This study investigates the tectonic setting, sediment provenance, paleoweathering, paleoclimate, and hydrothermal influences on the Upper Cretaceous deposits of the Lok-Karabakh Zone using geochemical and mineralogical data. The results indicate that the sediments were primarily derived from volcanic arc-related mafic to intermediate rocks and deposited in an arc-related basin. Major and trace element analysis suggests that the sediments originated predominantly from volcaniclastic and terrigenous sources. The Chemical Index of Alteration (CIA) values range from 52 to 95, indicating a low to moderate degree of weathering, with most samples reflecting a cold and arid climate. Mineralogical data further support moderate chemical weathering, with montmorillonite as the dominant clay mineral, along with kaolinite, chlorite, and illite. The A-CN-K ternary diagram suggests plagioclase weathering as the dominant alteration pathway, with limited potassium enrichment. Elemental discrimination diagrams confirm a minimal hydrothermal influence, as evidenced by the Al–Fe–Mn ternary diagram and metalliferous index values exceeding 0.4. Tectonic discrimination diagrams reveal that the sediments were deposited in an arc-related basin influenced by subduction-driven processes. The geochemical proxies indicate that the Lok-Karabakh sedimentary basin was characterized by a scarcity of coarse-grained sediments, leading to a predominance of fine-grained, feldspar-rich deposits such as greywackes, which adversely affected reservoir properties. These findings contribute to a better understanding of the geodynamic evolution of the Lok-Karabakh zone during the Late Cretaceous, highlighting the interplay of arc volcanism, climate, and weathering processes in shaping the sedimentary record. Additionally, the results provide insights into sedimentary basin evolution and reservoir potential in similar geological settings.

Keywords: Upper Cretaceous, Lok-Karabakh zone; paleoweathering; hydrothermal influence; provenance; tectonic setting.

Date submitted: 11.10.2024     Date accepted: 14.02.2025

References

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The scientific justification of the geodynamic impact of small and strong earthquakes that occurred in Azerbaijan between 2003 and 2024 on the structural layers within the South Caspian Basin (exemplified by the Bulla-Deniz oil and gas field) has been provided. Based on the epicentral distance distribution of the earthquakes, earthquakes with a magnitude of M ≥ 3, that occurred in this structure between 2018 and 2024, were selected. The effect of these earthquakes on the field and the changes in production were analyzed comparatively. In this analysis, only the epicentral distance of the earthquakes was considered, and the potential geodynamic effect of the earthquakes on the field was studied using a different methodological approach. The effect radius corresponding to the earthquake energy distribution and the accumulation time of the potential elastic strain energy were calculated. Based on these calculations, earthquakes that could potentially impact the field were selected, and a table was constructed showing the changes in energy accumulation period and impact distance. Thus, using a new methodological approach, the impact of earthquakes with a magnitude of M≥3 that occurred in Azerbaijan between 2003 and 2024 in the Bulla-Deniz field was determined. In this context, an analysis was conducted to identify the parameters of earthquakes that could cause anomalous variations in the field, taking into account the impact distances of the earthquakes. In the study area, the geodynamic impact and the energy store period of the earthquakes were considered in evaluating their effect on oil production in exploitation wells.

Keywords: South Caspian Basin; Bulla-Deniz oil and gas field; earthquake; hydrocarbon-bearing formations; oil production.

Date submitted: 25.10.2024     Date accepted: 03.03.2025

References

1. Yetirmishli, G. J., Valiyev, G. O., Kazimova, S. E., et al. (2019). Technologies for extracting residual oil. Geology and Geophysics of the South of Russia, 1, 84–96.
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This paper investigates the genesis of the Productive Series sediments within the uplift zone of Pirallahi Island, focusing on the distribution conditions and lithofacies characteristics of different origins. For this purpose, the lithofacies characteristics and conditions of the Lower Pliocene Productive Series sediments in the Pirallahi Island structure have been analyzed, particularly based on geophysical well logging (GWL) data. Using a significant number of well logging diagrams, the distribution of sand and shale lithologies for the productive horizons were determined, systematically classified, and correlation schemes were established. The research includes a detailed analysis of the sedimentary environments to interpret depositional patterns, integrating GWL data with lithological core analyses where available. The facies analysis on Pirallahi Island has included
nearly all the boreholes drilled in the field, with the distribution of facies considered from top to bottom across the study area. In addition, the study includes a quantitative assessment of porosity, permeability and clay content to comprehensively evaluate the reservoir potential. Well log analysis allowed interpretation of the effective porosity of the rocks and their shale content, providing a clearer understanding of reservoir heterogeneity. The main objective of the study reported in this paper is to demonstrate lithofacies variability in both horizontal and vertical directions using cross section and lithofacies modeling techniques. The developed facies model is thus demonstrated on a number of surfaces, providing a predictive framework for identifying favorable reservoir zones. The resulting regularities are discussed, highlighting the implications of facies variability for hydrocarbon exploration and production strategies.

Keywords: oil; gas; Pirallahi field; lithofacies feature; facies composition; facies model; correlation.

Date submitted: 12.09.2024     Date accepted: 23.01.2025

References

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16. Shikhova, L. F. (2017). Litho-facial models of Pirallahi field’s oil deposits on geophysical well logging data. Geophysical Journal, 39(2), 126-136.
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This study investigates the source rock intervals within the Agbada Formation in the Niger Delta, utilizing biostratigraphic analysis, source rock assessment, and basin modeling. The study addresses the need to understand the geological history of the formation, focusing on wells DRM1 and DRM2. Biostratigraphic data, integrating foraminifera and palynological analyses, precisely determine the age and stratigraphy of the studied interval, identifying it as the Pliocene to late Miocene paralic Agbada formation. Notable peaks in foraminiferal abundance correspond to specific periods on the Global Sea Level Cycle Chart, geochemical analyses, including Rock-Eval Pyrolysis and vitrinite reflectance, reveal immature to early mature source rocks with a gas-prone nature in the Miocene Agbada Formation. Total organic content and hydrogen index indicate good to very good organic richness, while kerogen type analysis identifies type III kerogen. A one-dimensional basin model, using Petromod software, evaluates burial and thermal histories. The model indicates insufficient burial for thermal maturation and hydrocarbon generation in both wells, despite DRM-1 being within the early oil zone. Differential burial history explains DRM-2's immature source at present-day. This integrated approach offers valuable insights into the age, stratigraphy, and thermal history of the Agbada Formation. The findings contribute to source rock characterization and basin understanding in the Niger Delta, with implications for hydrocarbon exploration and resource assessment.

Keywords: one-dimensional modeling; biostratigraphy; Agbada shale; Niger Delta; source rock assessment, hydrocarbon exploration.

Date submitted: 18.06.2024     Date accepted: 27.01.2025

References

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The research is aimed at developing a new method of active resistance of deep well casing strings to increase their strength and durability under conditions of plastic salt flow. This study used methods of systematic analysis of geological conditions, design of well structures and evaluation of the effectiveness of fastening technologies aimed at solving problems related to drilling and operation of wells in difficult geological conditions of Turkmenistan. The conducted experiments have shown that the use of this method allows for reducing deformations and minimizing the risk of string damage in complex geological conditions. The data analysis showed that the applied method is able to increase the operational life of strings, which is a significant achievement in the field of drilling technologies. In addition, a comparative analysis with traditional methods confirmed the economic feasibility of the new approach, as it reduces maintenance and repair costs. Additionally, the results of the study revealed that the use of the new method leads to a 25 per cent reduction in the probability of cracking and fracture formation in casing strings compared to conventional approaches. It was also found that the method actively influences drilling dynamics by reducing the time it takes to raise and lower the string into the well, which improves the overall efficiency of drilling operations. Finally, the findings open up prospects for further study of the influence of different geological conditions on active drag efficiency, which may contribute to the creation of more adaptive and sustainable technologies in drilling practice.

Keywords: geological conditions, operational life, drilling technologies, active resistance, strength characteristics.

Date submitted: 12.08.2024     Date accepted: 03.03.2025

References

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The optimization of cluster pad structures and drilling planning is a key factor in enhancing efficiency and reducing costs in oil and gas field development. This study focuses on the application of machine learning algorithms, mathematical modeling, and digital technologies for the rational placement of well clusters. By integrating production wells within a single infrastructure zone, cluster drilling improves resource allocation, minimizes environmental impact, and optimizes field development. The study also explores modern well trajectory control techniques to minimize wellbore intersections and reduce drilling complexity, ensuring operational safety and cost-effectiveness. A major challenge in well clustering is the lack of universal criteria for well grouping. This study proposes a clustering methodology that considers these factors, enabling optimal well placement while reducing infrastructure costs. The research also investigates offshore field development, determining the optimal number of fixed platforms for efficient drilling using machine learning techniques. The results demonstrate that machine learning algorithms significantly enhance the accuracy of optimal well pad placement. Systematic modeling and scenario analysis have reduced the number of required fixed platforms without compromising production efficiency, leading to substantial capital savings. A standardized well grouping methodology has been developed, ensuring a structured approach to well pad design and minimizing drilling risks. These findings contribute to the advancement of modern drilling technologies and provide a framework for improving efficiency in field development. The proposed solutions offer practical applications for reducing costs, optimizing well distribution, and ensuring sustainable oil and gas production.

Keywords: well clustering; modeling; cluster pad; optimization; drilling; machine learning.

Date submitted: 18.10.2024     Date accepted: 12.03.2025

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The article is devoted to a comprehensive study of the processes of oil extraction during in-circuit flooding using the example of various tectonic and stratigraphic elements of carbonate reservoir deposits in the Volga-Ural oil and gas province. As a criterion for the efficiency of the production of residual oil reserves, the possibility of introducing into the processes of analysis and interpretation of geological and field data an impact factor on deposits, defined as the product of the current density of the well grid and the ratio of producing wells to injection wells, is considered. The choice of this coefficient is due to both the possibility of interpreting data and making appropriate design decisions in conditions of uncertainty, and its high informativeness, taking into account the specifics of the placement of wells within the studied area of the field. Additionally, in order to improve scientific and methodological approaches to evaluating the effectiveness of the current development system using computer modeling systems, it is recommended to take into account the values of productivity coefficients obtained at the time of stabilization of the optimal flow rate of wells after cleaning the bottomhole formation zone and determined by multidimensional regression models for certain tectonic zones, stratigraphic elements or, in general, objects. Conclusions are drawn about the existence of a close correlation between the oil recovery coefficient and various technological indicators, in particular with the proposed coefficients of impact on deposits, which allows us to apply the results obtained in solving various fundamental problems of oil field development.

Keywords: intra-contour flooding; tectonic and stratigraphic elements; well grid density; oil recovery coefficient; deposits of the Volga-Ural oil and gas region; production of residual oil reserves.

Date submitted: 25.10.2024     Date accepted: 11.03.2025

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The most common way to exploit deposits of high-viscosity and ultra-viscous oil is through various combinations of thermal development methods. But the geological and physical limitations of this technology are: increased water saturation in the roof of the formation, layered heterogeneity due to the presence of clay and aquiferous lenses, small thickness of the formation - up to 10 m, high vertical and horizontal heterogeneity. The experience of operating ultra-viscous oil deposits in terrigenous reservoirs shows that for the production of reserves, one of the priorities is the use of wells with horizontal termination in combination with thermal methods, however, there are certain geological and physical limitations of the application in the form of a layer thickness of at least 10 m. Based on the results of numerical studies, it can be argued that the assessment of the effectiveness of a multi-hole well with a horizontal end, including the choice of a trajectory, the required number of additional conditionally horizontal shafts with optimal length, should be carried out using hydrodynamic modeling. Since the increase in the number of conditionally horizontal trunks, their proximity to each other, the small lengths of conditionally horizontal trunks, the presence of smooth divorces from each other lead to great interference and thereby reduce the productive characteristics per unit of their length.

Keywords: terrigenous reservoir; vertical directional borehole; multi-hole borehole with horizontal termination; conditionally horizontal trunk; interference between conditionally horizontal trunks; geological and technological model; well drainage area.

Date submitted: 25.10.2024     Date accepted: 11.03.2025

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One of the possibilities for improving oil field development performance is the use of various new technologies in various geological and technical measures (GTM). The choice of geological and technical measures is complicated by the subjectivity of interpretation and uncertainty of data on geological conditions, the current state of field development, expressed multicriteria, multifactoriality, ambiguity, etc. This article provides an algorithm and a corresponding calculation scheme, which provides for data collection, processing, statistical analysis with the construction of models expressing the dependence of the effectiveness indicators of individual geological and technical measures on various factors. The purpose of the research in this article is to improve models and algorithms within the framework of a decision-making system to increase the efficiency of geological and technical measures at an oil production well. The presence of uncertainties determines the importance of using in this case, along with the methods of mathematical statistics, methods that allow for and consider above mentioned the uncertainties. As part of the study, a method allowing to give a predictive assessment of the efficiency indicators of various geological and technical measures in various physical, geological and technical and technological conditions using the example of limiting water inflows was proposed. Also, as part of the research, a calculation scheme for the implementation of geological and technical measures was developed, based on a multi-criteria assessment of their effectiveness, including statistical analysis of factors, assessment of their significance, fuzzy cluster analysis and construction of statistical and fuzzy models. The resulting models allow making decisions under uncertainty and determining the optimal performance of equipmen.

Keywords: Technical-technological conditions; geological and technical measures; multi-criteria; cluster analysis; oil recovery.

Date submitted: 24.07.2024     Date accepted: 21.11.2024

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This study focuses on developing and optimizing the formulation of a water shutoff agent and evaluating its static properties for application in Kalamkas field conditions. The proposed composition consists of modified starch (MS), unsaturated amides (UAM), a gelling agent (Y1), and a crosslinking agent (TN), which undergo polymerization to form a robust three-dimensional gel matrix. The research includes an assessment of the influence of reagent ratios and crosslinker concentration on the gel's rheological properties and water shutoff capacity. Experimental results demonstrate that the optimal concentration of the primary reagents – modified starch and unsaturated amides – lies in the 3.5-4.5 % range. The optimal UAM/MS ratio lies between 0.7 and 2.0, ensuring a balance between the mechanical strength and elasticity of the gel structure. The crosslinking agent concentration significantly affects gelation and structural integrity. It has been established that concentrations ranging from 0.08% to 0.10% provide an optimal crosslinking degree, preventing excessive rigidity while maintaining high-pressure resistance. The final formulation, SG-k (Strong Gel Kalamkas), was developed considering technical and economic factors. The optimized composition ensures a high-viscosity gel with a gelation time of approximately 20 hours, making it suitable for in-situ applications in the Kalamkas field. The presented results confirm that optimizing the composition of the water shutoff agent significantly improves its properties, which is critically important for reducing water inflow and leveling the profile leveling of injectivity. The findings contribute to advancing water inflow control technologies by providing a reliable and cost-effective water shutoff solution. 

Keywords: profile leveling; water shutoff treatments; gelation; polymers; crosslinking.

Date submitted: 21.12.2024     Date accepted: 06.03.2025

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The article proposes the design of the cutting part and its reinforced material, which allows to prevent intensive work of the cutter in its central part and maximise the destructive potential of the tool. In this regard, a rational geometric parameter of the milling cutter's cutting part is determined by creating and studying a mechanical-mathematical model of the interaction process between the milling tool and the object to be destroyed, based on the theory of wear of mating surfaces. Since in the process of destruction there is a detachment of fine chips from the emergency facilities, contributing to intensive and uneven wear of the reinforcing structure, a milling tool whose cutting part is equipped with a cavitation-exciting element is developed. Possible dynamic loads on the rock-cutting tool due to the creation of cavitation loads have been experimentally determined and the possibility and necessity of drilling operations with the use of cavitator in the drilling tool arrangement have been confirmed. To address the uneven wear of the cutting part of the milling tool and to strengthen the radial hardening contours from the periphery to the centre when using a composite alloy with a non-uniform composition of granular solid filler, the analogy of the process of actualisation of composite surfacing with the Markov process was used. For this purpose, on a special bench, studies were carried out with a measurement step of 30 min. to synthesise the areas of compatibility of operational parameters with physical and mechanical properties of the destroyed emergency facilities, reinforcing parameters and design of downhole cutting tools.

Keywords: milling machine; reinforcing parameters; theory of contacting sphere's wear; cavitation element; Markov process; operational parameters; granulometric alloy.

Date submitted: 08.09.2024     Date accepted: 28.02.2025

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This manuscript investigated the corrosion inhibition and adsorption behavior of Dioscorea alata leaf extract on mild steel to explore their bioactive anti-corrosion potentials in 1M H2SO4 environment. It used chemical and electrochemical methods and phytochemical screening. The weight loss measurement revealed that samples with 1 to 5 g/300 ml extract recorded maximum inhibitory efficiency of 72.4, 78.4, 81.1, 81.5, and 83.3 %, respectively, within their first 5 days. Generally, their inhibitory efficacy has been observed to decrease with greater exposure time, while the computed Gibbs free energy of the adsorption process (ΔG°ads) values from the weight loss data ranged from -9.5491 to -9.7165 kJ mol-1, and the adsorption isotherm measurements corresponds well with the Temkin adsorption isotherm, demonstrating a physisorption reaction between the extract molecules and the surface of the coupons. Phytochemical screening showed steroids, saponins, and terpenes were active ingredients in the extract. On the other hand, the potentiodynamic test produced maximum percentage inhibition efficiency of 97.99, 31.51, 97.30, and 98.17 %, respectively, for 1 to 5 g/300 ml extract concentrations. The highest corrosion rate of 9.905e+003 mpy was obtained from the sample without extract. Based on the corrosion inhibition effectiveness of the extract obtained through both methods, it is suggested that the extract be added in the production of paints that are used to cover pipelines in the oil and gas industry. This is because it has chemicals in it like saponins, terpenes, and steroids that can stick to the metal's surface and inhibit corrosion in acidic media.

Keywords: sulfuric acid; adsorption isotherm; phytochemical compounds; Dioscorea alata; mild steel.

Date submitted: 20.12.2024     Date accepted: 19.02.2025

References

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In light of the water and energy crises around the world in general and Libya in particular, and the constant endeavor to provide visions and solutions to resolve these crises. This study is one of the efforts to contribute to this topic, as the study aims to increase the efficiency of a desalination plant that operates with gas turbines. The study aims to increase the efficiency of the total plant (the desalination plant that operates with turbines) by using part of the exhaust gas resulting from operating the turbines in the presence of a combined cycle. The study also aims to clarify how this can be applied to raise the efficiency of the total station, taking into account achieving the highest efficiency, the lowest cost rate, and the lowest environmental pollution rate while maintaining the default for the station. This was done through different methodologies, as the descriptive method was used. To describe the variables and data, the quantitative and scientific methodology in collecting data, determining the applied framework, and the comparison methodology in comparing the results. The analysis methodology was also used to analyze and evaluate the results. The results indicated that the best way to raise the station's overall efficiency is to use the combined cycle with a higher percentage of exhaust gas. The obtained efficiency is 34.5%, with a total cost of 20% and an emissions rate of 35%, while maintaining the plant's life span as 35% of the exhaust gas was used. 

Keywords: desalination plant; Gas turbines; exhaustive Gas; combined cycle; efficiency; pollution rate; life Span.

Date submitted: 09.12.2024     Date accepted: 18.02.2025

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The adsorption process has established itself as one of the best technologies for cleaning process liquids and gases worldwide, and activated carbon, zeolites, silica gel, etc. are undoubtedly considered universal adsorbents for removing various types of pollutants. However, the extensive use of industrial adsorbents is sometimes constrained by their high cost. Attempts have been made to develop inexpensive adsorbents using numerous agro-industrial and municipal wastes. The use of waste as inexpensive adsorbents is attractive due to their contribution to reducing waste disposal costs, thereby promoting environmental protection. This review presents the main stages of gas emission formation at a petrochemical plant and their possible composition, and analyzes the negative impact of sulfur compounds on thermal power equipment. Based on the literature review, an extensive list of low-cost adsorbents (obtained using various types of waste) from the world literature was analyzed and compiled and their adsorption capacities for sulfur compounds were presented. It is evident from the literature review that various low-cost adsorbents have shown good potential for the removal of sulfur compounds from petrochemical industrial gas emissions. However, there are several problems associated with the use of low-cost adsorbents, which were discussed in this paper. Based on the literature review, several adsorption compositions prepared from the sludge of water treatment plants of thermal power plants were developed and presented for use as an adsorbent of sulfur compounds from gas emissions of petrochemical industries. The developed compositions had sulfur capacity similar to the literature data.

Keywords: Adsorbents; industrial waste; gas emissions; hydrogen sulfide; petroleum refinery.

Date submitted: 17.07.2024     Date accepted: 04.10.2024

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The cost of sustainable development and achieving carbon neutrality has increasingly become a focus of research. Rare-earth elements are considered critically important to the green economy, as reducing carbon dioxide emissions is challenging without their involvement. This article analyzes various pathways for oil and gas companies to achieve carbon neutrality, with a specific focus on the demand for rare-earth elements. A classification of the primary pathways to carbon neutrality available to oil and gas companies is presented, along with a qualitative assessment of their associated rare-earth elements demand. Reports from leading global and Russian oil and gas companies (by market capitalization) were reviewed to identify the strategies they employ. All pathways to carbon neutrality for oil and gas companies was also classified in terms of rare-earth elements demand for its implementation. However, it was found that calculating the direct demand for rare-earth elements is feasible for wind power projects. Consequently, this study provides calculations of rare-earth elements demand for wind power projects implementation by international (11049.3 tons) and Russian (54 tons) oil and gas companies. Information about these projects and their rated capacity was taken from company reports and other open sources. Additionally, the carbon footprint associated with the mining and processing of the required rare-earth elements for these projects was calculated. For international companies, the carbon footprint is 211196.32 tons of carbon dioxide equivalent, while for Russian oil and gas companies, it is 1033.13 tons of carbon dioxide equivalent. 

Keywords: REE; pathways to carbon neutrality; greenhouse gas emissions; oil and gas companies; carbon footprint; wind power.

Date submitted: 23.11.2024     Date accepted: 03.03.2025

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This study provides an in-depth assessment of Azerbaijan's wind energy potential using ERA5 reanalysis data from 1940 to 2023. Using statistical analysis based on the Weibull distribution, the study examines wind characteristics at 24 strategically selected locations across the country. A Python-based automated process facilitated the analysis of over 70 million hourly wind speed observations, yielding detailed estimates of wind power density and providing critical data for renewable energy development planning. Azerbaijan has significant renewable energy resources, with an estimated onshore wind capacity of 3000 MW out of a total renewable capacity of 26940 MW. The analysis identified coastal areas such as Baku, Sumgait and Gobustan as having the highest wind energy potential, with Baku having an average wind speed of 8.01 m/s at 100 meters above ground level (AGL) and a wind power density of 628.5 W/m². Inland regions such as Khizi and Naftalan show moderate potential, suitable for smaller wind energy projects. The methodology integrates long-term meteorological data with advanced statistical techniques to ensure the reliability of the results. Weibull distribution parameters were calculated to characterize wind regimes and effectively predict energy yields. However, the study recognizes the limitations of ERA5's spatial resolution in capturing the complexity of mountainous terrain and highlights the need for localized, high-resolution measurements to improve accuracy. This research outlines priority areas for wind energy development and provides a robust framework for policy makers and stakeholders. By advancing the understanding of wind energy potential, the findings support Azerbaijan's strategic goals of enhancing energy security, achieving sustainable development, and addressing climate change challenges through renewable energy integration.

Keywords: renewable energy; wind energy; Weibull distribution; wind potential; Azerbaijan; ERA5.

Date submitted: 15.11.2024     Date accepted: 24.03.2025

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In the study, the release processes of doxorubicin immobilized in the pH-sensitive water-swellable hydrogel sample obtained from the crosslinking of polyacrylic acid with an average molecular weight of 230 kDa with 10% (mass) N,N'-methylene-bis-acrylamide were investigated. The immobilization of doxorubicin on the water-swelling polyacrylic acid-based hydrogel was carried out by the sorption method. The immobilization was monitored for 24 hours and continued until the equilibrium concentration of the drug in the medium was reached. It was found that the immobilization of doxorubicin on the polyacrylic acid-based gel occurs through non-covalent chemical interactions, including hydrogen bonding, electrostatic forces, and hydrophobic interactions. It has been shown that the immobilized organic substance, localized both inside and on the surface of the gel, retains its physicochemical properties for an extended period of time. The controlled release process was studied in a buffer medium of pH=7, which is close to the small intestine medium. The drug release was quantitatively characterized as a function of time. The kinetic data of the release were fitted to various kinetic equations such as zero order, first order, Higuchi square root law, Korsmeyer-Peppas and Hixson-Crowell cube root. It was found that the release of doxorubicin occurs by a non-Fickian diffusion mechanism and the direction of release fits well with the Higuchi model. Thus, the effective viscosity of polyacrylic acid and its ability to complex with metal ions to form gel systems provide the basis for its use in the preparation of materials for isolation formation water and sand protection in oil and gas industry applications.

Keywords: polyacrylic acid; hydrogel; immobilization; controlled release; kinetic models.

Date submitted: 23.12.2024     Date accepted: 11.02.2025

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We consider the 2b-order linear elliptic systems

in the generalized local mixed Morrey spacesand generalized mixed Morrey spaces, where the principal coefficientsare functions with vanishing mean oscillation. We obtain local regularity results for the strong solutions to L(x,D) in the spacesand. Solutions to the linear elliptic systems with discontinuous coefficients are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. We can apply this local regularity results in generalized local mixed Morrey spaces to study the regularity in generalized local mixed Morrey spaces of of the Navier-Stokes equations. Solutions to the Navier-Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier-Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. The possibilities nowadays to exploit supercomputers and highly developed numerical methods for nonlinear partial differential equations allow us to determine even the general solutions to the Navier-Stokes equations. However the difficulties become greater with increasing Reynolds number. This has to do with the particular structure of the solutions at high Reynolds numbers. Note that in the limiting case of high Reynolds numbers, most of these exact solutions have a boundary-layer character.

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

Date submitted: 20.12.2024     Date accepted: 17.03.2025

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