On the Problem of Determining the Distance Between Ventilation Boreholes When Driving Horizontal Workings on the Basis of the Economic Factor

P. V. Akimochkin

(Presented by Prof., Doctor of Technical Sciences I. A. Balashov)

The search for internal reserves of an enterprise proceeds along the path of increasing labor productivity, saving materials and electric power, and making full use of machines and mechanisms. During the driving of preparatory workings, as the face advances, the length of the ventilation pipes and cables changes, as does the haulage distance. A local ventilation fan is installed in the fresh-air current and remains there throughout the entire period of driving the working. It is known that as the length of a pipeline increases, its resistance increases, leakage grows, and consequently the required power of the fan installation increases.

In considering the schemes for driving main haulage workings in newly constructed mines of the Kuzbass, it may be noted that, in order to shorten construction periods and create the necessary working front, the driving of the main haulage working is intensified first of all; the length of this working sometimes reaches up to 2000 m. Ventilating a blind working of such length creates great difficulties.

The local ventilation fans currently available, of the “Prokhodka” type, provide reliable and effective ventilation by a single fan for a working 300–500 m long. For ventilating longer workings, a cascade connection of several fan installations is used.

In order to reduce the consumption of electric power for ventilation, it is necessary to reduce the resistance of the pipelines through which air is supplied. This can be achieved by channeling the air not through pipes, but through the entire cross-section of the working, using the general mine depression.

When ventilating long blind workings, we distinguish two schemes:

a) ventilation with installation of the fan at the beginning of the working being driven, for the entire period of its driving;

b) ventilation with transfer of the fan to a borehole drilled as the working advances.

Let us carry out an economic comparison of these two schemes in terms of the costs of ventilation and of driving a ventilation borehole.

In calculations of local ventilation installations, the required quantity of air is determined: a) by the number of people simultaneously working at the face; b) by the greatest consumption of explosives; c) by methane emission.

According to the greatest of these, a fan is selected, which is interlocked with the face mechanisms and operates around the clock. To compare ventilation schemes, let us take a blind working during the period of its driving. When the length \(L\) is reached, the costs of ventilation, with the fans located at the beginning of the working, will increase to such a magnitude that it will be economically advantageous not to increase the length of the pipeline, but to drill a borehole and bring the fan closer to the face, thereby creating, from the standpoint of ventilation, the conditions of the initial driving of the working (Fig. 1).

Fig. 1. Ventilation schemes for long blind workings

To determine the energy costs for ventilation according to the first scheme, we compose the equation:

\[ dA = a \cdot N \cdot dt, \tag{1} \]

where
\(A\)—the cost of the electric energy consumed over the entire period of driving the working;
\(N\)—the power consumed by the fan at the given moment of time, kW;
\(a\)—the cost of one kWh, in rubles;
\(t\)—the time of driving the working, in hours.

The power consumed by the fan depends on the length of the pipeline; therefore, to calculate the consumption of electric energy, we integrate equation (1):

\[ A = \int_{0}^{t} a \cdot N \cdot dt . \tag{2} \]

We express the fan power as

\[ N = \frac{Q \cdot H}{102 \cdot \eta}, \tag{3} \]

where \(Q\) is the air flow rate, \(\mathrm{m^3/sec}\);
\(H\) is the depression, mm water column;
\(\eta\) is the efficiency of the fan.

We determine the depression of the fan from the formula:

\[ H=\frac{6.5 \cdot \alpha \cdot L \cdot Q^2}{d^5}, \tag{4} \]

where \(\alpha\) is the aerodynamic coefficient of pipe resistance;
\(L\) is the length of the pipeline, m;
\(d\) is the pipe diameter, m.

The length of the pipeline can be determined from the expression:

\[ L=V \cdot t \frac{1}{30 \cdot 24}, \tag{5} \]

where \(V\) is the rate of driving the working, m/month.

In this case we assume that the rate of driving the working will be a constant quantity. Substituting the values \(N\), \(L\) into equation (2), then

\[ A=\int_{0}^{t}\frac{a \cdot Q \cdot 6.5 \cdot \alpha \cdot V \cdot t \cdot Q^2}{102 \cdot \eta \cdot d^5 \cdot 30 \cdot 24}\,dt \tag{6} \]

and, taking \(Q\), \(V\), \(d\) as constant quantities, we obtain:

\[ A=\frac{6.5 \cdot \alpha \cdot a \cdot Q^3 \cdot V}{30 \cdot 24 \cdot 102 \cdot d^5 \cdot \eta}\int_{0}^{t} t \cdot dt, \tag{7} \]

whence

\[ A=\frac{3.25 \cdot \alpha \cdot a \cdot Q^3 \cdot V \cdot t^2}{30 \cdot 24 \cdot 102 \cdot d^5 \cdot \eta}. \tag{8} \]

The costs of moving the fan and pipes are not taken into account, in view of their insignificant magnitude.

The costs of ventilation according to the second scheme will differ in practice from the first by the total cost of driving (drilling) the borehole, which can be expressed by the equality

\[ A_1=a_1 \cdot \frac{h}{\sin \beta}, \tag{9} \]

where \(A_1\) is the full cost of the borehole or raise;
\(a_1\) is the cost of one running meter of borehole, rub.;
\(\beta\) is the angle of inclination of the borehole or raise;
\(h\) is the depth of the working from the surface or upper horizon, m.

To find the rational length of the working, upon reaching which it is economically advantageous to drill a ventilation borehole, the following condition must be satisfied:

\[ A=A_1 \]

or

\[ \frac{3.25\cdot \alpha \cdot a \cdot Q^3 \cdot V \cdot t^2}{30\cdot 24\cdot 102\cdot d^5\cdot \eta} = a_1 \cdot \frac{h}{\sin \beta}, \tag{10} \]

whence

\[ t= \sqrt{ \frac{a_1\cdot h\cdot 30\cdot 24\cdot 102\cdot d^5\cdot \eta} {3.25\cdot \alpha \cdot a \cdot Q^3\cdot V\cdot \sin \beta} }. \tag{11} \]

Substitute the value of \(t\) into equation (4); then:

\[ L= \frac{d^2\cdot V}{4.8\cdot Q} \sqrt{ \frac{a_1\cdot h\cdot d\cdot \eta} {\alpha\cdot a\cdot Q\cdot \sin \beta} }. \tag{12} \]

Using the formula obtained, it will be possible to make an economic comparison of two ventilation schemes and to determine the advisability of drilling a ventilation borehole.

It should be noted that, in addition to the economic determination of the distance between boreholes in a working, the technical and mining-geological conditions of driving it must be taken into account.

Example. A working is given with the following initial parameters: \(Q=3.5\ \text{m}^3/\text{s}\), \(d=400\ \text{mm}\), \(a_1=200\) rubles (when drilling through coal), \(a=0.12\) rubles, \(h=80\ \text{linear m}\), \(\alpha=0.0003\), \(\eta=0.6\), \(\sin\beta=1\), \(V=50\ \text{linear m/month}\).

\[ L= \frac{50\cdot 150\cdot 0.3^2}{30\cdot 24\cdot 3.5} \sqrt{ \frac{200\cdot 80\cdot 0.3\cdot 0.6} {0.12\cdot 0.0003\cdot 3.5\cdot 50\cdot 1} } =510\ \text{m}. \]

Conclusions

1. Ventilation of long blind workings without driving additional workings leads to an increase in ventilation costs.

2. To reduce ventilation costs, it is advisable to drill boreholes. Determination of the distance between boreholes according to the economic factor can be carried out using the proposed formula (12).