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18 pages, 914 KB  
Article
Fractal Characteristics of Coal Structure and Fluid Transport During Compression Failure Process
by Teng Teng and Wang Yuming
Fractal Fract. 2026, 10(6), 421; https://doi.org/10.3390/fractalfract10060421 (registering DOI) - 21 Jun 2026
Abstract
The fractal characteristics of coal pore–fracture networks and their evolution under compression are essential for predicting rock mass failure and fluid transport. This study combines micro-CT scanning with fractal theory and seepage mechanics to investigate the structural evolution of coal under uniaxial compression [...] Read more.
The fractal characteristics of coal pore–fracture networks and their evolution under compression are essential for predicting rock mass failure and fluid transport. This study combines micro-CT scanning with fractal theory and seepage mechanics to investigate the structural evolution of coal under uniaxial compression and its impact on fluid transport. CT scans were performed at four characteristic stages (initial, elastic, plastic, and failure) to reconstruct three-dimensional fracture networks. Quantitative analysis reveals that fracture porosity increases sequentially from 0.44% to 5.01%, with the failure stage reaching 11.4 times the initial value. Fracture length and aperture distributions follow power-law scaling, and their fractal dimensions exhibit distinct evolution patterns: length dimension increases from 2.43 to a peak of 2.56 in the plastic stage and then drops to 2.47 at failure, while aperture dimension decreases from 2.29 to a trough of 2.12 before rebounding to 2.26. These patterns reflect a dynamic adjustment of network complexity, transitioning from primary fractures to micro-fracture dominance and finally to main fracture coalescence. Based on the Knudsen number, three diffusion regimes of Fick, transition and Knudsen are identified. A fractal permeability model is developed by idealizing the pore space as tortuous capillaries, showing that permeability scales with the fourth power of the maximum pore diameter and is positively influenced by the fractal dimension and the number of large pores. Furthermore, a coupled seepage–stress model is derived, incorporating pressure transmission, shear transmission, and crack opening coefficients. The damage variable is expressed as a function of stress level and fractal dimension. These findings provide theoretical support for predicting gas transport and failure behavior in coal under coupled hydro-mechanical conditions. Full article
(This article belongs to the Special Issue Fractal and Fractional Modelling in Deep Mining and Geomechanics)
19 pages, 3554 KB  
Article
The Bifurcation Characteristics and Dynamical Evolution Rule of Non-Isothermal Seepage Mechanical Model in Fractured Rock Mass
by Zhengzheng Cao
Processes 2026, 14(12), 1985; https://doi.org/10.3390/pr14121985 - 18 Jun 2026
Viewed by 161
Abstract
Aiming at the non-isothermal seepage phenomena in fractured rock mass, this paper conducts nonlinear dynamic research on the coupled seepage problem. Based on solid–fluid heat conduction energy equations and the mutual coupling of temperature and seepage fields, the non-isothermal seepage constitutive relation of [...] Read more.
Aiming at the non-isothermal seepage phenomena in fractured rock mass, this paper conducts nonlinear dynamic research on the coupled seepage problem. Based on solid–fluid heat conduction energy equations and the mutual coupling of temperature and seepage fields, the non-isothermal seepage constitutive relation of fractured rock is derived, and a one-dimensional nonlinear dynamic governing model is established. Theoretical analysis indicates the equilibrium solution of non-isothermal seepage is more complex than that under the isothermal condition. Numerical calculations reveal that temperature variation shifts equilibrium positions and alters the occurrence conditions of hysteresis bifurcation, verifying temperature as a core regulatory factor for seepage dynamic responses. Successive sub-relaxation iteration stability analysis demonstrates obvious differentiated convergence speeds: the seepage field converges markedly faster than the temperature field when the coupled system reaches steady state. Compared with the isothermal seepage, the temperature effect changes the location of abrupt transition points and critical threshold of control parameters, rendering fractured rock seepage systems easier to trigger abrupt structural mutation even at low rock fragmentation degrees. This study clarifies the internal nonlinear dynamic mechanism of thermal–fluid coupled seepage, identifies potential mutation risks in petroleum exploitation and geothermal development, and supplies essential theoretical support for related engineering applications. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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18 pages, 9556 KB  
Article
Numerical Investigation of Thermally Induced Damage Mechanisms in Hydraulic Fracturing of Deep Shale Reservoirs
by Hongke Wang, Zhiyu Luo and Qianli Lu
Processes 2026, 14(12), 1970; https://doi.org/10.3390/pr14121970 - 17 Jun 2026
Viewed by 151
Abstract
To clarify how injection-induced cooling and reservoir properties jointly control rock damage during hydraulic fracturing of deep shale reservoirs, this study develops a coupled thermo–hydro–mechanical phase-field model incorporating fracture pressurization, matrix seepage, heat transfer, thermoelastic stress redistribution, and tensile damage evolution. The hydraulic [...] Read more.
To clarify how injection-induced cooling and reservoir properties jointly control rock damage during hydraulic fracturing of deep shale reservoirs, this study develops a coupled thermo–hydro–mechanical phase-field model incorporating fracture pressurization, matrix seepage, heat transfer, thermoelastic stress redistribution, and tensile damage evolution. The hydraulic fracture component is verified against the classical KGD analytical benchmark, and the thermal damage component is benchmarked against a ceramic quenching experiment. The phase-field formulation is constructed using tensile-compressive strain-energy decomposition so that only the tensile part of the elastic energy contributes to damage evolution, while the compressive stiffness is retained. The results show that low-temperature fluid injections produce a steep but spatially limited cooling zone near the fracture wall. The constrained contraction of the cooled rock generates additional thermoelastic tensile stress, strengthens fracture-tip stress localization, and accelerates phase-field damage accumulation. In the baseline case, thermal cooling increases the peak tensile stress near the fracture tip along profile c from 10.2 MPa in the hydraulic-only case to 22.5 MPa at t = 2 h, while the phase-field damage value increases from 0.03 to 0.77. Five-case sensitivity analyses show that, as αT increases from 0.5 × 10−5 to 1.5 × 10−5 1/°C, the fracture-tip tensile stress at t = 2 h increases from approximately 18.6 MPa to 25.7 MPa, and the damage value increases from approximately 0.80 to 0.96. As permeability increases from 0.0001 mD to 0.01 mD, the pore pressure at 2 m from the fracture wall increases from approximately 50.4 MPa to 71.2 MPa, and the tensile stress along profile c increases from approximately 16.4 MPa to 21.8 MPa. These results demonstrate that coupled thermal and hydraulic effects govern fracture initiation, localization, and propagation tendency during thermally assisted hydraulic fracturing in deep shale reservoirs. Full article
(This article belongs to the Section Energy Systems)
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25 pages, 7299 KB  
Article
Hydro–Mechanical Seepage Characteristics and Composite Permeability Modeling of Post-Peak Fractured Coal
by Wenlong Zhang and Qingwang Lian
Energies 2026, 19(12), 2872; https://doi.org/10.3390/en19122872 - 17 Jun 2026
Viewed by 175
Abstract
Fractured coal in the residual-strength stage is a primary medium for gas migration and drainage in deep mining areas. To investigate the hydro–mechanical seepage response of post-peak fractured coal under constant-pressure-difference conditions, triaxial CO2 seepage tests were conducted on coal specimens collected [...] Read more.
Fractured coal in the residual-strength stage is a primary medium for gas migration and drainage in deep mining areas. To investigate the hydro–mechanical seepage response of post-peak fractured coal under constant-pressure-difference conditions, triaxial CO2 seepage tests were conducted on coal specimens collected from the Xinyuan Coal Mine. A Weibull-based damage constitutive model was established to characterize the confining-pressure-induced hysteresis in the damage-evolution path. The flow-rate evolution and Reynolds number analysis indicated that gas flow remained within the linear Darcy regime. A controlled-variable analysis was used to examine the competing effects governing permeability evolution. Mechanical compaction induced an exponential decrease in permeability, whereas the decrease in permeability with increasing pore pressure was interpreted, within the proposed model framework, as the combined effect of possible adsorption-induced matrix swelling and weakened gas slippage. To address the limitations of conventional constant-slip-factor models, a pressure-dependent slip modulation coefficient was introduced into a composite permeability equation incorporating effective stress, adsorption-related deformation, and dynamic gas slippage. Global nonlinear fitting yielded R2 = 0.97 and an RMSE of 0.1909, with the residuals generally distributed around zero, supporting the fitting reliability of the model within the investigated stress–pressure range. Response-surface analysis identified mechanical compaction as the dominant controlling mechanism, while adsorption-related deformation and gas slippage acted as secondary correction mechanisms. The proposed framework provides a quantitative basis for distinguishing the mechanical and fluid-related effects governing permeability evolution in post-peak fractured coal. Full article
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19 pages, 2488 KB  
Article
Time–Lapse Electrical Resistivity Tomography for Evolving Water–Bearing Fractures Ahead of Tunnels: An Improved Inversion Framework and Synthetic Verification
by Chuanqi Qu, Shuchen Li, Yaohui Liu, Zeen Wan and Zhongzhong Liu
Appl. Sci. 2026, 16(12), 5833; https://doi.org/10.3390/app16125833 - 10 Jun 2026
Viewed by 131
Abstract
Water–bearing fractures and seepage–prone zones ahead of tunnel faces may evolve rapidly under excavation–induced disturbance, making early identification and process tracking essential for risk mitigation. Cross–hole electrical resistivity tomography (ERT) is sensitive to fluid–controlled conductivity contrasts, but time–series interpretation based on independently inverted [...] Read more.
Water–bearing fractures and seepage–prone zones ahead of tunnel faces may evolve rapidly under excavation–induced disturbance, making early identification and process tracking essential for risk mitigation. Cross–hole electrical resistivity tomography (ERT) is sensitive to fluid–controlled conductivity contrasts, but time–series interpretation based on independently inverted snapshots is often unreliable due to ill–posedness, noise, and temporal inconsistency. In this study, we propose an improved time–lapse ERT inversion framework for monitoring evolving water–bearing fractures ahead of tunnels. The method is formulated as a baseline–anchored, Occam–consistent difference inversion that directly estimates resistivity changes relative to an initial state, incorporating error–aware weighting of differenced data and anisotropic regularization adapted to cross–hole sensitivity, so that temporal coherence is enforced during inversion rather than through post hoc differencing. Synthetic verification is conducted using three dynamic scenarios representing horizontal, vertical, and diagonal migration of conductive water–bearing pathways between boreholes. Quantitative comparison against independent inversion across all scenarios and time steps demonstrates that the proposed framework substantially reduces the root mean square error and mean relative error of the recovered resistivity, while significantly improving the spatial correlation coefficient between the recovered and true models, with the largest improvements observed in the diagonal–migration scenario. The reconstructed change maps exhibit more compact anomaly geometry and delineate evolution corridors aligned with the prescribed trajectories, whereas independent inversion produces diffuse and epoch–dependent change patterns. These results indicate that the proposed time–lapse inversion framework provides a more reliable basis for interpreting evolving seepage–related conductive structures in tunnel–ahead investigations. Full article
(This article belongs to the Section Civil Engineering)
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33 pages, 7792 KB  
Review
Recent Advances in Characterization Techniques for the Physical Properties of Multiphase Flows and Seepage Mechanisms
by Shu Tang, Rui Shen, Wei Xiong, Shengchun Xiong, Jiale Shi, Weimin Chen, Guo Wang and Zhengyong Luo
Processes 2026, 14(11), 1827; https://doi.org/10.3390/pr14111827 - 5 Jun 2026
Viewed by 289
Abstract
The transport behavior of multiphase flow in porous media is governed by the cross-scale coupling between fluid properties and pore structure, and serves as the theoretical foundation for core processes in fields such as energy development, underground carbon storage, and environmental remediation. Accurately [...] Read more.
The transport behavior of multiphase flow in porous media is governed by the cross-scale coupling between fluid properties and pore structure, and serves as the theoretical foundation for core processes in fields such as energy development, underground carbon storage, and environmental remediation. Accurately characterizing the intrinsic relationship between physical properties and seepage responses is crucial for enhancing engineering prediction capabilities and optimizing operational strategies. However, the inherent heterogeneity and multiscale nature of natural reservoirs, coupled with the limitations of traditional experimental methods in terms of optical opacity and spatiotemporal resolution, severely hinder a deep understanding of the mechanisms of multiphase flow at the pore-scale. This paper systematically reviews the methodological framework for characterizing physical properties and seepage mechanisms in multiphase flow systems, with a focus on cutting-edge breakthroughs in experimental measurement and visualization technologies over the past decade. Starting with classical and emerging testing methods for key physical properties such as saturation, relative permeability, capillary pressure, and interfacial tension, the paper evaluates the applicability, accuracy advantages, and inherent limitations of different techniques. The paper focuses on the latest advancements in pore-scale visualization technologies, covering microfluidic models, high-resolution X-ray CT, synchrotron rapid dynamic imaging, and multimodal, multiscale imaging fusion strategies; it also explores AI-enabled image processing and data analysis methods, as well as the application potential of cross-scale numerical coupling models in revealing transient seepage mechanisms and correlating them with macroscopic responses. Based on this, an integrated analytical framework of “physical property measurement—visualization characterization—theoretical modeling—engineering application” is established, and the core challenges and future pathways for advancing multiphase flow and seepage research toward “quantification of mechanisms, cross-scale correlation, and adaptation to in situ real-world conditions” are identified. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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18 pages, 14867 KB  
Article
Spherical Permeation Grouting Mechanism of Cement-Bentonite Slurry in Porous Media Based on Fractal Theory
by Jiakun Gong, Jie Chen, Chenxi Xu and Jun Yan
Fractal Fract. 2026, 10(6), 384; https://doi.org/10.3390/fractalfract10060384 - 2 Jun 2026
Viewed by 226
Abstract
Cement-bentonite grout is widely employed for seepage control and dike reinforcement in hydraulic infrastructure projects. The time-varying viscosity of the slurry, the particle-size distribution, and the tortuosity of fluid flow path are important factors affecting the slurry diffusion in a spherical permeation grouting [...] Read more.
Cement-bentonite grout is widely employed for seepage control and dike reinforcement in hydraulic infrastructure projects. The time-varying viscosity of the slurry, the particle-size distribution, and the tortuosity of fluid flow path are important factors affecting the slurry diffusion in a spherical permeation grouting process. However, they are not fully considered in the current theoretical models. In this study, a theoretical spherical permeation grouting model for cement-bentonite slurry is established. Fractal theory is introduced to characterize the particle-size distribution and the tortuosity of fluid flow path. A series of experiments are performed to investigate the rheological properties of cement-bentonite slurry and validate the theoretical model proposed in this study. The impacts of grouting time, grouting pressure and bentonite content on the slurry diffusion process are examined through numerical simulation. The results show that the proposed model predicts slurry diffusion distance with an error of less than 3% under all tested conditions. Compared to models neglecting tortuosity or time-varying viscosity, the proposed model improves prediction accuracy by 20–30% and 8–10%, respectively. Numerical simulations further reveal that increasing bentonite content from 0% to 3% reduces diffusion radius by 71.2%, while doubling grouting pressure increases diffusion radius by up to 47.5%. This indicates that the proposed model can better describe the process of slurry permeation and provide valuable support for related grouting projects. Full article
(This article belongs to the Special Issue Fractal and Fractional in Geotechnical Engineering, Second Edition)
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22 pages, 4612 KB  
Article
Hydrodynamic Characteristics of Seepage Beneath Underwater Structures Under Complex Geological and Geometric Boundaries
by Meng Zhu, Jun Hu, Yanan Zhang and Enjin Zhao
J. Mar. Sci. Eng. 2026, 14(11), 1008; https://doi.org/10.3390/jmse14111008 - 29 May 2026
Viewed by 272
Abstract
The spatiotemporal evolution of seepage fields and the associated hydrodynamic risk of subsequent internal erosion pose a critical threat to the structural integrity of marine and hydraulic infrastructure. To quantify these complex fluid–solid interactions, this study develops a high-fidelity numerical model—coupling the Navier–Stokes [...] Read more.
The spatiotemporal evolution of seepage fields and the associated hydrodynamic risk of subsequent internal erosion pose a critical threat to the structural integrity of marine and hydraulic infrastructure. To quantify these complex fluid–solid interactions, this study develops a high-fidelity numerical model—coupling the Navier–Stokes equations with the Darcy–Forchheimer resistance model and the Volume of Fluid (VOF) method—to investigate transient hydrodynamics within porous foundations under complex geometric and geological boundary conditions. Parametric analyses reveal that spatial porosity distribution fundamentally dictates the system’s seepage capacity; notably, relocating a highly permeable stratum to the shallow sub-surface eliminates upper hydraulic bottlenecks and significantly escalates total volumetric discharge. Furthermore, the study systematically evaluates the hydrodynamic efficacy of multi-dimensional seepage control structures. Results demonstrate that while increasing the vertical depth of a cutoff wall is highly efficient in restricting bulk volumetric flux, it inadvertently induces intense localized streamline convergence and flow acceleration at the structural tip. Conversely, lateral expansion of the wall base, though yielding only a moderate reduction in total seepage, successfully diffuses this concentrated flow and substantially attenuates peak pore fluid velocities. Ultimately, a combined design paradigm is proposed for practical coastal engineering applications: prioritizing vertical penetration to optimize bulk seepage reduction, concurrently integrated with moderate lateral base expansion to redistribute concentrated hydrodynamic shear stresses, thereby minimizing the hydrodynamic potential for localized piping and ensuring long-term stability against seepage-induced degradation. Full article
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19 pages, 14231 KB  
Article
Development Mechanism of Ultra-Deep Effective Reservoirs in the Cretaceous Bashijiqike Formation of the Kelasu Structural Belt, Kuqa Depression, Tarim Basin
by Lu Zhou, Xiaolong Sun, Hong Lou, Yuxin Wang, Jian Wang, Chaoqun Shi, Xinyue Zhao, Yin Liu and Li Peng
Minerals 2026, 16(6), 577; https://doi.org/10.3390/min16060577 - 27 May 2026
Viewed by 283
Abstract
As a key target for hydrocarbon exploration in clastic rocks in the Tarim Basin, reservoir characteristics of the Cretaceous Bashijiqike Formation in the Kuqa Depression vary significantly in different areas, especially ultra-deep reservoirs. Understanding the development mechanism and controlling factors of effective reservoirs [...] Read more.
As a key target for hydrocarbon exploration in clastic rocks in the Tarim Basin, reservoir characteristics of the Cretaceous Bashijiqike Formation in the Kuqa Depression vary significantly in different areas, especially ultra-deep reservoirs. Understanding the development mechanism and controlling factors of effective reservoirs is critical for ultra-deep hydrocarbon exploration. This study focuses on typical gas reservoirs in the Bozi (BZ) and Keshen (KS) areas. Core observation, polarizing microscope, cathodoluminescence microscope, scanning electron microscope, X-ray diffraction analysis, porosity and permeability test, and imaging logging interpretation have been used to systematically investigate reservoir petrology, diagenesis, physical property, and fracture characteristics. The results indicate that the BZ8 and BZ9 reservoirs experienced weak paleostress and tectonic deformation, resulting in relatively weak tectonic compaction, abundant primary intergranular pores, and sparse fractures. Reservoir cements are dominated by dolomite, indicating diagenesis was mainly affected by lagoonal fluids. In contrast, the KS31 reservoir is characterized by strong paleostress and deformation, leading to intense compaction and negligible primary pores but well-developed fractures. The reservoir is dominated by calcite, quartz and albite cements, suggesting a dominant influence of meteoric water. Furthermore, reservoirs are significantly affected by structural positions within an individual anticline. Compared with the anticlinal limbs, the anticline core undergoes overall upward arching and folding. The outer strata above the neutral surface develop intense horizontal tensile stress perpendicular to the fold hinge. This promotes fracture development and primary pore preservation, thus facilitating the seepage of diagenetic fluids and enhancing local dissolution. Full article
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19 pages, 5191 KB  
Article
Analysis of Grout Diffusion Law in 3D Rough Fractures Based on Fractal Characteristics of JRC Curves
by Ermeng Zhang, Lang Liu, Yiming Li and Huisheng Qu
Fractal Fract. 2026, 10(6), 352; https://doi.org/10.3390/fractalfract10060352 - 22 May 2026
Viewed by 246
Abstract
Understanding grout diffusion behavior in rough-walled rock fractures is essential for optimizing grouting design in mining and geotechnical engineering. This study couples fractal surface reconstruction with three-dimensional volume-of-fluid (VOF) simulation to systematically investigate grout diffusion in fractures characterized by the Weierstrass–Mandelbrot fractal function. [...] Read more.
Understanding grout diffusion behavior in rough-walled rock fractures is essential for optimizing grouting design in mining and geotechnical engineering. This study couples fractal surface reconstruction with three-dimensional volume-of-fluid (VOF) simulation to systematically investigate grout diffusion in fractures characterized by the Weierstrass–Mandelbrot fractal function. Twelve simulation cases, comprising four JRC profiles and three grout viscosities, are analyzed to elucidate the spatiotemporal evolution of grout filling. The results reveal a consistent three-stage diffusion pattern—initial filling, rapid diffusion, and stable equilibrium—across all conditions. Fracture fractal dimension emerges as the dominant factor controlling seepage velocity and diffusion zoning, while grout viscosity plays a secondary, roughness-modulated regulatory role. The equivalent hydraulic aperture is identified as the core parameter governing zone proportions. Engineering guidelines for viscosity selection and injection strategy under different roughness conditions are proposed. Full article
(This article belongs to the Section Engineering)
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31 pages, 4870 KB  
Article
Evolution of Wellbore Interfacial Debonding Induced by Fracturing Fluid Invasion in Eccentric Wellbores: A 3D Stress-Seepage Coupled Numerical Modeling Study
by Yan Xi, Zhiheng Shen, Haoyuan Zheng, Liwei Yu, Shimao Zheng, Hailong Jiang and Yumei Li
Processes 2026, 14(10), 1613; https://doi.org/10.3390/pr14101613 - 16 May 2026
Viewed by 210
Abstract
Hydraulic fracturing is critical for unconventional oil and gas development, yet perforation-induced initial damage impairs the integrity of the casing–cement sheath–formation assembly, causing fracturing fluid channeling and reduced stimulation efficiency. A stress-seepage coupling numerical model was established to simulate interface fracture initiation, propagation, [...] Read more.
Hydraulic fracturing is critical for unconventional oil and gas development, yet perforation-induced initial damage impairs the integrity of the casing–cement sheath–formation assembly, causing fracturing fluid channeling and reduced stimulation efficiency. A stress-seepage coupling numerical model was established to simulate interface fracture initiation, propagation, and sealing failure, quantifying axial and circumferential channeling evolution at the cement–formation interface. Key parameters (casing eccentricity, cement elastic modulus, injection rate, and minimum horizontal in situ stress) were systematically analyzed. Results show fluid preferentially migrates through perforation-weakened zones, with channeling initiating via axial debonding, then circumferential propagation, and finally dominant axial extension. Casing eccentricity exacerbates channeling, while higher cement elastic modulus or in situ stress mitigates it significantly; injection rate affects channeling length but not fracture initiation/propagation pressures. This study provides theoretical and practical guidance for fracturing channeling risk control. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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22 pages, 7732 KB  
Article
Numerical Modeling of Coastal Foundation Pits Using Fluid–Soil–Structure Coupling and Dynamic Seepage Boundaries
by Wei Huang, Linying Que, Senkai He, Yang Li, Zemin Ma and Zhibo Chen
Water 2026, 18(10), 1181; https://doi.org/10.3390/w18101181 - 13 May 2026
Viewed by 421
Abstract
A growing number of coastal foundation pits are being constructed. Based on an actual coastal deep foundation pit project, this study develops a finite element model that incorporates fluid–soil–structure coupling and dynamic seepage boundaries to simulate tidal fluctuations. The model investigates the influence [...] Read more.
A growing number of coastal foundation pits are being constructed. Based on an actual coastal deep foundation pit project, this study develops a finite element model that incorporates fluid–soil–structure coupling and dynamic seepage boundaries to simulate tidal fluctuations. The model investigates the influence of seawater and river water on the deformation behavior of the foundation pit. Results demonstrate the feasibility of the proposed modeling approach, which integrates fluid–soil–structure coupling with dynamic seepage boundaries and employs appropriate constitutive models for different soil layers. Under tidal action, deformation of the soil on the seaward side of the pit is significantly greater than at other locations. Pore pressure and pit deformation exhibit periodic fluctuations synchronized with the tidal cycle. Compared to static water conditions, pore pressure and surface settlement increase markedly, whereas horizontal displacement shows no significant final difference. An increase in the mean sea level leads to greater horizontal displacement of the diaphragm wall but reduces ground settlement outside the pit. Although river water level changes affect deformation through a mechanism similar to that of mean sea level, its impact is considerably weaker due to the greater distance from the pit and relatively stable water level. Therefore, tidal effects should be prioritized in the design and risk assessment of coastal foundation pits. Full article
(This article belongs to the Special Issue Coastal Engineering and Fluid–Structure Interactions, 2nd Edition)
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27 pages, 10513 KB  
Article
A Physics-Informed Neural Network Model for Reservoir Seepage in Porous Media Based on Darcy’s Law
by Yun Zhang, Xiaofan Chen, Kuanguo Li and Yifan Zou
Processes 2026, 14(10), 1578; https://doi.org/10.3390/pr14101578 - 13 May 2026
Viewed by 297
Abstract
Purely data-driven machine-learning methods are currently limited by weak physical interpretability; meanwhile, the sparsity of well-site data in oil and gas fields further degrades the prediction performance of deep learning models for reservoir seepage simulation. To overcome this bottleneck, this study embeds Darcy’s [...] Read more.
Purely data-driven machine-learning methods are currently limited by weak physical interpretability; meanwhile, the sparsity of well-site data in oil and gas fields further degrades the prediction performance of deep learning models for reservoir seepage simulation. To overcome this bottleneck, this study embeds Darcy’s law-based seepage equations as physical constraints into the loss function of a deep learning framework, thereby constructing a physics-informed neural network (PINN) for seepage flow in porous media of oil and gas reservoirs. Numerical simulations are performed in heterogeneous porous media to compare the predictive performance of the proposed PINN against conventional purely data-driven approaches, via evaluation metrics including the coefficient of determination (R2) and root mean square error (RMSE). The results show that both models achieve comparable predictive accuracy with sufficient training samples. In contrast, the PINN retains high predictive accuracy even with a reduced number of samples, and it delivers prominent superiority under conditions of sparse well data and strong reservoir heterogeneity. This study clarifies the applicable scenarios of the two aforementioned methods (physics-informed neural networks and purely data-driven machine-learning models) for fluid flow simulation in porous media and provides a solid theoretical and technical foundation for the accurate prediction of reservoir seepage fields and the optimization of oil and gas reservoir development. This work also offers a validated physics-constrained deep learning framework to guide the deployment of intelligent algorithms in practical subsurface flow engineering. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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20 pages, 11777 KB  
Article
Risk Assessment of Tunnel Construction Deformation Under Spatial Variation in Hydraulic Parameters
by Shangyou Jiang, Qihao Jiang, Xinlei Lyu, Xiaoxi Feng, Dongming Zhang and Hongwei Huang
Appl. Sci. 2026, 16(9), 4512; https://doi.org/10.3390/app16094512 - 4 May 2026
Viewed by 363
Abstract
Tunnel construction in soft soil environments involves significant geological and hydraulic uncertainty, particularly where permeable sandy interlayers within soft clay are prone to seepage-induced instability and excessive settlement. Although hydraulic–mechanical coupling is widely recognized, the spatial variability of key soil parameters (e.g., permeability [...] Read more.
Tunnel construction in soft soil environments involves significant geological and hydraulic uncertainty, particularly where permeable sandy interlayers within soft clay are prone to seepage-induced instability and excessive settlement. Although hydraulic–mechanical coupling is widely recognized, the spatial variability of key soil parameters (e.g., permeability and elastic modulus) is often inadequately represented, limiting quantitative evaluation of heterogeneous ground effects on construction-induced deformation. In this study, statistical analyses of site investigation and monitoring data are conducted to characterize parameter distributions and transverse settlement trough morphology, supporting model validation. A fluid–solid hydro-mechanical coupled numerical model in ABAQUS demonstrates that groundwater flow increases maximum surface settlement from 3.18 cm to 3.58 cm, confirming the significance of hydraulic coupling. To quantify spatial variability effects, a stochastic finite element framework based on random field theory is developed, showing that variations in vertical correlation length influence both the mean and dispersion of maximum settlement. Specifically, under a settlement control threshold of 40 mm, the failure probability decreases from 24.21% to 1.01% as the vertical correlation length increases from 1.5 m to 6 m. Finally, an engineering-oriented risk assessment framework is established using settlement trough area as the core loss indicator; its lognormal distribution is verified, and failure probability and reliability indices are integrated with code-based thresholds to evaluate construction risk under different scenarios, with the resulting risk levels ranging from Relatively High (Level III) to Moderate (Level II). Full article
(This article belongs to the Special Issue Advances in Smart Underground Construction and Tunneling Design)
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19 pages, 13864 KB  
Article
Mechanism of Water Invasion Zone Damage on Multi-Cycle CO2 Huff-n-Puff Recovery in Tight Oil Reservoirs
by Fenglan Zhao, Danfeng Tao, Shijun Huang, Shengchen Xie and Chaoshuo Wang
Processes 2026, 14(9), 1402; https://doi.org/10.3390/pr14091402 - 27 Apr 2026
Viewed by 251
Abstract
Tight oil reservoirs are characterized by poor petrophysical properties. After hydraulic fracturing, the low flowback rate of fracturing fluid readily leads to the formation of a water invasion zone in the near-wellbore region, which severely restricts the performance of Carbon dioxide (CO2 [...] Read more.
Tight oil reservoirs are characterized by poor petrophysical properties. After hydraulic fracturing, the low flowback rate of fracturing fluid readily leads to the formation of a water invasion zone in the near-wellbore region, which severely restricts the performance of Carbon dioxide (CO2) huff-n-puff. To clarify the damage mechanism of the water invasion zone on CO2 huff-n-puff in tight oil reservoirs and determine the key regulatory parameters, tight cores with a relative water invasion zone length Δδ = 0.3 were adopted as the research subject. Five groups of injection–soaking–production time combinations were designed, and single-factor analysis was implemented using the control variable method. Integrated with numerical simulation and nuclear magnetic resonance (NMR) testing, the influence of the water invasion zone, pore crude oil mobilization characteristics, and parameter regulation effects were systematically explored. The results demonstrate that the water invasion zone occupies effective pore throats to form a continuous water-phase barrier, hindering CO2 seepage and mass transfer. After four huff-n-puff cycles, the cumulative recovery factor of the water-invaded model is 4.13 percentage points lower than that of the water-free model. After four huff-n-puff cycles, the cumulative recovery factor of the water-invaded model is 4.13 percentage points lower than that of the water-free model. The NMR T2 spectra of cores with and without water invasion exhibit remarkable discrepancies: the water-free core presents a unimodal structure, while the water-invaded core features a distinctive bimodal structure, with obvious staged characteristics in crude oil mobilization. The recovery factor declines nonlinearly and sharply with the increase of Δδ, verifying that the water invasion zone length is the dominant controlling factor. The regulation effects of injection, soaking, and production time differ significantly: injection time serves as the pivotal parameter for enhancing oil recovery. Prolonging injection time can strengthen displacement intensity and dismantle the water-phase barrier, thereby elevating the recovery factor, whereas soaking time and production time have no significant improvement effect. The results can provide valuable references for the parameter optimization of CO2 huff-n-puff in water-invaded tight oil reservoirs. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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