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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".

Deadline for manuscript submissions: 30 November 2019.

Special Issue Editors

Guest Editor
Dr. Anis Younes

Laboratoire d'Hydrologie et de Geochimie de Strasbourg, CNRS, UMR 7517, University of Strasbourg, Strasbourg, France
Website | E-Mail
Phone: +03 68 85 04 41
Interests: Modeling flow and transport in saturated/unsaturated porous media; advanced numerical methods; coupled fluid flow with mass and energy transport; global sensitivity and uncertainty analysis; Bayesian parameter estimation
Guest Editor
Dr. Philippe Ackerer

Laboratoire d'Hydrologie et de Geochimie de Strasbourg, CNRS, UMR 7517, University of Strasbourg, Strasbourg, France
Website | E-Mail
Phone: +03 68 85 05 61
Interests: Flow and transport modeling in porous media; parameter estimation by inverse modeling; laboratory experiments, real field simulations
Guest Editor
Dr. Marwan Fahs

Laboratoire d'Hydrologie et de Geochimie de Strasbourg, CNRS, UMR 7517, University of Strasbourg, Strasbourg, France
Website | E-Mail
Phone: +03 68 85 04 48
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 1600 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 (8 papers)

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Research

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
Received: 28 July 2019 / Revised: 30 July 2019 / Accepted: 7 August 2019 / Published: 11 August 2019
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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
Received: 25 June 2019 / Revised: 24 July 2019 / Accepted: 27 July 2019 / Published: 29 July 2019
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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
Received: 3 May 2019 / Revised: 30 May 2019 / Accepted: 3 June 2019 / Published: 8 June 2019
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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
Received: 28 April 2019 / Revised: 19 May 2019 / Accepted: 21 May 2019 / Published: 24 May 2019
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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
Received: 2 April 2019 / Revised: 27 April 2019 / Accepted: 1 May 2019 / Published: 5 May 2019
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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
Received: 22 March 2019 / Revised: 16 April 2019 / Accepted: 17 April 2019 / Published: 20 April 2019
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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
Received: 27 March 2019 / Revised: 16 April 2019 / Accepted: 17 April 2019 / Published: 19 April 2019
Cited by 1 | PDF Full-text (4533 KB) | HTML Full-text | XML Full-text
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
Received: 28 February 2019 / Revised: 18 March 2019 / Accepted: 19 March 2019 / Published: 2 April 2019
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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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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.

Laboratory Experiments of Drainage and Rainfall Characterized by Image Analysis Method and Numerical Simulations

by Benjamin BELFORT *, Sylvain WEILL, Marwan FAHS and François LEHMANN

Université de Strasbourg, CNRS, ENGEES, LHyGeS UMR 7517, F-67000 Strasbourg, France

* Correspondence: [email protected]

Abstract: Two laboratory experiments consisting in drainage / imbibition and rainfall are 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 throughout 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 has been applied and validated for a large experimental tank of internal dimensions 180 cm long, 120 cm wide and 4 cm deep which has been homogenously packed with monodisperse quartz sand. The calibration curve relating water content and reflected light intensities is 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 (Theta probes, Type ML2x), pressure head (Pressure transmitters, Keller Druckmesstechnick), temperature, and cumulative outflow. Besides, 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 others benefits of our approach are also assessed using numerical simulations with a state-of-the-art computational code that solves the Richards’ equation.

Keywords: image processing, water content maps, unsaturated porous media, laboratory experiment, flow tank, drainage / imbibition, rainfall, 2D numerical simulations

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