Generalized ray expansion for pulse propagation and attenuation in fluid-saturated porous media

A theory suitable for studying pulses propagating through a layered fluid-saturated porous medium is presented. Biot's theory is used to describe the constitutive equation of a fluid-saturated porous solid. Since fast and slow compressional waves exist in a Biot solid even at normal incidence, there is mode conversion at the interface and, therefore, the transmission and reflection coefficients are 2x2 matrices. We use matrix methods in developing the solution of the wave propagation problem. A generalized ray expansion algorithm is obtained by using the Gauss-Seidel matrix iterative method. The arrivals of the fast and the slow waves are easily identified. A compact computational algorithm is developed using combinatorial analysis and the Cayley-Hamilton theorem.     

Erosion and deposition of solid particles in porous media: Homogenization analysis of a formation damage

The aim of the paper is to model at a large scale, the formation damage in porous media by erosion and deposition of solid particles. We start from the equations governing the pore-scale processes of erosion, deposition, convection and diffusion. The macroscopic equivalent behaviour is investigated by using a homogenization method. Four characteristic models with different dominating phenomena at the pore scale are determined. The main results are twofold: first dispersion-deposition and dispersion-erosion phenomena are shown at the macroscopic scale for peculiar values of the dimensionless numbers; furthermore, and contrarily to phenomenological models, erosion and deposition generally occur in regions of intense and slow flow, respectively.     

A study of two-dimensional dispersion in unconsolidated porous media

An experimental and numerical investigation into the magnitude of longitudinal and transverse dispersion in a two-dimensional flow field over a particle Peclet number range of 50–8500 is reported. Numerical modelling using a Galerkin finite element method is used to test various models, notably those of Fried and combarnous and Koch and Brady. Dispersion at low Peclet numbers (< 200) is found to be described adequately by either model, which at large Peclet, the degree of dispersion is significantly underestimated. An improved dispersion model for Peclet numbers greater than 200 is proposed. The transverse dispersion term and the choice of inlet boundary condition are found to have a negligible effect on the shape of the breakthrough curve.Nomenclature A (z) Polynomial in the z plane - B (z) Polynomial in the z plane - C Concentration - C _f Feed concentration - C _o Concentration at the entrance - D Dispersion tensor - D _f Molecular diffusion coefficient - D ₁ Longitudinal dispersion coefficient - D _p Particle diameter - D _t Transverse dispersion coefficient - k Permeability/viscosity - k Dimensionless permiability in the Koch and Brady model - P Pressure - Pe _k Modified Peclet number, Pe _p k - Pe _p Particle Peclet number vD _p /D _f - v Velocity - z Axial coordinate or complex variable Greek letters Solution domain - Boundary - Porosity     

A computerized technique for measuringin-situ concentrations during miscible displacements in porous media

A technique for measurement of thein-situ concentration in an unconsolidated porous medium has been developed. The method involves measurement of electrical conductivityin-situ, under dynamic conditions, for flow involving brine of differing concentrations, at selected locations along the porous medium and relating it to the brine strength. Data acquisition and analysis is carried out using a Hewlett — Packard micro-computer and its interface. A user-friendly software was designed and developed for the system. The measurement technique was evaluated by studying the effect of brine concentration, brine flow rate, and by conducting miscible displacements experiment. The experimentally measured dispersion coefficients for the porous medium agreed closely with the value predicted by the correlation available in the literature.     

Application of a wave transform to pressure transient testing in porous media

Solutions to the diffusion equation for nonuniform media are difficult to obtain in a form that can be easily evaluated. Often the solutions are written as the inverse Laplace transform of an inverse Fourier transform. In this paper, I show that the wave transform of Bragg and Dettman (1968) coupled with the Cagniard-de Hoop method for solving the wave propagation problem results in simplified solutions to the problem of pressure transient testing in linear composite reservoirs. The potential usefulness of an inverse wave transform, which would transform measured pressure data (smooth) into a wave signal propagating at the velocity of the square root of the diffusivity, is demonstrated by a synthetic example. In the example, diffusivity of the source region is estimated from the time of the direct wave arrival, while diffusivity of a second, higher diffusivity region is estimated from the velocity of the head wave. In the wave domain the time-like variable has units of (time)^1/2 which makes the units of velocity equal to L T-^(1/2). I also demonstrate, using synthetic data, that it is difficult, but perhaps possible, to invert the wave transform numerically.     

Contributions to numerical developments in shock waves attenuation in porous filters

The paper deals with the numerical method of the compressible gas flow through a porous filter emphasizing the treatment of the interface between a pure gaseous phase and a solid phase. An incident shock wave is initiated in the gaseous phase interacting with a porous filter inducing a transmitted and a reflected wave. To take into account the discontinuity jump in the porosity between the gaseous phase and the porous filter, an approximate Riemann solver is used to compute homogeneous non-conservative Euler equations in porous media using ideal gas state law. The discretization of this problem is based on a finite volume method where the fluxes are evaluated by a “volumes finis Roe” (VFRoe) scheme. A stationary solution is determined with a continuous variable porosity in order to test the numerical scheme. Numerical results are compared with the two-phase shock tube experiments and simulations of a shock wave attenuation and gas filtration in porous filters are presented.      

A pore scale study on turbulent combustion in porous media

This paper presents pore scale simulation of turbulent combustion of air/methane mixture in porous media to investigate the effects of multidimensionality and turbulence on the flame within the pores of porous media. In order to investigate combustion in the pores of porous medium, a simple but often used porous medium consisting of a staggered arrangement of square cylinders is considered in the present study. Results of turbulent kinetic energy, turbulent viscosity ratio, temperature, flame speed, convective heat transfer and thermal conductivity are presented and compared for laminar and turbulent simulations. It is shown that the turbulent kinetic energy increases from the inlet of burner, because of turbulence created by the solid matrix with a sudden jump or reduction at the flame front due to increase in temperature and velocity. Also, the pore scale simulation revealed that the laminarization of flow occurs after flame front in the combustion zone and turbulence effects are important mainly in the preheat zone. It is shown that turbulence enhances the diffusion processes in the preheat zone, but it is not enough to affect the maximum flame speed, temperature distribution and convective heat transfer in the porous burner. The dimensionless parameters associated with the Borghi–Peters diagram of turbulent combustion have been analyzed for the case of combustion in porous media and it is found that the combustion in the porous burner considered in the present study concerns the range of well stirred reactor very close to the laminar flame region.     

Method of homogenization applied to dispersion in porous media

The theory of homogenization which is a rigorous method of averaging by multiple scale expansions, is applied here to the transport of a solute in a porous medium. The main assumption is that the matrix has a periodic pore structure on the local scale. Starting from the pores with the Navier-Stokes equations for the fluid motion and the usual convective-diffusion equation for the solute, we give an alternative derivation of the three-dimensional macroscale dispersion tensor for solute concentration. The original result was first found by Brenner by extending Brownian motion theory. The method of homogenization is an expedient approach based on conventional continuum equations and the technique of multiple-scale expansions, and can be extended to more complex media involving three or more contrasting scales with periodicity in every but the largest scale.     

多孔介质中二维对流传热的分叉

本文利用分叉理论研究了流体饱和的二维多孔介质从底部加热所引起的自然对流,用有限差分方法确定对流的分叉进程;揭示其模式转换机理及分叉对非正常流动图象形成的影响;同时确定了矩形截面宽高比与临界端利数的关系。还提出了一个判别分支稳定笥的简明方法。     

Surface deposition from fluid flow in a porous medium

The changes to porosity and permeability resulting from surface deposition and early dissolution in an initial rhombohedral array of uniform spheres are studied. Very rapid decreases in permeability result from early deposition, with 48 percent reduction predicted in permeability from 8 percent reduction in porosity. After deposition has caused about a 1 percent increase in the radii of the spherical array, relative permeability reductions vary approximately as the square of relative changes in porosity. These theoretical results are matched with experimental data of Itoi et al. and Moore et al. on deposition of silica. Satisfactory results are obtained in some cases, but for other cases a more complex model of the porous medium is needed.     

Freezing and thawing porous media: experimental study with a dielectric capacitive method

A capacitive sensor-based apparatus has been used to study the ice/water phase change in consolidated porous media subjected to freezing and thawing. This technique relies on the dielectric properties of water, ice, air, and the mineral substrate in the radio-frequency range. It gives directly the freezing and thawing temperature depressions and indirectly provides an estimation of pore size distribution through the Gibbs–Thomson relation. It also holds good promise for evaluating the amount of liquid water in frozen porous media by combining drying and freezing tests. To cite this article: T. Fen-Chong, A. Fabbri, C. R. Mecanique 333 (2005).     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

Numerical study of the linear stability of immiscible displacement in porous media

In this paper the linear stability of immiscible displacement in porous media is examined by numerical methods. The method of matched initial value problems is used to solve the eigenvalue problem for displacement processes pertaining to initially mobile phases. Both non capillary and capillary displacement in rectilinear flow geometries is studied. The results obtained are in agreement with recent asymptotic studies. A sensitivity analysis with respect to process parameters is carried out. Similarities and differences with the stability of Hele-Shaw flows are delineated.This is a revised version of paper SPE 13163, presented at the 59th Annual Technical Conference of the Society of Petroleum Engineers, Houston, Texas, 16–19 Sept. 1984.     

Application of generalised effective-medium theory to transport in porous media

The use of effective-medium treatments to estimate bulk properties pertaining to transport (of, for example, fluids, heat, particles or electricity) through random composite media (such as reservoir rocks), is widespread. This is because they are relatively simple, often reasonably accurate (on occasion, remarkably so) and in many cases yield closed-form expressions for the properties concerned. However, the single-bond effective-medium treatment (EMT) of random resistor networks that has been used to determine transport coefficients for various transport problems in pore networks is limited to some special isotropic networks with nearest-neighbour connections. We demonstrate here that transport through two different fracture system models, with stress-induced anisotropy, can be treated using an EMT originally applied to anisotropic resistor networks. The main purpose of the present contribution, however, is to present a new, more general effective medium formalism applicable to networks of arbitrary topology. This new generalised EMT is used to obtain a new criterion for percolation of an arbitrary conducting network under random dilution. A specific application to unsaturated flow through a pore network with nearest- and next-nearest-neighbour connections is also given.     

An experimental study of steam injection into a uniform water flow through porous media

An experimental study of steam injection into a porous media was carried out in a 2-dimensional plane porous channel. The steam was injected into a uniform downward water flow in a vertically aligned porous channel. The steam-water interface was carefully observed to understand the underlying physics. Two steam injection rate bounds were found for a given water flow rate and water subcooling. The upper bound is the steam flow rate at which the steam zone grows without limit and the lower bound is the steam flow rate at which a steam zone is just initiated. The bounds were determined experimentally for a porous channel with different permeabilities and thermal conductivities. For large particle size, chaotic oscillation of steam water interface was observed. The oscillation is believed to enhance heat and momentum transfer mechanisms. The steam zone size and shape were measured to evaluate heat transfer characteristics. The average Nusselt number is presented in terms of steam and water Reynolds numbers and the Stefan number.     

Shock compression of some porous media in conical targets: numerical study

Axially symmetric flows in conical solid targets filled by porous aluminum, graphite or polytetrafluoroethylene under impact of an aluminum plate with the velocity of 2.5 km/s are simulated numerically within the framework of the model of the hypoelastic ideal-plastic solid. The porosity of the samples is taken into account by conservation laws at the leading shock wave; the medium behind that is supposed to be nonporous. Equations of state for all materials in question are used to describe thermodynamic properties of the impactor and target over a wide range of pressures and temperatures taking into account phase transformations. The maximal over space and time pressure as a function of the initial relative density is presented and discussed.     

Application of a lattice-gas numerical algorithm to modelling water transport in fractured porous media

A 2D lattice-gas numerical algorithm was used to simulate liquid infiltration into unsaturated porous media with a parallel sided central crack. The chosen model, the interacting liquid-gas model of Appert and Zaleski, has dynamic properties leading to a phase transition and liquid and gas phases can be simulated by the model. These two phases are used to simulate biphasic flow in porous media. Fourteen numerical experiments of liquid infiltration were carried out which differed in the morphology of the microporous matrix, in the aperture of the central crack and in the amount of liquid supplied. For the same microporous matrix, the infiltration dynamics in the dual media depended upon the ratio between the amount of liquid supplied and the crack aperture. Variations in water storage over time and liquid flow regimes within the cracks are discussed.     

Permeability anisotropy due to consolidation of compressible porous media

The characterisation of flow through porous media is important for all solid–liquid separation and fluid transport realms. The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy ratios for lignite, as well as for other materials including sand, clay and kaolin.