Viscous Fingering Instability in Porous Media: Effect of Anisotropic Velocity-Dependent Dispersion Tensor

The viscous fingering of miscible flow displacements in a homogeneous porous media is examined to determine the effects of an anisotropic dispersion tensor on the development of the instability. In particular, the role of velocity-dependent transverse and longitudinal dispersions is investigated through linear stability analysis and nonlinear simulations. It is found that an isotropic velocity-dependent dispersion tensor does not affect substantially the development of the instability and effectively has the same effect as molecular diffusion. On the other hand, an anisotropic velocity-dependent dispersion tensor results in different instability characteristics and more intricate finger structures. It is shown that anisotropic dispersion has profound effects on the development of the fingers and on the mechanisms of interactions between neighboring fingers. The development of the new finger structures is explained by examining the velocity field and characterized qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the sweep efficiency and relative contact area.     

Automaton Simulations of Dispersion in Porous Media

A thermodynamic lattice gas (automaton) model is used to simulate dispersion in porous media. Simulations are constructed at two distinctly different scales, the pore scale at which capillary models are constructed and large scale or Darcy scale at which probabilistic collision rules are introduced. Both models allow for macroscopic (pore scale) phase separation. The pore scale models clearly show the effect of pore structure on dispersion. The large scale (mega scale) simulations indicate that when the pressure difference between the displacing phase and displaced phase is properly chosen (representing the average pressure gradient between the phases). The simulation results are consistent with both theoretical predictions and experimental observations.     

Dispersion and Chemical Reactions in Porous Media

The effect of chemical reactions on the process of admixture transport by a flow through a porous medium is considered. On the basis of a number of examples it is shown that the dispersion coefficient depends on the chemical reaction rate constant.     

Dispersion Measurements in Highly Heterogeneous Laboratory Scale Porous Media

Laboratory experiments and numerical simulations investigate conservative contaminant transport in a heterogeneous porous medium. The laboratory experiments were performed in cylindrical columns 1m long and 3.5cm inside diameter filled with spherical glass beads. Concentration breakthrough curves are measured at a scale much finer than the size of the heterogeneity. Numerical simulations are based on a random walk in a known constant velocity field. The heterogeneity is a distinct, discontinuous change in the local permeability field. Fluid flow is miscible, flowing in a saturated porous medium. Previous work has shown this to be a very poorly understood phenomenon. The measurements reported here help to better understand how dispersion evolves through and past a heterogeneity.     

Dispersion in Heterogeneous Porous Media: One-Equation Non-equilibrium Model

In this paper, the method of large-scale averaging is used to develop two different one-equation models describing dispersion in heterogeneous porous media. The first model represents the case of large-scale mass equilibrium, while the second represents the asymptotic behavior of a two-equation model obtained by large-scale averaging. It is shown that a one-equation, non-equilibrium model can be developed even when the intrinsic large-scale averaged concentrations for each region are not equal. The solution of this non-equilibrium model is equivalent to the asymptotic behavior of the two-equation model.     

Dispersion Stability and Transport of Nanohybrids through Porous Media

Single-walled carbon nanotube-silica nanohybrid particles are a very promising material that could be used for enhanced oil recovery because of their interfacial activity. To demonstrate the basic principle, aqueous nanohybrid particle dispersions were evaluated by looking at the effect of pH, surfactant, and polymer. The results showed that pH did not have significant effect on the dispersion stability of nanohybrid particles. Although surfactant could improve the dispersion stability, it reduced the interfacial activity of the nanohybrid particles, causing them to stay in the aqueous phase. The best nanohybrid particle dispersion stability was found upon polymer addition, where the dispersions were stable for more than a week even at low polymer concentration (50?ppm). One-dimensional sand-pack studies were performed to evaluate the flow of the nanohybrid particles through porous media. The results showed that most of the nanohybrid particles (>99%) could pass through a column packed with glass beads while a measurable fraction of the particles was retained in the column packed with crushed Berea. When the columns contained a residual saturation of decane, additional nanohybrid particles were retained at the oil/water interface in both glass beads and crushed Berea sand media. The sand pack studies showed that not only can the nanohybrid particles flow through porous media but also about half of the particles injected will go the O/W interface when the porous medium contains a residual saturation of hydrocarbon, where they could be used to support a catalytic conversion of components of the oil in reservoirs.     

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

A two-dimensional numerical model is used to study the nonlinear behavior of density gradients on transverse dispersion. Numerical simulations are conducted using d ³ f, a computer code for simulation of density-dependent flow in porous media. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersivity. Changing salt concentration significantly affects fluid properties. This physical behavior of the fluid involves a non-linearity in modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from the tracer case due to the spatial variation of permeability, described by statistical parameters, at the local-scale. Indeed, the presence of vertical flow velocities induced by permeability variations is responsible for the reduction of the mixing zone width in the steady state in the case of a high density gradient. Uncertainties in the model simulations are studied in terms of discretization errors, boundary conditions, and convergence of ensemble averaging. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and limitations of the nonlinear model of Hassanizadeh (1990) and Hassanizadeh and Leijnse (1995) (Adv Water Resour 18(4):203–215, 1995) in heterogeneous porous media are investigated. We found that the main cause of the nonlinear behavior of dispersion, which is the interaction between density contrast and vertical velocity, needs to be explicitly accounted for in a macro-scale model.     

Investigation of Hydrodynamic Dispersion and Intra-pore Turbulence Effects in Porous Media

Transport in Porous Media - The aim of the present paper is to evaluate and compare the pore level hydrodynamic dispersion and effects of turbulence during flow in porous media. In order to compute...     

Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry

The coefficient of dispersion, D _ij , and the dispersivity, a _ijkl , appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium, e.g., a stratified porous medium, with alternating layers, and show that in such a medium, the dispersivity is governed by six independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.     

Dispersion Phenomena in Thermal Diffusion and Modelling of Thermogravitational Experiments in Porous Media

In a TIPM paper published in 1992, the authors presented a simple model of thermogravitational diffusion in packed columns (TPC). Though qualitatively in agreement with the experimental results, this model exhibited a systematic discrepancy with respect to the magnitude of the permeability of maximum separation in the TPC experiments. Here, the results of a re-examination of the classical phenomenology of irreversible thermodynamics in porous media, applied to TPC, are described. Through the interpretation of additional TPC experiments, we show that the effective thermal diffusion coefficient in TPC includes a dependency upon the fluid velocity. This dependency is consistent with a nonlinear extension of irreversible thermodynamics, and the model so amended accounts for a correct re-interpretation of the experiments.     

Numerical Modeling of Momentum Dispersion in Porous Media Based on the Pore Scale Prevalence Hypothesis

Transport in Porous Media - A macroscopic model that accounts for the effect of momentum dispersion on flows in porous media is proposed. The model is based on the pore scale prevalence hypothesis...     

Theoretical Analyses of the Effects of Solute Dispersion on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

This article deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including solute dispersion effects. Since the solute equilibrium concentration is much smaller than the molar density of the dissolvable mineral in a mineral dissolution system, a limit case, in which the ratio of the solute equilibrium concentration (in the pore fluid) to the molar density of the dissolvable mineral (in the solid matrix of the porous medium) approaches zero, is considered in the theoretical analysis. Under this assumption, the critical condition under which a planar chemical-dissolution front becomes unstable has been mathematically derived when solute dispersion effects are considered. The present theoretical results clearly demonstrated that: (1) the propagation speed of a planar chemical-dissolution front in the case of considering solute dispersion effects is the same as that when solute dispersion effects are neglected. This indicates that solute dispersion does not affect the propagation speed of the planar chemical-dissolution front in a fluid-saturated porous medium. (2) The consideration of solute dispersion can cause a significant increase in the critical Zhao number, which is used to judge whether or not a planar chemical-dissolution front may become unstable in the fluid-saturated porous medium. This means that the consideration of solute dispersion can stabilize a planar chemical-dissolution front, because an increase in the critical Zhao number reduces the likelihood of the planar chemical-dissolution front instability in a fluid-saturated porous medium. In addition, the present results can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of chemical dissolution fronts in two-dimensional fluid-saturated porous media.     

On the Nield-Kuznetsov Theory for Convection in Bidispersive Porous Media

We revisit the problem of thermal convection in a bidispersive porous medium, first addressed by Nield and Kuznetsov (Int. J. Heat Mass Transfer, 49: 3068–3074, 2006). We investigate the possibility of oscillatory convection by using a highly accurate Chebyshev tau numerical method. We also develop a nonlinear energy stability theory for the same problem. This yields a global stability threshold below which instabilities cannot arise. These thresholds together with the linear instability boundaries yield a zone where thermal instability may be found. The results and theory of Nield and Kuznetsov (Int. J. Heat Mass Transfer, 49: 3068–3074, 2006) are thus proven to be a highly important development in the modern theory of designer porous materials, cf. Nield and Bejan (Convection in Porous Media, Springer, New York, 2006), pp. 94–97. This work was supported in part by a Research Project Grant of the Leverhulme Trust—Grant Number F/00128/AK.     

Study of the Effect of Thermal Dispersion on Internal Natural Convection in Porous Media Using Fourier Series

Transport in Porous Media - Natural convection in a porous enclosure in the presence of thermal dispersion is investigated. The Fourier–Galerkin (FG) spectral element method is adapted to...     

Study of Dispersion in Porous Media by Pulsed Field Gradient NMR: Influence of the Fluid Rheology

Pulsed field gradient nuclear magnetic resonance (PFG-NMR) is used to measure the molecular displacements for the flow of a fluid through a capillary tube and a packed bed made of monodisperse PMMA beads. The molecules average displacement is studied using both the formalism of propagators and the cumulant method. In the Poiseuille case, the dispersion coefficients determined by the cumulant method compare satisfactorily with the theoretical values obtained. The technique is then extended to study the flow through a porous medium. We thus analyze Newtonian (water) and non-Newtonian (Xanthan) flows and put a particular emphasis on comparing the dispersion mechanisms between Newtonian and non-Newtonian fluids.     

Transport in Porous Media

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Transport in Porous Media     

Transport in Porous Media

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Transport in Porous Media     

Transport in Porous Media

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Transport in Porous Media