Techniczne nauki

D.Sc. Senkus V.V., Shchepetov A.V., Fomichev S.G.

Novokuznetsk branch-institute of FEI HPE "Kemerovo State University",

Russia, Novokuznetsk

The economic-mathematical model for a choice of parameters
of open technology of coal mining (open-pit mining)

Summary.

In article the economic-mathematical model for the analysis of technical and economic indicators of work of an extraction site of coal open-pit mine is offered. The model passes approbation on a number of coal open-pit mines of the South of Kuzbass (Russia).

Keywords: economic-mathematical model, coal mining, open technology, prime cost of coal, coal open-pit (open-cut) mine, quarry.

I. Introduction.

Important branch of economy of Russia is the coal industry which includes not only production (enrichment), but also processing (briquetting) of stone and brown coal. In itself coal mining is a removal it from an open surface of a field with the subsequent export from mine.

There are various ways of coal mining which depend on a depth of coal breeds. If depth of finding of coal layer makes to hundred meters – in this case coal mining is made in the open way. Today the volume of coal mining in a total amount of coal mining approximately makes in the open way 65% and its share allegedly will increase for the next decade still percent by ten.

Coal mining is made in the open way when coal lies superficially. In that case removal "vskrisha" (the overburden) then the drilling-and-blasting of coal is made. After an overburden (surface material covering the valuable deposit) coal by means of cars or automotive equipment is taken away from a production place.

At various stages of the activity coal open-pit mine decrease in economic efficiency of work, namely – growth of prime cost of extracted coal under the influence of various factors: as external, not depending on the enterprise and defined by economic policy pursued in the country, and internal, defined by the technical and economic solutions realized at the enterprise. The major known factor of growth of prime cost of the coal, being shown at a final stage of working off of fields, aging of geological fund which is connected with initial working off of more preferable stocks of coal and transition to working off of less preferable stocks is.

For an open way of production more preferable stocks of coal are concentrated on powerful layers under not a considerable layer of deposits with coal brands in demand in the market (with a low ash-content and the content of sulfur). To such stocks of coal fields located close also belong to the settlements providing the enterprises with labor, with the developed infrastructure (housing stock, population service, railroads and highways, high-voltage power lines, etc.).

Therefore, the set of factors which in aggregate form level of reached technical-economic indicators has impact on economic efficiency of work of cuts.

The analysis of publications of staff of Institute of coal of the Siberian office of the Russian Academy of Sciences in the last two years showed that not enough attention is paid to economic-mathematical modeling of parameters of open technology of coal (open-pit) mining.

The majority of scientific articles [1, 2] is devoted to idea of association of open and underground technologies of coal mining. A number of articles [3, 4] tries to estimate the capacity and stocks of the coal-mining enterprises. The part of scientific articles covers problems of safety and new technologies of underground production [5]. Some scientific articles [6, 7] are directed on increase of a resource of the mining-transport equipment. Offered mathematical models in articles [8-10] generally mention only topological parameters of coal fields. Therefore the problem of creation of adequate economic-mathematical models of technology of coal mining is actual.

II. Problem definition.

It is necessary to develop economic-mathematical model for a choice of parameters of open technology of coal mining on extraction sites. The model has to consider the following economic conditions:

1. Internal economic conditions of activity of the open-pit mine, defined by prime cost of extracted coal depending on various technological and geological parameters.

2. External economic conditions of activity of the open-pit mine – variations of market price of coal and a value added tax and other obligatory payments.

III. Results.

Internal economic conditions of activity of open-pit mine are defined by recurrence of technology of open-pit mining operations in the form of separate stages performed with the set sequence at working off of locally located extraction sites (Table 1, Figure 1).

Table 1 – The list and short characteristic of stages of a full production cycle open mining
operations on an extraction site of an open-pit mine

Carried-out stages mining operations		Short characteristic of stages mining operations
		Technological	Economic
Extraction of parts of a rock massif	1. Removal of a humus	There is no coal mining. Stages 1 and 2 are carried out consistently.	With third-party or own investments *
	2. Removal of deposits
	3. Removal of rock	Coal mining is made. Stages 3 and 4 alternate among themselves.	With financial means from sale of extracted coal
	4. Coal extraction
Rekultivation of the earth (rehabilitation)	5. Laying of deposits	There is no coal mining. Stages 5 and 6 are carried out with any sequence.	With third-party or own investments *
	6. Laying of rock
	7. Laying of a humus
* - own investments, are understood as the financial means saved up earlier or received now from sale of coal of a section got on another extraction sites or association of open-pit mines.

Full modelled prime cost of coal at working off of an extraction site С_р includes the sum of shares of prime cost of coal from costs of realization of stages of a production cycle, and also a share from the general expenses on an open-pit mine ΔС_об

С_р = ΔС_г + ΔС_н + ΔС_п + ΔС_у + ΔС_рн + ΔС_рп + ΔС_рг + ΔС_об, (1)

Ср	-	full prime cost of coal on an extraction site of an open-pit mine;
ΔСг	-	share of prime cost of coal from costs of removal of a humus;
ΔСн	-	share of prime cost of coal from costs of removal of deposits;
ΔСп	-	share of prime cost of coal from costs of removal of rock;
ΔСу	-	share of prime cost of coal from costs of coal extraction;
ΔСрп	-	share of prime cost of coal from costs of rock laying;
ΔСрн	-	share of prime cost of coal from costs of deposits laying;
ΔСрг	-	share of prime cost of coal from costs of humus laying;
ΔСоб	-	prime cost share from the general expenses on an open-pit mine falling on a fulfilled extraction site.

Figure 1 – General view of open excavations on the initial stages of working off
of an extraction site of open-pit mine and geological structure of a rock massif

The prime cost of coal С_р on an extraction site of open-pit mine with a full production cycle (1), and also each share in its structure on performance of stages of open mining operations are dependence on various studied technological and geological parameters F_i (Table 2).

С_р = f (F_i); (2)

ΔС_г, ΔС_н, ΔС_п, ΔС_у, ΔС_рп, ΔС_рн, ΔС_рг = f (F_i), (3)

Fi

-

studied technological and geological parameters on the extraction site fulfilled in the open way.

Table 2 – List of the key studied parameters

Name of studied parameters		Symbols
Technological parameters	1. Depth of open excavations in radical rock, m	Нк
	2. Length of an extraction site on pro-deleting of layers, m	Lп
	3. Step of transfer of the technological road on boards of developments, m	Lш
Geological parameters	4. Thickness of a layer of deposits, m	Нн
	5. Capacity of layer, m	m
	6. Corner of a bedding of layer, degree	α
	7. Coal brand	-

The technological parameters F_i in practice are set by borders of the mountain branch, established before protected objects, for example the railroad, the river, the settlement, etc. Therefore conditions of modeling are considered in the form of the borders of mountain branch forming a spatial arrangement of excavations on an extraction site in three directions:

the first direction in a cross of pro- deleting of layer – is set by borders in the form of two vertical planes П_к1 and П_к2 with distance between them equal the studied length L_п of an extraction field;

the second direction on layer pro-deleting – is set by borders in the form of two vertical П_п1 and П_п2 planes with distance between them Lk of an extraction field equal to settlement width L_к;

the third direction on a layer depth – is set by borders in the form of two horizontal planes, namely the bottom plane П_г1 passing on a bottom of developments, and the second border is an earth П_г2 surface with distance between them in equal to full depth of excavations Н.

The configuration of modelled surfaces of carried-out open excavations in deposits and radical rocks, and also transport communications, is set according to requirements of safety rules.

Volumes of taken parts of a rock massif are modelled in borders of open developments characteristic at the final stage of development of mining operations, namely at achievement of the set parameters on depth concerning an earth surface. Other sizes of excavations, for example their width L_к in a cross of pro-deleting of layers, are secondary since depend on their general depth Н = Н_к + Н_н and a corner of layers α.

Volumes of taken parts of a massif are modelled in borders of open developments characteristic at the final stage of development of mining operations, namely at achievement of the set parameters on depth concerning an earth surface. Other sizes of excavations, for example their width in a cross of pro-deleting of layers, are secondary since depend on their general depth and a hade of layers

Therefore, modeling conditions with restriction of depth of working off of an extraction site is initial for definition financial costs of realization of various stages of open mining operations. In this case development of mathematical model is comparable with design of cuts at which also depth of working off Н for which previously is set is settled an invoice taken volumes of parts of a massif.

External economic conditions of activity of cuts in developed model are defined by proceeds from sales of coal В_пр which act as economic criterion of an assessment of prime cost of coal С_р(F_i) (1)-(3). Determination of economically rational parameters F_i is reduced to the solution of the equation of balance of economic activity of the enterprise of transition representing a boundary condition from profitable work of an extraction site to unprofitable work (Figure 2).

В_пр = С_р(F_i), (4)

Впр

-

proceeds from sales of one ton of coal got on a site.

В_пр = Ц – НДС = Ц (1 – К_ндс), (5)

Ц	-	the price of got brand of coal on a sales market;
НДС	-	value added tax and other payments;
Кндс	-	the coefficient considering a value added tax.

The analysis of technical and economic indicators of work of an extraction site, is carried out with use of the software product at change of the various technological and geological parameters F_i in studied range

F_i.н ≤ F_i ≤ F_i.к, (6)

Fi.н	-	initial value of studied parameter Fi;
Fi.к	-	final value of studied parameter Fi.

Figure 2 – Schedules of dependences of economic indicators on the extraction
section site from change of studied parameter F_i

Economic efficiency of working off of any extraction site is estimated by receiving profit or the suffered losses from coal sale. Receiving profit on coal sale at change of studied parameters corresponds to a condition

П_пр(F_i) = В_пр – С_р(F_i) > 0, (7)

Ппр(Fi)

-

profit on sale of ton of coal as function from the studied parameters of technology Fi on an extraction site of aт open-pit mine.

Receiving profit on sale of coal П_пр corresponds to economically rational range of change of studied parameter F_i

F_i.min < F_i < F_i.max, (8)

Fi.min	-	the minimum recommended value of parameter Fi;
Fi.max	-	the maximum recommended value of parameter Fi.

Suffered losses from sale of coal corresponds to negative profit and unprofitable work of a section at not recommended range of change of studied parameter F_i

П_пр(F_i) = В_пр – С_р(F_i) < 0, (9)

where F_i < F_i.min and F_i > F_i.max. (10)

IV. Conclusions.

The offered economic-mathematical model allows:

1) to exclude economic situations at which the open-pit mine effectively working and possessing modern technology of coal mining, at change of conditions can be not profitable, for example:

- at incorrectly chosen technological parameters of open excavations, for example, working off depths;

- at economically irrational geological parameters of layers planned to working off on extraction sites, for example, thickness of a layer of deposits, capacities of layers, etc.;

- at change of economic conditions, for example, coal prices, etc.;

2) to receive the answer to the main question: that it is necessary to change in technology to leave a difficult economic situation or to improve indicators of work of a open-pit mine.

At present the model passes industrial approbation on coal open-pit mine «Stepanovsky» and on coal open-pit mine «Siberginsky» (Russia, Kemerovo region).

Literature.

1. Fedorin V.A. and others. About the priority directions of association of open and underground geotechnologies in uniform system of conducting mining operations in Kuzbass // Messenger KuzGTU. – 2012. – № 3. – Р. 102-107.

2. Shakhmatov V.Ya. The combined way of development of coal fields with use of infrastructure of adjacent mine // GIAB. – 2011. – № 7. – Р. 49-51.

3. Borisov I.L. Express a method of an assessment of the expected capacity of the coal-mining enterprises // Subsurface use the XXI century.– 2011. – №3. – Р. 30-33.

4. Shaklein S.V., Rogova T.B. Software of monitoring of reliability of stocks of the coal-mining enterprises // Messenger KuzGTU. – 2012. – № 1. – Р. 20-26.

5. Klishin V.I., Zvorygin L.V., Lebedev A.V., Savchenko A.V. Problems of safety and new technologies of underground mining of coal fields. – Novosibirsk: Publishing House «Novosibirsk Writer», 2011. – 524 р.

6. Gerike B.L., Doronin S.V. Modeling of influence of a rail track // Messenger KuzGTU. – 2011. – № 2. – Р. 47-50.

7. Gerike B.L., Gerike P.B. Vibration diagnostics of the concentrating equipment // Mining information and analytical bulletin. – 2011. – OV№ 3. – Р. 361-366.

8. Shaklein S.V., Pisarenko M.V. Multilevel geometrical models of coal fields // Markscheideria and subsurface use. – 2011. – № 4. – Р. 49-52.

9. Cherdantsev N. V., Preszler V. T. Modeling of a geomechanical condition anisotropic on durability of the non-uniform massif of coal // Messenger KuzGTU. – 2011. – № 3. – Р. 15-22.

10. Shaklein S.V., Pisarenko M.V. Development of approaches to an assessment of ambiguity of geometrical models of coal fields // High technologies of development and use of mineral resources. – Novokuznetsk, 2011. – Р. 148-152.

11. Aksenov V.V., Efremenkov A.B., Rezanova E.V. Intense the deformed condition of the massif of the coal containing development with system of planimetric screw and longitudinal channels // Mining information and analytical bulletin. – 2011. – ОV № 2. – Р. 24-42.