Flow and residence time in a laboratory aquifer recharged by rainfall

2021 ◽  
Author(s):  
Eric Lajeunesse ◽  
Valentin Jules ◽  
Olivier Devauchelle ◽  
Adrien Guérin ◽  
Claude Jaupart ◽  
...  
Keyword(s):  
Water Table ◽  
Velocity Potential ◽  
Boussinesq Approximation ◽  
Propagation Rate ◽  
Hydrodynamic Dispersion ◽  
Vertical Flow ◽  
Pore Scale ◽  
Flow Equations ◽  
Artificial Rainfall ◽  
Travel Time Distribution

<p>During rainfall, water infiltrates the soil, and percolates through the unsaturated zone until it reaches the water table. Groundwater then flows through the aquifer, and eventually emerges into streams to feed surface runoff. We reproduce this process in a  two-dimensional laboratory aquifer recharged by artificial rainfall. As rainwater infiltrates, it forms a body of groundwater which can exit the aquifer only through one of its sides. The outlet is located high above the base of the aquifer, and drives the flow upwards. The resulting vertical flow component violates the Dupuit-Boussinesq approximation. In this configuration, the velocity potential that drives the flow obeys the Laplace equation, the solution of which crucially depends on the boundary conditions. Noting that the water table barely deviates from the horizontal, we linearize the boundary condition at the free surface, and solve the flow equations in steady state. We derive an expression for the velocity potential, which accounts for the shape of the experimental streamlines and for the propagation rate of tracers through the aquifer. This theory allows us to calculate the travel times of tracers through the experimental aquifer, which are in agreement with the observations. The travel time distribution has an exponential tail, with a characteristic time that depends on the aspect ratio of the aquifer. This distribution depends essentially on the geometry of the groundwater flow, and is weakly sensitive to the hydrodynamic dispersion that occurs at the pore scale.</p>

scholarly journals Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

2021 ◽  
Vol 126 (16) ◽  
Author(s):  
Alexandre Puyguiraud ◽  
Philippe Gouze ◽  
Marco Dentz
Keyword(s):  
Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale

Upscaling of pore-scale mixing and reaction through effective dispersion coefficients

2021 ◽  
Author(s):  
Alexandre Puyguiraud ◽  
Lazaro Perez ◽  
Juan J. Hidalgo ◽  
Marco Dentz
Keyword(s):  
Green Function ◽  
Molecular Diffusion ◽  
Early Time ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Dispersion Coefficients ◽  
Incomplete Mixing ◽  
Effective Dispersion ◽  
Structure Heterogeneity ◽  
Field Heterogeneity

<p>We utilize effective dispersion coefficients to capture the evolution of the mixing interface between two initially segregated species due to the coupled effect of pore-scale heterogeneity and molecular diffusion. These effective dispersion coefficients are defined as the average spatial variance of the solute plume that evolves from a pointlike injection (the transport Green function). We numerically investigate the effective longitudinal dispersion coefficients in two porous media of different structure heterogeneity  and through different Péclet number regimes for each medium. We find that, as distance traveled increases (or time spent), the solute experiences the pore-scale velocity field heterogeneity due to advection and transverse diffusion, resulting in an evolution of the dispersion coefficients. They evolve from the value of molecular diffusion at early time, then undergo an advection dominated regime, to finally reach the value of hydrodynamic dispersion at late times. This means that, at times smaller than the characteristic diffusion time, the effective dispersion coefficients can be notably smaller than the hydrodynamic dispersion coefficient. Therefore, mismatches between pore-scale reaction data from experiment or simulations and Darcy scale predictions based on temporally constant hydrodynamic dispersion can be explained through these differences. We use the effective dispersion coefficients to approximate the transport Green function and to quantify the incomplete mixing occurring at the pore-scale. We evaluate the evolution of two initially segregated species via this methodology. The approach correctly predicts the amount of chemical reaction occuring in reactive bimolecular particle tracking simulations. These results shed light on the upscaling of pore-scale incomplete mixing and demonstrates that the effective dispersion is an accurate measure for the width of the mixing interface between two reactants. </p>

Analysis of Mixed Convective Heat and Mass Transfer on Peristaltic Flow of Fene-P Fluid with Chemical Reaction

2015 ◽  
Vol 32 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Z. Asghar ◽  
N. Ali
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Wave Length ◽  
Linear Equations ◽  
Pressure Rise ◽  
Boussinesq Approximation ◽  
Flow Equations ◽  
Highly Nonlinear ◽  
Concentration Changes

AbstractThis study presents the influence of heat and mass transfer on peristaltic transport of Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid in the presence of chemical reaction. It is assumed that all the fluid properties, except the density are constant. The Boussinesq approximation which relates density change to temperature and concentration changes is used in formulating buoyancy force terms in the momentum equation. Moreover, we neglect viscous dissipation and include diffusion-thermal (Dufour) and thermal-diffusion (Soret) effects in the present analysis. By the consideration of such important aspects the flow equations become highly nonlinear and coupled. In order to make the problem tractable we have adopted widely used assumptions of long wave length and low Reynolds number. An exact solution of the simplified coupled linear equations for the temperature and concentration has been obtained whereas numerical solution is obtained for dimensionless stream function and pressure gradient. The effects of different parameters on velocity field, temperature and concentration fields and trapping phenomenon are highlighted through various graphs. Numerical integration has been performed to analyze pressure rise per wavelength.

Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion

2021 ◽  
Author(s):  
Marco Dentz ◽  
Alexandre Puyguiraud ◽  
Philippe Gouze
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Sandstone Sample ◽  
Flow Variability

<p>Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and Péclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Péclet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability. </p>

Water Table Depth and Soil Salinization: From Pore‐Scale Processes to Field‐Scale Responses

2020 ◽  
Vol 56 (2) ◽  
Author(s):  
Salomé M. S. Shokri‐Kuehni ◽  
Bernadette Raaijmakers ◽  
Theresa Kurz ◽  
Dani Or ◽  
Rainer Helmig ◽  
...  
Keyword(s):  
Water Table ◽  
Soil Salinization ◽  
Water Table Depth ◽  
Pore Scale ◽  
Field Scale

scholarly journals NUMERICAL STUDIES OF NATURAL CONVECTION IN A SQUARE CAVITY

2006 ◽  
Vol 5 (1) ◽  
pp. 68
Author(s):  
Viviana Cocco Mariani ◽  
Ivan Moura Belo
Keyword(s):  
Boussinesq Approximation ◽  
Square Cavity ◽  
Flow Equations ◽  
Nusselt Numbers ◽  
Numerical Studies ◽  
Numeric Simulation ◽  
Different Temperatures ◽  
Convection Problem ◽  
Volume Method ◽  
Rayleigh Numbers

In the present work a numeric study of thermal and fluid dynamics behavior of natural air convection in a bi-dimensional square cavity is presented, in a laminar flow. The square cavity has two walls heated with different temperatures and two isolated walls, the Boussinesq approximation is used and a constant Prandtl number. The Finite Volume Method is used for the discretization of flow equations. The staggered load of variables is adopted and Power-Law and SIMPLE models are used. The numeric simulation is made up of several Rayleigh numbers, 104 Ra 106, and the results of average Nusselt numbers are compared to values obtained in the literature. Flow and isotherm lines are presented and analyzed. The numerical results presented here in this work agree with the ones available in the literature and can be used by researchers who work in the convection problem numeric simulation area.

scholarly journals Analytical solutions to the stream-aquifer interaction problem: a critical review

2013 ◽  
Vol 12 (2) ◽  
pp. 126-139
Keyword(s):  
Analytical Solution ◽  
Mathematical Models ◽  
Ground Water ◽  
Water Flow ◽  
Water Table ◽  
Analytical Solutions ◽  
Stream Flow ◽  
Boussinesq Equation ◽  
Ground Water Flow ◽  
Flow Equations

The aim of the present paper is to give a systematic and critical presentation of important existing analytical solutions for transient stream-aquifer interaction, which can be used to give answers to simple interaction problems or to verify mathematical models. Stream-aquifer interaction is the most common subject of papers discussing surface water-ground water interaction and a review of analytical solutions to the problem is lacking from the literature. The analytical solutions presented in the paper are firstly distinguished based on whether only the ground water flow equations or both the ground water and stream flow equations are solved for their derivation and secondly based on the type of aquifer (confined or unconfined) interacting with the stream and on the type of equations solved. The literature review showed that there is only a small number of publications, where the authors consider both the ground water and the stream flow equations for the development of the analytical solutions. The majority of the available analytical solutions of stream-aquifer interaction are derived by solving only the ground water flow equations, taking into account the stream water level as a boundary condition. For each analytical solution presented in the paper, its accuracy, its ease of application to simple interaction problems and its suitability for the verification of mathematical models are discussed in detail. Specifically for the case of predicting the water table level in unconfined aquifers interacting with streams, an analytical solution of the non-linear Boussinesq equation is compared to two analytical solutions of different linearized forms of the Boussinesq equation, in order to quantify the error in estimating the water table level when using a linear solution. Among the very few analytical solutions found in the literature, where the authors consider both the stream flow and ground water flow equations for their development, the most comprehensive one is chosen to give an application example, which can be used as a benchmark case for the verification of integrated stream-aquifer mathematical models.

Mass Dispersion Coefficients for Turbulent Flow in an Infinite Porous Medium

Volume 1 ◽  
2004 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Medium ◽  
Control Volume ◽  
Fluid Phase ◽  
Pore Scale ◽  
Simple Method ◽  
Flow Equations ◽  
Mass Dispersion ◽  
Spatially Periodic ◽  
Linear Effects ◽  
Control Volume Approach

In this work, mass dispersion tensors were calculated within an infinite porous medium formed by a spatially periodic array of longitudinally-displaced cylindrical rods. For the sake of simplicity, just one unit-cell, together with periodic boundary conditions for mass and momentum equations, and Neumann conditions for the mass concentration, was used to represent such medium. The numerical methodology herein employed is based on the control volume approach. Turbulence is assumed to exist within the fluid phase. High and low Reynolds k-e models were used to model such non-linear effects. The flow equations at the pore-scale were numerically solved using the SIMPLE method applied to a non-orthogonal boundary-fitted coordinate system. Integrated mass fraction results were compared with existing data in the literature.

Movement of solutes associated with intermittent soil-water flow .I. Tritium and bromide

Soil Research ◽  
1991 ◽  
Vol 29 (2) ◽  
pp. 175 ◽  
Author(s):  
DR Scotter ◽  
RW Tillman
Keyword(s):  
Water Flow ◽  
Hydraulic Properties ◽  
Molecular Diffusion ◽  
Tritiated Water ◽  
Potassium Bromide ◽  
Hydrodynamic Dispersion ◽  
Silt Loam ◽  
Dilute Solution ◽  
Soil Hydraulic Properties ◽  
Flow Equations

The movement of tritiated water and bromide through columns of repacked silt loam was examined in the laboratory. A pulse (5 mm) of a dilute solution of potassium bromide in tritiated water was applied, left for 3 or 10 days, and then leached further down the column of soil with 30 mm of distilled water. Twelve days after the solute pulse was applied, the columns were sectioned, and the distributions of water, tritiated water and bromide were measured. The bromide moved only slightly further than the tritiated water, indicating little anion exclusion. The bromide peaks were much sharper than those for tritiated water. This reflects the slower diffusion of bromide during the periods of several days between leaching and the termination of the experiment, and the importance of molecular diffusion relative to hydrodynamic dispersion. Given the soil hydraulic properties, the behaviour of water, tritiated water and bromide could be simulated by coupling the water flow equations with the convection-dispersion equation, and by using solute diffusivity and dispersivity values from the literature. A significant assumption was which cation was mostly convected with, and hence diffused with, the bromide. The use of the diffusion coefficient for calcium bromide rather than potassium bromide resulted in a better description of the observed bromide profiles in the soil.

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