B. Thermokinetic Oscillations Thermokinetic Oscillations accompanying Propane Oxidation BY PETER AND R. J. MOULE GRAY,J. F. GRIFFITHS Department of Physical Chemistry The University Leeds LS2 9JT Received 7th August 1974 Gaseous hydrocarbon oxidations are often accompanied by remarkable non-iso thermal pheno- mena such as oscillatory cool flames and complex ignitions. These owe their existence to an inter- play between kinetics and self-heating via thermal feedback in a system involving chain branching. The present work illustrates these phenomena and provides a quantitative assessment of thermo- kinetic concepts applied to them. Propane is oxidised in a stirred closed reactor. Characteristically time-dependent oscillations occur in the pressure range 40-100kNm-2at vessel temperatures between 570 and 660K.Sub-stantial temperature changes accompany the oscillating reaction rate and these changes are measured by a fine (25 pm) thermocouple and rapid recording equipment. Oscillating temperatures may vary in form from roughly sinusoidal with damping to steep cusp-like maxima of hardly diminished amplitude multiple events being terminated abruptly by the consumption of fuel. Thermokinetic oscillations depend vitally on thermal feedback and hence on heat transfer :by the deliberate variation of heat transfer properties such as heat capacities and thermal conductivities (with diluting gases) and intensities of stirring we are able to test this dependence. The spontaneous oxidation of hydrocarbons in the gaseous phase not only shows " slow " and explosive modes of reaction but also may be accompanied by periodic pulses of light emitted during repetitive bursts of enhanced rea~tivity.~'~ The light emission is very feeble and an associated pulse in gas temperature is generally less than 200 K; these phenomena are called " cool flames " to distinguish them from normal explosive burning5 Cool flames are now recognised as oscillatory reactions in closed reactors up to 11 successive events are observed,6 and in open systems they may be sustained indefinitel~.~The temperature attained in a cool flame pulse varies between about 5 and 200 K according to the initial reactant temperature and concentration,8 though in closed reactors successive flames become progressively weaker since moderate proportions of reactants are consumed in each of them (up to 20 %).9 The earliest recognition of oscillatory reaction attracted contrasting interpretations.At first isothermal explanations were offered based on superficial analogy to the Lotka-Volterra autocatalytic scheme already applied in some electrochemical and biological contexts. However this simple isothermal explanation fails to offer a satisfactory interpretation of hydrocarbon cool flames. Amongst the reasons why the Lotka-Volterra mechanism does not survive detailed scrutiny are (i) its failure to predict an alternate growth and decay in concentrations of intermediates that is not determined by the initial composition (it predicts conservative oscillations not limit cycles),l and (ii) the impossibility of making a satisfactory chemical identification with the participants of the isothermal kinetic model.* Recent more elaborate iso- thermal models are hardly more acceptable since schemes that predict limit cycles have to invoke chemically unlikely elementary reactions.' 3*l4 (The best success so far with 103 THERMOKINETIC OSCILLATIONS an isothermal scheme seems to be that of Field and Noyes Is who have fitted the rigorous criteria for isothermal oscillatory models to the chemical framework of the Belousov l6 reaction.Autocatalysis in their kinetic mechanism occurs via chain branching.) In hydrocarbon oxidation there is an obvious alternative feedback mechanism to isothermal autocatalysis. This is thermal feedback which takes account of the strongly exothermic properties of reaction.The earliest thermal feed back model was proposed by Salnikoff l7 who showed that two consecutive first order reactions (viz. A 3 B -+ C) will generate sustained oscillations in the concentration of the inter- mediate (B) provided that certain (plausible) criteria apply to the exothermicities and Arrhenius parameters of each step. Present day thermokinetic models such as that of Gray and Yang or of Halstead Prothero and Quinn l9 remain simple though now they feature chain branched autocatalysis. Through it these schemes predict not only oscillatory regimes but also other striking and unusual features of hydrocarbon oxidation such as the negative temperature-dependent heat-release rate the single and multiple-stage ignitions and the " lobes " associated with the ignition limit in a pressure-temperature ignition diagram.Implicit in each of these treatments is that simply to devise a plausible model chemical scheme is not enough proper analytical methods must be applied to prove that stable oscillatory behaviour is possible. Moreover extension beyond a qualita- tive test requires not only correct information on stoichiometries kinetic constants and thermochemistry but also correct thermal parameters of the system. We need to supplement conventional kinetic investigations with measurements of heat release and loss rates and of how they depend on temperature. Where theoretical treatments have been simplified such as by assuming spatially uniform temperatures and concen- trations we need to devise experimental techniques in which nature is made to imitate art.Accordingly the present paper describes new investigations of the thermal effects accompanying propane oxidation. A closed reactor is used in which the temperature excess of reactants is made uniform by mechanical stirring. Heat-loss rates are measured and by deliberately changing them the dependence of cool flame oscillations on thermal feed back is tested. THEORETICAL FOUNDATION Most order has been brought into the classification and analysis of oscillatory reactions by phase-plane analysis. Even in systems that are chemically as complex as hydrocarbon oxidations many of the features can be rationalised in terms of a single key intermediate participating in branching and termination processes.l8* The starting point for analysis of a thermokinetic model is the pair of expressions for the generation and loss of heat and for the generation and loss of the chain branching species (X). These conservation equations may take the general forms for energy ;CF= %(T,P,X)-Z(S/ Y)(T-T~) (1) for mass; X = -f(~, x> (2) where B(T,P,X) is the rate of heat release per unit volume andf(T X) is a function involving the rates of reactions from which X is formed or in which X is removed. Each of these parameters depends upon the concentration of X. I is the heat transfer coefficient between gas and reactor walls (T-To)is the spatially averaged temperature P.GRAY J. F. GRIFFITHS AND R. J. MOULE I05 excess of the reactants c is their heat capacity per unit volume and S/Yis the surface to volume ratio for the reactor. Solutions of these equations for Tand X begin by location of singular points in the (T,X)plane and identifying the behaviour close to them. Closed-curve trajectories in the (T,X)plane correspond to oscillatory behaviour in time illustrated by either T(t)or X(t). This connection causes us often to describe the experimental time- dependent observations of undiminished sustained oscillations by phase-plane terminology i.e.,as " limit cycle behaviour ". Experimentally T(t)may be observed via direct measurements of temperature (as in our experiments ** 2o and in those of others 4* l) or X(t)by following the changing concentration of one or more appropriate intermediate species.So far experimental evidence demonstrating the alternate growth and decay of chemical intermediates in cool flames is scant 21* 22 ;this is because the important branching intermediates are extremely difficult to identify and measure continuously. EXPERIMENTAL MATERIALS Propane (instrument grade B.O.C. Ltd,) and acetaldehyde (Analar B.D.H. Chemicals Ltd.) were distilled in vacuu before use. Oxygen and diluent gases (B.O.C.Ltd.) were taken directly from cylinders. APPARATUS AND PROCEDURE The apparatus and general procedure have been described previously.2o* 23 Good mixing of reactants was achieved by a double-vaned rotor spinning round a vertical axis within the reactor (Pyrex 0.5 dm3 spherical).The rotor magnetically driven was made of stainless steel previously coated with a ceramic layer to minimise surface reactions. The reactor was thermostatted in a re-circulating air furnace to 1 K over its surface in the range 550-650 K. Propane oxygen and reactive additives or inert diluents were pre-mixed and stored in a conventional Pyrex vacuum line. Reactants were admitted to the reactor via an electro-magnetic valve opened reproducibly for 0.1 s. Initial pressures in the reactor (typically 30-100 kN m-2) were measured from the output e.m.f. of a pressure transducer (Ether Ltd. UP4). To detect and follow accurately the temperature changes in gaseous reactions the measur- ing device must have a fast response a very small thermal capacity low thermal conductivity adequate sensitivity and it must be of robust construction.Our thermocouples gas welded from very fine Pt-Pt/l3 % Rh wire (25 pm diam.) come close to satisfying these criteria. Their response time is less than 20 ms in moving gas 24 and so they are able to give a faithful record of all behaviour except hot ignitions. A very fine junction coated with a thin layer of silica from a methanol+silicon oil flame was situated within the reactor and the reference junction (100pm diam. wire) was placed on the outside of the vessel wall. The e.m.f. generated from these junctions was amplified and displayed on a light sensitive chart by an ultra-violet recorder (Southern Instruments Ltd.). The interior probe was moveable across a horizontal diameter of the reactor so that temperature-time histories could be obtained at any position across the reactor.Temperature-time records for the same initial conditions but for different positions of the probe were combined to allow temperature-position profiles to be mapped at successive instants of reaction. Records for the same propane+ oxygen+ additive mixtures at different initial temperatures and pressures were combined to map the various types of non-isothermal behaviour on pressure-temperature ignition diagrams. Heat transfer coefficients (I) for all of the reactant mixtures were measured at various temperatures and pressures in additional experiments. With knowledge of vessel dimensions and of reactant heat capacities I may be evaluated from the measured temperature excess of THERMOKINETIC OSCILLATIONS reactants (eqn (1)).Two routes are open; either via a steady slate ti-= 0) if energy is supplied at a known rate,". 23 so that Z(S/V)(T'-T") = &!is (3) or by a dynamic method from the rate of exchange of heat between the gas and reactor walls. If 9= 0 as is the case when inert gas is heated or cooled adiabati~ally,~~ T = (ZS/C Y)(T-To) = (1 /z)( T-7-01 AT = ATo exp (-t/z). The heat transfer coefficient has a natural identity with the characteristic relaxation time (2)for heat dissipation between the gas and reactor walls.25 We have chosen this dynamic method to measure 1. Gas was expanded adiabatically from the reaction vessel and the temperature-time history was folIowed as the residua1gas warmed back to ambient tempera-ture.The characteristic relaxation time (2) was derived from the gradient of the graph of log AT against time. RESULTS TEMPERATURE UNIFORMITY HEAT LOSS RATES AND HEAT TRANSFER COEFFICIENTS We have measured 23 the spatial variation of temperature in the reactor. Except near the walls the effect of stirring is to make temperature excesses very nearly uniform across the reactor. It is this which is the experimentalists' justification for expressing heat loss rates in a Newtonian form (eqn (I) (3) and (4)) and is consistent with some theoretical models for cool flame l7-I9 and other 26* 27 non-isothermal gaseous reactions. Similar spatial temperature distributions prevail for stirring speeds in the range 1200-2400r.p.m.Heat loss coefficients are determined for different gas mixtures in a variety of conditions by a dynamic method. A typical adiabatic quenching and relaxation curve is shown in fig. 1 and with it a semi-logarithmic plot of log AT against time -2.0 -A & RELAXATION 1 e -1.5 I h W I h -8 W -1.0 0 0.I 0.2 0.3 0.4 0.5 0.6 0.7 time/s FIG.1.-Curve (a) An adiabatic cooling followed by thermal relaxation back to ambient temperature (620 K) for nitrogen at 50 kN m-' in a stirred reactor (0.5 dm3). Temperaturechanges are measured directly by a Pt-PtlRh (13 %) thermocouple (25 pm diam. wire). Curve (b) A plot of log (T-To) against time for thermal relaxation. The relaxation time from which I is evaluated (eqn (4)) is determined from the gradient of this line.Values for z and I at various conditions are given in table 1. The actual values of I may be expected to depend on transport properties especially ;L (here altered by dilution) on density (here varied by varying pressure) and on P. GRAY J. F. GRIFFI’krib AND R. J. MOULE stirring efficiency (here varied by the speed of the rotor). The lowest values of / prevail at the lowest pressures and stirring rates (table 1). High concentrations of propane yield high values of 2 thus the simple expedient of dilution with inert gases of low thermal conductivity and heat capacity gives scope to reduce the heat transfer coefficient. T is hardly dependent on pressure the variation of 2 arises mainly from the pressure dependence of c.TABLE 1.-HEAT TRANSFER COEFFICIENTSFOR GASEOUS MIXTURES IN A SPHERICAL VESSEL (0.5 dm3) AT VARIOUS CONDITIONS composition/mol % pressure/kN m-2 temp./K rotor speed/r.p.m. T Is l/W K-1 m-2 N2 = 100 40.0 623 2400 0.16 19.9 53.3 26.2 66.6 32.5 C3Hs = 8 40.0 623 2400 0.18 27.9 N = 92 53.3 34.4 66.6 45.2 CSHs = 33 40.0 623 2400 0.26 28.8 Nz = 67 53.3 38.6 66.6 50.2 623 1 200 0.32 23.0 28.8 36.0 623 2400 0.27 36.4 44.8 54.0 C3Hs = 50 40.0 623 1200 0.34 26.8 N2 = 50 53.3 35.6 66.6 44.4 TEMPERATURE-TIME RECORDS FOR EXOTHERMIC OXIDATION The four main types of non-isothermal behaviour during propane oxidation are depicted in our (temperature time) records. These are (i) a damped oscillatory approach to a quasi-steady state (fig.2a b and c) (ii) nearly undamped oscillations ending abruptly (fig. 24 (iii) a monotonic approach to a quasi-steady state (fig. 2e) and (iv) two-stage ignition (fig. 2f). In damped oscillations successive amplitudes diminished appreciably even after the first temperature peak. For pure propane + oxygen mixtures all multiple cool flames show damped characteristics their damping factors depending upon the initial conditions of temperature and pressure. Fig. 2a shows cool flame oscillations typical of those observed at low temperatures (roughly in the range 580-62OK). Although amplitudes clearly diminish the damping factor is low ; oscillations occur up to the end of reaction. Initial amplitudes are large ( > 100 K) and the peaks have a cusp-like shape interspersed by periods longer than 1 s.At higher temperatures (beyond about 620 K) damping is sufficiently high for oscillations to have died away before the fuel is completely consumed (fig. 2c). These temperature histories are roughly sinusoidal starting with a maximum amplitude that is usually less than 100 K and sometimes as low as 5 K. Periods are generally very short (<2 s). THERMOKINETIC OSCILLATIONS Cool flame oscillations with barely diminished amplitudes occur at low tempera- tures in the oxidation of propane to which acetaldehyde is added (even small amounts say <0.5 mol %). They have steep cusp-like maxima interspersed by shallow minima ;::I50-1 1) -2004 0246 0 24 6810 200-I 50i I 001 I 0 2 4 6 8 1012 02 4 time/s FIG.2.-(Temperature time) histories for propane oxidation at different conditions in a stirred reactor (0.5 dm3).(a)to (d)multiple oscillations ;(a)C3H8(50 mol %) To = 610 K P = 75 kN m-2 ; (6) C3Hs (47mol %)+CH3CH0 (3 rnol %) To = 635 K,P = 65 kN m-2 ; (c) C3H8 (50 rnol %), To = 640 K P = 84 kN m-’ ; (d)C,H (47 rnol %)+CH3CH0 (3 rnol %) To = 600K P = 60kN rn-’ ; (e) slow reaction ; C3H8 (50 mol %) To = 640 K P = 60 kN m-2 ; (f)two-stage ignition ;C3H8 (47 rnol %)+ CH,CHO (3 rnol %) To = 590 K P = 85 kN m-2.and they give the impression of sustained oscillations. That is to say if fuel were to be fed continuously to the system they would propagate indefinitely; in our closed reactor they terminate abruptly when no fuel remains (fig.24. Amplitudes vary between 50 and 150 K and periods from 3 to 15 s the highest temperature excess and largest times being associated with the lowest reactor temperatures (c590 K). These “ sustained ” oscillations occur below about 630 K above which there is a marked change to damped sinusoidstl oscillations (fig.2b). P. GRAY J. F. GRIFFITHS AND R. J. MOULE Slow reaction may be sufficiently exothermic to increase the reactant temperature monotonically (by up to 35 K) to a quasi-steady state (fig. 2e). In two-stage ignition the temperature rises by about 200 K characteristic of a cool flame. This is followed instantly however by a violent hot ignition sometimes after the temperature has begun to fall from its first maximum (fig.2f). Induction times to the occurrence of these non-isothermal phenomena may extend from several seconds to several hours. For this reason fig. 2a d and e are drawn with an arbitrary time zero. Generally the longest induction times are associated with the lowest initial temperatures and pressures but they are reduced dramatically by the addition of acetaldehyde (or other reactive compounds 28). Induction times in hydrocarbon oxidations are rarely exactly reproducible ;they are susceptible to changes of surface such as the deposition of carbon during a hot ignition. PRESSURE-TEMPERATURE IGNITION DIAGRAMS It is most convenient to display these varieties of non-isothermal behaviour according to the initial reactor temperature and the initial reactant pressure for each reactant composition i.e.as a (P,To)ignition diagram (fig. 3 and 4). Because the 90 \ I 80 I N I E I I / E 70 ;ti 60 50 40‘ I I I I I I I J 570 S@CJ ‘330 600 610 620 630 640 650 ambient temperat ure/K FIG.3.-Ignition and cool flame boundaries in a stirred reactor (0.5 dm3) for propane (50 mol %) and oxygen. precise location of boundaries is affected by the reactor dimensions and its surface treatment each experimentalist has to map his own diagram :experimental ignition diagrams usually agree qualitatively but rarely quantitatively. The ignition diagram is divided into the main regions of slow reaction ignition and THERMOKINETIC OSCILLATIONS oscillatory reaction (cool flames) ;it is this last region that is of particular interest to us.Between 1 and 7 consecutive cool flames occur during propane oxidation and fig. 3 and 4 indicate the approximate pressure and temperature locations of their boundaries. However as the temperature histories show (fig. 2aand d) at least for low temperatures in closed conditions the number of successive oscillations appears to be limited by complete consumption of fuel :the exact number is of less significance than their existence. At high temperatures oscillations characteristically die away before reaction is complete (fig. 2b and c). The ignition diagram for pure propane +oxygen mixtures (fig. 3) differs from that when acetaldehyde is added to the reactants (fig. 4). When CH3CH0 is present the cool flame zone extends to lower temperatures (570 K compared with 590 K for pure C3H8/O mixtures) moving with it the two-stage ignition boundary.Moreover there is sufficient distinction between weakly damped and strongly damped oscillations to justify a boundary between them in the (P,To)ignition diagram. For C3H8/02 mixtures damping increases progressively through the oscillatory region. 1 IGNlTlO \ ‘-A’ \ I \WEAKLY DAM? E0 ‘SSCI LLATIONS/ ‘\ / i NS I.. . /I * / \ / \ -\ 3 50 SLOW ---L I GEACTIONS qgfL I I I I I 1 I -1 570 580 50C 530 610 620 630 640 650 700 ambient temperat ure,K FIG.4.-Ignition and cool flamc boundaries in a stirred reactor (0.5 dm3) for propane (47 mol %) and oxygen with acetaldehyde (3 mol %) added.When diIuting inert gases (N2and Ar) are added the cool flame boundary moves to higher pressures. As far as we can tell the new position is determined exactly by the partial pressure of inert diluent. This restricts our studies because the region in which more than 3 cool flames occurs is moved beyond the pressure limit of our system \vhen sufficient diluent is added to affect I markedly. P. GRAY J. F. GRIFFITHS AND R. J. MOULE THE EFFECT ON TEMPERATURE HISTORIES OF VARIATIONS IN HEAT TRANSFER RATES The dependence of the non-isothermal behaviour on the magnitude of 2 is tested most effectively in the closed reactor by altering the stirring rate. As table 1 shows a decrease of 50 % in the speed of the rotor causes an approximately 30 % decrease of 1.Fig. 5 exemplifies how multiple oscillations in the combustion of a 1 1 propane+oxygen mixture are changed when I decreases from 45 W K-’ m-2 (at 2400 r.p.m.) to 35 W K-l m-2 (at 1200 r.p.in.). In particular as I decreases so the damping factor decreases and amplitudes of temperature oscillations are increased. 1501 0 4 8 12 04812 tiinels FIG.5.-(Teniperature time) histories in a stirred reactor (0.5dm3)at 625 K for propane (50 mol %) and oxygen at 60 kN nr2. Curve (a)stirring rate = 2400 r.p.m. Curve (6) stirring rate = 1200 r.p.m. DISCUSSION HEAT TRANSFER RATES Over our ranges of temperature pressure reactant compositions and stirring rates I varies from 20-55 W K-’ ni-2 for the corresponding relaxation times 0.16-0.34s.These values for 1 agree satisfactorily with those that we have determined in other ways using stationary 29 and quasi-stationary 23 methods. A value for I = 25 W K-l m-2 implies that when a reaction is producing 1.5 W dr3 (e0.15 kJ mol-I s-l at 0.5 atm and 620 K) a 1 K temperature excess will be maintained in a spherical reactor. Altering the stirring speed changes heat losses; but even in an unstirred system at appreciably less than 0.5 atm. convection is ~ignificant,~~ so that further forced convection enhances the heat loss coefficient less than linearly. Stirring of the reactants not only produces temperature uniformity and enhanced heat loss rates but also destroys any flame structure. (Temperature time) histories thus become a better mirror of a uniform system.8 PRESSURE-TEMPERATURE IGNITION DIAGRAMS So far as (P,To)diagrams are concerned the areas on them are identified by different temporal behaviour the properties of which correspond to those of the singularities in the (T,X) phase-plane that are experimentally accessible from fixed initial temperatures in closed reactors i.e.limit cycles (“sustained ” oscillations) stable foci (damped oscillations) stable nodes (slow reaction) and unstable saddle points (two-stage ignition). The boundaries between each of these in the (P,To) THERMOKINETIC OSCILLATIONS diagram which represent criticality in the experimentalists’ sense (viz. marginal achievement of ignition or marginal achievement of oscillation) in the phase-plane correspond to the merging of singularities.THE DEPENDENCE OF THERMOKINETIC OSCILLATIONS ON THERMAL PARAMETERS Multiple cool fiames are sensitive to changes of reactor temperature and heat transfer coefficients :increases of each cause decreases in amplitudes and increases in frequency and damping factors (fig. 2 and 5). A logical connection between the cause and effect which can be tested by our results is provided by phase-plane analysis.l8 For example the damping factor depends on (d%/dT-I); if d%/dT becomes negative as is thecase in propane oxidation 2o when reactor temperatures extend through the range 610-650 K or if I is increased then damping of oscillations is enhanced. CONCLUSIONS Although theoreticians have stressed the link between the occurrence of spatial and temporal oscillations and dissipative systems far from equilibrium combustion systems have rarely been invoked as illustrations.They are excellent examples reaction starts far from equilibrium and proceeds through a complex path network to multiple steady states ;it is strongly exothermic and is accompanied by large changes of free energy. Commonly the concept of feedback is interpreted in chemical terms taking the form of either an autocatalytic or an inhibitory kinetic me~hanism.~~ In oscillatory combustion systems chemical autocatalysis even with the unusually responsive changes of rate induced by chain branching only partly describes what is happening. There is also a thermal contribution to a feedback mechanism which because of the Arrhenius temperature dependence of elementary reaction rates is very strongly non-linear.Isothermal oscillatory systems are apt to depend on artificial reaction schemes with elementary steps of order greater than two in active intermediates; the corres- ponding degree of non-linearity may be more easily and naturally attained via the temperature dependence of velocity constants. G. J. Minkoff and C. F. H. Tipper Chemistry of Combustion Reactions (Butterworth London 1962) p. 200. ’R. Ben-Aim and M.Lucquin Oxidation and Combustion Reviews Vol. 1 ed. C. F. H. Tipper (Elsevier Amsterdam 1966) p. 1. B. Lewis and G. von Elbe Combustion Flames and Explosions of Gases (Academic Press New York 1962). 4R.Hughes and R.F. Simmons Twelfth Symposium (International) on Combustion (The Combustion Institute 1969) p. 449. M. Prettre Bull. Sac. Chim.France 1932 51 1132. R. E. Ferguson and C. R. 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