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Kinetic Analysis in the Maximum Temperature of Oil Generation by Thermogravimetry in Spanish Fossil Fuels M. A. Olivella and F. X. C. de las Heras* Escola Universita` ria Polite` cnica de Manresa (UPC), Av Bases de Manresa 61-73, 08240-Manresa, Catalonia, Spain Received February 28, 2002
Low-rank coals characterized by a high content of sulfur from Mequinenza (type III-S), Calaf (type III), and Utrillas (type III) basins, as well as type I-S oil shales from Ribesalbes were analyzed by thermogravimetry for deriving kinetic parameters from many TG curves recorded with different heating rates (5, 15, and 25 K/min) in maximum temperature of oil generation (Tmax) using a equation defined by Zsako´. These results are contrasted with those obtained by NLS (nonlinear least squares) algorithms which derive kinetic parameters nearby Tmax from single TG curve. Furthermore, analytical determination of organic sulfur has allowed the comparison of different maximum temperatures of oil generation, as well as apparent activation energies, to establish general trends when different types of kerogen are compared. Finally, a method to compare the kinetic parameters at different heating rates (5, 15, and 25 K/min) is applied nearby the maximum temperature of oil generation (Tmax) obtaining similar kinetic values and therefore concluding that the applied method is correct for these selected coals and oil shales.
1. Introduction Sulfur incorporation in ancient lakes, which generated sulfur-rich spanish low-rank coals and oil shales, was due generally to the lixiviation through fluvial systems of sulfate salts widespread in the catchment area (Triassic and Liassic gypsum) into lacustrine basins.1-3 Such an increase of salt, in reducing sedimentary conditions, resulted in a massive microbiological sulfate-reduction process by generating (poly)sulfides, which can be combined with the sedimentary iron, forming pyrite, or with the sedimentary organic matter, forming organic sulfur compounds. The role of sulfur in petroleum generation has been of considerable interest because the presence of sulfur in kerogens and coals are related to the early oil and hydrocarbon generation. The explanation offered for the early generation is that lower activation energies are required to break carbon-sulfur bonds compared to those of carbon-carbon bonds.4-6 In this paper, thermogravimetry is used to derive the kinetic parameters from TG curves suggesting that the apparent activation energies Ea vary inversely with sulfur contents, in parallel with previous results.6,7 (1) Cabrera, L.; Sa´ez, A. J. Geol. Soc. 1987, 144, 451-461. (2) Querol, X.; Chincho´n, S.; Lo´pez-Soler, A. Int. J. Coal Geol. 1989, 11, 171-189. (3) Anado´n, P.; Cabrera, L.; Julia`, R.; Roca, E.; Rosell, L. Palaeogeogr. Palaeoclimat. Palaeocol. 1989, 70, 7-28. (4) Orr, W. L. Org. Geochem. 1986, 10, 499-516. (5) Tannenbaum, E.; Aizenshtat, Z. Org. Geochem. 1985, 8, 181192. (6) Baskin, D. K.; Peters, K. E. AAPG Bull. 1992, 76, 1-13. (7) Hunt, J. M.; Lewan, M. D.; Hennet, R. J. C. AAPG Bull. 1991, 75, 795-807.
Most petroleum (oil and gas) is formed through the partial decomposition of kerogen in response to thermal stress during subsurface burial in a sedimentary basin.8,9 The knowledge of the mechanisms and kinetic of this process allows the determination of the extent and timing of oil and gas formation.10 Most kinetic models are based on first-order reaction by estimating quantitatively the hydrocarbon evolution as a function of burial time.11 Kinetic modeling of hydrocarbon generation assumes that the transformation of organic matter during thermal treatment can be described by a series of parallel reactions involving cracking of kerogen. Calculation of Ea allows the kinetic evolution of organic matter to be described. However the use of these kinetic parameters is questionable because there is not definitive proof that kerogen follow a first-order reaction.12 Maximum temperature Tmax from kinetic predictions is mainly ascribed as the main hydrocarbon generation stage.10 The kinetic behavior of kerogens has also been shown to represent a very critical element in modeling hydrocarbon generation from source rocks.9,13 Extrapolation of laboratory-derived kinetic parameters to geological conditions is a matter of debate, (8) Hunt, J. M. Petroleum Geochemistry and Geology, 2nd ed.; Freeman: New York, 1996. (9) Tissot, B. P.; Pelet, R.; Ungerer, P. AAPG Bull. 1987, 71, 14451466. (10) Di Primio, R.; Horsfield, B. Org. Geochem. 1996, 24, 999-1016. (11) Ko¨k, M. V.; Hughes, R.; Price, D. J. Thermal Anal. 1997, 49, 609-615. (12) Landais, P.; Michels, R.; Elie, M. Fuel 1994, 73, 1691-1696. (13) Tegelaar, E. W.; Noble, R. A. Org. Geochem. 1993, 22, 543574.
10.1021/ef020051c CCC: $22.00 © 2002 American Chemical Society Published on Web 10/05/2002
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especially when the nonuniqueness of kinetic parameters (compensation effect) is taken into account.14-16 Determination of kinetic parameters for hydrocarbon generation is a process consisting in an artificial maturation experiments followed by fitting of kinetic parameters to the laboratory data. One of the used artificial maturation techniques is thermogravimetry (TG).17 Generally in TG, heterogeneous reactions as
A(solid) f B(solid) + C(gas)
(1)
are studied under nonisothermal conditions. Usually the fractional reaction, R is defined in terms of the change in mass of sample [R ) (mo - m)/(mo mf)], where mo is the initial mass and mf the mass of the sample when reaction is completed. The kinetic reaction 1 may be studied by using two types of approximations: model and homogeneous approximations. By using the first formalism kinetic equations are derived taking into account the nucleation, the growth of germs, or the diffusion of the product, etc.18-20 The last formalism of homogeneous kinetics is applied by considering that the reaction rate, defined by means of the conversion degree R, might be given as the product of an apparent rate constant, depending on the temperature and a certain conversion function as it is indicated by the following equation
dR/dt ) k(T)f(R)
(2)
where f(R) is the differential function of the conversion degree and k(T) is a function of temperature. The temperature dependence is expressed according to the Arrhenius equation:
k(T) ) A exp(-E/RT)
(3)
and very often the conversion function is presumed to be an nth-order homogeneous reaction:
f(R) ) (1 - R)n
(4)
For nonisothermal experiments a convenient change of the variable time t into temperature T turns eq 2 into
1 dR/dT ) k(T)f(R) β
(5)
Upon introducing Arrhenius equation into eq 5, and the function f(R) as given by eq 3 and eq 4, respectively, where β is the heating rate, eq 6 is obtained:
A dR/dT ) ‚exp[-E/RT]‚(1 - R)n β
(6)
According to eq 6, from the kinetic point of view the reaction 1 may be characterized by means of three (14) Lakshmanan, C. C.; White, N. Energy Fuels 1994, 8, 11581167. (15) Lakshmanan, C. C.; Bennett, M. L.; White, N. Energy Fuels 1991, 5, 110-117. (16) Nielsen, S. B.; Dahl, B. Mar. Petrol. Geol. 1991, 8, 483-492. (17) Fuller, E. L.; Kopp, O. C.; Rogers, M. R. In Coal Science; Pajares, J. A., Tasco´n, J. M. D., Eds.; Elsevier: Oviedo, 1995, pp 889-900. (18) Sesta´k, J.; Satava, V. V.; Wendlandt, W. W. Thermochim. Acta 1973, 7, 333-336. (19) Fe`vre, A.; Murat, M. J. Thermal Anal. 1975, 7, 429-453. (20) Sesta´k, J.; Berggren, G. Thermochim. Acta 1971, 3, 1-12.
parameters, A (preexponential order, min-1); E (activation energy, kJ/mol); and n (reaction order). Many methods have been developed to derive these parameters from TG data.21,22 In this paper NLS (nonlinear least-squares) algorithms and an equation defined by Zsako´21 have been applied. From the mathematical point of view, the NLS procedure implies the use of a variational method by choosing function 6, containing three variational parameters and by determining the parameter values ensuring the minimum deviation of experimental points from theoretical curves. The Zsako´ equation21 derives kinetic parameters from the maximum rate temperatures Tmax observed at different heating rates, based on the best linearity of a set of values. Consequently, the kinetic parameters (A, E, and n) have no clear physical meaning and they do not characterize the chemical reaction itself, but only the whole complexity of processes occurring during the pyrolysis under the given experimental conditions. Hence they are designated as apparent values.21,23 Recently Font et al.24 have proposed a method for comparing the kinetic constants due to the interrelation among the preexponential factor, the reaction order and the apparent activation energy. This method consists on applying a comparison factor that represents the kinetic rate for a common temperature Tmax close to that where decomposition rate is maximum and a fractional conversion of 0.64; therefore,
comparison factor ) ki exp[-E/RTmax]0.64ni (7) where ki is the kinetic constant for the reaction “i” whose order is “ni”; 0.64 is an optimized constant.24 This method has been applied for homogeneous (cellulose) and heterogeneous (tannery waste) materials.24 For heterogeneous materials the comparison factor can be used for the analysis of different fractions. In this paper we focus on the use of the comparison factor in the fraction related with oil and hydrocarbon generation to determine the kinetic values for coals and oil shales selected for this study. According to Font et al.24 by deriving the kinetic values and the preexponential factor the decomposition of the volatile fraction must be considered in the interval of the study. If the data are correlated without considering the fraction of volatiles, the result of the correlation could vary, and therefore, to obtain different preexponential factor values, the following relationship was deduced:24
ki(ν∞ - na)nwhen_va_is_considered ) ki(ν∞)nwhen_va_is_NOT_considered (8) 2. Experimental Section 2.1. Samples Description. The designation, origin, and kerogen type of different low maturity (vitrinite reflectance 10%) in 8-Me and Calaf coals but the sulfur nature seems to be completely different. The sulfur in 8-Me coal is almost organic (91%) while in Calaf coal about 62% is in the inorganic form. Utrillas (Can˜izara) coal has intermediate sulfur concentration: about 50% is a sum of pyritic and sulfate sulfur and the remaining 50% is in organic form. The total sulfur concentration in Ribesalbes oil shales is relatively low ( 3 for NLS analysis). Good correlation coefficients have been obtained (R2 > 0.95) (Table 3) using Zsako´ equation;21 however, the kinetic parameters could not to be representative of pyrolysis process in the maximum point. More than a kinetic behavior, the first-order reaction could reflect a good correlation between the kinetic parameters with the heating rate mainly due to the compensation effect. A familiar manifestation of the compensation effect is the decrease in the values of both Ea and ln A at higher heating rates. Worthy of attention is also the fact that Ea values are well correlated (R2 > 0.98) with ln A at 5, 15, and 25 K/min heating rates in these selected samples for this study,30 showing that kinetic parameters are well correlated with heating rates due to the compensation effect. Both this decrease and the related compensation effect can result from increased thermal lag at higher heating rates.31 Thus, this linearity between preexponential factors and activation energies when increasing the heating rate has been also reported by Mianowski et al.32 The increase of the reaction order hardly influences the activation energy and preexponential factor in Mequinenza and Can˜izara coals probably due to the homogeneous decomposition and the minor compensation effect.30 On the other hand this mentioned effect is more significant in Ribesalbes oil shales and Calaf coal and it has more incidence in both apparent activation energy and preexponential factor values.30 This fact could be due to the more complex decomposition and the major compensation effect. By supposing first-order reaction as a fixed parameter, the kinetic parameters obtained by NLS analysis from a single curve for all samples are unrealistic (negative ln A, apparent activation energy too low).30 This shows that a first-order reaction in the maximum temperature of oil generation cannot be assumed in selected samples for this study. To assume a first-order reaction in the Tmax would be valid when the thermal decomposition calculated by any method based from one curve takes place via a firstorder equation as the decomposition of cellulose.33 In many fine particle pyrolysis and combustion studies found in the literature, the value of the reaction order equals unity, which is interpreted as a homogeneous decomposition inside the particle, where the (29) Olivella, M. A.; Palacios, J. M.; Vairavamurthy, A.; del Rı´o, J. C.; de las Heras, F. X. C. Fuel 2002, 81, 405-411. (30) Olivella, M. A. Ph.D. Thesis, Universitat Polite`cnica de Catalunya, Catalonia, Spain, 2000, 325 pp. (31) Narayan, R.; Antal, M. J. Ind. Eng. Chem. Res. 1996, 35, 17111721. (32) Mianowski, I. A.; Radko, T. Fuel 1993, 72, 1537-1540. (33) Antal, M. J.; Grφnli, M.; Va´rhegyi, G. Ind. Eng. Chem. Res. 1999, 38, 2238-2244.
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Table 3. Kinetic Parameters Obtained by Zsako´ Equation Derived from TG/DTG Curves at 5, 15, and 25 K/min Heating Rates and NLS Algorithms Based on Single Curve at 5 K/min Heating Ratea Zsako´ equation
NLS algorithms
samples
ln A/ln min-1
Ea/kJ/mol
n
R2
ln A/ln min-1
Ea/kJ/mol
n
χ2(×10-6)
8-Me Can˜izara Calaf Rib-3 Rib-7
23.31 27.44 17.67 20.21 18.82
147.8 179.2 93.00 139.8 134.5
1 1 1 1 11
0.998 0.999 0.971 0.938 1
26.9 32.5 43.4 32.8 27.0
165.0 200.4 193.7 211.5 186.4
5.2 6.5 22.6 14.5 27
8.2 3.2 17.3 0.4 0.4
a n is the reaction order; Ea, apparent activation energy; R2, Correlation Coefficient; A, Preexponential Factor; χ2, the objective function.
reaction rate varies proportionally with the nonreacted mass.34 Nevertheless, some values of the reaction order different from unity can be found in the literature;27,28 these values can be due to the presence of a heterogeneous material, to the variation of reaction surface when the reaction takes place,34 and also to the considerable influence of mass diffusion effects.35 Lewan36 is one of the authors who assumes that the generation of expelled oil can be described as a firstorder reaction rate. This hypothesis has been strongly criticized by Burnham37 who bases his claim that assuming a first-order rate is dangerous on the inference that the heterogeneous composition of the kerogen typically varies with the conversion. Lewan36 considers dR/dt ) 0 in isothermal experiments, because he supposes that the first-order reaction rate is uniform. To suppose dR/dt ) 0 in isothermal experiments is similar to considering it constant (dR/dt ) ct) in nonisothermal experiments at constant heating rate. The major weight loss could be associated with kerogen decomposition in 8-Me and Can˜izara coals, where the variation of the conversion with the temperature (dR/dT) is rather constant and uniform; on the contrary, conversion is not so linear with the temperature in Calaf coal and oil shales from Ribesalbes, probably due to a greater complexity of the reactions occurring during the decomposition and the heterogeneity of the sample.30 In reference to the obtained results in selected coals and oil shales and considering that our experiments were performed in nonisothermal conditions, the supposition of a first-order reaction rate could be misleading. From this analysis, to suppose a first-order reaction in the maximum temperature of oil generation can lead to erroneous results in future predictions of oil and gas generation. Many authors21,23 obtained unrealistic kinetic parameters derived from many curve methods. On the contrary, the curves simulated on bases of the kinetic parameters obtained at 5 K/min heating rate by NLS analysis offer a good fit (see Figure 6 for 8-Me coal) with experimental data in all samples tested by the low χ2 values (Table 3). Also, high reaction orders have been obtained by NLS analysis in Calaf coal and Ribesalbes oil shales. According to many authors,24,38 high-order reactions can give some indication of simultaneous multiple reactions that (34) Font, R.; Garcı´a, A. N. J. Anal. Appl. Pyrolysis 1995, 35, 249258. (35) Levenspiel, O. The Chemical Reactor Omnobook; OSU Book Stores: Corvallis, OR, 1979; pp 55.24-55.25. (36) Lewan, M. D. Geochim. Cosmochim. Acta 1998, 62, 2211-2216. (37) Burnham, A. K. Geochim. Cosmochim. Acta 1998, 62, 22072210. (38) Wilburn, F. W. Thermochim. Acta 1999, 340-341, 77-87.
Figure 6. Experimental data and the best-fitting curve by NLS analysis for 8-Me coal at 5 K/min. Table 4. Atomic Ratio of Organic Sulfur vs Carbon (Sorg/C), Maximum Temperature (Tmax) and Apparent Activation Energies (Ea) for Mequinenza (8-Me), Calaf, and Utrillas (Can ˜ izara) Coals at 5 K/min Heating Rate coals
type
Sorg/C (daf)
Tmax/°C
Ea/kJ/mol
8-Me Calaf Can˜izara
III-S III III
0.075 0.041 0.016
436.6 303.6 468.4
165.0 193.7 200.4
Table 5. Atomic Ratio of Organic Sulfur vs Carbon Content (Sorg/C), Maximum Temperature (Tmax), and Apparent Activation Energies (Ea) for Ribesalbes (Rib-3 and Rib-7) Oil Shales at 5 K/min Heating Rate oil shales
type
Sorg/C
Tmax/°C
Ea/kJ/mol
Rib-3 Rib-7
I-S I-S
0.048 0.056
485.6 480.7
211.5 186.4
can take place probably due to the heterogeneity of the solid or variable values of activation energy occurring during a reaction. In this paper, kinetic parameters in maximum temperature of oil generation have been evaluated in Spanish fossil fuels, not reported previously. 3.2. Relationship between the Maximum Temperature of Oil Generation Tmax and Kerogen Type. By comparing apparent activation energies obtained from NLS analysis, an inverse relationship between organic sulfur content in low-rank coals (Table 4) and oil shales (Table 5) and the peak of hydrocarbon generation Tmax derived from DTG curves is observed, which is consistent with observations made previously.7,39 As it was shown by Klomp and Wright,39 the early breakdown of sulfur rich kerogens is due to the cleavage of weak C-S and S-S bonds, whereas the higher activation energy is due to the C-C bond cleavage. According to this trend the maximum temperatures of oil generation are lower when increasing the organic sulfur content. The maximum temperature observed in Calaf coal is lower than the maximum temperatures obtained by (39) Klomp, U. C.; Wright, P. A. Org. Geochem. 1990, 16, 49-60.
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Table 6. Comparison of Kinetic Values before (k) and after Applying the Comparison Factor (k′) for the Decomposition of Mequinenza (8-Me) and Utrillas (Can ˜ izara) Coals and Ribesalbes (Rib-3, Rib-7) Oil Shales in Nitrogen heating rate (K/min)
5
15
25
standard deviation
k ) Ae-Ea/RTmax k′ ) Ax exp(E/RTmax)0.64n
Mequinenza (Tmax ) 734.4 K) 0.85 0.71 7.76 × 10-03 9.21 × 10-03
k ) Ae-Ea/RTmax k′ ) Ax exp(E/RTmax)0.64n
2.61 1.03 × 10-03
k ) Ae-Ea/RTmax k′ ) Ax exp(E/RTmax)0.64n
Ribesalbes-3 (Tmax ) 789.3 K) 2.0 1.65 × 10+6 2.26 × 10-05 2.21 × 10-08
2.67 × 10+24 2.51 × 10-24
1.18 × 10+24 1.0 × 10-05
k ) Ae-Ea/RTmax k′ ) Ax exp(E/RTmax)0.64n
0.195 2.5 × 10-05
Ribesalbes-7 (Tmax ) 782.8 K) 1.11 × 10+4 1.43 × 10-11
1.82 × 10+4 2.85 × 10-13
6.5 × 10+3 1.1 × 10-05
Can˜izara (Tmax ) 764.1 K) 5.30 1.58 × 10-03
8-Me and Can˜izara coals because the peak temperature is attributed to the dipolysulfidic and elemental sulfur decompositions, which have a lower thermal stability than aliphatic sulfur, not present in Calaf coal.29 Significant polysulfide content in addition to sulfide binding is suggested by the atomic S/C ratios for sulfur rich samples.4 Also, Tables 4 and 5 also confirm previous data obtained in type I kerogens6,9 where sulfur-rich organic matter is thermally more labile than sulfur-poor organic matter. Additionally, it is shown that type I-S kerogens from Ribesalbes show higher stability (with apparent activation energies of 211.5 and 186.4 kJ/mol for Ribesalbes-3 and Ribesalbes-7 respectively) than type III-S coal from 8-Me (with lower apparent activation energy 165.0 kJ/mol). The higher apparent activation energy was found, as expected, in the type III coals (193.7 kJ/mol for Calaf and 200.4 kJ/mol for Can˜izara coals). It is worthwhile mentioning that the study of influence of organic sulfur in oil generation by type III coals with a vitrinite reflectance
