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A free energy based model for water transfer in amphiphilic soils
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-14 DOI: 10.1016/j.advwatres.2025.104915
Florian Cajot, Claude Doussan, Philippe Beltrame
A 3D macroscopic gradient-dynamics model is developed and applied to sandy soil in presence of exopolysaccharides (EPS), to mimic a soil influenced by root exuded mucilages (rhizospheric soil). Depending on water content, amphiphilic soil has a hydrophilic or hydrophobic behavior which impacts water transfer and retention. To model this saturation-dependent wettability, we propose a nonequilibrium thermodynamic approach based on the definition of the free energy of the system. The free energy functional contains gravity energy, the free surface energy of the water and the effective interaction (attractive and repellent) between water and the porous matrix with the amphiphilic matter. The latter defines the wettability of the porous medium. Water flow dynamics is derived from Onsager’s variational principle leading to a non-linear fourth order PDE on the saturation generalizing the Richards equation. The new formulation reproduces a range of water flow regimes encountered in soil with EPS: (i) the stoppage of imbibition front in a homogeneous soil leading to equilibrium where moist regions coexist with a dry region, (ii) a decrease in capillary height in comparison with a sand without amphiphilic matter and (iii) the existence of a threshold of amphiphilic concentration for which the capillary rise is stopped at the dry layer containing the amphiphilic matter. After calibrating the parameters of our model, numerical simulation is in qualitative and quantitative agreement with experiments from the literature.
{"title":"A free energy based model for water transfer in amphiphilic soils","authors":"Florian Cajot,&nbsp;Claude Doussan,&nbsp;Philippe Beltrame","doi":"10.1016/j.advwatres.2025.104915","DOIUrl":"10.1016/j.advwatres.2025.104915","url":null,"abstract":"<div><div>A 3D macroscopic gradient-dynamics model is developed and applied to sandy soil in presence of exopolysaccharides (EPS), to mimic a soil influenced by root exuded mucilages (rhizospheric soil). Depending on water content, amphiphilic soil has a hydrophilic or hydrophobic behavior which impacts water transfer and retention. To model this saturation-dependent wettability, we propose a nonequilibrium thermodynamic approach based on the definition of the free energy of the system. The free energy functional contains gravity energy, the free surface energy of the water and the effective interaction (attractive and repellent) between water and the porous matrix with the amphiphilic matter. The latter defines the wettability of the porous medium. Water flow dynamics is derived from Onsager’s variational principle leading to a non-linear fourth order PDE on the saturation generalizing the Richards equation. The new formulation reproduces a range of water flow regimes encountered in soil with EPS: (i) the stoppage of imbibition front in a homogeneous soil leading to equilibrium where moist regions coexist with a dry region, (ii) a decrease in capillary height in comparison with a sand without amphiphilic matter and (iii) the existence of a threshold of amphiphilic concentration for which the capillary rise is stopped at the dry layer containing the amphiphilic matter. After calibrating the parameters of our model, numerical simulation is in qualitative and quantitative agreement with experiments from the literature.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"198 ","pages":"Article 104915"},"PeriodicalIF":4.0,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interaction between corner and bulk flows during drainage in granular porous media
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-13 DOI: 10.1016/j.advwatres.2025.104914
Paula Reis , Gaute Linga , Marcel Moura , Per Arne Rikvold , Renaud Toussaint , Eirik Grude Flekkøy , Knut Jørgen Måløy
Drainage of a liquid by a gas in porous media can be broken down into two main mechanisms: a primary piston-like displacement of the interfaces through the bulk of pore bodies and throats, and a secondary slow flow through corners and films in the wake of the invasion front. In granular porous media, this secondary drainage mechanism unfolds in connected pathways of pendular structures, such as capillary bridges and liquid rings, formed between liquid clusters. To represent both mechanisms, we proposed a dynamic dual-network model for drainage, considering that a gas displaces a wetting liquid from quasi-2D granular porous media. For this model, dedicated analyses of the capillary bridge shapes and hydraulic conductivity were conducted so that the secondary drainage mechanism could be properly quantified at finite speeds. With the model, an investigation of the wetting-phase connectivity and flow during drainage was carried out, covering a broad range of flow conditions. Results indicate that the span of liquid-connected structures in the unsaturated region, as well as their ability to contribute to flow, varies significantly with Capillary and Bond numbers.
{"title":"Interaction between corner and bulk flows during drainage in granular porous media","authors":"Paula Reis ,&nbsp;Gaute Linga ,&nbsp;Marcel Moura ,&nbsp;Per Arne Rikvold ,&nbsp;Renaud Toussaint ,&nbsp;Eirik Grude Flekkøy ,&nbsp;Knut Jørgen Måløy","doi":"10.1016/j.advwatres.2025.104914","DOIUrl":"10.1016/j.advwatres.2025.104914","url":null,"abstract":"<div><div>Drainage of a liquid by a gas in porous media can be broken down into two main mechanisms: a primary piston-like displacement of the interfaces through the bulk of pore bodies and throats, and a secondary slow flow through corners and films in the wake of the invasion front. In granular porous media, this secondary drainage mechanism unfolds in connected pathways of pendular structures, such as capillary bridges and liquid rings, formed between liquid clusters. To represent both mechanisms, we proposed a dynamic dual-network model for drainage, considering that a gas displaces a wetting liquid from quasi-2D granular porous media. For this model, dedicated analyses of the capillary bridge shapes and hydraulic conductivity were conducted so that the secondary drainage mechanism could be properly quantified at finite speeds. With the model, an investigation of the wetting-phase connectivity and flow during drainage was carried out, covering a broad range of flow conditions. Results indicate that the span of liquid-connected structures in the unsaturated region, as well as their ability to contribute to flow, varies significantly with Capillary and Bond numbers.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"198 ","pages":"Article 104914"},"PeriodicalIF":4.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mapping dissolved carbon in space and time: An experimental technique for the measurement of pH and total carbon concentration in density driven convection of CO2 dissolved in water
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-13 DOI: 10.1016/j.advwatres.2025.104916
Hilmar Yngvi Birgisson , Yao Xu , Marcel Moura , Eirik Grude Flekkøy , Knut Jørgen Måløy
We present an experimental technique for determining the pH and the total carbon concentration when CO2 diffuses and flows in water. The technique employs three different pH indicators, which, when combined with an image analysis technique, provides a dynamic range in pH from 4.0 to 9.5. In contrast to usual techniques in which a single pH indicator is used, the methodology presented allows not only to produce a binary classification (pH larger or smaller than a given threshold) but to access a much more complete continuous spatial distribution of pH and concentration levels in the system. We calibrate the method against benchmark solutions and further demonstrate its potential by measuring the pH and total carbon concentration in a density driven convection (DDC) of carbon-enriched water. The motivation for testing the method in this particular experiment comes from the fact that DDC plays a pivotal role in the efficiency of engineered carbon storage processes. The application of the technique presented here provided a tool for the analysis of the spatial distribution of captured carbon in the DDC flow.
{"title":"Mapping dissolved carbon in space and time: An experimental technique for the measurement of pH and total carbon concentration in density driven convection of CO2 dissolved in water","authors":"Hilmar Yngvi Birgisson ,&nbsp;Yao Xu ,&nbsp;Marcel Moura ,&nbsp;Eirik Grude Flekkøy ,&nbsp;Knut Jørgen Måløy","doi":"10.1016/j.advwatres.2025.104916","DOIUrl":"10.1016/j.advwatres.2025.104916","url":null,"abstract":"<div><div>We present an experimental technique for determining the pH and the total carbon concentration when CO<sub>2</sub> diffuses and flows in water. The technique employs three different pH indicators, which, when combined with an image analysis technique, provides a dynamic range in pH from 4.0 to 9.5. In contrast to usual techniques in which a single pH indicator is used, the methodology presented allows not only to produce a binary classification (pH larger or smaller than a given threshold) but to access a much more complete continuous spatial distribution of pH and concentration levels in the system. We calibrate the method against benchmark solutions and further demonstrate its potential by measuring the pH and total carbon concentration in a density driven convection (DDC) of carbon-enriched water. The motivation for testing the method in this particular experiment comes from the fact that DDC plays a pivotal role in the efficiency of engineered carbon storage processes. The application of the technique presented here provided a tool for the analysis of the spatial distribution of captured carbon in the DDC flow.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"198 ","pages":"Article 104916"},"PeriodicalIF":4.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The role of injection method on residual trapping: Insights into bridging scales and heterogeneity
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-11 DOI: 10.1016/j.advwatres.2025.104913
Catherine Spurin , Sharon Ellman , Tom Bultreys , Takeshi Kurotori , Sally Benson , Hamdi A. Tchelepi
CO2 injection into subsurface reservoirs provides a long-term solution to anthropogenic emissions. A variable injection rate (such as ramping the flow rate up or down) provides flexibility to injection sites, and could influence the amount of residual trapping. Observations made in cm-scale samples showed that starting at a low flow rate established a flow pathway across the core at a low capillary pressure, leading to a long-term reduction in pore space utilization, as increases in flux were accommodated with little change in saturation. In this work, the scalability of these observations is evaluated by performing experiments with variable injection rates in larger samples: 5 cm diameter and 12 cm length, compared to 2.5 cm diameter and 4.5 cm length in previous work (Spurin et al., 2024). We observed that starting at a low flow rate did not lead to a long-term reduction in pore space utilization. Instead, saturation increased significantly with increased flux, leading to a higher pore space utilization than experiments where injection started with the higher flow rate. The difference in observations depending on sample size and the role of heterogeneity highlights potential uncertainties in upscaling experimental observations to field-scale applications.
{"title":"The role of injection method on residual trapping: Insights into bridging scales and heterogeneity","authors":"Catherine Spurin ,&nbsp;Sharon Ellman ,&nbsp;Tom Bultreys ,&nbsp;Takeshi Kurotori ,&nbsp;Sally Benson ,&nbsp;Hamdi A. Tchelepi","doi":"10.1016/j.advwatres.2025.104913","DOIUrl":"10.1016/j.advwatres.2025.104913","url":null,"abstract":"<div><div>CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> injection into subsurface reservoirs provides a long-term solution to anthropogenic emissions. A variable injection rate (such as ramping the flow rate up or down) provides flexibility to injection sites, and could influence the amount of residual trapping. Observations made in cm-scale samples showed that starting at a low flow rate established a flow pathway across the core at a low capillary pressure, leading to a long-term reduction in pore space utilization, as increases in flux were accommodated with little change in saturation. In this work, the scalability of these observations is evaluated by performing experiments with variable injection rates in larger samples: 5 cm diameter and 12 cm length, compared to 2.5 cm diameter and 4.5 cm length in previous work (<span><span>Spurin et al., 2024</span></span>). We observed that starting at a low flow rate did not lead to a long-term reduction in pore space utilization. Instead, saturation increased significantly with increased flux, leading to a higher pore space utilization than experiments where injection started with the higher flow rate. The difference in observations depending on sample size and the role of heterogeneity highlights potential uncertainties in upscaling experimental observations to field-scale applications.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"197 ","pages":"Article 104913"},"PeriodicalIF":4.0,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403028","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}
引用次数: 0
Solving the discretised shallow water equations using neural networks
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-09 DOI: 10.1016/j.advwatres.2025.104903
Boyang Chen , Amin Nadimy , Claire E. Heaney , Mohammad Kazem Sharifian , Lluis Via Estrem , Ludovico Nicotina , Arno Hilberts , Christopher C. Pain
We present a new approach to the discretisation and solution of the Shallow Water Equations (SWE) based on the finite element (FE) method. The discretisation is expressed as the convolutional layer of a neural network whose weights are determined by integrals of the FE basis functions. The resulting system can be solved with explicit or implicit methods. Expressing and solving discretised systems with neural networks has several benefits, including platform-agnostic code that can run on CPUs, GPUs as well as the latest processors optimised for AI workloads; the model is fully differentiable and suitable for performing optimisation tasks such as data assimilation; easy integration with trained neural networks that could represent sub-grid-scale models, surrogate models or physics-informed approaches; and speeding up the development of models due to the available functionality in machine-learning libraries. In this paper, we investigate explicit and semi-implicit methods, and FE discretisations of up to quartic-order elements. A variety of examples is used to demonstrate the neural-network–based SWE solver, ranging from idealised problems with analytical solutions to laboratory experiments, and we finish with a real-world test case based on the 2005 Carlisle flood.
{"title":"Solving the discretised shallow water equations using neural networks","authors":"Boyang Chen ,&nbsp;Amin Nadimy ,&nbsp;Claire E. Heaney ,&nbsp;Mohammad Kazem Sharifian ,&nbsp;Lluis Via Estrem ,&nbsp;Ludovico Nicotina ,&nbsp;Arno Hilberts ,&nbsp;Christopher C. Pain","doi":"10.1016/j.advwatres.2025.104903","DOIUrl":"10.1016/j.advwatres.2025.104903","url":null,"abstract":"<div><div>We present a new approach to the discretisation and solution of the Shallow Water Equations (SWE) based on the finite element (FE) method. The discretisation is expressed as the convolutional layer of a neural network whose weights are determined by integrals of the FE basis functions. The resulting system can be solved with explicit or implicit methods. Expressing and solving discretised systems with neural networks has several benefits, including platform-agnostic code that can run on CPUs, GPUs as well as the latest processors optimised for AI workloads; the model is fully differentiable and suitable for performing optimisation tasks such as data assimilation; easy integration with trained neural networks that could represent sub-grid-scale models, surrogate models or physics-informed approaches; and speeding up the development of models due to the available functionality in machine-learning libraries. In this paper, we investigate explicit and semi-implicit methods, and FE discretisations of up to quartic-order elements. A variety of examples is used to demonstrate the neural-network–based SWE solver, ranging from idealised problems with analytical solutions to laboratory experiments, and we finish with a real-world test case based on the 2005 Carlisle flood.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"197 ","pages":"Article 104903"},"PeriodicalIF":4.0,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical study of nonlinear consolidation effect on contaminant transport in an aquitard coupling diffusion and adsorption
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-06 DOI: 10.1016/j.advwatres.2025.104912
Zhaofeng Li , Xi Zou , Wen Zhang , Xiaoli Wu , Yue Hu , Genxu Wang , Walter A. Illman
Aquitards, which widely occur throughout sedimentary basins or alluvial plains, play important roles in groundwater storage and contaminant transport. In this study, a mathematical model for one-dimensional contaminant transport which considered the combined effects of diffusion, adsorption and nonlinear consolidation deformation processes in an aquitard (NCD model) was formulated. An analytical solution was then derived using the separation variable method and the generalized integral transformation technique approach, and the accuracy of the above analytical solution was verified by a numerical model. During the nonlinear consolidation process of the aquitard, the drawdown, Darcy velocity and void ratio remained unstable until the end of consolidation, and contaminants entry into the aquitard exhibited hysteresis influenced by aquitard consolidation. Increasing drawdown of the adjacent confined aquifer, compression index, initial hydraulic conductivity, initial effective stress of the aquitard as well as decreasing values of aquitard thickness, initial void ratio and partitioning coefficient were all found to reduce the breakthrough time of contaminant transport in an aquitard undergoing nonlinear consolidation. Compared with contaminant transport in non-deforming porous medium, where transport parameters identical to those of the aquitard before consolidation (ND model) and after finishing consolidation (NDf model), the breakthrough time of contaminant transport for the NCD model (133.3 years) was significantly greater than that of the ND model (68.9 years), and it was slightly less than that of the NDf model (140.6 years). The difference in breakthrough times, at which the contaminants reach 0.01 times the initial concentration, between the NCD and NDf models had an obvious linear positive correlation with the consolidation factor and the cumulative water release from the aquitard.
{"title":"Analytical study of nonlinear consolidation effect on contaminant transport in an aquitard coupling diffusion and adsorption","authors":"Zhaofeng Li ,&nbsp;Xi Zou ,&nbsp;Wen Zhang ,&nbsp;Xiaoli Wu ,&nbsp;Yue Hu ,&nbsp;Genxu Wang ,&nbsp;Walter A. Illman","doi":"10.1016/j.advwatres.2025.104912","DOIUrl":"10.1016/j.advwatres.2025.104912","url":null,"abstract":"<div><div>Aquitards, which widely occur throughout sedimentary basins or alluvial plains, play important roles in groundwater storage and contaminant transport. In this study, a mathematical model for one-dimensional contaminant transport which considered the combined effects of diffusion, adsorption and nonlinear consolidation deformation processes in an aquitard (<em>NCD</em> model) was formulated. An analytical solution was then derived using the separation variable method and the generalized integral transformation technique approach, and the accuracy of the above analytical solution was verified by a numerical model. During the nonlinear consolidation process of the aquitard, the drawdown, Darcy velocity and void ratio remained unstable until the end of consolidation, and contaminants entry into the aquitard exhibited hysteresis influenced by aquitard consolidation. Increasing drawdown of the adjacent confined aquifer, compression index, initial hydraulic conductivity, initial effective stress of the aquitard as well as decreasing values of aquitard thickness, initial void ratio and partitioning coefficient were all found to reduce the breakthrough time of contaminant transport in an aquitard undergoing nonlinear consolidation. Compared with contaminant transport in non-deforming porous medium, where transport parameters identical to those of the aquitard before consolidation (<em>ND</em> model) and after finishing consolidation (<em>ND<sub>f</sub></em> model), the breakthrough time of contaminant transport for the <em>NCD</em> model (133.3 years) was significantly greater than that of the <em>ND</em> model (68.9 years), and it was slightly less than that of the <em>ND<sub>f</sub></em> model (140.6 years). The difference in breakthrough times, at which the contaminants reach 0.01 times the initial concentration, between the <em>NCD</em> and <em>ND<sub>f</sub></em> models had an obvious linear positive correlation with the consolidation factor and the cumulative water release from the aquitard.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"197 ","pages":"Article 104912"},"PeriodicalIF":4.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422633","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}
引用次数: 0
Effect of an interface undulation on convective dissolution of CO2
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-05 DOI: 10.1016/j.advwatres.2025.104904
R.M. Lucena , J. Pontes , F. Brau , A. De Wit , N. Mangiavacchi
When a partially miscible fluid dissolves into a host phase below it, buoyancy-driven fingering develops when the diffusive boundary solution created is denser than the underlying solvent. In many situations, the interface between the two fluids may present level variations introduced by geometrical irregularities. We study here numerically the influence of this interface undulation on the properties of the convective dissolution and on the resulting transfer flux. Two-dimensional time dependent numerical simulations are performed, assuming that the flow is governed by Darcy’s law, along with the Boussinesq approximation, to account for buoyancy effects introduced by a concentration dependent density. The velocity field is modeled by a vorticity–stream function formulation. The resulting equations are solved through the Taylor–Galerkin Finite Element Method, using a Crank–Nicolson time discretization. It is observed that the onset of the fingering instability is delayed in the inclined regions between the peaks and valleys of the undulation and that the fingers develop mainly in the horizontal regions. Additionally, at the valleys, there is an accumulation of the solute and a thickening of the boundary layer caused by the recirculation which induces the nucleation and by the anchoring of the fingering process at that location. This anchoring is maintained up to the later shutdown stages for cases with large interface undulations. While the flux is larger during the diffusive and initial fingering stages, the asymptotic flux is not strongly influenced by the undulation.
{"title":"Effect of an interface undulation on convective dissolution of CO2","authors":"R.M. Lucena ,&nbsp;J. Pontes ,&nbsp;F. Brau ,&nbsp;A. De Wit ,&nbsp;N. Mangiavacchi","doi":"10.1016/j.advwatres.2025.104904","DOIUrl":"10.1016/j.advwatres.2025.104904","url":null,"abstract":"<div><div>When a partially miscible fluid dissolves into a host phase below it, buoyancy-driven fingering develops when the diffusive boundary solution created is denser than the underlying solvent. In many situations, the interface between the two fluids may present level variations introduced by geometrical irregularities. We study here numerically the influence of this interface undulation on the properties of the convective dissolution and on the resulting transfer flux. Two-dimensional time dependent numerical simulations are performed, assuming that the flow is governed by Darcy’s law, along with the Boussinesq approximation, to account for buoyancy effects introduced by a concentration dependent density. The velocity field is modeled by a vorticity–stream function formulation. The resulting equations are solved through the Taylor–Galerkin Finite Element Method, using a Crank–Nicolson time discretization. It is observed that the onset of the fingering instability is delayed in the inclined regions between the peaks and valleys of the undulation and that the fingers develop mainly in the horizontal regions. Additionally, at the valleys, there is an accumulation of the solute and a thickening of the boundary layer caused by the recirculation which induces the nucleation and by the anchoring of the fingering process at that location. This anchoring is maintained up to the later shutdown stages for cases with large interface undulations. While the flux is larger during the diffusive and initial fingering stages, the asymptotic flux is not strongly influenced by the undulation.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"197 ","pages":"Article 104904"},"PeriodicalIF":4.0,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379233","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}
引用次数: 0
A training trajectory random walk model for upscaling colloid transport under favorable and unfavorable conditions 有利条件和不利条件下胶体迁移的训练轨迹随机游走模型
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-01 DOI: 10.1016/j.advwatres.2024.104878
Bashar M. Al-Zghoul , William P. Johnson , Diogo Bolster
In this study, we present a general random walk model for upscaling colloid transport and retention in two-dimensional porous media. The model is based on direct sampling from spatial and temporal jump distributions of single-interceptors, colloids that first enter the near-surface zone within 200 nm of a collector surface, derived from mechanistic pore-assembly trajectory simulations. This framework facilitates the connection and transition between the interception space and physical space, thereby enabling the upscaling of spatial and temporal distributions of single interceptors to full retention profiles and total residence time distributions. Additionally, the proposed random walk model has been tested across a range of advection and diffusion scenarios, demonstrating both accuracy and efficiency in predicting retention profiles and total residence time distributions. Overall, with the appropriate inputs, this model provides a reliable and efficient framework for predicting colloid transport and retention in porous media without the need for extensive computational sources.
在这项研究中,我们提出了二维多孔介质中胶体迁移和保留的一般随机游走模型。该模型基于单拦截剂的空间和时间跳跃分布的直接采样,胶体首先进入收集器表面200 nm内的近表面区域,从机械孔装配轨迹模拟中得出。该框架促进了拦截空间与物理空间之间的连接和转换,从而使单个拦截器的时空分布升级为完整的保留剖面和总停留时间分布。此外,所提出的随机游走模型已经在一系列平流和扩散场景中进行了测试,证明了预测滞留剖面和总停留时间分布的准确性和效率。总的来说,通过适当的输入,该模型为预测多孔介质中的胶体运输和保留提供了一个可靠而有效的框架,而不需要大量的计算源。
{"title":"A training trajectory random walk model for upscaling colloid transport under favorable and unfavorable conditions","authors":"Bashar M. Al-Zghoul ,&nbsp;William P. Johnson ,&nbsp;Diogo Bolster","doi":"10.1016/j.advwatres.2024.104878","DOIUrl":"10.1016/j.advwatres.2024.104878","url":null,"abstract":"<div><div>In this study, we present a general random walk model for upscaling colloid transport and retention in two-dimensional porous media. The model is based on direct sampling from spatial and temporal jump distributions of single-interceptors, colloids that first enter the near-surface zone within 200 nm of a collector surface, derived from mechanistic pore-assembly trajectory simulations. This framework facilitates the connection and transition between the interception space and physical space, thereby enabling the upscaling of spatial and temporal distributions of single interceptors to full retention profiles and total residence time distributions. Additionally, the proposed random walk model has been tested across a range of advection and diffusion scenarios, demonstrating both accuracy and efficiency in predicting retention profiles and total residence time distributions. Overall, with the appropriate inputs, this model provides a reliable and efficient framework for predicting colloid transport and retention in porous media without the need for extensive computational sources.</div></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"196 ","pages":"Article 104878"},"PeriodicalIF":4.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142975198","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}
引用次数: 0
Incorporating geological structure into sensitivity analysis of subsurface contaminant transport 将地质构造纳入地下污染物运移敏感性分析
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-01 DOI: 10.1016/j.advwatres.2024.104885
Lisa Bigler, Tara LaForce, Laura Swiler
Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. The results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.
在千米尺度上模拟地下污染物的运移通常需要模拟复杂地质构造内部的反应流动和运移。这些构造通常是手工网格化的,因此地质构造通常由一个或几个确定性生成的地质模型来表示,用于地下流动和输送的不确定性研究。地质结构的不确定性会对污染物的运移产生重大影响。在这项研究中,地质结构对页岩地层中污染物示踪剂运输的影响进行了研究,以建立一个用于永久处置乏核燃料的简化通用深层地质储存库。采用开源建模框架,对地质构造层间界面位置不确定的通用乏燃料库中两种示踪剂的输运进行敏感性分析研究。自动化工作流程使用地质构造模型的采样实现以及嵌套灵敏度分析中的不确定流量参数。在储存库内、储存库下游的观测点上的示踪剂浓度被用作确定模型对输入参数和地质实现的敏感性的兴趣量。研究结果表明,地层界面在地质构造中的位置对示踪剂输运具有一级影响,并且这种影响可能大于不确定流动参数的影响。
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引用次数: 0
On the permeability-surface area-porosity relationship for dissolving porous media
IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES Pub Date : 2025-02-01 DOI: 10.1016/j.advwatres.2025.104900
Kai Li , Ran Hu , Ya-Nan Zhang , Zhibing Yang , Yi-Feng Chen
Dissolution in porous media is widespread in natural and engineered systems, accompanied by the evolution of geometric structure, permeability and surface area of the porous matrix. Although extensive research has examined dissolution dynamics in porous media, there is a lack of quantitative characterization of the relationships among permeability, surface area and porosity, which depend on dissolution patterns. Here, we combine dissolution experiments and pore-scale simulations of millimeter-scale porous media to delve into the transitions of dissolution patterns, permeability-porosity relation and surface area-porosity relation. The pore-scale model incorporates the improved volume-of-solid formulation and is subsequently validated by experimental results. Based on a large number of 2D porous media dissolution simulations with different flow rates, reaction rates, and spatial heterogeneity of the pore space, we identify three distinct dissolution patterns and propose a theoretical equation to describe the transitions between these patterns. We further correlate dissolution patterns with the evolution of permeability and surface area as functions of porosity, and quantitatively characterize permeability-porosity and surface area-porosity relationships for different patterns. Finally, we develop a predictive model for the correction factor of surface area, thereby completing the system for modeling the flow-dissolution processes at the Darcy scale. This work is pivotal for upscaling the flow properties and dissolution properties for the Darcy scale and advances field-scale modeling techniques. It also deepens our understanding of dissolution dynamics in porous media and is instructive for underground engineering.
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引用次数: 0
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Advances in Water Resources
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