Laboratory Experiments on Solute Transport in Non-Homogeneous Porous Media

1986 ◽  
Vol 17 (4-5) ◽  
pp. 305-314 ◽  
Author(s):  
Anders Refsgaard
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Solute Transport ◽  
Laboratory Experiments ◽  
Heterogeneous Porous Media ◽  
Heterogeneous Porous Medium ◽  
Dispersion Parameters ◽  
Homogeneous Porous Media ◽  
Flow Through ◽  
Good Agreement

Solute transport in groundwater is a process which has become of major importance during the last decades due to increasing contamination of ground water. This process usually occurs in a medium heterogeneous with respect to hydraulic conductivity and porosity, properties that affect the dispersion of the solutes. The present paper describes an experimental investigation of the solute transport process in heterogeneous porous media, especially the connection between the statistical properties of their hydraulic conductivity distributions and the dispersion parameters governing the spreading of the solutes. The experimental results are compared to theoretical solutions derived for the same case of a solute pulse in an average uniform flow through a heterogeneous porous medium. Generally there is good agreement between the theory and the experiments. In field applications this means that the dispersion parameters can be more readily determined from the soil properties. Furthermore, the deviations between dispersivities determined in laboratory columns and dispersitivies found under field conditions can be explained quantitatively by the differencies in the length scales and in the variances of the hydraulic conductivity distributions.

scholarly journals Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model

Water ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 53 ◽  
Author(s):  
Elise Wright ◽  
Nicole Sund ◽  
David Richter ◽  
Giovanni Porta ◽  
Diogo Bolster
Keyword(s):  
Porous Media ◽  
Markov Model ◽  
Heterogeneous Porous Media ◽  
Lagrangian Model ◽  
Small Scale ◽  
Heterogeneous Porous Medium ◽  
The Mean ◽  
Fully Resolved Simulation ◽  
Solute Mixing ◽  
Good Agreement

In this work, we develop a novel Lagrangian model able to predict solute mixing in heterogeneous porous media. The Spatial Markov model has previously been used to predict effective mean conservative transport in flows through heterogeneous porous media. In predicting effective measures of mixing on larger scales, knowledge of only the mean transport is insufficient. Mixing is a small scale process driven by diffusion and the deformation of a plume by a non-uniform flow. In order to capture these small scale processes that are associated with mixing, the upscaled Spatial Markov model must be extended in such a way that it can adequately represent fluctuations in concentration. To address this problem, we develop downscaling procedures within the upscaled model to predict measures of mixing and dilution of a solute moving through an idealized heterogeneous porous medium. The upscaled model results are compared to measurements from a fully resolved simulation and found to be in good agreement.

scholarly journals Mathematical Treatment of Saturated Macroscopic Flow in Heterogeneous Porous Medium: Evaluating Darcy’s Law

Hydrology ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 4
Author(s):  
R. William Nelson ◽  
Gustavious P. Williams
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Flow Field ◽  
Laboratory Experiments ◽  
Heterogeneous Media ◽  
Darcy’S Law ◽  
Heterogeneous Porous Media ◽  
Darcy's Law ◽  
Mathematical Treatment ◽  
Heterogeneous Porous Medium

We present a rigorous mathematical treatment of water flow in saturated heterogeneous porous media based on the classical Navier-Stokes formulation that includes vorticity in a heterogeneous porous media. We used the mathematical approach proposed in 1855 by James Clark Maxwell. We show that flow in heterogeneous media results in a flow field described by a heterogeneous complex lamellar vector field with rotational flows, compared to the homogeneous lamellar flow field that results from Darcy’s law. This analysis shows that Darcy’s Law does not accurately describe flow in a heterogeneous porous medium and we encourage precise laboratory experiments to determine under what conditions these issues are important. We publish this work to encourage others to perform numerical and laboratory experiments to determine the circumstances in which this derivation is applicable, and in which the complications can be disregarded.

Historical development of soil-water physics and solute transport in porous media

2007 ◽  
Vol 7 (1) ◽  
pp. 59-66 ◽  
Author(s):  
D.E. Rolston
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Solute Transport ◽  
Soil Water ◽  
20Th Century ◽  
Water Flow ◽  
Unsaturated Soils ◽  
Transport Processes ◽  
Transport In Porous Media ◽  
Unsaturated Hydraulic Conductivity

The science of soil-water physics and contaminant transport in porous media began a little more than a century ago. The first equation to quantify the flow of water is attributed to Darcy. The next major development for unsaturated media was made by Buckingham in 1907. Buckingham quantified the energy state of soil water based on the thermodynamic potential energy. Buckingham then introduced the concept of unsaturated hydraulic conductivity, a function of water content. The water flux as the product of the unsaturated hydraulic conductivity and the total potential gradient has become the accepted Buckingham-Darcy law. Two decades later, Richards applied the continuity equation to Buckingham's equation and obtained a general partial differential equation describing water flow in unsaturated soils. For combined water and solute transport, it had been recognized since the latter half of the 19th century that salts and water do not move uniformly. It wasn't until the middle of the 20th century that scientists began to understand the complex processes of diffusion, dispersion, and convection and to develop mathematical formulations for solute transport. Knowledge on water flow and solute transport processes has expanded greatly since the early part of the 20th century to the present.

Incorporation of Interfacial Areas in Models of Two-Phase Flow

1999 ◽  
Author(s):  
William G. Gray ◽  
Michael A. Celia
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Single Phase ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Hydraulic Gradient ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Α Phase ◽  
Flow Through

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα . Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.

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