PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number
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Ivano-Frankivsk Department of Shevchenko Scientific Society
INCREASING THE PRODUCTIVITY OF OIL WELLS IN CONDITIONS OF CONTAMINATION OF THE BOTTOM HOLE ZONE
The efficiency of oil field development is largely influenced by the productive characteristics of wells. One of the main reasons for the decline in oil production rates is contamination of the near-wellbore zone, which occurs during the opening of formations by drilling and subsequent operation of wells. The intensification of hydrocarbon production is a key direction for ensuring the stable development of the oil and gas industry. An effective method for increasing the productivity of oil wells is hydrochloric acid treatment of the near-wellbore zone of the formation. For the conditions of a hypothetical oil well, the effect on oil flow rate of different values of the treated zone radius (0.5; 1; 1.5; 2; 2.5; 3; 3.5; 4 m), the multiplicity of the increase in the permeability of the treated zone (by 1.5; 2; 3; 4; 5; 6; 7; 8; 10 times) and the dynamic viscosity coefficient of oil (2; 5; 10; 50; 100; 200 mPa·s). The research results are presented in the form of tables and graphical dependencies of oil flow rate on determining factors. According to the results of statistical processing of the calculated data for the conditions of the example considered, the optimal value of the radius of the treated zone is about 1.809 m, and the optimal value of the multiplicity of the increase in the permeability of the treated zone is about 3.76 times. At the same time, the optimal values of the radius of the treated zone and the multiplicity of the increase in its permeability almost do not depend on the dynamic viscosity coefficient of oil.
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MODELING THE THERMAL EFFECT ON DEPOSITS WITH HIGH-VISCOSITY OILS
The reasons for using thermal methods to increase oil well productivity in conditions of acute shortage of hydrocarbon raw materials are described. The introduction of cyclic in-situ combustion in fields with a sparse well layout is proposed. To evaluate the effectiveness of the cyclic ICF process and its technological characteristics, mathematical modeling of the process was performed. A mathematical model was developed, described by a system of eight equations with eight unknowns, which are functions of distance and time with corresponding initial and boundary conditions. The calculation of heat exchange between the heat carrier and the skeleton of the porous medium was performed based on a two-temperature model. The mathematical model itself was developed with an emphasis on the temperature conditions in the formation and the phenomena associated with temperature increase. According to the calculation results, depending on the characteristics of oil and productive deposits, there are optimal values for the flow rate and time of air injection and the total volume of air injected, at which the maximum technological effect is achieved in terms of total oil production and the duration of the well's operation at an increased flow rate. The studies conducted indicate the high efficiency of the cyclic intra-formation combustion process.
STUDYING THE IMPACT OF WELL LOCATION ON OIL RECOVERY RATES
Various well placement systems in oil fields were analyzed, and the impact of their configuration on the oil recovery factor was determined. A hypothetical field created in the Petrel simulator was selected as the object of study, for which standard geophysical parameters were set and a model was constructed. As part of the study, a simulation of the field was created, wells were designed, and calculations were made of the impact of their location on development efficiency. The simulation nresults made it possible to assess the relationship between the geometry of well placement and the level of oil recovery from the formation. A geological and hydrodynamic model of the field was constructed, on the basis of which the possibilities for increasing oil recovery were investigated. Three field development strategies were developed and analyzed, and the results were compared in terms of key performance indicators. Based on the results of computer modeling, the most optimal option for further development was determined, ensuring the highest level of oil recovery. The method for increasing oil recovery was selected for a circular well layout system, which, according to the flow rate data obtained, demonstrated the best performance. Thus, the circular well layout system proved to be promising in terms of field development efficiency, uniform reservoir drainage, and rational use of reserves. The results obtained can be used to improve design solutions and increase the productivity of oil fields in real conditions.
REVIEW OF PROMISING SOURCES OF UNCONVENTIONAL HYDROCARBONS IN THE FIELDS OF UKRAINE
Examples of alternative sources of raw materials are given, the features of the geological structure of typical sedimentary basins and deposits are described, possible depths of occurrence and physical and mechanical properties of hydrocarbon-bearing rocks are indicated. The conditions of formation and occurrence of unconventional types of hydrocarbons confined to various structures and formations are analyzed. The definitions of shale gas, shale oil, tight rock gas, coalbed methane, gas hydrates, oil sands, etc. are given. The factors influencing the choice of equipment and technology for oil and gas industry operations are given, taking into account the localization of deposits of each type of unconventional hydrocarbons. In particular, it is noted that the main ones are economic profitability and the cost of the extracted It is shown that today the most promising among all the listed types are shale gas and shale oil due to the fact that technologies for traditional oil and gas deposits can be used for their extraction. It is shown that coalbed methane is a promising associated mineral with significant reserves. An analysis of the conditions for the distribution of gas hydrate deposits in the Azov-Black Sea basin and the prospects for the oil and gas bearing capacity of impact structures in Ukraine is carried out. The issues of environmental protection and ensuring safe working conditions for personnel are briefly considered. The importance of unconventional types of hydrocarbons for increasing the mineral raw material base of the fuel and energy sector of the country is shown. The possibilities of biogas production and application from various sources, in particular organic waste and wastewater, are briefly analyzed.
EXPERIMENTAL ESTIMATION OF DOUBLE AMPLITUDE OF THE OSCIRAL PROCESS OF TORQUE CHANGE ON A BIT
The article aims to establish, based on the results of bench-top experimental studies, the influence of external independent factors, which include axial static load, rotational speed n, stiffness C, and damping coefficient β of the drilling tool, on the double amplitude of the dynamic component of the torque on the bit. Bench studies were made using method ofrational design experiments, so that a combination of studies of independent officials occurs only once. A planned factorial experiment was carried out on sandstone blocks of the Vorotyshchenska Svita, folded between two layers with a hardness of 1440 and 2050 MPa. Constant factors during the drilling period in the bench washes were the type and diameter of three roller bits and the amount of washing liquid (water). The results of the investigations were based on empirical models of multiple nonlinear correlations between the variable amplitude of the colliding process, changing the overturning moment on the bit, and changing agents for inlays. Sand hardness is 1440 and 2050 MPa. An analysis of the influx of changeable officials was carried out to determine the main patterns of change in partial deposits and the type of rock hardness.
LIGHTWEIGHT PLUGGING FLUIDS TO IMPROVE THE QUALITY OF WELL CEMENTING IN THE CONDITIONS OF THE VERKHNYOMASLOVETSKE FIELD OF PJSC “UKRNAFTA”
Analyzing the literature and professional publications, it was found that a significant number of oil and gas fields in Ukraine are classified as hard-to-recover deposits. However, such fields provide a significant amount of production and are a reserve for increasing the production potential. The article provides a brief overview of mining and geological conditions and describes the peculiarities of well construction at the Verkhnyomaslovetske field of PJSC “Ukrnafta”, which belongs to the category of fields with hard-to-recover hydrocarbon reserves. The basic technological solutions were used for cementing production strings are analyzed. Based on the carried researches of typical lightweight plugging muds, the article reveals that these materials do not meet the conditions of high-quality casing and cementing, which is caused by violation of the technological parameters of the plugging mud and low strength characteristics of cement stone. Risks are characterized and disruptions of the technological process during cementing of production casings are identified. A new type of lightweight plugging material with a cement batter density of 1.25 g/cm3 was developed and the main technological parameters of the cement slurry and physical and mechanical properties of cement stone were researched. The designed plugging system was tested in accordance with the technological and thermobaric conditions of wells cementing in the Verkhnyomaslovetske field. The structure-forming features of the developed material were researched. The results of the researches indicate the stability of the plugging system and high strength characteristics of the lightweight plugging material. The X-ray fluorescence spectroscopy and X-ray structural analysis confirmed the forming of the main crystallizing phases of cement stone, which confirms the rapid kinetics of structure-forming of the designed plugging system. Carried complex researches and the obtained results indicate the advantages of the developed plugging material in terms of both technological and operational properties over the base materials.
VIBRATION ISOLATION DEVICES DEVELOPED AT IVANO-FRANKIVSK NATIONAL TECHNICAL UNIVERSITY OF OIL AND GAS AND REGULATORY DOCUMENTS GOVERNING THEIR APPLICATION
The designs of vibration protection devices (VPDs) developed by four groups of scientists from the Ivano-Frankivsk National Technical University of Oil and Gas under the leadership of Doctors of Technical Sciences, Professors P.I. Ogorodnikov, V.I. Vekeryk, L.M. Zamikhovsky and V.M. Moisyshyn are considered. The design features of six vibration protection devices that reduce the vibration levels of rock-breaking tools are analyzed, and the technical characteristics of the considered VSDs are presented. Technological regulations for deepening wells with VZP layouts, developed based on industrial research, and general characteristics of five instructional documents intended for selecting the parameters of the drill string layouts, bottom, and the rotary drilling mode of wells are presented.
Factors for the successful use of fluid baths to eliminate complications during deep well drilling
The article presents data from a comprehensive expert analysis of problems encountered during well drilling in the Carpathian oil and gas region between the 1960s and 2000s. It is noted that, despite the use of drilling fluids with a high inhibiting effect on unstable rocks, conditions may also arise that require the additional use of fluid baths to strengthen these rocks. A review of scientific works devoted to the problem of increasing the effectiveness of the use of liquid baths, both for the elimination of sticking and for the strengthening of unstable rocks, has been carried out. It was noted that most scientific works are devoted to the problem of perfecting the chemical formulations of liquid baths, while some organizational and technical-technological problems have been overlooked by researchers. As a result, the article describes a complete set of works on the installation of liquid baths, from planning to implementation at the drilling site. At the same time, organizational, technical and technological factors and the factor of perfection of the chemical formula of the bath under certain conditions of its application are analyzed. Some directions for improving the effectiveness of eliminating geological complications with the help of fluid baths are proposed, in particular, the direction related to maintaining the stability of the bath in the well during its exposure time. It is indicated at which stages of work on the installation of a fluid bath additional employees of the drilling organization are involved, what their role is in the successful performance of production operations to eliminate complications, and how they form a temporary working group from the point of view of a project approach. An equation is proposed that determines the basic conditions for the use of fluid baths in a well from the point of view of economic feasibility. To develop new chemical formulations for fluid baths, both for eliminating sticking and for strengthening unstable rocks, it is proposed to use the classification of reagents according to O.V. Aniskovtsev.
DETERMINANT METHODS OF OPTIMIZATION OF OPERATING MODES OF GAS TRANSPORTATION SYSTEMS
The principles of studying non-stationary processes in main gas pipelines under conditions of their incomplete loading are considered, which are based on the use of frequency methods, in particular, the construction of amplitude-frequency characteristics under static and dynamic loads. The purpose of the work is to develop methods for rational planning of gas transportation systems operating modes based on the use of frequency characteristics according to the criterion of the minimum duration of the non-stationary process. An equation was analytically obtained that allows establishing the dependence of the propagation speed of small disturbances in the gas flow on the linear coordinate under the conditions of the stationary regime; analysis of the calculation results shows that the discrepancies between the values ​​of the sound speed determined by different methods are 2.1% - 5.8%, and the smaller the real propagation speed of pressure disturbances, the greater the discrepancy between the values. The conducted research will allow to improve the method of diagnosing small leaks from the gas pipeline. A method of using frequency approaches is proposed, which is considered in the problems of applying impedance in the calculations of non-stationary processes, for estimating the frequency range of gas pipeline operation, conducting a simplified analysis of gas pipeline modes, numerical methods for implementing operational equations, in the analysis of gas pipeline operation by statistical dynamics methods, equations of unsteady gas movement through the gas pipeline.
RESEARCH OF THE PROCESS OF NON-NEWTONIAN LIQUID PRESSURE FROM A GAS PIPELINE
The process of cleaning main gas pipelines with cuff-type cleaning pistons from liquid accumulations, which are characterized by non-Newtonian properties, is considered. Based on analytical studies of the nature of the movement of a liquid accumulation under the action of a solid body (cleaning piston) moving at a constant speed, the nature of the distribution of linear velocities over the cross-sectional area of ​​the pipeline and along the length of the moving liquid accumulation has been established. The dependences of the pressure distribution in the liquid phase environment have also been constructed. The obtained regularities of the distribution of linear velocities and pressure over the cross-sectional area of ​​the pipeline and along the length of the moving liquid accumulation, together with the regularities of deformation of the sealing elements of the cleaning device, made it possible to construct a picture of the flow of the liquid phase through the moving boundary into the piston space, which leads to a deterioration in the efficiency of gas pipeline cleaning. The study was conducted to displace water and non-Newtonian fluid from the gas pipeline; Their results show a significant influence of the properties of the liquid accumulation on the magnitude of the flows through the moving boundary, which must be taken into account when planning the cleaning of gas pipelines.
FEATURES OF STRESS-STRAIN STATE CALCULATION FOR COMPLEX SYSTEMS OF OVERHEAD PIPELINE CROSSINGS
The article is dedicated to the improvement of the methodology for calculating the stress-strain state of complex systems of overhead pipeline crossings, particularly two-string multi-span structures where pipelines are positioned one above the other. The relevance of the research is driven by the growing need for laying pipelines in mountainous areas and the necessity of utilizing existing support systems to reduce construction costs. It is shown that traditional approaches, based on simplified assumptions regarding the equality of bending moments in spans and at supports, do not reflect the actual operating conditions of the crossings and can significantly underestimate maximum stresses, especially in the edge sections. The paper develops a detailed methodology that involves the stepwise determination of pipeline geometric parameters and loads from self-weight, product, snow, ice, and wind effects. The stress-strain state of the upper and lower strings is calculated based on the three-moment equation, followed by the determination of support reactions and the construction of bending moment and shear force diagrams. For the lower pipeline, the additional influence from the upper string is taken into account, which is modeled through applied forces equivalent to the support reactions. Special attention is paid to determining deflections: for complex statically indeterminate systems, the initial parameters method is applied, which ensures high accuracy in calculating displacements at any point of the beam. The proposed methodology allows for obtaining reliable values for forces and displacements, which is essential for verifying the strength and stiffness of overhead crossings and ensuring their reliable operation in difficult terrain conditions.
RATIONAL INDICATORS OF GAS TRANSPORTATION BY GAS TRANSPORTATION SYSTEMS UNDER THE CONDITION OF THEIR INCOMPLETE LOAD
The work is devoted to establishing the regularities of technological processes in gas transportation systems for optimizing operational control of operating modes under conditions of their incomplete loading. A mathematical model of non-stationary processes in a gas pipeline was created taking into account the influence of compressor stations on the basis of classical equations of gas flow energy and continuity using Dirac source functions. The implementation of the created mathematical model allowed obtaining in analytical form a dependence that reflects the law of oscillation in time of mass flow and pressure. The constructed dependences of the productivity trend of the gas transportation system at its beginning and at the end showed the influence of the placement of the compressor station in the gas transportation system, in particular its serial number on the route number, on the nature of the non-stationary process caused by its stop, in particular on the duration of non-stationarity.. Based on the research results, a principle of optimizing the operating modes of the gas transportation system under conditions of incomplete loading was proposed according to the criterion of minimum energy consumption for gas transportation at the maximum level of gas supply reliability.,
STUDY OF THE ACCURACY OF EQUATIONS OF STATE FOR PREDICTING THE PARAMETERS OF LEAKAGE OF HYDROGEN GAS MIXTURES UNDER THE CONDITIONS OF GAS DISTRIBUTION NETWORKS
In order to create a scientifically sound basis for improving the methods of calculating the parameters of the leakage of gas-hydrogen mixtures, a quantitative assessment of the accuracy of the common cubic equations of state was carried out. The adequacy of the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) models for determining the physical properties of mixtures under conditions corresponding to the operation of gas distribution networks was investigated. Multivariate thermodynamic modeling of the compressibility factor, adiabatic index and sound speed was carried out in the PVTsim Nova software package. The study was performed for ten different component compositions of natural gas, taking into account the variability of its composition, with a molar concentration of hydrogen from 0 to 20%. Calculations were carried out in the range of absolute pressures from 0.1 to 1.3 MPa and temperatures from 243.15 K to 323.15 K. The obtained data were compared with the reference results calculated using the fundamental equation of state GERG-2008. It was found that both cubic equations of state provide high accuracy for the studied conditions. It was determined that the average relative error for the SRK equation is: for the compressibility factor – 0.23%, for the adiabatic index – 2.31%, for the speed of sound – 1.11%. For the PR equation, the corresponding errors are 1.04%, 1.61% and 0.76%. The key patterns of the influence of pressure, temperature and hydrogen content on the studied properties are identified and quantitatively described. In particular, it was established with a high degree of approximation reliability that the dependence of the speed of sound on the relative density of the mixture under fixed thermobaric conditions is linear. The results of the study confirm that the common cubic equations of state are a reliable and adequate theoretical basis for the development of new methods for calculating production and technological gas costs.
PROSPECTS AND PROBLEMS OF USING HYDROGEN AS AN ENERGY CARRIER
It is shown that the process of using hydrogen additives to natural gas has a number of significant advantages, including an increase in the specific heat of combustion, which significantly reduces (with constant energy demand) the volume of energy supply to the consumer, and a reduction in the harmful effects of combustion products on the environment, since the use of a hydrogen-gas mixture significantly reduces carbon dioxide emissions into the atmosphere. The disadvantages of using hydrogen as an additive to natural gas as an energy carrier include, first of all, the problematic issues of industrial volumes of hydrogen production, associated with energy costs for technological processes; in addition, the presence of hydrogen in pipelines will lead to the process of decarbonization of steel, which will cause a decrease in its mechanical characteristics and ultimately an increase in the accident rate of pipeline transport of the energy carrier; storage of a gas-hydrogen mixture during the non-heating season in the cavity of gas transport mains requires a significant increase in energy costs. The use of hydrogen as an energy carrier on an industrial scale requires significant technical and technological changes in the state's energy system as a whole, which poses a number of important problems for the energy supply system that require an urgent solution; for their implementation, a method for optimizing the use of a gas-hydrogen mixture as an energy carrier according to the criterion of minimum energy costs for pipeline transport is proposed.
MATHEMATICAL MODELING OF NON-STATIONARY GAS FLOW PROCESS IN A GAS PIPELINE CAUSED BY AN EMERGENCY GAS LEAK
The article addresses the pressing issue of estimating gas losses during pipeline transportation, the importance of which has increased during the period of military action due to the risk of external destructive influences. The purpose of the study is to create a mathematical model of the non-stationary gas flow process in a gas pipeline caused by an emergency leak. A model based on the equations of motion and continuity was developed to describe the pressure and mass flow rate oscillations of the gas that occur during leak formation. The system of differential equations is reduced to a linearized equation, which includes the Dirac delta function for modeling concentrated gas withdrawal at the leak point. The solution to the equation is found using the integral sine transformation under initial (stationary linear pressure distribution) and boundary conditions (constant pressure at the beginning and end of the section). Based on the resulting dependencies for pressure and mass flow rate, a methodology for quantitative determination of total gas losses is formulated as the sum of the initial mass of gas in the emergency section and gas overflows from adjacent sections during the time until the linear valves are closed. Numerical calculations of the relative value of gas flow rates are performed, taking into account the overflows. Graphs show that the mass flow rate of gas at valve No. 1's cross-section instantly increases after a leak and then smoothly declines, while at valve No. 2's cross-section, a sharp drop is observed, followed by stabilization and a possible reverse flow. The modeling results ensure improved accuracy in estimating gas losses. The obtained results can be used to improve methods for diagnosing and predicting gas losses in gas transportation systems.
RESEARCH STRESS CORROSION ON PIPE STEELS
As a simple analysis shows, MG (in those areas where stress corrosion is detected) have a large diameter and are operated under high operating pressure. This leads to the fact that the mechanical stress in the MG wall is significantly higher than in the walls of other pipelines. Due to the action of the operating pressure, the annular stress is approximately 2 times greater than the axial stress. This explains the fact that most of the detected stress corrosion cracks are oriented in the longitudinal direction - perpendicular to the largest circumferential stress. Thus, one of the factors determining the conditions for the development of stress corrosion is the presence of high tensile stress in the pipeline wall. Therefore, the closer the stress is to the yield point of the metal, the faster stress corrosion develops. This conclusion is contained in the second name of the phenomenon - stress corrosion cracking. Stress corrosion cracking of main gas pipelines is a consequence of three main processes related in place and time: corrosion (electrochemical), mechanical (deformation) and sorption (adsorption and absorption). Depending on the predominant importance of one or another process, different mechanisms of stress corrosion cracking are possible, including at different stages of crack development. Any dangerous phenomenon on pipelines and methods of protection against it should be indicated in design standards, building codes and regulations. However, as the analysis of documents shows, the current building codes and regulations do not contain any mention of stress corrosion, do not offer measures to protect MG from this type of destruction. However, statistical data on failures on MG make it possible to establish the following: Stress corrosion is observed on gas pipelines Dy> 1020 mm. Failure time due to stress corrosion is from 4 to 26 years. Almost 40% of failures were observed at a distance of up to 25 km from compressor stations. And cathodic polarization can both slow down and accelerate the development of corrosion cracks.
THE INFLUENCE OF STATIC FORCES AND INITIAL CONDITIONS ON GAS PIPELINE DEFLECTIONS DURING THE PASSAGE OF A CLEANING PISTON
When cleaning pistons pass through gas pipeline beam crossings, forced oscillations of the pipe axis occur. It is important to take into account all the force factors associated with these vibrations, starting with static forces. In this paper, only static forces are taken into account, namely the weight of the pipes at the beam transition and the weight of the cleaning piston. The aim of the study was to determine the deflections of the pipeline axis and the bending moments of their pipes at the beam transition during the passage of the cleaning piston through it, with and without the initial condition. The initial condition is caused by the weight of the pipes at the transition and causes the deflection of the pipeline axis and bending moments of its pipes before the cleaning piston enters the beam transition. This condition was obtained as a result of solving a fourth-order differential equation with consideration of the boundary conditions corresponding to the pinching of the ends of the beam transition pipes. The problem was solved by the Fourier method. The eigenfunctions of the problem of free oscillations of the beam were used. The right-hand side of the inhomogeneous differential equation was represented as an infinite series of the product of the eigenfunction of the free oscillations of the beam and an unknown time function. After finding this unknown time function, the Fourier method was used to obtain the solution of the problem in the form of deflections of the axis of the beam transition, taking into account the initial condition. In the obtained solution, the deflections of the axis of the pipes of the beam transition caused by the initial condition are represented by a polynomial, and the deflections caused by the passage of the cleaning piston through the transition are obtained as an infinite sum. By performing a double differentiation of the deflection function of the axis of the beam transition, the function of bending moments of pipes at the gas pipeline transition is found, taking into account the initial condition. Using the analytical formulas for the deflections of the pipe axis at the beam transition and the bending moments of their pipes, the deflections of the gas pipeline axis at the beam transition and the bending moments were calculated both with and without taking into account the initial condition. Analysing the results, it should be noted that the deflections caused by one initial condition are three times higher than the deflections caused by the passage of the cleaning piston through the transition. The maximum deflections correspond to the cross-sectional area of the crossing x = 15 m. The maximum deflection caused by one initial condition is 6.2 mm, and the total maximum deflection is 8.2 mm. The maximum deflection caused by the cleaning piston itself is 2 mm. The curves in the bending moment plot for different time points are close together. This indicates that the passage of the cleaning piston through the transition has little effect on the value of the bending moments of the pipes at the transition. The maximum modulus values of the bending moments of the pipes at the transition, with and without taking into account the initial condition, are -183.2 kN∙m and -50.02 kN∙m, respectively. Keywords: beam transition; differential equation; bending moments of pipes at the transition.
IMPROVING GAS SUPPLY RELIABILITY BASED ON IMPROVING TECHNICAL
The operational reliability of the gas transportation system is considered from the point of view of providing consumers with energy carriers in specified volumes. The purpose of the study is to establish the trends in the technical condition of gas transportation systems and, on their basis, to develop a principle for calculating the time of trouble-free operation and the terms of technical maintenance to ensure a given level of reliability. A mathematical model for determining the reliability of a gas transportation system based on the simplest failure flow of the linear part and control systems is obtained, shown and considered on a practical example of the methodology as a calculation of the terms of technical research to ensure a given reliability of gas supply. Based on the conducted studies in production conditions, it is established regularity of influence of external factors, in particular barometric pressure, temperature and humidity of atmospheric air, as well as relative density of fuel gas on power and economy of gas pumping units, which will allow to ensure effective operation of compressor station as an element of gas transportation system. It is shown on the basis of statistical research that influence of natural factors depends on failure of gas pipeline route.
PRINCIPLES OF THERMAL-HYDRAULIC CALCULATIONS OF HEAT PUMP CONNECTION SYSTEMS
The article is devoted to the principles of thermal-hydraulic calculations of a heat pump (HP) connection system that utilizes low-potential heat sources for the energy-efficient heating of high-viscosity crude oil during its transportation through main pipelines. The transportation of high-viscosity oil requires continuous heating due to its cooling in the soil and the associated risk of pipeline blockage. Traditional heating methods based on fuel combustion are energy-intensive and environmentally hazardous. Therefore, this study examines the use of heat pumps that convert low-potential heat into higher-temperature heat to maintain the required pumping regime. The main purpose of the research is to develop a methodology for designing the heat-exchange equipment of this system, which includes the installation of an additional recuperative heat exchanger in the first (brine) circuit of the heat pump. The paper provides a detailed algorithm for thermal-hydraulic calculations covering: determination of the geometric parameters of the recuperative heat exchanger; selection and calculation of the physical properties of the working fluid for the brine circuit; hydraulic calculation of the brine circuit and pumping unit for hot heat carrier supply, including pump selection; and constructive thermal calculation of the recuperative heat exchanger. The calculation concludes with a comparison of the calculated and actual heat-exchange areas to refine the design. The proposed methodology makes it possible to optimize the design of heat-exchange equipment and ensure reliable and energy-efficient operation of the oil heating system.
RATIONAL MAINTENANCE OF GAS PUMPING UNITS AT THE COMPRESSOR STATION OF AN UNDERGROUND GAS STORAGE
A mathematical model for determining the reliability of a compressor unit based on the simplest failure rate is obtained, shown and considered on a practical example, a methodology for predicting the technical condition of the machine and based on technical diagnostics with the aim of ensuring the specified reliability. Based on mathematical modeling of the optimization process of servicing piston gas pumping units in the conditions of compressor stations of underground gas storage facilities, the dependences of the influence of production factors on the power and efficiency of the unit were obtained, which allow us to determine the rational operating modes of piston gas pumping units in the conditions of compressor stations, which made it possible to propose a methodology for selecting rational operating modes of piston gas pumping units. The objective function of increasing the efficiency of operation of piston gas pumping units when conducting parametric diagnostics of the compressor cylinder was constructed and the permissible energy losses and the maintenance interval for the components of the cylinder cavity of the compressor cylinder were determined.
ANALYSIS OF THE CHARACTERISTICS OF INTERNAL COMBUSTION ENGINES OF CONSTRUCTION MACHINES USED IN THE CONSTRUCTION AND REPAIR OF PIPELINES
The internal combustion engine is a key invention that has determined the development of transport. Its simplicity, power and versatility have made it indispensable in all sectors of the economy. In internal combustion engines, fuel burns directly inside the working cylinder or in the combustion chamber of the engine. This engine is compact and much more efficient than other types of engines. They are chosen depending on whether the machine is mobile or stationary, as well as on the nature of the loads that arise during the operation of the machines and the duration of the load on the drive systems of the machine components. Internal combustion engines are the main type of power plants used in machines for the construction and repair of pipelines. This type of engine has advantages over other engines: low specific gravity (weight to power ratio), constant readiness for operation, high efficiency, the ability to adjust the engine speed. The disadvantages of internal combustion engines include: the inability of the engine to withstand heavy overloads, the inability to start under load, and shorter durability compared to other types of engines. Despite the development of alternative types, internal combustion engines will remain in use for a long time due to: a wide and developed infrastructure, relatively low cost of the car fleet, greater range and refueling speed, ease of use.
ANALYSIS OF THE INFLUENCE OF NATURAL GAS COMPRESSIBILITY FACTOR DETERMINATION METHODS ON THE VOLUME OF PRODUCTION AND TECHNOLOGICAL GAS LOSSES IN THE GAS TRANSMISSION SYSTEM
The article presents a comparative analysis of the current Ukrainian regulatory methodologies (based on SOU/NDTOV) and the international reference standard (ISO 20765-1/AGA8) for determining the volume of production and technological gas losses (PTL) that occur during planned maintenance operations on main gas pipelines. The critical influence of the gas compressibility factor (Z) on the accuracy of the final calculated PTL volume is investigated. The relevance of the study is dictated by the exceptional strategic importance of the Ukrainian Gas Transmission System (GTS). Given the unstable loading and high wear of the infrastructure, the regular execution of planned preventative maintenance (PPM) is an indispensable condition for ensuring reliability. Every such operation involves technological gas losses, the volume of which, according to regulations, is determined by calculation. The accuracy of these calculations directly affects the formation of the fuel and energy balance of the GTS Operator. Underestimation or overestimation of PTL volumes leads to financial risks and distortion of performance data regarding operational efficiency. Particular attention is paid to the gas compressibility factor (Z), which is a key parameter for converting gas volumes from operating conditions to standard conditions. The use of simplified formulas, which do not account for the full chemical composition of the gas, creates a systematic error. Minimizing this error is a direct pathway to enhancing market transparency and energy efficiency. In the context of European integration processes, the alignment of national calculation methodologies with international standards becomes a matter of primary importance. Thus, ensuring maximum accuracy in PTL accounting is a critical task for the financial sustainability and technical reliability of the Ukrainian GTS. Based on hypothetical initial data for a typical section of a main gas pipeline, it is demonstrated that the application of the simplified methodology (Method 2) leads to systematic gas under-accounting, as its calculated coefficient significantly differs from the reference one.
ANALYSIS OF METHODS AND DEVICES FOR INCREASING THE EFFICIENCY OF STORAGE OF OIL AND OIL PRODUCTS IN TANK TANKS
During the storage of oil and petroleum products in tanks, significant bottom sediments of paraffin and various impurities accumulate over time. The sediment falls out within 1-2 months and compacts into a solid mass within about 6 months. When storing oil and petroleum products in tanks, there are two most popular methods of combating bottom sediments: periodic decommissioning of the tank (emptying), its preparation and removal of accumulated bottom sediments; the use of various additives and devices to prevent sedimentation.
MODELING OCCUPATIONAL AND MILITARY RISKS FOR SAFETY AND CIVIL DEFENSE IN THE OIL AND GAS SECTOR
Функціонування нафтогазових підприємств України відбувається в умовах безпрецедентного поєднання традиційних промислових небезпек та прямих військових загроз. Повномасштабна агресія перетворила об'єкти галузі на мішені для ракетних та безпілотних атак, що може ініціювати каскадний розвиток техногенних катастроф. Існуючі моделі управління ризиками є критично недостатніми, оскільки вони не були розроблені для протидії навмисним зовнішнім впливам та не враховують синергетичний ефект поєднання виробничих збоїв з військовими загрозами. Це створює нагальну науково-практичну проблему, яка потребує негайного вирішення для забезпечення стійкості критичної інфраструктури. Розробити науково-методичний підхід до комплексної оцінки ризиків на нафтогазових підприємствах, який, на відміну від існуючих, враховує синергетичний вплив традиційних виробничих факторів: техногенних, організаційних, людських та прямих військових загроз. Розробка такого підходу дозволить науково обґрунтувати пріоритетні превентивні заходи, спрямовані на підвищення стійкості та захисту об'єктів у умовах воєнного часу. Підхід базується на синтезі системного аналізу, положень стандарту ISO 31000 та елементів кількісної оцінки ризиків. Запропоновано комплексну класифікацію внутрішніх виробничих та зовнішніх військових ризиків. Кожен окремий фактор ризику кількісно оцінюється за класичною формулою, яка враховує ймовірність його виникнення та тяжкість потенційних наслідків, визначених шляхом організованої експертної оцінки. Розроблено модель, яка дозволяє розраховувати інтегральний показник ризику як зважену суму середніх ризиків для кожної групи з урахуванням їх стратегічної важливості, що визначається ваговими коефіцієнтами. Тестування моделі на прикладі компресорної станції продемонструвало її практичну застосовність та показало, що в сучасних умовах найбільший внесок у загальний рівень небезпеки вносять фактори прямого військового впливу та людський фактор, посилений психологічним стресом. Запропонований підхід слугує інструментом модернізації корпоративних систем управління промисловою безпекою та цивільним захистом. Він дозволяє обґрунтувати інвестиційні пріоритети у фізичний захист об'єктів, психологічну підтримку персоналу та адаптацію стратегій безпеки до динамічних умов воєнного часу. Модель може бути масштабована для інших секторів критичної інфраструктури в Україні.
ASSESSMENT OF PARAMETERS OF THE AREA OF GAS CONTAMINATION OF THE SOIL DURING EMERGENCY GAS LEAKS FROM GAS PIPELINES
The article considers the problem of emergency leaks of natural gas from gas pipelines caused by corrosion damage to the pipe walls, and their impact on the environment. It is shown that during the leak, the gas enters the soil, forming an area of ​​gas contamination, which over time spreads to the surface, polluting the atmosphere. The magnitude of the leak, its intensity and the depth of the gas pipeline determine the speed and nature of the formation of the gasification zone. A significant role is played by the filtration properties of the soil, in particular its permeability and resistance to the movement of gas in the pores, which determines the complex nature of the relationship between gas leaks and the laws of its filtration. In addition to material losses associated with the loss of gas, leakage processes cause soil contamination, a decrease in its ecological quality and a potential explosion hazard when critical concentrations of methane in the air are reached. The paper analyzes existing studies devoted to the diagnosis of leaks by temperature changes in the soil, determining its filtration characteristics and modeling non-stationary filtration processes. At the same time, it is noted that there are no comprehensive studies in the scientific literature that combine the analysis of gas leakage from the pipeline and the formation of the contamination area. Analytical studies of the process of gas leakage through a corrosion hole and modeling of the formation of the area of ​​soil gasification were carried out. A mathematical model was proposed that allows determining the time parameters of gas filtration to the soil surface, the volume of the formed gasification zone and the amount of gas losses. Particular attention was paid to the two-phase nature of the process - the period of gas reaching the soil surface and the subsequent stationary stage of filtration. The results of the study can be used in assessing the technical condition of gas pipelines, predicting the consequences of emergency situations, developing leak monitoring systems and improving methods of environmental safety of gas distribution networks.
IMPROVEMENT AND RESEARCH OF WELLBORE PACKER SEAL
The article describes the problem of increasing the tightness of the seals of well packers, which are important elements of operational and technological equipment of oil and gas wells. Packers isolate separate well intervals, which is necessary to perform technological operations, such as hydraulic fracturing of a productive horizon, injection of water or gas to maintain productive horizon pressure, carry out thermal and acid treatments and tests of casing and mouth equipment. The effectiveness of these processes, the safety of staff and the prevention of accidents in the well depends on the tightness of the packer. The article analyzes the design of the packers sealing units and the factors that affect their work. It is shown that the main problem when using traditional smooth rubber cuffs is the uneven distribution of contact stresses along the surface of the seal. This is the cause of intense wear of rubber, reducing tightness and increasing the risk of breakthrough of the working environment. It is established that seals materials should meet the requirements for resistance against aggressive environment, high temperatures and pressures, as well as deformation. To study the functioning of the sealing unit, simulation modeling was made by the method of finite elements using a model of Muni -Rivlin, which adequately describes the nonlinear behavior of rubber materials. The model allowed to determine the distribution of contact pressure between the cuff and the casing, as well as to evaluate the effect of the geometry of the seal, the friction coefficient and the installation efforts on the tightness of the system. On the basis of modeling results, an advanced structure of the sealing element with a corrugated surface was developed, which provides a more uniform distribution of stresses and increase contact pressure in contact areas. Our research have shown that the use of a corrugated cuff allows to increase the sealing capacity by 15-20% with the same or smaller installation efforts regarding to a standard smooth seal. It is also established that the increase of the friction coefficient between the rubber and the metal surface causes partial unloading of the upper seal, which can cause loss of tightness. To reduce this effect, it is recommended to use special lubricants and surface coatings that provide stable friction and improve the fit of the cuffs to the casing. The results of the article have of great practical importance for improving the new generation well packers.
EFFECT OF TEMPERATURE ON THE STRESS-STRAIGHTENING STATE OF A TWO-SUPPORT LOCKING THREADED CONNECTION OF WEIGHTED DRILL PIPES
The article presents the results of a study of the effect of temperature on the stress-strain state of a screwed two-support lock threaded connection of weighted drill pipes. It has been established that temperature significantly affects the geometric parameters, fit accuracy, and strength of threaded connections, since thermal expansion changes the tightening forces that determine the tightness and durability of the connection. For the study, a three-dimensional model of an NC50 double-support connection was constructed, which takes into account the effect of the temperature gradient (from 20 °C inside to 100 °C outside) and the tightening torque. Modeling was performed in SolidWorks FlowSimulation with subsequent export of thermal loads to Simulation to determine the stress-strain state. It was shown that the temperature distribution in the connection is uneven. A comparative analysis of the distribution of equivalent stresses in the recesses of the nipple coils, taking into account the temperature gradient and the tightening torque, showed both their increase and decrease relative to the case of only the tightening torque acting on a two-support ZRZ. This confirms the significant influence of the temperature field on the stress-strain state of the connection. The greatest reduction in stresses is observed in the first and last threads of the nipple, which can contribute to an increase in the durability and fatigue strength of the threaded connection, but at the same time there is a possibility of deterioration in its tightness. The results obtained are consistent with known experimental data and confirm the feasibility of taking thermomechanical factors into account when calculating the strength of drill strings. The modeling method used can be adapted to analyze other types of oil and gas equipment connections, in particular pump and compressor pipes and casing pipes operating in high-temperature conditions, with a view to further improving them to increase reliability, durability, and operational safety.
MEASURES TO PREVENT EXPLOSION AND FIRE HAZARDS IN THE OIL AND GAS INDUSTRY
One of the main dangers of the oil and gas industry is a sufficiently high level of risk of explosions and fires caused by the presence in the processes of extraction, transportation and storage of significant masses of hydrocarbons, which under certain conditions can create explosive and fire-hazardous concentrations of flammable gases or vapors. To prevent the occurrence of such conditions, safety regulations provide for a number of design and planning standards and means of a technical, technological and organizational nature. Ventilation of explosion-hazardous premises plays an important role in preventing the occurrence of dangerous situations. One of the important purposes of ventilation is to prevent the formation of explosive concentrations of flammable gases, vapors or dust. Therefore, the prevention of explosion and fire hazards in the oil and gas industry is relevant. The purpose of the work is to clarify the methodology for determining indicators that regulate explosion and fire hazards at fuel and energy complex facilities. To achieve the set goal, the following tasks were solved: substantiation of the definition of indicators regulating explosion and fire hazards at oil and gas facilities and measures to prevent explosion and fire hazards. Due to certain terminological and substantive changes that have occurred during the formation of the regulatory framework for labor protection in recent decades, the definition of the lower concentration limit of explosion and the lower concentration limit of flame propagation, which regulate explosion and fire hazards, requires clarification. Measures to prevent explosion and fire hazards within working areas that do not have spatial restrictions are based primarily on controlling air gas contamination in order to promptly detect dangerous concentrations and prevent the presence of sources of ignition (ignition) of gas-air mixtures in dangerous areas (principles of "concentration and localization"). Measures for preventing explosion and fire hazards within working areas that do not have spatial restrictions are presented, and a refined methodology for determining indicators that regulate explosion and fire hazards at fuel and energy complex facilities is provided. Keywords: Exhaust emergency ventilation, concentration, probability of mixture non-ignition, degree of mixture heterogeneity, explosive situation.
To the theorem on differentiation of inequalities between convex functions
The following statement is proved in the article: For any constant $K > 1$, there exist upper unbounded convex functions $f$ and $g$ on $[0;+\infty)$ such that the inequality $f(x) \le g(x)$ holds for all $x \ge 0$, and for the set $$ E_1=\{ x \ge 0\,:\, f_{+}^{'}(x)\le K g_{+}^{'}(x) \} $$ holds $$ dE_{1} =\varliminf\limits_{R\to +\infty}\frac1{R}\text{\rm meas }(E_1\cap[0,R])=\frac {K-1}{K}, $$ where $f_{+}^{'}$ and $g_{+}^{'}$ are the right-hand derivatives of the functions $f$ and $g$, respectively.
STRUCTURE OF CONTINUOUS SYMMETRIC POLYNOMIALS ON THE SPACE OF ABSOLUTELY SUMMABLE SEQUENCES
The work is devoted to the study of symmetric continuous homogeneous polynomials on the Banach space $\ell_1$ over the field $\mathbb{K}\in\{\mathbb{R}, \mathbb{C}\}$ of all absolutely summable sequences of elements of $\mathbb{K}.$ We consider the notion of symmetry in the following sense. Every bijection $\tau$ on $\mathbb{N}$ generates some isometrical isomorphism $J_\tau: \ell_1\to\ell_1$ that rearranges elements of the standard Schauder basis according to $\tau.$ As a result, every subgroup $S$ of the group of all bijections on $\mathbb{N}$ generates the group $G_S$ of corresponding isometrical isomorphisms on $\ell_1.$ The structure of $G_S$-symmetric homogeneous continuous $\mathbb{K}$-valued polynomials on $\ell_1$ is investigated in the present work.
ON THE ABSENCE OF AN EXCEPTIONAL SET IN THE RELATION FROM WIMAN’S THEOREM
Let $S(a,b),$\ $-\infty\le a<b\le +\infty,$\ be a class of functions analytic in $\Pi(a,b)=\{z: a<\text{\rm Re}\, z<b\}$ such that $$(\forall x\in(a,b))\colon\ M(x,F):=\sup\{|F(t+iy)|: a<t\le x, y\in{\mathbb R}\}<+\infty,$$ and $L(x,F)=(\ln M(x,F))'_+$ is the right derivative. By $S_{\infty}(a,b)$ we denote a subclass of the class $S(a,b)$, which consists of those functions $F\in S(a,b),$ such that $ L(x,F)\to +\infty \quad (x\to b-0)$, and by $S_0$ we denote the class of functions $F\in S_{\infty}(0, +\infty)$ for which there exists a function $\delta(r)\colon\mathbb{R}_{+}\to \mathbb{R}_{+}$ such that $\delta(r)\nearrow +\infty$ $(0\leq r\uparrow +\infty)$ and the inequality $$\big|L\big(r\pm \delta(r)/L(r,F),F\big)-L(r,F)\big|\leq L(r,F)/\delta(r) \quad (r\geq r_0) $$ is satisfied. Let $$B_{F}(r)=\sup\{\hbox{Re~}F(z)\colon \hbox{Re~}z<r\},\quad A_{F}(r)=\inf\{\hbox{Re~}F(z)\colon \hbox{Re~}z<r\}. $$ The following theorem is proved: Let $F\in {S}_0$, then the asymptotic relations $$ M(r,F)=(1+o(1))B_{F}(r)=-(1+o(1))A_{F}(r), $$ hold as $r\to +\infty.$
IDENTIFICATION OF FUNCTIONS IN HARDY SPACE ON A HALF-STRIP DOMAIN
This paper explores a signal identification problem using a convolution. We identify the signal with some function belonging to the Hardy space in a domain outside the half-strip. For this, we use a test function belonging to the Hardy space in the half-strip. Signals generated by point singularities and singularities generated by a segment are considered. The exponential test functions are chosen. For some cases, the exact solutions are found, for others, a convolution is found, and the possibility of finding the desired signal is analyzed.
ON SOME COUNTABLY GENERATED ALGEBRA OF ENTIRE FUNCTIONS OF BOUNDED TYPE ON THE SPACE OF ALL BOUNDED SEQUENCES OF COMPLEX NUMBERS AND ITS SPECTRUM
Let $\ell_\infty$ be the complex Banach space of all bounded sequences of complex numbers. In this paper we study the Fr\'{e}chet subalgebra $H_{b\mathcal{P}}(\ell_\infty)$ of the Fr\'{e}chet algebra of all entire functions of bounded type $H_b(\ell_\infty),$ generated by some fixed countable set $\mathcal{P}$ of continuous algebraically independent complex-valued homogeneous polynomials on the space $\ell_\infty$ such that the set $\mathcal{P}$ contains an infinite number of elements that share the same degree of homogeneity. We investigate the form of elements of this subalgebra. Furthermore, we show that every linear multiplicative functional, acting from $H_{b\mathcal{P}}(\ell_\infty)$ to $\mathbb{C},$ can be uniquely identified with the sequence of its values on the elements of $\mathcal{P}$ and we prove that this sequence grows no faster than some geometric progression. We use these results to describe the spectrum of the algebra $H_{b\mathcal{P}}(\ell_\infty).$
SUBSYMMETRIC LINEAR CONTINUOUS FUNCTIONALS ON SPACES OF LEBESGUE INTEGRABLE FUNCTIONS ON THE SEMI-AXIS
The work is devoted to the study of subsymmetric continuous linear functionals on real and complex topological vector spaces of Lebesgue integrable functions on the semi-axis. We consider the class of such spaces satisfying some natural conditions. The complete description of the structure of a subsymmetric continuous linear functional defined on an arbitrary representative of this class has been found. Specifically, we show that every such a functional can be represented as an integral of its argument up to multiplication by a constant.
STRUCTURE OF DEFECTIVE VECTORS FOR ASSOCIATED ENTIRE CURVES WITH LINEARLY DEPENDENT COMPONENTS
We study the structure of the set of exceptional vectors in the sense of Nevanlinna for associated entire curves of finite order with linearly dependent components. It is shown that even if an entire curve has linearly independent components, its associated entire curve may nevertheless have linearly dependent components. It is known that the set of all Nevanlinna exceptional vectors of a finite-order entire curve with linearly dependent components, together with a given subspace }$A_0=\left\{\overrightarrow{a}\in {\boldsymbol{C}}^p:\overrightarrow{G}\left(z\right)\cdot \overrightarrow{a}?0\right\}$\textit{, can be expressed as at most a countable union of subspaces }$A_j$\textit{, satisfying }$\omega\le \mathrm{dim} A_j\le p-1$\textit{ and }$A_j\supset A_0$\textit{. Furthermore, it is established that the corresponding associated entire curve }${\overrightarrow{G}}_l:\boldsymbol{C}\ \to {\boldsymbol{C}}^q$, where $q=C^l_p$, also has $\omega^*\ge C^l_p{-C}^l_{p-\omega}$\textit{ linearly dependent components. For this associated entire curve, the set of its Nevanlinna exceptional vectors, together with the subspace }${\mathrm{A}}^*_0=\left\{\overrightarrow{b}\in {\boldsymbol{C}}^q:\overrightarrow{G}\left(z\right)\cdot \overrightarrow{b}\equiv 0\right\}$\textit{, constitutes at most a countable union of subspaces }${\mathrm{A}}^*_j$\textit{ of dimension not exceeding }$\mathrm{q}\mathrm{-1}$\textit{, where }${{\mathrm{A}}^*_j\supset \mathrm{A}}^*_0$\textit{. In addition, for each }${\mathrm{A}}^*_j$\textit{, there exists a so-called special vector }${\overrightarrow{b}}_j\in {\boldsymbol{C}}^q$\textit{, orthogonal to }${\mathrm{A}}^*_j$.
DIRICHLET PROBLEM IN A HALF-SPACE FOR EQUATIONS OF THE DIFFUSION TYPE WITH INERTIA
The article investigates the first boundary value problem in a half-space for an equation of the diffusion type with inertia, where inertia depends on four groups of variables with degeneracy of parabolicity, each group is subordinated to a certain number of variables. To establish the existence of solutions of boundary value problems, the limit transition and asymptotic expansion of the equation are used. We investigate the first boundary value problem in a half-space for a degenerate parabolic equation of the diffusion type with inertia. We use the explicit form of the fundamental solution of the Cauchy problem and the properties of its derivatives for a degenerate parabolic equation, and by the method of potentials we reduce the first boundary value problem in a half-space to the solution of the corresponding singular integral equation in classes of exponentially decreasing differential functions, such that the integral operator is a compression operator for small t. The uniqueness of the solution of the first boundary value problem in a half-space follows from the maximum principle in classes of bounded functions. In this article we have established the existence and uniqueness of the solution of the Dirichlet problem for one class of degenerate equations of the diffusion type with inertia in the case of three groups of degenerate variables, by the method of potentials. The uniqueness of the solution of the problem follows from the maximum principle in classes of bounded functions.
FINITE AND INFINITE ELEMENTARY DIVISORS IN THE CONSTRUCTION OF FACTORIZATIONS OF SYMMETRIC POLYNOMIAL MATRICES
In many applied problems, factorization of symmetric polynomial matrices with real and complex coefficients is used to construct synthesized locally optimal control, to construct integrated systems of classical mechanics, in particular, to solve the Euler-Arnold problem of the motion of a multidimensional rigid body, billiards in spaces of constant curvature. For -symmetric polynomial matrices, the conditions for factorization with a singular factor with a predetermined canonical Smith form and a system of infinite elementary divisors over a ring with involution are obtained. The correspondence between the factorizations of -symmetric singular polynomial matrices and -symmetric regular polynomial matrices is established, which is carried out using the concepts of the reversal and -reversal matrix polynomials and the system of infinite elementary divisors. This correspondence is based on the properties of the transformations of the reversal and -reversal of matrix polynomials and the concept of infinite elementary divisors of a factorized matrix. Necessary and sufficient conditions for the existence of a factorization of a -symmetric invertible matrix of degree , in which the factor is an invertible polynomial matrix and has degree , are obtained. In such factorizations, the condition is satisfied that the sum of the powers of the factored factors is equal to the power of the factored matrix. If this condition of equality of degrees is not satisfied, then the existence of a factorization of a -symmetric invertible matrix is connected with the existence of an inadmissible factorization of a -reversal polynomial matrix. Keywords: regular polynomial matrix, factorization of -symmetric polynomial matrix, the Smith canonical form, reversal and -reversal matrix polynomial, finite and infinite elementary divisors.
RESEARCH OF THE MODULUS OF ELASTICITY OF CEMENT STONE BASED ON PORTLANDCEMENT PCT-IG USING CORRELATION-REGRESSION ANALYSIS
This paper presents the results of a comprehensive study of the influence of the physico-mechanical properties of cement stone on its elastic modulus using correlation-regression analysis methods. The research was conducted considering curing temperature regimes simulating real conditions of well cementing in the oil and gas industry. The main focus was on establishing the relationship between prism strength, deformation parameters, and the elastic modulus. For this purpose, three types of regression models were constructed and analyzed: the full model, the simplified model (Backward Elimination), and the Lasso regression model. The application of these approaches allowed not only to identify the key predictors but also to assess their significance under different temperature conditions. Special attention was paid to model diagnostics: testing the normality of residuals, presence of autocorrelation, and heteroscedasticity. Model validation was performed using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). The results demonstrated that prism strength is the primary factor determining the elastic modulus, while deformation parameters have a secondary influence, which increases with temperature rise. This highlights the necessity of considering the temperature factor when predicting the mechanical properties of cement stone. The practical significance of the research lies in the possibility of applying the obtained dependencies to optimize the composition of well cementing slurries, taking into account specific geothermal conditions of wells. This will contribute to enhancing the durability of the cement sheath, reducing the risk of intercolumn flows, and ensuring the integrity of the casing. Thus, the study contributes to the development of predictive methods for the mechanical properties of cement stone and has both theoretical and practical relevance for the oil and gas industry.
MODELING HEAT AND MASS TRANSFER DURING THE MASSECUITEDRYING PROCESS VIA SYSTEM OF TWO LINEAR PARABOLIC EQUATIONS AND THE LANGMUIR EQUATION
The paper presents a mathematical model of massecuite drying in a rotary drum dryer, taking into account heat and mass transfer between the gas and solid phases. A system of differential equations was developed to describe the temperature and moisture dynamics of massecuite along the drum length, considering its inclination angle and rotation speed. The model incorporates real dryer geometry, kinetic properties of the material, microstructural characteristics of sucrose crystals, and the convective nature of heat transfer. Numerical simulation was performed using Langmuir equations to represent adsorption–desorption phenomena on the particle surface. An analytical dependence was derived to determine the optimal drying zone length for various drum inclination angles (α = 2–6°) and air velocities (u = 1–3 m/s). Graphical results show a nearly linear decrease in air temperature and a nonlinear increase in massecuite temperature along the drum. The modeling results confirmed the adequacy of the developed mathematical model and enable evaluation of the effect of key technological parameters on drying efficiency. The proposed approach can be applied to the design and optimization of rotary drum dryers in the sugar industry. Keywords: massecuite, rotary drum dryer, heat and mass transfer, mathematical model, Langmuir equation, convection, inclination angle, temperature, moisture
IMAGE PROCESSING BY KRAVCHUK POLYNOMIALS: OPEN QUESTION
The study focuses on constructing spectral models of functions based on classical orthogonal polynomials, particularly Kravchuk polynomials, which serve as discrete analogs of continuous orthogonal bases. The use of such bases increases computational stability and speed, reduces approximation errors, and ensures the analytical representation of diagnostic signals in digital form. Discrete-variable bases are shown to be the most suitable for the development of software in non-destructive testing and diagnostic systems, as they eliminate the need for complex numerical integration. Special attention is paid to the analytical properties of Kravchuk polynomials, their recurrence relations, and their potential application in spectral transformations of functions. The problem of applying Kravchuk polynomials of several variables for image/speeach processing is formulated.