Determination of the Design Service Life of a Level in an Operating Coal Mine

V. V. Proskurin

The annual output of a mine is the most important technical-and-economic indicator in its design, construction, and operation. As a rule, it is adopted for the entire design (incomplete) service life of the mine or for the period until its reconstruction, and is secured by industrial reserves within the corresponding boundaries of the mine field.

The technical design of a mine establishes the principal parameters of the elements of the mine field: the height of a level, their number, the service life, and the industrial reserves of each of them. The latter, especially for lower-lying levels, is usually adopted in projects in preliminary form. Therefore, when designing the opening of a lower-lying horizon of a mine, the question often arises of refining or changing the industrial reserves of the level and its service life, as compared with those previously adopted in the technical design. This is most often caused by a combination of the following circumstances:

1) a possible change in the height of the level in connection with the improvement of mining systems, the introduction of new, more progressive means of mechanization and methods of work organization;

2) refinement, by detailed exploration, of the industrial reserves as a whole and by categories within the boundaries of the level adopted in the technical design;

3) the necessity and possibility of adding reserves at the expense of neighboring areas;

4) additional capital investments in connection with converting the mine to work with stowing, or in connection with refinement of the expected methane content of the coal seams (driving auxiliary shafts, near-shaft workings, chambers, etc.);

5) a reduction in the time of simultaneous mining of two levels during the transition of mining operations to the lower-lying horizon, and other factors.

Taking the above into account, the following two problems may be proposed for solution:

1. To refine the service life of the lower-lying level being opened, in connection with insignificant changes in its industrial reserves, as compared with those adopted in the technical design of the mine.

Such a problem can be solved by applying the known formula:

\[ t=\frac{Z_{\mathrm{e}}}{A}, \tag{1} \]

where \(t\) is the design service life of the level, years;
\(Z_{\mathrm{e}}\) is the industrial reserves of the level, \(t\);
\(A\) is the annual output of the mine, \(t\).

Since, by condition, \(Z_{\mathrm{e}}\) is a fixed quantity, the design service life of the level \(t\) will also be fixed.

1. To find the optimal service life of the lower level being opened up, in connection with the possibility of an “unlimited” change in its commercial reserves.

Such a formulation of the problem is quite realistic and has great production significance, since labor productivity in the mine and the cost of a ton of coal are, to some extent, functions of time; it also undoubtedly has a certain scientific interest in the sense of the novelty of the theoretical formulation of the question.

In this case the calculated service life of the level may be determined on the basis of the principle of the least costs per 1 \(t\) of its commercial reserves. As is known, this principle was used in analytical calculations by previous investigators [1; 2; 3] as applied to the solution of the problem of determining the most advantageous dimensions of a mine field along the strike and the dip. Making full use of the achievements of previous investigators, we consider it absolutely necessary to supplement them, in solving the problem posed by us, with two further factors:

1) taking into account additional operating costs connected with maintaining the level in working condition during the period when mining operations are transferred to the lower horizon; and 2) taking into account the number and ventilation capacity of group and separate drifts in accordance with the existing “Safety Rules in the Coal and Shale Industry.”

The latter is an important factor in determining the parameters of development, especially of deep and, as a rule, methane-bearing coal deposits.

In solving the problem posed, the following typical initial data have been adopted for the calculation: the mine field is double-winged; the opening scheme is by centrally located vertical shafts and main level crosscuts; the commercial reserves of the level are uniformly distributed along the haulage drifts; the vertical height of the level is chosen in accordance with the level of development of mining technology and organization of work; the vertical height of the mine field is according to the technical design of the mine; the costs and volumes of mine workings in the calculations must be adopted according to the current norms, estimates, and unit prices; the cost of maintaining mine workings is to be taken according to actual data for the overlying level already worked out.

The cost of the works connected with extracting all the commercial reserves of the level, taking into account the growth of labor productivity and the reduction in production cost over the calculated period of its service, may be expressed by the formula:

\[ q_{\mathrm{э}}\cdot Z_{\mathrm{э}}, \tag{2} \]

where \(q_{\mathrm{э}}\) is the average cost of mining 1 \(t\) of coal.

As applied to the conditions of the problem posed:

\[ q_{\mathrm{э}} = q_1 + q_2, \tag{3} \]

where \(q_1\) is the average cost of mining 1 \(t\) of coal in terms of costs independent of the commercial reserves of the level (stoping extraction, hoisting, drainage, etc.);
\(q_2\) is the average cost of mining 1 \(t\) of coal in terms of costs repaid by the commercial reserves of the level or dependent on them (driving of opening workings, maintenance of drifts, haulage, etc.).

The second term of equation (3) can be expressed as follows:

\[ q_2=\frac{\sum C_i}{Z_{\mathrm{э}}}, \tag{4} \]

then expression (2) will take the form:

\[ q_{\mathrm{e}} Z_{\mathrm{e}} = q_1 Z_{\mathrm{e}} + \sum C_i, \tag{5} \]

where \(C_i\) are costs repaid by the industrial reserves of the level or dependent on them.

In proceeding to calculate the costs \(C_i\), we shall bear in mind that the dimensions of the mine workings, their support, and other parameters in the calculations must be adopted in accordance with the annual productivity of the mine and the level of mechanization and organization of work in the period to which they will pertain.

Thus, let us write all costs repaid by the industrial reserves of the level, or dependent on them, in general form.

1. Driving mine shafts within the limits of the level

\[ \sum K_{\mathrm{stv.}} \cdot h, \tag{6} \]

where \(\sum K_{\mathrm{stv.}}\) is the total cost of driving and equipping 1 linear m of all shafts within the limits of the level;
\(h\) is the vertical height of the level, m.

1. Driving the shaft station, near-shaft workings, and chambers

\[ D, \tag{7} \]

where \(D\) is the cost of the shaft station and all near-shaft workings and chambers in the level.

1. Driving the main crosscut

\[ K_{\mathrm{kv.}} \cdot l, \tag{8} \]

where \(K_{\mathrm{kv.}}\) is the cost of driving 1 linear m of the main crosscut with roundings;
\(l\) is the length of the main crosscut, m.

1. Maintenance of group and isolated drifts on the haulage and ventilation horizons

\[ \frac{S}{2} \cdot \frac{t}{2} \cdot 2 \cdot 2 \cdot \sum r_{\mathrm{shtr}} = S t \sum r_{\mathrm{shtr}}, \tag{9} \]

where \(S\) is the strike length of the mine field, m;
\(t\) is the design service life of the level, years;
\(\sum r_{\mathrm{shtr}}\) is the total cost of maintaining 1 linear m of all group and isolated drifts on the haulage and ventilation horizons per year.

1. Transport of loads along drifts

\[ \left(Z_{\mathrm{e}} + Z_{\mathrm{e}} \cdot a_{\mathrm{e}}\right) \frac{S}{4} q_{\mathrm{shtr}} = \frac{Z_{\mathrm{e}}(1+a_{\mathrm{e}})S q_{\mathrm{shtr}}}{4}, \tag{10} \]

where \(a_{\mathrm{e}}\) is the coefficient of equivalent loads, accounting for the transport of rock, stowing material, materials, and equipment;
\(q_{\mathrm{shtr}}\) is the cost of transport along drifts per tonne-meter.

1. Energy for moving air along drifts. We shall have in view a central ventilation scheme. In our case the path of air movement along the haulage drifts in each wing varies from 0 to \(\frac{S}{2}\) and on average is equal to \(\frac{S}{4}\). The same along the ventilation drifts is \(\frac{S}{4}\); in each wing \(\frac{S}{2}\), and within one level \(S\).

When air \(Q_{\sh}\ \mathrm{m^3/sec}\) is supplied to the mine, one wing will receive

\[ \frac{Q_{\sh}}{2}, \]

and one drift,

\[ \frac{Q_{\sh}}{2 n_{\mathrm{d}}}, \ \mathrm{m^3/sec}, \tag{11} \]

where \(Q_{\sh}\) is the quantity of air entering the mine, \(\mathrm{m^3/sec}\);
\(n_{\mathrm{d}}\) is the number of group and isolated drifts on one wing.

The cost of energy for moving air through a mine working over the entire period of its existence will be equal to \([3, 41]\):

\[ \frac{\alpha \cdot P_{\mathrm{v}} \cdot l_{\mathrm{v}} \cdot Q_{\mathrm{v}}^3 \cdot 24 \cdot 365 \cdot t_{\mathrm{v}} \cdot \gamma} {102 S_{\mathrm{v}}^3 \eta}, \tag{12} \]

where \(\alpha\) is the coefficient of resistance of the mine working to air movement;
\(P_{\mathrm{v}}\) is the perimeter of the mine working, \(\mathrm{m}\);
\(l_{\mathrm{v}}\) is the length of the ventilated working, \(\mathrm{m}\);
\(Q_{\mathrm{v}}\) is the quantity of air flowing through the working, \(\mathrm{m^3/sec}\);
\(t_{\mathrm{v}}\) is the ventilation time, years;
\(\gamma\) is the cost of \(1\ \mathrm{kWh}\) of electric power;
\(S_{\mathrm{v}}\) is the cross-sectional area of the working, \(\mathrm{m^2}\);
\(\eta\) is the efficiency of the ventilation installation.

As applied to the problem under consideration, and taking into account that the length of the wing is equal to

\[ \frac{S}{2}, \]

the average path of air movement on the haulage horizon is

\[ \frac{S}{4}; \]

with two wings and two horizons, from (12) we have:

\[ l_{\mathrm{v}}=\frac{S}{2 \cdot 2}\cdot 2 \cdot 2=S. \]

From the preceding (11 and 12) we have:

\[ Q_{\mathrm{v}}=\frac{Q_{\sh}}{2 n_{\mathrm{d}}}, \]

but

\[ Q_{\sh}=\frac{A \cdot q \cdot C_y}{300 \cdot 60}; \]

therefore

\[ Q_{\mathrm{v}}= \frac{A \cdot q \cdot C_y} {300 \cdot 60 \cdot 2 \cdot n_{\mathrm{d}}}, \tag{13} \]

where \(q\) is the minimum quantity of air per \(1\ \mathrm{t}\) of daily output, in \(\mathrm{m^3/min}\), in accordance with the methane emission rate of the mine;
\(C_y\) is a coefficient allowing for air leakage and ventilation of reserve stoping faces;
\(300\) is the number of working days of the mine per year.

Finally, from expression (12) it follows that \(t_{\mathrm{v}}=t\).

In the adopted notation, the cost of energy for moving air for the ventilation of all group and isolated drifts of the haulage and ventilation horizons over the calculated service life of the level will be:

\[ \frac{\alpha \cdot P_{\mathrm{v}} \cdot 24 \cdot 365 \cdot \gamma} {102 \cdot S_{\mathrm{v}}^3 \cdot \eta} \left( \frac{A \cdot q \cdot C_y} {300 \cdot 60 \cdot 2 n_{\mathrm{d}}} \right)^3 S t. \tag{14} \]

Let us denote:

\[ C_{\text{shtr}}=\frac{\alpha \cdot P_{v}\cdot 24.365\cdot \gamma}{102\cdot S_{v}^{3}\eta} \left(\frac{A\cdot q\cdot C_{y}}{300\cdot 60\cdot 2n_{\text{shtr}}}\right)^{3}, \tag{15} \]

where \(C_{\text{shtr}}\) is the cost of ventilating 1 linear m of all group and isolated drifts of the haulage and ventilation levels of the floor per year.

Then we obtain:

\[ C_{\text{shtr}}\cdot S\cdot t. \tag{16} \]

1. The part of the cost of all surface structures of the mine, amortized by the reserves of the underlying floor being opened,

\[ \frac{Bh}{H}, \tag{17} \]

where \(B\) is the cost of all surface structures of the mine, amortized by the reserves of the entire mine field;

\(H\) is the difference between the absolute elevations of the upper and lower boundaries of the mine field, or the vertical height of the mine field in m, adopted in the technical design of the mine.

1. The part of the cost of sinking and equipping all mine shafts from the ground surface to the level of the upper boundary of the mine field, amortized by the reserves of the underlying level being opened,

\[ \frac{\sum K_{0}\cdot H_{0}\cdot h}{H}, \tag{18} \]

where \(\sum K_{0}\) is the total cost of sinking and equipping 1 linear m of all mine shafts from the ground surface to the level of the upper boundary of the mine field;

\(H_{0}\) is the distance from the collars of the mine shafts to the level of the upper boundary of the mine field, m.

1. Additional operating costs associated with the simultaneous operation of two floors during the period of transition of mining operations to the lower of them. These include:

\(a_{1}\) — costs for servicing the shaft station area (maintenance of shaftmen, their assistants, tipple operators, winchmen, cage attendants, duty electricians, etc.);

\(a_{2}\) — costs for servicing transport on the level (maintenance of the electric-locomotive depot, track repair, traffic control, accounting for incoming loads, etc.);

\(a_{3}\) — costs for servicing the ventilation system of the level (maintenance of ventilation supervision, door attendants, ventilation workers, etc.);

\(a_{4}\) — additional energy costs for hoisting loads and for shunting operations, for water drainage, for excess mileage of the electric-locomotive fleet, etc.;

\(a_{5}\) — costs for maintaining workings during the simultaneous operation of two floors.

If we denote

\[ \sum a=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}, \tag{19} \]

then we have:

\[ \sum a\cdot t_{0}, \tag{20} \]

where \(\sum a\) is the additional operating costs associated with the simultaneous operation of two floors, per year;

\(t_{0}\) is the period of simultaneous operation of two floors, years.

Bearing in mind that

\[ Z_e = A \cdot t, \qquad h_n=\frac{h}{\sin\alpha} \quad \text{and} \quad S=\frac{A \cdot t \cdot \sin\alpha}{h\sum PC}, \]

where \(h_n\) is the inclined height of the level, \(m\);
\(\alpha\) is the dip angle of the group of seams;
\(P\) is the productivity of the seam, \(t/m^2\);
\(C\) is the mineral recovery coefficient, formula (5), after transformations, will take the form:

\[ q_e = q_1 + \frac{\sum K_{stv}\cdot h}{A\cdot t} +\frac{D}{A\cdot t} +\frac{K_{kv}\cdot l}{A\cdot t} +\frac{t\sin\alpha\cdot \sum r_{shtr}}{h\sum PC} + \]

\[ +\frac{At(1+a_e)q_{shtr}\cdot \sin\alpha}{4h\sum PC} +\frac{C_{shtr}\cdot t\cdot \sin\alpha}{h\sum PC} +\frac{B\cdot h}{H\cdot A\cdot t} + \]

\[ +\frac{\sum K_0 H_0\cdot h}{H\cdot A\cdot t} +\frac{\sum a\cdot t_0}{A\cdot t}. \tag{21} \]

From equation (21) it is evident that

\[ q_e=f(t). \]

Solving the equation \(f'(t)=0\), we find the minimum of this function:

\[ -\frac{\sum K_{stv}\cdot h}{A\cdot t^2} -\frac{D}{A\cdot t^2} -\frac{K_{kv}\cdot l}{A\cdot t^2} +\frac{\sum r_{shtr}\cdot \sin\alpha}{h\sum PC} + \]

\[ +\frac{A(1+a_e)q_{shtr}\cdot \sin\alpha}{4h\sum PC} +\frac{C_{shtr}\cdot \sin\alpha}{h\sum PC} +\frac{B\cdot h}{H\cdot A\cdot t^2} + \]

\[ +\frac{\sum K_0\cdot H_0\cdot h}{H\cdot A\cdot t^2} -\frac{\sum a\cdot t_0}{A t^2} =0, \]

whence

\[ t= \sqrt{ \frac{ \left[ \left(\sum K_{stv}\cdot h+D+K_{kv}\cdot l+\sum a\cdot t_0\right) +\frac{h\left(B+H_0\sum K_0\right)}{H} \right]h\sum PC }{ \left[ \left(\sum r_{shtr}+C_{shtr}\right) +\frac{A(1+a_e)q_{shtr}}{4} \right]A\sin\alpha } } \ \text{years}. \tag{22} \]

Example. For mine A (steep dip), according to the design the following was adopted:

\[ \begin{aligned} \sum K_{stv} &= 18400\ \text{rubles},& B &= 48000000\ \text{rubles},& a_e &= 0.25,\\ h &= 100\ m,& \sum K_0 &= 18400\ \text{rubles},& q_{shtr} &= 0.00095\ \text{rubles},\\ D &= 12870000\ \text{rubles},& H_0 &= 50\ m,& \sum PC &= 60.8\ t/m^2,\\ K_{kv} &= 2700\ \text{rubles},& \alpha &= 65^\circ,& A &= 1500000\ m,\\ l &= 920\ m,& \sin 65^\circ &= 0.9063,& q &= 1.0\ m^3/\text{min}\\ \sum a &= 1184400\ \text{rubles},& H &= 400\ m,& &\quad \text{per }1\ t\text{ of daily output},\\ t_0 &= 5\ \text{years},& \sum r_{shtr} &= 108\ \text{rubles}.& \end{aligned} \]

\[ C_y = 1{,}5 \quad \text{and} \quad C_{shtr} = \frac{0{,}0015 \cdot 12{,}8 \cdot 24 \cdot 365 \cdot 0{,}13}{102 \cdot 9{,}5^3 \cdot 0{,}53} \left( \frac{1500000 \cdot 1 \cdot 1{,}5}{300 \cdot 60 \cdot 2 \cdot 3} \right)^3 = 4{,}02, \]

\[ t = \sqrt{ \frac{ \left[ (18400 \cdot 100 + 12870000 + 2700 \cdot 920 + 1184400 \cdot 5) + \frac{100(48000000 + 18400 \cdot 50)}{400} \right] 100 \cdot 60{,}8 }{ \left[ (108 + 4{,}02) + \frac{1500000(1 + 0{,}25)0{,}00095}{4} \right] 1500000 \cdot 0{,}9063 } } \]

\[ t = 17{,}75 \text{ years; according to the design, } t = 18 \text{ years was adopted.} \]

Let us investigate equation (21), \(q_e = q_1 + f(t)\), using the calculated data adopted in the example. By successively assigning values to \(t\), we obtain:

Table

The table shows, by means of a particular example, the influence of individual factors on the choice of the optimal service life of a level. The influence of individual factors under different conditions has different significance; for example, when working a deep deposit and coal that is exceptionally methane-bearing, the importance of the ventilation factor among the others increases sharply; the same may be said when converting a mine to operation with stowing, etc.

Conclusion

1. In analytical calculations for determining the principal dimensions of the elements of coal-deposit development, a solution is given for the first time for finding the rational service life of a level when opening the underlying horizon.

2. In formulas for determining the principal parameters of the mine field, it is necessary to take into account the additional costs associated with the simultaneous operation of two levels, as well as the number of group and separate drifts and their ventilation capacity.

3. Formula (22) may be used in the practical activity of design organizations and in instructional work at mining higher educational institutions.

LITERATURE

1. Popov A. S. Establishing the annual productivity and field dimensions for an individual mine in the development of hard-coal deposits. Publishing Bureau of the Moscow Mining Institute, 1934.

2. Zvyagin P. Z. Design and calculations of development elements for bedded deposits. ONTI, 1935.

3. Shevyakov L. D. Fundamentals of the Theory of Coal-Mine Design. Ugletekhizdat, 1950.