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Date submitted2023-03-16
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Date accepted2023-12-27
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Date published2024-04-25
Comprehensive assessment of deformation of rigid reinforcing system during convergence of mine shaft lining in unstable rocks
Operation of vertical mine shafts in complex mining and geological conditions is associated with a number of features. One of them is a radial displacement of the concrete shaft lining, caused by the influence of mining pressure on the stress-strain state of the mine workings. A rigid reinforcing system with shaft buntons fixed in the concrete lining thus experiences elastoplastic deformations, their value increases with time. It results in deviation of conductors from design parameters, weakening of bolt connections, worsening of dynamic properties of geotechnical system “vehicle – reinforcing”, increase of wear rate of reinforcing system elements, increase of risks for creating an emergency situation. The article offers a comprehensive assessment of displacements of characteristic points of the bunton system based on approximate engineering relations, numerical modeling of the deformation process of the bunton system and laser measurements of the convergence of the inner surface of the concrete shaft lining. The method was tested on the example of the reinforcing system of the skip-cage shaft of the potash mine. Displacement of the characteristic points of the reinforcing system is determined by the value of radial displacements of the surface of the concrete shaft lining. Evaluation of the radial displacements was made using monitoring measurements and profiling data. The results obtained make it possible to justify the need and timing of repair works. It is shown that the deterioration of the reinforcing system at different levels occurs at different rates, defined, among other things, by mechanical properties of the rock mass layers located at a given depth.
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Date submitted2021-02-09
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Date accepted2023-09-20
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Date published2024-02-29
Analysis of experience in the use of preformed particle polymer gels in the development of high-water-cut production facilities in low-temperature oil reservoirs
- Authors:
- Sergei V. Galkin
- Yuliya A. Rozhkova
Foreign practice of oil production in high-water-cut conditions suggests using the technology of injection of preformed particle gel (PPG) suspension into injection wells. After swelling, the polymer particles become elastic and are able to penetrate through highly permeable watered intervals into the remote reservoir zone, forming a polymer “plug”. Thus far, the domestic experience of application of this technology boiled down to testing foreign compounds. We have looked into the possibilities of PPG technology application in geological and technological conditions of high-water-cut fields of Perm Krai. The paper proposes PPG reagents effective in low-temperature reservoirs (20-35 °С) and at relatively high salinity of formation water (more than 200 g/l). The world experience of PPG technology application was analyzed to identify the principal scheme of reagent injection, to establish variants of sequence of injection of PPG particles of different sizes, as well as the possibility of regulating the morphological characteristics of polymer gel particles during synthesis depending on the porosity and permeability of the reservoir. A prerequisite for the technology is the ability to remove PPG particles after treatment from the bottom-hole zone of the formation; for this purpose, tests were carried out on a breaker compound based on sodium persulfate with synergizing additives. PPG technology is effective in reservoirs with high permeability heterogeneity. Two types of high-water-cut production facilities potentially promising for PPG realization have been identified for oil fields of Perm Krai. The first type includes carbonate Tournaisian-Famennian reservoirs with pronounced macrofracturing, in which the PPGs are used for colmatation of flushed large fractures. The second type is terrigenous Visean deposits with increased oil viscosity from 5 to 100 mPa∙s and high permeability of reservoirs (> 0.5 μm2). For both types of reservoirs, areas have been selected that are promising for the implementation of PPG technology.
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Date submitted2022-06-27
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Date accepted2023-06-20
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Date published2023-12-25
Analysis of the problems of high-quality drinking water extraction from underground water intakes on Vysotsky Island in the Vyborg district of the Leningrad region
This article presents the results of drilling, experimental filtration work and laboratory studies aimed at assessing the resources and quality of groundwater in the licensed area of Vysotsky Island located in the Leningrad region, in the Gulf of Finland in accordance with the requirements of regulatory documents. Analysis of the results of hydrochemical studies and their comparison with data on water intakes in adjacent areas gives the right to conclude that it is possible to classify a hydrogeological unit as a different type of resource formation than those located in the surrounding areas. Groundwater in this area is confined to an unexplored deep fractured regional high-pressure zone. According to the received data, the explored water intake can be attributed to a unique groundwater deposit, which has an uncharacteristic composition of groundwater in the north of the Leningrad region, which may be due to the mixing of modern sediments and relict waters of the Baltic glacial lake. The stability of groundwater characteristics is confirmed by long-term monitoring.
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Date submitted2022-09-15
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Date accepted2022-11-17
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Date published2022-12-29
Comprehensive assessment of hydraulic fracturing technology efficiency for well construction during hydrocarbon production
The oil and gas industry has been an integral and fundamental sector of the Russian economy for the past few years. The main problems of this industry have traditionally been the deteriorating structure of oil reserves; depreciation of main assets; slowdown and decline in oil production. Recently these have been complicated by a number of new negative trends related to underinvestment, limited financial resources, deteriorating access to new equipment and technologies. The task of the research is to make a comprehensive assessment of hydraulic fracturing technology during well construction and to increase the recovery and intensification of hydrocarbons production. In this research, modeling techniques were used to assess the productivity of each fracture. Geophysical methods (seismic survey) were used to determine the geomechanical properties of the formation. Comprehensive assessment of hydraulic fracturing technology during well construction was carried out, which allowed to increase vertical permeability and unite disparate parts of the reservoir in practice, and to determine the development efficiency of the hydrocarbon field.
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Date submitted2021-11-17
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Date accepted2022-04-06
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Date published2022-11-10
Method for predicting the stress state of the lining of underground structures of quasi-rectangular and arched forms
- Authors:
- Maksim A. Karasev
- Tien Tai Nguyen
A method for predicting the stress-strain state of the lining of underground structures, the shape of the cross-section of which is different from the circular outline, is considered. The main task of the study is to develop a methodology for assessing the influence of the parameters of the cross-section shape of underground structures on the stress state of the lining. To solve this problem, a method for calculating the stress state of the lining for arched tunnels with a reverse arch and quasi-rectangular forms is substantiated and developed. The methodology was tested, which showed that the accuracy of the prediction of the stress state of the lining is sufficient to perform practical calculations. An algorithm for multivariate analysis of the influence of the cross-sectional shape of underground structures of arched and quasi-rectangular shapes on the stress state of the lining is proposed. Parametric calculations were performed using the developed algorithm and regularities of the formation of the stress state of the lining of underground structures for various engineering and geological conditions, as well as the initial stress state field, were obtained. A quantitative assessment of the influence of geometric parameters of tunnels on their stress-strain state was performed.
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Date submitted2021-03-18
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Date accepted2021-09-10
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Date published2021-12-16
Development of blocking compositions with a bridging agent for oil well killing in conditions of abnormally low formation pressure and carbonate reservoir rocks
- Authors:
- Dmitrii V. Mardashov
Production well killing before workover operations in late-stage oil and gas-condensate fields can be complicated by abnormally low formation pressure, carbonate type of reservoir rocks, and high gas-oil ratio. These complications lead to the intensive absorption of technological fluids by the formation and gas ingresses, which, in its turn, increases the time of killing wells and putting them on production, reduction of productivity, and additional costs. Therefore, it is crucial to develop a high-performance well-killing composition that would allow improving the efficiency of killing wells in complicated geological, physical, and technological conditions at the expense of reliable overlapping of the perforation interval (or open wellbore) to prevent gas intakes and gas outflow from the formation. To develop blocking compounds, a set of laboratory tests has been carried out, including physical and chemical (determination of density, viscosity, thermal stability, sedimentation stability, etc.) and research of blocking and filtration properties of compositions during simulation of a fractured reservoir. In the course of laboratory tests, the choice of fractional composition and polymer filler concentration was substantiated in the blocking emulsion and polymer compositions to increase the efficiency of their application under the complicated conditions of killing oil wells. As a result of laboratory research and field tests, the emulsion and polymer blocking compositions containing bridging agent (microcalcite) were developed, which increase the oil well killing efficiency by preventing the absorption of technological fluids in the formations and, as a result, preserving its productivity.
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Date submitted2020-09-09
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Date accepted2021-03-29
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Date published2021-09-20
Developing features of the near-bottomhole zones in productive formations at fields with high gas saturation of formation oil
The article studies the formation features of the bottomhole zones in productive formations during operation of production wells in the north of the Perm Territory. Their distinctive feature is the high gas saturation of formation oil. The most widely used parameter in Russian and world practice – the skin factor was used as a criterion characterizing the state of the bottomhole zone. Analysis of scientific publications has shown that one of the main problems of applying the skin factor to assess the state of bottomhole zones is the ambiguity of interpretations of its physical meaning and the impossibility of identifying the prevailing factors that form its value. The paper proposes an approach to identifying such factors in the conditions of the fields under consideration, based on multivariate correlation-regression analysis. Choice of this tool is due to the complexity of the processes occurring in the “formation – bottomhole zone – well” system. When describing complex multifactorial processes, the chosen method demonstrates a high degree of reliability. For a large number of wells in the region, significant material was collected and summarized, including the results of determining the skin factor (1102 values) during hydrodynamic investigations, as well as data on the values of various geological and technological indicators, which can probably be statistically related to the value of the skin factor. A series of multidimensional mathematical models has been built; the skin factor was used as a predicted parameter, and data on the values of geological and technological indicators were used as independent indicators. Analysis of the constructed models is a key stage of this study. Set of parameters included in the multidimensional models, sequence of their inclusion and contribution to the total value of the achieved determination coefficient as the main indicator for the performance of the constructed models were studied. It has been established that the main factor influencing the state of the bottomhole zone is oil degassing. Significant differences in the formation features of the skin factor in the terrigenous and carbonate sediments at the fields under consideration have been determined.
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Date submitted2020-07-02
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Date accepted2021-02-16
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Date published2021-04-26
Development of viscoelastic systems and technologies for isolating water-bearing horizons with abnormal formation pressures during oil and gas wells drilling
Article provides a brief overview of the complications arising during the construction of oil and gas wells in conditions of abnormally high and abnormally low formation pressures. Technological properties of the solutions used to eliminate emergency situations when drilling wells in the intervals of catastrophic absorption and influx of formation fluid have been investigated. A technology for isolating water influx in intervals of excess formation pressure has been developed. The technology is based on the use of a special device that provides control of the hydrodynamic pressure in the annular space of the well. An experiment was carried out to determine the injection time of a viscoelastic system depending on its rheology, rock properties and technological parameters of the isolation process. A mathematical model based on the use of a special device is presented. The model allows determining the penetration depth of a viscoelastic system to block water-bearing horizons to prevent interformation crossflows and water breakthrough into production wells.
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Date submitted2020-06-15
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Date accepted2020-06-15
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Date published2020-06-30
Description of steady inflow of fluid to wells with different configurations and various partial drilling-in
- Authors:
- Valery A. Iktissanov
There are many equations of steady inflow of fluid to the wells depending on the type of well, presence or absence of artificial or natural fractures passing through the well, different degrees of drilling-in of the wellbores. For some complex cases, analytical solutions describing the inflow of fluid to the well have not yet been obtained. An alternative to many equations is the use of numerical methods, but this approach has a significant disadvantage – a considerable counting time. In this regard, it is important to develop a more general analytical approach to describe different types of wells with different formation drilling-in and presence or absence of fractures. Creation of this method is possible during modeling of fractures by a set of nodes-vertical wells passing from a roof to floor, and modeling of a wellbore (wellbores, perforation) by a set of nodes – spheres close to each other. As a result, based on this approach, a calculation algorithm was developed and widely tested, in which total inflow to the well consists of the flow rate of each node taking into account the interference between the nodes and considering the impermeable roof and floor of the formation. Performed modeling confirmed a number of known patterns for horizontal wells, perforation, partial drilling-in of a formation, and also allowed solving a number of problems.
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Date submitted2019-08-08
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Date accepted2019-09-16
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Date published2020-02-25
Testing of preformed particles polymer gel technology on core filtration models to limit water inflows
In order to reduce watering of wells and equalize their injectivity profiles, the prospects of introducing PPG technology in Russian fields are considered, in which preformed particles polymer gel are pumped into the injection well. These particles, being a supersorbent based on polyacrylamide, absorb water, become elastic, which allows them to shrink and tear in narrow filtration channels. When the polymer is filtered along permeable layers saturated with water, polymer particles accumulate in waterlogged intervals and thus they form a polymer plug, which redistributes the filtration flows and increases the coverage of the formation by the process of oil displacement. More than 4000 downhole operations have been carried out in the fields of China and the USA using PPG technology by now. In domestic fields in Western Siberia, there is limited experience in applying a similar technology in high-temperature formations with low mineralization of formation water. Due to the absence of hydrolytic processes in polyacrylamide, well-known domestic compositions are not applicable due to the low absorption capacity in the conditions of low-temperature deposits with increased mineralization of formation water. The authors synthesized a polymer based on polyacrylamide by block polymerization, which allows to obtain a high absorption capacity, including for low-temperature formations with high mineralization of formation water, which is typical for Perm Territory fields. Filtration experiments were carried out on core models with the composition developed by the authors, this composition focused on low formation temperatures and high mineralization of formation water. As a result of the experiments, it was found that the swollen particles of the gel are able to pass into fractures with a diameter less than their own size at least 20 times. With a significant increase in the viscosity of the dispersion medium, the stability of the suspension increases. Particles of polymer gel have the necessary strength for injection in the field conditions. The fracture permeability during polymer injection decreases by several times and becomes comparable with the permeability of pore collectors.
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Date submitted2019-07-13
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Date accepted2019-08-31
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Date published2019-12-24
Method for predicting the stress-strain state of the vertical shaft lining at the drift landing section in saliferous rocks
The article proposes a method for predicting the stress-strain state of the vertical shaft lining in saliferous rocks at the drift landing section. The paper considers the development of geomechanical processes in the saliferous rock in the landing area, the support is viewed as a two-layer medium: the inner layer is concrete, the outer layer is compensation material. With this in view, the paper solves the problem of continuum mechanics in a spatial setting, taking into account the long-term deformation of salts and the compressibility of the compensation layer. Long-term deformation of saliferous rocks is described using the viscoplastic model of salt deformation into the numerical model, and the crushable foam model to simulate the deformation of the compensation layer. This approach considers all stages of the deformation of the compensation layer material and the development of long-term deformations of saliferous rocks, which makes it possible to increase the reliability of the forecast of the stress-strain state of the vertical shaft lining.
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Date submitted2019-04-28
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Date accepted2019-06-28
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Date published2019-10-23
Determination of Optimal Fluorine Leaching Parameters from the Coal Part of the Waste Lining of Dismantled Electrolytic Cells for Aluminum Production
- Authors:
- N. V. Nemchinova
- A. A. Tyutrin
- V. V. Somov
When aluminum is obtained by electrolysis of cryolite-alumina melts when the baths are sent for capital repairs, a solid technogenic product is formed – waste lining of electrolytic cells (WLEC). The volume of formation of WLEC is 30-50 kg per 1 ton of aluminum. Currently, it is mainly stored at landfills near industrial enterprises, causing harm to the environment. However, this technogenic raw material contains valuable components (fluorine, aluminum, sodium) that can be extracted to produce fluoride salts, which are in demand during the electrolytic production of aluminum. The objects of research were samples of the coal part of the waste lining of dismantled S-8BM (E) type electrolytic cells of «RUSAL Krasnoyarsk» JSC (Krasnoyarsk) of RUSAL company. According to the X-ray experiment diffraction analysis (using a Bruker D8 ADVANCE diffractometer) of the phase composition of the samples, it was found that the main fluorine-containing compounds are cryolite, chiolite, sodium and calcium fluorides. The total fluorine content in the studied samples averaged 13.1 %. We conducted studies on the leaching of fluorine from WLEC with a solution of caustic alkali (NaOH concentration – 17.5 g/dm 3 ). The process was carried out in a mechanically agitated reactor using a BIOSAN MM-1000 top drive laboratory stirrer with a two-blade nozzle. By the method of mathematical planning of a three-factor experiment, the mutual influence of three leaching conditions on the optimization parameter was established – the extraction of fluorine in solution (in percent). The maximum recovery of fluorine from WLEC to the leach solution averaged 86.4 % and was achieved with the following indicators:processtemperature–95 ° C, the ratio ofliquidtosolidphase–9:1,duration– 210 min.
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Date submitted2019-01-11
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Date accepted2019-03-17
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Date published2019-06-25
Improving methods of frozen wall state prediction for mine shafts under construction using distributed temperature measurements in test wells
- Authors:
- L. Yu. Levin
- M. A. Semin
- O. S. Parshakov
Development of mineral deposits under complex geological and hydrogeological conditions is often associated with the need to utilize specific approaches to mine shaft construction. The most reliable and universally applicable method of shaft sinking is artificial rock freezing – creation of a frozen wall around the designed mine shaft. Protected by this artificial construction, further mining operations take place. Notably, mining operations are permitted only after a closed-loop frozen section of specified thickness is formed. Beside that, on-line monitoring over the state of frozen rock mass must be organized. The practice of mine construction under complex hydrogeological conditions by means of artificial freezing demonstrates that modern technologies of point-by-point and distributed temperature measurements in test wells do not detect actual frozen wall parameters. Neither do current theoretical models and calculation methods of rock mass thermal behavior under artificial freezing provide an adequate forecast of frozen wall characteristics, if the input data has poor accuracy. The study proposes a monitoring system, which combines test measurements and theoretical calculations of frozen wall parameters. This approach allows to compare experimentally obtained and theoretically calculated rock mass temperatures in test wells and to assess the difference. Basing on this temperature difference, parameters of the mathematical model get adjusted by stating an inverse Stefan problem, its regularization and subsequent numerical solution.
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Date submitted2018-11-18
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Date accepted2019-01-17
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Date published2019-04-23
Calculation of elastoviscoplastic displacement of well walls in transversal and isotropic rocks
- Authors:
- A. G. Gubaidullin
- A. I. Moguchev
The relevance of the work is justified by the need to improve the technical and economic indicators of well construction based on forecasting and preventing drilling tools sticking due to the narrowing of an open well bore in the intervals of transversely isotropic rocks. A mathematical model of elastic-viscous-plastic displacement of the walls of inclined and horizontal wells has been developed during the narrowing of the open borehole due to rock creep in the intervals of transversely isotropic rocks. In the program developed based on this mathematical model, the calculation of the elastic-viscous-plastic displacement of the walls of an obliquely directed and horizontal well in the reservoir of argillite from the Western Siberia deposit was carried out. As a result of the calculation, it was established that after opening the rock with bits, the cross-section of the open borehole due to the rock creep eventually takes the form of an ellipse, the small axis of which is in the plane of the upper wall of the well and decreases with time.
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Date submitted2018-09-01
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Date accepted2018-10-28
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Date published2019-02-22
Mathematical modeling of rock crushing and multiphase flow of drilling fluid in well drilling
The aim of the work is a mathematical modeling of the rock crushing during drilling and removal of the drilling cuttings (sludge) to the surface by drilling fluid. The process of rock destruction is described using the mathematical theory of fragmentation. The distribution of sludge particles in size and mass depends on such factors as the properties of the drilled rock, the rate of penetration, the type of bit, and the output power. After the formation of sludge, the process of its removal to the surface is modeled. The drilling fluid together with the rock particles is considered as a heterogeneous multiphase medium in which the carrier phase – the drilling fluid – is a non-Newtonian fluid. The flow of such a medium is described using a mixture model in the framework of the multi-fluid approach. This results in a system of nonlinear partial differential equations, for which a new closure relation is derived. To solve the system, the SIMPLE algorithm is used. As a result, the flow properties are studied with the inclusion of particles of various sizes. In particular, for particles of small size due to the action of plastic stresses in a non-Newtonian drilling fluid, an equilibrium mode arises in which the particles move with the drilling fluid without slipping. This is the fastest mode of delivery of sludge to the surface. The specific dimensions of such particles depend on the parameters of the drilling process. In particular, the appropriate size range can be adjusted by changing the parameters of the drilling fluid.
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Date submitted2016-09-22
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Date accepted2016-11-14
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Date published2017-02-22
Technological problems and fundamental principles of methods of engineering-geocryological exploration during construction and exploitation of wells in permafrost rock mass
- Authors:
- Z. N. Cherkai
- E. B. Gridina
The article describes peculiarities and complicating factors when constructing wells in cryolithic zones. It also presents fundamental principles of methods of pilot parametric drilling for complex exploration of engineering-geocryological conditions of multiple-well gas production platforms. The article describes peculiarities of geophysical examinations within the complex of parametric drilling for clarification and correlation of log sheet, and identifying non-commercial gas reservoirs and interpermafrost head oil-filed water horizons in permafrost rock mass. We defined main ecological issues of parametric drilling and presented potential environment pollutants from well drilling in cryolithic zones. It concludes a list of factors, which should be considered during gas well drilling in northern zones for meeting the «safety – sustainability – low waste» criteria.
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Date submitted2015-08-03
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Date accepted2015-10-06
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Date published2016-04-22
Technical and technological solutions to ensure stability of downhole drilling motors
- Authors:
- M. V. Dvoinikov
- Yu. D. Muraev
The article shows research analysis of engineering and technological solutions that aimed at improving the efficiency of drilling wells using optimization of dynamic of work downhole drill-ing motors. As the technical solutions that reduce vibration, considered two options of construc-tion of the power section. A first embodiment involves the production of a hollow rotor which can reduce its moment of inertia. The second solution is the production of modular rotor, which are changing the eccentricity (misalignment) of rotating parts of the engine. The research of fluctuations throughout the length of the power section of the working bodies and the spindle of the engine, taking into account changes in its energy characteristics has been con-ducted to ensure stable operation of the engine in a well, identifying optimal loading parameters. Indicators of shaft speed ensuring minimum vibration amplitude of the engine has been Iden-tified. Optimal speed range of the rotor to prevent buckling of the BHA and to sustain its operation is shown to be between 15-20 % of the frequency of the engine at idle. The maximum reduction in speed during the drilling process should not exceed 30 % by conducted research.
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Date submitted2009-10-16
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Date accepted2009-12-07
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Date published2010-09-22
Geomechanical and geodynamic problems ассompanying the мining of hydrocarbon deposits
Rock mechanics in petroleum industry is used for determination of geomechanical models of rock mass, calculating parameters of rock subsidence, stability of oil and gas wells, problems relevant to geodynamics. The present paper describes the analytical and numerical analyses of compaction in reservoir, following reduction in filter-capacity performance and well productivity.
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Date submitted2009-10-09
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Date accepted2009-12-12
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Date published2010-09-22
Stress condition of prefabricated tunnel linning with initial release
- Authors:
- E. A. Karasev
3d finite element model of soil and prefabricated tunnel lining interaction with appropriate boundary condition is given in this article. Stresses distribution on inner and outer part of the tunnel lining is analyzed. Relationship between stress state at top and sides of the tunnel lining and deformation module magnitude is shown.
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Date submitted2009-07-25
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Date accepted2009-09-13
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Date published2010-04-22
Specific behaviour of prefabricated tunnel linings
- Authors:
- E. A. Karasev
Analysis of different methods to model prefabricated tunnel lining is done. The description of main advantages and disadvantages of existing method is given. Method of detailing stress state prediction of prefabricated lining based on 3d finite elements method with complicated interaction between lining segment and soil is proposed.
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Date submitted2009-07-17
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Date accepted2009-09-09
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Date published2010-04-22
Numerical modelling of the lining stress stateof column stations without lateral platforms
- Authors:
- D. N. Petrov
- P. A. Demenkov
- D. A. Potemkin
Geomechanical forecast of stress-strain state of deep underground subway station is considered. Static work of structures of subway station based on complex approach is shown, including in situ testing and numerical modelling (finite elements method) during different stages of construction.
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Date submitted2009-07-02
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Date accepted2009-09-11
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Date published2010-04-22
Application of solid oxygen-containing substances for higher productivity of oil wells
- Authors:
- A. T. Karmansky
- E. V. Goncharov
The technological principles and results of realization of exothermal reactions in oil-and-gas productive wells are presented. Unique comfinations of chemical reagents on base of chlorates, saltpetres, etc ensured the simplicity, low prices and efficiency of technological operations for intensive influxes of oil and gas. High efficiency is reached not only due to reduction of oil viscosity and removal of paraffin and asphaltenes, but also due to re-forming of the reservoir rocks by relief of rock pressure and extension of fractures.
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Date submitted2008-10-18
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Date accepted2008-12-24
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Date published2009-12-11
Higher efficiency in drilling of oil and gas wells under complicated conditions
- Authors:
- N. I. Nikolaev
- A. I. Ivanov
The results of researches of properties of the new native waterswelling polymer «Petrosorb» are given. Description is given to the design of plugging-up tool for liquidation of catastrophic absorption of flushing fluid in the course of drilling of oil and gas wells.
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Date submitted1948-07-10
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Date accepted1948-09-24
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Date published1949-11-04
Determination of the density of the stoping zone fastening
- Authors:
- O. B. Bokii
When designing the standards for the consumption of timber for coal mining, it is especially important to correctly determine the consumption of timber for the lining of workings, which is from 50 to 70% of the total timber consumption for coal mining. The purpose of this work is to attempt to provide a method for the theoretical determination of the required density of lining of working faces based on the theory of limiting and equivalent spans developed by V.D. Slesarev. In accordance with this goal, the first two paragraphs of the work provide a brief exposition of the theory of limiting and equivalent spans according to V.D. Slesarev; § 3 provides an application of this theory to the issue of determining the magnitude of rock pressure on the lining of workings with a constant width; § 4 presents the method of successive approximations proposed by the author for calculating the expected pressure on the lining of working faces; § 5 provides a formula for determining the required density of lining of a working face; § 6 provides the results of calculating the pressure according to the proposed method for a specific case of practice—the 1st eastern face at Mine B in the Donetsk Basin.