I n d . E n g . C h e m . Res. 1995,34, 1081-1091
1081
Cellulose Thermal Decomposition Kinetics: Global Mass Loss Kinetics Ivan Milosavljevict and Eric M. Suuberg* Division of Engineering, Brown University, Providence, Rhode Island 02912
The kinetics of cellulose pyrolysis have received considerable attention during the past few decades. Despite intensive study, there remains controversy in the literature even on a topic as basic as the global kinetics of pyrolysis. The reported kinetics have been reconsidered in light of new experimental results that suggest a simple resolution to that part of the controversy concerning the activation energy of pyrolysis. It appears that the reported kinetics are sensitive to the heating rate employed in the experiments used to deduce them. Experiments in which the cellulose is rapidly heated to above 600 K give apparently “low” activation energies, mainly between about 140 and 155 kJ/mol, in the case of the material studied here. This applies to both “isothermal” and high heating rate temperature-ramp experiments. Alternatively, cellulose heated more slowly to temperatures below 600 K appears to lose mass with a n activation energy that is about 218 kJ/mol. The mathematical modeling of processes involving pyrolysis of cellulosic materials (e.g., biomass conversion processes, fire phenomena) can be strongly influenced by which kinetics are assumed, since the kinetic constants from one regime will not accurately predict mass loss in the other.
Introduction
A Review of Global Cellulose Pyrolysis Kinetics
There has been an ongoing debate in the literature concerning the “true” global kinetics of cellulose pyrolysis. Global kinetics are of interest in modeling cellulose decomposition in many applications in which trying to represent the full complexity of the cellulose degradation process makes no sense. The number of recent references cited below attests to the continuing attempts to resolve this issue. The work in this laboratory has been carried out in connection with a larger study on the behavior of combustible charring solids. Modeling the combustion behavior of such systems is generally highly complex, as it involves the interplay of fluid mechanics, heat transfer, mass transfer, and chemical reaction processes in both gas and solid phases. There is a need to keep the details in any one part of the overall model to a minimum, including the details of the pyrolysis (Kashiwagi and Nambu, 1992;Desrosiers and Lin, 1984; Lede et al., 1987; Kothari and Antal, 1985; Wichman and Atreya, 1987;Kung, 1972;Kansa et al., 1977; Curtis and Miller, 1988; DiBlasi, 1993). Global pyrolysis kinetics applied to cellulose are generally intended to predict the overall rate of volatiles release (i.e., mass loss) from the solid. It has been reported that different volatile products are released in different temperature ranges (e.g., Hajaligol et al., 1982) and in response to different temperature histories (e.g., Kilzer and Broido, 1965). This fact has not diminished the int6rest in global kinetics for various reasons. One is that, under certain conditions, tar is a dominant product of pyrolysis for a significant part of the process (e.g., Hajaligol et al., 1982; Martin, 19651, so that prediction of total mass loss would allow prediction of tar release rates. A second is that global kinetics are looked to as offering a clue to the key mechanistic steps in the overall cellulose breakdown process.
The kinetics and mechanism of cellulose pyrolysis have been reviewed a t varying levels of detail by a great many investigators (e.g., Shafizadeh, 1968,1975,1985; Roberts, 1970; Lewin and Basch, 1978; Welker, 1970; Antal, 1982, 1985). Often the reviews have been concerned with the behavior of wood or biomass, for which the pyrolytic behavior is more complex because of the existence of other components (hemicellulose and lignin). Here, we focus exclusively on pure cellulose behavior. It has often been noted that the global kinetics of pyrolysis tend to cluster about certain values. Roberts (1970) noted that the activation energy data on the pyrolysis of wood and related materials tended to cluster around two values, one a t about 235 kJ/mol and the other a t 125 kJ/mol. Various reasons were advanced, including the possible role of catalysis and sample-size related issues. Antal et al. (1980) noted three clusters of activation energy data from the literature: the first between 210 and 250 kJ/mol, in which temperature recording devices were “decoupled” from the samples; the second between 138 and 210 kJ/mol, in which coupling was through the gas; and the third between 109 and 138 kJ/mol, in which coupling was direct. It was noted that the relationship between coupling of sample and thermocouples might be coincidental, and indeed, in later more careful work on the topic, one of the authors has concluded that values in the highest range are among the most reliable (Varhegyi et al., 1989). We nevertheless agree wholeheartedly with the concerns expressed by Antal et al. (1980) about the potential for serious heat transfer limitations and associated temperature measurement problems in “routine” non-isothermal thermogravimetric (TGA) studies of kinetics. We observed the problem in our own studies, and have addressed it directly, as described below. Thus there is not particularly good agreement as to the global kinetics of the process. For our purposes, involving fire modeling (e.g., Milosavljevic and Suuberg,
* To whom correspondence should be addressed. Present address: Advanced Fuel Research, Inc., East Hartford, CT. +
0888-5885/95/2634-1081$09.00/0
0 1995 American Chemical Society
1082 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
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Varhegyi, 80 Lewellen, 24,000 Hajaligol, 60,000 --c Hajaligol, 21,000 Hajaligol, 6000 - A- Ramiah, isothermal - c Alves, isothermal . - 0 Raissi, 120 - 0- Lipska, isothermal . . o . Shivadev, 4000-low T - o- Shivadev, 4000-high T . . E . Antal, 22.4 - B- Antal, 55.0 Shafizadeh, isothermal -mSuuberg, 1000 ...*... Suuberg, 100 -This study, 15-60
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Figure 1. Summary of mass loss kinetics obtained at high heating rates ( > 10 Wmin). The values next to author names indicate the heating rate, in kelvin per minute, or the fact that the run was nominally “isothermal”, in which case the heating rate was generally quite high. The following are specific references: Varhegyi, Varhegyi et al. (1989); Lewellen, Lewellen et al. (1977); Hajaligol 60,000, Hajaligol et ai. (1982); Hajaligol 21,000 and 6000, Hajaligol (1980); Ramiah, Ramiah (1970); Alves, Alves and Figueiredo (1988); Raissi, Tabatabaie-Raissi et al. (1989); Lipska, Lipska and Wodley (1969); Shivadev, Shivadev and Emmons (1974); Antal, Antal et al. (1980); Shafizadeh, Shafizadeh and Bradbury (1979); Suuberg, Suuberg and Dalal (1987).
19921, we noted that in modeling the pyrolysis of bulk cellulose a single set of global rate constants was inadequate to describe the process. This led to the present experimental investigation of the kinetics. A preliminary examination of some of the many kinetics presented in the literature is presented in Figures 1and 2. The choice to present the kinetic summaries in terms of high and low heating rate experiments was guided by our initial observation that high heating rate kinetics, such as those obtained by Lewellen et al. (1977) and Suuberg and Dalal(1987),matched better the pyrolysis rate behavior of the rapidly heated surface layers of our bulk samples, whereas the higher activation energy kinetics often seen in slow heating experiments appeared to match better the pyrolysis rates of the slowly heated interiors of the samples. Figures 1and 2 show either the actual pyrolysis rates, or the rates calculated from reported constants, measured by various investigators. In all cases, an attempt was made to show the actual temperature range over which data were obtained. In cases in which the actual rates were not reported a t various temperatures, the kinetic parameters obtained were applied to the reported temperature range of the experiments. In the case of standard non-isothermal TGA experiments, an attempt was always made t o identify from the raw TGA curves what the temperature range of active mass loss was, and this is what is reported in Figures 1 and 2. The arbitrary choice was made to group into Figure 1 the data obtained in experiments involving heating at rates exceeding 10 Wmin. This choice was guided by some results obtained in our laboratory, as will be presented further below. In some cases, the experiments were conducted in normal or modified TGA systems, using controlled ramp heating (Varhegyiet al., 1989; Tabatabaie-Raissi, 1989; Antal et al., 1980). In
other cases, the samples were rapidly heated in the folds of an electrically heated wire mesh (Lewellen et al., 1977; Hajaligol et al., 1982; Hajaligol, 1980; Suuberg and Dalal, 1987), or radiatively (Shivadev and Emmons, 1974). Figure 1 also included a number of studies in which “isothermal” pyrolysis was examined (Rami&, 1970; Alves and Figueiredo, 1988; Lipska and Wodley, 1969; Shafizadeh and Bradbury, 1979). In these cases, the heating was generally very rapid, up t o the level of the isothermal experiment. ks may be seen from Figure 1, the many results cluster around a single band that appears to define a single activation energy over a very broad range of temperatures. There is about an order of magnitude spread in rates. If all of the results of Figure 1are averaged by taking only the end points of the curves defined by each study, a mean activation energy of 140 kJ/mol is calculated. The results for slow heating rate experiments are shown in Figure 2. All were obtained using the standard non-isothermal TGA technique at low rates of heating ( < l o Wmin). It should be noted that some studies contributed to both Figures 1 and 2, as they spanned the relevant range of heating rates (Varhegyi et al., 1989; Antal et al., 1980; Ramiah, 1970).,*While the temperature range of the studies included in Figure 1 was quite broad (500-1273 K), the range covered in Figure 2 is necessarily narrower (473-773 K),simply because in slow heating experiments the mass loss processes are completed before high temperatures are reached. Nevertheless, there is a significant overlap in the temperature range of interest in the two figures. While there is clearly more scatter in Figure 2 than in Figure 1, it is still possible to state with reasonable confidence that the results of Figure 2 imply a somewhat higher activation energy. By employing the same somewhat arbitrary averaging procedure as in the case
Ind. Eng. Chem. Res., Vol. 34,No. 4,1995 1083
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-Klose, 3 Varhegyi, 10 -Ramiah, 4-High T - - + . Ramiah, 4-LOW T -Cooley, 1 . - 0 . Cooley, 2 - + Cooley, 5 . - 8 . Broido, 4.5 - t Tang, 3-low T s Vovelle, 1 - Q- Vovelle, 10 . Akita, 0.23-2.4 - I+ Antal, 2.16 -mAntal, 5.65 -Rogers, 1 and 5 - - - Q - - - Min, 3-30 &Kashiwagi, 0.5-5 -+ This study, 0.1-6
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1OOOlT Figure 2. Summary of mass loss kinetics obtained a t low heating rates ( < l o Wmin). The values next to author names indicate the heating rate, in kelvin per minute. The following are specific references: Klose, Klose (1994); Varhegyi, Varhegyi et al. (1989); Ramiah, Ramiah (1970); Cooley, Cooley and Antal (1988); Broido, Broido and Weinstein (1970); Tang, Tang and Neil1 (1964); Vovelle, Vovelle et al. (1982); Akita,Akita and Kase (1967); Antal, Antal et al. (1980); Rogers, Rogers and Ohlemiller (1980); Min, Min (1977); Kashiwagi, Kashiwagi and Nambu (1992).
of Figure 1,the results of Figure 2 imply an activation energy of 193 kJ/mol. It should be emphasized that this activation energy is not the “correct” activation energy for fitting all these data. It is instead likely that there were several studies included in this figure which reported much “better” activation energies, which were different from this crude average. The point to be made is that the value that emerges from a consideration of data from this range of heating rates is definitely different from that obtained at higher heating rates, in Figure 1. Thus there appears to be a separation of large numbers of different results, based on the heating rate employed in the experiments, into two different kinetic regimes. This is not to deny that there are a few obvious cases of sets of data included in one figure that look as though they might be more appropriate in the other. We cannot draw conclusions about why this happens. Still, the overall trends are fairly well defined. We would also emphasize that it would be inappropriate to conclude on the basis of the above analysis that any of the individual reported activation energies are Uc~rrect7’ or “incorrectn. For one thing, the purity of the samples surely determines the degree t o which catalytic pathways are followed, and there is no reason to believe that a sample with catalytic impurity should exhibit the same activation energy as a sample with little such impurity. This might, in fact, be an important explanation for the spread of the data in both Figures 1 and 2. Keeping in mind the goal of providing a useful framework for modeling cellulose pyrolysis in complicated systems, the significant trend with heating rate of the sample is notable. A suggestion that heating rate may influence the course of cellulose pyrolysis is nothing new. Such an effect was embodied in a model proposed by Kilzer and Broido (19651,the essence of which may be represented by
, dehydrocellulose
cellulose
char
+
gases
1 tars
The route to dehydrocellulose was postulated to dominate at 473-553 K, whereas the route to tars was postulated to dominate at higher temperatures. In support of this model, Lipska and Parker (1966)and Broido and Nelson (1975)have confirmed that heat pretreatment of samples at 500 K and above does indeed enhance char formation. Meanwhile, Lewellen et al. (1977)and Martin (1965)have suggested that at high heating rates char formation can be substantially suppressed. There is, however, still some concern as to the validity of this particular model, and whether it is really related to the observations of lower char yields in the higher heating rate experiments (Varhegyi et al., 1994). We prefer, therefore, to consider this model only in the context of the historically important role it has played in shaping the thinking on cellulose decomposition. The activation energy for the tar formation step in the above model has been estimated by Williams (1974) to be about 230 kJ/mol, by Agrawal(1988) to be about 196 kJ/mol, and by Broido (1976)to be about 222 kJ/ mol. The data that were being fit by the various investigators were different. Again, it comes as little surprise that since there exist differences in reported mass loss rates, differences should appear in more detailed kinetic modeling as well. It should also be recalled that in some of the very high heating rate work shown in Figure 1, the main mass loss product is tar, and char yield is low. Thus, the activation energy for tar formation is essentially the reported global mass loss activation energy, and is lower than any of the three values cited here. In fact, mass transfer might also play a significant role in determining the release rates under certain
1084 Ind. Eng. Chem. Res., Vol. 34,No. 4,1995 conditions (Hajaligol et al., 1993). The inert gas pressure applied to pyrolyzing cellulose has been shown to affect tar yields significantly (Agrawal and McCluskey, 1985; Hajaligol et al., 1993). In order to model this effect, Hajaligol et al. (1993)invoked a model in which primary tar formation had an activation energy of 78 kJ/mol. Thus there is no question that the simple competitive reaction model above is a gross simplification of a number of very complicated phenomena, and general agreement on the next level of sophistication does not yet exist. It is again for this reason that global mass loss models will continue t o be attractive as many issues continue to be sorted out. In addition t o the question about appropriate Arrhenius parameters for the global mass loss, there is also uncertainty concerning the order of reaction. While there is throughout the literature a tendency to model the decomposition using first order decompositional kinetics, several careful studies clearly suggest that other order kinetics are more appropriate. We explore this issue further in the present work as well. In this paper, we explore this subject further using thermogravimetric analysis (TGA). We have also employed differential scanning calorimetry (DSC)to study the problem, and these results will be presented elsewhere. There are two objectives in this paper, in light of the above background. First, it will be demonstrated that the “shift”in kinetic parameters with heating rate is reliably observable using a single experimental technique. This will help lend credence to the conclusions drawn in light of Figures 1 and 2. Second, the issue of reaction order will be examined further.
Experimental Section This work was carried out as part of a larger experimental program, concerned with the behavior of cellulosic materials under simulated fire conditions. Other results from this work have been reported previously (Milosavljevic and Suuberg, 1992). The interest in the behavior of bulk solids under fire conditions dictated the general range of heating rates to be below 100 Wmin. The pyrolysis behavior of purified cellulose was studied in a standard TGA (Du Pont Instruments Model 951). All TGA experiments were conducted in an inert gas environment (nitrogen) with a purge flow rate of 50 mUmin. Temperature calibration of the TGA was of particular concern, since in this device the thermocouple was not in direct contact with the sample. The temperatures reported by the “standard” instrument thermocouple were observed to be significantly in error (over 20 K, see below) depending upon how the experiments were performed. Generally, high heating rates and large mass loadings led to larger discrepancies. Gas environment also made a difference, in that helium, with a high thermal conductivity, tends to give closer agreement with actual temperatures than does nitrogen. To obtain correct temperatures, an experimental protocol was adopted in which pairs of identical experiments were performed. One experiment is conducted in the usual manner for a TGA of this kind. Then a second experiment is conducted under identical conditions, but with a fine thermocouple (0.076 mm wire) actually embedded in the sample powder. The presence of the thermocouple did not allow for accurate mass measurement in the second experiment, which is why pairs of experiments were performed. Using this procedure, we obtained quite satisfactory results, in terms
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I 400
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Temperature [K] Figure 3. Non-isothermal thermogravimetric curves for cellulose pyrolysis in inert gas. The heating rates are indicated on the graph. The solid lines are data, and the dashed curves are predictions using a first order model and E = 218 kJ/mol and A = 9.23 x 1017 min-’ (see text).
of agreement with other work reported in the literature, as well as with our own DSC kinetics. The actual mass of samples used in experiments involving the above temperature “correction”procedure was about 30 mg. This sample was spread into a layer about 1 mm deep on the sample pans. The use of such a large amount of sample would normally be undesirable in TGA work in which large reaction endotherms occur. But because of the spreading of the sample into a thin layer and the fact that the temperature was measured directly, we have confidence in the results. The reliability of the correction procedure was demonstrated by experiments a t very low heating rates (e1 Wmin), in which the “corrected” temperature and furnace temperature results perfectly coincided, showing that when temperature changes occur slowly and the endotherm is not large, the sample tracks the furnace temperature quite well. The cellulose used for all TGA work was a Whatman CF-11 fibrous cellulose powder that was used asreceived. This cellulose was prepared from high purity cotton of 99% a-cellulose content. The ash content was 0.009% by mass. The molecular weight of this material was in the range 36 000-45 000 daltons. The diameter of the fibers was 10-30 pm.
Results and Discussion Non-Isothermal TGA Experiments. Typical results from ordinary “dynamic” TGA experiments (i.e., those involving fully non-isothermalhistories) are shown in Figure 3. All of these results are presented in terms of actual measured sample temperatures, as discussed above. These are rather ordinary-looking TGA curves for cellulose pyrolysis. They are represented in terms of conversion of the raw sample (shown as fractional remaining mass, MlMo),where M is the remaining mass at any time and MO is the initial mass of sample, including moisture. In the present case, asymptotic char yields (MF’Mo) appeared to be between 8 and 10%. There was a very slight trend toward higher char yields with slower heating rates, in line with earlier discussions, but there was not a wide variation over the approximately 2 orders of magnitude heating rate studied. In the case of the experiments at 0.092 and 0.93 Wmin, however, the rapid pyrolysis period terminated at a residual mass
of between 15 and 20%, followed by a very slow mass loss process that eventually achieved 7.0-9.6% char yields. The focus in this work is on the rapid mass loss processes that yield significant amounts of tar, rather than the late degassing of char. For this reason, the char yields in the 0.092 and 0.93 Wmin experiments will be taken to be those at the end of the rapid mass loss process of main interest. Having an accurate definition of what is meant by "char yields" is one element of the correct global kinetic modeling of cellulose pyrolysis. This is particularly the case in pyrolysis of bulk samples that apparently reach an asymptotic char yield, simply because of a existence of a significant temperature profile. The temperature profile dictates that the sample will reach what appear to be "complete" pyrolysis conditions, but in fact, may have some massloss pathways still open to it a t higher temperatures (Milosavljevic and Suuberg, 1992). Another complication in determining char yields is the role that mass transfer limitations might play. In a separate study, we have examined how the mass of cellulose affects our char yields. It was noted that the yield of char could be reduced t o below 5% by reducing the mass of sample examined in the TGA. At all but the slowest heating rates ('1 Wmin) the yield of char was increased by only about 2%, when we were forced to use large enough samples so as to bury the thermocouple completely. There was excellent agreement between the kinetics obtained by differential scanning calorimetry (to be discussed in a future paper), in which sample sizes were small (order 1-10 mg) and char yields were in the low range cited, and the TGA results reported here. We, therefore, do not believe that our mass-loss kinetics were significantly influenced by the secondary reaction processes that led to the slightly "high" char yields, relative to smaller sample sizes. It is possible to calculate directly from the data of Figure 3 pseudo first order rate constants for the cellulose decomposition reaction. This can be done by selecting any particular level of conversion, and determining the instantaneous rate and temperature at that conversion. As usual, for an nth order decomposition reaction
W l d t = -kMp"
(1)
where t is time, k is the reaction rate constant = A exp(-EJRT), M is the total sample mass at any time, and M p is the remaining pyrolyzable mass = M - Mf. The final char mass Mf is here for convenience treated as a constant, as though char were present as a pseudo-inert component throughout the process. This is obviously not true in reality, since char yield is a dynamically determined quantity. Equation 1may be rewritten by substituting f = Md(M0 - M f ) ,yielding
dfldt = -k'f"
(2)
where k' = k(M0 - Mf)"-l. The quantity f is physically the fractional unrealized mass loss. This quantity would be equivalent to 1minus conversion, but for the fact that the cellulose contains a small amount of moisture (5-6%), which is lost during the early heating period. By adjusting results to a dry basis, the direct interpretation in terms of conversion would be established, but this has not been done in Figure 3. Returning to eq 1, by assuming first order ( n = 11, and dividing the instantaneous mass loss rate ( d M / d t ) by the remaining pyrolyzable mass (M&, a pseudo first
Figure 4. Data of Figure 3 analyzed assuming a first order rate model with a rate constant k. The different symbols indicate the results from different levels of conversion (mass loss). Solid squares, 20%mass loss; triangles, 30%;crosses, 40%;open squares, 50%;diamonds, 60%;circles, 70%.
order rate constant can be calculated for all times. Since each time is associated with a particular temperature, an Arrhenius-type plot can be constructed from such results. The results are displayed for various values of M/Moin Figure 4 . It should be recalled that, for any particular conversion, each datum in Figure 4 comes from a different heating rate. Results of two replicate runs are shown, and establish the high degree of reproducibility in the experiments. The results of the experiments are shown for 0.3 I M/Mo I 0.8. At M/MQ = 0.9, the results do not appear to fit the trends, perhaps because there is an initiation period. At very low values of M/Mo, the trend is again not followed. The results of Figure 4 seem to suggest that the results obtained from the low heating rate experiments (0.092 and 0.93 Wmin) give points that all cluster below about lOOO/T = 1.65 (or below about 600 K),and that all follow a single straight line. The activation energy for this process is 218 kJ/mol, and preexponential9.23 x 1017 min-'. There is a clear indication that the assumption of a first order decomposition is appropriate during most of the process, and this yields kinetic constants not much different than many others reported in the literature, mainly among the studies cited in Figure 2. The actual fit to the raw data is displayed in Figure 3. The fit is generally adequate, but it is clear that there is a divergence from the low heating rate curves at high conversions, as expected from the inability to fit the high conversion data onto the straight line portion of Figure 4. It should be emphasized that a better fit to the data of Figure 3 could have naturally been achieved by ordinary curve-fitting procedures, but this was not the intention here. Rather, it was felt that the results of the fit t o the linear portion of the low heating rate data should be tested against the whole data set. A failure to achieve a good fit indicates where the postulated model is not adequate. Clearly, the high heating rate data are not fit very well. The high heating rate experiments (14.7 and 64.9 Wmin) both gave points only above 600 K in Figure 4. These points do not define a trend as did the lower temperature points. Instead, it appears that each conversion gives a separate curve on the Arrhenius plot. The activation energies obtained from different conversions range from 141 to 190 kJ/mol. In all cases, the activation energies are lower than that observed at the lower heating rates and temperatures, supporting the
1086 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1, 0.51
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Figure 5. The 14.7 and 64.9 Wmin data of Figure 3, analyzed utilizing eq 3. The slope of the regression line is -0.88, implying an apparent order of 0.12.
trends established in connection with Figures 1and 2. It is also worth noting that the data obtained a t 5.8 Wmin heating rate did not cleanly fit into either trend, but rather fell somewhere between the data from the high and low heating rates. The apparent shifting of kinetic curves in the high heating rate data of Figure 4 is an indication of the possibility of an incorrectly assumed order. It is possible to determine an apparent order from these data. Using (2), but not assuming any particular value for n, it is possible to rearrange (2) t o ln[(-df/dt)/fl= In k’
+ (n - 1)l n f
(3)
The quantity k‘ is the true rate constant, and the left hand side of (3) is what is shown in Figure 4 as the ordinate. By interpolation of the data of Figure 4, the values of the lefi hand side of (3) may be obtained at a single temperature for all values off, such that k’ is a true constant. Then a plot of the left hand side of (3) as a function of f yields (n - 1) as a slope. This procedure is illustrated in Figure 5 and yields a value of n which is approximately 0.12, meaning that, in this situation, the reaction apparently occurs with almost zero order, rather than first order. For a zero order reaction, W/dt is the rate constant, and the high heating rate data of Figure 4 are replotted in this fashion in Figure 6. The result is a reasonably good fit to a single zero order rate constant, with an activation energy of 165 kJ/mol and preexponential factor of 2.9 x 1013min-’. The conclusion of zero order will, however, be demonstrated below to be particular to this situation, and not generally true in the high temperature regime. The reason is that the apparent order comes about in the ill-defined transition from the low temperature decomposition regime into the high temperature decomposition regime. It is clear that there is a abrupt increase in rates in the 5.8 and 14.7 Wmin data, relative t o what would have been extrapolated from the lower temperature data, suggesting a sudden shift in mechanism near 1000/T = 1.65 (i-e., about 600 K). Attempting to establish a “reaction order”, even an apparent order, near such a jump will be of questionable validity a t best. This will be discussed further below. Thus there is a clear indication of a shift in kinetics at near 600 K from a first order process with an activation energy of near 218 kJ/mol below this temperature, to a process with a lower activation energy
1.54
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1000/T[K] Figure 6. The 14.7 and 64.9 Wmin data of Figure 3, analyzed assuming a zero order reaction. The regression line implies an activation energy of 165 kJ/mol in this temperature interval. The different symbols represent different levels of conversion (mass loss). Squares, 20% mass loss; x’s, 30%; circles, 40%; diamonds, 50%; crosses, 60%; triangles, 70%.
above this temperature. The values of activation energy obtained in this phase of the study are only in crude agreement with the average activation energies obtained from Figures 1and 2, but this is not surprising, since those values were only gross averages. Nevertheless the observation of lower activation energies at higher heating rates is confirmed. When samples are heated rapidly enough such that most decomposition occurs above 600 K,pyrolysis occurs with what has been termed “high heating rate kinetics”. When significant decomposition occurs below 600 K,the “low heating rate pathway” is involved. It is not the heating rate per se that determines the decomposition pathway, but rather, the temperature at which most decomposition occurs: higher heating rates favor decomposition a t higher temperatures. Figure 3 shows how difficult such a subtle shift is to observe, using only raw TGA curves. While the fit to the higher heating rate data, using low heating rate kinetics, is poorer than that to the lower heating rate data, it might still sometimes be accepted as “adequate”, considering the wide range of heating conditions involved. Thus it becomes easy to understand how the shift in mechanism might have been overlooked in some earlier studies, particularly when a wide range of heating rates was not examined. The examination of the data in a different light, such as that in Figure 4, begins to reveal the true nature of the problem. Further, it appears that the competitive reaction model of Kilzer and Broido is not the relevant model for the kinetic shift in question. This is concluded on two bases. First, the temperature range of the low temperature pathway in the Kilzer and Broido model is too low to explain the behavior observed here, where the transition occurs at near 600 K. Second, both pathways of interest here yield copious amounts of tar: there is not a clear “char-forming“pathway distinct from a “tar-forming“ pathway. Isothermal TGA Experiments. To study the heating rate-linked mechanism question further, a number of experiments were performed which are similar to the many “isothermal” experiments found in the literature. In these experiments, samples were heated at a rate of 60 Wmin to a final temperature, at which samples were held isothermally for an extended period of time. For comparison, another series of experiments was per-
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1087 100
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1
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r
remaining mass (%) 70 60 50
40 30 20
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..-.
400
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\ 561 K
K 600
E , (kJ/mol) 226 219 224 226 234 217
A (l/min) 5.30 x 1018 1.21 x 10’8 3.46 x 1018 5.44 x 1018 2.50 x 1019 4.85 x 1017
\
504 K
601
Table 2. Kinetic Parameters for Cellulose Decomposition from Isothermal Experiments below 600 K, following 60 Wmin Heating
I
800
1000
Time [min] Figure 7. Results of typical “isothermal” decomposition experiments performed in the thermogravimetric analyzer. In this case, the samples were heated a t a rate of 1 Wmin to the final isothermal temperature. Zero time in this case refers to the start of the 1 Wmin heating period. Table 1. Kinetic Parameters for Cellulose Decomposition from Isothermal Experiments following 1 Wmin Heating remaining mass (%) E , (kJ/mol) A (l/min) 225 2.89 x 10l8 80 215 3.46 1017 70 224 3.23 x 10l8 60 50 215 5.28 1017 212 3.35 x 1017 40 214 6.90 1017 30 225 2.81 x 10l8 20
formed, involving heating at 1 Wmin t o the final isothermal temperature. Typical curves from these latter experiments are shown in Figure 7. By taking the natural logarithm of (11, and then taking the derivative with respect to reciprocal temperature, the activation energy is calculable independently of any assumptions of order, provided the calculations are performed at constant remaining pyrolyzable mass, Mp: d[ln(-dM/dt)I/d[l/Tl = -Ea/R
(4)
This means that the calculation must be performed at constant M - Mf. There is again an issue of what to use for Mf in this case, since char yield can be a function of experimental conditions. The values cited in connection with the non-isothermal work appeared to be relevant here as well. In testing the derived kinetic parameters for sensitivity to variation of a few percent in the assumed values of Mf, the variation proved unimportant . When samples were heated at 1Wmin to their final reaction temperature, the analysis of the isothermal reaction rate data by the above technique revealed an activation energy that was invariant with conversion, and fairly constant a t around 220 kJ/mol, as shown in Table 1. This is in excellent agreement with the activation energy obtained from the non-isothermal data under the low heating rate conditions. A similar analysis of data obtained by heating at 60 Wmin to temperatures below 600 K is shown for comparison in Table 2. The activation energies are indistinguishable from those obtained from both the non-isothermal studies and from the isothermal kinetic studies involving heating at 1 Wmin. This is strong confirmation that it is not heating rate per se that is the important variable determining the kinetic con-
Table 3. Kinetic Parameters for Cellulose Decomposition from Isothermal Experiments above 600 K, following 60 Wmin Heating remaining mass (%) E , (kJ/mol) A (l/min) 70 128 1.34 x 1O’O 60 136 7.92 x 1O’O 50 145 4.42 x 10” 40 152 1.93 x 10l2 30 160 9.60 x 10l2 20 177 3.17 1014
stants, but rather the temperature at which the decomposition occurs. When the above procedure was carried out using data obtained following heating a t a rate of 60 Wmin to temperatures above 600 K, a different picture emerged. The values are shown in Table 3. There is a trend toward higher activation energies as conversion proceeds, and the values approach the 165 kJ/mol obtained from the non-isothermal, high temperature experiments only a t high conversions. The reaction order of pyrolysis was also available from the isothermal data. Starting with (2), it is possible to integrate t o obtain f as a function of time:
The integration is straightforward, yielding for n = 1: In f = -k,’t
+ constant
(6)
and for other values of n: l/fn-l = (n - 1)k’t
+ constant
(7)
The reaction orders were determined from the isothermal experimental data by plotting the data in the forms given in the left hand sides of eqs 6 and 7. Obviously the correct choice of order should give fairly linear behavior. The different functional forms are compared by plotting the isothermal data on the same set of axes. For this purpose, a normalization is introduced, which merely scales the data properly for plotting:
where F represents the left hand sides of eqs 6 and 7 and subscripts ‘“inn and “max” refer to the minimum and maximum value in a particular data set. The results of this procedure are shown in Figures 8-10. Figure 8 shows the isothermal experiment a t 584 K, for the 1 Wmin heating rate. Because of the low heating rate in this case, there is already some 30% mass loss prior to the beginning of the isothermal period (these data are not shown). Figure 8 again shows quite convincingly that the overall order for the low temper-
1088 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
n
r
01
01
300
320
360
340
380
400
420
Time [min] Figure 8. Examination of reaction order for an isothermal experimentperformed at 584 K, followingheating at 1 Wmin. Only the isothermal period is shown. Results for zero, first, and second orders are shown. 1
Om8
0.2
4
I
t
i
.
1.25
5
6
7
a
9
10
11
Time [min] Figure 9. Examination of reaction order for an isothermal experiment performed at 648 K, following heating at 60 Wmin. Results are shown for reaction orders of 0, 0.5, 1, 1.25, and 2. 1
0.8 A
0.6
r'
v
0
0.4
0.2
5
10
15
20
Time [min] Figure 10. Examination of reaction order for an isothermal experiment performed at 608 K, following heating at 60 Wmin. Results are shown for reaction orders of 0, 1, and 2.
ature reaction regime, even quite near the transition temperature, is essentiaIly unity throughout the middle part of the process. Figures 9 and 10 provide the results for experiments in the high temperature regime (648 and 608 K, respectively). In these cases, the order also appears to be near unity for a significant part of the process. From Figure 9, it is seen that approximately 20% of initial mass loss occurs in a process that is not clearly part of
0.2 -
0
20
40
60
80
100
120
140
Time [min] Figure 11. Examination of reaction order for an isothermal experiment performed at 584 K, following heating at 60 Wmin. Results are shown for reaction orders of 0, 1, and 2.
the main first order process, and there is also a departure near high conversions. In Figure 10, the actual onset of the first order period is a bit more difficult t o discern, but there is little question that first order is better than zero or second order kinetics. In neither case is zero order a good assumption. Since noninteger orders have been occasionally cited in the literature, this issue is also explored in Figure 9. Two arbitrary choices-0.5 order and 1.25 o r d e r a r e shown on this figure. Neither is an adequate representation of the kinetics, and first order is clearly the appropriate choice over most of the process. The question of order following rapid heating to a temperature very near the 600 K transition is examined in Figure 11. The temperature in this case is 584 K, just as in Figure 8. In this case, the sample was quickly heated (60 Wmin) through the low temperature reaction zone, so the essentially the full decomposition process is displayed in Figure 11. There is an early period of time during which the reaction appears to be perhaps better modeled by zero than first order. Following this, the order for the middle part of the process is again seen to be unity, consistent with the results of Figure 8, until there is a deviation again very near the end of the process (when only a few percent mass remains). We therefore agree with Lipska and Parker (1966)and Tang and Neil1 (19641,who also concluded that the first order period is preceded by an apparently zero order period. This zero order initiation period should not be confused with the apparently near-zero order observed near the transition temperature of 600 K. In this case of the earlier-discussednon-isothermal results at 14.7 and 64.9 Wmin., we believe that it was the abrupt change in mechanism near 600 K that led to the appearance of zero order. In that period, the reaction also appeared to have a higher activation energy (165 W/mol) than that determined from the isothermal experiments above 600 K, so the evidence strongly suggests transition from one regime to another. Summary Discussion
It appears that much of the confusion in the literature on global kinetics of cellulose pyrolysis may have derived from a failure to recognize that there are two easily accessible reaction rate regimes. The above results show how easy it is to encounter a "mixed kinetics" regime, under quite ordinary laboratory or practical conditions. The separation of the data as was done in
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1089 experiments performed with a cellulose pulp similar to that used in this study, and these gave quite similar results to those from the paper. It has been earlier noted there is fair agreement between the data of Figure 12 and the results of similar experiments performed at even higher heating rates (Lewellen et al., 1977). The curves shown in Figure 12 were calculated assuming first order decomposition kinetics and using these rate parameters. In this case, we are again interested in (1)subject to a linear increase in temperature with time, just as in the TGA
1-
0.8.
0.6
-
0.4
-
0.2
-
Z0
a
dT1dt = mh 01 500
(9)
I 550
600
650
700
750
800
TEMPERATURE [K] Figure 12. Results on pyrolysis of cellulose in inert gas from the heated wire mesh reactor studies of Suuberg and Dalal (1987). The dotted curves are obtained using the kinetic constants of Lewellen et al. (1977). The solid curve is obtained using the TGA kinetics obtained at 5.8 Wmin in the present study (see text).
Figures 1 and 2, based upon heating rates, is quite tricky, since the actual conditions of transition (temperature) are not yet well-defined, particularly when samples of very different nature are considered. Reports of fractional or zero orders are easy to understand in terms of both existence of an initiation period and the possible crossing between the two distinct rate regimes. Furthermore, since the reason for the transition from one regime t o another has not been mechanistically explained, there is reason t o believe that different samples with different impurities might still behave differently in either or both regimes. This suggests that the search for better global kinetics is not an easy task, even if the existence of two regimes is now recognized. As the results of Table 3 showed, the isothermal high heating rate TGA results gave an activation energy that is slightly above the commonly cited 140 kJ/mol. Similar cellulose has been briefly examined using another pyrolysis technique, the so-called heated wire mesh (Suuberg and Dalal, 1987). In this technique, a sample is held in the folds of a resistively heated wire mesh. This method allows attainment of much higher heating rates than are available in the TGA (up t o orders of thousands of degrees per second: see Suuberg et al. (1978)). There have been concerns expressed about temperature measurement uncertainties in such systems (Solomon et al., 19921, but if the system is not pushed to very high heating rates and the contact between mesh, sample, and thermocouple is good, then it is felt that reliable results can be obtained. In the work in question, the heating rate was kept well below those that prompt concerns. Figure 12 shows the results of experiments performed at both high and low heating rates in the heated wire mesh reactor. Each datum represents the char residue yield from an isothermal experiment in which the sample is heated a t the indicated rate to the abscissa temperature, and then allowed to cool a t a rate of between 200 and 400 Ws. Mass loss during cooling is generally quite small compared to that during heating. The cellulose used to obtain Figure 12 was an acidwashed paper (Munktell’s OWS2-80-200), with an ash content of 0.007%. It had a thickness of 168 f 8 pm, and was cut into rectangles 1 x 2 cm for these experiments. It was therefore not the same cellulose as studied in the TGA. There were, however, a few
In the case of the high heating rate studies, the cooling rate -m, will also be of interest. It is also possible that the temperature history of a sample will involve an isothermal period of duration ti. Exact integration of (1)subject to this temperature history is not possible, but a good approximation is available for the case of (EaIRT) >> 1,viz.,
M~ = M ~ ,exp{-[(Rla/E)(mc-l ,
+ mh-’) + tilA exp(-EalRT)} (10)
where MP,ois the pyrolyzable mass at time zero. Again, the actual total mass of cellulose a t time zero consists of this decomposable fraction, as well as a “char forming“ mass (Mf) and the moisture (Mm):
+ +
M , = MP,,Mf Mm
(11)
For any later time, the remaining mass is calculable from
M=Mp+M,
(12)
where (10) is used to calculate Mp, since it is assumed that moisture is lost a t lower temperatures than are of interest here. In fitting the results of Figure 12, we assume Mm = 0.06, based upon measurements, and assume that Mf = 0.08, based upon the results of the high heating rate experiments. In the experiments of Figure 12, there is no isothermal period so ti = 0. The kinetic constants of Lewellen et al. (1977) are A = 4.07 x lo1’ min-’ and E = 140 kJlmol. These kinetic constants are seen to fit the data at 100 and 1000 Wmin quite well. This may not be considered surprising, since Lewellen et al. used a very similar experimental technique. Nevertheless, they derived their kinetic constants from experiments conducted a t 400 Ws (24 000 Wmin), so their constants appear to apply over 2 orders of magnitude of heating rate variation. The rates predicted by the Lewellen et al. constants are close t o those predicted using the kinetic results from this TGA study. For reference, a t 625 K, the Lewellen et al. constants predict a rate constant K = 0.81 min-’, whereas a mean rate, based upon the data of Table 3, would predict a rate of 0.43 min-I. It is unclear how much significance can be attached to such a difference for two reasons. First, the samples that gave these rates are different, and second, the results which yielded the values in Table 3 were still close to the “transitionnregime. The Lewellen et al. constants perform considerably more poorly, in terms of predicting the rates a t 5 Wmin. There is a considerable overprediction of rates.Thus the need for different sets of heating-rate-dependent global parameters is again illustrated. The results of the TGA
1090 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
experiments of this study were used to obtain a better fit. It was noted above in connection with the results obtained at 5.8 Wmin (shown in Figures 3 and 4) that these results were squarely in the transition region. Nevertheless, it is only a short extrapolation from the purely low temperature regime (the points in question are those in Figure 4, just beyond the end of the solid line fit to the low temperature data). The extrapolation of the low temperature data underpredict the rates at 5.8 Wmin only by about a factor of 1.6. If it is assumed that the low temperature activation energy can still be applied and if the preexponential factor is increased by 1.6 (to 1.48 x 10l8min-l), then the fit shown in Figure 12 is obtained. Considering the crudeness of the correction procedure, the agreement is quite reasonable. Finally, we briefly consider the question of heat transport effects as possibly responsible for the apparent shift in kinetic parameters a t high temperatures. We believe this to be unlikely for several reasons. First, considering the analysis by Hajaligol et al. (1988), it appears that in spite of the endothermic nature of the pyrolysis reactions involved, the particles examined here are too small to be subject to an internal heat transfer limitation. For example, using our measured heat of pyrolysis at high heating rates (about 340 J/g), a particle half-thickness of 100 pm, our measured thermal diffusivity and heat capacity of order 0.1 mm2/s and 1.75 J/(gK), respectively, and the Lewellen kinetics, then from Figure 19 of Hajaligol et al. the assumption of an isothermal particle is seen to be quite good. Further, it is difficult to rationalize why heat transfer limitations would result in the behavior seen in Figure 12, in which apparent kinetics stay constant over several orders of magnitude in heating rate (from the 100 Wmin in Figure 12 to the 400 Ws of Lewellen et al.). Thus it seems quite unlikely that an internal heat transport limitation is the cause of the observed variation in kinetic parameters. It is also difficult to rationalize an external heat transfer limitation as the cause of an artifact. Throughout this work, the thermocouples are of comparable size to the particles, so it would be expected that if the particles can track a temperature change, so too can the thermocouples. In summary, it appears that a model consistent with what has been observed here is one of the following form:
, dehydrocellulose
cellulose
-----A
tarsi
+
gasesl
tars2
+
gases2
char
+
gases
The Kilzer and Broido low temperature competitive pathway is retained, since it is clear that heating cellulose a t very low temperatures for extended times does increase the char yield. What is necessary is the recognition of two separate pathways t o the main tar products of pyrolysis. Whether there are measurable differences in the products labeled 1 and 2 is unclear. The evidence from Hajaligol et al. (1982) indicates that tar yield is suppressed and gas yield increased as the heating rate is increased, but all of that work was performed a t heating rates of the order 100 Wsec or greater. The conventional wisdom has been that high heating rates increase tar yields, but this is based on consideration of the same low heating rate conditions that led to the Kilzer and Broido model. It is clearly necessary to reconsider the classical competitive models in light of what the newer, very high heating rate results suggest.
It is also worth noting that the work by hseneau (1971) suggested reconsidering the form of the original Kilzer and Broido model to include another competitive reaction. It has been shown that depolymerization products that cannot escape rapidly enough can undergo secondary reactions and thus contribute to char. The same feature has been included in a model proposed by Mok and Antal (1983). The basic structure of the model we propose here could very easily and consistently fit into the framework of the Mok and Antal model, as a second pathway to tar, which may then undergo the secondary char forming reactions. We have not chosen to develop this level of complexity in this paper, since the objective was to offer a simple global kinetic scheme. We will present other results in a forthcoming discussion of DSC results that will take up these questions.
Conclusions It appears as though the confusing state of the literature on global kinetics of cellulose pyrolysis may be a t least partly attributed to a previously unrecognized shift in mechanism near 600 K. Depending upon the heating rate used t o examine the kinetics, different values can easily emerge. We believe that the low temperature regime is characterized by an activation energy around 218 kJ/mol and an order that seems to go from zero, very early in the process, to first through most of the process. The high temperature regime is characterized by a lower apparent activation energy. We obtained values between 128 and 160 kJ/mol under conditions which might still have been near the transition, and near 140 kJ/mol for a similar sample of cellulose that clearly was decomposing in the high temperature regime. Thus an activation energy of about 140 kJ/mol is strongly suggested. The overall order is also unity in this regime. The latter activation energy is clearly the most reasonable for applications involving pulverized combustion, or pyrolysis of small cellulose particles under intense heating, or the pyrolysis of bulk cellulose samples under intense surface heat fluxes. For fire modeling applications, both kinetic regimes might, however, be of interest, since the interior of bulk samples would only heat slowly. Another conclusion of this study is that there appears to be enough variability in cellulose samples from study to study to make the use of any particular global kinetics from the literature highly dangerous, unless a match with the sample of interest is very well established. There appears to be a need for more studies on “standardized’’ cellulose samples, to allow more interlaboratory comparisons of kinetic data to be made. Only by identifylng such samples and characterizing their pyrolysis behavior very well can those interested in measuring and modeling more complicated engineering phenomena utilize published kinetics with confidence, and avoid the need for additional detailed kinetic measurements on their particular model systems.
Acknowledgment The support from the Center for Fire Research of NIST under Grant 60NANBOD1042 is gratefully acknowledged.
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IE9405089 Abstract published in Advance A C S Abstracts, March 15, 1995. @
