Advances in Water Resources最新文献

{"title":"Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation","authors":"Yuanzhe Wang ,&nbsp;Yifei Zong ,&nbsp;James L. McCreight ,&nbsp;Joseph D. Hughes ,&nbsp;Michael Fienen ,&nbsp;Alexandre M. Tartakovsky","doi":"10.1016/j.advwatres.2025.105024","DOIUrl":"10.1016/j.advwatres.2025.105024","url":null,"abstract":"<div><div>We evaluate the performance of the Karhunen–Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen–Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters.</div><div>We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105024"},"PeriodicalIF":4.0,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144335446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transient forcing in heterogeneous aquifers drives solute containment and chaotic mixing","authors":"Satoshi Tajima ,&nbsp;Marco Dentz","doi":"10.1016/j.advwatres.2025.105021","DOIUrl":"10.1016/j.advwatres.2025.105021","url":null,"abstract":"<div><div>Transient forcing of flow in compressible porous media due to tidal fluctuations, recharge cycles, and fluid injection–withdrawal processes, is a key driver of solute dispersion and mixing in geological and engineered systems. The combination of periodic forcing, medium heterogeneity, and compressibility leads to intricate spatio-temporal flow, dispersion, and mixing patterns. We analyse these patterns using detailed numerical simulations based on a stochastic representation of the spatial medium heterogeneity. Solute dispersion is characterised by the interface length and width, and mixing by the dilution index and the distribution of concentration point values. Poincaré sections show how the interplay of heterogeneity and compressibility creates stable regions that inhibit the advancement and dispersion of the mixing interface, and stochastic regions of chaotic advection that enhance solute mixing. This means that spatial heterogeneity in combination with temporal forcing leads to the containment of solute, promoting mixing at the same time. Meanwhile, incorporating local dispersion weakens this confinement, whereas further enhancing mixing. These findings have implications for a diverse range of environmental and industrial applications, including seawater intrusion in coastal aquifers, groundwater remediation, and geological storage activities.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105021"},"PeriodicalIF":4.0,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144289929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new Matrix Equivalent Discrete Fracture Network model for variable density flow in fractured porous media","authors":"Anis Younes","doi":"10.1016/j.advwatres.2025.105037","DOIUrl":"10.1016/j.advwatres.2025.105037","url":null,"abstract":"<div><div>Modeling variable density flow (VDF) in fractured reservoirs is a challenging task because of (<em>i</em>) the high contrast of permeability between the fractures and the matrix, (<em>ii</em>) the complexity of the fracture network and (<em>iii</em>) the nonlinearities induced by density variation. The dual-porosity model (DPM) and the discrete fracture-matrix (DFM) model are among the most used models for the simulation of flow in fractured reservoirs. The DPM is efficient as it uses an implicit representation of the fractures but is not sufficiently accurate since it cannot account for the effect of individual fractures. The DFM model uses an explicit representation of the fractures but suffers from lack of efficiency induced by the poor quality of meshes in the case of complex fracture networks.</div><div>In this study, a new efficient model named matrix-equivalent discrete fracture network (MEDFN) model is developed for VDF in fractured porous media. The main idea of the VDF-MEDFN model is to use an explicit representation of the high-conductive fractures and to replace the low-permeable matrix by an equivalent rectangular fracture network. The flow and the transport equations are then solved on the global fracture network formed by the combination of the initial high-conductive fracture network and the fictitious rectangular low-permeable fracture network representing the matrix.</div><div>The VDF-MEDFN model is developed in this work leveraging the method of lines (MOL) with the upwind finite volume method for the spatial discretization and high-order methods for the time integration. Performed numerical experiments show the validity of the new model and highlight its high performances against the VDF-DFM model, based on DFM and the mixed finite element method.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105037"},"PeriodicalIF":4.0,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144289930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental study on the dynamic filtration characteristics of supercritical CO2 foam fracturing fluid in porous media","authors":"Xudi Wu ,&nbsp;Xingyi Chen ,&nbsp;Jian Ma ,&nbsp;Yang Xu ,&nbsp;Baolun Niu ,&nbsp;Wei Liu","doi":"10.1016/j.advwatres.2025.105036","DOIUrl":"10.1016/j.advwatres.2025.105036","url":null,"abstract":"<div><div>Supercritical CO₂ (SC-CO₂) foam fracturing fluids are increasingly used in unconventional reservoir stimulation due to their water-saving advantages and potential for CO₂ storage. However, the filtration loss of SC-CO₂ foam into porous media significantly limits its fracturing effectiveness. This study employed a self-developed dynamic filtration testing system to investigate the rheological behavior and dynamic filtration characteristics of SC-CO₂ foam. A series of controlled experiments were conducted to examine the effects of foam quality, temperature, pressure, core permeability, and CO₂ phase transition on filtration behavior and core damage. The results demonstrate that SC-CO₂ foam is a shear-thinning non-Newtonian fluid whose viscosity increases with foam quality and pressure but decreases with temperature and shear rate. Compared with conventional fracturing fluids, SC-CO₂ foam exhibits superior filtration control without forming a filter cake. The filtration coefficient decreases with increasing foam quality (up to 80 %), but increases when the foam becomes unstable at 90 %. Phase transition of CO₂ leads to collapse of foam structure and loss of filtration control capacity. Core permeability significantly influences filtration loss, with higher permeability leading to increased fluid leak-off. The permeability damage rate ranges from 10 % to 30 %, and is most severe in low-permeability cores with high liquid-phase content. The key findings of this study are expected to provide theoretical guidance for evaluating the effectiveness of SC-CO₂ foam fracturing.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105036"},"PeriodicalIF":4.0,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A variational framework for inverse modeling: Case study in CO₂ sequestration","authors":"Zhen Zhang ,&nbsp;Xupeng He","doi":"10.1016/j.advwatres.2025.105034","DOIUrl":"10.1016/j.advwatres.2025.105034","url":null,"abstract":"<div><div>This study investigates probabilistic Bayesian inversion methods for CO₂ sequestration problems, focusing on the challenges of estimating subsurface properties in high-dimensional spaces, such as permeability and porosity, and accurately quantifying uncertainties. Traditional approaches, such as gradient-based optimization, Monte Carlo sampling, and Kalman filter-based methods, have notable limitations. Gradient-based methods are computationally efficient but fail to capture uncertainty and are prone to local minima. Monte Carlo methods, while effective in posterior estimation, become computationally infeasible in high-dimensional settings due to the curse of dimensionality. Kalman filter-based methods offer some uncertainty estimation but are limited by their reliance on Gaussian-shaped posterior and weakly nonlinear assumptions for the model-data relationships. To address these challenges, this study explores variational inversion (VI) techniques, recasting Bayesian inference as an optimization problem to efficiently approximate the posterior distribution. Specifically, we apply automatic differentiation variational inference (ADVI) and Stein variational gradient descent (SVGD) to 2D and 3D CO₂ sequestration inverse problems and compare their performance against Monte Carlo sampling and the ensemble smoother with multiple data assimilation (ES-MDA). Our results demonstrate that ADVI and SVGD offer significant computational advantages over traditional methods, while still be able to capture a reliable posterior estimation. ADVI provides more reasonable mean and uncertainty estimates than ES-MDA, even with smaller number of forward runs. SVGD delivers better mean and uncertainty estimates than both ADVI and ES-MDA, with the same computational cost as ES-MDA. Both ADVI and SVGD show better scalability than ES-MDA and MCMC, meaning they are less affected by the increasing dimensionality of the model parameters. These findings highlight the potential of ADVI and SVGD to offer a reliable alternative to traditional MCMC and ES-MDA methods.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105034"},"PeriodicalIF":4.0,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144289931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimation of relative permeability curves in porous media induced by electroosmotic flow through pore-scale two-phase flow simulations","authors":"Zhenlei Zhang ,&nbsp;Zhigang Sun ,&nbsp;Minghui Gao ,&nbsp;Wei Zhou ,&nbsp;Diansheng Wang ,&nbsp;Lei Zhu ,&nbsp;Ziqiang Wang ,&nbsp;Yudou Wang","doi":"10.1016/j.advwatres.2025.105035","DOIUrl":"10.1016/j.advwatres.2025.105035","url":null,"abstract":"<div><div>Given the limited research on two-phase electroosmotic flow within porous media, this paper conducts numerical simulations to investigate the pore-scale two-phase flow behavior and the relative permeability characteristics induced by electroosmotic flow. A two-phase slip velocity approximation model is employed to simulate water/oil two-phase electroosmotic flow in porous structures. The results indicate that, although the dragging capacity of the water phase increases with water saturation, the influence of capillary force and weak viscous coupling between small oil clusters and the water phase results in a non-monotonic trend in the relative permeability of the oil phase. Due to changes in the flow mechanism, the relative permeability of the water phase increases slowly before a certain level of water saturation. However, once the water saturation exceeds this threshold, the relative permeability of the water phase increases rapidly with further increases in water saturation. The increased flow resistance for the oil phase and the diminished electro-osmotic driving force for the water phase are the two primary factors responsible for the lowest oil-phase relative permeability observed in oil-wet porous media. The relative permeability curves for both the oil and water phases increase with the electric field strength under all three wettability conditions. Moreover, high electric field strength will reduce irreducible water saturation under water-wet conditions, but this phenomenon is not as pronounced under intermediate-wet and oil-wet conditions.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105035"},"PeriodicalIF":4.0,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enhancing hydrological modelling with reanalysis soil moisture: A data-driven approach for optimizing initial conditions through reanalysis integration","authors":"Lingxue Liu ,&nbsp;Yufeng Ren ,&nbsp;Zirui Li ,&nbsp;Li Zhou","doi":"10.1016/j.advwatres.2025.105023","DOIUrl":"10.1016/j.advwatres.2025.105023","url":null,"abstract":"<div><div>Hydrological models are fundamental tools for water resource management, flood mitigation, and ecological protection. Soil moisture (SM) critically affects the accuracy and reliability of these models by influencing rainfall infiltration and runoff generation. While previous studies have demonstrated the benefits of incorporating SM observations or products into hydrological simulations, there is still ample room to fully exploit their potential in developing the initial SM conditions and reducing the warm-up process before model calibration. In this study, we develop a novel strategy to enhance the utility of the European Centre for Medium-Range Weather Forecasts Reanalysis v5-Land (ERA5-Land) SM dataset in replacing the default initial SM of the Block-wise use of the TOPMODEL (BTOP) model without warm-up adjustments. This strategy involves establishing robust relationships between BTOP and ERA5-Land SM variables, grounded in their physical definitions, through various curve-fitting functions and Long Short-Term Memory (LSTM) model. The improved ERA5-Land SM series are then applied for the calibration of the BTOP model to assess their effectiveness in substituting initial SM conditions across Japan's Fuji and Shinano River Basins. The results show that the LSTM model outperforms traditional curve fitting in establishing relationships of various SM variable combinations, and the basin-scale LSTM provides a practical advantage for large basins with high computational costs, while still maintaining the reliability of relationship constructed. Furthermore, the proposed strategy for initial SM acquisition exhibits commendable performance in replacing the default initial conditions of the BTOP model, resulting in substantial improvements in hydrological simulations. During the calibration period, the metrics (<em>NSE</em> and <em>KGE</em>’) showed enhancements of up to 30.63 % and 15.03 %, respectively, while in the validation period, these metrics improved by 6.49 % and 25.11 %, further highlighting the effectiveness of the strategy. This satisfactory strategy helps preserve more data for the calibration and validation of hydrological models, particularly in data-scarce basins.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105023"},"PeriodicalIF":4.0,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic Mode Decomposition of 4D imaging data to explore intermittent fluid connectivity in subsurface flows","authors":"Aman Raizada ,&nbsp;Steffen Berg ,&nbsp;Sally M. Benson ,&nbsp;Hamdi A. Tchelepi ,&nbsp;Catherine Spurin","doi":"10.1016/j.advwatres.2025.105013","DOIUrl":"10.1016/j.advwatres.2025.105013","url":null,"abstract":"<div><div>The interaction of multiple fluids within a heterogeneous pore space gives rise to complex pore-scale flow dynamics, such as intermittent pathway flow. Synchrotron imaging has been employed to capture and analyze these dynamics. However, these imaging datasets are often extremely large (on the order of terabytes), and the spatial and temporal characteristics of the relevant flow phenomena are difficult to extract. As a result, identifying the locations of fluctuations that control fluid connectivity remains a significant challenge. In this work, a novel workflow is presented that uses Dynamic Mode Decomposition (DMD) to find critical spatio-temporal regions exhibiting intermittent flow dynamics. DMD is a data-driven algorithm that decomposes complex nonlinear systems into dominant spatio-temporal structures without relying on prior system assumptions.</div><div>The workflow is validated through three test cases, each examining the influence of viscosity ratio on flow dynamics while maintaining a constant capillary number. These scenarios demonstrate the capability of the DMD method to accurately capture underlying flow behavior and extract key intermittent structures from high-dimensional experimental data. DMD offers a powerful and computationally efficient approach for analyzing complex fluid dynamics in heterogeneous pore spaces. The proposed workflow enables rapid and objective identification of relevant time scales and spatial regions of interest. Given its speed and scalability, it holds strong potential as a diagnostic tool for the analysis of large synchrotron imaging datasets.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105013"},"PeriodicalIF":4.0,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144255428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep learning-based surrogate modeling for underground hydrogen storage","authors":"Shuojia Fu ,&nbsp;Shaowen Mao ,&nbsp;Alvaro Carbonero ,&nbsp;Bharat Srikishan ,&nbsp;Neala Creasy ,&nbsp;Hichem Chellal ,&nbsp;Mohamed Mehana","doi":"10.1016/j.advwatres.2025.105014","DOIUrl":"10.1016/j.advwatres.2025.105014","url":null,"abstract":"<div><div>Underground hydrogen storage (UHS) is critical for integrating intermittent renewable energy sources by storing excess energy as hydrogen during surplus periods and retrieving it during shortages. Effective UHS design requires accurate prediction of hydrogen plume migration and reservoir pressure evolution, typically achieved by high-fidelity numerical simulations. Although these physics-based simulations are accurate, they are computationally expensive and unsuitable for rapid decision-making. To address this, we develop efficient surrogate models for UHS prediction using Swin-Unet, a transformer-based deep learning architecture with a U-Net structure. Our results show that Swin-Unet accurately predicts the spatiotemporal evolution of hydrogen saturation and reservoir pressure in heterogeneous depleted gas reservoirs, offering a fast and reliable alternative to traditional simulations. Compared to surrogate models based on U-Net and Segmentation Transformer (SETR), Swin-Unet achieves higher pressure prediction accuracy while maintaining similar training costs. For hydrogen saturation prediction, Swin-Unet achieves higher accuracy than SETR and comparable accuracy to U-Net, while reducing GPU memory usage by about two-thirds and training time by approximately 75% relative to U-Net. This is the first study to apply Swin-Unet to surrogate modeling of UHS, demonstrating its potential as an accurate and efficient approximation for traditional physics-based simulations. Swin-Unet enables accurate and efficient UHS prediction in heterogenous geological formations, supporting sensitivity analysis, uncertainty quantification, and operational optimization for future UHS projects.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105014"},"PeriodicalIF":4.0,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Scale-dependent permeability in geologic formations: Renormalization group theory and finite-size scaling analysis","authors":"Misagh Esmaeilpour ,&nbsp;Cheng Chen ,&nbsp;Saeid Sadeghnejad ,&nbsp;Behzad Ghanbarian","doi":"10.1016/j.advwatres.2025.105019","DOIUrl":"10.1016/j.advwatres.2025.105019","url":null,"abstract":"<div><div>Understanding the scale dependence of permeability (<span><math><mi>k</mi></math></span>) of geologic formations at field scales is essential for precise modeling of flow and transport in subsurface, particularly for underground energy storage. In this study, we conducted extensive computations and investigated the scale dependence of <span><math><mi>k</mi></math></span> in random and heterogeneous formations by employing renormalization group theory (RGT) and finite-size scaling analysis. Based on the random permeability field and following the Gaussian distribution of <span><math><mrow><mtext>ln</mtext><mo>(</mo><mi>k</mi><mo>)</mo></mrow></math></span>, we first generated ten formations with different levels of heterogeneity at five dyadic domain sizes, <span><math><mi>L</mi></math></span> = 2ⁱ, <span><math><mrow><mi>i</mi><mi>∈</mi><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mi>…</mi><mo>,</mo><mn>7</mn></mrow><mo>}</mo></mrow></math></span>. The first formation reflects the permeability distribution of an actual reservoir, while the others were generated with varying degrees of heterogeneity. We then applied the RGT to determine the effective permeability (<span><math><msub><mi>k</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></math></span>) of each formation at various occupation probabilities <span><math><mi>p</mi></math></span> = 0.5, 0.6, 0.7, 0.8, 0.9 and 1. We next used finite-size scaling theory to further analyze the scale-dependent <span><math><msub><mi>k</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></math></span>. The <span><math><mrow><msub><mi>k</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub><mo>−</mo><mi>L</mi></mrow></math></span> plot for each formation was scattered. However, by applying the finite-size scaling analysis the data collapsed onto a single quasi-universal curve. It means that finite-size scaling theory could successfully incorporate the effect of large-scale heterogeneities in the scale dependence of permeability.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"203 ","pages":"Article 105019"},"PeriodicalIF":4.0,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}