To reduce the risks of making erroneous decisions aimed at improving the efficiency of oil deposits development in the carbonate reservoirs of the Volga-Ural oil and gas province, it is proposed to use the analogy method. An algorithm has been developed that allows using analog objects or groups of them to solve various fishing tasks. The search is proposed to be carried out using 20 parameters characterizing the geological, physical and physico-chemical properties of the formations and the fluids saturating them. The deep differentiation of objects allows to increase the degree of identification of objects.

Keywords: Volga-Ural oil and gas province; analogy method; differentiation; grouping; carbonate reservoirs.

Date submitted: 19.02.2024     Date accepted: 28.05.2024

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Hydrocarbon accumulations in the Lower Pliocene Productive Series of Apsheron Peninsula have formed owing to subvertical hydrocarbon migration from the underlying Maykop and Diatom source formations. This concept has been substantiated by the recent studies based on the molecular-isotopic characteristics of organic matter, oil and gas. The most notable feature of the Apsheron oils is the stable predominance of paraffin-naphthene HCs in all oil fractions, and this is true for all the fields considered. Meanwhile two geological features had major influence on formation of the composition and properties of Lower Pliocene oils in Apsheron Peninsula. In structures unaffected by tectonic erosion more mobile light components of oils happened accumulated in upper stratigrafically younger horizons due to natural fractionation of hydrocarbons on their upward migration routes. In anticlinal folds with washed out crestal part physical and biochemical degradation has caused the loss of light hydrocarbons, first of all of methane fraction, and in this way weighting up of oils. From top to bottom, towards the basal PS suites the distillate fractions show reduction in the light ends (gasoline and naphtha), which is predictably accompanied by an increase in the amount of bottoms. Compositional variation in oil hydrocarbons laterally and through the section of the peninsula is graphically demonstrated on the basis of gasoline, ligroin, kerosene and diesel cuts of oil. In terms of elemental composition, the deeper the stratigraphic occurrence of the reservoir, the more the whole oil is enriched in sulphur- and nitrogen-containing polar compounds.

Keywords: oil; hydrocarbon composition; Apsheron Peninsula; the Productive Series; Lower Pliocene.

Date submitted: 11.10.2023     Date accepted: 25.04.2024

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The article provides overview of the drilling fluids selection as reservoir fluids, which includes mineralogy study of the production interval such as X-Ray diffraction, fluid base selection based on capillary suction test and cation exchange capacity test used to pick up appropriate mud in the East offshore part of Russia. The described principals allowed to minimize non-productive time in overall well construction process with the increased production rate per well which was achieved by the successful planning stage work and offset data.

Keywords: planning stage; X-Ray diffraction; reservoir fluids; non-productive time; capillary suction test; production rate.

Date submitted: 06.06.2023     Date accepted: 25.04.2024

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The development of reserves contained viscous and highly viscous oil poses one of the major challenges in modern reservoir engineering. The poor performance of conventional waterflooding prompts the application of enhanced oil recovery (EOR) methods, of which thermal and chemical EOR are considered the most efficient. Reservoir simulation is a powerful tool for evaluating EOR performance. Serial runs of a history-matched model of a Bobrikovian reservoir are used to evaluate the incremental oil production due to each EOR technique and formulate the efficiency limits of the process performance criteria. In contrast to previous studies that evaluated EOR applications using reservoir simulation modeling, an entirely new quality model is derived through automatic history matching performed by solving an inverse problem. Another novel feature is the automated selection of the optimum field development scenario given a user-defined objective function. Evaluating the performance of hot water injection in a Bobrikovian reservoir suggests that this technology yields positive effects when the injected water temperature ranges from 50 °C to 90 °C. The surfactant–polymer flooding method is also investigated. The largest incremental oil production with a constant surfactant concentration of 0.5% is observed for a polyacrylamide concentration of 0.25%, which can be attributed to a water cut reduction due to plugging the well-drained and flushed reservoir zones. The greatest incremental oil production is achieved when injecting 1.5% surfactant and 0.25% polyacrylamide. The highest efficiency per ton of injected chemicals is obtained when injecting 0.5% polyacrylamide and 0.10% surfactant.

Keywords: High-viscosity oil; EOR; thermal methods; surfactant-polymer flooding; reservoir simulation; history matching; injection simulation scenario.

Date submitted: 03.10.2023     Date accepted: 14.05.2024

References

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Of key importance for planning the sustainable development of territories is the potential for stable production of hydrocarbon reserves, which can be expressed by the time of its duration. In the practice of developing oil and gas fields, two methods are known to stabilize production: through geological and technological measures that increase the productivity of wells and by regulating their operating modes. The second method, on the contrary, involves limiting the growth of selections at the initial stage of development. Due to this, the further decline in production turns out to be slower. Accordingly, the need for geological and technological measures is also decreasing. To describe the quantitative characteristics of production stabilization in both cases, a mathematical apparatus has been developed, based on the equations of state of hydrocarbons, the laws of underground hydrodynamics, as well as the work of specialists in the field of analysis and forecasting of the production of hydrocarbon reserves. It has been established that the processes of development of recoverable reserves of both oil and gas are subject to the same laws, and therefore can be described by means of one generalizing equation. Based on the equation, formulas are derived for calculating the duration of a stable production period depending on both the efficiency of intensification technologies and the degree of capacity redundancy, as well as the
availability of recoverable reserves and the degree of their production. Calculations of the duration of the stable production stage for specific geological and technological conditions are presented.

Keywords: hydrocarbon production; geological and technological measures; operating mode; reserves development.

Date submitted: 16.02.2024     Date accepted: 17.05.2024

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This article focuses on the issue of enhancing oil production by eliminating asphalt, resin, and paraffin deposits (ARPD). These deposits pose significant challenges, including equipment clogging, reduced well productivity, and increased maintenance costs. Moreover, paraffin deposits can damage well equipment, cause accidents, and halt hydrocarbon production. The study involved laboratory and field experiments at the Uzen field to evaluate the efficiency of removing and dissolving paraffin using an emulsion composed of gas gasoline and nitrite compound solutions. Previous studies conducted at NGDU Uzenneft were critically analyzed for comparison. The scientific innovation of this research lies in the development of an emulsion based on gas gasoline and nitrite compound solutions to remove ARPD. The composition was designed to exclude highly aggressive components. It utilized a previously developed emulsion base and incorporated ammonium nitrite, slightly acidified with hydrogen chloride (0.1% by mass), to promote an exothermic reaction.The effectiveness of this technology was measured by changes in daily oil production rates, the duration of the treatment's effect, and changes in the well productivity coefficient before and after treatment.Results indicate that the developed technology successfully removed paraffin from the bottomhole zone of oil wells and increased oil production in 5 out of 6 wells at the Uzen field. The positive effect lasted 17-27 days, with oil inflow increasing by 17-174%. This led to a total additional oil production of 1528 tons from the five wells.

Keywords: bottomhole formation zone; asphalt-resin-paraffin deposits; nitrite composition; surfactants; enhanced oil recovery.

Date submitted: 18.01.2024     Date accepted: 20.05.2024

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50. Efendiyev, G. M., Kuliyev, R. H., Karazhanova, M. K., et al. (2021). Decision-making in the production of hard-torecover oil reserves under uncertainty. In: 11th World Conference «Intelligent System for Industrial Automation» (WCIS-2020). Advances in Intelligent Systems and Computing, Springer, Cham.

The article proposes a new method for calculating the permeability of a geological model cell using probabilistic methods. It is proposed as an alternative to the generally accepted method, which is based on the use of empirical dependencies between porosity and permeability based on the results of laboratory core tests. The proposed method allows us to calculate the dependences of the probabilities of exceeding certain permeability values on porosity. These are of interest for studying the geological structure of oil and gas facilities in the process of their modeling. In this work, the boundary values of filtration properties corresponding to the boundaries of reservoir classes in the classification proposed by A. A. Khanin in 1969 were used. The article discusses the problems arising from the integration of different-scale levels. One of their solutions can be obtained by using the Monte Carlo method. In particular, its use helped to simulate the reservoir properties of rocks in a virtual cell of a geological model based on analyses of the results of previous studies of core samples in laboratory conditions. The approximation of the probabilities of exceeding the corresponding values of permeability from porosity allows us to calculate histograms of this parameter for each cell of the model. To do this, it is necessary to determine the differences in the probability functions that are used for neighboring permeability thresholds. In turn, this makes it possible to perform a differentiable assessment of hydrocarbon reserves for the corresponding reservoir classes in terms of permeability. The article discusses a methodology that allows you to perform all calculations in an automated mode. The text of the article provides the necessary description of the program for calculating the probabilities of exceeding the permeability thresholds, as well as a schematic diagram reflecting the main provisions of its work. The article substantiates the expediency of not using porosity thresholds for reservoir identification. Instead, permeability histograms are calculated for each cell. This methodological scheme makes it possible to calculate reserves associated with rocks of various permeability classes in an automatic mode.

Keywords: bottomhole formation zone; asphalt-resin-paraffin deposits; nitrite composition; surfactants; enhanced oil recovery.

Date submitted: 21.06.2023     Date accepted: 21.05.2024

References

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11.  Khanin, A. A. (1969). Rocks-reservoirs of oil and gas and their study. Mосква: Nedra.
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13. Ates, H., Bahar, S., El-Abd., S., et. al. (2003). Ranking and upscaling of geostatistical reservoir models using streamline simulation: A field case study. SPE Reservoir Evaluation & Engineering, 8(01), 22–32.
14. Kapustin, N., Grushevenko, D. (2019). Evaluation of long-term production capacity and prospects of the oil and gas industry of Russian Federation. E3S Web of Conferences – Energy Systems Research, 114, 02001.
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The study of gas phase dispersion at the intake of submersible pumping equipment is an actual issue, since changes in gas phase dispersion can lead to changes in natural separation. At the same time, the gas separation efficiency can be affected by the presence of solid phase in the well products, which would change the structure of gas-liquid mixture and operation mode of electric submersible pump. The results of the research are novel, which takes into account the influence of the properties of multi-component gas-liquid mixture on the character of operation of ESP well. The new dependences of gas bubble diameter at the submersible equipment intake on gas content for four model gas-liquid mixtures: «water – air», «water – surfactants – air», «water – air – solids» and «water – surfactants – air – solids» with the concentration of suspended particles in the flow of 1.0 g/l have been experimentally obtained in conditions of gauge pressure at the intake 0.04 - 0.05 MPa, gas content of mixture was increased up to 71%, liquid flow rate was changed in the range of values from 13 to 68 m3/day. High-speed video recording with fixing the structure of gas-liquid mixture in the near-intake space of the ESP was carried out during the tests. Visualization allows us to clarify the boundary of the flow regime transition from «bubble» to «slug/churn» compared to the Caetano method. There were developed new correlations of natural gas separation coefficient taking into account the influence of solid phase at different operating modes of ESP well.

Keywords: gas-liquid mixture (GLM); gas bubble; natural gas separation; solid particles; surfactants.

Date submitted: 03.10.2023     Date accepted: 30.05.2024

References

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At present, at almost all fields of the Republic of Kazakhstan the main technology of oil recovery enhancement is the traditional method of waterflooding of productive formations. Many oil and gas fields in Kazakhstan are at a late stage of development and are categorized as «mature» fields. In the global experience of mature field development, the key focus is on the application of enhanced oil recovery (EOR) techniques - chemical, thermal, gas and microbiological methods. This paper considers the application of chemical EOR at a number of Kazakh fields such as Zaburunye, North Buzachi, Kalamkas, East Moldabek. As the results of the pilot studies have shown, the most effective EOR here is the application of polymer flooding. It should also be noted that polymer flooding is successfully applied in Kazakhstan for high-viscosity oil fields such as North Buzachi (oil viscosity 316-417 mPa·s), East Moldabek (oil viscosity 246-377 mPa·s). In this case, water cut, smoothing of injectivity profile and, as a result, increase of oil production is achieved. Successful application of the technology largely depends on the parameters of physical and chemical impact at each stage - the volume of injection of gel-polymer composition, concentration of ingredients, the flow rate of filtered water, the presence and linear size of cracks, the permeability of pore channels and etc. Polymer flooding applied in Kazakhstan showed its technological and economic efficiency on the example of pilot tests, laboratory studies, which reduces water cut and increases oil production. Widespread use of EOR methods would allow increasing recoverable oil reserves by at least 5-10 %.

Keywords: Enhanced Oil Recovery (EOR); gas Injection; hydrocarbon recovery methods; chemical EOR methods; thermal EOR methods; oil production; polymer flooding; oil recovery.

Date submitted: 10.01.2024     Date accepted: 31.05.2024

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The process of developing a single-well oil reservoir in an elastic mode is considered, described by the model of a nonstationary plane-radial filtration flow of a single-phase liquid in a porous medium. For the proposed model, the laws of change in the time of the well flow rate and the pressure at the bottom of the well are considered set. And the pressure distribution in the formation at the initial moment of time, as well as the pressure at the outer boundary of the formation, are considered unknown. The task of determining the dynamics of pressure distribution in the reservoir based on the proposed model is set. This problem belongs to the class of boundary inverse problems without initial conditions. First, a discrete analogue of the inverse problem is constructed using the method of difference approximation. A computational algorithm is proposed for the numerical solution of the resulting system of linear algebraic equations up to a predetermined time layer l. In this case, the pressure at the nodal points of a predetermined triangular region is not determined. And for solving a system of linear equations, starting from the time layer l + 1, a special representation is proposed. At the same time, at each time layer, the system of linear equations is split into two mutually independent linear subsystems, each of which is solved independently, independently of each other. As a result of splitting, an explicit formula for determining the approximate pressure value at the outer boundary of the formation and a recurrent formula for determining the pressure distribution in the formation, starting with l + 1 time layer, were obtained. Based on the proposed computational algorithm, numerical experiments were carried out for a model single-well oil reservoir.

Keywords: elastic development mode; single-phase filtration; plane-radial fluid flow; boundary inverse problem without initial conditions; difference approximation method.

Date submitted: 13.02.2024     Date accepted: 04.06.2024

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In this paper, the authors conducted a study devoted to determining the most optimal compositions for the implementation of measures to increase well productivity in the conditions of active development of the White Tiger field. The results of basic experiments in the field of selection of reagents for heat treatment of the bottomhole zone of wells, together with a comprehensive analysis of the geological conditions of the studied object, show that in order to restore and multiply the permeability of formations, it is necessary to use such compositions, the mechanism of interaction of which is based on the dissolution of asphalt-tar deposits and substances with a large molecular weight. In this regard, a number of theoretical calculations have been carried out for the «magnesium + hydrochloric acid» reaction in four variants with the gradual introduction of compositions of different chemical composition and origin. At each stage, the reaction temperature was determined using both the main and alternative methods in order to increase the representativeness of the results. Taking into account the imposed restriction on the deviation of the determined temperature from the bottom hole, the composition of the agent that can be recommended for the treatment of productive layers of the White Tiger deposit has been previously successfully determined. It is concluded that it is necessary to study the replication of its application at analog facilities in order to improve the technical and economic performance of oil and gas production departments.

Keywords: bottom-hole formation zone; thermal effect; reservoir temperature; reaction products; oil field development; well productivity improvement.

Date submitted: 05.02.2024     Date accepted: 07.06.2024

References

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The analysis of scientific research conducted in recent years shows that the drilling fluids used in the drilling of oil and gas wells can be described by different rheological models. These models do not take into account structural stability and relaxation time of drilling fluids. Currently, in most cases, these drilling fluids are characterized by visco-plastic (pseudo-plastic) properties depending on the different basis and composition. Despite the above, considering the existence of the fact that they have structural stability which determines its internal characteristic and relaxation properties which determines how quickly the fluid responds to changes in stress or deformation during the movement of drilling fluids and the importance and relevance of their attention, the article deals with the issues of rheological modeling of such systems and taking into account the violation of their structural stability. These properties must be taken into account because problems of increasing the efficiency of technological processes during well drilling can be further complicated due to the complex structure and relaxation properties of the applied drilling fluids. In the article, it is proposed to use the generalized exponential model for the description of 10 different oil-based drilling fluids and 8 different waterbased drilling fluids in the presence of shear deformation. As a result of the rheological test of oil-based drilling muds and water based drilling muds of different compositions on the basis of the mentioned model, the possibility of determining their structural stability coefficient and relaxation time has been shown.

Keywords: drilling fluid; rheological model; structural stability; relaxation time; viscosity; multiphase.

Date submitted: 19.01.2024     Date accepted: 11.06.2024

References

1. Ofei, T. N., Lund, B., Gyland, K. R., Saasen, A. (2020). Effect of barite on the rheological properties of an oil-based drilling fluid. Annual Transactions of the Nordic Rheology Society, 28, 81-90.
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7. Suleimanov, B. A., Veliyev, E. F., Vishnyakov, V. V. (2022). Nanocolloids for petroleum engineering: Fundamentals and practices. John Wiley & Sons.
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9. Ismayilov, G. G., Dzhalalov, G. I., Safarov, N. M. (2021). About one interpretation of the phenomenon of «phase inversion» in rheologically difficult water-oil emulsions. SOCAR Proceedings. 4, 87-94.
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16. Vishnyakov, V. V., Suleimanov, B. A., Salmanov, A. V., Zeynalov, E. B. (2019). Primer on enhanced oil recovery. Gulf Professional Publishing.

The article analyzes methods and technologies for predicting zones of abnormally high reservoir pressure (AHRP) when drilling oil and gas wells. Forecasting these zones is considered as one of the main methods for increasing the efficiency of drilling operations. Some methods of AHRP are reviewed, as well as the signs used for this purpose. The advantages of methods that use dependencies between technical drilling parameters are substantiated. Such methods enable us to predict high pressure zones in real time, and without stopping drilling. A brief chronology of the development and improvement of this class of methods is noted. A method included in this class is proposed. This method can also calculate the density of the weighted drilling mud to counteract the abnormal pressure. The method is based on the principle of mathematical calculation of the dependence of the mechanical drilling speed on a number of other mechanical drilling parameters. As a part of the SOCAR «Scientific Foundation» grant project, the use of AHRP forecasting methods in SOCAR practice was monitored and the results were provided. The feasibility of using a system created based on this method in SOCAR wells is substantiated. A brief summary of the principle of forecasting, the operation of functional blocks and the system is provided. An algorithm for the system's operation was developed. Based on this algorithm, a control program was written in the C⁺⁺ programming language. The operability of the system was tested using laboratory experiments based on the method of computer simulation.

Keywords: oil and gas wells; AHRP; accidents and complications in wells; forecasting AHRP; forecasting AHRP in SOCAR; modernized forecasting method; forecasting system.

Date submitted: 25.12.2023     Date accepted: 20.06.2024

References

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One of the reasons reducing the efficiency of well operation is formation of asphalt-resin-paraffin deposits (ARPD), which are deposited in the bottom-hole zone of wells and on the surface of oilfield equipment. A new inhibitor «NDP-22M» was developed to reduce the solidification temperature of highly paraffinic oils and prevent the formation of asphalt-resin-paraffin deposits (ARPD). In addition to preventing the formation of ARPD, «NDP-22M» significantly improves the rheological properties of highly paraffinic oil, which is important for its further transportation. The reagent reduces the solidification temperature and viscosity of oil, as well as facilitates its fluidity. The inhibitor contains a nonionic surfactant, a depressant agent and a solvent. The prepared inhibitor has the ability to reduce the pour point and viscosity of oil, as well as to prevent ARPD. The prepared inhibitor was studied on oil brought from the wells of the oil and gas production department of the production association «OGPB» (Oil and Qaz Production Board), «Oil Pipeline Administration». In this oil, the amount of paraffin is 10.8%. In the course of research, it was found that the effectiveness of adding 300 g/t of reagent to oil is 75%.

Keywords: inhibitor; paraffin deposits; oil production; dynamic viscosity.

Date submitted: 24.01.2024     Date accepted: 02.05.2024

References

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Pipeline transport is one of the most capital and metal-intensive types of transport. Being environmentally friendly during normal operation, it can cause irreparable damage to nature in case of accidents. Therefore, the issues of reliability and efficiency of operation of field and main oil and gas pipelines and control of energy characteristics during their operation are of no small importance. The amount of additional pressure in the system from hydrodynamic shocks is determined by the density and elasticity of the pumped liquid, as well as the elasticity of the walls of the pipeline itself. The article considers the problem of estimating the critical speed and dynamic loads during the movement of multiphase flows through pipelines, taking into account the interaction of the phases. Dynamic loads are calculated based on the change in critical speed for various structural forms formed as a result of the interaction of phases. These loads, compared to shell structures with separated phases, turned out to be less than when moving in a mold with dispersed bubble structures. The characteristics of the critical speed distribution are determined. It has been determined that the dynamic loads arising in multiphase flows with a predominance of the gas phase are many times higher than in systems where the liquid phase is the leading medium, and the dependence of the pressure distribution on the densities of the phases has been shown. The work analyzes various modes of hydraulic shock. The volume of oil caused by its compression during hydraulic shock was calculated. The results of calculating the increase in the volume of an oil pipeline due to a dynamic impact are presented.

Keywords: Critical speed; structural form; speed gradient; density; hydraulic shock; dynamic load; energy feature; elasticity; multiphase flow; flow structure.

Date submitted: 25.03.2024     Date accepted: 06.06.2024

References

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In the article, using a three-line symmetrical strain diagrams for metal, a technique is given for constructing a «moment-curvature» diagram, which is important for determining the deflections of steel beams. Approximations of the moment-curvature diagram by polynomials of the third and fifth degrees, which have high accuracy, are proposed. In numerical examples, it was established that when plastic deformations develop, it is not permissible to determine deflections using a linear model. In addition, numerical examples show that physical nonlinearity has little effect on internal forces in statically indeterminate systems, but has a strong effect on the stress-strain state.

Keywords: beam; physical nonlinearity; moment-curvature diagram; deflection.

Date submitted: 29.11.2023     Date accepted: 08.04.2024

References

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Oil and gas production on the continental shelf is carried out from offshore structures, a significant part of which are fixed platforms. Many of them have a core spatial structure as a supporting block, consisting of pipes of various diameters. The article proposes a method for analyzing and improving geometric shapes, taking into account the physical properties of the pontoon material, which allows solving specific practical problems. The influence of various factors on the stress distribution of pontoons has been revealed. A general method for linearization of thin-walled structures with variable geometric parameters characterized by accelerated convergence is proposed. An effective calculation method based on the small parameter method has been developed. Based on the developed methods, a computational algorithm was found and a set of application programs was compiled. The problems of moment and the general theory of shells were considered accordingly. In designs that provide sufficient strength and manufacturability, all real properties of materials were taken into account and more accurate design methods were found. For a large-scale class of problems of nonlinear structural mechanics, taking into account the physical properties of materials makes it possible to identify additional reserves of their strength. The use of nonlinear theory makes it possible to clarify the calculation of stresses and select the
optimal dimensions and cross-sectional shape of the pontoon element of the support block. Based on the calculation results, certain formulas and methods have been compiled that can be used in engineering practice.

Keywords: Pontoon; support block; offshore platform; shells of rotation; nonlinear model.

Date submitted: 26.01.2023     Date accepted: 31.05.2024

References

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In the current paper an asymptotic method to the problem of establishing the optimal program trajectory and optimal control in the movement of a sucker rod pumping unit of oscillatory systems with liquid damper is considered, where the plunger is inside the Newtonian fluid. In this case the mass of the head is large enough. From the properties of the plunger motion, the boundary conditions are taken to be periodic and the transition of motion from one mode to the second is described by impulse systems. By means of expedient transformations, the given equation of motion with fractional derivatives is reduced to the equation of fractional order containing a small parameter (the inverse of the mass of the head). Using the method of discretization of oscillatory systems with liquid dampers, a system of the first-order difference equations is reduced to the two-dimensional system. Using the given static data, the definition of fractional derivatives in subordinate terms is considered, a quadratic functional is constructed and this problem is investigated by the least squares method. Constructing the extended functional the discrete Euler-Lagrange equations are obtained. The control actions and the corresponding optimal program trajectory is found from the obtained system of discrete Euler-Lagrange equations using the Matlab software package and the algorithm of the calculation process is proposed. The results are illustrated with a specific, simple numerical example from practice and the graphs of optimal control and optimal program trajectory are given.

Keywords: asymptotic method; Newtonian fluid; Euler-Lagrange equations; algorithm of the calculation.

Date submitted: 01.04.2023     Date accepted: 29.05.2024

References

1. Rasulzade, A. F., Hajiyeva, N. S., Ismailov, N. A. (2022). Determination of the optimal program trajectory and control for discretized movement of the plunger in rod pumping equipment. Proceedings of IAM, 11(2), 203-220.
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A model and methods for determining the dynamic response at the suspension point of the rod during the flight of its certain part have been constructed. The boundary value problem has been solved. A technique was used that allows elasticity of the solution to this problem. The dynamic reaction at the suspension point of the rod during the flight of its certain part is determined. It is shown that when the rod is rigidly suspended, the dynamic reaction perceived by the suspension point is equal to the weight of the flying part of the rod. Numerical calculations were carried out for practical values of the system parameters. The results obtained will make it possible in each transverse case to determine the dynamic response at the point of suspension of the rod during the flight of its certain part and, as a result, to prevent violations of the tightness of the wellhead.

Keywords: dynamic response; differential equation; rod; spring stiffness; orthogonality.

Date submitted: 23.01.2024     Date accepted: 21.05.2024

References

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We study the regularity theory of linear elliptic systems with discontinuous coefficients in generalized local Morrey spaces. Precisely, we obtain local regularity results for the strong solutions to 2b-order linear elliptic systems 

where the principal coefficients A_α are assumed to be functions with vanishing mean oscillation (VMO).

Keywords: elliptic systems; generalized local Morrey space; vanishing mean oscillation.

Date submitted: 23.02.2024     Date accepted: 03.06.2024

References

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