A simple kinetic analysis to determine the intrinsic reactivity of coal chars

Fuel 84 (2005) 1920–1925 www.fuelfirst.com

A simple kinetic analysis to determine the intrinsic reactivity of coal chars Edwige Sima-Ella, Gang Yuan, Tim Mays* Department of Chemical Engineering, University of Bath, Bath BA2 7AY, UK Received 31 October 2004; received in revised form 17 March 2005; accepted 22 March 2005 Available online 19 April 2005

Abstract The intrinsic oxidation reactivity in air of an activated carbon char derived from bituminous coal was investigated using a new thermogravimetric analysis (TGA) method. Applying the new method, values of the Arrhenius activation energy E and pre-exponential factor A were estimated from TGA data obtained via heating samples at different constant rates. A novel statistical criterion was subsequently used to determine the heating rate at which optimum values of E and A were obtained. This is a valuable development, for in conventional non-isothermal TGA, while it is accepted that Arrhenius parameters vary with heating rate, there is no formal method for selecting one rate (and hence one set of values of E and A) over another. Using this new method, the following optimum values were obtained for the carbon at a heating rate of 25 8C minK1: EZ129.4 kJ molK1 and ln(A/sK1)Z10.4. These results are very similar to those calculated for the same material using more time consuming and less accurate isothermal TGA methods. It is therefore proposed that this new analysis method might be an improvement on conventional techniques to determine the intrinsic oxidation reactivity in air of coal chars. q 2005 Elsevier Ltd. All rights reserved. Keywords: Coal char characterisation; Intrinsic reactivity; Thermogravimetric analysis

1. Introduction Coal characterisation has been extensively studied over the years [1–15]. The physical and chemical properties of coal, and materials derived from coal, are of considerable importance in industrial coal utilisation, for example in combustion, gasification and steel-making processes. The aspect of coal characterisation that is considered in this paper is the intrinsic oxidation reactivity of coal chars. Understanding the kinetics of char oxidation is useful for the understanding, design and modelling of industrial processes. Also, this aspect may serve as an index to compare different coals and coal blends and predict process performance. It is therefore important that an accurate estimation of the reactivity parameters is made. Reactivity is characterised by the rate constant k which may be factored into the activation energy E and a preexponential factor A via the Arrhenius equation: kðTÞ Z A expðKE=RTÞ

(1)

* Corresponding author. Tel.: C44 1225 386528; fax: C44 1225 385713. E-mail address: [email protected] (T. Mays).

0016-2361/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2005.03.022

where T is the absolute temperature and RZ8.314! 10K3 kJ KK1 molK1 is the gas constant. Modern thermal analyses suggest that activation energy is the predominant factor in the reactivity equation [16]. Activation energy, essentially, affects the temperature sensitivity of the reaction rate, whereas the pre-exponential factor is related more to material structure. Char reactivity, therefore, may be sufficiently characterised by its activation energy value alone. The intrinsic reactivity of a coal char may conveniently be measured at low temperature, where mass transfer limitations are not an issue. Many combustion (or oxidation) kinetic measurements of chars have been obtained using thermogravimetric analysis (TGA). TGA is a common way of measuring intrinsic reactivity because of the low temperature range for this process, typically !1000 8C. In this work, reactivity is measured in air between 400 and 600 8C. At higher temperatures, diffusion of products and reactants to surfaces has a significant effect on reaction rate. In TGA, the weight of a char sample is determined as a function of time and temperature as it is subjected to a controlled temperature programme. TGA experiments are usually carried out in two ways: (i) isothermal, where the sample is heated at a constant temperature [3–8], and (ii) linear heating, where the sample is heated at a constant rate

E. Sima-Ella et al. / Fuel 84 (2005) 1920–1925

[9–15]. Isothermal TGA is not attractive because of the excessive time and multiple experiments required. At relatively low temperatures (!500 8C), the char might take up to 3 h to reach 50% conversion [17], and at least three experiments are necessary for assessing reactivity parameters. The non-isothermal option, on the other hand, presents several advantages: studying the reaction in one single experimental run, and achieving complete char conversion in a shorter period of time (approximately !2 h). However, two significant problems arise with this technique. First, the mathematical equations for linear heating, which incorporate activation energy and preexponential factor are not easily analysed. And second, kinetic parameters depend on heating rate in non-isothermal TGA [19–22] (as well as on other factors such as instrument sensitivity and particle size) so that unique values of these parameters are not well-defined. To circumvent this second problem, non-isothermal experiments using a given thermal analysis system and sample are conventionally performed at a single heating rate, usually 15 8C minK1 [17], or 8–12 8C minK1 [18]. As previously mentioned, this is not a reliable technique, as the activation energy value changes with heating rate. In the isothermal case, the analysis is more straightforward; this is why, non-isothermal TGA is not as popular as isothermal methods in char reactivity studies. In this work, a new and simple approach is presented for non-isothermal TGA which clearly identifies a heating rate that provides optimum estimates of Arrhenius parameters, and therefore resolves the second major problem with conventional methods mentioned above. The new approach identifies a way of obtaining optimum kinetic parameters using a simple statistical criterion. The parameter values obtained using the new method are then compared with values obtained using isothermal analysis in order to test their validity.

1921

be estimated from the intercept and slope, respectively, of an Arrhenius plot (ln k versus 1/T): ln k Z ln A K E=RTisothermal

(4)

2.2. Model equations—non-isothermal analysis In this case, temperature changes at a constant positive rate bZdT/dt. Hence, combining Eqs. (1) and (2) leads to Eq. (5) [29]: da Að1 K aÞ Z expðKE=RTÞ dT b

(5)

Solving Eq. (5) via integration, subject to the initial condition aZ0, TZT0 yields: ð A T expðKE=RTÞ (6) lnð1 K aÞ Z K b T0 Since there is no oxidation (aZ0) up to T0 (ignition temperatureZ400 8C), the limits of the integral are Ð conventionally changed to 0T expðKE=RTÞ, hence the function p(x)may be introduced such that: ðN Kx e dx (7) pðxÞ Z 2 x x where xZE/RT. Hence Eq. (5) reduces to: lnð1 K aÞ Z K

AE pðxÞ bR

(8)

2. Theoretical analysis

A problem with Eq. (8) is that it is not analytically solvable. The function p(x), however, can be expressed by some approximate equations. Many approximations have been derived and are still being discussed [29–31]. Here, two simple approximations to p(x) are used: Doyle’s approximation [32] and the Coats–Redfern approximation [33]. These have been selected for their simplicity and resulting ease of manipulation of Eq. (8) into linear forms. Doyle’s approximation of p(x) is derived by observing a linear relationship between lnp(x) and x:

2.1. Model equations-Isothermal analysis

pðxÞ zexpðK5:33 K xÞ

Although reactions of many substances are complex, the air oxidation of chars has been generally described as a global one step kinetic chemical reaction model [23–28]:

Hence Eq. (8) may be manipulated to a linear form to yield:     AE E ln½lnð1 K aÞ Z ln K K 5:33 K 1:052 (10) bR RT

da Z kð1 K aÞ dt

(2)

where aZ ð1K W=W0 Þ is the fractional weight conversion, where W is sample weight and W0 the original sample weight. Solution of Eq. (2) via integration, subject to the initial condition aZ0, tZ0 yields Klnð1 K aÞ Z kt

(3)

Hence k may be determined from the slope of a plot of Kln(1Ka) versus t. Subsequently, values of A and E may

(9)

Hence for a given heating rate, A and E may be estimated from values of the intercept and slope respectively of a plot of ln[ln(1Ka)] versus 1/T. In the Coats–Redfern approximation (see [34]) only the first term of an asymptotic expansion of p(x) is retained [35]: pðxÞ Z

eKx ½1 K ð2!=xÞ C ð3!=x2 Þ K ð4!=x3 Þ C/ x2 C ðK1Þn ððn C 1Þ!=xn Þ C/

(11)

1922

E. Sima-Ella et al. / Fuel 84 (2005) 1920–1925 Table 2 Reactivity values for isothermal oxidation of BPL in air

Hence: pðxÞ z

eKx x2

(12)

Eq. (12) may be incorporated into Eq. (8) to yield a linear equation:     Klnð1 K aÞ AR E (13) ln K Z ln 2 bE RT T Hence for a given heating rate, A and E may be estimated from the intercept and slope respectively of a plot of ln[Kln(1Ka)/T2] versus 1/T.

3. Experimental methods

Temperature (8C)

Reactivity, k (sK1!10K5)

475 500 525 550 575

3.834 6.416 15.578 25.259 34.224

heated at 10 8C minK1 to 400 8C (temperature at which oxidation initiates) and held at that temperature for 15 min. As the material contains no volatiles, this procedure ensured the BPL was totally dry before oxidation analysis. 3.4. Char oxidation

3.1. Raw material The material used in this investigation is BPL (Calgon), a steam activated carbon derived from bituminous coal. This is a highly homogeneous material used here as a convenient model for more variable coal chars. Some properties of BPL are shown in Table 1; other information may be found from the manufacturer [36]. 3.2. Thermobalance Char preparation and oxidation were carried out by means of a Setaram TG 92 thermogravimetric analyser (TGA) operating at atmospheric pressure. The system is controlled by a compatible PC, which registers the temperature measured by a thermocouple placed under the crucible. The crucible used is made of Al2O3. The sample is placed in the alumina crucible, suspended from a highly sensitive horizontal beam balance (!0.03 mg) located in the casing of the TGA apparatus, and heated to the reaction temperature. Sample weight is continuously recorded by the PC data acquisition system until the experiment is terminated at 100% conversion. The amount of sample used was around 50 mg. All reported data for weight change were analysed on a dry, ash-free basis. All weight measurement experiments were corrected for buoyancy following blank runs under the same heating conditions.

After pyrolysis, dry air (20% oxygen) was directly introduced into the TGA crucible region at similar conditions to nitrogen. Non-isothermal runs proceeded at heating rates of 5, 10, 15, 20, 30 and 50 8C minK1 from 20 to 600 8C. Isothermal runs, were carried out at 475, 500, 525, 550 and 575 8C up to 10% conversion in each run. Previous investigations showed that the conversion-temperature curve of BPL in air was independent of temperature below 600 8C; suggesting that the oxidation process was chemically controlled in these conditions.

4. Results and discussion 4.1. Isothermal analysis The rate constant values from the isothermal analysis are summarised in Table 2. As expected, reactivity increases with increasing temperature. The activation energy and pre-exponential factor were estimated from linear

-7.0

The activated carbon was treated under N2 (99.99% purity) flowing at 16.7 ml minK1 [STP]. The carbon was

ln (k,s-1)

-8.5

3.3. Char preparation

-10.0

Table 1 Some properties of BPL activated carbon Moisture, as packed Ash content Fixed carbon BET surface area Particle size

2 wt% 8 wt% 90 wt% 1, 004 m2/g 4 mm (max)

-11.5 0.140

0.145

0.150

0.155

0.160

0.165

1/RT (kJ mol -1)

Fig. 1. Determination of reactivity parameters, A and E, according to isothermal method during the air oxidation of BPL.

E. Sima-Ella et al. / Fuel 84 (2005) 1920–1925 Table 3 Kinetic parameters for the linear heating of BPL in air using Doyle and Coats–Redfern approximations Heating rate (8C minK1)

5 10 15 20 30 50

Doyle’s approximation

Coats–Redfern’s approximation

E (kJ molK1)

ln(A/sK1)

E (kJ molK1)

ln(A/sK1)

193.37 175.69 160.20 139.45 128.88 100.00

20.48 17.71 15.23 12.16 10.66 6.63

190.62 171.84 155.62 135.87 122.85 92.60

19.96 16.93 14.30 11.26 9.30 4.75

regression analysis of the data in Fig. 1. Values obtained were EZ123.3G10.9 kJ molK1 and ln(A/s)Z9.72G1.65. Error values are standard errors on the estimates at 95% confidence interval. 5 ˚C/min

1923

4.2. Non-isothermal analysis Table 3 shows values of E and A estimated from the nonisothermal TGA data using both the Doyle and Coats– Redfern approximations. Values of E and A are similar from both approximations for a given heating rate. Also, both parameters appear to decrease with increasing heating rate. There is a difference of almost 60 kJ molK1 in the value of E from using 5 or 30 8C/min heating rate. Similarly, the natural logarithm value of the pre-exponential factor is doubled in this range. As observed in Fig. 2 single heating rate experiments affect the shape of the conversiontemperature curve, and ultimately, the determination of true kinetic data. At 600 8C, more than 40% of the material has reacted at a heating rate 5 8C/min; whereas, only 3% of the original material has reacted when a heating rate of 50 8C/min is applied. 10 ˚C/min

1.00 0.95

0.80

0.85

0.60

0.75

0.40 400

450

500 550 Temperature (˚C)

600

15 ˚C/min

400

450

500 550 Temperature (˚C)

600

20 ˚C/min

1.00

1.00 0.98

0.95 0.96 0.94

0.90

0.92

0.85

0.90

400

450

500 550 Temperature (˚C)

600

30 ˚C/min

400

450

500 550 Temperature (˚C)

600

50 ˚C/min 1.00

1.00 0.99

0.99

0.98 0.97 0.98

0.96 0.95

0.97

400

450

500 550 Temperature (˚C)

600

400

450

500 550 Temperature (˚C)

600

Fig. 2. Comparison of the experimental TGA curve (—) with the calculated TGA curves using approximations from Doyle (—) and Coats–Redfern (—).

1924

E. Sima-Ella et al. / Fuel 84 (2005) 1920–1925 1.2%

6.0%

1.0%

5.0%

0.8%

4.0%

0.6%

3.0%

0.4%

2.0%

0.2%

1.0%

0.0%

0.0% 0

10

20

30

40

50

60

-1

Heating rate (ºC min )

Fig. 3. Standard error in the fit of TGA data calculated using Coats–Redfern (:) and Doyle (&) approximations.

To resolve this problem, a statistical analysis was developed to determine which heating rate yielded optimum values of E and A. Fig. 2 shows plots of actual and predicted conversion curves from the non-isothermal TGA for different rates. Graphically, there appears to be one rate that yields the best fit to the data using either approximation method. To clarify this, values of s, the root mean squared (RMS) difference between the actual and predicted values of a for the four different heating rates, were determined. Values of s are plotted as a function of heating rate in Fig. 3. Fig. 3 shows that for each approximation method there is a minimum value of s (and hence a best fit) for a particular value of heating rate. This optimum is observed at a heating rate of about 25 8C minK1 for the Coats–Redfern approximation, and about 17 8C minK1 for Doyle’s approximation. However, the RMS values for the Doyle method are about three times those for the Coats–Redfern method. Accordingly, it is suggested that an optimum approach is to use the Coats–Redfern method to analysis the non-isothermal TGA data. For this method, at 25 8C minK1, EZ129.4G 0.9 kJ molK1, and ln(A/sK1)Z10.34G0.05. These parameter values are in good agreement with those obtained using the isothermal analysis, though with much smaller standard errors.

5. Conclusions This study measured the intrinsic oxidation reactivity in air of BPL using isothermal and non-isothermal TGA methods. The reaction was modelled as a first order global kinetic, and reactivity parameters factored in terms of Arrhenius activation energy E and pre-exponential factor A. The conventional though tedious isothermal method, led to values of EZ123.3G10.9 kJ molK1 and ln(A/sK1)Z 9.72G1.65. In the non-isothermal case, kinetic parameters were derived from a simplified mathematical study. This

analysis has been presented in two parts: (i) eliminating the mathematical complexity by transforming the temperature integral equation into a linear form; (ii) identifying an optimum-heating rate at which true kinetic parameters are deduced. It was found that the Coats–Redfern approximation to the temperature integral [33] is simultaneously simple and accurate. The optimum-heating rate was observed as 25 8C minK1 for which EZ129.4G0.9 kJ molK1, and ln(A/ sK1)Z10.34G0.05. These values are not statistically different at the 95% confidence level from those obtained from the isothermal analysis, and are very similar to literature values for equivalent materials [17]. Finally, it is recommended that the non-isothermal TGA method presented here is sufficiently simple and accurate for kinetic measurement of intrinsic char reactivity. In addition, if optimum-heating rate is an instrument factor (i.e. dependent on TGA apparatus) rather than material specific (dependent on type of material) it only needs to be determined once the equipment is first purchased. The new procedure is considered to be of potential use in the study of coal char reactivity, where accurate and fast characterisation is required.

Acknowledgements The authors gratefully acknowledge financial support received in the form of a research grant by the British Coal Utilisation Research Association (Contract B56), United Kingdom.

References [1] Van Krevelen DW. Coal: typology—chemistry–physics-constitution. 3rd ed. Amsterdam: Elsevier; 1993. [2] Berkowitz N. An introduction to coal technology. 2nd ed.: Academic Press; 1994. [3] Lizzio AA, Piotrowski A, Radovic LR. Fuel 1998;67:1691–5. [4] Gale TK, Bartholomew CH, Fletcher TH. Energy Fuels 1996;10: 766–75. [5] Sørensen LH, Gjernes E, Jessen T, Fjellerup J. Fuel 1996;75:31–8. [6] Kajitani S, Hara S, Matsuda S. Fuel 2002;81:539–46. ´ lvarez T, Fuertes AB, Pis JJ, Ehrburger P. Fuel 1995;74:729–35. [7] A [8] Zolin A, Jensen A, Pederson LS, Dam-Johansen K, Torslev P. Fuel 1998;12:268–76. [9] Feng B, Jensen A, Bhatia SK, Dam-Johansen K. Energy Fuels 2003; 17:399–404. [10] Zolin A, Jensen AD, Jensen PA, Dam-Johansen K. Fuel 2002;81: 1065–75. [11] Lester E, Cloke M. Fuel 1999;78:1645–58. [12] Peralta D, Paterson NP, Dugwell DR, Kandiyoti R. Energy Fuels 2002;16:404–11. [13] Shemet VZh, Pomytkin AP, Neshpor VS. Carbon 1993;31:1–6. [14] Ceylan K, Karaca H, Onal Y. Fuel 1999;78:1109–16. [15] Alonso MJG, Alvarez D, Borrego AG, Menendez R, Marban G, et al. Energy Fuels 2001;15:413–28. [16] Vyazovkin SJ. Therm Anal Cal 2001;64:829–35. [17] Russell NV, Beeley TJ, Man C-K, Gibbins JR. Fuel Proc Technol 1998;57:113–30.

E. Sima-Ella et al. / Fuel 84 (2005) 1920–1925 [18] Ichihara S, editor. Thermal analysis fundamentals and applications. 3rd ed. Tokyo: Realize; 1994. p. 40. [19] Mackenzie RC, editor. Differential thermal analysis: fundamental aspects, vol. 1. London: Academic Press; 1970. p. 102–4. [20] Hatakeyama T, Zhenhai L, editors. Handbook of thermal analysis. Chichester: Wiley; 1998. [21] Zsako´, J. Ke`kedy E, Varhelyi Cs. Kinetic analysis of thermogravimetric data IV: influence of heating rate and sample weight on thermal decomposition. Thermal analysis, vol 2. Davos: Proceedings 3rd ICTAC; 1971. [22] Wendlandt WM. Thermal methods of analysis. Chemical analysis. vol. 19.: Interscience; 1964. [23] Walker Jr PL, Rusinko F, Austin LG. Gas reactions of carbon. Advances in catalysis and related subjects. vol. 11. London: Academic Press; 1959. [24] Smith IW, Tyler RJ. Fuel 1972;51:312–20. [25] Olofson J. Mathematical modelling of fluidised bed combustors. London: IEA Coal Research; 1980.

1925

[26] Hu YQ, Nikzat H, Nawata M, Kobayashi N, Hasatani M. Fuel 2001; 80:2111–6. [27] He R, Sato J, Chen Q, Chen C, et al. Combust Sci Technol 2002;174: 1741–8. [28] Hecker WC, Madsen PM, Sherman MR, Allen JW, Sawaya RJ, Fletcher TH. Energy Fuels 2003;17:427–32. [29] Brown ME, editor. Introduction to thermal analysis: techniques and applications. 2nd ed. London: Kluwer Academic; 2001. [30] Starink MJ. Thermochim Acta 2003;404:163–76. [31] Senum GI, Yang RT. J Therm Anal 1979;11:445–7. [32] Doyle CD. J Appl Polym Sci 1962;6:639–42. [33] Coats AW, Redfern JP. Nature 1964;201:68–9. [34] Murray P, White J. Trans Brot Ceram Soc 1955;54:204–38. [35] Zsako´ J, Zivkovic ZD, editors. Thermal analysis. Yugoslavia: University of Beograd; 1984. [36] Carbon Corporation. Product bulletin: BPL 4!10 granular activated carbon. Pittsburgh 1998. LC-103-08/98.