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G Q Chen - One of the best experts on this subject based on the ideXlab platform.

  • the asymptotic time variation of taylor Dispersivity for scalar transport in a two zone packed tube
    International Journal of Heat and Mass Transfer, 2015
    Co-Authors: G Q Chen
    Abstract:

    Abstract For transient scalar transport in a tube packed with two-zone heterogeneous porous media, presented in this paper is an extension of the existing study to determine the steady Dispersivity for the long term process of Taylor dispersion (Chen and Wu, 2012). For the initial phase of Taylor dispersion with essential implications to various applications, this work aims to illustrate the asymptotic time variation of the Dispersivity, by means of Aris’s method of concentration moments originally devised for the analysis of dispersion in a flow through an empty tube. The analytical solution of the Dispersivity covering both the initial and long term phases is rigorously derived to reflect the asymptotic structure of the Dispersivity as characterized by relevant dimensionless parameters which represent the relative magnitude of properties and the combined influences of two zones.

  • flow distribution and environmental Dispersivity in a tidal wetland channel of rectangular cross section
    Communications in Nonlinear Science and Numerical Simulation, 2012
    Co-Authors: Limin Zeng, G Q Chen
    Abstract:

    Abstract Presented in this paper is a theoretical analysis on flow distribution and environmental Dispersivity for a tidal wetland channel of rectangular cross-section. The analytical solution of velocity distribution for the tidal wetland flow is obtained and illustrated with a limiting case covering the known solution for a steady wetland flow. By use of Aris’s method of concentration moments, the environmental Dispersivity for a pulsed contaminant emission into the tidal wetland flow is rigorously derived and characterized in terms of dimensionless parameters. The solution is shown to be a generalization of the environmental Dispersivity for the corresponding steady wetland flow, taking into account the combined action of periodic oscillation and cross-sectional variation of superficial flow as well as the difference between superficial mass dispersivities in the vertical and lateral directions. For a long time evolution of the contaminant cloud, the environmental Dispersivity may approach a stable stage of oscillation with a period equal to the period of the superficial flow. The evolution of environmental Dispersivity at the initial stage for the tidal wetland flow is shown not monotonous as it does in the case of the steady wetland flow. It is also found that the period of superficial flow has no impact on the necessary time for the environmental Dispersivity to attain the stable stage.

Peter K Kitanidis - One of the best experts on this subject based on the ideXlab platform.

  • a mathematical and computational study of the Dispersivity tensor in anisotropic porous media
    Advances in Water Resources, 2013
    Co-Authors: Yuan Liu, Peter K Kitanidis
    Abstract:

    Abstract Dispersive transport in porous media is usually described through a Fickian model, in which the flux is the product of a dispersion tensor times the concentration gradient. This model is based on certain implicit assumptions, including slowly varying conditions. About fifty years ago, it was first suggested that the parameterization of the second-order dispersion tensor for anisotropic porous media involves a fourth-order Dispersivity tensor. However, the properties of the Dispersivity tensor have not been adequately studied. This work contributes to achieving a better grasp of dispersion in anisotropic porous media through a number of ways. First, with clearly stated assumptions and from first principles, we use the method of moments to derive a mathematical formula for the fourth-order Dispersivity tensor, and show that it is a function of pore geometry, fluid velocity, and pore diffusion. Second, by using pore-scale flow and transport simulations through orderly and randomly packed 2-D and 3-D porous media, we evaluate the effects of the three factors on Dispersivity. Different relationships with the Peclet number are observed for the longitudinal and transverse dispersivities and for orderly and randomly packed media. Third, we discuss the limitations of 2-D periodic media with simple structures in computing transverse Dispersivity, which is more accurately predicted in the 3-D periodic media and 2-D randomly packed media. Fourth, we exhibit through numerical simulations that the method of moments can, computational limitations notwithstanding, be extended to stationary porous media.

  • experimental determination of transverse Dispersivity in a helix and a cochlea
    Water Resources Research, 2006
    Co-Authors: Ioannis D Benekos, Olaf A Cirpka, Peter K Kitanidis
    Abstract:

    [1] In porous media, transverse dispersion plays a decisive role in the dilution of conservative solutes, the decay of concentration fluctuations, and the mixing of reactive solutes. One possible approach for measuring the transverse Dispersivity of homogeneous isotropic porous media is based on the principle of Taylor-Aris dispersion, where the longitudinal macrodispersion coefficient is inversely proportional to the pore-scale transverse dispersion coefficient. Taylor-Aris dispersion requires a shear flow situation. To achieve the latter in porous media, we use a helix, as previously proposed, and also a cochlea, which is spiral-shaped cavity resembling the interior a nautilus shell. We obtain experimental breakthrough curves from conservative tracer experiments and compare them to results of numerical simulation. By fitting the model we obtain the values of transverse Dispersivity in various tracer tests. In our experiments we investigate porous media with relatively uniform particle distributions. Estimates of the transverse Dispersivity are obtained for each experiment, and the relative advantages of each device are discussed. The two devices yield similar results. The estimated ratio of transverse Dispersivity to longitudinal Dispersivity agrees with the higher ratios reported in the literature.

G. Suresh Kumar - One of the best experts on this subject based on the ideXlab platform.

  • Effect of sorption intensities on Dispersivity and macro-dispersion coefficient in a single fracture with matrix diffusion
    Hydrogeology Journal, 2008
    Co-Authors: G. Suresh Kumar
    Abstract:

    Matrix diffusion and sorption are among the key processes impacting the efficiency of natural attenuation in the subsurface. While these processes have been studied extensively in fractured media, limited information exists on the sorption nonlinearity. To address this shortfall, a numerical model has been developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous-solute-source boundary condition. The influence of sorption intensities on Dispersivity and macro-dispersion coefficient is investigated using a method of spatial moments. Results suggest that mixing of solutes is significantly lowered by nonlinear sorptive behavior, with respect to the mixing caused by matrix diffusion for linearly sorbing solutes. Also, the magnitude of time dependent Dispersivity during the pre-asymptotic regime is lower for nonlinearly sorbing solutes with respect to the linearly sorbing solutes. Reduced mixing is also observed for nonlinearly sorbing solutes under combined mechanisms of matrix diffusion and decay. Les phénomènes de diffusion et de sorption comptent parmi les processus clés qui influent sur l’atténuation naturelle en subsurface. Si ces processus ont été massivement étudiés en milieu fracturé, il existe en revanche peu d’informations sur la non-linéarité de la sorption. Afin de combler cette lacune, un modèle numérique a été développé ; il couple la diffusion dans la matrice et la sorption non-linéaire à l’échelle d’une fracture unitaire en utilisant le concept de double porosité. La seule condition aux limites fixée pour toute l’étude est une source de soluté constante et continue. L’influence de l’intensité de la sorption sur la dispersivité et sur le coefficient de macro-dispersion est étudié via une méthode utilisant les moments spatiaux. Les résultats suggèrent que les mélanges de solutés sont significativement réduits par les phénomènes de sorption non-linéaires, comparativement aux mélanges causés par la diffusion pour des solutés à sorption linéaire. C’est pourquoi la dispersivité, dépendante du temps, est plus faible pour les solutés à sorption non-linéaire que pour les solutés à sorption linéaire, lors du régime pré-asymptotique. Des mélanges réduits ont également été observés pour des solutés à sorption non-linéaire, sous les mécanismes combinés de diffusion dans la matrice et de dégradation. La difusión intersticial y la adsorción se encuentran entre los procesos clave que impactan la eficiencia de la atenuación natural en el subsuelo. Mientras que estos procesos se han estudiado extensamente en medios fracturados existe información limitada acerca de la no linealidad de la adsorción. Para abordar esta situación se ha desarrollado un modelo numérico que acopla la difusión intersticial y la adsorción no lineal a la escala de una sola fractura usando el concepto de porosidad doble. El estudio se restringe a condiciones limitantes de fuente de soluto constante y continuo. Se investiga la influencia de las intensidades de adsorción sobre el coeficiente de dispersión-macro y dispersividad usando un método de momentos espaciales. Los resultados sugieren que la mezcla de solutos disminuye significativamente mediante comportamiento de adsorción no lineal, en relación con la mezcla causada por difusión intersticial para solutos con adsorción lineal. Se observa que la magnitud de la dispersividad dependiente del tiempo durante el régimen pre-asintótico es más baja para solutos con adsorción no lineales en relación a los solutos con adsorción lineal. También se observa mezcla reducida para solutos con adsorción no lineal bajo mecanismos combinados de difusión intersticial y desintegración.

  • Time dependent Dispersivity behavior of non-reactive solutes in a system of parallel fractures
    Hydrology and Earth System Sciences Discussions, 2006
    Co-Authors: G. Suresh Kumar, M. Sekhar, D. Misra
    Abstract:

    In order to obtain meaningful predictions of contaminant transport, an accurate way of quantifying Dispersivity needs to be developed. Results from the theoretical studies suggest that dispersion and the associated Dispersivity is non-fickian near the source of contaminant and it grows with travel time and distance. In most tests of a limited duration it is quite probable that the asymptotic regime is not reached, and a proper interpretation of the test should be based on the time-dependent results due to the difficulty associated with the expensive experimental setups added to the marked scarcity of field data. An attempt has been made using spatial moment analysis to evaluate the time dependent Dispersivity for a system of parallel fractures with matrix diffusion. The study is limited to non-reactive solutes, having a constant continuous source. An empirical relation to evaluate the Dispersivity was developed by us based on the sensitivity analysis, when distinct parallel fractures have constant aperture width and is found to be functions of matrix porosity, matrix diffusion coefficient and injected fracture velocity at pre-asymptotic stage. The system becomes more complex when the aperture widths of the distinct parallel fractures are varied, as it appears that the initial development period of non-fickian behavior may be long due to the continuous lateral mixing of the solute body. It is found that Dispersivity at pre-asymptotic regime increases with the coefficient of variation for distinct parallel fractures with varying aperture widths.

Suresh G Kumar - One of the best experts on this subject based on the ideXlab platform.

  • time dependent Dispersivity of linearly sorbing solutes in a single fracture with matrix diffusion
    Journal of Hydrologic Engineering, 2008
    Co-Authors: Muddu Sekhar, Suresh G Kumar, Debasmita Misra
    Abstract:

    Field studies show that the variance of travel distance often increases nonlinearly with time elapsed after release of solute tracers. The nonlinear relationship between variance of travel distance and time is attributed to the heterogeneity of the porous media. To describe the transport in such a heterogeneous system, a time-dependent Dispersivity is necessary. Though more attention has been devoted toward the study of non-Fickian dispersion at early time, there are no known studies that explicitly describe the Dispersivity behavior in a fracture–matrix-coupled system. The observation from numerical results suggests that Dispersivity has a time-dependent behavior and it reaches asymptotic values after a long time. The preasymptotic behavior of a solute front in fracture is characterized by increasing effective Dispersivity with time. The role of fracture and matrix transport parameters on this behavior is analyzed for linearly sorbing solutes. Approximate expression is provided for the time-dependent Dispersivity of the solute front in a single fracture with matrix diffusion and the expression for the time required to attain the asymptotic behavior is also obtained. A comparison of the front Dispersivity behavior between parallel multiple fractures with a constant aperture width model and smooth parallel multiple fractures with a varying aperture width model is done.

  • effect of sorption intensities on Dispersivity and macro dispersion coefficient in a single fracture with matrix diffusion
    Hydrogeology Journal, 2008
    Co-Authors: Suresh G Kumar
    Abstract:

    Matrix diffusion and sorption are among the key processes impacting the efficiency of natural attenuation in the subsurface. While these processes have been studied extensively in fractured media, limited information exists on the sorption nonlinearity. To address this shortfall, a numerical model has been developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous-solute-source boundary condition. The influence of sorption intensities on Dispersivity and macro-dispersion coefficient is investigated using a method of spatial moments. Results suggest that mixing of solutes is significantly lowered by nonlinear sorptive behavior, with respect to the mixing caused by matrix diffusion for linearly sorbing solutes. Also, the magnitude of time dependent Dispersivity during the pre-asymptotic regime is lower for nonlinearly sorbing solutes with respect to the linearly sorbing solutes. Reduced mixing is also observed for nonlinearly sorbing solutes under combined mechanisms of matrix diffusion and decay.

U M Scheven - One of the best experts on this subject based on the ideXlab platform.

  • Dispersivity of bidisperse packings of spheres and evidence for distinct random structures
    Physical Review Letters, 2018
    Co-Authors: U M Scheven
    Abstract:

    The intrinsic longitudinal and transverse Dispersivity of bidisperse random packings of spheres with size ratio 5∶1 was determined by pulsed field gradient nuclear magnetic resonance, in the dilute regime where small spheres occupy between 0% and 5% of the packings' volume. Small spheres plugging pores systematically raise the mechanical transverse and longitudinal Dispersivity above that of reference packings of monodisperse spheres. NMR-derived porosities, widths of velocity distributions, and dispersivities reveal distinct states of structural disorder above and below a relative sphere concentration n/N=1, where n and N are the number densities of small and large spheres.

  • pore scale mixing and transverse Dispersivity of randomly packed monodisperse spheres
    Physical Review Letters, 2013
    Co-Authors: U M Scheven
    Abstract:

    We show that transverse dispersion in flow through randomly packed monodisperse spheres (sphere diameter d) is a velocity-dependent superposition of three separable random processes-diffusion with coefficient D(r), intrinsic mechanical dispersion with Dispersivity l(m)=d/33 caused by advection on streamlines, and a newly identified coupled mechanical dispersion with Dispersivity l(c)=d/11, which arises by coupled advection and transverse diffusion at the pore scale. The velocity dependence of the transverse Dispersivity is derived from first principles. Our analysis is insensitive to details of the pore geometry and is verified by pulsed field gradient NMR experiments which covered 4.5 orders of magnitude in reduced velocity.

  • intrinsic Dispersivity of randomly packed monodisperse spheres
    Physical Review Letters, 2007
    Co-Authors: U M Scheven, R J Harris, Michael L Johns
    Abstract:

    Tracer dispersion in noninertial flow through random porous media is of considerable importance in catalysis, chromatography, ground water flows, oil production, and soil contamination, and it is a fundamental problem of hydrodynamics. Absent macroscopic stagnation zones, it is governed by differential advection in a nonuniform velocity field coupled to diffusion along velocity gradients perpendicular to the local flow. In laminar flow through a pipe [1‐3] the pipe radius a sets the spatial scale for the velocity gradients. In a simple isotropic random porous medium, realized approximately in the laboratory with a random pack of identical spheres (RP), the equivalent length is given by the volume to surface ratio of the pore