J. Phys. Chem. 1992, 96,6651-6656
6651
Temperature Patterns on a Catalytic Ribbon Heated by a Constant Electrical Current: Propylene Oxidation Georgios Philippou and Dan Luss* Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4792 (Received: January 31, 1992; In Final Form: April 15, 1992)
Complex periodic and chaotic variations in the overall reaction rate were observed during the oxidation of propylene in air on a thin platinum ribbon heated by a constant electrical current. Thermal images showed that the ribbon remained at a constant high temperature for most of the time. The temporal variations in the overall reaction rate are caused by a back and forth movement of either the right or left boundary of the high temperature region. The wave velocity is of the order of 0.3 cm/s. The amplitudeand frequency of oscillations decrease with increasing electrical current and their maximal value is close to the extinction current. The overall reaction rate oscillates at a higher frequency than the local temperature. The power spectrum of the overall reaction rate decays exponentially, while that of the local temperatures decays as a power law. The probability density function of the time interval between successive oscillations in the reaction rate is usually widely spread around two modes.
Introduction Many chemical, biological, and electrochemical reacting systems exhibit periodic, quasiperiodic, and chaotic behavior.'-' The coupling of chemical reactions and transport processes is known to lead in some cases to the formation of spatial and spatiotemporal structures of the reactive compounds. The discovery of the Belousov-Zhabotinski reaction12 generated significant interest in spatial and spatiotemporal patterns and waves in chemically repredict that acting homogeneous systems. Theoretical the propagating waves and dissipative structures also exist on heterogeneous catalytic surfaces. Experimental revealed spatial and spatiotemporal temperature patterns on pt and Ni surfaces on which catalytic oxidation reactions were carried out. It is important to gain an understanding of the cause of these spatiotemporal patterns, the conditions and reactions for which they occur, and their impact and potential applications. This work is an experimental study of the formation, characterization, and transitions of spatiotemporaltemperature patterns on a catalyst surface heated by a constant electrical current, and the relation between the oscillatory and chaotic behavior of the overall reaction rate and the local temperatures. Propylene oxidation on a platinum ribbon was used as the test reaction. A study of the oxidation of propylene on a platinum ribbon maintained at a set average temperature was reported p r e v i ~ u s l y . ~ ~ Experimental System The reaction was carried out on a 14.7cm long, 0.05 cm wide, and 0.0025 cm thick pure platinum ribbon (Johnson Mathey, Inc.) placed in a rectangular duct with a cross section of 0.93 cm X 22.9 cm and a height of 27 cm. The platinum ribbon was heated by a constant electrical current generated by a programmable power supply (Lambda, Inc.). A large resistor (approximately 10 s2 at 24 "C)was connected in series with the platinum ribbon to maintain a constant current in spite of any temporal changes in the average resistance of the platinum ribbon, which is 1.4 and 2.7 52 at 24 and 300 O C , respectively. Temporal variations in the current were of the order of kO.01 A. The ribbon was suspended in the center of the channel with the gaseous reacting mixture (linear velocity of 2.9 cm/s) flowing perpendicular to its length. The gases, extra dry grade oxygen, prepurified nitrogen, and propylene (99.0% minimum purity), were controlled by a mass flow controller, purified, dried, and mixed before entering the reactor at room temperature (24 "C).The catalyst was activated by heating to lo00 OC in air for 1 h before introducing 1% propylene to the air stream for about 14 h. The infrared radiation from the ribbon was measured by a thermal imager (AGEMA Thermovision 780) placed next to a Kodak IRTRAN 2 infrared To whom correspondence should be addressed.
transparent window in the reactor wall. Additional details of the system are reported in ref 23. The heat generated by the exothermic propylene oxidation on the ribbon was calculated from the difference in the electric power required with and without reaction. The time-dependent electric voltage across the wire was recorded simultaneously with the thermal images.
Results Experiments in which the platinum ribbon was heated electrically with a constant current were conducted using mixtures of air and propylene. Propylene feed concentrations between 0.03% and 0.5% were examined. In an experiment the current was changed in small steps at a fmed propylene concentration, in order to construct a bifurcation diagram of the overall rate of heat generated by the reaction per unit surface area, Qg,versus the current, I, heating the ribbon. A typical bifurcation diagram of Qe versus current for a mixture of 0.2% propylene is shown as Figure 1. In that case, a uniform extinguished state existed for all currents below 0.99 A. Either an extinguished or a chaotic state existed for currents between 0.99 and 1 .O A. This narrow region of two different states increased as the propylene concentration was increased. A chaotic state existed for currents between 1 .O and 1 .055 A. Either an oscillatory or a stationary fully ignited state could be obtained for currents between 1.055 and 1.13 A. The measurement noise prevented definite determination if these reaction rate oscillations were periodic or chaotic due to their small amplitude (about 0.1% of average value). If these small oscillations are periodic, then an additional transition from a periodic to a chaotic state may exist. The small amplitude of the oscillations prevented the finding out of that transition, if it exists. A stationary fully ignited state existed for currents exceeding 1.13 A. When the current was decreased, the ignited state disappeared while the oscillatory state remained stable at a current of 1.055 A. When the current was increased, the oscillations vanished with a transition to an ignited state at a current of 1.13 A. This hysteresis in the osciUatory states vanished for propylene concentrations above 0.3%. The amplitude of the oscillations decreased as the current was increased. The chaotic oscillations abruptly vanished at a current of 0.99 A. In order to construct the bifurcation diagram correctly, it was necessary to keep the step changes in the current as small as possible (about 0.014.02A). After each change the system was left for about an hour. When a transition from a stationary state to an oscillatory state occurred, small amplitude oscillations appeared approximately 1 h after the change in the current. The amplitude of the oscillations increased to a constant value over the next 4 to 5 h. Following a large current change from a high (stationary state) to a low value (oscillatory state) the oscillations appeared only after approximately 1 day. This long transient is most probably
0022-3654/92/2096-665 1 $03.00/0 0 1992 American Chemical Society
6652 The Journal of Physical Chemistry, Vol. 96, No. 16, 1992
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Figure 1. Overall rate of heat generated by the reaction versus current for a mixture containing 0.2% propylene. Bars denote amplitude of
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corresponding series of transient temperature profiles.
related to slow changes in the surface structure. A series of bifurcation diagrams for various feed concentrations was used to construct a bifurcation map of the operating conditions leading to qualitatively different states (Figure 2). For sflidently low average ribbon currents and propylene concentrations (region E in Figure 2), a uniform extinguished state with negligible reaction rate is obtained. For sufficiently high currents, a uniform ignited state exists (region I). For low currents next to region E, a region (E C) exists in which either an extinguished or a chaotic state is obtained. For low propylene concentrations (less than 0.3%) next to region I a region (I 0)exists in which either a uniform fully ignited stationary state or an oscillatory state exists. (The small amplitude prevented characterizationof the oscillatory nature.) Next to region (I + 0)a region C of chaotic states exists. For high propylene concentrations (larger than 0.35%) next to region I a region (I E) exists in which either a stationary ignited or extinguished state is obtained. It was not possible to determine the intersections of the boundaries of the various regions at low propylene concentrations, as the measurements became rather inaccurate for propylene concentrations below 0.03%. A moving temperature front was observed during the chaotic behavior. Figure 3 shows a series of temperature profiles along the ribbon during an oscillation in the heat generated by the reaction, Q8(Figure 3a). Initially the reaction rate is high and the ribbon is fully ignited (Figure 3b). Then the right boundary of the high temperature region starts moving (Figure 3c), decreasing the length of the high temperature region, and therefore decreasing the overall reaction rate. The mimimum in the overall reaction rate is found when the movement stops, Le., when the length of the high temperature region is the shortest. The temperature profile in Figure 3d is of a state close to the minimum of QB'Subsequently, the temperature front reverses its direction of movement, increasing the fraction of ribbon which is at the high temperature and therefore the overall reaction rate. Figure 3e is of a temperature profile during this stage. The backward movement continues until the front reaches the support and the ribbon is again fully ignited (as in Figure 3b). The front velocity is of the order of 0.3 cm/s. The oscillations may be due to either a right or leftward motion as illustrated in Figures 4 and 5. During an oscillation only one
of the two fronts bounding the high temperature region moves. Figure 4 is a series of five images of 1-cm sections along the 14.7 cm long ribbon. Each image was created from a different time series and corresponds to a similar pair of moving temperature fronts. The temperature is represented by various shades of gray, where black is the lowest and white the highest temperature. The position is measured from the center of the ribbon. Negative and positive values correspond to the left- and right-hand side, respectively. The images show that the ribbon remains fully ignited during most of the time. At first the right end front moves approximately to the center of the ribbon, then reverses its direction, and moves back to the support. The ribbon remained fully ignited for about 150 s, then a left-moving front moves to the center of the ribbon and then reverses its direction until it reaches the support. Figure 5 shows typical temporal oscillations of QB (top) and two temperature profiles approximately at the minimum of two Q8peaks. The times at which the temperature profiles were recorded are marked by arrows in Figure 5 (top). In the case marked by a, only the right front of the high temperature region moved, while in case b only the left front moved. Typical oscillations of the overall heat generation rate (top) and local temperature (bottom) at a point 5 cm to the right the center are shown in Figure 6. The reaction rate remains at the high value (fully ignited ribbon) for most of the time, and the oscillations are associated with decreased overall rates. In contrast to the local temperature, the amplitude of the rate oscillations is not constant. The overall reaction rate oscillates at a higher frequency than the local temperature. The reason is that Q8 changes by the movement of either the left or right front. On the other hand, the local temperature changes at the right-hand part of the ribbon are caused only by the movement of the right front of the high temperature region. The small short temporal temperature rise noted in Figure 6 (bottom) corresponds to temporal changes in the rate of heat generation. The movement of the left front of the high temperature region causes a rapid small increase in the current and hence in the local temperature at the right part of the ribbon. During the local temperature oscillations (Figure 6 bottom), the temperature remains at a high value (ignited zone temperature) most of the time and decreases rela-
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The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6653
Propylene Oxidation on Electrically Heated Pt
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tively quickly to a low value (extinguished zone temperature). The local temperature always drops to approximately the same low value, but the duration of the oscillation is not the same for the various peaks. The sharp peaks (short duration) were observed
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when the front reversed its direction shortly after passing the measurement point, while the broad peaks (long duration) were found when the front reversed its direction far from the measurement location. Changes in the current used to heat the ribbon did not change significantly the shape of the oscillations in the rate of heat
Philippou and Luss
6654 The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 0.50
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rate on the low temperature zone. Changes in the length of the fraction of the ribbon which is at the high temperature, caused by the moving temperature front, are responsible for the oscillations in the overall chemical reaction rate. The distinction between a periodic and chaotic behavior is mainly related to the frequency of the movement of the temperature fronts. The bifurcation map (Figure 2) indicates the existence of six regions with qualitatively different dynamic features. The transition between the extinguished state region (E in Figure 2) to the extinguished plus chaotic state (E + C) is via a boundary crisis bifurcation2*(CR in Figure 2). The transition between regions (I E) and E and between (E + C) and C is via a saddle-node bifurcation (SNin Figure 2). It is very difficult to characterize the other transitions since when the oscillations have a small amplitude (as in region (I 0))the noise prevents accurate clarification of their nature, i.e., are they periodic, quasiperiodic, or chaotic. If the small oscillations in region (I 0)are periodic, then they are bound by a saddlenode of periodic solutions (SNP) from above and by a subcritical Hopf bifurcation from below. The subcritical Hopf is transformed to a supercritical Hopf at a degenerate Hopf bifurcation, Le., the tangential intersection of the SNP and the Hopf bifurcation. The hysteresis in the small amplitude oscillations disappears for propylene concentrations exceeding that at the degenerate Hopf bifurcation (about 0.3%). This interpretation implies the existence of a (unobserved by us) bifurcation from periodic to chaotic oscillations. If the oscillatory behavior in region (I 0) is chaotic, then the upper boundary of that region is probably a saddle-node of chaotic solutions. Oscillations were observed when the ribbon was heated electrically either with a constant current or controlled at a set average temperat~re.2~ Signifcant differences were observed between the two types of experiments with respect to the nature of the moving temperature waves and the shape of the oscillations. In the constant current experiments the ribbon remained fully ignited most of the time, and the oscillations were caused by a back and forth movement of either the left or the right front of the high temperature zone. In the constant average temperature experiments, only a fraction of the ribbon was ignited (in some range of average temperatures) and both fronts of the wave moved simultaneously, changing the fraction of the ribbon which is ignited and therefore the reaction rate. While the temperatures of the ignited and extinguished section remained unchanged during the constant current experiments, changes in the temperatures of the ignited and extinguished zone (order of 20 "C)occurred in the constant average temperature experiments. The chaotic behavior of the reaction in the constant current experiments is due to the wide spread in the time intervals between successive wave movements. In the constant average temperature experiments the relative motion of the two sides of the temperature wave was the main cause of the chaotic behavior of the reaction. In general the oscillations in the constant average temperature experiments were less regular than in the constant current experiments. The time delay method29,30 was used to reconstruct the attractors of the overall reaction rate (Figure 9) and local temperature (Figure 10). The chaotic attractors of the overall rate of heat generation for a mixture containing 0.2% propylene (Figure 9) become leas complex as the current increases. The chaotic attractors of the constant current experiments were in general less complex and filled a smaller part of the phase space than those in the constant average temperature experiments.*' These differences are caused by the fact that in the constant current experiments, the reaction remained at a constant high rate (fully ignited ribbon) most of the time with some oscillations to lower reaction rates. Reconstructed attractors of the local temperature at two different locations along the ribbon for a mixture of 0.2% propylene and a current of 1.04 A are shown in Figure 10. A time delay (10 s) was used for reconstructing the two attracton which is the optimum time delay according to the mutual information meThe shape of the local temperature attractors is less complicated than that of the attractor of the overall reaction rate. The reason is that the local temperature always oscillates between
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Discussion The periodic and chaotic oscillations in the overall reaction rate (heat generation) during the oxidation of propylene on the Pt ribbon, heated by a constant electrical current, are due to the back and forth movement of a temperature front. The reaction occurs on the high temperature part of the ribbon, with negligible reaction
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The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6655
Propylene Oxidation on Electrically Heated Pt
1 o4
0.02 0.03 0.04 Frequency ( Hz ) Figure 11. Power spectrum of the overall rate of heat generation for a mixture of 0.2% propylene an a current of 1.04 A showing an exponential decay at high frequencies. 0.01
Local Temperatore at 6.0 cm k
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Frequency ( Hz ) Figure 12. Power spectrum of the local temperature for a mixture of 0.2% propylene and a current of 1.04 A showing a power law decay at high frequencies.
Figure 10. A three-dimensional reconstruction of the attractors of local temperatures at two different locations along the ribbon for a mixture of 0.2% propylene and a current of 1.04 A. A time delay of 10 s was used in the reconstruction.
the same high and low temperatures (see Figure 6) while the amplitude of the oscillations of the overall reaction rate is not constant. The local temperature oscillates between the high and low values and the shape of the attractor depends on the choice of the time delay and, in particular, the ratio between the time delay and the length of time during which the ribbon is at the low temperature. In the attractor shown in the top of Figure 10 (position -6.0cm) for some oscillations this period is longer than 3 times the time delay. In these cases we get instances in which T(t), T ( ~ + Tand ) , T ( ? + ~ Tare ) at the low temperature and the trajectory is A-B-C-D-E-F-A. For peaks with short duration the trajectory is A-B-A4-A-F-A. The attractor shown on the
bottom of Figure 10 (position -3.0 cm)has a different shape than that at position -6.0 cm as the temperature oscillations at this point last for a shorter period (less than 27). Thus, the trajectory cannot pass through a point at which all the three values are low (point D in Figure 10 top) but only through those in which at most two temperatures are low. Power spectral density3’J2is useful in characterizingdynamical . systems and distinguishing between deterministic and stochastic proce~ses.3~3~~ Figure 11 is a typical power spectrum of the overall rate of heat generation for a mixture of 0.2% propylene and a current of 1.04 A. The corresponding Qgas a function of time is shown in Figure 6 (top). The power spectrum has no significant peaks and decays exponentially suggesting that it corresponds to a chaotic deterministic system. A similar exponential decay of the power spectrum was observed in the constant average temperature experiment^.^^ Figure 12 is a typical power spectrum of the local temperature at a distance of 6 cm from the center of the ribbon, for propylene concentration of 0.2% and a current of 1.04 A. The corresponding temporal local temperature is shown in Figure 6 (bottom). Unlike the power spectrum of the overall rate of heat generation, that of the local temperatures decayed as a power law at high frequencies, suggesting a stochastic behavior. Similar features were observed in the constant average temperature experiment^.^^ . While certain similarities exist between the oscillations for the constant average temperature and the constant current experiments, several important differences exist. In the constant average temperature experimentsthe electrical heating plays an important role in the oscillatory behavior, and the‘controller,which maintains a set average temperature, is responsible for keeping part of the ribbon at a high temperature, with small temporal changes in its
6656 The Journal of Physical Chemistry, Vol. 96, No. 16, 199'2
temperature. S h e i n t u ~ hshowed ~ ~ that in the constant average temperature case a slow modification of the surface properties in a bistable system may lead to periodic changes in the reaction rate, assuming that a uniform but different activity exists in two sections of the ribbon. The oscillations are caused by deactivation of the high temperature region and activation of the low temperature region. He showed" that very complex dynamic features, including chaos, may be obtained when the ribbon consists of many sections. This analysis can predict all the observed qualitative features of the oscillations in the reaction rate.. However, it predicts that the temperature oscillations are of the antiphase type, Le., one section cools while another heats up, keeping a constant overall average temperature. This prediction does not agree with the observed back and forth moving temperature wave.23 The observed back and forth moving temperature front in the constant current experiments is rather surprising. To explain this behavior one needs to know what initiates the movement of the temperature front. The small fluctuations in the current (order of 0.01 A) could not be the cause of this chaos as their frequency is several orders of magnitude higher than that of the oscillations in the reaction rate. A plausible cause may be a reduction in the activity which causes local extinction. It is, however, not clear what is stopping the front and causing it to reverse its direction of movement. The fact that a front starts moving from both sides indicates that this behavior is not caused by an intrinsic nonuniformity in the activity of the ribbon or of the flow field. Electrically heated wires have been used in many studies to determine the Oscillatory features of exothermiccatalytic reactions. Clearly, any analysis or model of this behavior which ignores the spatiotemporal features of the wire will lead to pitfalls. A model of the system should account not only for the dynamic features of the observed reaction rate but also for the observed local features. It is of intrinsic academic interest to be able to predict a priori the type of reactions and operating conditions which cause the formation of the spatiotemporal patterns, the length of the ignited region, and nature and rate of movement of the reaction fronts. It is of practical importance to know the impact of the temperature patterns on the overall rate and how it can be affected by changes in the operating conditions such as reactant concentration, heating current, etc. Moreover, it is essential to study how robust or sensitive these patterns and the time averaged rate and/or selectivity are to slight variations in the activity of the catalyst or
Philippou and Luss to nonuniformities in the activity profile.
Acknowledgment. We are thankful to Professor M.Sheintuch and Dr. M. Graham for helpful discussions. We are thankful to the NSF and the Welch Foundation for support of this research. Re&W NO. CHzdHCHI, 115-07-1; Pt, 7440-06-4.
References and Notes (1) Field, R. J.; Burger, M. Oscillations and traveling waves in chemical systems; Wiley: New York, 1985. (2) Epstein, I. R. Physica D 1991, 51, 152. (3) Razen, L. F.; Chang, S.M.; Schmitz, R. A. Chem. Eng. Sci. 1986,41, 1561. (4) Lev, 0.; Wolffberg, A.; Pismen, L.M.; Sheintuch, M. J. Phys. Chem. 1989, 93, 1663. (5) Lev, 0.;Sheintuch, M.; Yarnitzky, C.; Pismen, L.M. Chem. Eng. Sci. 1990,45, 839. (6) Wang, Y.; Hudson, J. L.AIChE J . 1991, 37, 1833. (7) Bassett, M.R.; Hudson, J. L.J . Electrochem. Soc. 1990, 137, 1815. (8) Skinner, G. S.;Swinney, H.L. Physica D 1991, 1 , 16. (9) El-Hamdi, M.; Gorman, M.; Robbins, K. Submitted to Comb. Sci. Technol. (10) Herzel, H.; Plath, P.; Svensson, P. Physica D 1991, 48, 340. (1 1) Song, X.;Schmidt, L. D.; Aris, R. Chem. Eng. Sci. 1991'16, 1203. (12) Zaikin, A. N.; Zhabotinski, A. M. Nature 1970, 255, 535. (13) Pismen, L.Chem. Eng. Sci. 1980, 35, 1950. (14) Sheintuch, M.; Pismen, L. Chem. Eng. Sci. 1981, 36, 893. (15) Schmitz, R.; Tsotsis, T. Chem. Eng. Sei. 1983, 38, 1421. (16) Bykov, V.; Gorban, A.; Kamenshehikov, L.;Yabloskii, G. Kinet. Catal. 1983, 24, 520. (17) Barto, M.; Markos, J.; Bnmovska, A. Chem. Eng. Sci. 1991,46,2875. (18) Imbihl, R.; Cox, M. P.; Ertl, G. J. Chem. Phys. 1986, 84, 3518. (19) Ertl, G. Science 1991,254, 1750. (20) Pawlicki, P. C.; Schmitz, R. A. Chem. Eng. Prog. 1987, 83, 40. (21) Lobban, L.;Philippou, G.; Luss, D. J . Phys. Chem. 1989, 93, 733. (22) Lobban, L.; Luss, D. J . Phys. Chem. 1989, 93,6530. (23) Philippou, G.; Schultz, F.; Luss, D. J. Phys. Chem. 1991, 95, 3224. (24) Ganke, M.E.; Harold, M. P. Submitted to Chem. Eng. Sci. (25) Kellow, J. C.; Wolf, E. AIChE J. 1991, 37, 1844. (26) Kellow, J. C.; Wolf, E. Chem. Eng. Sci. 1990, 45, 2597. (27) Cordonier, G. A.; Schmidt, L. D. Chem. Eng. Sci. 1989,44, 1983. (28) Greboni. C.: Ott. E.: Yorke. J. A. Phvsica D 1983. 7. 181. (29j PackaFd; N.'H.; Crutchfield; J. P.; F a h e r , J. D.; Shaw, R. S. Phys. Rev. Lett. 1980, 45, 712. (30) Fraser, A. M.; Swinney, H. L. Phys. Reu. A 1987, 33, 1134. (31) Eckmann, J. P.: Ruelle. D. Rev. Mod. Phvs. 1985. 57. 617. (32) Bendat, J. S.; Piersol, A. G. Random d a t a Analysis and Measurement Procedures; Wiley: New York, 1985. (33) Sigeti, D.; Horthemke, W. Phys. Rev. A 1986, 35, 2276. (34) El-Hamdi, M.; Gorman, M.; Robbins, K. Submitted to Physica D. (35) Sheintuch, M. Chem. Eng. Sci. 1989, 44, 1081. (36) Sheintuch, M. J. Phys. Chem. 1990, 94, 5889.
