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INTRODUCTION

The study of thermogravimetric curves is commonly used to elucidate the likely processes

involved during pyrolysis, as well as to determine the corresponding kinetic parameters. One of

the main problems found in the determination of such parameters is their ability to couple each

other in such way that different sets of kinetic parameters can properly describe similar

conversion degree curves once a kinetic model has been selected. In order to diminish the effect

of the interrelation between kinetic parameters, procedures based on the utilisation on different

heating rates are suggested.

This topic has been treated extensively in bibliography, where most of the authors specially pay

attention to the compensation effect between activation energy and preexponential factor [1-4],

while there is another factor to have in mind: the reaction order. When speaking about kinetic

parameters interrelation, the compensation effect of the whole kinetic triplet should be

considered: activation energy, preexponential factor and conversion degree function considered

(given by a certain kinetic model). Depending of the values adopted by the kinetic triplet, a

different fit quality can be observed. Thus, the actual compensation effect between kinetic

parameters should be represented in four dimensional charts; for example, if the reaction order

model was considered, the four dimensional charts should represent any variable which couldrepresent the quality of the fit (as a variation coefficient) versus the activation energy-

preexponential fac tor-reaction order. Due to the impossibility of the construction of 4D graphs,

3D charts can be used alternatively. In this case, three different alternative 3D charts can be used,

since they can represent the variation coefficient versus two of the kinetic parameters (keeping

the third as a constant). Those zones of the 3D charts with the lowest variation coefficient should

correspond to the set of kinetic parameters which compensate each other in order to represent a

certain conversion degree curve.

In the present work, the interrelation between the kinetic triplet has been studied, considering the

reaction order model.

ACKNOWLEDGEMENTS

The authors of the work wish to thank financial support provided by the Spanish Comisin de

Investigacin Cientfica y Tecnolgica de la Secretara de Estado de Educacin, Universidades,

Investigacin y Desarrollo and the European Community (FEDER refunds) (CICYT CTQ2004-

02187) and by the Generalitat Valenciana (project GRUPOS03/159).

REFERENCES

1. N. Liu, R. Zong, L. Shu, J. Zhou, W. Fan. Kinetic Compensation Effect in Thermal

Decomposition of Cellulosic Materials in Air Atmosphere,

2. J. G. Rocha Poc H. Furlan and R. Giudici. A Discussion on Kinetic Compensation Effect and

Anisotropy,J. Phys. Chem. B 2002, 106, 4873-4877.

3. Andrew K. Galwey. Perennial problems and promising prospects in the kinetic analysis of

nonisothermal rate data, Thermochimica Acta, 407, (2003) 93103.

4. M. E. Brown, A. K. Galwey. The significance of compensationeffects appearing in

data published in Computational aspects of kinetic analysis: ICTAC project, 2000,

Thermochimica Acta 387 (2002) 173183.

ABOUT THE INTERRELATION BETWEEN KINETIC

PARAMETERSA.Marcilla*, J.C. Garca-Quesada and R. Ruiz.

Chemical Engineering DepartmentUniversity of Alicante. Apdo. 99, E-03080 Alicante, Spain. Tlf.:

+34 965 90 34 00 - Ext. 3003, Fax: +34 965 90 38 26, *E-mail: antonio.marcilla@ua.es

RESULTS

Different reference conversion have been generated at different heating rates using the reaction

order model and the same set of kinetic parameters: preexponential factor(ln A =), activation

energy (Ea/R=) and reaction order (n=1). Afterwards, new sets of curves were generated by using

different sets of kinetic parameters. Reference curves and generated curves were compared by

calculating a variation coefficient:

Depending on the parameter kept as constant, a different type of graph can be obtained. The 3D

graphs show surfaces with a valley. That zones with the lowest V.C. in the valley constitutes

a path in the surface, reflecting the the compensation effect between kinetic parameters, since it

corresponds to the zone where a set of kinetic parameters better reproduce the reference curve.

Although these surfaces seem to have a track of minimum

variation coefficient, they actually have a minimum which

correspond to the right set of kinetic parameters. It is shown as

an example in Figure 4 for the Type I of 3D charts.

INFLUENCE OF THE NUMBER OF HEATING

RATES USED

As commented above, multi heating rates analysys are usually suggested in order to reduce

parameters interactions between kinetic parameters. However, the question that arises concerns

about the number of different heating rates to use in kinetic analysis. In the present study the

different cases have been analysis, considering different heating rates between 0.5-40C/min. The

influence of the number of heating rates in the shape of the surfaces VC-Ea-lnA has been studied.

THE COMPENSATION EFFECT

Compensation effect between kinetic parameters can also be contemplated by analysis the shape

of the valley obtained in the 3D surfaces. Although activation energy and constant rate show

the more marked dependence, as already reported in bibliography [1-4], also a compensation

effect can be observed between these variables and the reaction order, as possible to observe in

Figure 5.

It is also worth metionning that the width of the valley also

represent the sensitibity of the fit quality with the kinetic

parameters considered. This sensitibity is associated to the

uncertainty in the determination of a certain kinetic parameters.

The narrowest valley, the lower uncertainty in the

determination of the kinetic parameters. Thus, according to

Figures 1-3, the fit quality is very sensible to activation energy

and in minor degree to preexponential factor and reaction

order.

Although these surfaces seem to have a track of minimum

variation coefficient track, where the variation coefficient is

apparently constant, they are actually paraboloids with a

minimum, which correspond to the right set of kinetic

parameters. It is shown as an example in Figure 4 for the Type

I of 3D charts.

2

2

2mod1mod

..

NCV

i

elieli

Type II. Preexponential factor constant

Figure 2

Type I. Reaction order constant

Figure 1

Type III. Activation energy constant

Figure 3

0.00

0.01

0.02

0.03

0.04

0.05

5.7 5.8 5.9 6.0 6.1 6.2 6.3

0.96

0.98

1.00

1.02

1.04V.C.

lnA(s-1)

n

0.000.01

0.02

0.03

0.04

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.96

0.98

1.00

1.02

1.04

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

Ea/R(K-1

)

0.00

0.02

0.04

0.06

0.08

0.10

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5.7

5.8

5.9

6.0

6.1

6.2

6.3

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

Ea/R(K-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Type III. Activation energy constant

Figure 4

V.C. contour profiles: Compensation effect between kinetic parameters

Figure 5

lnA(s-1)

5.7 5.8 5.9 6.0 6.1 6.2 6.3

Ea/R

(K-1)

6900

7000

7100

7200

7300

7400

7500

7600

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

lnA (s-1)

0.96 0.98 1.00 1.02 1.04

n

5.7

5.8

5.9

6.0

6.1

6.2

6.3

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

n

0.96 0.98 1.00 1.02 1.04

Ea/R

(K-1)

6900

7000

7100

7200

7300

7400

7500

7600

0.00

0.02

0.04

0.06

0.08

0.10

As expected the width of the valley, is markedly reduced when increasing the number of heating

rates to be considered, but even for 10 different heating rates, the surface obtained still shows a quite

wide valley. It indicates that compensation effect and interaction between kinetic parameters still

may exist when using multi-heating rate analysis.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5.7

5.8

5.9

6.0

6.1

6.2

6.3

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

Ea/R(K-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5.7

5.8

5.9

6.0

6.1

6.2

6.3

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

Ea/R(K-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

5.7

5.8

5.9

6.0

6.1

6.2

6.3

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

Ea/R(K-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5.7

5.8

5.9

6.0

6.1

6.2

6.3

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

Ea/R(K-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.160.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5.7

5.8

5.9

6.0

6.1

6.2

6.3

69007000

71007200

73007400

75007600

V.C.

lnA

(s-1)

E/R(K-1)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.140.16

1 heating rate

Figure 6

2 heating rates 4 heating rates

6 heating rates 10 heating rates