Temperature fronts and pulses on catalytic ribbons

Physica A 188 (1992) 68-77 North-Holland

Temperature fronts and pulses on catalytic ribbons Dan Luss Department of Chemical Engineering, University of Houston, Houston, TX 77204-4792, USA

Infrared temperature images show that standing and moving temperature fronts and moving temperature pulses exist on the surface of an electrically heated thin catalytic ribbon on which a chemical reaction occurs. The dynamic behavior when the electrical current maintains a constant resistance differs from that under constant current heating. A mathematical model shows that when the reaction leads to activation-deactivation of the catalytic surface four qualitatively types of pulse motions exist in addition to chaotic temperature patterns.

I. Introduction

Electrically heated catalytic wires and ribbons have been used for m a n y years to study the kinetics and dynamics of m a n y reactions [1-6]. The advantages of these systems include: easy determination of the reaction rate f r o m the rate of heat generation, simple geometry, easy and rapid t e m p e r a t u r e control and lack of kinetic disguise by interpellet diffusion. The electrical heating is usually done either in the constant t e m p e r a t u r e m o d e , in which a controller keeps the ribbon at a constant set resistance [5, 6], or in the constant current m o d e [6]. Most early studies analyzed and interpreted the data assuming that the surface t e m p e r a t u r e and concentration of the reactants are uniform [1-6]. H o w e v e r , recent theoretical and experimental studies indicate that this is not always valid, and that symmetry breaking may lead to formation of both stationary and spatio-temporal t e m p e r a t u r e patterns. These patterns m a y cause large deviation between the observed rate and that corresponding to a uniform surface at the average temperature. Thus, m a n y of the previously p r o p o s e d kinetic models and associated parameters may be falsified by these patterns. T h e discovery of these nonuniform temperature patterns and waves raises some important and interesting questions, namely: What are the various types of spatio-temporal patterns and their characteristic sizes and frequencies? Which pattern features are universal and which are reaction specific? What is 0378-4371/92/$05.00 (~) 1992- Elsevier Science Publishers B.V. All rights reserved

D. Luss / Temperaturefronts and pulses on catalytic ribbons

69

the influence of initial conditions and symmetry on these patterns? What are the stability features of these patterns and what types of bifurcations between patterns exist? Finally, it is of interest to know the organization of regions with qualitatively different patterns in the parameter space. I shall outline here the dynamics of electrically heated catalytic ribbons, and especially of one kept at a constant resistance, i.e., average temperature.

2. Stationary fronts- constant resistance experiments The coupling between many catalytic exothermic reactions may lead to steady-state multiplicity. Razon and Schmitz [7] reviewed recently the corresponding literature. Some of the multiplicity features, such as the ignition temperature, have been used to determine kinetic parameters [2-4]. The electrical resistance of a catalytic ribbon is usually a linear function of temperature, i.e., R ( T ) = R(Ta) [1 + a ( T -

(1)

Ta) ] ,

where T a is the ambient temperature. The energy balance of the ribbon can be written as OT pcpA - ~ = A A

oZT OX 2

+ a(Qg + QE - QR)

(2)

where A is the cross section of the ribbon, a the perimeter, A the effective conductivity. Qg, QE and QR are the rate of heat generated by the reaction, the electrical heating, and heat removal. Specifically, (3)

Qg = ( - A H ) r ( T ) ,

QR. QE h+(h . . . a

a

1) .

T - T. + ~

(4)

A uniform temperature steady states satisfies the relation Qg = Q R - QE.

(5)

Fig. 1 shows the sigmoidal Qg and the essentially linear QR- QE" The intersections between the curves are steady-state solutions. When the prescribed temperature is between A and C (defined by eq. (6)) in fig. 1 and the end effects are small, a nonuniform steady state may be obtained in which part

D. Luss / Temperature fronts and pulses on catalytic ribbons

70

QR " QE

QR" Q~

-h/ct

Fig. 1. Graphical determination of steady-state solution. A standing front can be obtained when the two hatched areas are of equal size.

of the ribbon is at the low temperature A and the rest at the high temperature C. A sharp temperature front separates the two regions. The relative size of the two regions depends on the prescribed average temperature. The temperatures A and C at the edges of the standing wave satisfy the condition [8] c

f ( Q g - QR - Q E ) dT = O. A

(6)

Thus, the two hatched areas in fig. 1 must be of equal size. Sheintuch and Schmidt [9] were the first to claim that such solutions must exist in order to explain certain observed multiplicity features. Lobban et al. [10] found experimentally these standing front profiles by an IR imager during the oxidation of ammonia in air on a platinum ribbon. Typical results are shown in fig. 2.

3. Moving temperature w a v e - constant resistance experiments

In many catalytic reactions the activity of the surface is modified by the chemical reaction. In such cases, a stationary, sharp temperature front cannot exist for a ribbon kept at constant resistance, i.e., average temperature. Instead moving high temperature pulses, bounded by sharp fronts, are found. An experimental study of the oxidation of propylene on a Pt ribbon revealed the existence of back and forth moving high temperature pulses [11]. At relatively high average temperatures the pulse occupies a relatively large

D. Luss / Temperature fronts and pulses on catalytic ribbons

I

300

I

71

I

T,,+= 282 °C

1.0% N H 3

?

200

0 10-8

-4

0 Position

4

8

( cm )

Fig. 2. Standing fronts observed during the oxidation of 1% ammonia in air on a platinum ribbon kept at various constant temperatures via electrical heating [10]. fraction of the ribbon length (fig. 3). The leading and trailing fronts tend to m o v e at different velocities causing a periodic change in pulse length. This leads to a periodic change in the observed reaction rate. Moreover, the controller, which maintains a constant average temperature, causes periodic small changes (order of 20°C) in the t e m p e r a t u r e of the pulse. For average t e m p e r a t u r e s close to the extinction point the high temperatures pulses are rather short (fig. 4) and their m o v e m e n t leads to chaotic changes in the observed rate. The distinction between periodic and chaotic behavior is related mainly to the m o v e m e n t of the t e m p e r a t u r e pulse. The overall reaction rate oscillates at a higher frequency and in a much less regular fashion than the local t e m p e r a t u r e . The power spectrum of the overall reaction rate decays exponentially, while that of the local t e m p e r a t u r e decays as a power law. 4OO

i

i

300

~.

200

"i',

Tavg.,~= 269 C

100

-4

0 Position ( c m )

\

4

Fig. 3. Profiles of three moving temperature pulses (a, b, c) on a platinum ribbon kept at average temperature of 269°C on which 0.2% propylene in air is oxidized [11].

72

D. Luss / Temperature fronts and pulses on catalytic ribbons

Time (sec)

0.2~O0

750,

1000,

1250

E 0.22

0.20

0.18 400

i

i

i

i

i

i

-4

0

4

I

30O

200

1008

8

Position ( cm ) Fig. 4. Chaotic reaction rate and corresponding moving temperature pulses during the oxidation of 0.2% propylene on a platinum ribbon kept at an average temperature of 229°C [11].

Sheintuch [12, 13] analyzed the behavior of the moving temperature pulses, assuming that the reaction fronts are localized, either due to nonuniformities in the ribbon or to slow front propagation. His analysis predicts that antiphase temperature oscillations exist so that two or more sections of the ribbon oscillate out of phase to maintain the prescribed average temperature. While the analysis predicts, as observed, complex oscillations in the reaction rate, it fails to predict the back and forth observed movement of the temperature wave. We have recently studied a model of a ribbon which undergoes deactivationactivation [14]. It was found that in addition to an irregular chaotic temperature pattern four types of pulse motion were observed: - A n t i p h a s e oscillations in which the temperature increases on one side and decreases on the other while the front position is stationary during most of the cycle (fig. 5). - Unidirectional moving pulse, generated next to one support and disappearing at the other (fig. 5, temperature contours in fig. 6a).

D. Luss / Temperature fronts and pulses on catalytic ribbons

4 ~I

'"

73

i'41

%__

UNI-DIRECTIONAL i

I

Fig. 5. Schematic of the four types of pulse motions - antiphase oscillations, unidirectional pulse, source point, and back and forth moving pulse.

a

b

c

POSITION Fig. 6. Temperature contours o0served for (a) unidirectional pulse, (b) pulses emanating from a source point, (c) back and forth moving pulse.

74

D. Luss / Temperature fronts and pulses on catalytic ribbons

- A source point from which two pulses emanate and move in opposite directions (figs. 5, 6b). - B a c k and forth moving pulse (figs. 5, 6c). O t h e r motions, which are combinations and transitions among these, were found. It should be noted that in a study of the endothermic decomposition of methylamine on an electrically heated ribbon both antiphase oscillations [15] and pulses emanating from a source point [16] were observed. However, these patterns have not yet been observed for exothermic reactions. R a t h e r intricate transitions between the various pulse motions were noted. The transition from periodic to chaotic motion was usually via a quasiperiodic behavior. The transition from back and forth to unidirectional motion was gradual and not abrupt, and occurred via a continuous change in the fraction of the unidirectional waves.

4. Moving f r o n t - constant current experiments Kinetic experiments are sometimes carried out using constant current electrical heating, as this mode of operation is easier to implement than constant resistance heating [6]. In these cases no feedback and interaction exists between the electrical heating and the chemical reaction rate. Thus, it is interesting to determine if t e m p e r a t u r e pulses can be formed in the system and their nature. Recent experiments by Philippou [17] on the oxidation of propylene on a Pt ribbon heated by a constant electrical current indicate that t e m p e r a t u r e pulses exist also in this system for a bounded range of currents exceeding that at extinction. Regions of operating conditions under which oscillations in the overall rate are observed are denoted as O in the bifurcation m a p (fig. 7).

1.2

•

-

-

,

•

•

.

S N P

i I

i + ~

0 E

•~ 1.1

•

-

I

0.9

I

Oscillatory Extinguished

1.0

•-

•

Ignited

E

.

.

.

.

.

O.2

.

.

.

.

0.4

.

.

SL 0.6

% Propylene Fig. 7. Map of regions with qualitatively different dynamic features. SN refers to a saddle-node bifurcation, SL saddle-loop, H 1 supercritica| Hopf, H 2 subcritical Hopf and SNP saddle-node of periodic orbits [17].

D. Luss / Temperature fronts and pulses on catalytic ribbons

0 ~00o, .~ m.~

0.5

850

900

Time (sec) 950 1000 1050 1100 a

0.2% Propylene I = 1.04 (Amps)

0.4

~:~ 0.3

~

j

,

o~" 300f400 . . . . .~. . . . . . . . . . . .b. . . . . . . . . . . . . . .

~]

'°°I/

100 n . . . . . . . . . . . . . . . . . . 11 400~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~

i

,

I

i

i

75

,

I

,

i

,

I

,

i

,

I

,

400~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i

,

I

,

\1/

.

1

\1 Position (em) Fig. 8. (a) Oscillation in reaction rate during the oxidation of 0.2% propylene in air on a platinum ribbon heated by a 1.04 ampere current; (b-d) corresponding transient temperature profiles [17].

T h e thermal images showed that these oscillations are always caused by back and forth m o v e m e n t of one of the thermal fronts, which bound the high t e m p e r a t u r e zone (fig. 8). The m o v e m e n t starts at a support, stops at about the middle of the ribbon, and then reverses its direction. In contrast to the case of constant average t e m p e r a t u r e only one front is moving during the oscillation. T h e t e m p e r a t u r e s of the high and low t e m p e r a t u r e region do not change and the only variation between pulses is the distance they travel before reversing their direction. Thus, all t e m p e r a t u r e oscillations are between two fixed levels while the overall rate fluctuates between various values, as these depend on the distance the front moves (fig. 9). The moving t e m p e r a t u r e fronts are initiated at both supports with no preference to either side. The experiments raise the interesting question of what is the mechanism which initiates the front m o v e m e n t and what causes it to stop and reverse its direct. The fact that fronts are formed on both sides of the ribbon indicates that this behavior is not caused by an intrinsic nonuniformity in the activity of the ribbon or flow field.

76

D. Luss / Temperature fronts and pulses on catalytic ribbons ,

,

f

'

I

I

I

I

,

,

,

300

f

I

i

'

,

l

~J

-t

250

200 0.60

' ' I

I

I

i

i

I

i

i

i

i

i

r

I

i

i

i

I

i

i

i

h

i

i

I

0.50

"" 0.40 Propylene

0.2% I

=

1.04

(Amps)

0.30 0

0

0 Time (sec)

3000

000

Fig. 9. Oscillation in the local temperature and in the overall reaction rate during the oxidation of 0.2% propylene on a platinum ribbon heated by a 1.04 ampere current [17].

5. C o n c l u d i n g

remarks

Many previous studies of the steady or oscillatory rate of catalytic reactions on electrically heated ribbons assumed that the state of the surface is uniform. R e c e n t experiments show that this is an erroneous assumption, which may lead to pitfalls in the development of a kinetic model explaining the behavior. The recent d e v e l o p m e n t of instrumental techniques capable of detecting changes in local surface t e m p e r a t u r e , concentration and structure [18] should enhance our knowledge and understanding of these spatio-temporal structures. That information can hopefully be used to carry out reactions which will not proceed on uniform surfaces, and to assess the impact of the t e m p e r a t u r e fronts and pulses on the p e r f o r m a n c e of commercial catalysts.

Acknowledgements

Thanks are due to the NSF for support of this research and to Professor M. Sheintuch, Dr. G. Philippou and Mr. U. Middya for helpful discussions.

D. Luss / Temperature fronts and pulses on catalytic ribbons

77

References [1] W. Davies, Philos. Mag. 17 (1934) 233; 19 (1935) 308. [2] D.A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics (Plenum, New York, 1969). [3] L. Hiam, H. Wise and S. Chaikin, J. Catal. 10 (1968) 272. [4] C.G. Radar and S.W. Weller, AIChE J. 20 (1974) 515; 21 (1975) 176. [5] M.A. Cardoso and D. Luss, Chem. Eng. Sci. 24 (1969) 1698. [6] Yu.E. Volodin, V.V. Barelko and P.I. Khalzou, Chem. Eng. Commun. 18 (1982) 271. [7] L.F. Razon and R.A. Schmitz, Chem. Eng. Sci. 42 (1987) 1005. [8] V. Barelko, I.I. Kurochka, A.G. Merzhanov and K.G. Shkadinskii, Chem. Eng. Sci. 33 (1978) 805. [9] M. Sheintuch and J.W. Schmidt, Chem. Eng. Commun. 44 (1986) 33. [10] L. Lobban, G. Philippou and D. Luss, J. Phys. Chem. 93 (1989) 733. [11] G. Philippou, F. Schultz and D. Luss, J. Phys. Chem. 95 (1991) 3224. [12] M. Sheintuch, Chem. Eng. Sci. 44 (1989) 1081. [13] M. Sheintuch, J. Phys. Chem. 94 (1991) 5889. [14] U. Middya, M. Sheintuch and D. Luss, Physica D, submitted for publication. [15] G.A. Cordonier, F. Schuth and L.D. Schmidt, J. Chem. Phys. 91 (1989) 5374. [16] G.A. Cordonier and L.D. Schmidt, Chem. Eng. Sci. 44 (1989) 1983. [17] G. Philippou and D. Luss, J. Phys. Chem., in press. [18] G. Ertl, Science 254 (1991) 1750.