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Steady flow toward a fully penetrating well takes place in a natural porous formation, where the erratic spatial variations, and the raising uncertainty, of the hydraulic conductivity K are modeled within a stochastic framework which regards the log‐conductivity, ln K, as a Gaussian, stationary, random field. The study provides second order moments of the flow variables by regarding the variance of the log‐conductivity as a perturbation parameter. Unlike similar studies on the topic, moments are expressed in a quite general (valid for any autocorrelation function of ln K) and very simple (from the computational stand point) form. It is shown that the (cross)variances, unlike the case of mean uniform flows, are not anymore stationary due to the dependence of the mean velocity upon the distance from the well. In particular, they vanish at the well because of the condition of given head along the well’s axis, whereas away from it they behave like those pertaining to a uniform flow. Then, theoretical results are applied to a couple (one serving for calibration and the other used for validation purposes) of pumping tests to illustrate how they can be used to determine the hydraulic properties of the aquifers. In particular, the concept of head‐factor is shown to be the key‐parameter to identify the statistical moments of the random field K. Plain Language Summary Flow toward a single well takes place in a porous formation, where the hydraulic conductivity is regarded as a random space function to account for its irregular spatial variability. A simple solution to this difficult problem is achieved by adopting some simplifying assumptions which apply to numerous real settings. Theoretical results are applied to a series of pumping tests in order to demonstrate their utility in the identification of aquifers' hydraulic properties. Key Points A simple, general formulation to compute second‐order moments is presented The head factor is introduced for a robust identification of aquifers' statistical parameters The application to pumping tests is illustrated and discussed

Horizontal wells play a crucial role in enhancing shale gas reservoir production. This study employs transient multiphase simulation to investigate the impact of well trajectory on production optimization throughout a well’s life cycle. The research uses OLGATM as a simulator to examine six well trajectories: toe-up, toe-down, smooth horizontal, undulated toe-up, undulated toe-down, and undulated horizontal. Initial findings indicate comparable production rates across different trajectories during the early production phase, with toe-up wells showing slightly better performances due to minimal slugging. However, as the reservoir pressure decreases, the well trajectory significantly influences production. Horizontal wells achieve the highest accumulated gas production rates due to minimal liquid holdup and back pressure. Toe-up wells experience early liquid accumulation and severe slugging, leading to increased back pressure and smaller production. The study highlights the positive effects of lateral undulations on toe-up and toe-down wells in terms of liquid unloading, however some emphasis is also put on their adverse influence on horizontal wells.

Well‐type flow takes place in a heterogeneous porous formation where the transmissivity is modeled as a stationary random space function (RSF). General expressions for the covariances of the head and flux are obtained and analyzed. The second‐order approximation of the mean radial flux is represented as the product between the solution valid in a homogeneous domain and a distortion term , which adjusts according to the medium heterogeneity. The spatial dependence of the function is studied. In view of the formation identification problem, the equivalent T(eq) and apparent T(ap) transmissivity are computed. The important result is the relationship ( may be either “eq” or “ap”), where TH and TG represent the harmonic and the geometric means of the transmissivity, respectively. The position‐dependent weight is explicitly calculated. Indeed, close to the well, it yields , which is understandable in view of the fact that the limit is equivalent to I → ∞, which is the heterogeneity structure of a stratified formation. Nevertheless, the effective transmissivity of a stratified formation is precisely TH. In contrast, far from the well, one has , with the flow being slowly varying in the mean there. It is shown that grows with increasing . In the case of T(eq), the rate of growing is found (similar to Dagan and Lessoff (2007)) to be strongly dependent upon the position in the flow domain, whereas T(ap) is a more robust property. Finally, it is shown how the general results can be used for practical applications. Key Points Analysis of well‐flows in heterogeneous porous media Analytical expressions of the second‐order moments of the flow variables Application to the formation identification problem

To establish premature optimal well operation modes, it is necessary to consider the process of well operation within the framework of ongoing processes in the common reservoir-well hydrodynamic system and take into account the peculiarities of changes in the properties of the gas condensate mixture and the thermobaric conditions of the reservoir in it. Therefore, the object of the study is the operation of a gas condensate well in the event of technological complications in it, which requires the selection of the necessary optimal operating mode to prevent these complications by comprehensively taking into account the factors influencing this process in the “reservoir-well” system. The article proposes a calculation scheme for establishing the optimal operating mode of a gas condensate well without the formation of a liquid plug at the bottomhole, taking into account the formation deformation during field development in the depletion mode. The problem is solved by determining the required current working volume of produced gas (as well as condensate), bottomhole and contour values of reservoir pressure, condensate saturation and reservoir porosity. As a result of the study, it was revealed that the determined characteristics of the selected optimal mode of a gas condensate well are significantly affected by a change in the reservoir properties of the reservoir (for example, the permeability of the reservoir), which in turn leads to a change in the optimal working gas flow rate of the well. The considered problem has not been previously studied in its full formulation, which is presented in this article, where the solution of the problem under study is achieved taking into account the change in the physical properties of the reservoir fluid and gas, as well as the reservoir properties of the reservoir under conditions of a change in the state of the reservoir system due to emerging deformation processes in the reservoir

Underground coal mining destroys overlying strata, and phreatic aquifer above the panel is destabilized, causing phreatic water level (PWL) variation. On-site monitoring of the PWL variation throughout the mining period is of great significance to the management and conservation of groundwater resources in arid and semiarid mining areas. The research on the decline of the PWL when phreatic aquifer leakage is concentrated, but there is little research on the fluctuation characteristics of PWL under the condition of phreatic aquifer without leakage. Therefore, using the #108 coalface in the Jinjitan colliery of the Yushenfu mining area as a case study to carry out the research on PWL fluctuation induced by underground coal mining. First, phreatic water without leakage throughout the coal mining period in the #108 coalface was determined. Second, considering surface subsidence induced by mining activities and PWL in fluviograph comprehensively, true PWL fluctuation characteristics were analyzed throughout the whole coal seam mining period. It is concluded that the buried depth of PWL presented a trend of “decreasing sharply—increasing sharply—decreasing slowly—increasing slowly—becoming stable” in the monitoring period of 1 year. Furthermore, a well flow model was established to simulate the PWL variation process before and after coal mining and to predict the PWL recovery time after coal mining. On these bases, the error analysis of the measured and predicted PWL recovery time, the relationship between the PWL fluctuation and the residual aquiclude thickness, the impact of rainfall on PWL recovery, the response of surface vegetation eco-environment, and phreatic water resources management and conservation were discussed. These research results are important for achieving a win–win situation strategy that balances the exploitation of coal resources and the conservation of phreatic water resources, promoting the sustainable development of coal mining.

The relevance of the technical and economic evaluation of the application of enhanced oil recovery methods at oil fields at the final stage of development is related to the need to recover the remaining reserves, including hard-to-recover (HTR) reserves, the share of which is growing annually. Currently, there are many effective enhanced oil recovery (EOR) methods for different process conditions, but their application has different effects based on the combination of methods, techniques and production conditions. The aim of this study was to approach the scaling of the effect of the application of modern EOR using the methodology of the clustering of wells with similar technological characteristics. This paper proposes a methodology for the selection of candidate wells to form clusters based on a set of indicators that determine the choice of enhanced oil recovery technology in oil fields at the final stage. The technological efficiency of sidetracking and multistage hydraulic fracturing application was evaluated based on the analytical method of well flow rate estimation. By applying cluster analysis to selected wells, three clusters were formed, each including three wells, united by the geological properties of their reservoir rocks and the filtration–capacitive properties of the oil. After this, the optimal technologies were selected for two clusters—hydraulic fracturing and sidetracking. The accumulated oil production, recovered due to the application of the technologies, from six wells for the first 7 years after the operation was estimated at 306.92 thousand tons of oil. Due to the achieved technological effect, the economic efficiency of the development of the studied oil field will increase due to the proceeds from the sales of the extracted additional oil. The results of this study can be used in the calculation of technical and economic efficiency at oil fields with similar conditions.

This study presents a comprehensive computational analysis of flow rate efficiency during uranium extraction via the In Situ Recovery method. Using field data from a deposit located in Southern Kazakhstan, a series of mathematical models were developed to evaluate the distribution and balance of leaching solution. A reactive transport model incorporating uranium dissolution kinetics and acid–rock interactions were utilized to assess the accuracy of both traditional and proposed methods. The results reveal a significant spatial imbalance in sulfuric acid distribution, with up to 239.1 tons of acid migrating beyond the block boundaries. To reduce computational demands while maintaining predictive accuracy, two alternative methods, a streamline-based and a trajectory-based approach were proposed and verified. The streamline method showed close agreement with reactive transport modeling and was able to effectively identify the presence of intra-block reagent imbalance. The trajectory-based method provided detailed insight into flow dynamics but tended to overestimate acid overflow outside the block. Both alternative methods outperformed the conventional approach in terms of accuracy by accounting for geological heterogeneity and well spacing. The proposed methods have significantly lower computational costs, as they do not require solving complex systems of partial differential equations involved in reactive transport simulations. The proposed approaches can be used to analyze the efficiency of mineral In Situ Recovery at both the design and operational stages, as well as to determine optimal production regimes for reducing economic expenditures in a timely manner.

In situ leaching represents an efficient and safe method for uranium mining, where a suboptimal well flow rate distribution leads to solution imbalances between wells, forming stagnant zones that increase operational costs. This study examines a real technological block from the Budenovskoye deposit, applying reactive transport modeling to optimize well flow rates and reduce operational time and reagent consumption. A reactive transport model was developed based on mass conservation and Darcy’s laws coupled with chemical kinetics describing sulfuric acid interactions with uranium minerals (UO2 and UO3). The model simulated a technological block with 4 production and 18 injection wells arranged in hexagonal cells over 511–542 days to achieve 90% uranium recovery. Six approaches for well flow rate redistribution were compared, based on different weighting factor calculation methods: advanced traditional, linear distance, squared distance, quadrilateral area, and two streamline-based approaches utilizing the minimum and average time of flight. The squared distance method achieved the highest efficiency, reducing operational costs by 5.7% through improved flow redistribution. The streamline-based methods performed comparably and offer potential advantages for heterogeneous conditions by automatically identifying hydraulic connections. The reactive transport modeling approach successfully demonstrated that multi-criteria optimization methods can improve ISL efficiency by 3.9%–5.7% while reducing operational costs.

The Nubian sandstone aquifer is the only water source for domestic use and irrigation in the Kharga oasis, Egypt. In this study, 46 pumping tests are analyzed to estimate the transmissivity of the aquifer and to derive a spatial distribution map by geostatistical analysis and kriging interpolation. The resulting transmissivity values are log-normally distributed and spatially correlated over a distance of about 20 km. Representative values for the transmissivity are a geometric average of about 400 m2/d and a 95% confidence interval of 100–1475 m2/d. There is no regional trend in the spatial distribution of the transmissivity, but there are local clusters with higher or lower transmissivity values. The error map indicates that the highest prediction accuracy is obtained along the central north-south traffic route along which most agricultural areas and major well sites are located. This study can contribute to a better understanding of the hydraulic properties of the Nubian sandstone aquifer in the Kharga oasis for an effective management strategy.

Empirical formulas to estimate the radius of influence, such as the Sichardt formula, occasionally appear in studies assessing the environmental impact of groundwater extractions. As they are inconsistent with fundamental hydrogeological principles, the term “radius of influence myth” is used by analogy with the water budget myth. Alternative formulations based on the well-known de Glee and Theis equations are presented, and the contested formula that estimates the radius of influence by balancing pumping and infiltration rate is derived from an asymptotic solution of an analytical model developed by Ernst in 1971. The transient state solution of this model is developed applying the Laplace transform, and it is verified against the finite-difference solution. Examining drawdown and total storage change reveals the relations between the presented one-dimensional radial flow solutions. The assumptions underlying these solutions are discussed in detail to show their limitations and to refute misunderstandings about their applicability. The discussed analytical models and the formulas derived from it to estimate the radius of influence cannot be regarded as substitutes for advanced modeling, although they offer valuable insights on relevant parameter combinations.