On the Kinetics of Thermal Decomposition of Solid Fuel
Abstract Generated abstract
This paper addresses the determination of kinetic parameters for the thermal decomposition of solid fuels under nonisothermal heating, where temperature dependent rate constants complicate direct integration of kinetic equations. It reviews limitations of existing derivatographic approaches based on DTA, DTG, or TG curves alone, and proposes a simpler graphical method using both DTG and TG curves to estimate the rate of volatile release and calculate effective rate constants. Applied to brown coal from the Itat deposit, the method indicates that volatile release up to the maximum rate is satisfactorily described by a first order equation, with an effective activation energy of about 9 kcal/mol.
Full Text
On the Kinetics of Thermal Decomposition of Solid Fuel
Ya. A. Belikhmaer, K. K. Stramkovskaya
(Presented by the scientific-methodological seminar of the Chemical-Technological Faculty)
Recently, the method of derivatography has found wide application for studying the process of thermal decomposition of solid fuels. The essence of the derivatographic method consists in the simultaneous recording, during heating, of the change in TG weight, the rate of change in DTG weight, and thermophysical properties (DTA thermal effects). With the aid of DTA curves, judging by the position and depth of exo- and endothermic effects, one can assess the differences in the character of the reactions of thermal destruction of solid fuels. Thermodynamic analysis in combination with DTA will evidently make it possible to give not only a qualitative but also a quantitative assessment of the thermal effects of the process of thermal destruction of the organic mass of solid fuels.
A change in temperature in the course of the reactions of thermal destruction of solid fuels leads to the fact that, in the differential equations describing the kinetics of the reactions, the rate constants prove to be variable quantities. If the change in temperature is specified by the experimenter, i.e., the temperature is a known function of time, then all the rate constants prove to be specified functions of time [1].
The differential equation in the general case has the form:
\[ \frac{dx}{d\tau}=K \cdot x^n, \tag{1} \]
where \(x\) is the concentration;
\(K\) is the rate constant;
\(n\) is the reaction order.
At a constant heating rate, instead of time in equation (1) one may introduce temperature as the variable, since in this case
\[ \frac{dT}{d\tau}=C, \]
where \(C\) is a constant [2]:
\[ \frac{dx}{dT}=\frac{K}{C}\cdot x^n. \tag{2} \]
The reaction rate constant can be written as a function of temperature with the aid of the Arrhenius equation. Then equation (2) is written as:
\[ \frac{dx}{dT}=\frac{a_0}{C}\cdot e^{-\frac{E}{RT}}\cdot x^n. \tag{2a} \]
Separating the variables, we obtain:
\[ \frac{dx}{x^n}=\frac{a_0}{C}\cdot e^{-\frac{E}{RT}}\cdot dT. \tag{3} \]
The dependence of the reaction-rate constant on time considerably complicates the integration of differential equation (3). In this connection, a graphical method for determining the kinetic parameters directly from the derivatogram appears much simpler.
N. T. Borchard and F. Daniels proposed a method for determining the kinetic characteristics of thermal decomposition reactions of inorganic substances from DTA curves [2]. However, this method is unacceptable for solid fuels, since for the latter it is difficult to determine the position of the zero line [3]. N. G. Dave used, for calculating the kinetic parameters of a reaction, the DTG curve [4]. The method is laborious, since it is associated with determining the area under the DTG curve. M. Weltner performed kinetic calculations only on the basis of TG curves, assuming first order for reactions of thermal destruction of coal [5].
Fig. 1. Derivatogram of Itat brown coal
Fig. 2. DTG and TG curves—derivatograms
We propose using DTG and TG curves for kinetic calculations. Let us consider the calculation method for a specific example. Figure 1 presents the derivatogram of brown coal from the Itat deposit. The DTG curve for the case of thermal destruction of coal describes the rate of release of volatile products
\[ \frac{dx}{d\tau}=K_{\mathrm{eff}}(x_0-x_\tau)^n, \tag{4} \]
where \(K_{\mathrm{eff}}\) is the effective rate constant for the release of volatile products,
\(x_0\) is the initial coal sample weight,
\(x_\tau\) is the decrease in weight over time \(\tau\),
\(n\) is the order of the process.
The numerical value of the rate of release of volatile products is determined as follows (Fig. 2). Through the maximum point on the DTG a straight line \(AC\) is drawn perpendicular to the zero line until it intersects
Fig. 3. Dependence of \(\lg K_{\mathrm{eff}}\) on \(1/T\) for the process of volatile release during thermal destruction of brown coal
the TG curve. At the inflection point \(C\), a tangent is drawn. The rate of release of volatile products is determined as the tangent of the angle of inclination of the tangent,
\[ V_m=\operatorname{tg}\alpha=\frac{\Delta G}{\Delta \tau}. \]
Since the rate of release of volatile products is proportional to the deviation of the DTG curve from the zero line, then
\[ V_m=L_m\cdot M, \]
where \(L_m\) is the deviation of the DTG curve from the zero line (mm),
\(M\) is the scale of the rate of release of volatile products.
Having determined the scale of the rate of volatile release, one can calculate the rate at any point of the DTG curve.
Substituting into equation (4) the value \(dx/d\tau\) found from DTG, and the values \(x_0, x_c\) found from TG, one can determine, for a given \(n\), the value \(K_{\mathrm{eff}}\). The effective activation energy is determined from the tangent of the angle of inclination of the straight-line dependence of \(\lg K_{\mathrm{eff}}\) on \(1/T\).
It is evident from Fig. 3 that, up to the maximum rate, the process of volatile-product release is satisfactorily described by a first-order equation. The effective activation energy is \(9\ \mathrm{kcal/mol}\).
Conclusions
A simple method is proposed for determining the kinetic parameters of thermal-decomposition reactions from the DTG and TG curves of the derivatogram.
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