TOWARD A UNIFIED COMBUSTION THEORY R. H. ESSENHIGH
J. B. HOWARD
rl
I THE PYROLYSIS AND COMBUSTION MECHANISM OF CARBONACEOUS SOLIDS
A
I n hybrid propellant rocket systems the fuels most commonly used have been rubbers and organic PO&mers, though the experimental use of carbon and euen coal is not unknown. The hybrid is therefore the latest member o f a class o f somewhat similar Combustion systems of which the others are industrial processes. This article considers the possibility that the classical literature o f industrial heterogeneous cornbustion swtems may contain something o f value to the propulsion problem
arbonaceous solids always contain carbon, generally hydrogen, often contain oxygen, may sometimes contain other elements such as chlorine, nitrogen, sulfur, and are frequently associated with extraneous material such as moisture and inorganics. Because reaction of such materials with oxygen is generally exothermic, many are capable of being used as fuel; many have, in fact, been investigated for their pyrolysis behavior and combustion properties, in degrees varying from the superficial to the intensive, either because of potential use as fuel or because of potential fire hazard. The practical situations involving such materials range widely. They include combustion of coal and similar material for industrial reasons (steam raising and industrial process furnaces), ignition and combustion of particulate matter in prevention of dust explosions, ignition and combustion of woods and other cellulosic materials in connection with fire research and spread of flame, ignition of solids by high density radiation from nuclear explosions, and mechanism and control of flame in hybrid propellant systems using solid fuels and fluid oxidants. In this last situation of hybrid rocket propulsion, the fuels most often used have been rubbers and organic polymers such as Lucite and polystyrene, but the use of carbon and even of coal is not unknown. Indeed, according to Green (23) who quotes a private communication from Wolfgang Noegerrath, coal reacting with gaseous nitrous oxide was the fuel employed in the first fluid-solid propellant combination, developed in 1937 in the I. G. Farben Laboratories at Ludwigshaven (39). Green (23) also quotes Bernard Smith as authority for information about experiments conducted about the same time (1938-41) by the California Rocket Society using a fluted carbon bar with gaseous oxygen. In the context of rocket propellant systems, interest naturally centers on those materials that can react fast enough with fluid oxidants to be used in propulsion devices. The fundamental problem, however, is still the mechanism of combustion of pyrolyzing solids, so the different practical systems cited above have the same essential basis at the fundamental level-they differ primarily by having different time scales for the reaction time, different intensity scales for the energy release rate and energy density in the system, and different relative magnitudes of the various heat transfer, mass transfer, and rate control mechanisms. In principle, therefore, it should be possible to describe the combus-
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tion behavior of pyrolyzing solids even in such a wide range of practical systems by the same set of simultaneous differential equations, with the different practical systems determined by different rate constants, physical constants, and boundary conditions. From this point of view, the propulsion device is then seen as the latest member of a class of somewhat similar combustion systems, though it is the one having the highest combustion intensity and shortest reaction time. Study of some of the other members of the class and their behavior could, therefore, be of value for purposes of comparison and of interpretation of the behavior in the propulsion chamber. One essential difference that must be taken into account and that might invalidate any useful comparison between propulsion systems and the rest is that in most of the systems (steam boilers, etc.), the fuel usually cokes (forms a solid residue that is either carbon or hydrocarbon of considerable stability), whereas in the propulsion system the fuel must not coke because of its then generally lower reactivity and the possibility of considerable combustible loss from the combustion chamber in the form of ablated solid particles. Conversely, because such coking behavior is known to be a problem in hybrid propulsion units, knowledge of coking behavior could be of use, either in specifying requirements for the appropriate choice of fuel that will not coke, in arranging combustion conditions to prevent coking, or in providing knowledge of how to deal with coke if it should form. Because the literature on combustion of pyrolyzing solids goes back approximately three centuries and is too vast to be cataloged here, it is possible that it may contain something of value to the propulsion problem. The purpose of this paper is, therefore, to examine and discuss some of the pyrolysis and combustion results found in the past during investigation of industrial and similar processes involving combustion of pyrolyzing solids, and to examine these conclusions from the point of view of their relevance and significance to behavior in the combustion chambers of hybrid propulsion devices. Background and Problem Breakdown
Because most of the relevant research of the past has been on coal, this is the material to which most attention will be given in this paper, though other materials involved as subjects of relevant research have included VOL. 5 8
NO. 1
JANUARY 1966
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SURPRISINGLY, MANY DETAILS OF COMBUSTION ARE STILL OBSCURE lignites, coal tars, petroleum tars, celluloses and cellulosic derivatives, woods, resins, sugars, feedstuffs, grains, agricultural produce and waste, rubbers, organic polymers, and a wide range of metals. A brief survey of pertinent literature on these materials is given below. In addition, the following data may also help to place these materials in some sort of mental context. Coal today is usually finely pulverized to be burned in larger boilers, at 1 atm. of pressure (at rates up to 250 tons per hour) and at combustion intensities about 35,000 B.t.u./cu. foot hour atm.; for purposes of comparison, the optimum combustion intensity in Longwell's bomb (38) was estimated at 300 X 106 B.t.u./hour cu. foot atm.; and, in addition, a simple relation between combustion intensity, specific impulse, and thrust is outlined at the end of this article. The size distribution of the coal is about the same as in a liquid spray, though the burning times are longer, being about 1 second at 35,000-B.t.u. combustion intensity. This, however, is not the limit, it is usually held down to this because of slagging problems. Where slagging can be allowed, combustion intensities have been raised, and a figure in excess of 1 million B.t.u./cu. foot hour atm. is said to have been achieved in a special combustor to be used for MHD generation, with flame temperatures over 2000' C. (3600' F.). This is in the region of propulsion combustion intensities, though not of thrusts because of the low operating pressure. In explosion flames, burning times would appear to be shortened by an order of magnitude to about 0.1 second (compared with 0.001 to 0.05 second in liquid fuel thrust chambers). However, with the use of oxygen in place of air, it should be possible to shorten burning times and increase combustion intensities still further, by a factor approaching' a further order of magnitude. Of greater interest and value are the figures on time-toignition and rates of heating which, it now appears, are crucial in determining both the degree of devolatilization at the moment of ignition and (in consequence) the mechanism of ignition. If heating is fast enough, coal evidently does not devolatilize significantly (30, 37), so ignition must occur on the solid particle surface and not in the volatiles, as has generally been assumed in the past. This result, yet to be confirmed independently, was obtained by us using a plug flow reactor in which we found heating rates of lo4 degrees/second; in jet flames they may be an order of magnitude higher. Though these values are four or five orders of magnitude slower than those obtained in the shock tube, they are nevertheless a similar number of orders of magnitude faster than can be obtained by linear pyrolysis and similar devices. Because the flame system we have used can be run for hours at a time, determination of much fine detail of behavior at time intervals of about 0.01 second can be obtained with relatively crude sampling devices and at considerable leisure. If oxygen is used, 16
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
the higher flame speeds and flow rates should spread out the reaction zone over an even longer distance, but covered in a shorter time, so that time intervals between sampling points could probably be reduced to 0.001 second. The results of these and other investigations have been to clarify a picture in broad outline, though a surprising number of the details of the processes are still obscure or unknown. What is clearly established is that, for lumps on a grate, devolatilization is the first event to occur as the particles heat. But with fine particles (less than 100 microns) in dust flames, significant devolatilization starts only after ignition. In either system, at the end point of principal devolatilization, devolatilization is either partial or complete (this is still not regarded as certain), again depending upon the particle size and rate of heating. The tail of the flame is then burn-out of a solid residue by normal heterogeneous reaction of oxygen with the solid surface. Because as the reaction rate increases the degree of devolatilization evidefitly drops, it may become insignificant as the combustion intensities approach those found in propulsion units. Whether this is the case is one of the many still unsolved questions of detailed behavior, to be examined here, in addition to the following questions :
Ignition. Particularly for the coking materials, when ignition starts in the volatiles, is this determined just by production of volatiles or by a specific threshold rate of production? Pyrolysis. Is the rate of devolatilization controlled by the breakup rate of the material, by the escape rate from the interior to the surface, or by the escape rate from the surface to the main oxidant-gas stream? Pyrolysis Mechanism. Is this a first-order volumetric reaction, a surface reaction, or an internal surface reaction? Coking Control. What are the mechanics or chemistry of breakup, and under what conditions is a coke produced? Conversely, what conditions will not produce a coke from a material that will not otherwise melt or flow at the reaction temperature? Volatile Products. W7hatcontrols the nature of these products? Is the primary decomposition reaction supplemented by secondary reactions such as the water-gas and shift reactions?
R. H . Essenhigh is Associate Professor of Fuel Science, Combustion Laboratory, The Pennsylvania State University. When this article was written, J . B. Howard was also with the Department of Fuel Science; he is now Assistant Professor of Chemical Engineering at Massachusetts Institute of Technology.
AUTHOR
SCIENTISTS HAVE PUBLISHED ON COAL COMBUSTION SINCE 1667 Combustion. How does pyrolysis behavior affect the combustion mechanism and the location of the reaction surface? Solid Combustion Mechanitm. What is the mechanism, and what is the dominant rate-controlling process? Is it reaction-control by a diffusion boundary layer, by active surface adsorption, by active surface desorption, or by internal surface reaction? Our own views on the answers to these questions can be summarized fairly concisely, but as there is still argument about the interpretation of the data on which
the views are based, there is still no general agreement on the specific behavior. For that reason, before summariziig our views, we outline first some of the pertinent literature on these points. Hirlory and LHVQIUN
Interest in pyrolysis and combustion of solids originated with studies of coal behavior some indeterminate time ago, and research has now been in progress for about three centuries. The first scientific communication on the subject, to the Royal Society of London, was dated 1667 (77). The early studies were largely confined to the engineering aspects of gas making, for commercial distribution, by coal pyrolysis in coking ovens. Interest in the combustion behavior of solids probably started nearly two centuries later, with Faraday, as a result of hia experiments on the ignition properties of coal dusts (79) following his investigation, with Lyell, of the Haswell Colliery explosion in 1844 (20). One sigdicant result of this work was the original formulation of the distillation or volatiles theory of ignition which is still current today. During the rest of the century, research was largely dominated by the engineering aspects of coal behavior on grates. A more significant scientific contribution was provided by the research on dust explosions, which reached a high level in the first two decades of this century, notably under Wheeler’s direction (60); this resulted in production of many significant data that recently have been reviewed and evaluated (72). Significant contributions here to combustion behavior induded: results of pyrolysis establishing the main pattern of volatiles production from carbonaceous solids (both in rates and components) (7), the demonstration of inflammation at low thermal intensities depending primarily on the first evolved volatile components (8), and the indication that in fast explosion flames there was probably not time for volatiles to be generated (78). At the same time, interest in the explosion hazard potential of other dusts was also developed. Concerning the pattern of volatiles production, it is generally found that materials are reasonably stable to heat, up to a fairly
specific decomposition temperature when breakdown coking starts with a sudden rapid evolution of volatiles, mmewhat as a pulse. In the 1920’s, research on dust explosions was finally carried over into the study of pulverized coal combustion (which had developed to the point of commercial application 40 years earlier). This brought the problem to the attention of a new group, one result being the rise of the physical as opposed to the chemical school of combustion theorists. The effective originator of this was Nusselt (46), with his diffusion theory of reaction control [strongly supported by Hottel (70, 27, 47, 58)],which has only in the past five years been shown to be less general than had originally been thought (4, 54) and evidently does not apply to small particles or systems with thin boundary layers. Apart from the unpublicized &et work in Germany mentioned above, the next developments were in the mid-l94O’s, when a further branching of strong interest developed with lire research investigations into the mechanism of spread of flame in houses and industrial plants. Somewhat parallel with this,in both time and concepts, was the work on spread of flame in forests and on ignition by thermal radiation from nuclear explosions. A key paper frequently quoted is that by Bamford, Crank, and Malan (2) who proposed that ignition occurred at some threshold value of the volatiles evolution; this has undertones of Clark and Wheeler’s proposal (8) that ignition occurred in the first flash of the most easily generated volatiles. However, the two ideas are somewhat at variance. We would suggest that volatiles evolution, being rapid when once started (as a strong pulse), will go through any threshold value so quickly that a threshold has no real significance. That ignition (at slow heating rates) certainly starts in the volatiles, as proposed by Faraday (77, 79, ZO), was demonstrated by photography (27), which also showed that flame then flashed back to the solid surface from the initiation point. This type of system, with heating by radiation [described in more detail by Simms and associates (36,50)]has also been examined recently by Weatherford and Sheppard (59) in connection with lire research problems. In the rocket chamber this type of ignition problem is probably irrelevant, though the influence of the radiation could be significant. In parallel with the combustion and ignition investigations there was also considerable further activity in pyrolysis studies, in addition to the conventional ones used for three centuries, with the application of both D.T.A. (dating from 1914) (26) and T.G.A. techniques (from 1926) (7). The particular value of these techniques has been the use of D.T.A. to detwt compositional changes during breakup by analysis of the thermograms produced, and the use of T.G.A. to get activation energies for the decomposition. More recently these latter have been supplemented by measurements from linear V O L 5 8 NO. 1 J A N U A R Y 1 9 6 6
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pyrolysis studies (3, 44). The essential conclusions of these various studies [partly reviewed by van Krevelen (33) and Howard ( Z S ) ] have been that breakup is a complex process that can, nevertheless, be represented approximately over part of the process by a monomolecular volumetric reaction even for coking materials. At this point we find a number of discrepancies. I n the first place, volatiles escape, or loss of sample weight at constant temperature must be undergoing a two-stage process. Initially, rapid evolution occurs, followed by a long slow outgassing in which the rate is substantially independent of time. This could be due to either the progression of a thermal wave through the solid, as suggested by Weatherford and Sheppard (59) [also Blackshear and Murty (6)] ; or to an initial escape of the surface volatiles, followed by escape from the interior being controlled by diffusion (13). A second point is that early values of decomposition activation energies for both coals and a range of polymers (33, 40,41)are mostly in the range of 50 to 60 kcal. More recent measurements or adopted values (3, 24, 36, 44, 50, 59), including our own current work, seem to be in the range 15 to 30 kcal. Finally, the linear pyrolysis studies showed experimentally that, if a material breaks up completely without coking, it breaks up at the surface, which then regresses, usually quite steadily. It is difficult to see then why a volumetric reaction rate should be almost universally assumed for pyrolysis of coking materials. The problem is akin to extracting a brick from a wall-it is easier to knock one off the edge than to pull one out of the center, unless the wall has a number of somewhat unstable holes. Pyrolysis and Combustion Mechanism
Prevailing Views. In collating the prevailing views on the detailed behavior of the points listed above, the following would seem to be a fair summary. Excluding our recent findings (30, 31), which are being prepared for evaluation by publication, it has generally been accepted that ignition starts in the volatiles. An important exception to this that is possibly significant for propulsion systems is that with the application of thermal fields of high intensity, the material does not have time to coke, but simply ablates (59) ; the ablated material then breaks up further and burns in the gas phase. However, when coking does occur, it is generally assumed to be complete, the solid residue being carbon. Ignition otherwise is thought to be determined by the establishment of the threshold production rate of volatiles as described earlier (59). Production of the volatiles is assumed to be controlled by a first-order volumetric reaction but this results effectively in the creation of a decomposition or pyrolysis wave’s moving further and further into the solid; the thermal conductivity wave does likewise because of the falling temperature profile that exists from the solid surface into its interior. The practical effect of this is to provide at least superficial resembIance to the shrinking drop model proposed elsewhere (73). The material ignited at this stage was 18
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
identified by Martin (42) as Levoglucosan; this would appear to have been something of a catch-all name for the paraffinic and tarry material generally and, in conjunction with the behavior of Hz, CH4, C2He, etc., shows a qualitatively identical pattern to that found by Wheeler (7, 8) for coals and substantiated by many further experiments since then. The mechanism of breakup is obscure. Van Krevelen (33) has suggested that it is controlled by breaking C-C bonds, this conclusion being reached by comparison of activation energies and bond energies, but this is arguable-cf. Hansel and McAlevy (25) on behavior of polystyrene. The location of the reaction surface is assumed to be somewhere in the gas phase during the volatiles evolution, but possibly it shifts to the solid surface when devolatilization has terminated. The control of this surface mechanism is another point of controversy. Following Nusselt (46) and Hottel (10, 27, 47, 58), it was accepted for many years that reaction above 1000° C. would always be dominated by a diffusion boundary layer above the solid surface. I t has now been established (4, 54)that small particles at least (less than 100 microns) are not diffusion-controlled, though whether the control is shifted to adsorption or desorption is still not settled ( 73). It is our belief that this summarizes the majority opinion on the ignition-pyrolysis-combustion mechanism, though there are certainly many dissenters from detailed points. Martin (42), for instance, repudiates the threshold-rate theory of ignition and concludes instead that the prime requirement is for sufficient efflux of volatiles in the first instance that has to be maintained by a sufficient flow rate thereafter. This is substantially in accordance with our view. Two other points that he makes are: first, the possibility of secondary volatiles production by reaction of the incandescent char layer near the surface (at about GOO0 C.) with volatiles from the interior flowing through it; and second, that the actual ignition may be triggered by reaction intermediates possibly formed by the secondary reactions. This may be so. There is clear evidence from behavior of coals (above) and also of wood (48) that there is something in the nature of a two-stage decomposition occurring at two different temperatures leading to a change of activation energy. In certain instances, it is our view that, in coals, this respresents breakdown of two major constituents of the coals ( 7 6 ) , but another view that deserves attention (Q), summarized by Howard (29), is that changes in evolution behavior (and presumably of composition) are partially controlled by the ease and manner of the volatiles’ escape from the sample. Consequently, as the pyrolysis plane migrates further into the sample, the ease and manner of escape are continually altering, and it may be that these are responsible for changes of composition with temperature as the parametric link between the two processes. Authors’ Views. To some extent also, we subscribe to the views expressed above. In the cases where ignition is preceded by devolatilization, we agree with Martin’s view that a threshold evolution rate is prob-
ably irrelevant so far as ignition is concerned; we accept Wheeler’s view of a rapid initial efflux of volatiles going quickly fmm.something negligible to a value significantly above any necessary threshold; we do not see any sound gmund for not accepting Clegg’s view (9) as a strong possibility. What we disagree on principally is that devolatilization always starts at a ked temperature; that it is always a volumetric reaction; that evolution is always determined or controlled by the rate of breakup; and that devolatilization is always complete. Additionally (and subject to independent check of our experiments), we conclude that, at fast heating rates, there is no time for significant devolatiliation before ignition. The evidence for a variation in decomposition temperature is provided by our current experiments on the plug-flow reactor mentioned above (these also bring in the iinal point of completeness of devolatilization). A stationary flame is established in a vertical parallelsided duct, using a modified onedimensional flame furnace (5), and solid samples extracted at various p i n t s are analyzed for volatile content. Figure 1 is a typical curve of the results obtained as a function of both distance and time. The flame is stabilized against a water-cooled tube bank, and it is seen from the figure that the flame fmnt is established at a point 3 or 4 inches below this b a d and at a temperature of about 1000° C. (measured by suction pyrometer). Because helium tracer and other experiments showed the flame to be truly plug flow, the only heat transfer mechanism involved in flame stabilization was radiation to the particles. The particles then lost heat to the
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surrounding gas, so that their temperature would be somewhat higher than the gas, though insignificantly so according to our calculations, which showed that the particles b d gas were never far from temperature equilibrium in spite of the fast heating rate (this was also true for the particle centers). The suction pyrometer temperatures (generally believed to be intermediate between particles and gas) will, therefore, be fairly close to both though, if anything, slightly lower than the true particle temperatures. This gives further point to what follows in the temperature and time figures given below. Our original view and expectation, as expressed elsewhere (14, were that the ignition temperature would correspond to the decomposition temperature of the coal. This view does not hold for the fast heating raten obtained. The data show that the main devolatilization in the flame sets in a t about 1250’ C., und ujtm ignition. Because coals normally start to devolatiliie at about 350” or 400’ C. and will devolatilize almost completely at 1000° C., given time, we conclude that the discrepancy between the normal decomposition temperature and that found in the furnace must be due to the existence of an induction period of about 0.1-second duration. I n accounting for this induction period we present the following tentative suggestion: If liquids cooled carefully and slowly can be supercooled below their normal freezing point, might it not be possible that solids heated rapidly can indeed be superheated above their normal melting or decomposition point? If this is possible, it would then seem reasonable to conclude that any system such as an explosion flame with faster heating than this, (10’ degrees per second), and having burning times of the same period as the volatile evolution (0.1 second) will not be able to devolatilize and must burn as solid particles without decomposing. This was the view taken of explosion flames (12), somewhat against some previoua opinions [though in agreement with (78)l; there may be a close relation of this behavior to that found with intense thermal irradiation (see above) when the material ablated without decomposition. In line with this is the behavior shown by the material in the tail of the flame-again we had anticipated that the conventional view of complete devolatilization (at 1600” C.) would be borne out. Figure 1 shows that this is not so. After the initial rapid loss down to 5 or 6y0 V. M., the rate of loss suddenly drops to an almost negligible value, the residue corresponding to a C / H complex normally obtained at the coal’s “carbonization pole” (34) and corresponding roughly to C I O O H ~ ~ O On~ .grates with exposure times of minutes or longer, even this volatile residue is lost; again as the converse, it is reasonable to expect that less will be lost with shorter exposure times. The second point of disagreement listed, that concerning the volumetric nature of the reaction, is also a point on which evidence is supplied by Figure 1, in conjunction with other experiments. The key to determining the nature of the reaction is the nature of the theoretical prediction or assumption generally invoked. This is, as partially substantiated by van Krexelen (35), V O L 5 8 NO. 1 J A N U A R Y 1 9 6 6
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that the reaction, being first-order volumetric, will have a rate proportional to the volatile content, V , left. Thus : d V / d t = -kV (1) where k is a decomposition constant. Because this is independent cf particle size or thickness, then for a material uniformly heated, a rate of generation, or generation time, that is independent of particle size will denote a volumetric reaction; one dependent on particle size will indicate a nonvolumetric reaction. Now studies of single particles of coal (73) have shown that the evolution time is proportional to the square of the particle diameter in the range 300 microns to 4 mm., obeying the relation : t , = Kda (2) where K is an evolution or combustion constant; and do is the initial particle diameter. This was analyzed ( 7 3 ) on the basis of a shrinking drop model on which the generation rate was assumed to be determined by the rate of escape through a carbon matrix. In this shrinking drop analysis, the carbon matrix was treated as an inert porous body containing potential volatile material that was assumed to turn instantaneously into liquid which was then able to vaporize off at its equivalent surface. This was a fictitious device introduced to provide an argument for specifying the volatiles concentration at the drop surface, and must not be taken as implying the existence of a real physical liquid drop. If a real liquid drop existed, then the analysis of the drying of solids developed by Sherwood (49) would be relevant; however, in that case the drying rate period [see Norton (45)]would be controlled by capillarity behavior, not by gaseous diffusion. The drying process does, however, provide an interesting parallel. A closer parallel, in some respects, is the internal reaction process (for example, oxygen diffusing into carbon) first analyzed by Theile (52). However, this still differs in essentials because the reaction of the diffusing gas takes place throughout the volume from the exterior surface to some ill-defined combustion depth (which also goes vanishingly to zero as the temperature rises) whereas the pyrolysis process is assumed to be located at a thin surface only, at some location inside the particle. As both these previous analyses were inappropriate to the system, the shrinking drop model was developed and analyzed. The equation obtained did predict a squarelaw relation with particle diameter. I n general agreement with this, so far as the particle size influence is concerned, are the results obtained by Ishihama (32) on ignition limits of coal dusts. He found that the low limit concentration varied with particle size according to a rectangular hyperbola, substantially in agreement with other conclusions (72), with the limit being strongly dependent on particle size above 150 microns and largely independent below 50 microns. Finally, devolatilization times for the flame particles (mostly less than 50 microns), being about 0.1 second, are about an order of magnitude longer than those calculated from Equation 2. This shows that Equation 2 cannot be extrapolated 20
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
down to the small particles. In our opinion, the inference is that there is a change of control in the mechanism of volatiles escape, from a diffusional escape control above 150 microns to a chemical breakup mechanism below 50 microns. Theory of Volatiles Evolution. The final point of disagreement on the theory of volatiles evolution requires rather fuller treatment. Elements of the theory have already been sketched. The principal point of disagreement is whether the reaction is still volumetric when-as is almost universally assumed-the particle size or slab thickness is increased above 100 microns (2, 6, 48, 53,59). The central problems in the volumetric theory are these: why are the volatiles in the interior formed with as much ease (equal activation energy) as the volatiles at the periphery of the active area (described as the brick wall problem above) ; and how can the volatiles from the center escape, unless and until the material forms many major cracks for them to escape by. O n the shrinking drop model (73), the particle was regarded (as described above) as a porous carbon matrix containing fluid-forming material that could be treated as behaving as a liquid drop vaporizing at its exposed surface, and the rate of escape was determined by the diffusion through the carbon matrix. O n this view, we should expect to find some physical indications that can be detected by appropriate physical examination ; such expected indications have recently been provided by two independent sources. In the first, Blackshear and Murty (6) took x-ray photographs of cellulose disks during pyrolysis caused by combustion in air, and the existence of a more solid center shrinking with time is clearly evident. This was further substantiated by density traverses across the disk. A similar pattern was observed by Tinney (56) in another set of experiments on the combustion of wooden dowels. He found that polished cross-sections of part-burned dowels also showed a clearly defined unaltered central area of steadily reducing width as reaction proceeded. This, however, is by no means conclusive because of the temperature gradients found to exist (6, 48, 56, 59) inside the materials. Calculation (59) has shown that these could have been responsible for the density pattern observed. The situation is obscure because fairly thick slabs of material clearly must be affected in some degree by the temperature gradient. However, the main point at issue is whether the pyrolysis wave is generated : -exclusively by this gradient [as Weatherford and Sheppard (59) indicate] -by the surface pyrolysis process at the interface between the pyrolyzed and unpyrolyzed material (as assumed for the shrinking drop model) -by a combination of the two Now it is obviously possible to distinguish between the first and the second hypotheses by heating the material in such a way that the temperature gradient through the material is small or zero. If the reaction is then found to be uniformly volumetric, with no evidence of a
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pyrolysis wave, then the second is disproved. Alternatively, if the reaction shows evidence of a pyrolysis wave, the first is disproved. Some of the existing experimental results mentioned above do provide some information on this. First, in Ishihama's results (32), ignition, believed to depend on pyrolysis, was independent of particle size when this dropped below 50 microns. So, as explained above in discussing Equation 1, this denotes a volumetric reaction. For larger particles in the range up to 4 mm., both Ishihama's data and the single particle studies (73) show a dependence on particle size which rules out a volumetric reaction. However, calculations of the rate of heating, even of the 4-mm. particles, showed that the temperature of the particle centers was never far behind that of the surface. This would seem to disprove the first postulate for this size range. Unfortunately, these conclusions depend on inference rather than direct proof, so they still must be regarded with some reserve. The ambiguities of interpretation can be further illustrated by comparing the results of four methods of analysis of pyrolysis data given by Blackshear and Murty (6). Figure 2, taken from their paper, is reported as a typical weight l a curve obtained during their experiments: -Their own interpretation of these data was partially based on the Godsave-Lloyd (22, 37) analysis of the oil drop, as m d i e d in nomenclature by Spalding (57) [similarto the Nusselt (46) solid-particle analysis]. The mass transfer coetlicient then calculated from boundary layer diffusion theory was in fair agreement with experiment, regarding the behavior as equivalent to a heavy oil drop [with a combustion constant of the order of 1 V c.g.s. units; this is the order found for such materials (731. Such supeficial similarity with burning constants has been observed also in the case of coal particles (73), and the objections to treating the two as comparable systems have been discussed in that paper. For a diameter function, Blackshear and Murty then appealed to conductive heat transfer as discussed by Gross (24) to explain the diameter dependence found: proportional to 1/84 -If, however, we accept that the material is behaving l i e a liquid drop on the Godsave-Lloyd model, by the mass transfer equations we should expect a Nusselt type (diameter Squared) equation to apply, whether the material is a sphere (46)or a cylinder (24). In terms of mass variation with time, we get for a sphere (46), equivalent sphere, or cylinder (77) an equation of the form (M/Mo)'/," = 1 kt (3)
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0.0
Rgwc 2. Lkta from Blackham and MUrry (6)demmutrotd tha a m tipitim in intmpetdon of I h r k explaining thc evolution of oolati[O. (Top)ty&al w& lass CUIW for a pUrolyzing cyIindn of cellulose auring canhution; (midle) th data me compared with predictiow from E@atiom 3 and 4; (bottom) th same data platkd (15 in Egua1' lion 5. All of thm intaprrroriaUfit tha exQ&nmtal datafairly well
where Ma is the initial weight and k is the decomposition or decay constant (Equation 1) which differs only by the numerical factor of 0.215 if the system is a cylinder rather than a sphere. This gives a relation proportional to 8.w. -Alternatively, if we assume a rate of breakup proportional to the sphere or cylinder equivalent diameter, we have
. ....a'-
I
V O L 5 8 NO. 1 J A N U A R Y 1 9 6 6
21
(M/MO)1/2 = 1 - kt
(4)
-Finally, as a rate of escape problem, by internal diffusion, extension to a cylinder of the sphere theory, given elsewhere (6) and summarized at the end of this article, gives us
( M / M o )[l -
'/z
In ( M / M o ) ]= 1 - kt
(5)
Figure 2 (middle and bottom) shows the data of Figure 2 (top) plotted according to these equations. It is clear from this, plus the representations given by the authors, that the data are reasonably consistent with all four interpretations. This shows clearly the perils of assuming that agreement with an equation is necessarily a confirmation of a theory or a mechanism. I t is, therefore, clear that definitive experiments will have to be set up to distinguish between the various possibilities. Discussion and Conclusion
'The foregoing shows that detailed pyrolysis behavior of burning solids is still obscure. What is reasonably established is that ignition of large particles does start in the volatiles, though for small particles heated quickly it evidently starts on the solid. For systems already burning (such as pulverized flames), flame is selfsustaining and there is no real ignition problem. For materials being heated in an intense thermal field, ignition probably starts at some ill-defined temperature or generation rate ; the sole requirement when devolatilization is important seems to be that the generation rate shall be reasonable rapid, which is generally the case. For small particles (less than 50 microns), and probably also for thin sheets, we conclude that devolatilization (when it occurs) is almost certainly a volumetric reaction. For particles and thick sheets, the generation rate certainly becomes dependent on size and thickness. What is still obscure is what then controls the rate of volatiles loss-whether it is the temperature distribution through the solid, operating on a volumetric reaction, or whether it is the diffusional rate of escape through the solid. I n either case, however, the effective behavior is as though a pyrolysis wave were propagating through the solid at a rate that is controlled, either by the rate of conduction of heat from the solid surface inward, or by the rate of diffusional escape of the volatiles from the interior outward. Because the conduction and diffusion equations have essentially similar forms, this may account for the ambiguity of interpretation of the rival theories in accounting for the pyrolysis behavior. If the rate of volatiles production is fast enough, it can sweep the surface clear of oxidant and prevent surface reaction. If generation is slow, simultaneous reaction at the exposed coke surface can occur. If this reaction is fast enough for the solid surface to regress faster than the propagation of the pyrolysis wave, there will be no pyrolysis. The reason for such regression of the solid surface could be direct oxygen attack, as suggested, or it could be due to ablation caused by an intense thermal field. In the first instance, the location 22
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
of the reaction surface will be at the solid surface; in the second it will be in the gas phase. Reaction control, in the first instance, will be the rate of surface reaction; in the second instance, it will be the ablation rate. Location of the reaction surface or zone, under ablation, is also indeterminate. I t is generally presumed to be in the boundary layer. This is the thought behind such analyses of those of Marxman and Gilbert (43) and of Tsuji (57). However, it is also possible that, in turbulent flow conditions, reaction may take place uniformly across the stream flow as in the carbon channel analysis given elsewhere (55). As shown in that analysis, reaction can be velocity-dependent even when the transport processes (molecular or turbulent diffusion) are too fast to be significant resistances. It seems to us that this type of analysis may deserve more attention. The relevance of this to hybrid rocket combustion systems is somewhat repetitive. A solid with sufficient carbon in it to remain solid at reaction temperatures, and not to flow or shear, may cause difficulty if the ablation or regression rate of the surface is slower than the propagation rate of the pyrolysis wave. Under such conditions, it can be anticipated that there will be a n initial efflux of volatiles from a surface layer, perhaps 50 to 100 microns deep, followed by a steadier efflux as the pyrolysis wave moves into the solid. This presumably can be eliminated if the fuel characteristics are so chosen that regression of the surface is always faster than the propagation of the pyrolysis wave at the thermal intensities involved. This would seem, therefore, to define the central problem-determination of the characteristics of carbonaceous solids that will enable prediction of the rate of regression of the unchanged surface, and speed of propagation of the pyrolysis wave, under the conditions of temperature, pressure, and flow involved in propulsion combustion chambers. Background Information
Relation between Combustion Intensity, Spec;f;c Impulse, and Thrust. Define the combustion intensity I , as:
I, = mAH/PVc where AH is the heat of combustion; P, the pressure (in atmospheres) ; m,the firing rate; V,, the combustion volume ; and define
v6 = c2/2 JAH where vt is the internal efficiency (usually between 0 and 50%); J , the mechanical equivalent of heat; and c, the exhaust velocity. Then, because the specific impulse I , is given by
Is
= c/g
where g is the gravitational constant, by elimination we get
I?
=
(2 v , ) ( ~ c ~ / g 2 ~ J ) I ,
so that, for a given combustion chamber operating at a
given pressure and flow rate, the specific impulse rises with the square root of the combustion intensity (for q* assumed constant). Because also for the thrust
F = I,mg then
F2 = (2 d ( V 2 m ) I e or
F = (2
176)
(V,P/g>( I O / I J
Derivation of Devolatilization Rate Equation from Permeability Analysis. The analysis given here follows that given previously (73). The chief difference is the change from a sphere to a cylinder which alters the forms of certain equations, not the method of analysis. The pyrolyzing material is regarded as a cylindrical porous matrix of radius ao, with a permeability Po to the passage of vaporized volatiles of viscosity 7 being expelled. A diminishing cylindrical reservoir of liquid volatiles has radius a. At any radial surface r, the flow rate of vaporized volatiles is u, given by Darcy’s equation u =
- ( P o / v )(dc/dr)
where (dcldr) is the radial concentration gradient. the liquid surface the flow rate is u, where u, = u ( r / a ) =
At
At the matrix surface (r = ao) the volatiles concentration is co; at the liquid surface (r = a ) it is pure volatile of constant concentration ca. Hence, integrating gives
- CO)
By one method of analysis, and depending on the further assumptions made, (c, - CO) appears to be constant; by another, there are indications that it could be proportional to 2. If it is taken first as constant, because v, is the mass rate of change (per unit area) of liquid to vapor [ ( d m / d t ) / 4 ~ a ~then: ] ] , vu = -u(V/lOO)(da/dt) = c,(P0/7)/a In (ao/u)
(6)
where Q is the solid density and V is the volatile percentage of the material. Integrating again and substituting ( M / M o ) for (u/ao)2 we get
( M / M o )[l - In ( M I M o ) ] = 1
- kt
(7)
Test of this equation against the experimental data shows that it does not fit. However, taking into account the effect of the concentration term co and a possible dependence of this on a2, the modification to the equation is addition of a term in a to the denominator of the right-hand term of Equation 6. This then becomes [a ba In ( u o / a ) ] , where b is constant. The effect of integrating is to change the left-hand side of Equation 7 to ( M / M o )[l - f In ( M I M o ) ]where f is some fraction to be determined. Indications are that f can take the value of 1/2, so the final equation reads
+
( M / M o )[l -
l/2
In (M/Mo)J = 1 - kt
(1) Audibert, E., Rev. Ind. Minirale 115 (1926); Chem. Abs. 20, 2239 (1926). (2) Bamford, C. H., Crank, J., Malan, D. H., Proc. Cambr. Philosophical SOC.42, 166 (1945). (3) Barsh, M. K., Anderson, W. H., Bills K., Moe, G., Schultz, R. D., Reu. Sa’. Instr. 29, 392 (1958). (4) Beer, J. M., Essenhigh, R. H., Nature 187, 1106 (1960). (5) Beer, J. M., Thring, M. W., Essenhigh, R. H., Combust. Flame 3,557 (1959). (6) Blackshear, K. A., Murty, P. I& Tenth Symp. (International) on Combustion, 911 (19651, The Combustion Institute, Cambridge (England). (7) Bur ess, M. J., Wheeler, R. V., Trans. Chem. SOC.97, 1924 (1910); 99, 649 (1911y. (8) Clark, A. H., Wheeler, R. V., Ibid., 103, 1754 (1913). (9) Clegg, K. E., Illinois State Geol. Survey, Rep. Investigations No. 190 (1955). (10) Davis, H., Hotte1,H. C., IND.ENa. CHEM.26, 889 (1934). (11) Derry, G. H., Williams, T. I., “A Short History of Technology,” p. 506, Oxford, 1960. (12) Essenhigh, R. H., Colliery Eng. 38, 534 (1961); 39, 23, 65, 103 (1962). (13) Essenhigh, R. H., J . Eng. Power 85, 183 (1963). (14) Essenhigh, R. H Csaba J Ninth Sym (International) on Combustion, Cornell, 1962, p. lli: Acadehchress, N. Y. $963). (15) Essenhigh, R. H Fells, I Disc. Faraday Society, T h e Physical Chemistry of Aerosols, p. 208, Brystol, Engiand, September 1960. (16) Essenhigh, R. H., Howard, J. B., “Combustion Ehenomena in Coals and the Two Component Hypothesis of Coal Constitution Paper 44, American Conference on Coal Science, June 1964 (Penn. State U&.) (to be published). (17) Essenhigh, R. H., Yorke, G. C., Fuels44, 177 (1965). (18) Explosions in Mines Comm., 4th Rept. p. 9 et seg., H.M.S.O., London (1913). (19) Faraday, M., Lyell, C., Phil. Mag. 26, 16 (1845). (20) Faraday, M.,,Lyell, C. “Report t o the Home Secretary on the Explosion a t the Haswell Colliery” on September 28, 1844 (Report of 1845). (21) Fire Research, Joint Fire Research Organization (London), Ann. Rept. for 1954 (1955). (22) Godsave G. A. E Nature 164, 708 (1949)’ 166 111 (1950). 4th Symp. (InternatioAal) on Co‘kbustion, p. 84, Cambridge, 1d52, Williams and Wilkins, Baltimore, 1953. (23) Green, Leon, Jr., Introductory Considerations in Hybrid Rocket Combustion p 451 “Heterogeneous Combustion ” Vol. 15 Progress in Astronautics and A;ron&tics Series, H. G. Wolfard, I. blassman, :nd Leon Green, Jr., eds., Academic Press, New York, 1964. (24) Gross. D.. J . Res. Natl. Bur. Std. 66C. , 99 (1962). . , (25) Hansel, I. G., McAlevy R. F., A.I.A.A. Second Aerospace Meeting, Paper No 65-68 New York 1965) (26) Hollinis, H Cobb’ J. W’ J. Gas Li htin 126, 917 (1914); Fuel 2, 322 (1923). Stedart,I.’M., IND.&Q. &HEM. 32,719 (1940). (27) Hotte1,H. (28) Howard, H. C., Supplement t o Chemistry of Coal Utilization, Ch. 9, p. 340. (29) Ibid., p. 369. (30) Howard J B., Ph.D. thesis, Fuel Science Dept., The Pennsylvania State University,’ 1665. (31) Howard, J. B., Essenhigh, R. H., Com6ust. Flame 7, 337 (1965). (32) Ishihama, W., Studies of the Lower Critical Explosive Concentration of Coal Dust Clouds, 11th International Conf. of Directors of Safety in Mines Res., Warsaw (Poland), October 1961. (33) Krevelen, D. W. van, “Coal Science,” chap. 14, Elsevier, Amsterdam, 1957. (34) Krevelen, D. W. van, Fuel 29, 269 (1950). (35) Krevelin, D. W. van, Heerden, C. van, Huntjens, F. S.,Ibid., 30, 253 (1951). (36) Lawson, D. I., Simms, D. L., Brit. J . Appl. Phys. 3, 288, 394 (1952). (37) Lloyd, E., Proc. Inst. Mech. Eng. 159, 220 (1948). ENQ.CHEM.47, 1634 (1955). (38) Longwell, J. P., Weiss, M. A., IND. (39) Lutz, O., Akad. Luflfnhrtjorrchungen 37, 13 (1943). (40) Madorsky, S. L., J.PolymerSci. 9, 133 (1952); 11, 391 (1953). (41) Madorsky, S . L., Straws, S.,J . Res. Natl. Bur. Std. 53, 361 (1954). (International) on Combustion, 877 (1965), (42) Martin S. Tenth Sym The Combusti’on Institute, &&bridge, England. (43) Marxman, G., Gilbert M Ninth Symp. (International) on Combustion, Cornell, 1962, p. 371, Academic Press, 1963. (44) Nachbar, W., Williams F A. “ O n the Analysis of Linear Pyrol sis Experiments,” p. 345, Ninth Sykp: (Ihternational) on Combustion, Acadkmic Press, 1963. (45) Norton, F. H., “Refractories,” chap. 7, p. 157, McGraw-Hill, New York, 1949. (46) Nusselt, W., VDI60, 102 (1916); 68, 124 (1924). (47) Parker, A. S., Hottel, H. C., IND. ENG.CHEM.28, 1334 (1936). (48) Roberts A. F Clough G Ninth Symp. (International) on Combustion, p. 158, Coxkll, 1562, Academii Press, 1963. (49) Sherwood, T. K.,IND. ENO.CHEM.21 (12), 976 (1929); 24,307 (1932). (50) Simms, D. L., Combust. Flame 4, 293 (1960); 5, 369 (1961); 6, 303 (1962); 7,253 (1963). (51) Spalding, D. B., Proc. Inrt. Mech. Engrs. 168, 545 (1954). ENQ.CHEM.31, 916 (1939). (52) Theile, E. W., IND. (53) Thomas, P. H., Trans. Faraday SOC.56, 833 (1960); 57, 2007 (1961); Proc. Roy. Soc. 262A, 192 (1955). (54) Thring, M. W., Beer, J. N., Proc. Anthracite Conf., Mineral Industries Experiment Station Bull. 75, p. 25, T h e Pennsylvania State University, University Park, Pa. (1961). (55) Thring, M. W., Essenhigh, R. H., Suppl. t o Chemistry of Coal Utilization, chap. 17, p. 768, Wiley, 1963. (56) Tinney, E. R., Tenth Symp. (International) on Combustion, 925 (1965), The Combustion Institute, Cambridge, England. (57) Tsuji, H., Ninth Symp. (International) on Combustion, p. 384, Cornell, 1962, Academic Press, 1963. (58) Tu, C. M., Davis, H., Hottel, H . C., IND.ENO.CHEM.26,749 (1934). (59) Weatherford, W. D., Shep ard, D: M., Tenth Symp. (International) on Combustion, 897 (1965), The eombusuon Institute, Cambridge, England, (60) Wheeler, R. V., Trans. Chem. SOC.103, 1715 (1913).
6,
-( r / a ) ( P o / d ( d c / d r )
In (sola) = (Po/qu,a)(c,
LITERATURE C I T E D
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JANUARY 1 9 6 6
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