On the Effect of the Use of Pneumatic Mechanisms in a Mine on the Temperature of Mine Air

B. M. Titov

The technical operating rules in force in the USSR stipulate that the temperature of mine air in stoping and development workings must not exceed 25°C; therefore, in connection with the transition of operations in some mines of the Donbass (and in the future also in mines of the Kuzbass) to depths of up to 1000 m and more, the question of combating high temperatures in mines is becoming extremely urgent.

Along with other factors, the energy used in the mine has an influence on the temperature of mine air. For example, it is customary to consider that the use of electrical energy causes heating of the mine air, while pneumatic energy causes cooling; however, reliable numerical values of this heating are, as a rule, not given in the literature.

Considering the operation of a mine pneumatic installation as analogous to the operation of an air-compressor refrigerating unit operating with continuous renewal of the working medium, one may expect that the use of pneumatic energy in a mine will lead to appreciable cooling of the mine air.

To determine the cooling effect of pneumatic energy, we propose using an entropy diagram and carrying out the calculations as follows.

Let us assume that the compressed air at the point where the pipeline enters the mine shaft has a pressure \(P_1 = 6.0\) atm, a temperature \(t_1 = 80^\circ\mathrm{C}\), and that the pressure drop in the pipeline from the compressor to the consumers is equal to 1.5 atm.

For the parameters of the mine (ventilation) air at the place where the pneumatic mechanisms operate, let us take \(P_{\mathrm{m}} = 1.1\) ata, \(t_{\mathrm{m}} = 24^\circ\mathrm{C}\), \(\varphi_{\mathrm{m}} = 85\%\).

Assuming that during the movement of the air through the pipeline its temperature decreases to the ambient temperature \(t_{\mathrm{m}} = 24^\circ\mathrm{C}\) at constant pressure [1,424], let us determine the amount of heat transferred to the mine air:

\[ Q_1 = c_p(T_1 - T_{\mathrm{m}}) = 0.24(353 - 297) = 13.5 \ \frac{\mathrm{kcal}}{\mathrm{kg}}. \]

Moving through the pipeline, the air stream overcomes its resistance, and as a result the air pressure drops (Fig. 1) from \(p_1\) to \(p_2\). If the air expanded adiabatically from pressure \(p_1\) to \(p_2\), then its temperature would decrease to the value \(T_{2ad}\), and subsequently, through its heating by the surroundings, the following amount of heat would be removed:

\[ Q_0 = c_p(T_{\mathrm{m}} - T_{2ad}). \]

In reality the situation is different [2,361]. The air, expanding from pressure \(p_1\) to \(p_2\), performs work, which is expended on 1) overcoming...

overcoming resistances in the pipeline and acceleration of the air stream as a result of the increase in the specific volume of the air.

The work of overcoming resistances in the pipeline, like the work of friction of solid bodies, is converted into heat and heats the compressed air (Fig. 1) to the temperature \(T_2\)

\[ Q_{tr}=c_p\left(T_2-T_{2ad}\right). \]

When heated, the specific volume of the air increases from \(v_{2ad}\) to \(v_2\), and it performs additional work, which goes to overcoming resistances in the pipeline and is equivalent to the quantity of heat \(Q_2\) (Fig. 1).

Fig. 1. Entropy diagram of the change of state of compressed air during its delivery through a pipeline and expansion in consumers of pneumatic energy.

\(1\)—\(2\) — process of cooling the air in the pipeline; \(2\)—\(3\) — process of pressure drop of the air owing to frictional resistances and constrictions in the pipeline; \(3\)—\(4\) — process of expansion of the air in consumers of pneumatic energy; \(4\)—\(5\) — process of heating the expanded air owing to the conversion of useful mechanical work into heat; \(5\)—\(6\) — process of heating the expanded air by heat taken from the surrounding medium.

The work expended on increasing the velocity of motion of the air stream from \(w_1\) to \(w_2\) is equivalent (Fig. 1) to the quantity of heat

\[ Q_w=A\,\frac{w_2^2-w_1^2}{2g}. \]

and, as calculations show, in mine pneumatic networks does not exceed \(0.001 \dfrac{\mathrm{kcal}}{\mathrm{kg}}\).

Thus, when the pressure in the pipeline drops from \(p_1\) to \(p_2\), the amount of heat \((Q_w-Q_z)\) is taken from the mine air, but within the limits of accuracy of our calculation it may be disregarded and it may be assumed that the air temperature in the pipeline remains constant and equal to the ambient temperature \(T_m\).

During air transport, about 20% of it [1,409] leaks through the imperfect tightness of the pipeline. The process of air leakage through leaks is analogous to the process of gas throttling, for which, as is known [2,253], the following expression is valid:

\[ i_1-i_2=A\left(\frac{w_2^2}{2g}-\frac{w_1^2}{2g}\right), \]

where \(i_1, i_2\) are the heat content of the gas before and after throttling, \(\dfrac{\mathrm{kcal}}{\mathrm{kg}}\);

\(w_1, w_2\) are the velocities of motion of the gas stream before and after throttling, \(\mathrm{m/sec}\).

In our case, the velocity of motion of the air stream in the direction of leakage before and after the gap in the pipeline is zero; therefore:

\[ i_1=i_2. \]

In the region in which gases obey the law

\[ p\cdot v=RT \]

the same heat content corresponds to the same temperature. Consequently, no absorption of heat from the environment or release of it occurs during leaks of compressed air.

The portion of the air that has reached the consumers of pneumatic energy with pressure \(p_2\) expands in them and performs useful work, for example: drilling, breaking, moving the mineral, supplying ventilation air, etc. If the process of air expansion in pneumatic mechanisms proceeded adiabatically, without heating due to internal energy losses to friction, turbulence, and leakage, then the air temperature at the end of expansion would be

\[ T_{\mathrm{ad}}=T_m\left(\frac{p_m}{p_2}\right)^{\frac{k-1}{k}} =297\left(\frac{1.1}{5.5}\right)^{0.286}=186^\circ\mathrm{K}. \]

In reality, owing to throttling, partial air leakage through leaks in the consumers of pneumatic energy, and heat conductivity of the housing walls, the air temperature at the end of expansion will not be \(T_{\mathrm{ad}}\), but \(T_z\). These internal energy losses neither heat nor cool the mine air.

The magnitude of the internal energy losses is customarily taken into account by the adiabatic power coefficient, which in the best case does not exceed the value \(\eta_{\mathrm{ad}}=0.5\).

Consequently, the amount of heat equivalent to the mechanical work performed is equal to

\[ Q_{\mathrm{mech}}=(1-K_{\mathrm{leak}})\,\eta_{\mathrm{ad}}\,c_p\,(T_m-T_{\mathrm{ad}}) \]

\[ =(1-0.2)\cdot0.5\cdot0.24\cdot(297-186)=10.6\ \frac{\mathrm{kcal}}{\mathrm{kg}}, \]

where \(K_{\mathrm{leak}}\) is the coefficient taking into account air leakage from the pneumatic network.

One part of this work, used to overcome friction in the mechanisms, to deliver ventilation air, and to move loads in the horizontal direction, is completely converted into heat \(Q_m\) and heats the air cooled during expansion (Fig. 1) to the temperature \(T_i\); the other part of the work, used to move the load vertically and to break intermolecular bonds, is not converted into heat. The ratio between these parts of the work in each individual case will be different and is not yet reliably known, but it may nevertheless be asserted that, in the main, the work performed by compressed air is converted into heat. As an approximation we shall take the part of the mechanical work converted into heat as equal to 80%.

Thus, for heating the air that has expanded in pneumatic mechanisms to the temperature \(T_i\), the following quantity of heat is taken from the surroundings:

\[ Q_z=(1-K_{\text{mech}})Q_{\text{mech}}=(1-0.8)\cdot 10.6=2.1\ \frac{\text{kcal}}{\text{kg}}, \]

where \(K_{\text{mech}}\) is a coefficient accounting for what part of the mechanical work is converted into heat.

Moistening after expansion has a considerably greater effect on the cooling of mine air.

During compression in the compressor and subsequent cooling, the relative humidity of the compressed air increases, while the absolute humidity decreases owing to the precipitation of moisture in the intermediate and aftercoolers, the air receiver, and the pneumatic network.

After expansion and heating of the air to the temperature of the surroundings, its relative humidity, owing to the increase in volume, decreases sharply, and then, through evaporation of the moisture present in the mine workings, becomes equal to the humidity of the mine air. The latent heat of vaporization is expended on evaporation of the moisture; this heat is taken from the surroundings and thereby lowers the temperature of the mine air.

Let us determine how much heat is absorbed as a result of humidifying the expanded compressed air when an aftercooler is installed after the compressor and when it is not.

If no aftercooler is installed after the compressor, it may be assumed that the compressed air enters the mine at a relative humidity \(\varphi_1=20\%\) \((t_1=80^\circ\text{C}\) and \(p_1=7\ \text{ata})\), and its absolute humidity is equal to [1,14]

\[ \gamma'_s=\varphi_1\cdot \gamma_s=0.2\cdot 0.293=0.059\ \text{kg}/\text{m}^3. \]

On cooling to the temperature \(T_{\!sh}\) and expanding to the pressure \(P_{\!sh}\), owing to the increase in volume, the absolute humidity of the air will be

\[ \gamma'_{\text{vl}}=\gamma'_s\,\frac{p_{\!sh}\cdot T_1}{p_1\cdot T_{\!sh}} =0.059\,\frac{1.1\cdot 353}{7\cdot 297} =0.011\ \text{kg}/\text{m}^3. \]

The absolute humidity of the mine air at \(\varphi_{\!sh}=85\%\) and \(t_{\!sh}=24^\circ\text{C}\) is

\[ \gamma''_{\text{v.p}}=\varphi_{\!sh}\cdot \gamma''_s =0.85\cdot 0.0218=0.0185\ \text{kg}/\text{m}^3, \]

therefore, in order to additionally humidify the expanded air, part of the moisture must evaporate from the surroundings and thereby cool them.

mine air, having absorbed the latent heat of vapor formation. Taking, according to \(p_{\mathrm{sh}}\) and \(T_{\mathrm{sh}}\), the specific weight of the air in the mine \(\gamma_{\mathrm{sh}}=1.26\ \mathrm{kg}/\mathrm{m}^3\), we obtain

\[ Q_3'=\frac{(\gamma'_{\mathrm{v.n}}-\gamma'_{\mathrm{v.p}})r}{\gamma_{\mathrm{sh}}} =\frac{(0.011-0.0185)\cdot 586}{1.26} =-3.5\ \frac{\mathrm{kcal}}{\mathrm{kg}}, \]

where \(r\) is the latent heat of vapor formation, \(\frac{\mathrm{kcal}}{\mathrm{kg}}\).

The release of heat from the cooling of the condensate by \((T_1-T_{\mathrm{sh}})\) degrees may be neglected within the accuracy of the calculation.

If, after the compressor, an aftercooler is installed and the compressed air is supplied to the mine at \(\varphi_1=100\%\), \(t_1=t_{\mathrm{sh}}=24^\circ\mathrm{C}\) and \(p_1=7\ \mathrm{ata}\), then its absolute humidity in the compressed state will be \([1,14]\):

\[ \gamma_s'=0.0218\ \mathrm{kg}/\mathrm{m}^3. \]

When the air expands from pressure \(p_1\) to \(p_{\mathrm{sh}}\) and is subsequently heated to the ambient temperature \(T_{\mathrm{sh}}\), its absolute humidity is equal to

\[ \gamma'_{\mathrm{v.p}}=\gamma_s'\frac{p_{\mathrm{sh}}}{p_1} =0.0218\frac{1.1}{7.0} =0.00343\ \mathrm{kg}/\mathrm{m}^3. \]

The absolute humidity of the mine air under the adopted conditions, as we have already calculated, is equal to

\[ \gamma''_{\mathrm{v.p}}=0.0185\ \mathrm{kg}/\mathrm{m}^3. \]

Consequently, in order to humidify the expanded air, part of the moisture will be evaporated from the surrounding medium and thereby the following amount of heat is taken from the mine air:

\[ Q_3''=\frac{(\gamma'_{\mathrm{v.p}}-\gamma''_{\mathrm{v.p}})\cdot r}{\gamma_{\mathrm{sh}}} =\frac{(0.00343-0.0185)\cdot 586}{1.26} =-7.0\ \frac{\mathrm{kcal}}{\mathrm{kg}}. \]

Thus, each kilogram of compressed air supplied to the mine at a pressure of \(6\ \mathrm{ata}\), after doing work in pneumatic mechanisms, transfers to the mine air at a temperature of \(24^\circ\mathrm{C}\) the following amount of heat:

a) without installing an aftercooler,

\[ \Delta Q'=Q_1+Q_2+Q_3'=13.5-2.1-3.5=+7.9\ \frac{\mathrm{kcal}}{\mathrm{kg}}; \]

b) with an aftercooler installed,

\[ \Delta Q''=Q_2+Q_3''=-2.1-7.0=-9.1\ \frac{\mathrm{kcal}}{\mathrm{kg}}. \]

Consequently, cooling of the mine air by using pneumatic energy is possible only when an aftercooler is installed after the compressor. If the air in the pipeline has time to cool to the ambient temperature, then the amount of heat absorbed by the compressed air directly at the place where the pneumatic energy is consumed does not depend on the installation of an aftercooler and is equal to

\[ \Delta Q_{\mathrm{zad}}=Q_2+Q_3''=-2.1-7.0=-9.1\ \frac{\mathrm{kcal}}{\mathrm{kg}}, \]

i.e., a person located directly near the pneumatic mechanisms will observe the cooling effect of pneumatic energy.

Let us recalculate the heating effect of compressed air (if no aftercooler is installed after the compressor) per 1 kWh of useful expended energy, taking [1, 409] that an energy expenditure of 1 kWh corresponds to a consumption of compressed air in the free state

\(V = 97.5\ \text{m}^3\);

\[ \Delta Q_{pn}=\Delta Q' \cdot V \cdot \gamma=7.9\cdot 97.5\cdot 1.2=930\ \frac{\text{kcal}}{\text{kWh}}. \]

Let us determine, for comparison, the quantity of heat transferred to the mine air when electric power is used in the mine.

The overall efficiency of the electrical installation is

\[ \eta=\eta_{tr}\cdot \eta_c\cdot \eta_{av}=0.96\cdot 0.95\cdot 0.85=0.77, \]

where \(\eta_{tr}\) is the efficiency of the transformer;
\(\eta_c\) is the efficiency of the mine network;
\(\eta_{av}\) is the average efficiency of electric motors.

Consequently, the heat liberation when electric power is used in the mine, taking into account the conversion of 80% of the mechanical work obtained into heat, will be:

\[ \Delta Q_{el}=102\cdot 3600\, A\left[\left(\frac{N}{\eta}-N\right)+K_{mech}\cdot N\right]= \]

\[ =\frac{102\cdot 3600}{427}\left[\left(\frac{1.0}{0.77}-1\right)+0.8\cdot 1.0\right]=950\ \frac{\text{kcal}}{\text{kWh}}. \]

Thus, if no aftercooler is installed after the compressor, pneumatic energy heats the mine air in the same way as electric power.

Conclusions

1. Cooling of the mine air when pneumatic energy is used occurs only if an aftercooler is installed between the compressor and the air receiver.

2. When compressed air is cooled in the pipeline to the ambient temperature, the liberation of cold at the places where consumers of pneumatic energy operate does not depend on the installation of aftercoolers after the compressor and is equal to about 9 kcal per kilogram of spent compressor air.

3. To increase the cooling effect of pneumatic energy, the compressed air must be cooled and dried on the surface by passing it through aftercoolers.

4. If no aftercooler is installed after the compressor, then pneumatic energy heats the mine air no less than electric power.

5. Aftercoolers must not only eliminate heating of the mine air, but also reduce the pressure loss in the pipeline, which, as is known, is directly proportional to the square of the air velocity.

6. Each kilogram of compressed air supplied to the mine at a pressure of 6 atm and with an aftercooler installed after the compressor absorbs, on average, about 9 kcal of heat, while during compressor operation without an aftercooler it liberates, on average, 8 kcal of heat.

LITERATURE

1. Il’ichev A. S. Mine Pneumatic Installations. Ugletekhizdat, 1953.
2. Shyule V. Technical Thermodynamics. Vol. 1, Book 1. ONTI, NKTP USSR, 1935.