Special Issue "Modeling of Flow and Transport in Saturated and Unsaturated Porous Media"

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydraulics and Hydrodynamics".

Deadline for manuscript submissions: 31 December 2020.

Special Issue Editors

Dr. Anis Younes
Website SciProfiles
Guest Editor
Laboratoire d'Hydrologie et de Geochimie de Strasbourg, CNRS, UMR 7517, University of Strasbourg, Strasbourg, France
Interests: modeling flow and transport in saturated/unsaturated porous media; density driven flow; numerical methods; parameter estimation by inverse modeling
Dr. Philippe Ackerer
Website
Guest Editor
Laboratoire d'Hydrologie et de Geochimie de Strasbourg, CNRS, UMR 7517, University of Strasbourg, Strasbourg, France
Interests: Flow and transport modeling in porous media; parameter estimation by inverse modeling; laboratory experiments, real field simulations
Dr. Marwan Fahs
Website SciProfiles
Guest Editor
Laboratoire d'Hydrologie et de Geochimie de Strasbourg, CNRS, UMR 7517, University of Strasbourg, Strasbourg, France
Interests: Contaminant transport and heat transfer in porous media; density driven flow; natural convection; multispecies reactive transport; numerical models and codes development; semi-analytical solutions; benchmarks

Special Issue Information

Dear Colleagues,

This Special Issue focuses on recent advances and future developments in the modeling of flow, mass and heat transfer in porous media. This includes, but is not limited to: saturated/unsaturated flow, multiphase flow, multicomponent reactive transport, heat transfer and coupled hydraulic, thermal, mechanical, chemical and biological processes.

All modeling steps (mathematical models, data assimilations, numerical methods, simulation, parallel computing, post-processing, validation, benchmarking, calibration, comparison against laboratory experiments, sensitivity and uncertainty analysis, field applications) are included.

A non-exhaustive list of possible contributions includes:

  • Extension of mathematical models for improving model realism
  • Modeling and simulation studies for new physical insights
  • Development and evaluation of models, new algorithms and numerical techniques
  • Stochastic and probabilistic modeling
  • Analytical and semi-analytical solutions, benchmarking issues
  • Inverse problems and characterization of soil and aquifer properties
  • Uncertainty and sensitivity analysis
  • Lab experimental studies and comparison against numerical simulations
  • Field applications of models, upscaling and calibration.

Dr. Anis Younes
Dr. Philippe Ackerer
Dr. Marwan Fahs
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Water is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Saturated, unsaturated and fractured porous media
  • Flow, mass and heat transfer
  • Coupled physical, chemical and biological transport
  • Multi-scale, multi-physics, nonlinear processes
  • New numerical methods and algorithms
  • Inverse modeling and parameter estimation
  • Sensitivity and uncertainty analysis
  • Laboratory and field investigations

Published Papers (21 papers)

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Open AccessArticle
A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers
Water 2020, 12(6), 1639; https://doi.org/10.3390/w12061639 - 08 Jun 2020
Abstract
We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural [...] Read more.
We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method. Full article
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Open AccessArticle
B-Spline Method of Lines for Simulation of Contaminant Transport in Groundwater
Water 2020, 12(6), 1607; https://doi.org/10.3390/w12061607 - 04 Jun 2020
Abstract
In this study, we propose a new numerical method, which can be effectively applied to the advection-dispersion equation, based on B-spline functions and method of lines approach. In the proposed approach, spatial derivatives are calculated using quintic B-spline functions. Thanks to the method [...] Read more.
In this study, we propose a new numerical method, which can be effectively applied to the advection-dispersion equation, based on B-spline functions and method of lines approach. In the proposed approach, spatial derivatives are calculated using quintic B-spline functions. Thanks to the method of lines approach, the partial differential equation governing the contaminant transport in groundwater is converted into time-dependent ordinary differential equations. After this transformation, the time-integration of this system is realized by using an adaptive Runge–Kutta formula. In order to test the accuracy of the proposed method, four numerical examples were solved and the obtained results compared with various analytical and numerical solutions given in the literature. It is proven that the proposed method is faster and more reliable than other methods referenced herein and is a good alternative for simulation of contaminant transport problems as a result of these comparisons. Full article
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Open AccessFeature PaperArticle
Simulation of Water and Salt Dynamics in the Soil Profile in the Semi-Arid Region of Tunisia—Evaluation of the Irrigation Method for a Tomato Crop
Water 2020, 12(6), 1594; https://doi.org/10.3390/w12061594 - 03 Jun 2020
Abstract
In Tunisia, water used for irrigation is often saline, increasing the risk of salinization for soils and crops. In this study, an experiment was conducted on a tomato crop cultivated on a silty-clay soil irrigated with three different water qualities: 0, 3.5, and [...] Read more.
In Tunisia, water used for irrigation is often saline, increasing the risk of salinization for soils and crops. In this study, an experiment was conducted on a tomato crop cultivated on a silty-clay soil irrigated with three different water qualities: 0, 3.5, and 7 dS·m−1. Experimental data were then used to calibrate and validate the Hydrus-1D model, which simulates water flow and salt transfer in soils. The successfully-calibrated and validated model was then used to study the combined effects of the soil osmotic and soil matrix potentials on root water uptake. The values of the root mean square error (RMSE), the coefficient of determination (CD), the modeling efficiency (EF), and the coefficient of residual mass (CRM) were close to their optimal values for both soil water content and soil electrical conductivity profiles, indicating the reliability of the model to reproduce water and salt dynamics. Relative yields (Yr), indirectly estimated using actual and potential root water uptake (transpiration), indicated that the multiplicative stress response model (using the S-shape model) satisfactorily simulates measured yields and reproduces the effects of irrigation with saline waters on crop yields. An alternative scenario using a reduction of water requirements by 50% was investigated to assess an irrigation method with considerable water savings. As the results show that relative yields, Yr, were only slightly reduced, the crop water requirements estimated by CROPWAT 8.0 must have been overestimated. The variation of the soil salinity in the root zone highlighted a high salinization risk in the short-term when water of 7 dS·m−1 is used for irrigation. Full article
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Open AccessArticle
Influence of Streambed Heterogeneity on Hyporheic Flow and Sorptive Solute Transport
Water 2020, 12(6), 1547; https://doi.org/10.3390/w12061547 - 28 May 2020
Abstract
The subsurface region where river water and groundwater actively mix (the hyporheic zone) plays an important role in conservative and reactive solute transport along rivers. Deposits of high-conductivity (K) sediments along rivers can strongly control hyporheic processes by channeling flow along [...] Read more.
The subsurface region where river water and groundwater actively mix (the hyporheic zone) plays an important role in conservative and reactive solute transport along rivers. Deposits of high-conductivity (K) sediments along rivers can strongly control hyporheic processes by channeling flow along preferential flow paths wherever they intersect the channel boundary. Our goal is to understand how sediment heterogeneity influences conservative and sorptive solute transport within hyporheic zones containing high- and low-K sediment facies types. The sedimentary architecture of high-K facies is modeled using commonly observed characteristics (e.g., volume proportion and mean length), and their spatial connectivity is quantified to evaluate its effect on hyporheic mixing dynamics. Numerical simulations incorporate physical and chemical heterogeneity by representing spatial variability in both K and in the sediment sorption distribution coefficient ( K d ). Sediment heterogeneity significantly enhances hyporheic exchange and skews solute breakthrough behavior, while in homogeneous sediments, interfacial flux and solute transport are instead controlled by geomorphology and local-scale riverbed topographies. The hyporheic zone is compressed in sediments with high sorptive capacity, which limits solute interactions to only a small portion of the sedimentary architecture and thus increases retention. Our results have practical implications for groundwater quality, including remediation strategies for contaminants of emerging concern. Full article
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Open AccessArticle
Porous Medium Typology Influence on the Scaling Laws of Confined Aquifer Characteristic Parameters
Water 2020, 12(4), 1166; https://doi.org/10.3390/w12041166 - 19 Apr 2020
Cited by 1
Abstract
An accurate measurement campaign, carried out on a confined porous aquifer, expressly reproduced in laboratory, allowed the determining of hydraulic conductivity values by performing a series of slug tests. This was done for four porous medium configurations with different granulometric compositions. At the [...] Read more.
An accurate measurement campaign, carried out on a confined porous aquifer, expressly reproduced in laboratory, allowed the determining of hydraulic conductivity values by performing a series of slug tests. This was done for four porous medium configurations with different granulometric compositions. At the scale considered, intermediate between those of the laboratory and the field, the scalar behaviors of the hydraulic conductivity and the effective porosity was verified, determining the respective scaling laws. Moreover, assuming the effective porosity as scale parameter, the scaling laws of the hydraulic conductivity were determined for the different injection volumes of the slug test, determining a new relationship, valid for coarse-grained porous media. The results obtained allow the influence that the differences among the characteristics of the porous media considered exerted on the scaling laws obtained to be highlighted. Finally, a comparison was made with the results obtained in a previous investigation carried out at the field scale. Full article
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Open AccessArticle
Transmissibility Upscaling on Unstructured Grids for Highly Heterogeneous Reservoirs
Water 2019, 11(12), 2647; https://doi.org/10.3390/w11122647 - 15 Dec 2019
Abstract
One critical point of modeling of flow in porous media is the capacity to consider parameters that are highly variable in space. It is then very challenging to simulate numerically fluid flow on such heterogeneous porous media. The continuous increase in computing power [...] Read more.
One critical point of modeling of flow in porous media is the capacity to consider parameters that are highly variable in space. It is then very challenging to simulate numerically fluid flow on such heterogeneous porous media. The continuous increase in computing power makes it possible to integrate smaller and smaller heterogeneities into geological models of up to tens of millions of cells. On such meshes, despite computer performance, multi-phase flow equations cannot be solved in an acceptable time for hydrogeologists and reservoir engineers, especially when the modeling considers several components in each fluid and when taking into account rock-fluid interactions. Taking average reservoir properties is a common approach to reducing mesh size. During the last decades, many authors studied the upscaling topic. Two different ways have been investigated to upscale the absolute permeability: (1) an average of the permeability for each cell, which is then used for standard transmissibility calculation, or (2) computing directly the upscaled transmissibility values using the high-resolution permeability values. This paper is related to the second approach. The proposed method uses the half-block approach and combines the finite volume principles with algebraic methods to provide an upper and a lower bound of the upscaled transmissibility values. An application on an extracted map of the SPE10 model shows that this approach is more accurate and faster than the classical transmissibility upscaling method based on flow simulation. This approach keeps the contrast of transmissibility values observed at the high-resolution geological scale and improves the accuracy of field-scale flow simulation for highly heterogeneous reservoirs. Moreover, the upper and lower bounds delivered by the algebraic method allow checking the quality of the upscaling and the gridding. Full article
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Open AccessArticle
A Spacetime Meshless Method for Modeling Subsurface Flow with a Transient Moving Boundary
Water 2019, 11(12), 2595; https://doi.org/10.3390/w11122595 - 09 Dec 2019
Cited by 1
Abstract
In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the [...] Read more.
In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the moving boundary is previously unknown. We solve the subsurface flow problems based on the Trefftz method, in which the Trefftz basis functions are obtained from the general solutions using the separation of variables. The solutions of the governing equation are then approximated numerically by the superposition theorem using the basis functions, which match the data at the spacetime boundary collocation points. Because the proposed basis functions fully satisfy the diffusion equation, arbitrary nodes are collocated only on the spacetime boundaries for the discretization of the domain. The iterative scheme has to be used for solving the moving boundaries because the transient moving boundary problems exhibit nonlinear characteristics. Numerical examples, including harmonic and non-harmonic boundary conditions, are carried out to validate the method. Results illustrate that our method may acquire field solutions with high accuracy. It is also found that the method is advantageous for solving inverse problems as well. Finally, comparing with those obtained from the method of fundamental solutions, we may obtain the accurate location of the nonlinear moving boundary for transient problems using the spacetime meshless method with the iterative scheme. Full article
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Open AccessArticle
Permeability Coefficient of Low Permeable Soils as a Single-Variable Function of Soil Parameter
Water 2019, 11(12), 2500; https://doi.org/10.3390/w11122500 - 27 Nov 2019
Abstract
Based on the results of experimental studies concerning the filtration coefficient, the Darcianity of the observed flows for eight cohesive soils at four hydraulic gradients was analyzed. It is observed that linear dependence of flow velocity on hydraulic gradient is an approximation only, [...] Read more.
Based on the results of experimental studies concerning the filtration coefficient, the Darcianity of the observed flows for eight cohesive soils at four hydraulic gradients was analyzed. It is observed that linear dependence of flow velocity on hydraulic gradient is an approximation only, and it is the worse the more cohesive a given soil is. Despite this, Darcy’s law can be a correct approximation of the empirical relationship between hydraulic gradient and the flow velocity, also in very cohesive soils. A statistical analysis was carried out to identify correlation between soil properties and permeability coefficient. For each soil, 109 parameters were analyzed, among others applying mercury intrusion porosimetry, scanning electron microscopy, dynamic image analysis, and laser diffraction. Ultimately, three single-variable models best fitted to the experimental data were found, using the plasticity index IP as the independent variable, the average pore diameter DP, and the convexity of silt fraction particles. All model parameters are statistically significant at p < 0.05. Comparison with reference multi-variable models showed that the best fit for experimental data is observed by the model with the plasticity index, while the results suggest low usability of single-variable models with structural parameters. Full article
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Open AccessFeature PaperArticle
Laboratory Experiments of Drainage, Imbibition and Infiltration under Artificial Rainfall Characterized by Image Analysis Method and Numerical Simulations
Water 2019, 11(11), 2232; https://doi.org/10.3390/w11112232 - 25 Oct 2019
Cited by 2
Abstract
Two laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based [...] Read more.
Two laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based on photographs. This method requires classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The procedure was applied and validated for a large experimental tank of internal dimensions 180 cm long, 120 cm wide and 4 cm deep that had been homogenously packed with monodisperse quartz sand. The calibration curve relating water content and reflected light intensities was established during the main monitoring phase of each experiment, making this procedure very advantageous. Direct measurements carried out during the water flow experiments correspond to water content, pressure head, temperature, and cumulative outflow. Additionally, a great advantage of the proposed method is that it does not require any tracer or dye to be injected into the flow tank. The accuracy and other benefits of our approach were also assessed using numerical simulations with state-of-the-art computational code that solves Richards’ equation. Full article
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Open AccessArticle
Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits with Partial Penetrating Curtains in Sand and Gravel Strata
Water 2019, 11(10), 2182; https://doi.org/10.3390/w11102182 - 19 Oct 2019
Cited by 2
Abstract
The dewatering of deep foundation pits excavated in highly permeable geology usually requires waterproofing technologies to relieve groundwater flow. However, no effective prediction formula is yet available for determining water inflow in the presence of partial penetrating curtains. In this study, a dewatering [...] Read more.
The dewatering of deep foundation pits excavated in highly permeable geology usually requires waterproofing technologies to relieve groundwater flow. However, no effective prediction formula is yet available for determining water inflow in the presence of partial penetrating curtains. In this study, a dewatering project with partial penetrating curtains is analyzed via a finite difference method to show evident three-dimensional (3D) seepage characteristics. The standard curve and distortion functions are established under the assumption of an equivalent well by quantifying the blocking effects; thus, the empirical inflow prediction formulas for steady flow are further developed. Moreover, a dewatering design method based on the prediction formulas is proposed and applied to the field dewatering project in sand and gravel strata. Measured results show that dewatering efficiency is considerably enhanced by 3D flow, forming appropriate pressure distributions for dewatering construction. The uplift pressure below the pit bottom is controlled within a 25% safety margin to verify the reliability of the design method. Full article
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Open AccessFeature PaperArticle
A Modeling Platform for Landslide Stability: A Hydrological Approach
Water 2019, 11(10), 2146; https://doi.org/10.3390/w11102146 - 15 Oct 2019
Abstract
Landslide events are among natural hazards with many fatalities and financial losses. Studies demonstrate that natural factors such as rainfall and human activities such as deforestation are important causes of triggering a landslide. In this study, an integrated two-dimensional slope stability model, SSHV-2D, [...] Read more.
Landslide events are among natural hazards with many fatalities and financial losses. Studies demonstrate that natural factors such as rainfall and human activities such as deforestation are important causes of triggering a landslide. In this study, an integrated two-dimensional slope stability model, SSHV-2D, is developed that considers various aspects of hydrological effects and vegetation impacts on the stability of slopes. The rainfall infiltration and water uptake of roots change the water content of the unsaturated zone. The temporal and spatial distribution of water content is estimated in the hydrological unit of the developed model. The vegetation unit of the model considers interception loss due to the existence of canopies and trunks, soil reinforcement effect by roots, root water uptake, the impact of root on hydraulic conductivity, and the influence of vegetation weight on slope stability. Benchmark problems with and without vegetation are solved for the model verification. The analyses demonstrate that the consideration of matric suction in the unsaturated zone can increase the safety factor more than 90%. It is also observed that the existence of trees with high density on a slope can increase the factor of safety about 50% and prevent shallow landslides. The present model is a platform for further development of more comprehensive and elaborative slope stability models. Full article
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Open AccessArticle
Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment
Water 2019, 11(8), 1660; https://doi.org/10.3390/w11081660 - 11 Aug 2019
Cited by 1
Abstract
Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this [...] Read more.
Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations. Full article
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Open AccessArticle
Smoothing of Slug Tests for Laboratory Scale Aquifer Assessment—A Comparison among Different Porous Media
Water 2019, 11(8), 1569; https://doi.org/10.3390/w11081569 - 29 Jul 2019
Cited by 2
Abstract
A filtering analysis of hydraulic head data deduced from slug tests injected in a confined aquifer with different porous media is proposed. Experimental laboratory tests were conducted in a large-scale physical model developed at the University of Calabria. The hydraulic head data were [...] Read more.
A filtering analysis of hydraulic head data deduced from slug tests injected in a confined aquifer with different porous media is proposed. Experimental laboratory tests were conducted in a large-scale physical model developed at the University of Calabria. The hydraulic head data were deduced from the records of a pressure sensor arranged in the injection well and subjected to a processing operation to filter the high-frequency noise. The involved smoothing techniques are the Fourier transform and two types of wavelet transform. The performances of the filtered hydraulic heads were examined for different slug volumes and four model layouts in terms of optimal fitting of the Cooper’s analytical solution. The hydraulic head variations in the confined aquifer were analyzed using wavelet transform in order to discover their energy contributions and frequency oscillations. Finally, the raw and smoothed hydraulic heads were adopted to calculate the hydraulic conductivity of the aquifer. Full article
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Open AccessFeature PaperArticle
A Comparative Study of Water and Bromide Transport in a Bare Loam Soil Using Lysimeters and Field Plots
Water 2019, 11(6), 1199; https://doi.org/10.3390/w11061199 - 08 Jun 2019
Cited by 1
Abstract
The purpose of this methodological study was to test whether similar soil hydraulic and solute transport properties could be estimated from field plots and lysimeter measurements. The transport of water and bromide (as an inert conservative solute tracer) in three bare field plots [...] Read more.
The purpose of this methodological study was to test whether similar soil hydraulic and solute transport properties could be estimated from field plots and lysimeter measurements. The transport of water and bromide (as an inert conservative solute tracer) in three bare field plots and in six bare soil lysimeters were compared. Daily readings of matric head and volumetric water content in the lysimeters showed a profile that was increasingly humid with depth. The hydrodynamic parameters optimized with HYDRUS-1D provided an accurate description of the experimental data for both the field plots and the lysimeters. However, bromide transport in the lysimeters was influenced by preferential transport, which required the use of the mobile/immobile water (MIM) model to suitably describe the experimental data. Water and solute transport observed in the field plots was not accurately described when using parameters optimized with lysimeter data (cross-simulation), and vice versa. The soil’s return to atmospheric pressure at the bottom of the lysimeter and differences in tillage practices between the two set-ups had a strong impact on soil water dynamics. The preferential flow of bromide observed in the lysimeters prevented an accurate simulation of solute transport in field plots using the mean optimized parameters on lysimeters and vice versa. Full article
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Open AccessArticle
A Unified Equation to Predict the Permeability of Rough Fractures via Lattice Boltzmann Simulation
Water 2019, 11(5), 1081; https://doi.org/10.3390/w11051081 - 24 May 2019
Cited by 5
Abstract
In this paper, the fluid flow through rough fractures was investigated via numerical simulation based on the lattice Boltzmann method (LBM). The accuracy of LBM was validated through the numerical simulation of the parallel plate model and the verification of the mass conservation [...] Read more.
In this paper, the fluid flow through rough fractures was investigated via numerical simulation based on the lattice Boltzmann method (LBM). The accuracy of LBM was validated through the numerical simulation of the parallel plate model and the verification of the mass conservation of fluid flow through rough fracture. After that, the effect of roughness on fluid flow was numerically conducted, in which, the geometry of fractures was characterized by the joint roughness coefficient (JRC), fractal dimension (D) and standard deviation (σ). It was found that the JRC cannot reflect the realistic influence of roughness on the permeability of single fracture, in which, an increase in permeability with increasing JRC has been observed at the range of 8~12 and 14~16. The reason behind this was revealed through the calculation of the root mean square of the first derivative of profile (Z2), and an equation has been proposed to estimate the permeability based on the aperture and Z2 of the fracture. The numerical simulations were further conducted on fluid flow though synthetic fractures with a wide range of D and σ. In order to unify the parameter that characterizes the roughness, Z2 was obtained for each synthetic fracture, and the corresponding relationship between permeability, aperture and Z2 was analyzed. Meanwhile, it was found that the fluid flow behaves differently with different ranges of Z2 and the critical point was found to be Z2 = 0.5. Based on extensive study, it was concluded that Z2 is a generic parameter characterizing the roughness, and the proposed equation could be used to predict the permeability for fluid flow in fracture. Full article
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Open AccessArticle
Assess Effectiveness of Salt Removal by a Subsurface Drainage with Bundled Crop Straws in Coastal Saline Soil Using HYDRUS-3D
Water 2019, 11(5), 943; https://doi.org/10.3390/w11050943 - 05 May 2019
Cited by 2
Abstract
The low permeability of soil and high investment of salt management pose great challenges for implementation of land reclamation in coastal areas. In this study, a temporary soil leaching system was tested in which bundled maize straw (straw drainage module, SDM) was operated [...] Read more.
The low permeability of soil and high investment of salt management pose great challenges for implementation of land reclamation in coastal areas. In this study, a temporary soil leaching system was tested in which bundled maize straw (straw drainage module, SDM) was operated as a subsurface drainage tube and diluted seawater was used for leaching. A preliminary field experiment was conducted in coastal soil-filled lysimeters to examine the system’s feasibility and a numerical model (HYDRUS-3D) based on field measured data was designed to simulate the entire leaching process. The simulation results showed that the soil water velocity and the non-uniformity of salt distribution were apparently enhanced in the region approaching the drain outlet. The mass balance information indicated that the amount of water drained with SDM accounts for 37.9–66.0% of the total amount of leaching water, and the mass of salt removal was about 1.7 times that of the salt input from the diluted seawater. Additional simulations were conducted to explore the impacts of the design parameters, including leaching amount, the salinity of leaching water, and the number of leaching events on the desalination performance of the leaching system. Such simulations showed that the salt removal efficiency and soil desalination rate both were negatively related to the seawater mixture rate but were positively associated with the amount of leaching water. Increasing the leaching times, the salt removal efficiency was gradually decreased in all treatments, but the soil desalination rate was decreased only in the treatments leached with less diluted seawater. Our results confirmed the feasibility of the SDM leaching system in soil desalination and lay a good foundation for this system application in initial reclamation of saline coastal land. Full article
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Open AccessArticle
On Solving Nonlinear Moving Boundary Problems with Heterogeneity Using the Collocation Meshless Method
Water 2019, 11(4), 835; https://doi.org/10.3390/w11040835 - 20 Apr 2019
Cited by 2
Abstract
In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary conditions. We adopt the collocation Trefftz [...] Read more.
In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary conditions. We adopt the collocation Trefftz method (CTM) to approximate the solution using Trefftz base functions, satisfying the Laplace equation. An iterative scheme in conjunction with the CTM for finding the phreatic line with over–specified nonlinear moving boundary conditions is developed. To deal with flow in the layered heterogeneous soil, the domain decomposition method is used so that the hydraulic conductivity in each subdomain can be different. The method proposed in this study is verified by several numerical examples. The results indicate the advantages of the collocation meshless method such as high accuracy and that only the surface of the problem domain needs to be discretized. Moreover, it is advantageous for solving nonlinear moving boundary problems with heterogeneity with extreme contrasts in the permeability coefficient. Full article
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Open AccessArticle
Improved Solutions to the Linearized Boussinesq Equation with Temporally Varied Rainfall Recharge for a Sloping Aquifer
Water 2019, 11(4), 826; https://doi.org/10.3390/w11040826 - 19 Apr 2019
Cited by 2
Abstract
Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The [...] Read more.
Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate. Full article
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Open AccessArticle
Effect of Pilot-Points Location on Model Calibration: Application to the Northern Karst Aquifer of Qatar
Water 2019, 11(4), 679; https://doi.org/10.3390/w11040679 - 02 Apr 2019
Cited by 1
Abstract
In hydrogeological modelling, two approaches are commonly used for model calibration: zonation and the pilot-points method. Zonation assumes an abrupt spatial change in parameter values, which could be unrealistic in field applications. The pilot-points method produces smoothly distributed parameters compared to the zonation [...] Read more.
In hydrogeological modelling, two approaches are commonly used for model calibration: zonation and the pilot-points method. Zonation assumes an abrupt spatial change in parameter values, which could be unrealistic in field applications. The pilot-points method produces smoothly distributed parameters compared to the zonation approach; however, the number and placement of pilot-points can be challenging. The main goal of this paper is to explore the effect of pilot-points number and locations on the calibrated parameters. A 3D groundwater flow model was built for the northern karst aquifer of Qatar. A conceptual model of this aquifer was developed based on MODFLOW software (United States Geological Survey). The model was calibrated using the parameter estimation and uncertainty analysis (PEST) package employing historical data of groundwater levels. The effect of the number and locations of pilot-points was examined by running the model using a variable numbers of points and several perturbations of locations. The calibration errors for all the runs (corresponding to different configurations of pilot-points) were maintained under a certain threshold. A statistical analysis of the calibrated parameters was then performed to evaluate how far these parameters are impacted by the pilot-point locations. Finally, an optimization method was proposed for pilot-points placement using recharge and observed piezometric maps. The results revealed that the pilot-points number, locations, and configurations have a significant effect on the calibrated parameter, especially in the high permeable regions corresponding to the karstic zones. The outcome of this study may help focus on areas of high uncertainty where more field data should be collected to improve model calibration. It also helps the placement of pilot-points for a robust calibration. Full article
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Review

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Open AccessReview
Application of Fractional Flow Theory for Analytical Modeling of Surfactant Flooding, Polymer Flooding, and Surfactant/Polymer Flooding for Chemical Enhanced Oil Recovery
Water 2020, 12(8), 2195; https://doi.org/10.3390/w12082195 - 04 Aug 2020
Abstract
Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important [...] Read more.
Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important to revisit the application of fractional flow theory to CEOR at this stage. For surfactant flooding, the effects of surfactant adsorption, surfactant partition, initial oil saturation, interfacial tension, and injection slug size have been systematically investigated. In terms of polymer flooding, the effects of polymer viscosity, initial oil saturation, polymer viscoelasticity, slug size, polymer inaccessible pore volume (IPV), and polymer retention are also reviewed extensively. Finally, the fractional flow theory is applied to surfactant/polymer flooding to evaluate its effectiveness in CEOR. This paper provides insight into the CEOR mechanism and serves as an up-to-date reference for analytical modeling of the surfactant flooding, polymer flooding, and surfactant/polymer flooding CEOR process. Full article
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Other

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Open AccessTechnical Note
Experimental Study on the Permeability Characteristic of Fused Quartz Sand and Mixed Oil as a Transparent Soil
Water 2019, 11(12), 2514; https://doi.org/10.3390/w11122514 - 28 Nov 2019
Abstract
An accurate estimation of soil permeability is essential in geotechnical engineering. Transparent soil provides a promising experimental material to visualize pore-scale fluid flow, although the permeability characteristic of transparent soil remains unclear. As a result of the replacement of the fluid and solid [...] Read more.
An accurate estimation of soil permeability is essential in geotechnical engineering. Transparent soil provides a promising experimental material to visualize pore-scale fluid flow, although the permeability characteristic of transparent soil remains unclear. As a result of the replacement of the fluid and solid phase, the permeability coefficient of transparent soil is usually several times or even more than ten times smaller than that of natural soil with the same particle size distribution and porosity. Fused quartz sand is used as the solid phase in this proposed transparent soil, which exhibits a similar mechanical behavior but different permeability to those of natural sand. Due to its low cost and eco-friendly characteristic, a mixture of mineral oil and aliphatic hydrocarbon is proposed as the liquid phase, which can achieve the same refractive index as the fused quartz sand after calculating the material proportion. Through a series of laboratory tests, the permeability of the transparent soil is obtained; the permeability is affected by the fluid dynamic viscosity, fluid density, particle size, particle size distribution, void ratio, and pore morphology. A hierarchical approach is introduced to quantitatively evaluate the effect of the particle shape on the permeability. Based on the experimental results, a modified Kozeny–Carman model is proposed for the prediction of transparent soil permeability, which can guide the preparation of transparent soil samples in further experimental studies. Full article
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

 

Title: Coupling Transport and Chemistry in Porous Media: Algorithms and Validation Examples

Authors: Laila Amir 1 and Michel Kern 2

Affiliations: 1 Faculté des sciences et techniques, UCAM, Marrakech, Morrocco
2 Inria, Paris, France

Abstract: Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs.

In previous work [1,2], the authors introduced a method for the simulation of reactive transport. The method is a globally coupled approach, where transport and chemistry are solved together, but keeps the transport and chemistry modules separate . At each time step, the large nonlinear system of algebraic equations representing the coupling of all chemical species at all mesh points is solved by a Newton–Krylov method. The linearized system at each Newton iteration is solved by an iterative method (usually GMRES) It was also shown in [2] that a suitable non-linear preconditioning substantially improved the performance of the method. This paper extends the method first to handle mineral precipitation and dissolution reactions, using an interior point Newton method, and second to 2D heterogeneous geometries, using a black transport code. We detail the methods and algorithms for the individual modules,and for the coupling step, paying particular attention to the precondtioning steps. We show numerical examples to validate the method.

References: [1] L. Amir and M. Kern. A global method for coupling transport with chemistry in heterogeneous porous media. Computat. Geosci., 14:465–481, 2010. 10.1007/s10596-009-9162-x.
[2] L. Amir and M. Kern. Preconditioning a coupled model for reactive transport in porous media. Int. J. Numer. Anal. Model., 16(1):18–48, 2019.

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