Method for Determining the Total Heats of High-Temperature Gasification of Organic Fuels

N. N. Bakhval, V. I. Braginsky

(Presented at the scientific seminar of the Department of Radiation Chemistry)

The total heat of gasification \(Q\) (the amount of heat expended on heating and decomposition of a substance) is a very important characteristic of fuels used both in hybrid engines and in ordinary solid-fuel engines. However, at present there are no sufficiently convenient and reliable methods for determining it.

One of the methods for studying high-temperature decomposition is the thermographic method [1]. This method makes it possible, with comparatively slow heating of a substance, to determine the temperature of phase transitions, and also to estimate approximately the magnitudes of the corresponding thermal effects.

In contrast to the conditions of a thermographic experiment (quasi-isothermal decomposition, constancy of temperature throughout the entire volume of the substance), during combustion of a fuel in a hybrid engine, as well as during combustion of ordinary disordered heterogeneous mixtures, heating and gasification of the fuel proceed under substantially nonisothermal conditions. In this connection, one cannot unconditionally use data obtained by the thermographic method in determining the regularities of the high-temperature decomposition of fuels that occurs in hybrid and mixed systems [2].

In work [3], a method was developed for determining the total heats of gasification of fuels directly from high-temperature pyrolysis experiments using a block calorimeter. The method makes it possible to determine, with good accuracy, the values of the thermal effects of gasification of various fuels.

The disadvantages of the method include the difficulty of determining \(Q/\tau\) for heat-resistant polymers, since it is necessary to maintain a high block temperature so that the pyrolysis time is ...

considerably less time than the thermal relaxation of the block. Thus, to determine \(Q_{г}\) for polystyrene, the block temperature must be no lower than \(700^\circ\mathrm{C}\). If a condensed residue is formed during pyrolysis of the fuel, then application of this method for determining \(Q_{г}\) becomes difficult.

We have developed a simple method for determining the total heats of high-temperature gasification of fuels, based on combustion of small quantities of these substances in a thermite composition.

The method of introducing inert substances that lower the combustion temperature has been used to study combustion processes in a number of works \([4,5,6]\). In \([7]\), a certain dependence was found between the heat expenditures for gasification of an additive and the decrease in the burning rate of explosives when these additives are introduced into them. However, in such a system it is very difficult to isolate the influence of the quantity of heat absorbed by the additive on the burning rate, since the decomposition products of the additive may participate in the combustion process of the explosive. In addition, the combustion process of explosives itself is multistage, which complicates the picture still further.

It is known \([8]\) that, during combustion of a thermite composition, the main reaction proceeds in the condensed phase. It may be assumed that small quantities of fuels introduced into a thermite composition will behave as an inert additive, reducing the burning rate of the thermite by consuming heat for their gasification. The more heat the additive requires for its gasification, the greater will be the decrease in the burning rate of the thermite.

It is assumed that the additive acts only to lower the combustion temperature of the thermite, without changing either the activation energy \(E\) of the process or the constants of the thermite composition. This will be fulfilled only when the decomposition products of the additive do not react with the components of the main composition. Considering that the additive behaves as an inert substance, according to the theory of combustion \([9]\) the following relations can be introduced:

Let

\[ U = A e^{-E/2RT} \]

be the burning rate of the thermite composition with an organic additive, and

\[ U_0 = A e^{-E/2RT_0} \]

be the burning rate of the thermite composition without the additive. Here:

\[ A \]

is the pre-exponential factor,

\(E\) — activation energy,
\(R\) — universal gas constant,
\(T_r\) — combustion temperature of thermite with an additive,
\(T_0\) — combustion temperature of thermite without an additive.

Let us determine the ratio of the combustion rate of thermite with an additive to the combustion rate of thermite without an additive:

\[ \frac{u}{u_0} = e^{\frac{E}{2R}\left(\frac{1}{T_0}-\frac{1}{T_r}\right)} \tag{1} \]

Taking the logarithm of this expression,

\[ \ln \frac{u}{u_0} = \frac{E}{2R} \left( \frac{1}{T_0}-\frac{1}{T_r} \right) \tag{2} \]

The combustion temperature of the composition with an additive may be expressed as:

\[ T_r = T_0 - \frac{x}{1-x} \frac{Q_{\text{gas}}}{C_p} \tag{3} \]

where

\[ \frac{x}{1-x} \]

is the fraction of the additive in the thermite composition,

\(Q_{\text{gas}}\) — total heat of gasification of the additive,
\(C_p\) — specific heat capacity of the additive.

Determining \(T_r\) from equation (2) and substituting its value into equation (3), we obtain:

\[ T_0 - \frac{x}{1-x} \frac{Q_{\text{gas}}}{C_p} = \frac{1}{ \frac{1}{T_0} - \frac{2R}{E}\ln \frac{u}{u_0} } \tag{4} \]

Denoting \(\frac{u}{u_0}=Z\), after simple transformations we obtain the expression

\[ \frac{x}{1-x}Q_{\text{gas}} = \frac{ C_p T_0 \frac{2R}{E}\ln Z }{ \frac{2R}{E}\ln Z-\frac{1}{T_0} } \tag{5} \]

Hence we obtain the expression for \(\ln Z\):

\[ \ln Z = \frac{ \left(\frac{2R}{E}\ln Z-\frac{1}{T_0}\right) }{ C_p T_0 \frac{2R}{E} } \cdot \frac{x}{1-x}Q_{\text{gas}} \tag{6} \]

The method proposed by us is based on comparing the value of the thermite combustion rate upon introducing into it a substance with a known heat of gasification with the decrease in the thermite rate when introducing into it a substance with unknown thermal effects. Then, for the reference substance, according to equation (6), we have:

\[ \ln Z_{\mathrm{et}} = \frac{\dfrac{2R}{E}\ln Z_{\mathrm{et}}-\dfrac{1}{T_{r0}}} {C_p T_{r0}\dfrac{2R}{E}} \cdot \frac{x_{\mathrm{et}}}{1-x_{\mathrm{et}}}\,Q_{r,\mathrm{et}} . \tag{7} \]

Dividing equation (6) by equation (7), with the specific heat capacity \(C_p\) transformed, we obtain

\[ \frac{\ln Z}{\ln Z_{\mathrm{et}}} = \frac{\dfrac{2R}{E}\ln Z-\dfrac{1}{T_{r0}}} {\dfrac{2R}{E}\ln Z_{\mathrm{et}}-\dfrac{1}{T_{r0}}} \cdot \frac{\dfrac{x}{1-x}\,Q_r} {\dfrac{x_{\mathrm{et}}}{1-x_{\mathrm{et}}}\,Q_{r,\mathrm{et}}}. \]

Now one can obtain an expression for determining the desired heat of gasification:

\[ Q = \frac{x_{\mathrm{et}}(1-x)}{(1-x_{\mathrm{et}})x} \cdot Q_{r,\mathrm{et}}\, \frac{\ln Z}{\ln Z_{\mathrm{et}}} \cdot \frac{\dfrac{2R}{E}\ln Z_{\mathrm{et}}-\dfrac{1}{T_{r0}}} {\dfrac{2R}{E}\ln Z-\dfrac{1}{T_{r0}}}. \tag{8} \]

Expression (8) can be simplified by applying considerations regarding the temperature coefficient of the burning rate \(\beta\). According to [10], one may write:

\[ \beta = \frac{E}{2RT_0^2}. \]

Whence

\[ \frac{2R}{E}=\frac{1}{\beta_0 T_0^2}. \tag{9} \]

Substituting expression (9) into (8), we obtain

\[ Q_r = \frac{x_{\mathrm{et}}(1-x)}{(1-x_{\mathrm{et}})x}\, Q_{r,\mathrm{et}}\, \frac{\ln Z}{\ln Z_{\mathrm{et}}} \cdot \frac{-\ln Z_{\mathrm{et}}+\beta_0 T_0} {-\ln Z+\beta_0 T_{r0}}. \tag{10} \]

For real substances \(\ln Z\) varies within narrow limits \([2.3-0.5]\). For thermites, according to [8], \(\beta T_0 \approx 15\). Consequently,

\[ \frac{\beta_0 T_0-\ln Z_{\mathrm{et}}}{\beta_0 T_0-\ln Z}\approx 1. \]

Then we finally obtain:

\[ Q_r \approx \frac{x_{\mathrm{et}}(1-x)}{(1-x_{\mathrm{et}})x}\, Q_{r,\mathrm{et}}\, \frac{\ln Z}{\ln Z_{\mathrm{et}}}. \tag{11} \]

Or, when identical amounts of additions of the reference and the substance under investigation are used, we have:

\[ Q_{\text{gas}}=Q_{\text{gas, ref}}\cdot \frac{C_n \tau}{C_{n\text{ ref}}\tau_{\text{ref}}} \tag{12} \]

EXPERIMENTAL RESULTS

The main experiments were carried out on iron–aluminum thermite with different ratios between \(Fe_2O_3\) and \(Al\). Commercial grades of PP-4 aluminum powder and ChDA-grade \(Fe_2O_3\) were used. The composition was prepared by thorough mixing of the components on rolls with a rubber plug. Additions of organic combustible substances were introduced in amounts of 5–11% by weight above 100%. The prepared sample mixture was pressed into brass cups 10 mm in diameter. The specific pressing pressure was 1500 kg/cm\(^2\).

The samples were burned in a constant-pressure bomb, in an atmosphere of nitrogen at a pressure of 1 atm. The burning rate was measured using a sensitive piezoelectric pressure transducer and a loop oscillograph.

Polymethyl methacrylate (PMMA) was taken as the reference substance; its heat of gasification, according to [3], is 380 cal/g. In carrying out the experiments it was established that \(Q_{\text{gas}}\) does not depend on the ratio between \(Al\) and \(Fe_2O_3\) in the initial thermite. Thus, the value of the heat of gasification does not change when the \(Fe_2O_3\) content in the thermite is varied from 50% to 70%.

The largest number of experiments was carried out with the composition \(Fe_2O_3\)—60% and \(Al\)—40%, since with this ratio the maximum percentage of PMMA additive could be introduced. Thus, with 50% \(Fe_2O_3\), the thermite composition ceases to burn already upon introduction of 8% PMMA, whereas with 60% \(Fe_2O_3\) in the thermite composition it continues to burn steadily upon introduction of 11% PMMA.

It was established that, with an error of 10–15%, \(Q_{\text{gas}}\) does not depend on the percentage of additive in the thermite (Table I).

Table I

For some substances, the total heat expenditures for gasification were determined by burning them in an iron-magnesium thermite of composition \(Mg\ 30\% + Fe_2O_3\ 70\%\). Additives were introduced in an amount of 5% by weight in excess of 100%. The data are given in Table 3.

Table 3

It follows from Table 3 that \(Q_{\mathrm{gas}}\), with an error of 10%, does not depend on the composition of the thermite.

To check the proposed method, the total heat of gasification was additionally determined for all substances using a block calorimeter according to the procedure in [3]. These experiments were carried out jointly with V. B. Ulybina. The values of \(Q_{\mathrm{gas}}\) obtained by the thermite method and the block-calorimeter method are given in Table 4.

Table 4

Conclusions

1. A method is proposed for determining the total heats of high-temperature gasification of organic fuels.

2. Satisfactory agreement has been obtained between the data obtained and the results of measurements of the heat of gasification using a bomb calorimeter.

Literature

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3. B. N. Dmitriev, O. A. Kochetov, V. B. Ul’bin, A. S. Shteinberg, Fizika goreniya i vzryva, 1969, 5, I.

4. K. K. Andreev, in: Theory of Explosives. Moscow: Oborongiz, 1963, p. 419.

5. K. K. Andreev, Thermal Decomposition and Combustion of Explosives. Moscow: Nauka, 1966.

6. P. Gray, J. C. Lee, D. C. Taylor. 6th Symposium on Combustion, No. 4, 1957, 258.

7. V. J. Annikov, B. N. Kondrikov, N. A. Polyakova, Fizika goreniya i vzryva, 1969, 5, I.

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9. Ya. B. Zel’dovich, ZhETF, 1942, 12, II–12.

10. A. F. Belyaev, G. V. Lukashin, DAN, 148, 6, 1963.