Transcript Monolithic Reactors for Environmental Catalysis

Monolithic Reactors for
Environmental Catalysis
朱信
Hsin Chu
Professor
Dept. of Environmental Eng.
National Cheng Kung University
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1. Introduction


Minimize the pressure drop associated with
high flow rates
Allow the process effluent gases to pass
uniformly through the channels of the
honeycomb
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2. Chemical Kinetic Control




To be controlled by chemical kinetics rather than by diffusion
to or within the catalyst pore structure while the geses are
cold
When the surface becomes sufficiently hot, the rate will be
determined by mass transfer.
In the laboratory, when screening a large number of catalyst
candidates, it is important to measure activity at low
conversion levels to ensure that the catalyst is evaluated in the
intrinsic or chemical rate-controlling regime.
Good laboratory practice is to maintain all conversions below
20% for kinetic measurements. (adiabatic)
For highly exothermic reactions (i.e., △H > 50kcal/mol),
measurements should be made at conversions no greater than
10%.
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
A material balance across any reactor gives the
following equation assuming one-dimensional, plug
flow, steady-state operation:
d (vc)
 r
dz
where

v = velocity (cm/s)
C = molar concentration [(g‧mol)/cm3]
z = length (cm)
r = rate of reaction [(g‧mol)/(cm3‧s)]
When the conversion or the reactant concentration is
low, the reactor is considerd isothermal; hence
v
dc
 r
dz
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
Assume the oxidation of ethane to CO2 and H2O in a large
excess of O2 in a fixed bed of catalyst:
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C2 H 6  O2  2CO2  3H 2O
2

We can assume that the rate is independent of O2.
It obeys first-order kinetics (pseudo-zero-order in O2), so the
rate is expressed as:
v

dC(C2 H6 )
dz
 k ' C(C2 H6 )
where k’ = the apparent rate constant
Integrating from the reactor inlet (i) to outlet (o) gives:
ln
Co
k 'z

 k ' t
Ci

where t = actual residence time (s)
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


volume of catalyst
t = volumetric flow rate
Volumetric hourly space velocity (VHSV)
volume flow rate at STP
1
VHSV = volume of catalyst plus void  time at STP
The rate expression then becomes:
ln

Co
k"

Ci
VHSV
By varying the space velocity, the change in conversion can be
determined.
The slop of the plot yields the k” of the reaction at STP.
Next slide (Fig. 4.1)
Ethane conversion versus temperature at different space
velocities.
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3. Bulk Mass Transfer
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When experiments are conducted with extremely active
catalyst or at high temperatures, diffusional effects are
introduced, and the intrinsic kinetics of the catalytic material
is not determined accurately.
The activation energy will decrease as pore diffusion and bulk
mass transfer become more significant.
Stationary environmental abatement processes are designed to
operate in the bulk mass transfer regime where maximum
conversion of the pollutant to the nontoxic product is desired.
Diffusion processes have small temperature dependency (low
activation energies).
Chemical-controlled reactions have a high degree of
dependence on temperature (high activation energies).
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
Important benefit of diffusion processes:
the physical size and other geometric parameters of the
honeycomb for a required conversion can be obtained using
fundamental parameters of mass transfer.
v

dC
  k g aC
dz
Where kg = mass transfer coefficient (cm/s)
a = geometric surface area per unit volume (cm2/cm3)
C = reactant gas phase concentration [(g‧mol)/cm3]
Integrating,
ln
C
 k g at
Ci
Fractional conversion = 1- exp[-(kgat)]
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
Some dimensionless numbers
N sh 
N sc 
k g d ch
( sherwood number )

( schmidt number )
D
N Re  (

D
W d ch
)
(channel Reynolds number )
A 
where D = diffusivity of pollutant in air (cm2/s)
W = total mass flowrate to honeycomb catalyst (g/s)
A = frontal area of honeycomb (cm2)
dch= hydraulic diameter of honeycomb channel (cm)
ρ = gas density at operating conditions (g/cm3)
μ= gas viscosity at operating conditions (g/s‧cm)
ε=void fraction of honeycomb, dimensionless
Equation on last slide becomes:
Fractional conversion = 1- exp  N N(aN/  ) L 
sh

sc
Re

where L = honeycomb length (cm)
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
Next slide (Fig. 4.2)
Correlations for Nsh, Nsc, and NRe
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Example 1 Calculation for Mass Transfer Conversion
The removal of propane (C3H8) in a stream air at 300℃ and
atmospheric pressure with:
Flow rate, W= 1000 lb/h (126g/s)
Diameter of monolith, D=6 in. (15.24 cm)
Length of monolith, L=6 in.(15.24 cm)
Area of monolith, A=182.4 cm2
Monolith geometry, 100 cpsi (15.5 cells/cm2)
C3H8 feed fraction, X=1000 vppm (volume parts per million)
Sol: From the literature (Lachman and McNally, 1985)
dch = 0.083 in. (0.21cm)
ε=0.69
a = 33 in.2/in.3 (13 cm2/cm3)
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
Using Hodgman’s (1960) Handbook of Chemistry and
Physics
The density (ρ) and viscosity (μ) of air :
ρ at 300℃ = 6.16 × 10-4 g/cm3
μ at 300℃ = 297 × 10-6 g/s‧cm
Therefore,
NRe 

(W / A )dch


(126 g / s)(0.21cm) /(0.69 182.4cm2 )
 707.9
(297 106 g / s  cm)
To utilize Fig. 4.2, the following term must be
determined:
N Re d ch (707.9)(0.21cm)

 9.75
L
15.24cm
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
From Bird et al., 1960, the diffusivity for a binary system:
Da b  0.0018583
where
T 3 (1/ M A  1/ M B )
2
P AB
 D , AB
M =
P =
σAB=
T =
D, AB =

molecular weight of species, A=air;
B=C3H8 [g/(g‧mol]
total pressure (atm)
collision diameter for binary system (Å)
absolute operating temperature (K)
collision integral for binary system,
dimensionless
Using Table B-1 from Bird et al., 1960:

For air: MA = 28.97, σA=3.617Å, k  97.0 K
For C3H8: MB=44.09, σB=5.061Å, k  254K
where σ and  / k are Lennard-Jones parameters for the single
components.
A
B
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
The binary system:
1
2
1
2
 AB  ( A   B )  (3.617  5.061)  4.339 Ao
 AB

    
  A  B   (97)(254)  156.96 K
k
 k  k 
kT
 AB


573K
 3.65
156.96 K
Using this value and Table B-2 from Bird (1960),
D, AB  0.903
Therefore,
(573)3 (1/ 28.97  1/ 44.09)
D  0.0018583
 0.359cm2 / s
2
(1)(4.339) (0.903)

297 106 g / cm
and N Sc 

 1.34
 D (6.16 104 g / cm3 )(0.359cm2 / s)
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
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Using Figure 4.2,
NRedch/L=9.75→Nsh/Nsc0.56=3.8
Therefore, Nsh=4.4
Fractional conversion = 1  exp  N

=
(a /  ) L 

N sc N Re 
sh
 (4.4)(13cm2 / cm3 / 0.69)(15.24cm) 
1  exp  

(1.34)(707.9)


= 0.736 = 73.6% (done)
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4. Reactor Bed Pressure Drop
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Pressure drop (△P)
a. flow contracts within the restrictive channel diameter
b. washcoat on the surface of the honeycomb channel creates
friction
The basic equation for △P derived from the energy balance:
1 dP 2 f  2


 dL g c d ch

where P = total pressure (atm)
f = friction factor, dimensionless
gc = gravitational constant (980.665 cm/s2)
υ= velocity in channel at operating conditions (cm/s)
ρ= gas density at operating conditions (g/cm3)
Next slide (Fig. 4.3)
Friction factor correlation to NRe
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
The velocity in the channel (υ)


w
 A
whereε = void fraction (percent open frontal area of the
honeycomb)
A = cross-sectional area of honeycomb
Simplify the basic equation for △P
2 fLch
P 
gc dch

2
Next slide (Fig. 4.4)
△P versus flow rate
To select the optimum honeycomb geometry (volume, crosssectional area, length, cpsi, etc.) for a given application
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