On the Determination of Kinetic Parameters of Thermal Decomposition Processes of Solid Fuels from Derivatograms
Abstract Generated abstract
This paper addresses the determination of kinetic parameters for thermal decomposition of solid fuels using derivatographic data, with attention to simplifying calculations from DTA, DTG, and TG curves. Assuming that decomposition of solid combustible minerals can often be formally described as a first-order process, the authors derive a transformed expression for estimating activation energy from characteristic temperatures on the gas-evolution-rate curve, especially the onset temperature and the temperature of maximum evolution rate. Application of the proposed method to peat gives effective activation energies of about 33.5 to 46 kJ/mol, reported to be in good agreement with published values.
Full Text
Tomsk Order of the October Revolution and Order of the Red Banner of Labor
Polytechnic Institute named after S. M. Kirov
Vol. 259 1975
On the Determination of Kinetic Parameters of Thermal Decomposition Processes of Solid Fuels from Derivatograms
S. I. Smolyaninov, V. I. Lozbin
(Presented by the scientific-methodological seminar of KhTF)
Thanks to advances in experimental technique, considerable attention has recently been given to the study of the kinetic regularities of the processes of thermal decomposition of solid combustible minerals by the methods of thermography and thermogravimetry. A special effect is achieved by the use of derivatography, which combines the properties of the indicated methods [1].
A number of authors have proposed methods for calculating kinetic parameters from DTA, DTG, and TG curves [2–5]; however, these methods are either complicated for calculation or make it difficult to choose characteristic sections on the indicated curves.
On the basis of a number of studies [6–7], it may be assumed that in most cases the process of thermal decomposition of solid combustible minerals can formally be described by a first-order equation, represented in our case as
\[ (a-x)=ae^{-K\tau}, \tag{1} \]
where
\[ \begin{aligned} \tau &\text{— time;}\\ a &\text{— total yield of volatiles;}\\ x &\text{— yield of volatiles by time } \tau;\\ K &\text{— reaction-rate constant;} \end{aligned} \]
and the rate constant as a function of temperature:
\[ K=Be^{-\frac{E}{RT}}, \tag{2} \]
where
\[ \begin{aligned} B &\text{— frequency factor;}\\ E &\text{— activation energy;}\\ R &\text{— universal gas constant;}\\ T &\text{— absolute temperature.} \end{aligned} \]
The reaction rate will have the form:
\[ \frac{dx}{d\tau} = B\cdot e^{-\frac{E}{RT}}\cdot a\cdot e^{-B\tau e^{-\frac{E}{RT}}}. \tag{3} \]
Let us denote:
\[ \frac{dx}{d\tau}=W \text{— rate of decomposition;} \]
\[ -\frac{E}{R}=m; \]
\[ \frac{1}{T}=n; \]
$T_0$ — temperature at the onset of gas evolution, °K;
$b$ — rate of temperature rise, $\dfrac{\text{deg}}{\text{min}}$;
\[ T=T_0+b\tau,\quad \text{whence } \tau=\frac{T-T_0}{b}=\frac{1-nT_0}{bn}. \]
Differentiating equation (3) with respect to $n$ and setting the differential equal to zero, we obtain for the extremum of the function:
\[ \frac{mbn^2}{B}+e^{mn}\left(1-mn+mn^2T_0\right)=0, \tag{4} \]
where $\dfrac{mbn^2}{B}\ll 1$, i.e., this expression may be neglected without appreciable error;
$e^{mn}$ is expanded in a series:
\[ e^{mn}=1+\frac{mn}{1!}+\frac{m^2n^2}{2!}+\ldots; \]
taking the first two terms of the series, as a result we have the equation
\[ m^2(n^3T_0-n^2)+mn^2T_0+1=0, \tag{5} \]
\[ m_{1,2}=\frac{-nT_0\pm\sqrt{\,n^2T_0^2-4(nT_0-1)\,}}{2n(nT_0-1)}. \tag{6} \]
Substituting the values of $m$ and $n$, taking into account that $T=T_m$, i.e., the temperature of the maximum rate of gas evolution, we obtain
\[ \left(-\frac{E}{R}\right)_{1,2} = \frac{ -\dfrac{T_0}{T_m} \pm \sqrt{ \dfrac{T_0^2}{T_m^2} -4\left(\dfrac{T_0}{T_m}-1\right) } }{ \dfrac{2}{T_m}\left(\dfrac{T_0}{T_m}-1\right) }. \tag{7} \]
In the equation obtained, the denominator is a negative quantity. In order for the right-hand side to be a positive number, the condition must be satisfied
\[ \frac{ -\dfrac{T_0}{T_m} - \sqrt{ \dfrac{T_0^2}{T_m^2} -4\left(\dfrac{T_0}{T_m}-1\right) } }{ \dfrac{2}{T_m}\left(\dfrac{T_0}{T_m}-1\right) }, \]
since in the numerator one always has
\[ \left| \sqrt{ \dfrac{T_0^2}{T_m^2} -4\left(\dfrac{T_0}{T_m}-1\right) } \right| > \left| \dfrac{T_0}{T_m} \right|. \]
Thus, the final equation for determining the activation energy of first-order reactions has the form:
\[ E= \frac{ \dfrac{T_0}{T_m} + \sqrt{ \dfrac{T_0^2}{T_m^2} -4\left(\dfrac{T_0}{T_m}-1\right) } }{ \dfrac{2}{T_m}\left(\dfrac{T_0}{T_m}-1\right) }\cdot R. \tag{8} \]
The effective activation energies of the process of thermal decomposition of peat, determined by the proposed method, lie within the range $33.5$–$46\ \dfrac{\text{kJ}}{\text{mol}}$, which agrees well with literature data [7].
Conclusions
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A transformed first-order equation has been proposed for determining kinetic parameters.
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The characteristic temperatures for determining the activation energy are readily found from the gas-evolution-rate curve.
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The calculated effective activation energy of the thermal decomposition of peat agrees with the literature data.
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