This article presents a mathematical framework for evaluating dual-phase electroosmotic flow in a vertical annulus partially filled with a porous material, consisting of immiscible fluid. Phase one occupies the inner porous region with crude oil, while phase two occupies the outer region as a clear Newtonian fluid. The model incorporates electrokinetic effects through linearized Poisson–Boltzmann equations, slip boundary conditions at the oil–water interface with shear stress jump, and Brinkman-Darcy flow in the porous phase. Exact solutions are obtained for both regions in terms of modified Bessel functions of first and second kinds. For optimization purpose, such solutions are tailored to oil enhancement applications to ascertain the role of each parameter entering flow formation. Findings demonstrate that negative values of the electric field parameter (Ezp<0) actively assist flow formation, eliminate boundary flow stagnation, and accelerate crude oil mobilization, whereas positive values retard transport. Furthermore, quantitative sensitivity analyses reveal that the outer radius ratio, the porous-fluid interface position, and the viscosity parameter exert dominant control over the system pressure gradient and interfacial velocity. Parametric evaluations confirm that optimized electrokinetic configurations yield substantial enhancements in core fluid discharge and production efficiency, providing a robust predictive foundation for designing electro-assisted enhanced oil recovery in vertical annular wellbores.
Uranium mineral prospectivity mapping is of great significance for uranium exploration and the identification of prospective mineralized areas. Hard labels constructed from buffer zones around known uranium occurrences tend to discretize continuously varying mineralization responses, making it difficult to adequately characterize the continuous variation in mineral prospectivity and the uncertainty associated with mineralization boundaries. To address this issue, this study focuses on sandstone-hosted uranium deposits in the Beverley–Four Mile area, South Australia, and introduces a self-distillation strategy into the ResNet50 model. Soft labels generated by the model are employed to supplement the differences in mineral prospectivity and spatial transitional information that are difficult to represent using hard labels, thereby enhancing the model’s ability to learn mineralization-related features. Experimental results show that, after incorporating the self-distillation strategy, ACC, AUC, F1, and PR-AUC are improved by 3.13
Cloud cover in rice-growing regions obscures optical observations and weakens phenological signals, undermining growth-stage monitoring. Thus, we must address disrupted continuity of normalized difference vegetation index under cloud cover, lack of phenology-aware imputation, and limited evaluation of imputation effects on downstream classification.Therefore, we propose a phenology-aware multisensor fusion framework maintaining growth-stage discriminability under cloud cover while aligning outputs with operational needs. It integrates optical–synthetic aperture radar fusion, phenology-aware imputation, classification, and temporal resolution optimization. It is evaluated via temporal-first splitting, ablation tests, and out-of-distribution (OOD) robustness testing across the spatiotemporal domain. Evaluations are performed on 4,500 samples across four major rice-producing provinces in Thailand, covering diverse agro-ecological conditions, ensuring robustness under real-world variability. Results demonstrate significantly improved classification performance of the proposed framework over SAR-only and nonimputed baselines: overall F1 score reaching 0.88, a Cohen’s kappa coefficient of 0.82, and consistent gains under high-cloud-cover scenarios. Fusion improves data coverage and stabilizes classification performance under cloud cover, preserving spectral–structural coherence; phenology-aware imputation retains temporal patterns and reduces bias from missing data; and robustness-oriented evaluation incorporates temporal resolution analysis and OOD testing under degraded observation conditions, ensuring reliable model assessment. Our system generates rice growth stage maps at 10-day intervals together with confidence scores, enabling irrigation scheduling, targeted rice field inspection, and risk alert issuance when reliability and spatial confidence thresholds are satisfied. By enabling reliable rice-growth-stage monitoring under persistent cloud cover, the framework represents a methodological advancement and practical, scalable solution for supporting efficient water allocation, timely input management, and climate-risk mitigation for stakeholders.
Electrical Resistivity Tomography (ERT) is a widely used geophysical method for subsurface investigations, applied in engineering, geology, and environmental studies. ERT data often contain outliers caused by measurement errors, electrode malfunctions, or environmental noise, which can significantly affect the inversion results and lead to misinterpretations of subsurface structures. Traditional outlier detection techniques, such as manual data filtering or statistical thresholding, often lack robustness and adaptability to complex datasets. In this study, we propose a novel automated approach utilizing the RANdom SAmple Consensus (RANSAC) algorithm to identify and correct erroneous measurements in ERT datasets. The proposed approach applies RANSAC with polynomial regression to each depth horizon independently, allowing for improved detection of local anomalies while preserving the overall resistivity distribution. To validate the methodology, we generate synthetic ERT data using the pyGIMLi library and introduce controlled noise to simulate realistic measurement errors. Additionally, the method is tested on the field dataset, enabling an evaluation of its practical performance under actual survey conditions. The performance of the proposed method is assessed by comparing resistivity distributions obtained from filtered datasets with the original synthetic model free of errors. The results demonstrate that RANSAC-based filtering enhances the quality of ERT data, leading to more accurate inversion outcomes. The proposed approach provides a robust and automated solution for geophysical data processing, reducing the influence of erroneous measurements without requiring manual intervention. The methodology is highly adaptable and can be applied to various geophysical techniques and other geological datasets where outlier detection and correction are crucial.
Climate change poses a severe threat to Pakistan and the wider South Asian region, where shifting temperature and precipitation patterns increasingly jeopardise agricultural productivity, water security, and socio-economic stability. This study examines the spatially resolved, seasonally varying drivers of temperature across 161 Pakistani districts (1981–2023) by incorporating surface pressure, wind speed, precipitation, relative humidity, and aerosol optical depth into a Geographically and Temporally Weighted Regression (GTWR) framework, treating temperature as the dependent variable. Bandwidth and kernel parameters were optimised via a corrected Akaike Information Criterion grid search. Benchmarked against global (OLS), spatial-only (GWR), and temporal-only (TWR) regressions, GTWR achieves the lowest AICc and residual sum of squares (2.04 vs. 62.5–123.3), and reduces mean residual Moran's I to 0.016 from 0.35–0.40, confirming that jointly modelling spatial and temporal non-stationarity substantially improves fit and residual independence rather than yielding only marginal gains in variance explained (R2 = 0.9997). Spatial patterns show the strongest warming signals in southern and urbanised districts, with temperature extremes concentrated in the northeast and moderated in the southwest. Marked seasonality emerges across the DJF, MAM, JJA, and SON periods, with the South Asian monsoon identified as a dominant control on summer precipitation across Pakistan's heterogeneous topography. This analysis quantifies region- and season-specific climatic dynamics that remain sparsely documented in the Pakistani context, offering geospatially resolved, policy-relevant evidence for adaptation planning, including water resource management, agricultural resilience, and national climate-action policy, with a transferable methodological template for other topographically complex, monsoon-influenced regions.
This article develops and analyzes an expanded mixed virtual element method for the Sobolev equation with a convection term. The proposed formulation relaxes certain restrictions inherent in the classical mixed approach and provides a flexible framework for the underlying model problem. The well-posedness of the resulting semi-discrete problem is established. For temporal discretization, a fully discrete scheme is constructed using the backward Euler method, ensuring stability and robustness. Optimal a priori error estimates are derived for both the semi-discrete and fully discrete schemes through the introduction of a novel intermediate projection operator, along with its corresponding approximation properties. Lastly, a set of numerical experiments is presented to support the theoretical findings.
Efficient and scalable linear solvers are critical for implicit reservoir simulation, where the linear solver can account for up to 90 OPM simulator on Norne , SPE11C , and Sleipner benchmarks. The resulting framework, , matches or improves upon default OPM solvers ( and ) in a sequential setting (1 MPI rank) and delivers 2– 4× speedups in strong-scaling tests with up to 2048 MPI ranks on a single domain.
Accurately predicting the peak shear strength (PSS) of rock joints is of great significance for rock engineering and mining engineering. In this study, the whale optimization algorithm (WOA) and the sparrow search algorithm (SSA) were used to optimize the hyperparameters of the extreme gradient boosting (XGBoost) model, and two hybrid models, WOA-XGBoost and SSA-XGBoost, were established for predicting PSS. The performance of these two hybrid models was compared with XGBoost, gene expression programming (GEP), group method of data handling (GMDH), and two empirical models. The results show that the hybrid SSA-XGBoost model has the highest prediction accuracy, with its coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE), Willmott's Index of Agreement (WIA), and Legates-McCabe's Index (LM) being 0.9906, 0.2861 MPa, 0.1312 MPa, 0.9994, and 0.9591, respectively. Additionally, the SHapley additive explanations (SHAP) method was used to analyze the importance of each parameter on PSS.
In current image super-resolution reconstruction of digital rock images, most existing networks focus either on single-scale local convolutional features or on a single form of global attention modeling, while lacking the capability to jointly model multi-scale pore structures, high-frequency boundary textures, and long-range connectivity geometry. To address these challenges, this paper proposes a frequency–spatial collaborative enhanced super-resolution network, termed FSCNet, which enables fine-grained reconstruction of pore microstructures with a lightweight architecture. FSCNet incorporates four key innovative components, each targeting a specific challenge in digital rock reconstruction. First, the multi-scale dynamic convolution module (MSDC) is introduced to address the difficulty of modeling heterogeneous pore structures with different sizes, orientations, and spatial distributions, thereby improving the reconstruction of pore boundaries, bedding structures, and micro-fractures. Second, the multi-scale spatial attention (MSSA) module is designed to alleviate the insufficient emphasis on structurally important regions by enhancing pore edges, mineral interfaces, and texture connectivity areas. Third, the frequency–spatial bridge (FSB) module establishes interaction between the frequency and spatial domains to overcome the weak recovery of high-frequency information, improving restoration of pore boundaries and fine mineral textures. Finally, the adaptive expert blending (AEB) module mitigates the imbalance between local detail extraction and global structural modeling by adaptively fusing the local dynamic convolution branch and the sparse global attention branch according to lithological structures. Extensive experiments on the Carbonate2D and Sandstone2D digital rock datasets demonstrate that FSCNet achieves competitive PSNR and SSIM performance, validating its effectiveness for digital rock image super-resolution reconstruction.
With advances in computational mechanics and computer science, the assessment of variability in engineering system responses has become feasible. This study evaluates the limit state of doubly eccentric loaded footing settlements in a 3D finite element model of a two-layer stratified soil domain. The Drucker–Prager constitutive model and Modified Cam Clay model are implemented within a high-fidelity finite element framework. The spatial variability of key soil parameters, including the reload path slope κ , the hydraulic permeability k (governing Darcy’s law), and the critical state line inclination c, is investigated using crude Monte Carlo simulations, with Latin hypercube sampling employed as the sampling strategy. Despite the strong nonlinearity of the system response, the Gaussian stochastic nature of the input variables is preserved in the output variables. Soil configurations with cohesive clay layers in the upper strata tend to produce higher statistical moments of the limit loads. In contrast, sandy soils, in several cases, yield higher mean values of maximum displacement and footing rotation. Similar trends are observed in the corresponding measures of output variability. Furthermore, the probabilities associated with the initiation point of the Meyerhof curve are estimated. The proposed computational framework can therefore support footing settlement design and decision-making processes.
This study introduces a probabilistic transformation of fracture representations to improve the accuracy and transferability of deep-learning surrogates for predicting steady-state pressure fields in fractured porous media. Discrete Fracture Network simulations generated 20,000 paired fracture–pressure samples, comprising 10,000 single-fracture and 10,000 two-fracture cases; a balanced mixed dataset was constructed from both categories. Three representations were evaluated: (1) parametric descriptors mapped through a CNN decoder, (2) binary masks, and (3) continuous super-Gaussian probability density functions (PDFs) implemented within a U-Net framework. The probabilistic transformation converts discrete fracture traces into smooth, fixed-dimensional fields suitable for convolutional learning. The wider PDF representation (σ = 0.02) consistently achieved the lowest errors, with test MSEs of 0.301 × 10⁻3 and 0.545 × 10⁻3 for the dedicated single- and two-fracture models, respectively. The mixed-trained model achieved MSEs of 0.425 × 10⁻3 and 0.538 × 10⁻3 on the corresponding single- and two-fracture test subsets. These results represent 20.0 − 49.3
This work presents a novel framework for approximating multiphase chemical equilibrium in porous media flow simulations. This framework facilitates the development of approximation schemes that, by leveraging equilibrium data from previous time steps, significantly reduce computational costs when integrated within a global mass conservation formulation of reactive transport in porous media. The formulation ensures the conservation of mass for an arbitrary number of chemical species distributed across multiple fluid and solid phases, while rigorously enforcing chemical equilibrium and pore volume conservation, and being compatible with the incorporation of additional kinetic reactions when needed. Comparative tests between the approximate schemes and a fully implicit reference version across three test configurations with increasing complexity demonstrates good performance. Additionally, a criterion is introduced to assess the validity of the proposed approximations, enabling adaptive switching to higher-fidelity equilibrium models when required. This adaptive methodology achieves results comparable to the fully implicit scheme while minimizing computational demands.
During the freezing of frozen soil, the processes of temperature migration, moisture redistribution, and ice-water phase transitions are intricately interrelated, leading to governing equations characterized by pronounced nonlinearity and competing constraints. Conventional numerical approaches generally depend on grid discretization and nonlinear iterative schemes, whereas traditional physics-informed neural networks (PINNs) often encounter challenges such as loss term trade-offs and difficulties in optimizing over extended time steps when applied to strongly coupled phase-change phenomena. To overcome these limitations, this study introduces a Physical Information Extreme Learning Machine (PIELM) framework for simulating the coupled water-heat dynamics in frozen soils. By utilizing spatiotemporal coordinates as inputs and temperature and saturation as outputs, the proposed method employs a fixed stochastic hidden layer mapping alongside analytical derivative computations to systematically integrate initial conditions, Dirichlet and Neumann boundary conditions, experimental anchor points, and partial differential equation (PDE) residuals into a unified weighted linear system. Concurrently, Picard iteration is applied to linearize nonlinear closed-form expressions, including the ice-to-water ratio, diffusion coefficient, and hydraulic conductivity. Validation against clay freezing experimental data demonstrates that the comprehensive PIELM approach accurately reconstructs the final moisture content distribution and the temporal evolution of the hydrothermal field, achieving a root mean square error (RMSE) of 0.387
Naturally fractured reservoirs are essential for subsurface energy production and storage. However, the complexity and uncertainty inherent to fracture network properties make it difficult to characterise fluid flow within them. This study presents an unsupervised machine learning workflow that constrains uncertainty by establishing a systematic link between the pressure transient response observed at the well and the underlying fracture network properties. We generate a geologically consistent ensemble of 4,850 discrete fracture networks (DFNs) and simulate pressure transient responses for the same geometries under three matrix-fracture permeability configurations. For each dataset, we group pressure derivative responses into geologically interpretable flow behaviour clusters using Dynamic Time Warping (DTW) based K-medoids clustering. The resulting cluster medoids provide representative pressure derivative responses that summarise the dominant flow regime sequence within each class. The workflow consistently identifies four stable clusters across all datasets, each characterised by a distinct and repeatable sequence of diagnostic flow regimes consistent with a bounded range of fracture network properties. Feature importance ranking and SHAP values derived from a random forest classifier show that fracture intensity, wellbore fracture length, and backbone fracture fraction provide the strongest geological controls on cluster separation and hence on the emergent diagnostic signatures. Comparing clusters across datasets shows that 64.1
When data are assimilated in a reservoir history matching problem, not all resulting models are equally reliable for forecasting the future behavior. Not only are many of the model assumptions incorrect, but the assimilation methods themselves are imperfect. In fact, even in the perfect model scenario in which all assumptions are correct, the data assimilation algorithm itself may be imperfect, and the posterior ensemble from a given data assimilation procedure may be much different from the correct posterior. In these cases, it is not the correctness of the scenario that is of ultimate importance, but rather the usefulness of the individual model realizations for determining forecast quality. In this paper, the forecast realizations are stacked after history matching to improve predictability. The effectiveness of the approach is demonstrated on applications with redundant observations for which the fit to observed data provides a good surrogate for the fit to true data, and for problems with noisy fitness landscapes that allow minimizations to models with poorly matched data. Although the goal is not to identify the correct scenario, incorrect scenarios were either eliminated or heavily downweighted in some cases. Computation of the stacking weights requires only the solution of a constrained linear optimization problem and does not require alteration of the data assimilation methods or high computational cost.
Predicting permeability from Nuclear Magnetic Resonance (NMR) data is a fundamental yet challenging task in reservoir characterization, primarily due to the uncertainty associated with surface relaxivity ( ρ ) parameters. In this work, we investigate the feasibility of using Machine Learning (ML) to estimate permeability from T_2 distributions and quantify how ρ uncertainty affects predictive accuracy. To address this, we generated a dataset of 15,000 synthetic 3D porous media representing granular sedimentary rock samples. We employed efficient in-house implementations of a Random Walk algorithm (governed by Bloch-Torrey physics) to simulate magnetization decay and obtain T_2 distributions, alongside a Finite Element Method (FEM) solver for the Stokes equations to compute absolute permeability, assuming 100 ρ . In the first experiment, we simulated T_2 distributions by assigning a constant ρ value for all synthetic porous media. In the second experiment, we applied a different ρ value to each synthetic porous medium to emulate real-world uncertainty, representing the scenario where ρ is unknown. The third experiment extends the second by converting the T_2 distributions into surface-to-volume ratio distributions using the specific ρ value assigned in the second experiment to each medium. We systematically compared the Multilayer Perceptron (MLP) performance against the industry-standard Schlumberger-Doll-Research (SDR) model. Overall, the MLP yielded strong predictive performance. The second experiment presented a performance drop for both models, confirming the impact of ρ uncertainty. The main contribution of this work is the systematic quantification of the sensitivity of predictive permeability models to ρ , establishing a controlled benchmark that addresses and reduces existing uncertainties. Additionally, these findings demonstrate that the MLP provides a robust and competitive alternative for permeability estimation in scenarios where ρ is unknown.
Geothermal energy is a key option for decarbonizing heating and cooling in the energy transition. Forecasting geothermal production has inherent uncertainty due to the heterogeneity of geological formations that host the geothermal resource and the limited data available to characterize and quantify these heterogeneities. This uncertainty leads to operational risks such as early thermal breakthrough. Identifying the most valuable monitoring data and data acquisition strategies for operators is key to constraining uncertainties and ultimately de-risking operations in a reliable and cost-effective way. Data-worth analysis quantifies the value of data provided by existing observations or proposed data collection strategies. This study combines Ensemble Smoother with Multiple Data Assimilation and data-worth analysis to constrain uncertainty in production forecasts and reservoir response for a geothermal doublet system located in a clastic, channelized fluvial reservoir. The main monitoring data includes production temperature, injection pressure, and temperature and pressure profiles along the well paths. We show that production temperature and injection pressure alone only can constrain uncertainties in production forecasts. Using observations of well temperature and pressure profiles demonstrates a threefold increase in data worth, which improves both the quantification of production forecasts and reservoir dynamics. At constant injection rates in doublet system, temperature profiles monitored along the wells provide higher data worth compared to pressure profiles. Data from a deviated monitoring borehole is advantageous. Early-time (first year) observations of temperature and pressure profiles along the injector, producer, and monitoring borehole already constrain production uncertainty prior to thermal breakthrough. Data-worth analysis is shown to be most beneficial when conducted across multiple plausible geological scenarios to ensure a more reliable assessment of collection strategies. The findings of this study yield insight into designing informative data-acquisition strategies for direct-use geothermal systems.
This paper presents a comprehensive study of the fluid pressure distribution in a fractured porous medium, taking into account fluid flow through both fractures and matrix blocks. The intricate flow patterns induced by porous networks in the medium result in unusual behavior in flow characteristics. The fractional Darcy’s law is considered to address the type of ambiguity present in these scenarios. Accounting for this, a system of fractional differential equations describing the fluid flow through a fractured medium is developed, and the existence and uniqueness of its solution are discussed. To validate the model and investigate the solution behavior, two independent numerical methods are developed and analyzed: an unconditionally stable finite difference scheme and a spectral method based on fractional Jacobi functions that yields a closed-form polynomial approximation. Convergence analysis for the spectral scheme is carried out, and stability is examined for the finite difference method. The characteristic of the solution is found to depend strongly on the permeability ratio between the matrix and fracture domains, as well as on the order of the fractional derivative. The interplay between medium permeability, fractional derivative order, and the resulting pressure distribution is examined in detail.
Hyperspectral image classification assigns a class label to each pixel in images with hundreds of spectral bands, and recent deep learning methods have achieved strong performance. However, many existing approaches suffer from high computational complexity, leading to long training and inference times as well as heavy memory consumption. Moreover, they often extract redundant spectral information while insufficiently exploiting local spatial context, which limits efficiency and generalization. To address these challenges, we propose an efficient central spectral–spatial context attention framework that emphasizes informative spectral characteristics while incorporating discriminative local spatial information. The framework introduces a Center Sub-Cube Attention (CeSCA) block embedded within residual blocks built using separable convolutions. Motivated by the higher discriminative power of central spectral features, the CeSCA block derives attention from a central sub-cube to jointly capture spectral and local spatial cues. This attention mechanism recalibrates the full three-dimensional feature map, enhancing discriminative spectral–spatial representations while reducing redundancy and computational cost. Extensive experiments on the Indian Pines, Pavia University, and Salinas Scene datasets demonstrate that the proposed method achieves state-of-the-art accuracy under both 10
