
Goal: To calculate the overall rate!
Mass Transfer Chemical reactions 10-42
Overall rate of reaction across this film is:
2
1 1 2 1ir n c
We must calculate the flux n1 for concentrated solutions:
dc11 vc
dzn
ow e ux rom convec on s
0 n1nncv
So the e uation for flux n can be written as: n1dc
Mass Transfer Chemical reactions 10-43
DDcdz
11
. . 1 10z = l: c1 = c1i
Solving forn1 gives:
1 1 21 1
10
r n ln( 1) 1 ( 1)c / c
whereD
k
(2c10/n1 is large) the
following diagram shows
the rate relative to that ofdilute solutions:
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Consider studying cracking of oil by flowing it over a hot plate.
If the molecular wei ht of the roduct is onl 25% of that of the oil,
by how much the convection introduced mass transfer changes
the cracking reaction rate?
1 molecule oil = x 0.25 molecules of the product.
= - .
the above figure:%40
rateactual
The convection REDUCES the reaction rate when the effect of
Mass Transfer Chemical reactions 10-45
reaction on the mass transfer coefficient is neglected.