Transport in Porous Media最新文献

A Data-Driven Approach for Efficient Prediction of Permeability of Porous Rocks by Combining Multiscale Imaging and Machine Learning 结合多尺度成像和机器学习，高效预测多孔岩石渗透性的数据驱动方法

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-04-02 DOI: 10.1007/s11242-025-02167-3

Iman Nabipour, Maysam Mohammadzadeh-Shirazi, Amir Raoof, Jafar Qajar

{"title":"A Data-Driven Approach for Efficient Prediction of Permeability of Porous Rocks by Combining Multiscale Imaging and Machine Learning","authors":"Iman Nabipour, Maysam Mohammadzadeh-Shirazi, Amir Raoof, Jafar Qajar","doi":"10.1007/s11242-025-02167-3","DOIUrl":"10.1007/s11242-025-02167-3","url":null,"abstract":"<div><p>Digital rock physics has increasingly become an emerging field in which advanced numerical simulation and high-resolution imaging are combined to accurately predict rock properties. In this context, multiscale imaging is crucial for fully capturing the inherent heterogeneity of natural rocks. However, limitations in resolution and field of view (FOV) present significant challenges. Direct numerical simulations at large scales are often not computationally practical or may be too expensive. The compromise between FOV and resolution is particularly pronounced in the complex multiscale pore structures of porous rocks, including carbonates in particular. To address this issue, we propose an innovative machine learning technique that integrates multiscale imaging data at varying resolutions. For the rock sample, we used the imaging data published by Nabipour et al. (Adv Water Resour 104695, 2024) in three resolutions. Our approach employs an optimized neural network design combined with a transfer learning strategy, enabling the identification of complex cross-scale correlations that were previously unattainable with conventional methods. The results demonstrate that this multiscale neural network approach effectively estimates permeability by analyzing various aspects of pore morphology across different scales. In particular, we achieved high accuracy, as evidenced by R-squared coefficients of 0.966 for training and 0.836 for testing in low-resolution domains, and also significantly enhanced computational efficiency, reducing the overall computational time. Despite being tested for images of carbonate rocks, the developed method is adaptable to a wide range of multiscale porous materials and offers a promising solution to the persistent challenge of balancing imaging resolution with FOV.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-025-02167-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Lightweight Multi-scale Neural Network for Inversion of NMR Relaxation Measurements in Porous Media

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-29 DOI: 10.1007/s11242-025-02164-6

Gang Luo, Branko Bijeljic, Sihui Luo, Lizhi Xiao, Rongbo Shao, Martin J. Blunt

{"title":"A Lightweight Multi-scale Neural Network for Inversion of NMR Relaxation Measurements in Porous Media","authors":"Gang Luo, Branko Bijeljic, Sihui Luo, Lizhi Xiao, Rongbo Shao, Martin J. Blunt","doi":"10.1007/s11242-025-02164-6","DOIUrl":"10.1007/s11242-025-02164-6","url":null,"abstract":"<div><p>Nuclear magnetic resonance (NMR) can be used to find fluid type and pore size distribution in rocks. Low-field NMR employs Carr–Purcell–Meiboom–Gill pulse sequences to measure reservoir rock properties, where echo signals are inverted to determine <i>T</i><sub>2</sub> relaxation times. Further analysis provides petrophysical parameters and fluid classification. However, noise and the ill-posed nature of inversion lead to low-resolution <i>T</i><sub>2</sub> spectra, complicating fluid quantification. This study introduces LMsNN, a lightweight multi-scale neural network, to enhance the accuracy of <i>T</i><sub>2</sub> spectrum inversion. By incorporating physical response equations and constraints, LMsNN reduces artifacts and enhances optimization robustness. We validate the method using numerical simulations and direct rock sample measurements, comparing it with two traditional inversion techniques. Results show that LMsNN effectively processes low signal-to-noise ratio, improving fluid identification across rock types. We further applied LMsNN to NMR well log data, where the porosity derived from the inverted <i>T</i><sub>2</sub> spectra closely matched direct rock sample measurements. These findings demonstrate that LMsNN significantly improves NMR relaxation spectrum resolution, offering a more reliable and robust approach for fluid characterization.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Open Boundaries, Anomalous Diffusion and the Darcy-Bénard Instability

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-25 DOI: 10.1007/s11242-025-02160-w

A. Barletta, D. A. S. Rees, M. Celli, P. V. Brandão

引用次数: 0

Impact of Structural Variations in Gas Diffusion Layers on Effective Mass Transfer in PEMFCs Using the Lattice Boltzmann Method

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-24 DOI: 10.1007/s11242-025-02163-7

Khanh-Hoan Nguyen, Kyoungsik Chang, Sadia Siddiqa

{"title":"Impact of Structural Variations in Gas Diffusion Layers on Effective Mass Transfer in PEMFCs Using the Lattice Boltzmann Method","authors":"Khanh-Hoan Nguyen, Kyoungsik Chang, Sadia Siddiqa","doi":"10.1007/s11242-025-02163-7","DOIUrl":"10.1007/s11242-025-02163-7","url":null,"abstract":"<div><p>In this paper, a thorough computational model is used to investigate the heterogeneous mass transport properties in the gas diffusion layers (GDLs) of proton exchange membrane fuel cells (PEMFCs). In PEMFCs, the GDL is essential for the movement of reaction gases and the expulsion of water generated during the process. One strategic way to improve PEMFC performance is to alter the GDL structure. Therefore, this paper introduces the structural modifications in the GDL to improve and optimize fuel cell efficiency. The GDLs are stochastically reconstructed in four distinct configurations: fixed-diameter fibers, fixed-diameter spheres, random-diameter spheres, and a combination of fixed-diameter fiber/spherical. These structures are considered to quantify their influence on diffusion within the GDL. The lattice Boltzmann method (LBM) is employed to simulate the GDL model via OpenLB. The results reveal that variations in structure, thickness, and porosity lead to changes in pore size, shape, and distribution, thereby significantly influencing mass transport properties. The findings indicate that the flow of flux through the entire GDL is easier in a spherical structure as compared to a fiber structure. This analytical approach provides valuable insights into microscopic flow phenomena within porous structures and their consequential impact on macroscopic transport properties.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Density Effects on Mixing in Porous Media: Multi-dimensional Flow-Through Experiments and Model-Based Interpretation

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-22 DOI: 10.1007/s11242-025-02161-9

Yu Ye, Sen Liu, Gabriele Chiogna, Chunhui Lu, Massimo Rolle

{"title":"Density Effects on Mixing in Porous Media: Multi-dimensional Flow-Through Experiments and Model-Based Interpretation","authors":"Yu Ye, Sen Liu, Gabriele Chiogna, Chunhui Lu, Massimo Rolle","doi":"10.1007/s11242-025-02161-9","DOIUrl":"10.1007/s11242-025-02161-9","url":null,"abstract":"<div><p>Density effects can strongly impact flow, solute transport and mixing processes in porous media. In this study, we systematically investigate and compare variable-density flow and transport in quasi two-dimensional and fully three-dimensional porous media using laboratory flow-through experiments and numerical simulations. Sodium chloride was used as conservative tracer in the experiments, with injected concentrations of 4.8 and 20 g/l, respectively. Average flow velocities of 1, 3, 9 and 27 m/d were selected to represent a wide range of advection-dominated flow conditions (Péclet number 3–100). Numerical simulations were performed to quantitatively interpret the bench-scale experiments, as well as to extend the investigation to a larger domain, allowing the analysis of the impact of a wider range of injected concentrations (0.01–65 g/l) and average flow velocities (0.5–30 m/d). Our results reveal distinct plume patterns, including fingering instabilities, sinking and secondary motion, depending on the density difference, on the average flow velocity and on the dimensionality of the system. The latter plays a key role in causing convective rolls, in the rapid sinking of the injected electrolyte plume, and in preventing the onset of fingering instabilities in the 3-D setups. The outcomes of the flow-through experiments, numerical simulations, and Shannon entropy analysis of mixing enhancement by density gradients illuminate a different mixing behavior, under distinct advection-dominated flow regimes, in quasi 2-D and fully 3-D flow-through systems.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Temporally Relaxed Theory of Nonequilibrium Solute Transport in Porous Media With Spatial Dispersivity Involving Flexible Boundary

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-22 DOI: 10.1007/s11242-025-02162-8

Joseph Antoine Nyoumea, Thomas Tjock-Mbaga, Ali Zarma, Jean Marie Ema’a Ema’a, Patrice Ele Abiama, Germain Hubert Ben-Bolie

{"title":"A Temporally Relaxed Theory of Nonequilibrium Solute Transport in Porous Media With Spatial Dispersivity Involving Flexible Boundary","authors":"Joseph Antoine Nyoumea, Thomas Tjock-Mbaga, Ali Zarma, Jean Marie Ema’a Ema’a, Patrice Ele Abiama, Germain Hubert Ben-Bolie","doi":"10.1007/s11242-025-02162-8","DOIUrl":"10.1007/s11242-025-02162-8","url":null,"abstract":"<div><p>Groundwater is a vital drinking water source in tropical regions and supports many human activities. However, its pollution poses significant challenges. Researchers study pollutant behavior in porous media using advection–dispersion equations (ADEs), which account for Fickian and non-Fickian solute transport. This study presents a novel approach to solute transport in a medium with spatially variable dispersivity based on the temporally relaxed theory of Fick's Law. The methodology introduces two relaxation times accounting for solute particles' collisions and attachment, deriving a new ADE. The Darcy velocity is considered as a linear spatial function, and the dispersion coefficient is assumed to be proportional to the square of the velocity. Our findings indicate that the temporally relaxed theory can reproduce the solute transport behavior described by the existing two-stage models, equilibrium models in medium with constant and variable dispersivity. Additionally, the relaxation times significantly affect the temporal and spatial distribution of solute concentration and the remediation time. The effects depend on the input distribution, the position, and the heterogeneity parameter. The relaxation times possess similar properties to the transport parameters in the mobile-immobile and rate-limited sorption models. Time laggings can capture non-linear phenomena, including memory effects, nonequilibrium dynamics, multi-scale behavior, and anomalous transport, such as superdiffusion, subdiffusion, and long-tailed transport. This model can be applied to accurately predict transport parameters from soil column experiments and actual field conditions. This innovative approach provides a deeper insight into solute transport and its impact on groundwater contamination.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Discrete Exterior Calculus Method for Groundwater Flow Modeling 地下水流建模的离散外部微积分方法

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-18 DOI: 10.1007/s11242-025-02159-3

Jin Xu, Wenfan Zhang, Zheng Chen

{"title":"Discrete Exterior Calculus Method for Groundwater Flow Modeling","authors":"Jin Xu, Wenfan Zhang, Zheng Chen","doi":"10.1007/s11242-025-02159-3","DOIUrl":"10.1007/s11242-025-02159-3","url":null,"abstract":"<div><p>A numerical formula for modeling groundwater flow is presented in this study, derived from the principles of discrete exterior calculus (DEC). The study begins with transforming the governing equations for unsteady flow into formulas in the framework of exterior calculus, utilizing differential forms and their operators. The spatial discretization of the exterior calculus formula is based on the conception of simplicial complex and its dual mesh, while the time derivative term is discretized using the difference numerical scheme. Following the above discretization scheme, a mixed numerical formulation was developed, with flux and pressure as primary variables. To evaluate the DEC-based method’s effectiveness and accuracy in modeling groundwater flow, an extensive numerical study is conducted. The assessment includes comparisons with analytical solutions, such as Theis’s solution for a single well, as well as numerical results obtained from simulating multi-well pumping scenarios using established methods. The solutions exhibit a high degree of consistency with both analytical and numerical results. Furthermore, the results demonstrate the applicability of the proposed approach in more complex settings, ranging from pit dewatering with a waterproof curtain to three-dimensional flow with cutoff barriers. The results illustrate the potential of the DEC method as an effective groundwater solver, distinguished by its excellent local mass conservation.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Diffusion Model-Based Generation of Three-Dimensional Multiphase Pore-Scale Images

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-17 DOI: 10.1007/s11242-025-02158-4

Linqi Zhu, Branko Bijeljic, Martin J. Blunt

{"title":"Diffusion Model-Based Generation of Three-Dimensional Multiphase Pore-Scale Images","authors":"Linqi Zhu, Branko Bijeljic, Martin J. Blunt","doi":"10.1007/s11242-025-02158-4","DOIUrl":"10.1007/s11242-025-02158-4","url":null,"abstract":"<div><p>We propose a diffusion model-based machine learning method for generating three-dimensional images of both the pore space of rocks and the fluid phases within it. This approach overcomes the limitations of current methods, which are restricted to generating only the pore space. Our reconstructed images accurately reproduce multiphase fluid pore-scale details in water-wet Bentheimer sandstone, matching experimental images in terms of two-point correlation, porosity, and fluid flow parameters. This method outperforms generative adversarial networks with a broader and more accurate parameter range. By enabling the generation of multiphase fluid pore-scale images of any size subject to computational constraints, this machine learning technique provides researchers with a powerful tool to understand fluid distribution and movement in porous materials without the need for costly experiments or complex simulations. This approach has wide-ranging potential applications, including carbon dioxide and underground hydrogen storage, the design of electrolyzers, and fuel cells.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-025-02158-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

3D Visualization of Viscous Fingering in Miscible Fluids Flow in Porous Materials

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-17 DOI: 10.1007/s11242-025-02157-5

Jiaxi Yang, Toshifumi Mukunoki, Laurent Oxarango

{"title":"3D Visualization of Viscous Fingering in Miscible Fluids Flow in Porous Materials","authors":"Jiaxi Yang, Toshifumi Mukunoki, Laurent Oxarango","doi":"10.1007/s11242-025-02157-5","DOIUrl":"10.1007/s11242-025-02157-5","url":null,"abstract":"<div><p>Viscous fingering is a type of flow instability that occurs when a less viscous fluid displaces a more viscous fluid, causing instability at the displacement front. Owing to the opaque nature of porous media, experimental studies on the structure of viscous fingering and its development over time have been mostly limited to 2D porous media or Hele–Shaw cells. In this study, we used a micro-focused X-ray computed tomography scanner to investigate the 3D characteristics of viscous fingering in porous media. A low-viscosity iodine brine solution was injected in 3D-printed porous samples initially saturated by a high-viscosity syrup solution. The resulting miscible invasion was monitored by a sequence of X-ray tomography. Seven experiments were conducted to explore a large range of Péclet number and viscosity ratio. It allowed to identify the 3D morphology of fingering patterns and to quantitatively evaluate changes in physical properties such as iodine concentration in miscible fluids. As already identified in 2D experiments, characteristic events such as tip splitting, shielding, and coalescence were observed in 3D viscous fingering. At relatively low Péclet numbers, the fingering of the brine phase was more prone to breakthrough at certain points, forming a slender finger structure. As the Péclet number increased, the instability of the brine phase flow increased, making it easier to form multiple finger structures, and the tips were more prone to splitting into small finger structures. When the viscosity ratio decreased, the brine phase flow became more unstable. After halving the viscosity ratio of the miscible solution, multiple finger structures were formed at lower Péclet numbers, with small finger structures continuously splitting at the tips.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-025-02157-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Relevance of Local Dispersion on Mixing Enhancement in Engineering Injection and Extraction Systems in Porous Media: Insights from Laboratory Bench-Scale Experiments and Modeling 多孔介质中工程注入和抽提系统中局部分散对混合增强的相关性：实验室台阶实验和建模的启示

IF 2.7 3区工程技术

Transport in Porous Media Pub Date : 2025-03-01 DOI: 10.1007/s11242-025-02155-7

Francesca Ziliotto, Mónica Basilio Hazas, Markus Muhr, Navid Ahmadi, Massimo Rolle, Gabriele Chiogna

{"title":"Relevance of Local Dispersion on Mixing Enhancement in Engineering Injection and Extraction Systems in Porous Media: Insights from Laboratory Bench-Scale Experiments and Modeling","authors":"Francesca Ziliotto, Mónica Basilio Hazas, Markus Muhr, Navid Ahmadi, Massimo Rolle, Gabriele Chiogna","doi":"10.1007/s11242-025-02155-7","DOIUrl":"10.1007/s11242-025-02155-7","url":null,"abstract":"<div><p>This work investigates the dynamics of flow, transport and mixing in subsurface porous media during an engineered injection–extraction (EIE) system. We perform laboratory bench-scale experiments mimicking an EIE system in an unconfined aquifer, and we explore the role of local dispersion on mixing enhancement. The experimental setup is equipped with four wells operated in a sequence, one at a time, creating transient flows and a fluctuating water table impacting the transport dynamics of an injected dye tracer plume. A high-resolution imaging technique is applied to monitor the spatial and temporal evolution of the plume concentration. The experiments are performed in porous media with fine and coarse grain sizes and considering two different sequences of injection and extraction. The plume spreading and mixing are quantified by computing the spatial moments and the plume area, respectively. The Okubo–Weiss parameter is calculated over the plume area to correlate mixing enhancement with changes in flow topology. The results indicate that the operation of EIE system significantly enhances mixing and spreading, particularly when the effective Okubo–Weiss parameter is higher. Furthermore, the mixing enhancement is larger in the experiments performed in the coarse porous media, indicating the importance of local dispersion as a factor for mixing enhancement in EIE systems.</p></div>","PeriodicalId":804,"journal":{"name":"Transport in Porous Media","volume":"152 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11242-025-02155-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0