Energy & Fuels 1990,4, 171-177 apparent activation energy is 14.6 kcal/mol, and the A factor is 4.6 X lo6 (O/C)(day)-'. 3. There is a significant relative increase in the amount of oxidized organic sulfur during 295 K oxidation of Powder River Basin coal even though the total amount of
171
organic oxygen remains almost constant. The extent of organic sulfur oxidation at the surface can therefore be used as a rough indicator for the extent of prior weathering. Registry No. COz, 124-38-9; water, 7732-18-5.
Autocorrelations of Kinetic Parameters in Coal and Char Reactions Robert H. Essenhigh*pt and Mahendra K. Misraf Department of Mechanical Engineering, The Ohio State University, 206 West 18th Avenue, Columbus, Ohio 43210 Received October 26, 1989. Revised Manuscript Received January 11, 1990
For a wide range of coal reactions, the values of the preexponential constants (ko)and activation energies ( E )are shown to be so highly correlated that the presumption is that they are autocorrelated. The reactions involved include total pyrolysis; pyrolytic release of tar,hydrocarbons, and low molecular weight gases; volatile combustion; and char-gas reactions. The presumption of autocorrelation is supported by a simple analysis based on the assumption that variations in ko and E are a statistical consequence of random errors of measurement, and this carries the associated inference that the primary rate measurements belong to a common data set in spite of the wide range of KO and E values extracted (often by different procedures in data reduction). This conclusion also implies such a surprising degree of commonality in the two main reaction groups (pyrolysis and char-gas reactions) that requires the reactions to be substantially independent of coal rank.
Introduction In the measurement of the two principal kinetic constants required to describe chemical reaction rates, k, and E , it is no surprise to find wide variations reported in values of these two parameters for different reactions since it is reasonable to assume a priori that ko and E are independent. In a number of cases, however, the ko and E values have been found to be correlated, and sometimes so highly correlated that they may be considered to be autocorrelated. This is particularly the case for coal pyrolysis and combustion reactions. Uncertainty of prediction due to variations in kinetic parameter vaues has been a particular problem in modeling coal and char reactions, and establishment of such autocorrelations is of particular value in coal flame modeling as this reduces the number of independent kinetic parameters from two to one. In this paper, therefore, we have several objectives. The first is to illustrate E-ko correlations, or lack thereof, for a range of coal and char reactions, using immediately available data; the second is to examine the conditions under which the identified correlations may be regarded as autocorrelations, with corresponding utility to modelers in reducing (unwanted) degrees of freedom and with an associated improvement in the confidence level of the model predictions; and the third is to invite enlargement of the data base reported here to fill in gaps and to determine the extent to which the data show or fail to show autocorrelations, with the associated objective of identif'E. G . Bailey Professor of Energy Conversion. Graduate Research Fellow.
*
0887-0624/90/2504-0171$02.50/0
ying the sources of the wide parameter variations that currently exist.
Data Correlations for Coal and Char Reactions Figures 1-15 illustrate correlation plots of ko against E , using mostly literature data, for the following reactions: coal pyrolysis (Figures 1 and 2); release from pyrolyzing coal of tar (Figure 3), hydrocarbons (Figure 4), and the gases H20, C 0 2 , CO, and H2 (Figure 5); volatile matter (VM) combustion (Figure 6); char oxidation (Figures 7-9); catalyzed oxidation (Figure 10); low-temperature oxygen adsorption (Figure 11); oxide film desorption (Figure 12); steam gasification (Figure 13); C 0 2 gasification (Figure 14); and hydrogenation (Figure 15). The majority of the values used in these plots are from updates of previously compiled data sets described in refs 1 and 2 for, respectively, pyrolysis and the char-gas reactions. The basis for the latter was Table 19.6 in ref 2, which provides all necessary source references. Additional values were mainly obtained from recent publications with easy accessibility, notably data we have developed in current experiments on VM c o m b u ~ t i o n(Figure ~ * ~ 6 ) and (1) Misra, M. K.; Essenhigh, R. H. Energy Fuels 1988, 2,371-385. (2)Essenhigh, R. H. Fundamentals of Combustion, In Chemistry of Coal Utilization: Second Supplementary Volume;Elliot, M. A., Ed.; Wiley: New York: 1981; Chapter 19. (3) Shaw, D. W. Determination of Global Kinetics of Coal Volatiles Combustion. Poster paper presented at the Twenty-Second Symposium (International) on Combustion, Seattle, August 1988. (4)Zhu, X.Private communication on continuation of ref 3 investigations, Department of Mechanical Engineering, The Ohio State University, 1989.
0 1990 American Chemical Society
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Figure 1. Correlation of preexponentialfactor (ko)and activation energy ( E )for pyrolysis of coal treated as a one-step first-order process (56 determinations; see ref 1).
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Figure 4. Correlation of preexponentialfactor (kd and activation energy ( E ) for hydrocarbon release in coal pyrolysis.
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Figure 3. Correlation of preexponentialfactor (ko) and activation energy ( E ) for tar release in coal pyrolysis.
data (Figure 7) from the Quarterly Reports of Sandia National Laboratories Combustion Research Facility.6 These last have particular interest because these are measurements obtained over a period of 2 years in the same experimental device (particles injected into gas flames) operated by the same investigators using only a limited set of chars; by comparison, the other graphs for the most part represent results obtained by numerous investigators in widely different experiments. Additional values on the oxidation plot of Figure 8 are the commonly cited and widely used value extracted from Field‘s data? a value obtained recently’ by reanalysis of Davis and Hottel’s data,s and a value used by Goldman et al.9 in (5) Hardesty, D. R. Quarterly Reports of the Sandia National Laboratories Combustion Research Facility, July 1987-June 1989. (6) Field, M. A. Combust. Flame 1969, 13, 237-252. (7) Essenhigh, R. H. Stefan Flow Effects in Boundary Layer Diffusion during Carbon Particle Combustion. Presented at the Spring Meeting of the Central States Section of the Combustion Institute, Argonne National Laboratory, Chicago, IL, May 1987; paper CSS/CI-71-87. (8) Davis, H.; Hottel, H. C. Ind. Eng. Chem. 1934, 26, 889-892. (9) Goldman, J.; Xieu, D. V.; Oko, A.; Milne, R.; Essenhigh, R. H. Proceedings of the Twentieth Symposium (International)on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; pp 1365-1372.
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Figure 6. Correlation of preexponential fador (k,) and activation energy ( E ) for volatile combustion (data source refs 3 and 4).
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Figure 9. Correlation of preexponential fador (ko)and activation energy ( E ) for char combustion (units g/(gs)) (data source ref 2 update; see text).
Catalysis
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Figure 10. Correlation of preexponential factor (k,) and activation energy (E)for catalytic oxidation (data source ref 2 update; see text).
modeling fixed-bed gasification (with additional values from the same source on the gasification plots of Figures 13 and 14). Trend lines are included in all cases but one (Figure 14) to assist inspection, and the empirical correlations obviously vary from good to indifferent but mostly are good.
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Statistical Source of Autocorrelation Correlations between values of E and ko first appears to have been described by Constable in 1925loJ5in a study of catalysis of gas reactions on oxidized metal surfaces, and related work has ~0ntinued.ll-l~In that and the related work, in general, there were variations in the catalyst treatments that reasonably led to the conclusion that the E-ko variations were due to real changes in material properties, and that the reasons for the variations could
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Figure 8. Correlation of preexponential factor (ko)and activation energy ( E ) for char combustion in various units (data source ref 2 update; see text).
1962;pp 139-147.
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Figure 11. Correlation of preexponential factor (KO) and activation energy ( E )for low-temperature adsorption (data source ref 2 update; see text).
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Figure 13. Correlation of preexponential factor (ko) and activation energy ( E )for steam gasification of char (data source ref 2 update; see text). 10
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Figure 12. Correlation of preexponential factor (ko) and activation energy ( E ) for oxidation desorption (oxide film decomposition) (data source ref 2 update; see text).
Figure 14. Correlation of preexponential factor (ko) and activation energy ( E )for C02 gasification of char (data source ref 2 update; see text).
be explained mechanistically, with the correlation in the kinetic parameters referred to in several cases (e.g., ref 13) as the “compensation effect” of the theta rule. In the correlations shown in Figures 1-15, some of the variations may be due to real variations in reactivity; however, it is our belief that much if not most can be explained as a consequence of random statistical sampling of implied data sets where the true kinetic constants are invariant. This is quite a different explanation from that previously advanced1*13 and is the focus of the analysis following which we believe is presented here for the first time. We may suppose that, in carrying out experiments, we obtain subsets of (experimental) values of velocity constants that are randomly selected (and error-loaded) samples abstracted from a true ”universal” data set of velocity constants, k , at different temperatures, T. We assume that the universal data set has “true” kinetic parameters, ko and E, which are defined in the usual way by the Arrhenius expression:
The actual measurements of the (error-loaded) subset of velocity constants, k*, then generate the approximate kinetic-constant values, k0* and E*, also defined by the Arrhenius expression: = ko* exp(-E*/Rr) (2)
k*(n
[note that the dimensions of the k’s will depend on reaction order and the basis of measurement]. The experimental data set of k’s and 7“s will be measured over some defined temperature range having some midpoint or median value, To*,and the set will have a There will center of gravity with coordinates [k(To*),To*]. be a corresponding reduced set of data points from the universal set in the same temperature range, with center of gravity coordinates [k(TO),TO].In any random sampling of points, however, the highest probability will be that the two centers of gravity of the two data sets will approximately coincide so we can take To* = To and k(To*)= k(To). Thus, we can equate eqs 1and 2 at T = To,so that, after rearranging we have In ko* = [In ko - E/RTo] + ( l / R T o ) E * (3)
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Energy & Fuels, Vol. 4, No. 2, 1990 175 1
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Figure 15. Correlation of preexponential factor (k,) and activation energy (E)for char hydrogenation (data source ref 2 updatq
see text).
This is the basis for proposing the existence of statistical autocorrelation between ko* and E*; and eq 3 is thus the autocorrelation equation between the two parameters if the originating experimental data points are true subsets of the universal set. It is the equation of a straight line with slope (l/RTo) so that the autocorrelation can apparently fail if the measurements have sufficiently different midpoint values of To. It can also apparently fail if the centers of gravity are not sufficiently coincident. In general, however, these will only be sources of random variation about the autocorrelation line. Otherwise, when In (ko*) correlates well with E*, the highest inference is that the originating experimental data points are subets of a common set. The inference is further supported if the slope of the correlating line is close to (l/RTo). This is the case, for example, in Figure 7 where the experimental temperature range was 1400-2000 K, for a midpoint value of Toof 1700 K, which is close to the value obtained from the slope of the graph. Likewise, there is adequate but lesser agreement in Figure 11where Tocalculated from the slope was about 500 K which was the upper limit of the reported experimental temperature range. There is also an important inverse of the above argument. Let us suppose that there exists a set of Arrhenius plot lines with sufficiently common centers of gravity that eq 3 is obeyed, but that the data sets are not subsets of a common universal set (i.e., they are different reactions). This can only happen if these independent and randomly determined reactions just happen to have reaction rates that are all (approximately) the same at the arbitrarily chosen midpoint temperature, T,. The probability of such an occurrence is believed to be improbably low; conversely, where the correlation is obtained, it is a reasonable inference that the existence of the correlation most probably implies an autocorrelation: that is, one that is not randomly based. If the existence of an autocorrelation is accepted or established, this can have major value in limiting the range of options for selecting joint values of E and lz,; but the procedure, obviously, does not provide the true values. We may reasonably suppose, however, that the ko* and E* values are as likely to be high as low, in which case the determinations overall are likely to be normally distributed along the autocorrelation line so that the best estimate of the true value would be expected to be at about the mid-
point of the range. This identifies a factor for future evaluation.
Commentary on Data 1. Overall, the graphs show minor to major degrees of autocorrelation. Indeed, this principle was used in ref 1 (Figure 1)in analysis of pyrolysis behavior to reduce the number of degrees of freedom and constraints in determining best estimate kinetic values for the pyrolysis, with some approach to uniqueness in kinetic parameter determinations. Of the other data sets, Figure 7 is of particular interest for the reason already given, that the data are essentially “sole-sourcenmeasurements, with about half the measurements on the same material (Lower Wilcox char) in different flame conditions. Moreover, the outliers on this plot were for such sufficiently different experimental conditions that autocorrelation was not expected in those cases. The unexpected element is the astonishingly wide range of activation energies reported (10-65 kcal/mol) if, indeed, the data are in autocorrelating sets. It is otherwise necessary to suppose that materials of widely different reactivity properties (controlling the temperature coefficient of the reaction) happen to have very similar velocity constants at the arbitrarily selected midpoint temperature, To,of 1700 K. 2. Comparison between graphs shows some interesting agreements and differences. A detailed examination is out of place here as this calls for a major review article, but some of the highlights can be identified. In the pyrolysis group of figures, Van Krevelen’s data in Figure 2 appear to be out of place or anomalous in comparison with Figure 1, evidently because the particles used in the determinations were large enough that there was probably interference from diffusional escape of the volatiles, as shown in the detailed analysis documented in ref 1. In the wider range of pyrolysis results (Figures 1,3-5), there is no significant differentiation between the correlation lines for release of tar,hydrocarbons, H20,COz, CO, and total pyrolysis (with H2 arguable because of the limited data). If these are valid autocorrelations for the individual constituents, their kinetic constants can be described by eq 3 with common values of the equation constants which is an unexpected commonality; their relative rates, of course, can still be different if the “true” values of ko and Eo are different for each constituent; this is a separate problem again requiring more extensive examination that is out of place here. 3. For the char-gas reactions, the comparison between graphs is difficult in the first place because of the different units used, although cm/s and g/(cm2.s) should be very nearly the same since the first unit is converted to the second by multiplying by the coal density which is close to unity in cgs units. Dividing by the oxygen concentration then changes either of those unit systems by a factor of 10 at 10% oxygen; a t other oxygen values, the further changes are mostly trivial on the In (k,) scale. Another contributing factor to the disparate results may be that the determinations were carried out at sufficiently different temperatures. Nevertheless, taking all the gas-reaction results at face value (and with a temperature correction for the adsorption data) all the data points tend to lie close to one or other of the two lines in Figure 8, with the exception of the hydrogenation which is to be expected as this is a slow reaction. It is no surprise to find close agreement (within the limits of scatter) between steam and C 0 2 gasification, but what is particularly interesting is to find the steam and C 0 2 data so close to the lower oxygen line of Figure 8, and to the Sandia data line of Figure 7. This correspondence can, in fact, be interpreted mecha-
176 Energy & Fuels, Vol. 4, No. 2, 1990
nistically, if we assume that the reaction being followed is the same in all three cases. This would be so if (1)the oxygen transfer reaction by 02,C02,or H20 generates an adsorbed oxide film that is independent of the oxygentransfer species and (2) the reaction being followed in all cases is then the oxide film decomposition. The corollary to this is that the reaction being followed is intrinsically zero order with respect to the concentration of the oxygen-transfer species (though half-order if reaction is predominantly internal). This would also be in accordance with the higher activation energies mostly reported (in excess of 20 kcal/mol), which is a point already discussed more extensively in ref 2.
Discussion The correlations shown in Figures 1-15 taken as they stand have a significant quantitative value to the extent that they mostly describe quite narrow bands within which the “true” values of the kinetic constants can be expected to lie. This alone narrows margins of error in selecting kinetic constants quite substantially. The discussion can now be usefully extended to examine two questions raised by the reviewers of the first draft of this paper. These questions were as follows: (1) To what extent can the correlations be due to purely statistical correspondences of random data? (2) Do the correlations otherwise provide any further fundamental (mechanistic) information on the relevant rate processes? 1. The first question can be answered quite shortly. The well-known procedure used to obtain the correlation plots shown in Figures 1-15 is to determine values of E and k, from Arrhenius plots (log (k)-l/T spaces) and to remap onto log (ko)-E spaces. If the slopes of the lines (values of E ) on the Arrhenius space are limited (say to 0-100 kcal/mol) but the distribution of the lines is otherwise totally random and taken over the full possible range of values on this space (-m to +a in log (k),and 0 to +m in 1/79, then the transformation mapping onto the full field of the log @,)-E space is also random, with values of log (k,) also in the range --a, to +m (with values of E limited to the original selection). If the procedure is then repeated but with limits placed on the range of values of k and T in the Arrhenius space, this limitation reduces the degree of randomness in the log(ko)-E space, and nonzero regression coefficients can be obtained. This was examined directly by using a random number generator to create random values of E in the range 5-80 kcal/mol; these values were used to define the slopes of lines that were then assigned randomly to grid points in Arrhenius space bounded by -4 < log (k) < 0 and 5 X < 1 / T C 10 X From this random placing, associated values of log (k,) were determined for each line. As expected, the mapping to the log &,)-E space then showed well-defined bands in different repeats of the procedure, with quite high correlation coefficients, up to values of 0.85. The bounds of the bands were determined by the (artificial) bounds set on log (12) and 1/T. As the bounds were narrowed, the correlation coefficients increased. This procedure identified the extent to which randomness in the complete Arrhenius space is limited by restricting the space to within the bounds stated. In other words, bounding the data in this way progressively eliminates the degree of randomness, and selecting random data within defined bounds generates correlation coefficients whose values increase with the narrowness of the bounds, which is to be expected. This conclusion was also tested directly by splitting up the random data array, first into narrower temperature ranges over the full log (k)range and then into narrower log (k) ranges over the full range. As expected, the corre-
(l/n
Essenhigh and Misra lation coefficients increased, with values reaching 0.95. For comparison, it may be noted that the regression coefficient for the Figure 7 data is 0.995; it does not seem reasonable that this could be achieved by purely random data sets and it would also be an unwarranted reflection on the competence of the investigators involved. 2. If the ko-E correlations are real and are not just statistical artifacts, the question of developing advances in mechanistic interpretations from the correlations is a separate issue. The correlations have validity and value in their own right independently of more “fundamental” concerns. Nevertheless, an examination of the matter is appropriate at this point as a curtain raiser for future concerns. Most pertinently, the question of mechanistic interpretations of some solid reactions (primarily pyrolysis) was discussed extensively at the 1989 Gordon Research Conference (GRC) on Analytical Pyrolysis (New Hampton) as reported by Boom and de Leeuw.14 In focusing on pyrolysis they say, as summary of the GRC views: ”Another major outcome concerned the impossibility to perform kinetic studies using pyrolysis data: it is allowed to ‘Arrhenius’fit the data but mechanistic conclusions may not be drawn.” Part of the basis for this conclusion was based on a comparison of fast and slow pyrolysis from which it appeared that “real dissociation processes in the solid phase happen on the picosecond scale”.14 In our view, this position of abandoning mechanistic interpretations is somewhat extreme. For example, in developing the quantitative structure of the coal pyrolysis model described previously’ we relied heavily on physical concepts of coal model structure to determine what model concept component should be included and what could be (initially) excluded; without those mechanistic constructs, the model development would have been essentially impossible. Even more so is this the case for the carbon-gas reactions, where there is extensive theoretical basis for interpreting the reported results mechanistically. Indeed, abandonment of any mechanistic interpretation in the carbon-gas reactions creates additional problems of major practical significance. For example, in the carbon-gas reactions the experimental determination of reaction order ( n )with respect to the concentration ( p ) of the reactive gas is frequently determined and reportea on an empirical basis as an nth power, viz., pp“. The pressure, p g ,can be reported at normal pressure as either mole fraction or partial pressure: numerically, they are the same. If the absolute pressure is increased (as in studies of pressurized combustion or gasification), the empirical use of p provides no basis for extrapolating previous results to higher pressure: there may or may not be a pressure effect, and the empirical expression says nothing about this. The influence of pressure then has to be determined experimentally and independently without any guide to expected behavior from a theoretical extrapolation. Our view is, then, that even if mechanistic interpretations are difficult, they should be pursued nonetheless to provide some basis for extrapolating to other conditions. With regard to the autocorrelations, these cannot by themselves (by their statistical nature) provide information on mechanisms. They may do so, however, by cross-comparisons, as already noted, for example, in comparing the trend lines for the C-02, C-H20 (and C-C02) data, with the possible implication that the equations are essentially common because the reaction being followed is common; (14) Boon, J.; de Leeuw, J. Pyromail; FOM-Institute, AMOLF, Amsterdam, June 1989;letter no. 1. (15)We are indebted to one of the reviewers of this paper for bringing refs 10-13 to our attention.
Energy & Fuels 1990,4, 177-183 the mechanistic basis for this can be the decomposition of an oxide film which could have essentially the same structure whichever oxygen-transfer gas was involved. Extension of these mechanistic considerations is outside the scope of this paper, but it identifies one potentially fruitful line of argument to be considered in the future.
Conclusions The correlations demonstrated in the Figures 1-15 are believed to well support the proposition stated in the Introduction: that the values of E and k , are so highly correlated in many cases that this effectively reduces the number of independent kinetic degrees of freedom from 2 to 1. For modeling purposes, this can be of major value, as already noted.’ In effect, the correlations provide a basis for selecting paired values of ko and E for a given reaction, within a determinable level of error, even though the “true” values are unknown; at the same time, it provides a quantitative rule for simultaneous adjustment of the paired values for sensitivity studies. This procedure sets more precisely determinable bounds on the selection of possible
177
values of the kinetic constants of interest. The bounds can be improved still further by an update of the existing data base (which is incomplete) and by a careful analysis of the experimental details in each case so that the units used for the velocity constants can be adjusted to a common basis. The extent to which the procedure at this time does not identify the “true” values of the kinetic constants is then less of a failure of the procedure than a failure of experimental design and measurement that would accurately define and measure the true values. In that sense, an added benefit of the correlations is as an aid to defining and determining priorities in what is now needed for more accurate definition of needs and methods of measurement. Clearly, there is little point just in enlarging the data base by continued data gathering with no other objective, except where the data base is still very sparse (as in the C-C02) reactions. What is needed now is more carefully designed experiments that can lead to the true values of the relevant kinetic constants and that can also be used in identification of mechanisms.
Extended 8@(H)-Drimaneand 8,14-Secohopane Series in a Chinese Boghead Coal T.-G. Wang Petroleum Geochemistry Unit, Jianghan Petroleum Institute, Shashi City, Hubei, China
B. R. T.Simoneit* Petroleum Research Group, College of Oceanography, Oregon State University, Corvallis, Oregon 97331
R. P. Philp and C.-P. Yu Petroleum Geochemistry Group, School of Geology and Geophysics, University of Oklahoma, Norman, Oklahoma 73019 Received August 24, 1989. Revised Manuscript Received December 28, 1989 Extended C14-C23 8P(H)-drimane and C27-C32 8,14-secohopane series have been detected and identified in a Jurassic boghead coal from Lulong, Hebei, North China, by GC-MS and GC-MS/MS analysis and based on comparison with reference data and interpretation of mass spectra. The boghead coal is composed of alginite macerals and contains biomarkers of algal and microbial origins such as tricyclic terpanes, hopanes, pregnane, and steranes. It is proposed that the extended 8B(H)-drimane series most likely originates from multiple precursors, i.e., tricyclic terpanes, 8,14-secohopanes, and hopanes, by opening and/or cleavage of ring C, and an overall scheme is presented for their possible genesis.
Introduction It is well-known that the homologous series of polycyclic alkanes containing an extended side chain, e.g., tri- and tetracyclic terpanes as well as pentacyclic hopanes, are common constituents in many geological ~amples.l-~ In addition, certain individual compounds or homologous series of bicyclic terpanes and tetracyclic triterpanes have also been r e p ~ r t e d . ~ - ~ Philp et al.4 reported one C14, six C15, and three C16 bicyclanes in the Australian Rankin oil and in three oils
* Address correspondence to this author. 0887-0624/90/2504-Ol77$02.50/0
from the Gippsland Basin (Dolphin, Tuna, and Mackerel). On the basis of synthetic standards, Alexander et a1.6i6 (1) Aquino Neto, F. R.; Trendel, J. M.; Restle, A.; Connan, J.; Albrecht, P. Advances in Organic Geochemistry 1981; Wiley: London, 1983; pp 659-667. (2) Ensminger, A.; van Dorsselaer, A.; Spyckerelle, C.; Albrecht, P.; Ourisson, G.Aduances in Organic Geochemistry 1973; Editions Technip: Paris, 1974; pp 245-260. (3) Trendel, J. M.; Restle, A.; Connan, J.; Albrecht, P. J.Chem. Soc., Chem. Commun. 1982, 304-306. (4) Philp, R. P.; Gilbert, T. D.; Friedrich, J . Geochim. Cosmochim. Acta 1981,45, 1173-1180. (5) Alexander, R.; Kagi, R.; Noble, R. J. Chem. Soc., Chem. Commun. 1983, 226-228.
0 1990 American Chemical Society
