Diffusion Coefficients In Porous Media Research Articles

Analytical solution and analysis of solute transport in rivers affected by diffusive transfer in the hyporheic zone

Summary A model is presented for solute transport in rivers including transient storage in hyporheic zones. The model consists of an advection–dispersion equation for transport in the main channel with a sink term describing diffusive solute transfer to the hyporheic zone. This system of equations is solved analytically for instantaneous injection of a conservative tracer in an infinite uniform river reach with steady flow. The solution enables to estimate the temporal and spatial evolution of tracer concentrations downstream of the injection point with fewer parameters than any other model before. The solution is linked to a non-linear least squares optimisation algorithm to analyse breakthrough curves and estimate solute transport parameters. The model is applied to tracer experiments conducted in the Chillan River, Chile, which were previously analysed with a model including mass exchange between the river and a stagnant storage zone. The fit between observations and model results is good, except for some experiments where the tailing of the fitted curves is more pronounced than observed. Estimates of the water flow velocity are practically identical with previous findings, but the estimates of the cross-sectional area and the dispersion coefficient are markedly different. Estimated values for the diffusion coefficient in the hyporheic zone agree with values cited in literature and with the magnitude of chemical diffusion coefficients in porous media.

Experimental Investigation of the Diffusion Coefficients in Porous Media by Application of X-Ray Computer Tomography

Experimental Investigation of the Diffusion Coefficients in Porous Media by Application of X-Ray Computer Tomography

EFFECTIVE PROPERTIES OF POROUS AND COMPOSITE MATERIALS

Based on a previously modified version of Bruggerman's method, a dependence of the effective diffusion coefficient in porous media on the porosity is deduced and compared with available experimental data. Based on the same method, a dependency of the effective elastic coefficients of composite materials on the volume fraction of inclusions is deduced in the case of different types of inclusions. Comparison with available experimental data shows good agreement between the theory predictions and the experimental data. In the case of the elastic properties of laminated composite materials, application of the same method yields results identical to those obtained using the averaging procedure. A theory of effective viscosity of concentrated suspensions is applied for calculations of dependency of effective viscosity on applied shear rate using available experimental data.

Modeling the Reduction of Vapor Phase Emissions from Surface Soils Due to Soil Matrix Effects: Porosity/Tortuosity Concepts

ABSTRACT A major route for transport of volatile organic compounds within porous media is vapor phase diffusion. The diffusion rate through a porous medium is less than that through free-air due to the decreased cross-sectional area available for gas movement and the increased path length due to pore tortuosity. Numerous empirical expressions have been published that relate the diffusion coefficient in porous media to the diffusion coefficient in free-air (unobstructed gas phase). Published measurements of relative diffusivity and air-filled porosity were combined into a database. Empirical expressions available in the literature, including the popular Millington-Quirk equation, were evaluated along with a fourth-degree polynomial expression developed by the authors to determine the best type of equation to predict relative diffusivity as a function of air-filled porosity over the domain of values for porosity ranging from 0.071 to 1 for different types of materials. Mean square deviations were used as the statistical test to compare equations. The polynomial expression developed in this project produced a significantly different effective diffusion coefficient (1.3 x 10-6 m2/sec) compared to values of 9.2 x 10-6 m2/sec and 3.1 x 10-6 m2/ sec predicted by forms of the Millington-Quirk equation for a specific case.

Determination of effective macropore diffusion coefficients by digital image processing

AbstractIn this contribution, a new method is proposed for determining effective macropore diffusion coefficients in porous media by digitized microphotographs of porous support materials and random walk simulations. The method introduced allows calculation of the effective diffusion coefficient as a function of the mean free path length over a wide variety of values. A versatile method for the preparation of porous substances for light microscopy is described.The frequently applied model of an active shell, which is used to model particle/solid collisions, was found to give incorrect results in conjunction with the application of the first passage time algorithm, which was applied to save computing time in the simulation of gas diffusion. It was possible to show that more realistic results are obtained if a Knudsen layer is used to model particle/solid collisions. Furthermore, in investigating diffusion in two‐ and three‐dimensional representations of capillary tubes, it was found that results of simulations performed to calculate transport properties of fluids in porous media, based on two‐dimensional model systems, cannot in any case be transferred to the corresponding three‐dimensional systems.

Surface relaxation and the long-time diffusion coefficient in porous media: Periodic geometries.

The macroscopic diffusion coefficient, obtained in an ideal pulsed-field-gradient spin-echo (PFGSE) experiment in the long-time limit, should exactly equal that derived from the electrical conductivity only when the surface relaxivity \ensuremath{\rho} and surface electrical conductivity vanish. In general, the coefficient derived by PFGSE techniques can be either greater or less than its electrical counterpart, depending on the pore geometry and other factors. Formally, the effect of \ensuremath{\rho} can be seen from the structure of a perturbation expansion based on the \ensuremath{\rho}=0 time-dependent solutions of the pore-space diffusion problem. In addition, analytic results for periodic structures with partially absorbing boundary conditions and numerical simulations are used to illustrate the differences between the diffusion coefficients for \ensuremath{\rho}=0 and \ensuremath{\rho}\ensuremath{\ne}0. In treating disordered media, our simulations are limited to systems that are not heterogeneous beyond the PFGSE diffusion length scale.

The measurement of apparent diffusion coefficients in compacted clays: an assessment of methods

Diffusion coefficients are critical parameters for predicting migration rates and fluxes of contaminants through dense clay-based barrier materials used in many waste containment strategies. A number of methods have been developed to measure diffusion coefficients in porous media. Here we compare three methods, involving both in-diffusion (ID) and through-diffusion (TD) techniques, for measuring the apparent diffusion coefficient, D, of I − and Cs + in dense saturated bentonite. The clay was compacted to a dry density of about 1.3 Mg/m 3 and saturated with a Na-Ca-Cl-dominated solution having an ionic strength of 220 mol/m 3. The D values obtained are designated D p (from the concentration profile developed in ID studies), D g (from the concentration gradient measured in the TD method), and D t (from the “time-lag” technique in TD experiments). For I −, the mean D p value was 200 μm 2/s, D g was 300 μm 2/s and D t was 130 μm 2/s. The corresponding values for Cs + were 1.2 μm 2/s, 0.54 μm 2/s and 1.9 μm 2/s. The D values are lower for Cs + than for I − mainly because Cs + is sorbed to a greater extent on the clay. The D values obtained by the three methods for both diffusants are in reasonable agreement, and we conclude that any of the methods examined here can be used reliably to obtain D in compacted bentonite.

EXPERIMENTAL STUDY ON MASS TRANSFER IN POROUS RIVERBED

Mass transfer mechanism in porous riverbed was investigated using chloride tracer method and a hotfilm anemometer in two experimental open channels which have porous media composed of 1.9cm and 4.08cm diameter ceramic ball respectively. Water depth to particle diameter ratio was about 1.7 and surface flow mean velocity was 3.9cm/s-42cm/s.Flow over porous riverbed was found to have very high turbulent intensity near porous boundary, which was about 20% of surface flow mean velocity in all hydraulic conditions. Values of vertical-direction diffusion coefficient in porous media increased with increasing surface flow mean velocity, and were found to have the distribution pattern in porous media which shows linear decrease with depth. Observed values of diffusion coefficient near porous boundary satisfied the theoretical relationship between diffusion coefficient and turbulent intensity.

Diffusion coefficients in bidisperse porous structures

On the basis of theoretical analysis the reason for experimentally observed differences in effective diffusion coefficients in porous media when stationary and nonstationary methods are applied to the measurements has been explained. It has been shown that these differences appear as a function of the porous structure of the media and are especially significant for bidisperse porous pellets. In order to verify the theoretical conclusions effective diffusion coefficients were measured for five different porous pellets, one monodisperse and four bidisperse structures using the dynamic membrane method. The experimental results fully confirm the theoretical conclusion that the diffusion coefficients estimated from the zero and first moments of the response curves should be identical and thus equal to those obtained in the stationary methods. For all bidisperse structures considered values of diffusion coefficients estimated from the second moments on the basis of the formula for the monodisperse structure are lower than the diffusion coefficients estimated from the zero and first moments, thus fully supporting the theoretical conclusions.

A nonsteady state method for determining diffusion coefficients in porous media

A series of experiments was run to test the feasibility of determining diffusion rates in a porous medium using a nonsteady state method. The experimental procedure is based on a mathematical model of Crank (1970) and involves diffusion from a porous sheet of finite thickness into a finite homogeneous volume. By measuring the composition of the homogeneous volume as a function of time it is possible to calculate integral diffusion coefficients of salts in the porous medium.

Diffusion of Gases in Porous Solids. I. Theoretical Background and Experimental Method

In the past, some authors have not defined the diffusion coefficient appropriate to their experimental system, consequently, valuable data have been lost. We discuss the various diffusion coefficients referred to all possible frames of reference in relation to the choice of a suitable experimental system for the determination of gaseous diffusion coefficients in porous media. A modified Ney and Armistead type diffusion cell is described with an improved method of calculation of results from continuously monitored concentration changes in the diffusion cell.

Steady-state measurement of krypton-85-air diffusion coefficients in porous media

Steady-state measurement of krypton-85-air diffusion coefficients in porous media