Equivalent Dispersion Coefficient Research Articles

Single region substitute models for dual-porosity advection–dispersion migration process based on contaminant distribution

Dual-porosity (DP) model is recommended for describing the complex non-Fickian contaminant transport in soil, while advection–dispersion-equation (ADE) model is the most popular transport model due to its simplicity and convenience. In this study, single region substitute approaches for the DP model were established based on the contaminant distribution in the mobile and immobile phases. A time dependent parameter Ω was used to determine the participation degree of the immobile phase in contaminant transport. The single region substitute (SRS) model was modified by combining the mobile phase retardation factor with the adsorbed concentration of immobile phase. Furthermore, dispersion-modified SRS (DSRS) model was established for calculating the equivalent dispersion coefficient of the coupled mobile-immobile mass transfer and advection via Fourier transformation. Correlation analyses of the modified models shown that the SRS model fits DP well when advection velocity or the mobile-immobile mass transfer rate is relatively slow under both Cauchy and Dirichlet inlet boundary, whereas that the DSRS model is applicable when mobile-immobile mass transfer rate is relatively higher. Both SRS and DSRS models can provide better understanding to the contaminant transport process of DP model.

Impact of Electro-Magnetohydrodynamic Nature on Dispersion of solute in the Peristaltic Mechanism

The present article deals with the dispersion of a solute in peristaltic system. This mathematical model provides the analytical solution of electro-magnetohydrodynamic flow of biofluids through a channel. Treating blood as a Jeffrey fluid and considering homogeneous chemical reaction, the closed form of solution of effective dispersion coefficient is obtained by using Taylor’s limiting condition and long wave length approximation. The impacts of physiological parameters such as the electro osmotic velocity, electro kinetic, Jeffrey fluid parameter and Hartmann number on the Peristaltic movement have been investigated. It is found that the average equivalent dispersion coefficient is reduced with respect to the enhancement of homogeneous chemical reaction parameter and Hartmann number. It is pertinent to point out here that the electro osmotic velocity and electro kinetic parameter help to enhance average equivalent dispersion coefficient in comparison with the absence of applied electric field. The present analytical study provides useful information to artificial bio-processors.

A Photonic Approach to Linearly Chirped Microwave Waveform Generation With an Extended Temporal Duration

A photonic approach to linearly chirped microwave waveform generation with an extended temporal duration is proposed and experimentally demonstrated. The linearly chirped microwave waveform generation is realized based on spectral-shaping and wavelength-to-time mapping, in which a Fabry–Perot (FP) interferometer with a linearly increasing or decreasing free spectral range is used to as a spectral shaper, and the wavelength-to-time mapping is realized using a recirculating dispersive loop with a large equivalent dispersion coefficient realized by allowing the spectrally shaped optical pulse to travel in the dispersive loop multiple times. The generation of two linearly chirped microwave waveforms at two different frequency bands with two temporal durations of 25 and 42 ns and a time-bandwidth product (TBWP) of 210 is experimentally demonstrated.

Temperature, Humidity, and Airflow in the Emplacement Drifts Using Convection and Dispersion Transport Models

A coupled thermal-hydrologic-airflow model is developed, solving for the transport processes within a waste emplacement drift and the surrounding rock mass together at the proposed nuclear waste repository at Yucca Mountain. Natural, convective airflow as well as heat and mass transport in a representative emplacement drift, embedded in a three-dimensional, mountain-scale rock mass with edge cooling, are explicitly simulated for the first time in the literature, using the MULTIFLUX model. The conjugate, thermal-hydrologic transport processes in the rock mass are solved with the TOUGH2 porous-media simulator in a coupled way to the in-drift processes. The new simulation results show that large-eddy turbulent flow, as opposed to small-eddy flow, dominates the drift airspace for at least 5000 years following waste emplacement. The size of the largest, longitudinal eddy is equal to half of the drift length, providing a strong axial heat and moisture transport mechanism from the hot drift sections to the cold drift sections. The in-drift results are compared to those from simplified models using a surrogate, dispersive model with an equivalent dispersion coefficient for heat and moisture transport. Results from the explicit, convective velocity simulation model provide higher axial heat and moisture fluxes than those estimated from the previously published, simpler, equivalent dispersion models, in addition to showing differences in temperature, humidity, and condensation rate distributions along the drift length. A new dispersive model is also formulated for comparison, giving a time- and location-variable function that runs generally about ten times higher in value than the highest dispersion coefficient currently used in the Yucca Mountain Project.

On the use of large time steps with ELLAM for transport with kinetic reactions over heterogeneous domains

AbstractAn Eulerian Lagrangian localized adjoint method (ELLAM) is considered for the resolution of advection‐dominated transport problems in porous media. Contrary to standard Eulerian methods, ELLAM can use large time steps because the advection term is approximated accurately without any CFL restriction. However, it is shown in this article that special care must be taken for the approximation of the dispersive and reactive terms when large time steps are used over heterogeneous domains. An alternative procedure is proposed. It is based on an equivalent dispersion coefficient or an equivalent reaction rate when different zones are encountered during the tracking. Numerical experiments are performed with variable dispersion or variable reaction rates over space (including nonlinearity). When classical ELLAM require numerous time steps to handle heterogeneity, the alternative procedure is shown to perform with the same accuracy in a single time step. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Analytical solutions of one-dimensional macrodispersion in stratified porous media by the quadrupole method: convergence to an equivalent homogeneous porous medium

In this article, the quadrupole method is implemented in order to simulate the effects of heterogeneities on one dimensional advective and diffusive transport of a passive solute in porous media. Theoretical studies of dispersion in heterogeneous stratified media can bring insight into transport artefacts linked to scale effects and apparent dispersion coefficients. The quadrupole method is an efficient method for the calculation of transient response of linear systems. It is based here on the Laplace transform technique. The analytical solutions that can be derived by this method assists understanding of upscaled parameters relevant to heterogeneous porous media. First, the method is developed for an infinite homogeneous porous medium. Then, it is adapted to a stratified medium where the fluid flow is perpendicular to the interfaces. The first heterogeneous medium studied is composed of two semi-infinite layers perpendicular to the flow direction each having different transport properties. The concentration response of the medium to a Dirac injection is evaluated. The case studied emphasises the importance in the choice of the boundary conditions. In the case of a periodic heterogeneous porous medium, the concentration response of the medium is evaluated for different numbers of unit-cells. When the number of unit cells is great enough, depending on the transport properties of each layer in the unit cell, an equivalent homogeneous behaviour is reached. An exact determination of the transport properties (equivalent dispersion coefficient) of the equivalent homogeneous porous medium is given.

A Study of Sectionally Related Dispersion and Chemical Reaction Effects

This theoretical investigation is aimed at finding the influence ofthe cross-section on the equivalent dispersion coefficient of a solute in a non-Newtonian medium flowing through a channel by considering the Power law, Bingham plastic, Casson models of fluids and it has been noted that in the case of the first two, there is a steep rise with the increase of the width of the channel, but in the case of Casson model, equivalent dispersion coefficient attains a maximum atRla = 1.7. Some explanation is offered for this behaviour of the fluids

Tracer dispersion in sintered glass beads with a bidisperse size distribution

AbstractAn experimental study was made of tracer dispersion in bidisperse sintered glass materials prepared from mixtures of two sizes of beads with mean diameters of 325 and 95 μm. The equivalent dispersion coefficient increases by a factor of 30 when the porosity decreases from 30 to 12%; this variation is similar to that measured in monodisperse samples. The variation of dispersion can be characterized by the ratio R = ℓd/L1 where ℓd is a length scale deduced from the equivalent dispersion coefficient and L1 is obtained from conductivity and permeability measurements. It is shown that the increase of ℓd/L1 correlates with the loss of porosity during the sintering process. Lightly sintered samples with a percentage of small beads around the minimum of porosity display a nearly Gaussian behavior, with a dispersion coefficient close to that obtained in homogeneous equivalent mixtures. This result is in contrast with very large anomalies observed by other authors. These results imply that dispersion in consolidated samples is sensitive to large‐scale inhomogeneities of the materials rather than to their detailed structure.

Analysis of Hydrodynamic Dispersion in Discrete Fracture Networks Using the Method of Moments

Recent field investigations in crystalline rock give strong indications that water flows in largely isolated channels in fissured rock. The channels are located in fracture planes and may or may not connect to other channels in the same plane or at fracture intersections. In the present paper, hydrodynamic dispersion in such fracture networks is investigated using the concepts of residence time distribution theory. It is shown that from a set of simple relations, at least the first four statistical moments for the system response are easily obtained even for complicated networks. In particular, an equivalent dispersion coefficient may be calculated from the second central moment (variance). The effect of channeling generally decreases in systems with many mixing steps. A criterion, based on the coefficients of skewness and kurtosis, is derived for when the response of the system is in accordance with the diffusion‐dispersion model. Examples show that this limit may not be obtained under realistic repository conditions in fissured rock.

Comment on “Flux‐Averaged and Volume‐Averaged Concentration in Continuum Approaches to Solute Transport” by J. C. Parker and M. Th. van Genuchten

Water Resources ResearchVolume 21, Issue 8 p. 1299-1300 CommentariesFree Access Comment on “Flux-Averaged and Volume-Averaged Concentration in Continuum Approaches to Solute Transport” by J. C. Parker and M. Th. van Genuchten Gedeon Dagan, Gedeon DaganSearch for more papers by this authorEshel Bresler, Eshel BreslerSearch for more papers by this author Gedeon Dagan, Gedeon DaganSearch for more papers by this authorEshel Bresler, Eshel BreslerSearch for more papers by this author First published: August 1985 https://doi.org/10.1029/WR021i008p01299Citations: 11AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Bresler, E., G. Dagan, Unsaturated flow in spatially variable fields, 3, Solute transport models and their application to two fields, Water Resour. Res., 192, 429– 435, 1983. Dagan, G., The generalization of Darcy's law for nonuniform flows, Water Resour. Res., 151, 1– 7, 1979. Dagan, G., Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport, Water Resour. Res., 184, 835– 848, 1982. Dagan, G., Solute transport in heterogeneous porous formations, J. Fluid. Mech., 145, 151– 177, 1984. Dieulin, A., G. Matheron, G. deMarsily, B. Beaudoin, Time dependence of an “equivalent dispersion coefficient” for transport in porous media, Flow and Transport in Porous Media A. Verrujt, F. B. J. Barends, 199– 202, A. A. Balkema, Rotterdam, 1981. Matheron, G., G. deMarsily, Is transport in porous media always diffusive? A counterexample, Water Resour. Res., 165, 901– 917, 1980. Parker, J. C., M. Th. vanGenuchten, Flux-averaged and volume-averaged concentration in continuum approaches to solute transport, Water Resour. Res., 207, 866– 872, 1984. Saffman, P. G., A theory of dispersion in porous media, J. Fluid Mech., 6, 321– 349, 1959. Saffman, P. G., On the boundary conditions at the surface of a porous medium, Stud. Appl. Math., 12, 93– 101, 1971. Taylor, G. I., Diffusion by continuous movement, Proc. London Math. Soc., A20, 196– 212, 1921. Citing Literature Volume21, Issue8August 1985Pages 1299-1300 ReferencesRelatedInformation

A note on fracture flow dispersion mechanisms in the ground

Two mechanisms for spreading of a tracer pulse in fissured media are discussed: channeling and diffusion in the rock matrix. Dispersion has traditionally been treated as a random mechanism, comparable to diffusion. It is not quite clear if this is applicable to such geologic media as sparsely fissured rock or other stratified media. In this paper, two other mechanisms for dispersion are treated. One is stratified flow; the other is due to interaction with a solid material. A very idealized case of stratified flow is treated. A case is modeled where the medium flows in parallel channels. Each channel is assumed to consist of the space between two parallel plates. The flow is laminar. The various channel widths are assumed to be randomly distributed with a lognormal frequency distribution. This is a distribution which has been found experimentally in fissured crystalline rock. For this case, it is shown that an equivalent dispersion coefficient will increase with the distance between injection and observation point. For this case the normal Fickian diffusion dispersion description is not applicable if the usual assumption is made that the dispersion coefficient is constant. There are several interaction mechanisms of interest between a solute and the solid material. The one treated here is the diffusion of the solute into the porous rock matrix and sorption of the inner surfaces of the matrix. This interaction will also lead to the spreading of a tracer front, in a similar way to what other dispersion mechanisms do. It is demonstrated that if the solid material has very long extension, the dispersion due to this mechanism is so large that a Fickian dispersion coefficient cannot be evaluated without explicitly accounting for this mechanism. Attempts to evaluate Fickian dispersion coefficients by the method of moments will give values which are entirely dependent on the observation accuracy of the tail.

Dispersion in simple microfluid flows

We have discussed here dispersion of a solute matter in a simple microfluid flowing through channels and pipes. The effect of homogeneous first order chemical reaction rate has also been considered in the analysis. Using Taylor's limiting condition, equivalent dispersion coefficient has been determined and the effects of various parameters have been studied. Moreover, as the various viscosity coefficients for simple microfluid are known to depend on the volume concentration of suspended particles, its effect on the equivalent dispersion coefficient has also been studied. It is found that for given simple microfluid parameters the equivalent dispersion coefficient decreases as the chemical reaction rate constant increases, however it increases as the volume concentration of suspended particles increases.

Dispersion in non-Newtonian fluids: Effects of chemical reaction

The dispersion of a solute in non-Newtonian fluids flowing through channels and pipes has been studied by taking into account the homogeneous first-order chemical reaction. It is shown that for the same mean velocity of the flow the equivalent dispersion coefficient decreases as the rate of the chemical reaction increases. This decrease is enhanced due to non-Newtonian nature of the fluid.