Relevance. Establishment of sedimentation parameters of terrigenous reservoirs is an important aspect in predicting new deposits and rational exploitation of hydrocarbon systems. Boron concentration in sandstones serves as an informative indicator of paleosalinity of sedimentary conditions. As a rule, boron accumulation in marine sedimentation regimes is more pronounced compared to its accumulation in continental settings. In contrast, the formation of coal-bearing horizons is predominantly carried out in waterlogged paleolandscapes, where favorable conditions of anaerobic decomposition of organic matter promote peat accumulation. In this relation, the necessity to search for correlations between boron content and the amount of coal seams to reveal the facies of sedimentation is actualized. Aim. To determine the relative boron content and the number of coal interlayers in sandstones of the Tanopchi Formation of one of the Yamal Peninsula fields based on the data of geophysical borehole surveys and to identify correlations between these parameters and sedimentation conditions. Methods. Determination of geochemical parameters based on the data of geophysical well surveys, separation of coal seams based on the data of electrical, radioactive and induction logging methods, separation of electrofacial models using the methodology of V.S. Muromtsev, classical methods of determining the conditions of sedimentation based on the data of core and geophysical well surveys. Results and conclusions. The results of the study indicate high informative significance of relative boron content as an indicator of sedimentation conditions of reservoir rock formation. Determination of boron content normalized to clay content, together with estimation of the number of coal interlayers, allows us to reliably differentiate sedimentary strata of marine and continental genesis. Continental facies conditions show a negative linear regression between the boron content and the number of coal interbeds, which is due to the conditions characteristic of these environments: periodic waterlogging, fluctuations in the acid-alkaline balance, and reduced hydrodynamic activity of formation waters. Marine facies, on the contrary, are characterized by a positive linear relationship between the considered parameters, which can be interpreted in the context of the allochthonous model of coal formation.

In-situ chemical oxidation (ISCO) is a common method to remediate chlorinated ethene contaminants in groundwater. Monitoring the effectiveness of ISCO can be hindered because of insufficient observations to assess oxidant delivery. Advantageously, potassium permanganate, one type of oxidant, provides the opportunity to use its strong electrical signal as a surrogate to track oxidant delivery using time-series borehole geophysical methods, like electromagnetic (EM) induction logging. Here we report a passive ISCO (P-ISCO) experiment, using potassium permanganate cylinders emplaced in boreholes, at a chlorinated ethene contamination site, Naval Air Station Pensacola, Florida. The contaminants are found primarily at the base of a shallow sandy aquifer in contact with an underlying silty-clay confining bed. We used results of the time-series borehole logging collected between 2017 and 2022 in 4 monitoring wells to track oxidant delivery. The EM-induction logs from the monitoring wells showed an increase in EM response primarily along the contact, likely from pooling of the oxidant, during P-ISCO treatment in 2021. Interestingly, concurrent natural gamma-ray (NGR) logging showed a decrease in NGR response at 3 of the 4 wells possibly from the formation of manganese precipitates coating sediments. The coupling of time-series logging and well-chemistry data allowed for an improved assessment of passive ISCO treatment effectiveness.

Abstract Array induction logging technology plays a crucial role in the identification and fluids quantitative evaluation in oil and gas wells. In conventional inversion methodologies, software focusing is initially applied to raw data to derive key parameters, which serve as priors for subsequent inversion processes. Precise resistivity inversion is critical for identification of oil- and water zones/layers. Compared to the direct utilization of raw measurements, software focusing generates additional computational overhead and increases processing time, and it also exhibits slow convergence and a propensity to become trapped in local optima, limiting the inversion efficiency and robustness. To address these challenges, this paper proposes an efficient inversion method of long short-term memory (LSTM) neural networks, which directly processes raw array data, simplifying the inversion workflow and overcoming the limitations of traditional inversion methods. First, a fast forward algorithm for 2D horizontally layered formations in vertical wells was developed by numerical mode matching, and a sample database of array induction logging curves is generated. Second, a deep learning model of LSTM network was constructed, which was then trained and optimized to automatically capture the complex mapping relationship between logging responses and formation parameters based on the sample data. Finally, the optimized deep learning network is employed to inverse logging data. The results indicate that the proposed LSTM-based inversion method significantly enhances computational efficiency, reducing the single-point inversion time to less than 1 ms, which corresponds to a four to five orders of magnitude improvement over conventional approaches. Furthermore, the resistivity estimation exhibits a relative error predominantly within 5%, while the absolute error in the invaded zone radius remains largely within 0.1 m, demonstrating the method's high accuracy. Additionally, the robustness tests indicate that the method retains high accuracy even when dealing with samples exhibiting different relative noise levels. Further application of the network to complex synthetic formation models reveals that the inversion results are accurate, underscoring the strong generalization ability of the network.

In practical applications, conventional electrical anisotropy has certain limitations because it solely takes into account the resistivities along and perpendicular to the layering plane. To address more complicated electrical anisotropy issues, two parameters are used, namely anisotropic dip and anisotropic azimuth, to additionally capture the anisotropic properties in different sedimentary environments. Then the corresponding solution is proposed based on the dyadic Green function. Additionally taken into account are multilayer anisotropic issues. Using this proposed approach, the influence of various anisotropic dips and azimuths, as well as borehole dips and azimuths, is studied. Two angles are shown to exist by the Results: the critical anisotropy dip ψc and the critical borehole dip θc. Before and after these two angles, the axial components Hxx, Hyy, and Hzz show clear monotonic changes with variations in the borehole dip and anisotropy dip, respectively. The results also show that cross components (Hxy, Hyx, Hyz, Hzy, Hxz and Hzx) contain both borehole orientation and anisotropy orientation information. In layered geological models, triaxial induction responses are examined to further illustrate the correctness and robustness of the suggested approach.

Abstract Structural information about the subsurface near the borehole can be obtained from reconstructed conductivity distributions. These distributions may be reconstructed via the inversion of deep‐sensing electromagnetic induction log data. Unfortunately, these complex media often display anisotropy and structural variations in both horizontal and vertical directions, making the three‐dimensional inversion computationally demanding and ill‐posed. To address these challenges, we introduce a sequential inversion strategy of deep‐sensing electromagnetic induction logging data that is measured while drilling. For the inversion at each logging position, we employ a matrix‐free implementation of the adjoint integral equation method and a quasi‐Newton algorithm. To tackle the ill‐posed nature of the problem, we regularize the inverse problem by employing a multi‐dimensional inversion parameter technique that shifts from zero‐ to three‐dimensional parameterization. The model derived from the inversion of the data at multiple positions is incrementally integrated by utilizing the sensitivity data at each logging position. To validate our approach, we tested our method on simulated data using an anisotropic model. These experiments show that this approach produces a good reconstruction of the true conductivity for the whole track while only doing the inversion at a single position at a time.

В ситуациях, когда генераторная катушка прибора индукционного каротажа расположена в плоскости, перпендикулярной направлению слоев с различным удельным электрическим сопротивлением, электромагнитное поле является трехмерным, что делает расчеты таких полей вычислительно затратными. Ранее был предложен способ аппроксимации круговой катушки с током вертикальной квадратной рамкой, что позволило свести расчет такого трехмерного поля к решению нескольких двумерных задач и значительно сократить вычислительные затраты. В данной работе приводится описание вычислительных экспериментов, которые подтверждают адекватность такой замены формы источника в средах со значениями удельного электрического сопротивления среды и частоты тока, типичными для задач индукционного каротажа. When using induction logging in horizontal wells, the generator coil of the electromagnetic logging tool is located in a plane perpendicular to the direction of layers with different resistivity. The electromagnetic field excited by the generator coil is three-dimensional in this case. To reduce the computational costs, a method to approximate a loop coil with a vertical square frame was proposed earlier. In this approach, the calculation of a three-dimensional electromagnetic field is performed by solving several axisymmetric (two-dimensional) problems, which significantly reduces computational costs. However, such a replacement of the geometric configuration of the source certainly requires a verification. This article compares the field generated by sources of the regular polygons form containing 3 to 16 segments. To conduct computational experiments, a typical geoelectric model containing a layer of oil-saturated sandstone was used. We use three source current frequencies at 20, 100, and 250 kHz. For a square frame, the error value at a distance of 0.7 m from the center of the loop was less than 0.04 %. When changing the source current frequency and the resistivity of the medium, the error associated with replacing a circular loop with a square frame did not exceed the above values. The provided computational experiments have showed that the choice of a vertical square frame is sufficient in terms of the accuracy of the obtained magnetic field components in the receiver of a logging tool.

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper URTeC 4042140, “Regional Pore-Pressure Variations of the Wolfcamp, Dean, Spraberry, and Bone Spring Formations of the Midland and Delaware Basins in the USA,” by Shuvajit Bhattacharya, Ray Eastwood, and Katie Smye, The University of Texas at Austin, et al. The paper has not been peer reviewed. _ The authors study regional pore-pressure variations in the Leonardian and Wolfcampian producing strata (Wolfcamp, Bone Spring, Avalon, Dean, and Spraberry) in the Midland and Delaware Basins of West Texas and southeast New Mexico. Pore pressure is analyzed with a variety of subsurface data, including sonic logs and completions data. Results show that pore pressure is consistently higher in the Wolfcamp Formation (especially Wolfcamp B, C, and D) and Delaware Basin Bone Spring S3 than the Spraberry Formation in the Midland Basin. Introduction Over the years, several studies have been conducted on pore pressure in different shale reservoirs in the Permian Basin. A few recent studies used 3D seismic data to estimate and map pore pressure in the Permian. However, few published studies exist on basinwide variations of pore pressure in producing shale formations in the Permian. Uncertainty persists as to why pore pressure is different in age-equivalent formations in the Delaware and Midland Basins. The authors study regional pore-pressure variation in selected Leonardian and Wolfcampian shale formations at the basin scale, integrating well logs, completions, and reservoir data. The challenges and opportunities presented by different kinds of subsurface data in estimating pore pressure are discussed. Pore-pressure-gradient maps reveal vertical and lateral changes in pore pressure in the Permian Basin. Methods Pore pressure of the Wolfcamp, Dean, Spraberry, Bone Spring, and Avalon Formations in the Midland and Delaware Basins was studied with a combination of sonic logs, instantaneous shut-in pressure (ISIP), diagnostic fluid injection tests (DFIT), mud weight, and other approaches. Pore Pressure From Sonic Logs. Two methods were used for obtaining pore-pressure estimates from sonic logs: Eaton’s approach and the SOPI method that uses sonic, offset well, porosity, and formation-resistivity data. Although resistivity logs were more prevalent than sonic logs in the Midland and Delaware Basins, the presence of both induction logs and laterologs was encountered; mixing the results from both data types would complicate workflow and interpretations. Using Eaton’s approach, a shale normal compaction trend line varying with depth was established. Departures from this trend were used to compute pore pressure using observed sonic travel time. For the SOPI method, wells with petrophysical multimineral model results that accurately characterized variations in lithology and porosity for the formations of interest were used. The sonic log response was forward-modeled using the derived mineral composition and porosity from petrophysical inversion.

This work is dedicated to the development of a numerical inversion methodology for electrical logging data in sub-vertical and slightly inclined oil and gas wells. It examines the specific features of joint inversion of galvanic and induction logs combined in various configurations, depending on the equipment used. The axisymmetric two-dimensional geoelectric model of medium consists of homogeneous blocks separated with horizontal and coaxial cylindrical boundaries. The blocks are characterized by horizontal and vertical electrical resistivity, as well as dielectric permittivity. Numerical inversion is carried out until a minimal discrepancy is achieved between the measured signals and those simulated within the interpretive formation model. Unlike the traditional layer-based approach, this inversion method involves not only adjusting the sounding curves but also accounting for signal variations along the borehole. In this case, the resulting model aligns as closely as possible with the actual measurements. Inversion based solely on galvanic measurements can potentially yield unstable results near boundaries with high resistivity contrasts, underestimating the resistivity of layers adjacent to highly resistive ones. The ambiguity can be reduced through joint inversion of galvanic and induction logs, although this often requires the base formation model to be more complex. In particular, during drilling with fresh clay-based mud in reservoirs with mixed oil and mineralized formation water saturation, a low resistivity annulus forms. This zone is more electrically conductive than both the invaded zone and virgin formation due to the higher content of saline formation water. It cannot be detected through galvanic well logs analysis, but its influence on induction logs is significant. Therefore, the presence of an annulus may be a crucial factor to consider when constructing a geoelectric model of the formation that aligns with resistivity logs obtained with different logging methods. These specifics are illustrated with the results of inversion of real data measured in vertical wells in the intervals of Lower Cretaceous and Jurassic deposits of the Shirotnoe Priobie oil fields.

Relevance. The need to bring undeveloped sediments of the Bazhenov horizon to development in areas that are well explored and have developed infrastructure. Objects. Anomalous section deposits of the Bazhenov Formation (J3-K1bn) of Western Siberia within the Uvat oil and gas bearing region. Aim. To ascertain the spread boundaries and structure parametrization of sediments of the Bazhenov formation anomalous section within the Uvat oil and gas bearing region through an integrated analysis of the core material study results, GIS and seismic data. Methods. Photomaterials of three core samples and the results of macro- and micro-description of rocks, measurement of natural radioactivity on the core by the spectrometric gamma-ray logging, palynological and microfaunistic studies. To clarify the structure of the Bazhenov formation, geophysical well surveys and 3D seismic data were used. The logging materials are represented by 154 wells and include the following methods: intrinsic polarisation, gamma ray logging, induction, neutron and lateral logs. Results. The authors have carried out the analysis of the Bazhenov formation sediments within the Uvat oil and gas bearing area. They carried out the lithological and petrographic analysis of the formation sediments in thin sections and determined the contribution of radioactive elements to the total natural radioactivity, according to which, in combination with GIS data, the Bazhenov formation was differentiated into rocks of mainly siliceous composition, siliceous-carbonate rocks, mudstones and sandy-silty mudstones. Biostratigraphic studies of samples of the Bazhenov formation were analyzed. The deposits of the Bazhenov formation are dated by the Titonian (Volga) Stage, part of which is represented by a mixed composition containing both the amorphous organic matter typical of the Bazhenov formation and the Valanginian or Valanginian-Goterivian palynoforms of good preservation. The authors clarified the boundary of the Bazhenov formation anomalous section in the Uvat oil and gas area: in comparison with the previously established contours of distribution, the eastern boundary shifted to the west, due to which the total area of the anomalous section reduced almost twofold; the contours of the north-eastern border of Bazhenov formation anomalous section were slightly revised and shifted to the south-west direction. The obtained data indicate that the Bazhenov formation anomalous section formation was caused by the introduction of Valanginian-Gotterivian deposits into the Tithonian-Berriasian deposits of protobagenite, which confirms the geomechanical model of the Bazhenov formation anomalous section formation.

Summary The lamination characteristics of shale are one of the sources of anisotropy in shale reservoir resistivity, with significant differences in horizontal and vertical resistivity, and usually with vertical resistivity greater than horizontal resistivity. Therefore, the resistivity anomaly caused by anisotropy in horizontal wells of shale reservoirs seriously interferes with the logging evaluation of shale reservoirs. Based on the 3D finite element method, the electromagnetic field distribution of array induction logging was simulated, and the influence of resistivity, anisotropy, and well inclination angle on resistivity in laminated shale formations was analyzed. A resistivity correction chart was constructed using the sensitivity differences of each subarray of array induction logging in anisotropic formations. Finally, resistivity anisotropy correction is achieved based on actual logging data. Research has shown that in anisotropic formations of horizontal wells, the effects of formation resistivity, anisotropy, and well inclination angle on each subarray of array induction logging are different, resulting in significant deviations between the measured resistivity values and the actual formation resistivity values. Through the construction of resistivity correction charts with different sensitivities of each subarray, anisotropy correction was performed on the actual well data. The corrected resistivity can approximately represent the horizontal resistivity of the reservoir, laying the foundation for evaluating shale reservoirs using resistivity data.

A hybrid inversion algorithm to obtain the resistivity of the uninvaded zone based on the array induction log

The article analyzes the features characterizing the Lower Kura depression (LKD). A number of hydrocarbon deposits have been discovered in this oil and gas region. The Kalmas underground gas storage facility, which has the largest volume in Azerbaijan, is also located in this area. In the LKD, all PS formations can be traced throughout the entire well section. The reservoir properties of the rocks were considered to study the features of the area. In order to study the reservoir properties in the well section, the field applies data obtained by using a complex of well logging (WL) methods (laterolog, spontaneous potential logging, induction logging, gamma logging, neutron logging, acoustic logging) and analyses of rock samples. The graphs were constructed to evaluate the relationship between petrophysical parameters (porosity, permeability, etc.) determined in the rocks involved in the well sections of the object of research. In the article, maps of porosity distribution, permeability and permeability of sandy siltstone rocks and fractions greater than 0.1 of the Productive Series of the South-Eastern Gobustan and Baku Archipelago, which are part of the Low Kura Depression, are plotted and analysed. Plots showing the porosity distribution of the Low Kura Depression by depth were also constructed and some results were obtained. Based on reservoir properties, the region is divided into 6 groups, and in each group intermediate values of the porosity and permeability coefficient are determined. In general, the porosity coefficient ranges within 5-25%, permeability – 1-250 mD. The reservoir properties of rocks vary over area from worse to better. The capacitance-filtration properties of rocks were studied. The rock samples analysed identified rocks with good and low reservoir characteristics. To study the variation in the determining factors, maps of the distribution of reservoir properties indicators (fractions greater than 0.1 mm; porosity and permeability in sand-siltstone-containing rocks) were compiled by area and their causes were determined by comparison with other oil and gas fields. It was found that with distance from the mouth of the Kura River (towards the right and left banks), the reservoir properties of the rocks deteriorate. This is due to an increase in the amount of clay in rocks. It is also clarified that the change in porosity coefficient does not depend on depth. The content of sand-siltstone composition in the rocks along the section is 20-50%.

Abstract Quantitative interpretation of the data from controlled‐source electromagnetic methods, whether via forward modelling or inversion, requires solving a considerable number of forward problems, and multigrid methods are often employed to accelerate the solving process. In this study, a new extrapolation cascadic multigrid method is employed to solve the large sparse complex linear system arising from the finite element approximation of Maxwell's equations using secondary potentials. The equations using secondary potentials are discretized by the classic nodal finite element method on nonuniform rectilinear grids. The resulting linear systems are solved by the extrapolation cascadic multigrid method with a new prolongation operator and preconditioned Stabilized bi‐conjugate gradient method smoother. High‐order interpolation and global extrapolation formulas are utilized to construct the multigrid prolongation operator. The extrapolation cascadic multigrid method with the new prolongation operator is easier to implement and more flexible in application than the original one. Finally, several synthetic examples including layered models, models with anisotropic anomalous bodies or layers, are used to validate the accuracy and efficiency of the proposed method. Numerical results show that the extrapolation cascadic multigrid method improves the efficiency of 3D controlled‐source electromagnetic forward modelling a lot, compared with traditional iterative solvers and some state‐of‐the‐art methods or software (e.g., preconditioned flexible generalized minimal residual method, emg3d) in the considered models and grid settings. The efficiency benefit is more evident as the number of unknowns increases, and the proposed method is more efficient at low frequencies. The extrapolation cascadic multigrid method can also be used to solve systems of equations arising from related applications, such as induction logging, airborne electromagnetic, etc.

Abstract The purpose of the study is to establish the depth of the free water level (FWL), the zone of oxidized oil, the oil-water transition zone, the zone of maximum and decreasing resistivity. Correct understanding of initial oil saturation zonation in carbonate oil-bearing reservoirs is very important for development planning. The article proposes a method for express assessment of the FWL depth and initial oil saturation zonation in carbonate oil-bearing reservoirs based on electrical resistivity study. The values of electrical resistivity determined from induction logging curves in more than 200 wells were used as initial data. The vertical change in the electrical properties is considered using the resistivity values of oil-bearing reservoirs averaged over all wells. The initial oil saturation zonation was analysed using the graphs of electrical resistivity against depth. As a result of the work done, the following conclusions were made regarding the zonation of initial oil saturation and the possible geological characteristics of carbonate oil-bearing reservoirs: 1) based on the graphs of electrical resistivity against depth it is possible to distinguish 3 zones of initial oil saturation: oil-water transition zone above FWL, zone of maximum resistivity in the middle part of the deposit, and zone of decreasing resistivity in the upper part of the deposit; 2) in general, the initial oil saturation in the reservoir (as a function of the electrical resistivity) upward from the initial FWL depth does not grow exponentially, as in the Leverett function, but linearly in each zone. Proposed express method for initial oil saturation zonation in carbonate reservoirs provides novel information for formation testing and perforation planning. In oil-water transition zone it is recommended to use the gentlest methods of perforation and production intensification to preserve the integrity of the oxidized oil zone, since this zone is water confining and can prevent premature water flooding of the product.

An effective method of finding stable solutions of inverse problems of electric and induction logging along the well is proposed, which allows avoiding the influence of the resistance values of the neighboring formations on the determination of the geoelectrical parameters of the object under study. A highly efficient method was proposed for solving such an unstable inverse problem. This method is based on the application of a neural network with inverse error propagation of a simple architecture. Namely three-layer. The mathematical statement of the problem is given, both the topology of the neural network and all its parameters are described in detail. In the course of the numerical experiment, they were selected as optimal. The process of building a base for training a neural network is described in detail. Namely, how each of the examples of the learning base is built by solving a direct problem. With this cut parameter, the training for each example is chosen arbitrarily, which guarantees a comprehensive range for training the neural network. The number of examples in the training base is one hundred thousand examples. As the activation function, the sigmoid is chosen due to the fact that it is differentiable everywhere. The results of testing the written program are given. The learning rate was estimated to obtain the required small error. It is shown that this approach is stably convergent. For testing, the parameters of the layers of the cut, which are inherent to the geophysical parameters of the cuts of the Dnipro-Donetsk depression, were chosen. A complex of lateral logging sounding was chosen as the electrical logging equipment. Four-probe low-frequency induction logging equipment was chosen as induction logging equipment. Examples for induction and electrical logging are given separately. The obtained results are analyzed in detail. Ways of further improvement of the obtained neural network and its use for other problems of geophysics are given.

A novel and efficient modeling approach has been developed for simulating the responses of triaxial induction logging (TIL) in layered biaxial anisotropic (BA) formations. The core of this innovative technique lies in analytically calculating the primary fields within a homogeneous medium and approximating the scattered fields within layered formations. The former involves employing a two-level subtraction technique. Initially, the first-level subtraction entails altering the direction of the Fourier transform to mitigate the integral singularity of the spectral fields, particularly in high-angle and horizontal wells. Conversely, the second-level subtraction aims to further optimize integral convergence by creating an equivalent unbounded transverse isotropic (TI) formation and eliminating the corresponding spectral fields. With the two-level subtractions, the convergence of the spectral field has been enhanced by more than six orders of magnitude. Additionally, a strict recursive algorithm and approximation method are developed to compute the scattered fields in layered biaxial anisotropic media. The rigorous algorithm is based on a modified amplitude propagator matrix (MAPM) approach and serves as the benchmark for the approximation method. In contrast, the approximation method exploits the similarity between the spectral scattered field of the TI medium and the BA medium, establishing corresponding equivalent layered TI models for each magnetic component. Since the scattered field in TI models only involves a one-dimensional semi-infinite integral, the computational complexity is significantly reduced. Numerical simulation examples demonstrate that the new simulation method is at least two orders of magnitude faster than the current modeling approach while maintaining computational precision error within 0.5%. This significantly improved simulation efficiency provides a solid foundation for expediting the logging data processing.

Response characteristics and novel understandings of dual induction logging of horizontal wells in fractured reservoirs

The article studies the wells that opened clayey reservoirs of Paleogene age. When predicting the trajectory of a crack during hydraulic fracturing (HF), it is necessary to take into account the percentage of minerals in the rock, since cracks during hydraulic fracturing are formed at the contacts between mineral grains. This conclusion is indisputable, but obtaining complete information about the percentage of minerals in a rock is an expensive and not always feasible task. At the same time, the physical and mechanical characteristics of clayey rocks are no less significantly influenced by their porosity. Therefore, it is important to note that a reliable determination of the porosity coefficient from the exposed geological section will undoubtedly have a primary positive impact on the reliability of hydraulic fracturing modeling. Based on this, in wells that opened clayey reservoirs, the values of porosity coefficients determined by various methods were analyzed, including the direct one – analysis of core, cuttings and the indirect one – geophysical methods. During the work, a coincidence of the porosity coefficient in the core, cuttings and electrical logging was discovered. Based on the results of the study, it can be concluded that the porosity coefficient determined from acoustic logging (AL) significantly exceeds the values of the porosity coefficient determined from core, cuttings and induction logging. This is due both to the influence of clay content on the acoustic logging readings, and due to the low quality of AC materials induced by erosion of the wellbore. It should be noted that the calculations of porosity coefficients in the above-reference part – in the Batalpashinsky formation based on core and induction logging – coincide almost completely. However, in the sub-reference part of the formation the readings differ slightly. The porosity coefficient calculated is a maximum of 2% lower than the porosity coefficient determined from the core, which is quite acceptable.

The article proposes a method for rapid assessment of the initial position of oil-water contacts, oxidized oil zones, transition zones, zones of high and decreasing resistance in the Lower Carboniferous Tournaisian oil deposits at one of the oilfields of the Republic of Tatarstan. As initial data, the values of electrical resistivity of effective interlayers from the catalog of geological and geophysical data, determined from induction logging curves, were used. Well log data for more than 200 wells drilled in elevation areas were used in analysis. The change in the electrical properties of deposits vertically is considered using the average resistivity values of effective interlayers averaged over all wells. Conclusions are based on the results of the done work: according to the resistivity values in massive carbonate deposits of the Tournaisian age, it is possible to distinguish various zones of oil saturation along the vertical; initial oil saturation does not grow exponentially, as in the Leverett function, but linearly in each zone.

SUMMARY The deployment of electromagnetic (EM) induction tools while drilling is one of the standard routines for assisting the geosteering decision-making process. The conductivity distribution obtained through the inversion of the EM induction log can provide important information about the geological structure around the borehole. To image the 3-D geological structure in the subsurface, 3-D inversion of the EM induction log is required. Because the inversion process is mainly dependent on forward modelling, the use of a fast and accurate forward modelling tool is essential. In this paper, we present an improved version of the integral equation (IE) based modelling technique for general anisotropic media with domain decomposition pre-conditioning. The discretized IE after domain decomposition equals a fixed-point equation that is solved iteratively with either the block Gauss–Seidel or Jacobi pre-conditioning. Within each iteration, the inverse of the block matrix is computed using a Krylov subspace method instead of a direct solver. An additional reduction in computational time is obtained by using an adaptive relative residual stopping criterion in the iterative solver. Using this domain decomposition scheme, numerical experiments show computation time reductions by factors of 1.97–2.84 compared to solving the full-domain IE with a GMRES solver and a contraction IE pre-conditioner. Additionally, the reduction of memory requirement for covering a large area of the induction tool sensitivity enables acceleration with limited GPU memory. Hence, we conclude that the domain decomposition method is improving the efficiency of the IE method by reducing the computation time and memory requirement.