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Non-Arrhenius behaviour in the oxidation of two carbonaceous substrates
Journal of Loss Prevention in the Process Industries 16 (2003) 223–225 www.elsevier.com/locate/jlp
Short Communication
Non-Arrhenius behaviour in the oxidation of two carbonaceous substrates J.C. Jones ∗, S.C. Newman Department of Engineering, Fraser Noble Building, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland, UK
Abstract Two carbonaceous substances—a chemically activated carbon and a bituminous coal—are found, in microcalorimeter experiments, to display a temperature dependence of reaction rate at odds with the Arrhenius equation. Since Arrhenius behaviour is always assumed in tests for spontaneous heating of such substances, this places a question mark over the validity of such tests for at least some of the materials to which they might be routinely applied. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Carbon; Coal; Self-heating; Arrhenius parameters
1. Introduction The Arrhenius expression for the temperature dependence of the rate of a chemical reaction is as follows: k ⫽ Aexp(⫺E / RT). It has its origins in gas-phase kinetics (Moore, 1970), there being a connection (possibly a straightforward equality) between the pre-exponential factor and the molecular collision frequency. An equation of the same form has also found wide application to the oxidation of solid fuels. Usually here there is no mechanistic interpretation of A and E, simply an observed (or assumed) temperature dependence of rate that fits an equation of this form, with E having a value of the order of 102 kJ mol-1. Arrhenius behaviour is generally accepted as the norm across the entire range of chemical reactions, including biochemical ones (Bronk, 1973), whether or not there is a mechanistic basis for interpreting A and E. Accordingly, when non-Arrhenius behaviour is observed it is seen as a point of interest in itself. The present group have recently (e.g., Jones, 2000a,b,c) been closely examining currently widely used test procedures for assessing the propensity to spontaneous combustion of coals and carbons. A point of contention is that such
∗
Corresponding author. Tel.:+44-1224-272793; fax:+44-1224272497. E-mail address: [email protected] (J.C. Jones).
tests assume a single value for the activation energy E for all substances to which the tests might be applied, which is very difficult to justify. Improved procedures (Jones, 2000a,b) have been developed which address this, but even here the assumption is made that Arrhenius behaviour is expected therefore some value or other of the activation energy is applicable. If a coal or carbon does not obey Arrhenius kinetics this introduces a further dimension of uncertainty in the prediction of self-heating behaviour. The work by the present group has involved a good deal of microcalorimetry; coals and carbons have been examined at temperatures between just above room and about 360 K. Although the possibility of non-Arrhenius behaviour beyond the temperature range of the experiments had previously been discussed, and was indeed supported by limited indirect evidence (Jones, 1999), no direct evidence by way of nonlinear plots of log(rate) against 1/T, was observed. The reaction rate for a strong exothermic process can of course be expressed as a heat-release rate, viz.: q(T) ⫽ QAexp( ⫺ E / RT)
(1)
so that a plot of ln{q(T)} against 1/T is linear if the behaviour conforms to an Arrhenius temperature dependence of reaction rate. Many such plots displaying the expected linearity have been reported previously (Jones, 1998). In a continuation of this work (Newman, S.C. MEng thesis University of Aberdeen, in preparation) about 20 carbonaceous substrates were studied, two of which—an activated carbon and a bituminous coal—were found to display marked cur-
0950-4230/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0950-4230(02)00115-8
224
J.C. Jones, S.C. Newman / Journal of Loss Prevention in the Process Industries 16 (2003) 223–225
Nomenclature k A E R T q(T) Q
rate constant (unites s-1 if first order) pre-exponential factor (s-1) activation energy (J mol-1) Universal gas constant = 8.314 J K-1 mol-1 absolute temperature rate of heat release at temperature T(W kg-1) heat of combustion (J kg-1)
vature in their Arrhenius plots. Results from the substrates which did display Arrhenius behaviour—by far the majority—are of interest in identifying trends of self-heating propensity with factors including temperatures attained during processing (for carbons) and rank (for coals), and will be reported in due course. This paper is concerned solely with the non-Arrhenius behaviour.
2. Experimental The microcalorimeter used was a Thermometric 2277 Thermal Activity Monitor. A solid sample for testing was placed in a steel ampoule. The instrument had previously been stabilised at the desired temperature overnight. The ampoule containing the sample was then placed in the equilibration position. The reference ampoule, containing air only, was also placed in its equilibration position. Thermal equilibration of the samples took place over a one-hour period. The ampoules were then lowered into the measuring position and the signal followed at a potentiometric recorder connected to the instrument. The ampoules were left in the measuring position for about an hour, this being more than adequate for the signal to become steady. When the final heat release reading at the recorder was taken it was checked against that on the digital display on the microcalorimeter. Between each experiment, the ampoules were removed from the instrument and the ampoule containing the subject material was opened up to replenish its internal atmosphere. The instrument was recalibrated at each change of temperature setting, at least six hours having been allowed for stabilisation prior to calibration once the set temperature was reached. For each of the carbonaceous substances of interest heat-release rate measurements were made at five temperatures.
3. Materials The two substrates which displayed non-Arrhenius behaviour were: 1. A chemically activated carbon, manufactured by Norit UK and assigned by them the code CNR 115. The sample was supplied (along with several others)
by Norit UK, manufacturers. It was examined in the microcalorimeter at temperatures in the range 311– 338 K. 2. A Chinese bituminous coal. This had been obtained from a coal supplier in Aberdeen. It too was examined in the microcalorimeter at temperatures in the range 311–338 K. The plot of ln{q(T)} against 1 / T for the Chinese coal was obtained twice, that is, for two different samples of the coal each of mass 260 mg. The results obtained the first time were reproduced exactly the second time. The plot for the activated carbon was determined once only, with a 265 mg sample. However, the remarkably consistency of composition of these materials, reflected in reproducibility of heat release rates with very small samples, has already been observed and noted (Jones & Cook, 2000). It arises from stringent milling and blending techniques in manufacture.
4. Results Fig. 1 shows a plot of ln(q / W kg - 1) against 1 / T for the activated carbon and Fig. 2 the corresponding plot for the Chinese coal. In each case the non-linearity is clear therefore the description of the behaviour as being ‘non-Arrhenius’ is appropriate. The two plots of ln{q(T)} against 1 / T were fitted (using EXCEL) to polynomials of the form: y ⫽ ax3 ⫹ bx2 ⫹ cx ⫹ d
(2)
where y = ln{q(T)} and x = 103K / T. The coefficients a, b, c and d for the two substrates are given in Table 1 below. The standard test for spontaneous combustion propensity of coals and carbons previously referred to uses a set oven temperature of 140 °C. If the polynomials apply at this temperature, the heat-releases rates would be 11.8 W kg-1 for the activated carbon and 2.9 W kg-1 for the coal. More importantly, the fact that the plots are nonlinear means that for these substrates at least extrapolation from oven conditions to storage or transportation
J.C. Jones, S.C. Newman / Journal of Loss Prevention in the Process Industries 16 (2003) 223–225
225
ards. It is not possible to correlate the behaviour with the observable properties of the respective substrates since none of these can be demonstrated (or even postulated) to differ between the substrates which displayed Arrhenius behaviour and those which did not. Relevant properties include the nature and amounts of volatiles. The activated carbon, being chemically (rather than steam) activated, will have experienced only moderate processing temperatures and will therefore have retained some of the volatiles present in the parent material. 5. Concluding remarks
Fig. 1.
Plot of ln(q / W kg - 1) against 1 / T for the activated carbon.
Two carbonaceous materials have been shown to demonstrate, in the temperature range 311–338 K, a temperature dependence of reaction rate which does not conform to the Arrhenius equation. This adds an extra uncertainty to the application of tests for the propensity to self-heating of such materials since these always assume Arrhenius behaviour. Acknowledgements The authors thank J. MacDowall, chief chemist at Norit UK, Glasgow, for supply of the carbon sample and helpful advice, also Alex Noble, coal suppliers, Aberdeen, for donation of the sample of Chinese coal. The microcalorimeter was purchased by means of a grant from the University of Aberdeen Research Committee. References
Fig. 2.
Plot of ln(qW kg - 1) against 1 / T for the Chinese coal.
Table 1 Coefficients for use in eq. (2) Coefficient → Substrate ↓
a
Activated Carbon –4.1367 Chinese coal –50.319
b
+31.002 +427.52
c
d
–84.009 +82.845 –1214.4 +1151.2
conditions would not give a reliable prediction of haz-
Moore, W. J. (1970). Physical Chemistry. London: Longman. Bronk, J. R. (1973). Chemical Biology. Macmillan. Jones J. C. (2000a). New concepts and test procedures in the assessment of hazards due to spontaneous heating of transported combustible solids. Symposium for energy engineering in the 21st century vol. 3. New York: Begell House, pp. 1313-1320. Jones, J. C. (2000b). A new and more reliable test for propensity of coals and carbons to spontaneous heating. Journal of Loss Prevention in the Process Industries, 13, 69–71. Jones, J. C. (2000c). Commentary on the UN test for spontaneous heating of solid substances. Journal of Loss Prevention in the Process Industries, 13, 177–178. Jones, J. C. (1999). Towards an alternative criterion for the shipping safety of activated carbons Part 3. A case study. Journal of Loss Prevention in the Process Industries, 12, 331–332. Jones, J. C. (1998). Towards an alternative criterion for the shipping safety of activated carbons. Journal of Loss Prevention in the Process Industries, 11, 407–411. Jones, J. C., & Cook, B. (2000). Towards an alternative criterion for the shipping safety of activated carbons Part 5. Reproducibility checks. Journal of Loss Prevention in the Process Industries, 13, 175–176.
Short Communication
Non-Arrhenius behaviour in the oxidation of two carbonaceous substrates J.C. Jones ∗, S.C. Newman Department of Engineering, Fraser Noble Building, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland, UK
Abstract Two carbonaceous substances—a chemically activated carbon and a bituminous coal—are found, in microcalorimeter experiments, to display a temperature dependence of reaction rate at odds with the Arrhenius equation. Since Arrhenius behaviour is always assumed in tests for spontaneous heating of such substances, this places a question mark over the validity of such tests for at least some of the materials to which they might be routinely applied. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Carbon; Coal; Self-heating; Arrhenius parameters
1. Introduction The Arrhenius expression for the temperature dependence of the rate of a chemical reaction is as follows: k ⫽ Aexp(⫺E / RT). It has its origins in gas-phase kinetics (Moore, 1970), there being a connection (possibly a straightforward equality) between the pre-exponential factor and the molecular collision frequency. An equation of the same form has also found wide application to the oxidation of solid fuels. Usually here there is no mechanistic interpretation of A and E, simply an observed (or assumed) temperature dependence of rate that fits an equation of this form, with E having a value of the order of 102 kJ mol-1. Arrhenius behaviour is generally accepted as the norm across the entire range of chemical reactions, including biochemical ones (Bronk, 1973), whether or not there is a mechanistic basis for interpreting A and E. Accordingly, when non-Arrhenius behaviour is observed it is seen as a point of interest in itself. The present group have recently (e.g., Jones, 2000a,b,c) been closely examining currently widely used test procedures for assessing the propensity to spontaneous combustion of coals and carbons. A point of contention is that such
∗
Corresponding author. Tel.:+44-1224-272793; fax:+44-1224272497. E-mail address: [email protected] (J.C. Jones).
tests assume a single value for the activation energy E for all substances to which the tests might be applied, which is very difficult to justify. Improved procedures (Jones, 2000a,b) have been developed which address this, but even here the assumption is made that Arrhenius behaviour is expected therefore some value or other of the activation energy is applicable. If a coal or carbon does not obey Arrhenius kinetics this introduces a further dimension of uncertainty in the prediction of self-heating behaviour. The work by the present group has involved a good deal of microcalorimetry; coals and carbons have been examined at temperatures between just above room and about 360 K. Although the possibility of non-Arrhenius behaviour beyond the temperature range of the experiments had previously been discussed, and was indeed supported by limited indirect evidence (Jones, 1999), no direct evidence by way of nonlinear plots of log(rate) against 1/T, was observed. The reaction rate for a strong exothermic process can of course be expressed as a heat-release rate, viz.: q(T) ⫽ QAexp( ⫺ E / RT)
(1)
so that a plot of ln{q(T)} against 1/T is linear if the behaviour conforms to an Arrhenius temperature dependence of reaction rate. Many such plots displaying the expected linearity have been reported previously (Jones, 1998). In a continuation of this work (Newman, S.C. MEng thesis University of Aberdeen, in preparation) about 20 carbonaceous substrates were studied, two of which—an activated carbon and a bituminous coal—were found to display marked cur-
0950-4230/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0950-4230(02)00115-8
224
J.C. Jones, S.C. Newman / Journal of Loss Prevention in the Process Industries 16 (2003) 223–225
Nomenclature k A E R T q(T) Q
rate constant (unites s-1 if first order) pre-exponential factor (s-1) activation energy (J mol-1) Universal gas constant = 8.314 J K-1 mol-1 absolute temperature rate of heat release at temperature T(W kg-1) heat of combustion (J kg-1)
vature in their Arrhenius plots. Results from the substrates which did display Arrhenius behaviour—by far the majority—are of interest in identifying trends of self-heating propensity with factors including temperatures attained during processing (for carbons) and rank (for coals), and will be reported in due course. This paper is concerned solely with the non-Arrhenius behaviour.
2. Experimental The microcalorimeter used was a Thermometric 2277 Thermal Activity Monitor. A solid sample for testing was placed in a steel ampoule. The instrument had previously been stabilised at the desired temperature overnight. The ampoule containing the sample was then placed in the equilibration position. The reference ampoule, containing air only, was also placed in its equilibration position. Thermal equilibration of the samples took place over a one-hour period. The ampoules were then lowered into the measuring position and the signal followed at a potentiometric recorder connected to the instrument. The ampoules were left in the measuring position for about an hour, this being more than adequate for the signal to become steady. When the final heat release reading at the recorder was taken it was checked against that on the digital display on the microcalorimeter. Between each experiment, the ampoules were removed from the instrument and the ampoule containing the subject material was opened up to replenish its internal atmosphere. The instrument was recalibrated at each change of temperature setting, at least six hours having been allowed for stabilisation prior to calibration once the set temperature was reached. For each of the carbonaceous substances of interest heat-release rate measurements were made at five temperatures.
3. Materials The two substrates which displayed non-Arrhenius behaviour were: 1. A chemically activated carbon, manufactured by Norit UK and assigned by them the code CNR 115. The sample was supplied (along with several others)
by Norit UK, manufacturers. It was examined in the microcalorimeter at temperatures in the range 311– 338 K. 2. A Chinese bituminous coal. This had been obtained from a coal supplier in Aberdeen. It too was examined in the microcalorimeter at temperatures in the range 311–338 K. The plot of ln{q(T)} against 1 / T for the Chinese coal was obtained twice, that is, for two different samples of the coal each of mass 260 mg. The results obtained the first time were reproduced exactly the second time. The plot for the activated carbon was determined once only, with a 265 mg sample. However, the remarkably consistency of composition of these materials, reflected in reproducibility of heat release rates with very small samples, has already been observed and noted (Jones & Cook, 2000). It arises from stringent milling and blending techniques in manufacture.
4. Results Fig. 1 shows a plot of ln(q / W kg - 1) against 1 / T for the activated carbon and Fig. 2 the corresponding plot for the Chinese coal. In each case the non-linearity is clear therefore the description of the behaviour as being ‘non-Arrhenius’ is appropriate. The two plots of ln{q(T)} against 1 / T were fitted (using EXCEL) to polynomials of the form: y ⫽ ax3 ⫹ bx2 ⫹ cx ⫹ d
(2)
where y = ln{q(T)} and x = 103K / T. The coefficients a, b, c and d for the two substrates are given in Table 1 below. The standard test for spontaneous combustion propensity of coals and carbons previously referred to uses a set oven temperature of 140 °C. If the polynomials apply at this temperature, the heat-releases rates would be 11.8 W kg-1 for the activated carbon and 2.9 W kg-1 for the coal. More importantly, the fact that the plots are nonlinear means that for these substrates at least extrapolation from oven conditions to storage or transportation
J.C. Jones, S.C. Newman / Journal of Loss Prevention in the Process Industries 16 (2003) 223–225
225
ards. It is not possible to correlate the behaviour with the observable properties of the respective substrates since none of these can be demonstrated (or even postulated) to differ between the substrates which displayed Arrhenius behaviour and those which did not. Relevant properties include the nature and amounts of volatiles. The activated carbon, being chemically (rather than steam) activated, will have experienced only moderate processing temperatures and will therefore have retained some of the volatiles present in the parent material. 5. Concluding remarks
Fig. 1.
Plot of ln(q / W kg - 1) against 1 / T for the activated carbon.
Two carbonaceous materials have been shown to demonstrate, in the temperature range 311–338 K, a temperature dependence of reaction rate which does not conform to the Arrhenius equation. This adds an extra uncertainty to the application of tests for the propensity to self-heating of such materials since these always assume Arrhenius behaviour. Acknowledgements The authors thank J. MacDowall, chief chemist at Norit UK, Glasgow, for supply of the carbon sample and helpful advice, also Alex Noble, coal suppliers, Aberdeen, for donation of the sample of Chinese coal. The microcalorimeter was purchased by means of a grant from the University of Aberdeen Research Committee. References
Fig. 2.
Plot of ln(qW kg - 1) against 1 / T for the Chinese coal.
Table 1 Coefficients for use in eq. (2) Coefficient → Substrate ↓
a
Activated Carbon –4.1367 Chinese coal –50.319
b
+31.002 +427.52
c
d
–84.009 +82.845 –1214.4 +1151.2
conditions would not give a reliable prediction of haz-
Moore, W. J. (1970). Physical Chemistry. London: Longman. Bronk, J. R. (1973). Chemical Biology. Macmillan. Jones J. C. (2000a). New concepts and test procedures in the assessment of hazards due to spontaneous heating of transported combustible solids. Symposium for energy engineering in the 21st century vol. 3. New York: Begell House, pp. 1313-1320. Jones, J. C. (2000b). A new and more reliable test for propensity of coals and carbons to spontaneous heating. Journal of Loss Prevention in the Process Industries, 13, 69–71. Jones, J. C. (2000c). Commentary on the UN test for spontaneous heating of solid substances. Journal of Loss Prevention in the Process Industries, 13, 177–178. Jones, J. C. (1999). Towards an alternative criterion for the shipping safety of activated carbons Part 3. A case study. Journal of Loss Prevention in the Process Industries, 12, 331–332. Jones, J. C. (1998). Towards an alternative criterion for the shipping safety of activated carbons. Journal of Loss Prevention in the Process Industries, 11, 407–411. Jones, J. C., & Cook, B. (2000). Towards an alternative criterion for the shipping safety of activated carbons Part 5. Reproducibility checks. Journal of Loss Prevention in the Process Industries, 13, 175–176.