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Monolithic Reactors for Environmental Catalysis朱信Hsin ChuProfessorDept. 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), me△asurements 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:

where v = velocity (cm/s)C = molar concentration [(g mol)/cm‧ 3]z = length (cm)r = rate of reaction [(g mol)/(cm‧ 3 s)]‧

When the conversion or the reactant concentration is low, the reactor is considerd isothermal; hence

( )d vcr

dz

dcv rdz

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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:

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:

where k’ = the apparent rate constant Integrating from the reactor inlet (i) to outlet (o) gives:

where t = actual residence time (s)

2 6 2 2 2

72 3

2C H O CO H O

2 6

2 6

( )( )'C HC H

dCv k C

dz

'ln 'o

i

C k zk t

C

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t = Volumetric hourly space velocity (VHSV)

VHSV = The rate expression then becomes:

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.

volume of catalyst

volumetric flow rate

1volume flow rate at STP

volume of catalyst plus void time at STP

"ln o

i

C k

C VHSV

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3. Bulk Mass Transfer When experiments are conducted with extremely active catal

yst 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.

Where kg = mass transfer coefficient (cm/s)a = geometric surface area per unit volume (cm2/cm

3)C = reactant gas phase concentration [(g mol)/cm‧ 3]

Integrating,

Fractional conversion = 1- exp[-(kgat)]

g

dCv k aCdz

ln gi

Ck at

C

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Some dimensionless numbers

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

where L = honeycomb length (cm)

Re

( )

( )

( ) ( )

g chsh

sc

ch

k dN sherwood number

D

N schmidt numberD

dWN channel Reynolds number

A

( / )sh

sc Re

N a L

N N

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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 ConversionThe removal of propane (C3H8) in a stream air at 300 and a℃tmospheric 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=0.69a = 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,

To utilize Fig. 4.2, the following term must be determined:

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Re 6

( / ) (126 / )(0.21 ) /(0.69 182.4 )707.9

(297 10 / )chW A d g s cm cm

Ng s cm

Re (707.9)(0.21 )9.75

15.24chN d cm

L cm

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From Bird et al., 1960, the diffusivity for a binary system:

where M = molecular weight of species, A=air; B=C3H8 [g/(g mol]‧

P = total pressure (atm)σAB= collision diameter for binary system (Å)T = 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,

For C3H8: MB=44.09, σB=5.061Å,

where σ and are Lennard-Jones parameters for the single components.

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2,

(1/ 1/ )0.0018583 A B

a bAB D AB

T M MD

P

,D AB

97.0A Kk

254B Kk

/ k

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The binary system:

Using this value and Table B-2 from Bird (1960),

Therefore,

1 1( ) (3.617 5.061) 4.339

2 2o

AB A B A

(97)(254) 156.96AB A B Kk k k

5733.65

156.96AB

kT K

K

, 0.903D AB

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2

(573) (1/ 28.97 1/ 44.09)0.0018583 0.359 /

(1)(4.339) (0.903)D cm s

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4 3 2

297 10 /1.34

(6.16 10 / )(0.359 / )Sc

g cmand N

D g cm cm s

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Using Figure 4.2,

NRedch/L=9.75→Nsh/Nsc0.56=3.8

Therefore, Nsh=4.4 Fractional conversion =

=

= 0.736 = 73.6% (done)

( / )1 sh

sc Re

N a Lexp

N N

2 3(4.4)(13 / / 0.69)(15.24 )1

(1.34)(707.9)

cm cm cmexp

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4. Reactor Bed Pressure Drop Pressure drop ( P)△

a. flow contracts within the restrictive channel diameterb. washcoat on the surface of the honeycomb channel creates friction

The basic equation for P derived from the energy balance:△

where P = total pressure (atm)f = friction factor, dimensionlessgc = 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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c

1 2

g dch

dP f

dL

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The velocity in the channel (υ)

where ε = void fraction (percent open frontal area of the honeycomb)

A = cross-sectional area of honeycomb Simplify the basic equation for P△

Next slide (Fig. 4.4) P versus flow rate △To select the optimum honeycomb geometry (volume, cross-sectional area, length, cpsi, etc.) for a given application

w

A

2

c

2

g dch

ch

fLP