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Modeling Catalytic Converter for Oxidation of Hydrocarbon in the Exhaust Gas

Sanchita ChauhanUniversity Institute of Chemical Engg. and Tech.,

Panjab University,Chandigarh160014 Indiae-mail: sanchita_pu@yahoo.co.in

V.K. SrivastavaAcademy of Business & Engg. Sciences,

Vijay Nagar,Ghaziabad 201009 India

e-mail: iitdchemvks@yahoo.com

AbstractHydrocarbons are released to the atmosphere inappreciable quantities from the vehicular exhaust during thewarm-up period. In this paper the conversion of hydrocarbonpropylene is analysed in a monolithic converter using anunsteady state model. The results derived from the modeldepict the gas concentration, gas temperature and solidtemperature variation in the monolith during the cold start

period.

Keywords-catalytic reaction; propylene; unsteady state;monoliths

I.

INTRODUCTION

Pollutants released during transportation are a cause ofconcern as they are one of the major sources ofenvironmental pollution. Catalytic converters areextensively used to bring about a reduction in theconcentration of these polluting exhaust gases. As comparedto the earlier bed of particulate bead catalyst, monolithsexhibit higher conversion of pollutants due to increasedgeometric surface area and are also lighter in weight [1].

It was observed that the converters are effective inreducing pollution only after they have reached the desiredoperating temperatures [2]. It is the incoming hot exhaustgas that heats the converter to its operational temperature.After this the concentration of pollutant decreases due to theinitiation of the highly exothermic catalytic reactions. So itis during this warm-up period that a considerable amount ofhydrocarbons are released to the atmosphere untreated.

Modeling as compared to experimental testing isrelatively inexpensive and less time consuming [3].However a number of difficulties are encountered duringmodeling, they include complexities in reaction schemesand the rate expressions to be used for different catalyticformulations. The monolith behaviour during warm-upperiod can be adequately predicted by a one-dimensionalmodel [4].

In this study mass and energy balance equations forunsteady state model are formed for analysing theconcentration of the polluting hydrocarbon propylenereleased during the warm-up period of the converter. Themodel consists of a set of partial differential equationswhich are coupled. These equations are solved by theBackward Implicit Scheme method.

II.

KINETICS

The catalytic oxidation of propylene over platinumcatalyst dispersed over a substrate is considered.

C3H6+ 4.5 O23 CO2+ 3 H2O (1)

The rate expression for this reaction is:

(-r)cat = kcat exp(-Ecat/RTs)

CC3H6 (2)

where, activation energy Ecat is taken as 50,242 J/gmoland rate constant kcat is taken as 9.14104cm/s [5].

III.

MODELING

One-dimensional modeling is carried out for a channelof the converter taking into account the gas-solid heat andmass transfer, the axial heat conduction in the catalyst andthe chemical reactions the converter [6].

A.

Assumptions:

Some major assumptions made during modeling include:o Catalyst does not deactivate.o Noble metal concentration is kept constant.o

Gas phase concentration, temperature and velocityand the solid temperature are uniform across thecross-section of the monolith.

o

Diffusion in washcoat is neglected.o

The physical properties of monolith are constant andindependent of monolith temperature.

o

Negligible axial diffusion of mass and heat transfer ingas phase.

o Heat transfer by radiation within channel and heatexchange between the substrate and the surroundingsat both inlet and outlet faces of the monolith areneglected.

B.

Modeled Equations

Mass balance in gas phase:

v(dCg/dx) + kg S (Cg-Cs) = (dCg/dt) (3)

here Cg , Csrepresent concentrations in bulk gas phase

and at the solid surface (gmole/cm3), Tg is gas temperature

(K), kgis mass transfer coefficient (cm/s), S is the geometric

2009 Second International Conference on Environmental and Computer Science

978-0-7695-3937-9/09 $26.00 2009 IEEE

DOI 10.1109/ICECS.2009.66

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surface area per unit reactor volume (cm2/cm3), v is averagevelocity (cm/s) and t is time (s).

Mass balance in solid phase:

a (-r)cat = kgS (Cg- Cs) (4)

here a is catalytic surface area per unit reactor volume(cm2/cm3).

Energy balance in gas phase:

-gCpgv(dTg/dx) + hS(Ts-Tg) = gCpg(dTg/dt) (5)

here g represents gas density (g/cm3), Cp

g is specific

heat of gas (cal/g K), h is heat transfer coefficient (cal/cm2s

K) and (-H) is heat of reaction (cal/gmole).Energy balance in solid phase:

s(d

2T

s/dx

2)+ h S (T

g-T

s) + a(-H) (-r)cat = sCps(dTs/dt) (6)

here s

is thermal conductivity of wall (cal/cm s K), Cpsis specific heat of solid (cal/g K),

sis solid density (g/cm3)

and t is time (s).Entering gas concentration and temperature all times:

Cg(0,t) = Cg0 , Tg(0,t) = Tg

0 (7)

The solid catalyst at start is at the ambient temperature:

Ts(x,0) =Ts0

(8)

At the entrance and exit of the converter the boundaryconditions are:

at x = 0, dTs /dx = 0 (9)

at x = L, dCs /dx = 0 , dTg /dx = 0, dTs /dx =0 (10)

Equations (1), (3) and (4) are partial differentialequations that are coupled and nonlinear. As these arecoupled, their solutions are dependent on one another. Allthese equations are solved in dimensionless form using thefollowing expressions.

C = Cg / Cg0 , T'g=

Tg / Tg0

, T's= Ts/ Ts0

, z = x / L ,

t ' = t/t0 (11)

The mass balance equation becomes

(dC/dz) + 1C e-Ecat/RTs= - 2(dC/dt) (12)

where 1 = L a kcat/v and 2= L/v t0

The energy balance equation for gas phase reduces to:

(dT'g/dz) = 1 (T's-T'g) - 2(dT'g/dt) (13)

where 1 = 4 L h / v g Cpg d and 2= L/v t0

here d is the hydraulic diameter of the channel (cm).The energy balance equation for solid phase reduces to:

(dT's2/dz2) = - 3Ce

-Ecat/RTs+ 33(T's-T'g) + 3(dT's/dt') (14)

where 3= Cg0 a L2(-H ) kcat /sTg

0

33 = 4 h L2/ s d and 3 =s Cps L

2/ st0

Initial and boundary conditions:

C(0,t') = 1.0,T 'g(0,t') = Tg/Tg0, T's(x,0) = Ts/Ts

0 (15)

at z = 0.0, dT's /dz = 0 (16)

at z = 1.0, dT'g /dz = 0, dC/dz = 0 and dT's /dz = 0 (17)

The above partial differential equations are solved byBackward Implicit finite difference numerical scheme [7].

IV. RESULTS AND DISCUSSION

At the start of the operation, the converter is at 25 0C andpropylene gas entering the converter at 3270C heats up theconverter. The catalytic reaction starts once the converterreaches the operating temperature. Due to this reaction adecrease in the concentration of propylene is observed. Theinlet concentration of propylene (1900ppm) has adimensionless value of 1.0000 and the results are obtainedand analysed for decrease in the dimensionlessconcentration upto 0.1000. Discussion has been done with

the help Figs. 1 - 4.Fig. 1 shows the concentration variation of propylene

along the converter length with respect to time. Atdimensionless time 12.00 the concentrations are 0.9749,0.8829 and 0.7991 at axial lengths 0.10, 0.50 and 0.90respectively. As time increases to 14.70, the concentrationsdecrease to 0.7961, 0.3216 and 0.1346 at axial lengths 0.10,0.50 and 0.90 respectively, indicating that with passage oftime the conversion increases.

Fig. 2 shows variation of the gas temperature along theaxial length with respect to time for an inlet gas temperatureof 327.000C. At dimensionless time 12.00 the gastemperatures are 324.860C, 317.460C and 311.540C at axiallengths 0.1, 0.5 and 0.9 respectively, due to transfer of heat

from the warm gas to relatively cooler solid wall. Howeveraround dimensionless time 13.50 an increase in gastemperature towards the exit of the converter is observed. Itis caused by the transfer of heat from the solid catalyst tothe gas phase, due to highly exothermic reactions takingplace on the solid catalyst surface. Therefore atdimensionless time 14.70 the gas temperatures are332.800C, 352.080C and 365.620C at axial lengths 0.1, 0.5,and 0.9 respectively.

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Figure 1. Concentration variation with Axial Length for Propylene Gas.

Figure 2. Gas Temperature variation with Axial Length for PropyleneGas.

Figure 3. Solid Temperature variation with Axial Length.

Figure 4. Gas and Solid Temperature variation with Axial Length.

Fig. 3 shows variation of the solid temperature along theconverter length with respect to time. At dimensionless time12.00 the solid catalyst temperatures are 290.980C,290.440C and 289.930C at axial lengths 0.1, 0.5 and 0.9respectively. The results indicate an increase in the solidtemperature due to heat transferred by the hot incoming gasto the catalyst surface. At dimensionless time 14.70 the

solid catalyst temperatures are 441.020C, 428.890C and420.160C at axial lengths 0.1, 0.5 and 0.9 respectively. Theresults indicate a mixed effect of an increase in the solidtemperature due to heat released by the exothermic reactionstaking place on the catalyst surface and also the catalyticsurface being at a higher temperature than the gas causes theheat to be transferred from the solid to the gas phase,thereby resulting in the decrease of the solid temperaturealong the converter length.

Fig. 4 represents the variation of solid and gastemperature in axial direction with respect to time. Thecomparison is shown in axial direction for dimensionlesstimes 10.00, 13.00, 14.00 and 14.70. Already their effectshave been discussed in Figs. 2 and 3 respectively. Also from

Fig. 4 it is observed that at later values of time the solidtemperature at the entrance is higher than the gastemperature due to catalytic reactions taking place on solidsurface. However towards the exit gas temperature isincreased from its inlet value of 3250C indicating gas takingaway excess heat from the solid.

V. CONCLUSION

In the present study development of a model capable ofsimulating the components of an exhaust gas after-treatmentsystem using one-dimensional model for predicting thehydrocarbon propylene emissions from cold start conditionswas carried out.

Simultaneous changes in gas concentrations, gas

temperature and solid temperature, were analysed forpropylene gas present in the exhaust. It was observed thatinitially when the converter is started, the solid temperaturebeing very low does not favour the start of catalyticreactions. The conversion of propylene gas starts only afterthe incoming gas has heated the solid catalyst to itsoperating temperature.REFERENCES

[1] R.M. Heck, S. Gulati, and R.J. Farrauto, The application ofMonoliths for gas phase catalytic reactions, Chem. Engng. J., vol.82, 2001, pp. 149-156.

[2] J.M. Keith, H.C. Keith, D.T. Chang, and Jr Leighton, Designing afast igniting catalytic converter system, AIChE J., vol. 45, 2001, pp.603-614.

[3] W-S. Kim, A Computational approach to Modeling the Warm-Up

behavior of Automotive catalytic converter for reducing cold-startemissions, Proc. 2nd International Conference on ComputationalHeat and Mass Transfer, COPPE/UFRJ - Federal University of Rio deJaneiro, Brazil, Oct. 2001.

[4] R.H. Heck, J. Wei, and J.R. Katzer, Mathematical Modelling ofMonolithic Catalysts, AIChE J., vol. 22, 1976, pp. 477-484.

[5] T. Ahn, W.V. Pinczewski, and D.L. Trimm, Transient performanceof catalytic combustors for gas Turbine applications, Chem. Eng.Sci., vol. 41, 1986, pp. 55-64.

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[6] S. Chauhan and V.K. Srivastava, Modeling catalytic andhomogenous combustion of hydrocarbons in Monolithic Converters,Chemical Product and Process Modeling, vol. 3, 2008, art. 10

[7] S. Chauhan and V.K. Srivastava, Modeling exhaust gas pollutionabatement: Part I- single hydrocarbon Propylene, Computers andMathematics with Applications, vol. 55, 2008, pp. 319-330.

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