Numerical analysis of the transient performance of high-temperature monolith catalytic combustors: Effect of catalyst porosity

Pergamon

Chemical Enoineering Science, Vol. 50, No. 14, pp. 2255-2262, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All fights reserved 0009-2509/95 $9.50 + 0.00

0009-2509(95)00074-7

NUMERICAL ANALYSIS OF THE TRANSIENT PERFORMANCE OF HIGH-TEMPERATURE MONOLITH CATALYTIC COMBUSTORS: EFFECT OF CATALYST POROSITY A. N A K H J A V A N , t P. B J O R N B O M , M. F. M. Z W I N K E L S and S. G. J,AR,~,S Royal Institute of Technology, Department of Chemical Engineering and Technology, Chemical Technology, S-100 44 Stockholm, Sweden (Received 5 May 1994; accepted in revised form 1 February 1995)

Abstract--The transient response of a high-temperature monolith catalytic combustor was studied under various conditions. The aim of the study was to elucidate the significance of the catalyst porosity on the catalyst light-off. Numerical experiments were carried out using a one-dimensional mathematical model, which accounts for both heterogeneous and homogeneous reactions and allows heat conduction in the solid phase in the axial direction. The most significant feature of the model is that it considers the reactions on the interior surface as well as on the exterior surface of the catalyst. This allows us to study the significance of the catalyst porosity on transient behavior. The effect of the porosity was studied by varying the interior surface area, the washcoat thickness and the effective diffusivity. Each of these parameters is a measure of the effect of the catalyst porosity, directly or indirectly. The results of this study show that all of these parameters have an effect on the transient performance of the catalytic combustor except when the catalyst is preheated to a very high temperature. Thus, it is concluded that larger catalyst surface area will benefit catalytic ignition. The results also show that the effect is more important at transient state than at steady state and that it depends on the type of fuel used for the combustion.

INTRODUCTION Increasingly severe NOx emission regulations and the constant desire to achieve a more efficient combustion has caused an increasing interest in high-temperature catalytic combustion in recent years (Arai and Machida, 1991). Development work in this area is increasingly supported by theoretical studies. Reaction engineering calculations and modeling have proven to be important tools and direct utilities in industrial catalyst development (Beekman and Hegedus, 1991). Several numerical and computational analyses have been completed in high-temperature catalytic combustion, A feature of all models is that they use an apparent reaction rate (Lee, 1985), with a temperature dependence in the form of an Arrhenius expression and, as a result, consider the diffusion and reaction on the interior surface of the catalyst only under certain restrictive assumptions as discussed below [e.g., K u o et al. (1971); Cerkanowicz et al. (1977); Prasad et al. (1983); Bruno et al. (1983); Ahn et al. (1986) and Groppi et al. (1993)]. Pfefferle and Pfefferle (1987) have argued that the catalyst surface area has effect neither on combustion at opening temperature nor on light-off. On the other hand, Arai and Machida (1991) have claimed that a larger catalyst surface area should be preferred since catalytic surface reaction is required to heat the catalyst to the ignition temperature. They have neverthe-

tAuthor to whom correspondence should be addressed.

less suggested further study in this area to investigate the significance of this effect. The main objective of the current study was to investigate the effect of the catalyst porosity or, basically, the interior catalyst surface area on the transient performance of a high-temperature monolith catalytic combustor with emphasis on its effect on the heating of the catalyst to the ignition temperature. For that purpose a mathematical model, similar to the model developed by Ahn et al. (1986), was developed. This is a one-dimensional model that considers both heterogeneous and homogeneous reactions and allows heat conduction in the axial direction in the solid phase. However, the intrinsic reaction rate, combined with an effectiveness factor, is used in the model presented in this article and as a result the present model accounts for the pore diffusion in the washcoat and the reaction on the interior surface of the catalyst in a more general way than the above-mentioned models based on the apparent reaction rate. This is important in a study of the present type since the conditions during a light-off process may vary from the chemical reaction being rate-limiting, via the influence of strong pore diffusion resistance to conditions where external mass transfer resistance is rate-limiting. In conflict with this an apparent reaction rate equation, with temperature dependence of the Arrhenius type, is valid only under conditions where the chemical rate is invariably rate-limiting or under conditions with an invariable influence of strong pore diffusion resistance, the so-called falsified kinetics conditions (Fogler, 1992).

2255

A. NAKHJAVANet al.

2256

To examine the effect of the porosity a factorial (numerical) experiment was carried out. The interior surface area, the washcoat thickness and the effective diffusivity were the parameters that were varied in this experiment. Since the significance of the effect of the interior surface area depends on how fast the fuel reacts on the catalyst surface (Levenspiel, 1972; Lee, 1985; Fogler, 1992), the examination was performed for three types of fuel (with different intrinsic reaction rates on the catalyst). MODELING

A monolith consists of a large number of parallel channels that can be assumed to be identical. Thus, the model was developed only for one channel. This means that the interaction between channels was neglected. It has been suggested that such an interaction should not be ignored (Worth et al., 1993). However, since this study focuses more on comparison of results than on analysis of one result alone, a small error, caused by this assumption, should be negligible. The monolith can be made from one of several materials (e.g,, ceramic materials or metals) which is coated with catalyst material (washcoat). The washcoat is usually composed of modified A1203 with impregnated Pt or Pd (Zwinkels et al., 1993). The heterogeneous chemical reactions will take place on the Pt or Pd surface. An ideal plug-flow reactor (one-dimensional model) with homogeneous premixed fuel/air was assumed. The one-dimensional model can describe the process as well as a two-dimensional one but with a considerable reduction in computational effort (Ahn et al., 1986). A gas velocity equal to 18.0 m/s was used which results in a laminar flow. In addition the following assumptions were made to develop the model. • Accumulation of mass and energy in the gas phase is negligible, quasi-static gas-phase approximation (Ahn et al., 1986). • Axial dispersion in the gas phase is negligible (Ahn et al., 1986). • Thermal radiation may be neglected (Ahn et al., 1986). • Radial temperature gradients in the solid phase are negligible, due to the high solid conductivity and small wall thickness (Ahn et al., 1986). • The pressure drop along the reactor is very small; thus, a constant mean pressure was assumed (Ahn et al., 1986). • The physical properties and the velocity of the gas are only a function of gas-phase temperature. • The physical properties of the monolith are constant and independent of monolith temperature. • The physical properties of the washcoat are constant and independent of the washcoat temperature. The same physical property values as for the monolith material was assumed. Although there is usually a difference in porosity, etc., between washcoat and monolith material this ap-

proximation appears to be sufficient for the purpose of the present study since we are more interested in the patterns of change rather than in absolute values. • The surface reaction rate is expressed by the following equation: r~=k°exp{-E~)/C

~

\ RT"J / s.

(1)

This is the intrinsic kinetic rate and does not include the diffusion in the catalyst pores (Kuo et al., 1971). The choice of the surface reaction rate is discussed in detail later in this paper. • The global kinetic rate is used for the gas-phase reaction rate: 0 I/--Eg \ g g rg = kg exp ~-ff-~g ) C s C o 2 .

(2)

This is despite the fact that a detailed kinetic is needed to describe the homogeneous reaction because of the presence of radicals. However, as mentioned earlier, this study is based on comparative analysis and the focus of the study is the heterogeneous reaction, thus the global kinetic rate should fulfil the requirement of the study. • Both the surface and the gas-phase reactions are assumed to be irreversible (with complete combustion of the fuel). The assumed reaction is as follows: C, H4,, + (n + m)Oz ~ nCO2 + 2mH20. Using the principles of chemical engineering, applying the chemical reaction rate laws, material and energy balances, diffusion laws and the assumptions made above, the following equations were obtained: Gas-phase balance equations: mass balance ~x

+ aky(C°Y - Css) I + ro = 0

(3)

with the boundary conditions (C})~=o = C 7 C } = C ~ '° u=o °

atx=0 atx=0

(B1)

(B2) (B3)

energy balance c ~ , p ° l g ° ~ + trh(T o - T~) -- r, A H = 0

(4)

with the boundary condition (Tg)x=o = T °. Solid-phase balance equations: mass balance /~2 C ~ \

6dwS = k A C ~ -- C 7)

(B4)

(5) (6)

Numerical analysis of the transient performance of high-temperature monolith catalytic combustors with the boundary conditions

(0%

=o

/.,,

2257

Solving, combining and expanding all of these equations results in the following system of non-linear partial differential equations:

/~c~\

= o~6(roAH -- ~400 + ~sOs)

:

:

(12)

-

from eq. (9), energy balance

1 Ou _ aOg

~T~= ~ f ~ S A H

Cp, s P s ~ ' t

with the boundary condition

~T~

--=0

atx=0,L

dx

(13)

+ 2~-~t32T~+ ~ ( T o - T~) (7)

(B7)

substituting the gas-temperature spatial derivative in eq. (12) by eq. (13) and then substituting the gasvelocity spatial derivative in eq. (3) by the foregoing equation gives ~qJ

The additional equations resulting from stoichiometry and the assumptions made are as follows: - ~6u?(cc4®g- ~s®~)

(

~ (uCo~) = I - ~b_l b --

(uC})Oj

(8)

= constant

(9)

pu = constant.

(I0)

r,

dO~

d2®,

dz = ~TWf~o.) + ~ s - - ~ - + ~90g - ~100~ (15) where r g = c q l k o [ 1 - d p ( 1 - O g ~ F ) ] (~---~)

The initialconditions are as follows:

T , = T o for allx

(I1)

To=T °

for0
(I2)

C~=0

for0
(I3)

To = T o f o r x = 0

04)

C ) = C ~ "° f o r x = 0 .

(I5)

T,

= ~--6, To

O,

r~

fll

q

k: +

(18)

6k,

kf f12 = De'I® dwk f

(19)

,/ Siks"~ l/2

Finally, the constants used in these equations are as follows:

The variable F, the external diffusion-limiting factor, is defined as follows: C~-

=

(17)

c~

to

=

fll + f12tanh(O)

= -&-6, ~ = Cg:'° T~

~=-g, ~ - - - .

F

(16)

1

f(o.) = 1

Since it is always more convenient to work with dimensionless variables, the following variable substitutions are made:

o~

(14)

C 7 × 100%.

(11)

ak: ~1

- - - -

C}'°An ~

~2

TO

--4 cep

0 ~

O~3 =

kfC~' o toAH cv,spsTOsd '

~7= (Z9 ~

to T° h 0 ' Cp.~p~T~ d

C0,OCO

P u° = -L-' ~ = - A '

to2 L2ce, sp~

°is

toh ce,~p~d

~I0

- E~

2--

6

c~°a

T° cep°O

where 8

- - - -

1

a4 = oky T O, as = a k f T O, o~6 =

When C~~ goes to zero, it means that the heterogeneous reaction is totally limited by fuel mass transfer from gas to solid phase (external diffusion) and when C~" approaches C~, it indicates that the heterogeneous reaction is totally controlled by catalyst surface reaction. Hence, the following definitions are true. • The heterogeneous raction is totally controlled by external diffusion when F goes to 100%. • The heterogeneous reaction is totally controlled by catalyst surface reaction when F goes to 0%.

=

Ae A,

2258

A. NAKHJAVAN et al. THE CATALYTIC RATE EXPRESSION

As discussed earlier, the catalytic reaction rate expression used in this study is the intrinsic reaction rate. The apparent reaction rate is calculated continuously using eq. (17). This allows us to explore the significance of the catalyst porosity by varying the interior surface area, the washcoat thickness and the effective diffusivity in eq. (17). Note that the pore diffusion-related rate coefficient of eq. (17) (kffl 2 tanh(~)) cannot be substituted by a rate coefficient with an Arrhenius type of temperature dependence. For low values of the Thiele modulus, @, the temperature dependence of this coefficient reflects the activation energy of the chemical reaction while for high values of * we obtain an apparent activation energy of about half the activation energy of the chemical reaction. For intermediate D-values the temperature dependence of the pore diffusion-related coefficient cannot be described by an Arrhenius expression at all (Levenspiel, 1972; Lee, 1985; Fogler, 1992). The constants in the intrinsic catalytic rate expression were obtained from Kuo et al. (1971). These constants were found experimentally for two groups of fuels, slow oxidizing (HC I) such as methane and fast oxidizing (HC II) such as propene. It was observed by Kuo et al. that there existed influence of pore diffusion resistance at high temperatures. However, the intrinsic reaction rates and activation energies were obtained from data at low temperatures, where the chemical reaction was rate-limiting in their experiments. An imaginary group of fuels, extremely fast oxidizing (HC III), is also introduced in this paper. The idea was to investigate the possibility of conditions where the heterogeneous reaction approaches external mass transfer rate limitation very quickly. Under these conditions the influence of the interior surface area of the washcoat may be neglected even during light-off of a relatively cold washcoat. If such conditions are at all possible they should occur for an extremely fast oxidizing fuel. The constants in the rate expression for this fuel were calculated assuming that this fuel oxidizes as many times faster than HC II and HC II oxidizes faster than HC I. Table 1 lists the values of these intrinsic rate constants. It should be noted that these constants include information about the type of the catalyst. NUMERICAL S O L U T I O N M E T H O D

Using the finite difference method (Davis, 1984), the present system of nonlinear partial differential equaTable 1. Kinetic parameters of the fuel oxidation on the catalyst k° (cm/s) HC I HC II HC III

0.52 1.47 x 103 4.15 x 106

E, (J/mol) 64.58 × 83.06 x 101.58 x

10 3 10 3 10 3

tions was reduced to a system of nonlinear algebraic equations (Ames, 1992). The central difference approximation was used for the spatial derivatives and the backward difference operator for the time derivative. A program (in FORTRAN) was developed to solve this system of nonlinear algebraic equations. Subroutines from the NAG FORTRAN Library were used in this program to solve the system of nonlinear algebraic equations. These subroutines are based on the MINPACK routine HYBRD1 (More et al., 1974). Starting from initial values, the program solves the equations (the value of all variables at time t + dt for all x). Using the results of previous time step calculations the program follows the same procedure to solve the equations for the next step in time. The program continues to propagate in time until no changes are observed (or can be stopped before that if desired). RESULTSAND DISCUSSION The operating conditions used in this study were as follows. • The constant average pressure along the reactor was equal to 1 atm. • An equivalent ratio, ~b, was equal to 0.47 was assumed. • The gas inlet temperature was equal to 600K (950 K when HC I was used as a fuel). • The gas velocity at the inlet was equal to

18.0 m/s. • The monolith was preheated to 400 K. In addition to the above parameters the data listed in Tables 1-3 were use to stimulate the model. Table 2 lists the properties of the monolith used. For the base case the diffusivity of fuel was equal to 0.04cm2/s (Kuo et al., 1971). For this case typical values for the BET surface area and the wash coat thickness were chosen, 50m2/g and 0.005 crn, respectively. For each of the three fuels (HC I-HC III) numerical experiments were carried out according to a 2 3 factorial design using the effective diffusivity, the interior surface area and the washcoat thickness as independent variables. This factorial design is given in Table 3 together with the values of the + and - levels of the independent variables. The model was simulated for all three groups of fuels for the base case. To study the mechanism of the Table 2. Properties of the monolith (ceramic) Length (cm) Width (cm) Cell a r e a (cm 2) Wetted perimeter (cm) Thermal conductivity (J/cm s K) Density (g/cma) Heat capacity (J/g K) Wall thickness (cm)

10 0.15 2.3 x 10-2 0.62 2.32 x 10- 3 2.5 0.92 0.015

Numerical analysis of the transient performance of high-temperature monolith catalytic combustors Table 3. The variable values used in the factorial experiment

2259

Gas- and solid-phase temperature profiles ( H C II) 1400

+

:

I

~

v

1200

De, f

(cm2/s)

S (cm2/cm3) dw (cm)

0.l 100 × 104 0.01

0.01 10 × 104 0.001

catalytic combustion, the transient solid- and gasphase temperatures along the reactor and the conversion of fuels were followed (Figs 1 and 2, respectively). The change of external diffusion limitation were also studied using the variable F from eq. (11) (Fig. 3). Finally, to investigate the importance of the pore diffusion on the reaction rate, the Thiele modulus ¢I) from eq. (20) was also examined (Fig. 4). Figure 1 gives the temperature profiles, when HC II was used as a fuel for the base case. As Fig. 1 shows, at the beginning (t = 0-3 s), the gas is hotter than the solid and the heat is transferred from the gas phase to the solid phase. This continues until the solid temperature is high enough to allow combustion on the catalyst (t > 3 s). The heat produced by the heterogeneous reaction increases the solid temperature and now the heat is transferred from the solid to the gas. The gas temperature increases along the reactor from the inlet. This continues until the gas temperature is high enough to allow the homogeneous reaction (t = 25 s) at the outlet of the reactor. The gas-phase reaction is fast and the heat released from the reaction increases the gas temperature rapidly. The pattern was the same for HC III; however, the heterogeneous reaction starts earlier and consequently the process reaches steady state faster. When HC I was used no reaction took place when simulating with the gas inlet temperature equal to 660K. The temperature was increased to 950K and then the heterogeneous reaction started but no homogeneous reaction occurred. Note that the conditions were still far from steady state. Figure 2 shows the conversion of these fuels vs time for the base case. As expected, HC III lights off faster than HC II and HC II faster than HC I. For fuels HC II and HC III, after reaching a conversion of near 80%, the process approaches a condition where the heterogeneous reaction is almost totally controlled by external diffusion (the relatively flat part of t h e curves). The subsequent part of the curves indicate the start of the homogeneous reaction. The conversion of HC I is very low even though an inlet gas temperature of 950 K was used as the operating temperature. So for HC I neither mass transfer limitation nor homogeneous reaction is observed. As mentioned before, to illustrate the mass transfer limitation from gas to solid phase exclusively, the variable F was plotted vs axial direction of monolith at some particular times. Figure 3 shows the results when HC II was used as a fuel for the base case. F starts from 0% (no mass transfer limitation) and c a n approach a value of 100% (total mass transfer limita-

1000

400'

v

~

• Ts-0 × Tg-15 + Ts-25

200 ~/

0

|

I

I

I

I

v

v

w

v

v

~

I

I

• Tg-3 A Ts-3 * Ts-15 • Tg-25

I

I

|

I

0.l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 x/L

Fig. 1. Transient solid- and gas-phase temperature profiles along the reactor. HC II is used as fuel. Notation: for example, Tg-25 indicates gas-phase temperature at t = 25 s.

Exit c o n v e r s i o n vs time

e~ O

:.col,

-

.,cm

d 0

5

to

15

20

25

30

35

40

T i m e (see)

Fig. 2. The exit conversion vs time, for fuels HC I-HC IlL

tion). As expected F varies greatly in the axial direction, because of the temperature profile in the monolith. This is true until reaching the steady state. The same pattern was observed for HC III, though F increases much faster. In the case when HC I was used as a fuel, F does not exceed 10%. This means that catalytic combustion of HC I is constantly controlled by the surface reaction rate. The significance of the Thiele modulus is that one single quantity represents the importance of pore diffusion on the reaction rate (Lee, 1985). A reaction is unaffected by pore diffusion resistance, when the Thiele modulus is small (,~ 1), and strongly affected when the Thiele modulus is large ( > 3). Figure 4 shows how the Thiele modulus varies along the monolith for the base case. It can be seen how the reaction is transferred from the diffusion-free zone to the diffusion-limitedzone. Figure 4 gives the results of the simulation when HC II was used as a fuel. For HC

A. NAKHJAVANet al.

2260

The external diffusion limiting factor (HC II)

80'

7O -

~

6o' 5O 4O 30

• t=-15 s

A t=20 s × t=25 s

2O 10q 0.l

0.2

0.3

0.4

0.5

0.6 0.7

0.8

0.'9

I~0

x/L Fig. 3. The mass transfer limiting factor "F" along the reactor. HC II is used as fuel. Notation: for example, t = 25 indicates F at t = 25 s.

conditions where the effect of the porosity occurs or if the effect is always there. The results of the factorial experiments are illustrated in Figs 5 - 7 which show that the interior surface area is important everywhere. For several of the cases studied in the factorial experiments the chemical reaction is rate-limiting in the whole combustor over the whole time interval studied. This applies to cases 3 - 8 for the slow oxidizing fuel and to cases 7 and 8 for the fast oxidizing fuel. Here the conversion is a function of the product Sd,,, but independent of D e. For all other cases, including all the cases for the extremely fast fuel, the conversion depends on all three of the parameters De, S and dw. The patterns described above for F and the Thiele modulus for the base cases for the three fuel groups (HC I - H C III) are persistent in the factorial experi-

Slow oxidizing fuel (HC I) The thiele modulus (HC II)

1

4

~

~

~"

12

60

• 1=De+S+W+ • 2=oe-s+w+

I

50 [I

8 fi o

6

¢

4

•-

o

~ ~

0.I 0.2

•~.

• t=10 s • t=15 s :, t=20 s

~.

~

t, 3=De+S-W+ x 4=De-S-W+ . 5=De+S+W* 6=De-S+W+ 7=De+S-W-

. l V

,m

I

F

zl~" 2

~ .~

!

" 8=De-S-W-

.¢~ _..,.-Ja=~

0

5

20

30 I--

"

x t=25 s

0.3

.

.

0.4

0.5

.

-

0.6 0.7

g 0.8

-7 0.9

I0

I5

1.0

25

30

35

40

45

50

Time (sec)

x/L Fig. 4. The Thiele modulus along the reactor. H C II is used

as fuel. Notation: for example, t = 25 indicates Thiele modulus at t = 25 s.

III this transfer takes place much faster and for H C I the Thiele modulus remains constantly at values less than one. F r o m the above results and discussion, it is clear that, no matter how fast the fuel oxidizes on the catalyst diffusion limitation will not occur immediately. This suggests that a larger surface area would benefit the ignition of the fuel since the catalytic reaction is not initially diffusion-limited at least for the conditions of the base case. The catalytic reaction may be initially limited by external diffusion, only if the initial catalyst temperature is high enough. To investigate this, simulations were done, using H C II as a fuel, by varying the catalyst preheating temperature and following the Thiele modulus value. It was observed that above 800 K the catalytic reaction is totally limited by external diffusion already from the beginning. In order to explore further this effect of the interior surface on the heating of the catalyst to ignition temperature, the above-mentioned factorial experiments were carried out. The idea was to cover a wide range of conditions to see if there exists a limited area of

Fig. 5. The exit conversion vs time, for fuel HC I. Each curve represents the results of one factorial experiment. Notation: for example, 4 = De-S-W + indicates experiment no. 4, where the low values " - " for effective diffusivity and BET surface area and the high value" + "for wash-coat thickness are used for simulation. Note that curves 3-6 coincide, as do curves 7 and 8.

Fast oxidizing fuel (HC II) too I-* t--Dc+S+W+

4¢'"~FTF-------/--~-. . . .

L" 2=~-s+w+

/

T 1

90 F A 3=De+S-W+ ~,B . p . ~ L x 4=De-S-W+ ,,4r- ~..j8 o / ~ 5=oe+S+W- .¢" . = l /o 6=De-S+W- ~ 70 1-+ 7 = D e + S - W - f 60 - 8=De-S-W-

50

~

-

~ g

,,¢ l('.,¢',m .,~_~

d'_/-

1",,~

='- f

/'a"

~

4o 2O

10 0

0

5

10

15

20

25

30

35

40

Time (sec) Fig. 6. The exit conversion vs time, for fuel HC II. Each curve represents the results of one factorial experiment. Notation: the same as Fig. 5. Curves 3 and 6 coincide, as do curves 7 and 8.

Numerical analysis of the transient performance of high-temperature monolith catalytic combustors Extremely fast oxidizing fuel (HC III)

2261

perature (800 K). The conversion curve shifts slightly to the right or left, respectively. The transfer of F and the Thiele modulus, from low to high values, will also be either slightly slower or faster compared to the base case.

I00 9O

80 -

CONCLUSIONS /.~

A × t • + -

30 20 10 0 . . . .

0

2

4

6

8 Time

I l0

1 12

I 14

2=~-s+w+ 3=De+S-W+ 4=De-S-W+ 5=De+S+W6=De-S+W7=De+S-W8=De-S-Wbase case

I 16

I 18

I 20

(sec)

Fig. 7. The exit conversion vs time, for fuel HC III. Each curve represents the results of one factorial experiment. Notation: the same as Fig. 5. Curves 3 and 6 coincide.

ments as well. These diagrams confirm the conclusions drawn above from Figs 5-7. Although the conditions were varied within such wide limits in the factorial experiments we could not find any case where the effect of the interior catalyst surface area does not exist because of dominating external diffusion limitations.

Using a one-dimensional mathematical model, the transient performance of a high-temperature catalytic combustor was studied. It was observed that the transient performance depends on heat and mass transfer from and to the gas, as well as on the reaction rate with diffusion in the washcoat. The effect of porosity was examined by varying the interior catalyst surface area, the effective diffusivity and the washcoat thickness. It was shown that a larger catalyst surface area would benefit the catalytic ignition. It was also discussed that depending on operating conditions, especially the catalyst initial temperature the importance of this effect varies. The effect of the interior surface area appears to be more important at transient state than at steady state, especially for fuels with slow surface reaction rate.

Acknowledoement--This project has been financed by NUTEK, the Swedish National Board for Technical and Industrial Development. We wish to thank our colleague Christina H6rnell for her suggestions and helpful discussions.

A SENSITIVITYANALYSIS Because of the uncertainties in the mass and heat transfer coefficients, a sensitivity analysis was carried out. This was done by varying both of these parameters separately. The Thiele modulus, the variable F and the conversion of the fuels were followed. First the mass transfer coefficient was decreased by 50%. For fuels HC II and HC III, F now increased much more rapidly; however, F did not change much for HC I and remained below 10%. The Thiele modulus remained at low values (,~ 1), diffusion-free reaction, for HC I. For fuels HC II and HC III the Thiele modulus changed slower, from low to high values than for the base case. The heat transfer coefficient was also reduced by 50%. As expected, the catalytic ignition of the fuel takes place later relative to the base case. The pattern of the conversion curves does not change but only shifts to the right. Both F and the Thiele modulus also change (to higher values) compared with the base case, but the change is slower, It could be concluded that an increase of these parameters would affect the Thiele modulus in such a way that its variation becomes faster relative to the base case. The sensitivity of the outcome to the catalytic activation energy was also examined. This was done for fuel HC II by varying the activation energy by + 10% with the same rate constant at a mean tem-

Ae A~ B1-B7

Ce ce.~ C~ C~ C~~ C~ d dm dw

Df De,f Eg Es F h 11-15

k: k° k° L P rg

NOTATION cross-sectional area of each channel, cm 2 exterior surface of catalyst, cm 2 geometric surface of catalyst, cm 2 the boundary conditions gas specific heat capacity, J/g K monolith specific heat capacity, J/g K fuel concentration in the gas phase, mol/cm 3 fuel concentration in the solid phase, mol/cm 3 fuel concentration on the exterior surface of catalyst, mol/cm 3 oxygen concentration in the gas phase, mol/cm 3 wall thickness ( =dm + dw), cm monolith wall thickness, cm washcoat thickness, cm diffusivity coefficient, cm2/s effective diffusivity coefficient, cm2/s homogeneous activation energy, J/mol catalytic activation energy, J/mol the external diffusion limiting factor heat transfer coefficient, J/s cm 2 K the initial conditions mass transfer coefficient, cm/s homogeneous pre-exponential factor, cm3/ mol s heterogeneous pre-exponential factor, cm/s monolith length, cm wetted perimeter, cm homogeneous reaction rate, mol/cm3 s

2262

R

S t

to

r~ T~ X

Y

A. NAKHJAVAN e t al.

heterogeneous reaction rate, mol/cm2 s average heterogeneous reaction rate, at each radial point, on the catalyst, mol/cm2 s universal gas constant, J/tool K catalyst specific surface area, cm2/cm 3 time, s arbitrary time scale factor, s gas-phase temperature, K solid-phase temperature, K axial distance, cm radial distance, cm

Greek letters ratio of exterior surface area to catalyst geometric area AH combustion enthalpy, J/mol space velocity, 1/s @g dimensionless gas temperature ®s dimensionless solid temperature 2 monolith thermal conductivity, J/cm s K dimensionless axial distance p gas density, g/cm 3 Ps monolith density, g/cm 3 tr ratio of wetted perimeter to cross-sectional area, 1/cm T dimensionless time 0 gas velocity, cm/s ~b fuel to air equivalent ratio ( = actual fuel/air ratio/stoichiometric fuel/air ratio) Thiele modulus dimensionless fuel concentration in the gas phase Superscripts 0 initial condition or gas inlet property O gas phase s solid phase ss catalyst outer surface Subscripts exterior surface e fuel f g gas phase interior surface i monolith m oxygen 02 solid phase S washcoat w

REFERENCES

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