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Energy & Fuels 1997, 11, 972-977
Analysis of Pyrolysis Reactions of Various Coals Including Argonne Premium Coals Using a New Distributed Activation Energy Model Taisuke Maki, Akio Takatsuno, and Kouichi Miura* Department of Chemical Engineering, Kyoto University, Kyoto 606-01, Japan Received December 16, 1996X
A simple method presented by the author for estimating both f(E) and k0 in the distributed activation energy model (DAEM) was applied to analyze the pyrolysis reactions of 19 different coals, including 8 Argonne premium coals. First, f(E) and k0 for the changes in total volatiles were estimated using the thermogravimetric curves measured at three different heating rates for all the coals. It was found that f(E) curves were significantly dependent on coal rank, whereas the k0 vs E relationships were found to be little dependent on coal rank. This suggests the similarity of the pyrolysis reactions for all the coals. For the Argonne premium coals, the peak E value of f(E) curves shifted from 215 to 275 kJ/mol in accordance with the coal rank. The validity of the method was clarified by comparing the predicted thermogravimetric curves with the experimental ones. Next, fi(E) and k0i for the changes in the evolution of gas components and tar were also estimated using the formation rates measured and the k0 vs E relationships estimated above.
Introduction The so-called distributed activation energy model (DAEM) has been widely utilized to analyze complex reactions such as pyrolysis of fossil fuels, thermal regeneration reaction of activated carbon, etc.1-6 The model assumes that many irreversible first-order parallel reactions having different rate parameters occur simultaneously. When the model is applied to the analysis of coal pyrolysis, the change in total volatiles, V, against the time, t, is given by
1 - V/V* )
∫0∞exp(-k0 ∫0te-E/(RT) dt) f(E) dE
(1)
where V* is the effective volatile content of the coal, f(E) is a distribution curve of the activation energy to represent the differences in the activation energies of many first-order irreversible reactions, and k0 is the frequency factor corresponding to the E value. The distribution curve f(E) is normalized to satisfy
∫0∞f(E) dE ) 1
(2)
The distribution curve f(E) is generally assumed by a Gaussian distribution with mean activation energy E0 and standard deviation σ. On the other hand, the frequency factor k0 is assumed to be a constant in general for all reactions to avoid the complexity of the * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Pitt, G. J. Fuel 1962, 41, 267-274. (2) Suuberg, E. M.; Peters, W. A.; Howard, J. B. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 37-46. (3) Reynolds, J. G.; Burnham, A. K. Energy Fuels 1993, 7, 610619. (4) Solomon, P. R.; Hamblen, D. G.; Carangelo, R. M.; Serio, M. A.; Deshpande, G. V. Energy Fuels 1988, 2, 405-422. (5) Grant, D. M.; Pugmire, R. J.; Fletcher, T. H.; Kerstein, A. R. Energy Fuels 1989, 3, 175-186. (6) Niksa, S.; Kerstein, A. R. Energy Fuels 1991, 5, 647-665.
S0887-0624(96)00224-1 CCC: $14.00
analysis. However, the assumption of a constant k0 value may not be valid when f(E) spreads over a wide range of E values, since it is well-known that k0 and f(E) are interrelated.7,8 Furthermore, the assignment of the Gaussian distribution to f(E) does not always reflect real situations. Recently, one of the authors has presented a simple method to estimate both f(E) and k0 from three sets of experiments performed at different heating profiles without assuming any functional forms for f(E) and k0.9 The procedure to estimate f(E) and k0 is summarized below. (1) Measure V/V* vs T relationships at three different heating rates at least. (2) Calculate nominal rates k h ) dV/dt/(V* - V) at several but same V/V* values at the different heating rates, then make Arrhenius plots of k h at the same V/V* values. (3) Determine activation energies from the Arrhenius plots at different levels of V/V*, then plot V/V* against the activation energy E. (4) Differentiate the V/V* vs E relationship by E to give f(E), since the following relation holds approximately:
V/V* ) 1 -
∫E∞f(E) dE ) ∫0Ef(E) dE
(3)
(5) Calculate k0 corresponding to each E value at all the heating rates aj (j ) 1, 2, 3) using
0.545ajE 2
k0RT
) e-E/(RT)
(4)
then employ the averaged k0 value as a true k0 value. (7) Anthony, D. B.; Howard, J. B. AIChE J. 1976, 22, 625-656. (8) Du, Z.; Sarofim, A. F.; Longwell, J. P. Energy Fuels 1990, 4, 296302. (9) Miura, K. Energy Fuels 1995, 9, 302-307.
© 1997 American Chemical Society
Analysis of Pyrolysis of Coals
Energy & Fuels, Vol. 11, No. 5, 1997 973 Table 1. Ultimate and Proximate Analyses of 19 Coals Used ultimate analysis [wt % daf]
proximate analysis [wt % db]
coal
C
H
N
O (diff)
FC
VM
ash
Beulah-Zap (ND) Wyodak (WY) Illinois No. 6 (IL) Blind Canyon (UT) Lewinston-Stockton (ST) Pittsburgh No. 8 (PITT) Upper Freeport (UF) Pocahontas (POC) Soya (SY) Morwell (MW) Baiduri (BD) Onbilin (OB) Taiheiyo (TC) Ebeneza (EN) Tiger Head (TH) Tatung (TT) Ensyutohson (ET) Blair Athol (BS) Newlands (NL)
72.9 75.0 77.6 80.6 82.5 83.2 85.5 91.0 66.1 67.1 72.3 78.3 78.7 81.2 82.3 82.7 82.8 82.9 85.9
4.8 5.4 5.0 5.8 5.3 5.3 4.7 4.4 5.2 4.9 4.7 5.6 6.2 6.1 5.6 4.7 5.6 4.7 4.9
1.2 1.1 1.4 1.6 1.6 1.6 1.6 1.3 1.5 0.6 1.4 1.7 1.2 1.6 1.8 1.1 1.5 1.8 1.7
20.1 18.5 16.0 12.0 10.6 9.9 8.2 3.3 27.2 27.4 21.6 14.4 13.9 11.1 10.3 11.5 10.1 10.6 7.5
45.3 46.5 44.4 49.4 49.9 52.9 59.3 76.6 43.4 48.2 48.6 54.3 41.7 46.3 51.5 60.3 51.3 61.9 57.7
44.9 44.7 40.0 45.8 30.1 37.8 27.4 18.6 41.7 50.3 49.7 43.3 45.7 38.9 36.3 29.7 37.2 29.3 27.0
9.7 8.8 15.4 4.7 19.8 9.3 13.1 4.8 15.1 1.5 1.7 2.4 12.6 14.8 12.2 10.0 11.5 8.8 15.3
Equation 4 was obtained when approximating eq 1 by eq 3. No a priori assumptions were required for the functional forms of f(E) and k0(E). In other words, we could estimate k0 and E at any levels of V/V* by using the method. In this paper the method was applied to analyze the pyrolysis reactions of 19 coals, including the Argonne premium coals. First, the f(E) and k0 for total volatiles were estimated. Then those for the formation reactions of each gas species and tar were estimated. The validity of the presented method was examined through these measurements and analyses. Experimental Section Table 1 lists the ultimate analyses for the 19 coals used in this work. The weight change accompanying the pyrolysis of coal was measured by use of a sensitive thermobalance (Shimadzu TG-50) under three different heating rates (a) of 5, 10, and 20 K/min in a nitrogen atmosphere. Fine particles of less than 74 µm and small samples of around 2 mg were used to ensure uniform heating of the coal samples. The measured weight-time relationships were converted to the relationships of V/V* vs T. Pyrolysis using a Curie point pyrolyzer (Japan Analytical Industries JHP-2S) was also performed for several coals. In the pyrolyzer only coal samples wrapped by a pyrofoil are heated at 3000 K/s by high-frequency heating. The pyrolysis temperatures are determined by the Curie point temperatures of foils. The coal particles were heated to 280, 386, 485, 578, or 920 °C and kept for 10 s at the temperature. The V h value obtained at 920 °C was equated to V*, and then the V/V* value was calculated for each temperature. The gaseous products were analyzed continuously for CO, CO2, H2O, and CH4 at a ) 20 K/min by introducing directly the exit gas stream from the TG into a mass spectrometer (Shimadzu, GCMS-QP2000A). Since the amounts of other volatile products except for tar were negligibly small, the amounts of tar produced were estimated by subtracting the amount of the gaseous products from the total volatiles.
Results and Discussion f(E) Curves and k0 vs E Relationships Estimated for 19 Coals. Figure 1 shows the relationships of V/V* vs T measured at a ) 20 K/min. The temperature at which the reaction starts and the shape of the curves are significantly different among the coals. For the
Figure 1. V/V* vs T relationships measured at a ) 20 K/min for 19 coals.
Argonne premium coals, the lower rank coals start to be pyrolyzed at lower temperatures. The lowest rank coal, ND, shows a shape that is a little different from the other coals: it starts to be pyrolyzed at the lowest temperature, but the V/V* value is the lowest at 1000 K. Similar shapes were obtained for the lower rank coals such as MW, SY, and BD in Figure 1b. These suggest that the mechanism of the pyrolysis for these coals is different from other coals. Figure 2 shows typical Arrhenius plots performed to obtain E values at different V/V* levels for coal WY through procedures 1 and 2 given above. The relationships between V/V* vs E can be obtained by plotting the V/V* value against the corresponding E value through procedure 3 and are shown for the Argonne premium coals in Figure 3a and for the other coals in Figure 3b. When the curves are differentiated graphically by E (procedure 4), f(E) curves for the coals could be obtained as shown in Figure 4. The shapes of the curves are significantly different among the coals: the peaks appear at E ) 215-300 kJ/mol, and the activation energy E spreads from 150 to 400 kJ/mol. These results
974 Energy & Fuels, Vol. 11, No. 5, 1997
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Figure 2. Typical Arrhenius plots performed to obtain E values at different V/V* levels (WY coal).
Figure 4. f(E) curves estimated by the proposed method for 19 coals.
Figure 3. V/V* vs E relationships estimated by the proposed method for 19 coals.
clearly show that f(E) cannot be represented by a single Gaussian distribution. For the Argonne premium coals, the peak position shifted to higher E values with the increase of coal rank. This is well expected because the higher rank coals are decomposed at higher temperatures as shown in Figure 1. For the other coals, the order of peak position does not always follow the order of coal rank as shown in Figure 4b. This is probably because the properties of the coals, collected from various countries, are significantly different. Figure 5 shows the k0 vs E relationships estimated for all the coals. Interestingly, the relationships were little dependent on coal types except three low-rank coals, SY, MW, and BD. The difference in k0 was on the order of less than 102 at the same E without the lower rank coals. This means that the coal pyrolysis consists of similar reactions having almost the same rates for these coals. Only the proportions of the reactions are different among the coals, which is represented by the difference of f(E) curves. The k0 value increased from an order of 1010 to an order of 1025 s-1, while E increases from 150 to 400 kJ/mol. The following compensation effect approximately held between the k0 values and E for all the coals:
k0 ) R eβE (R, β are constants)
(5)
Figure 5. k0 vs E relationships estimated by the proposed method for 19 coals.
Figure 6. f(E) curves for the Argonne premium coals estimated by Burnham et al. using the conventional method.10
It is obvious that k0 cannot be assumed as constants for the pyrolysis of these coals. f(E) Curves Estimated by the Conventional Method. Figure 6 shows the f(E) curves obtained by
Analysis of Pyrolysis of Coals
Energy & Fuels, Vol. 11, No. 5, 1997 975
Figure 7. Comparison between the experimental V/V* vs T curves and calculated ones using f(E) and k0 estimated for four coals.
Burnham et al.10 for the Argonne premium coals by the conventional method. The peak position of f(E) is not in the order of the coal rank; the peak position of the lowest rank coal, ND coal, is at E ) 260 kJ/mol, whereas the peak position of the highest rank coal, POC coal, is at E ) 220 kJ/mol. This is probably because the k0 value assigned to ND coal is larger than that assigned to POC coal. In the conventional method the f(E) curve is dependent on the value of k0 assigned as stated above. This means that f(E) is just an adjustable curve if k0 was not assigned on some sound basis. Therefore, we must be careful in interpreting the meaning of the activation energy when we resort to the conventional method. The validity of the f(E) curve obtained by the conventional method for prediction use will be examined in the next section. Examination of the Validity of the Presented Method. To examine the validity of the presented method, the experimental TG curves were compared with the calculated curves for four coals as shown in Figure 7. The calculated curves were obtained by numerically integrating eq 1 using the f(E) curves and the k0 vs E relationships estimated by the presented method. The TG curves utilized for obtaining f(E) curves (a ) 5, 10, and 20 K/min) were well reproduced, indicating that the approximate equation (eq 3) employed for developing the method is valid. At a ) 3000 K/s (10 s of holding time at each final temperature) the experimental data and the calculated TG curves showed good agreement for the four coals. The experimental data obtained by Solomon et al.11 at a ) 30 K/min were also compared with the calculated curves for IL, PITT, and UF coals. Good agreement was obtained between the experimental and the calculated curves. These (10) Burnham, A. K.; Oh, M. S.; Crawford, R. W. Energy Fuels 1989, 3, 42-55. (11) Solomon, P. R.; Serio, M. A.; Carangelo, P. M.; Bassilakis, R.; Gravel, D.; Billargeon, M.; Baudais, F.; Vail, G. Energy Fuels 1990, 4, 319-333.
Figure 8. Comparison between the experimental data and several model calculations at 20 K/min for IL coal.
results show that the estimated f(E) and k0 values are well utilized for prediction purposes. Although the above discussion indicates well the validity of the presented method, the sensitivity of f(E) and k0 on the V/V* vs T relationship was investigated to examine further the validity of the method. Several model calculations performed by changing f(E) and/or k0 on purpose were compared with the experimental data obtained at a ) 20 K/min for IL coal in Figure 8. The broken lines were calculated by shifting the estimated f(E) curve by 10 kJ/mol to either larger E values (case 1-1) or smaller E values (case 1-2) without changing the k0 vs E relationship. On the other hand, the chain lines were calculated by either doubling (case 2-1) or halving (case 2-2) the estimated k0 values without changing f(E) curve. Both the broken lines and the chain lines were far from the solid line (calculated using the estimated f(E) and k0) and the experimental data. The V/V* values, for example, differ by as large as 0.05 when f(E) was shifted by 10 kJ/mol. Similar model calculations were performed at a ) 3000 K/s, where the
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Figure 9. Formation rates of CO, CO2, H2O, CH4, and tar for ND and IL coals: (a and b) measured at a ) 20 K/min in this work; (c and d) measured at a ) 30 K/min by Solomon et al.11
Figure 10. Distribution curves of E for the formation of each species, fi(E), for ND and IL coals: (a and b) estimated from the gas formation rates measured in this work; (c and d) estimated from the gas formation rates measured by Solomon et al.
V/V* value shifted by as large as 0.1 when f(E) was shifted by 10 kJ/mol. These results indicate that both f(E) and k0 affect the V/V* vs T relationship very sensitively. The dotted line was calculated using the f(E) curve (shown in Figure 6) and the k0 value (assumed to be a constant as 1.6 × 1012 s-1) estimated by Burnham et al. The curve did not agree with the experimental data for larger V/V* region. This may be partly because the experimental data used to estimate f(E) by Buhnham et al. are different from ours. However, the f(E) curve estimated by the conventional method may be just an adjustable curve when f(E) spreads over wide E values as stated earlier. So we think that a good fit between the experimental and calculated curves does not always show the validity of the conventional method.
Summarizing these discussion, we can well say that the presented method is valid for estimating f(E) and k0. fi(E) and k0i for the Formation Reaction of Each Species. Up to now we have discussed the f(E) and k0 values estimated from the weight loss curve. Since the weight loss is brought about by the formation of various components such as CO2, H2O, CO, CH4, tar, etc., f(E) is surely the sum of the distribution curves for such components. Then the distribution curve of E for the formation rate of the species i, fi(E), was estimated by the following procedure. Since we have estimated the relationship between k0 and E for each coal as shown in Figure 5, the relationship between E and T can be obtained for a selected heating rate, aj, by resorting to eq 4. By use of this
Analysis of Pyrolysis of Coals
relationship, the relationship between the normalized amount of the species i formed, Vi/Vi*, and the temperature, T, which was obtained experimentally, can be converted to the relationship of Vi/Vi* and E. Here, Vi* represents the ultimate amount of the species i formed. When the V/V* vs E relationship is differentiated by E, the distribution curve of E for the formation rate of the species i, fi(E), can be obtained. The k0i vs E relationship is the same as the k0 vs E relationship for each coal. Parts a and b of Figure 9 show the formation rates of CO, CO2, H2O, CH4, and tar for ND and IL coals measured at a ) 20 K/min, where the formation rate of tar was obtained by assuming that the volatile, except for CO, CO2, H2O, and CH4, is tar. The formation rates measured at a ) 30 K/min by Solomon et al.11 for the same species are also shown for comparison purpose in parts c and d of Figure 9. The fi(E) curves of CO, CO2, H2O, CH4, and tar were estimated from the corresponding formation rates in parts a and d of Figure 9 by following the above procedure and are shown in parts a and d of Figure 10, respectively. Almost the same fi(E) curves were obtained from the gas formation rate of our data (parts a and b of Figure 10) and from Solomon’s data (parts c and d of Figure 10), although the heating rates employed to measure the gas formation rates were different. This shows that fi(E) curves can be estimated from gas formation rates obtained at a single heating rate and that the presented procedure for estimating fi(E) is valid.
Energy & Fuels, Vol. 11, No. 5, 1997 977
We can see that the fi(E) curves of H2O, CO2, and tar have rather steep peaks at lower E values and that fi(E) curves of CO are rather broad. The shape of the fi(E) curve of CH4 was different between the two coals. The range of E values covered by each fi(E) curve is rather close to that covered by the distribution curve used by Solomon et al. in their FG-DVC model.4 Conclusion The new method presented by one of the authors for estimating both the distribution curve f(E) and the frequency factor k0(E) in the distributed activation energy model (DAEM) was applied to the analysis of the pyrolysis reaction of 19 coals. It was found that the f(E) curve spreads over 150-400 kJ/mol and that the frequency factor k0 increases from 1012 to 1025 s-1 with the increase of E. The shape of the f(E) curves was significantly different among the coals, whereas the k0 vs E relationship was little dependent on coal type except several low-rank coals. The validity of the proposed method was clarified through the comparison of the experimental weight loss curves with the weightloss curves calculated using the estimated f(E) and k0(E). The distribution curves of fi(E) for the formation of CO, CO2, H2O, CH4, and tar were also estimated for the Argonne premium coals by extending the proposed method. EF960224W
