Porous Medium (porous + medium)

Distribution by Scientific Domains
Distribution within Engineering

Kinds of Porous Medium

  • fluid-saturated porous medium
  • heterogeneous porous medium

  • Selected Abstracts

    Combustion of a substitution fuel made of cardboard and polyethylene: influence of the mix characteristics,modeling

    FIRE AND MATERIALS, Issue 7 2008
    S. Salvador
    Abstract The model proposed in this paper describes the combustion of a porous medium subjected to a radiative heat flux at its surface. There is no forced convection of air through the medium; hence this situation corresponds to the one encountered at the surface of fuel elements such as pellets, bricks or ballots, inside a furnace or kiln. Ash is not removed from the surface. No assumption is made a priori in terms of the limiting phenomena. The medium is composed of cardboard and polyethylene (PE). Based on previous experimental work (Fuel 2004; 83:451,462), the material is assumed to be a macroscopically homogeneous porous medium. Local thermal equilibrium is also assumed. Most of the parameters required for the modeling were determined from specific experiments. Good predictions of the sample mass evolution and of the temperature levels inside the sample body were obtained for a large range of densities and PE content. A devolatilization front of about 20,mm first propagates inside the medium. The volatile matter flux is advected to the surface, which leads to the formation of the flame above the surface. Then a second char oxidation front propagates, starting from the surface. The front thickness is approximately 25,mm under the experimental conditions. Copyright 2008 John Wiley & Sons, Ltd. [source]

    Full waveform inversion of seismic waves reflected in a stratified porous medium

    Louis De Barros
    SUMMARY In reservoir geophysics applications, seismic imaging techniques are expected to provide as much information as possible on fluid-filled reservoir rocks. Since seismograms are, to some degree, sensitive to the mechanical parameters and fluid properties of porous media, inversion methods can be devised to directly estimate these quantities from the waveforms obtained in seismic reflection experiments. An inversion algorithm that uses a generalized least-squares, quasi-Newton approach is described to determine the porosity, permeability, interstitial fluid properties and mechanical parameters of porous media. The proposed algorithm proceeds by iteratively minimizing a misfit function between observed data and synthetic wavefields computed with the Biot theory. Simple models consisting of plane-layered, fluid-saturated and poro-elastic media are considered to demonstrate the concept and evaluate the performance of such a full waveform inversion scheme. Numerical experiments show that, when applied to synthetic data, the inversion procedure can accurately reconstruct the vertical distribution of a single model parameter, if all other parameters are perfectly known. However, the coupling between some of the model parameters does not permit the reconstruction of several model parameters at the same time. To get around this problem, we consider composite parameters defined from the original model properties and from a priori information, such as the fluid saturation rate or the lithology, to reduce the number of unknowns. Another possibility is to apply this inversion algorithm to time-lapse surveys carried out for fluid substitution problems, such as CO2 injection, since in this case only a few parameters may vary as a function of time. We define a two-step differential inversion approach which allows us to reconstruct the fluid saturation rate in reservoir layers, even though the medium properties are poorly known. [source]

    Surface waves in a general anisotropic poroelastic solid half-space

    M. D. Sharma
    SUMMARY A method is introduced for studying surface waves in a general anisotropic poroelastic medium. The method is analogous to the one used for isotropic media and derives a complex secular equation to represent the propagation of surface waves at the stress-free plane surface of a non-dissipative porous medium. The point of importance is that the derived equation is, analytically, separable into real and imaginary parts and hence can be solved by iterative numerical methods. A root of this secular equation represents the existence of surface waves and calculates the apparent phase velocity along a given direction on the surface. Numerical work is carried out for the model of a crustal rock. The propagation of surface waves is studied numerically for the top three anisotropies (i.e. triclinic, monoclinic, orthorhombic). [source]

    The effect of inertial coupling on seismic reflection amplitudes

    Ashish Arora
    ABSTRACT A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves. [source]

    An electromagnetic modelling tool for the detection of hydrocarbons in the subsoil

    Electromagnetic geophysical methods, such as ground-penetrating radar (GPR), have proved to be optimal tools for detecting and mapping near-surface contaminants. GPR has the capability of mapping the location of hydrocarbon pools on the basis of contrasts in the effective permittivity and conductivity of the subsoil. At radar frequencies (50 MHz to 1 GHz), hydrocarbons have a relative permittivity ranging from 2 to 30, compared with a permittivity for water of 80. Moreover, their conductivity ranges from zero to 10 mS/m, against values of 200 mS/m and more for salt water. These differences indicate that water/hydrocarbon interfaces in a porous medium are electromagnetically ,visible'. In order to quantify the hydrocarbon saturation we developed a model for the electromagnetic properties of a subsoil composed of sand and clay/silt, and partially saturated with air, water and hydrocarbon. A self-similar theory is used for the sandy component and a transversely isotropic constitutive equation for the shaly component, which is assumed to possess a laminated structure. The model is first verified with experimental data and then used to obtain the properties of soils partially saturated with methanol and aviation gasoline. Finally, a GPR forward-modelling method computes the radargrams of a typical hydrocarbon spill, illustrating the sensitivity of the technique to the type of pore-fluid. The model and the simulation algorithm provide an interpretation methodology to distinguish different pore-fluids and to quantify their degree of saturation. [source]

    Simulations to Verify Horizontal Flow Measurements from a Borehole Flowmeter

    GROUND WATER, Issue 3 2006
    Scott C James
    This paper reports on experiments and simulations of subsurface flow from a slotted acrylic tube deployed in a sand-tank flow chamber for two different purposes. In the first instance, the slotted tube is used to represent a single fracture intersected by an uncased well. In the second instance, the slotted tube is used to represent a multislot well screen within a porous medium. In both cases, the scanning colloidal borescope flowmeter (SCBFM) measures ground water velocity within the well by imaging colloids traveling through a well to measure their speed and direction. Measurements are compared against model simulations. For the case of a slotted tube representing a single fracture, SCBFM and model results agree with respect to the flow direction and to within a factor of 1.5 for the speed near the well's center. Model and experimental agreement lend confidence that for an uncased well drilled in a fractured-rock medium, a calibrated SCBFM could be used to identify and quantify flowing features. Next, the SCBFM was deployed in a four-column multislotted casing with slots aligned with the flow direction. Another numerical model was developed to estimate the flow field within this well screen to evaluate the potential usefulness of employing the SCBFM in a screened well to estimate flow speed and direction in the surrounding porous medium. Results indicate that if the slots are not aligned with the flow, the SCBFM may only provide order-of-magnitude speed measurements and direction measurements with an uncertainty of approximately 25. [source]

    Determination of Transverse Dispersion Coefficients from Reactive Plume Lengths

    GROUND WATER, Issue 2 2006
    Olaf A. Cirpka
    With most existing methods, transverse dispersion coefficients are difficult to determine. We present a new, simple, and robust approach based on steady-state transport of a reacting agent, introduced over a certain height into the porous medium of interest. The agent reacts with compounds in the ambient water. In our application, we use an alkaline solution injected into acidic ambient water. Threshold values of pH are visualized by adding standard pH indicators. Since aqueous-phase acid-base reactions can be considered practically instantaneous and the only process leading to mixing of the reactants is transverse dispersion, the length of the plume is controlled by the ratio of transverse dispersion to advection. We use existing closed-form expressions for multidimensional steady-state transport of conservative compounds in order to evaluate the concentration distributions of the reacting compounds. Based on these results, we derive an easy-to-use expression for the length of the reactive plume; it is proportional to the injection height squared, times the velocity, and inversely proportional to the transverse dispersion coefficient. Solving this expression for the transverse dispersion coefficient, we can estimate its value from the length of the alkaline plume. We apply the method to two experimental setups of different dimension. The computed transverse dispersion coefficients are rather small. We conclude that at slow but realistic ground water velocities, the contribution of effective molecular diffusion to transverse dispersion cannot be neglected. This results in plume lengths that increase with increasing velocity. [source]

    Interpretation of Spring Recession Curves

    GROUND WATER, Issue 5 2002
    H. Amit
    Recession curves contain information on storage properties and different types of media such as porous, fractured, cracked lithologies and karst. Recession curve analysis provides a function that quantitatively describes the temporal discharge decay and expresses the drained volume between specific time limits (Hall 1968). This analysis also allows estimating the hydrological significance of the discharge function parameters and the hydrological properties of the aquifer. In this study, we analyze data from perennial springs in the Judean Mountains and from others in the Galilee Mountains, northern Israel. All the springs drain perched carbonate aquifers. Eight of the studied springs discharge from a karst dolomite sequence, whereas one flows out from a fractured, slumped block of chalk. We show that all the recession curves can be well fitted by a function that consists of two exponential terms with exponential coefficients ,1 and ,2. These coefficients are approximately constant for each spring, reflecting the hydraulic conductivity of different media through which the ground water flows to the spring. The highest coefficient represents the fast flow, probably through cracks, or quickflow, whereas the lower one reflects the slow flow through the porous medium, or baseflow. The comparison of recession curves from different springs and different years leads to the conclusion that the main factors that affect the recession curve exponential coefficients are the aquifer lithology and the geometry of the water conduits therein. In normal years of rainy winter and dry summer, ,1 is constant in time. However, when the dry period is longer than usual because of a dry winter, ,1 slightly decreases with time. [source]

    Turbulent Flow Through Porous Media

    GROUND WATER, Issue 5 2001
    Douglas W. Barr
    The pressure driving flow through porous media must be equal to the viscous resistance plus the inertial resistance. Formulas are developed for both the viscous resistance and the inertial resistance. The expression for the coefficient of permeability consists of parameters which describe the characteristics of the porous medium and the permeating fluid and which, for unconsolidated isotropic granular media, are all measurable. A procedure is proposed for testing for the occurrence of turbulence and calculating the effective permeability when it occurs. The formulas are applied to a set of data from 588 permeameter runs ranging from laminar to highly turbulent. The equations fit the data from the permeameter closely through the laminar flow conditions and quite closely through the turbulent conditions. In the turbulent range, the plotting of the data separates into three distinct lines for each of the three shapes of particles used in the tests. For the porous medium and fluid of these tests, turbulence begins at a head gradient of about 0.1. [source]

    Moderate Bioclogging Leading to Preferential Flow Paths in Biobarriers

    Katsutoshi Seki
    Permeable reactive barriers (PRBs) are an alternative technique for the biological in situ remediation of ground water contaminants. Nutrient supply via injection well galleries is supposed to support a high microbial activity in these barriers but can ultimately lead to changes in the hydraulic conductivity of the biobarrier due to the accumulation of biomass in the aquifer. This effect, called bioclogging, would limit the remediation efficiency of the biobarrier. To evaluate the effects bioclogging can have on the flow field of a PRB, flow cell experiments were carried out in the laboratory using glass beads as a porous medium. Two types of flow cells were used: a 20- 1- 1-cm cell simulating a single injection well in a one-dimensional flow field and a 20- 10- 1-cm cell simulating an injection well gallery in a two-dimensional flow field. A mineral medium was injected to promote microbial growth. Results of 9 d of continuous operation showed that conditions, which led to a moderate (50%) reduction of the hydraulic conductivity of the one-dimensional cell, led to a preferential flow pattern within the simulated barrier in the two-dimensional flow field (visualized by a tracer dye). The bioclogging leading to this preferential flow pattern did not change the hydraulic conductivity of the biobarrier as a whole but resulted in a reduced residence time of water within barrier. The biomass distribution measured after 9 d was consistent with the observed clogging effects showing step spatial gradients between clogged and unclogged regions. [source]

    Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid-saturated porous medium

    V.J. Bansod
    Abstract This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non-linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20300 [source]

    On the analytical solution of the Bejan-Khair equation arising in free convection in porous media

    V.J. Bansod
    Abstract This paper revisits the fundamental problem of free convection heat and mass transfer over a heated vertical surface embedded in a porous medium using analytical techniques. An integral procedure is applied to the boundary layer similar equation for the combined heat and mass transfer from a vertical surface in a porous medium. The analytical approximations have covered a wide range of governing parameters of the problem. The results for both Nusselt and Sherwood numbers agree well with numerical results published in the literature. 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20297 [source]

    Numerical and experimental investigation of heat and mass transfer in unsaturated porous media with low convective drying intensity

    Tao Lu
    Abstract The heat and mass transfer in an unsaturated wet cylindrical bed packed with quartz particles was investigated theoretically and experimentally for relatively low convective drying rates. The medium was dried by blowing dry air over the top of the porous bed which was insulated by impermeable, adiabatic material on the bottom and sides. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous medium using the energy and mass conservation equations for heat and mass transfer during the drying. The drying model included convection and capillary transport of the moisture, and convection and diffusion of the gas. The wet and dry regions were coupled with a dynamic boundary condition at the evaporation front. The numerical results indicated that the drying process could be divided into three periods: the initial temperature rise period, the constant drying rate period, and the reduced drying rate period. The numerical results agreed well with the experimental data, verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(5): 290,312, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20205 [source]

    Forced convective heat transfer for fluid flowing through a porous medium with internal heat generation

    Hua Du
    Abstract Forced convection in channels filled with packed beads with internal heat source was numerically analyzed by using the extended Darcy model for the flow and energy conservation equations with nonthermal equilibrium (NTE). The temperature difference between the matrix and fluid phases was discussed with three dimensionless parameters (Rep, H/dp, and ks/kf). It is concluded that the thermal equilibrium assumption may be adopted for the situation when the solid conduction dominated over the convection or when the heat transfer coefficient between the two phases is large at large Rep. The Nusselt number at the wall with the variation of Rep for different ks/kf was also investigated. 2001 Scripta Technica, Heat Trans Asian Res, 30(3): 213,221, 2001 [source]

    Solute movement through intact columns of cryoturbated Upper Chalk

    M. Mahmood-ul-Hassan
    Abstract Cryoturbated Upper Chalk is a dichotomous porous medium wherein the intra-fragment porosity provides water storage and the inter-fragment porosity provides potential pathways for relatively rapid flow near saturation. Chloride tracer movement through 43 cm long and 45 cm diameter undisturbed chalk columns was studied at water application rates of 03, 10, and 15 cm h,1. Microscale heterogeneity in effluent was recorded using a grid collection system consisting of 98 funnel-shaped cells each 35 cm in diameter. The total porosity of the columns was 047 002 m3 m,3, approximately 13% of pores were , 15 m diameter, and the saturated hydraulic conductivity was 1266 131 m day,1. Although the column remained unsaturated during the leaching even at all application rates, proportionate flow through macropores increased as the application rate decreased. The number of dry cells (with 0 ml of effluent) increased as application rate decreased. Half of the leachate was collected from 15, 19 and 22 cells at 03, 10, 15 cm h,1 application rates respectively. Similar breakthrough curves (BTCs) were obtained at all three application rates when plotted as a function of cumulative drainage, but they were distinctly different when plotted as a function of time. The BTCs indicate that the columns have similar drainage requirement irrespective of application rates, as the rise to the maxima (C/Co) is almost similar. However, the time required to achieve that leaching requirement varies with application rates, and residence time was less in the case of a higher application rate. A two-region convection,dispersion model was used to describe the BTCs and fitted well (r2 = 097,099). There was a linear relationship between dispersion coefficient and pore water velocity (correlation coefficient r = 095). The results demonstrate the microscale heterogeneity of hydrodynamic properties in the Upper Chalk. Copyright 2007 John Wiley & Sons, Ltd. [source]

    Solute transport in sand and chalk: a probabilistic approach

    E. Carlier
    Abstract A probabilistic approach is used to simulate particle tracking for two types of porous medium. The first is sand grains with a single intergranular porosity. Particle tracking is carried out by advection and dispersion. The second is chalk granulates with intergranular and matrix porosities. Sorption can occur with advection and dispersion during particle tracking. Particle tracking is modelled as the sum of elementary steps with independent random variables in the sand medium. An exponential distribution is obtained for each elementary step and shows that the whole process is Markovian. A Gamma distribution or probability density function is then deduced. The relationships between dispersivity and the elementary step are given using the central limit theorem. Particle tracking in the chalky medium is a non-Markovian process. The probability density function depends on a power of the distance. Experimental simulations by dye tracer tests on a column have been performed for different distances and discharges. The probabilistic approach computations are in good agreement with the experimental data. The probabilistic computation seems an interesting and complementary approach to simulate transfer phenomena in porous media with respect to the traditional numerical methods. Copyright 2006 John Wiley & Sons, Ltd. [source]

    The fundamental solution of poroelastic plate saturated by fluid and its applications

    P. H. Wen
    Abstract In this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis. Copyright 2009 John Wiley & Sons, Ltd. [source]

    Groutability of cement-based grout with consideration of viscosity and filtration phenomenon

    Jong-Sun Kim
    Abstract The groutability depends on the properties of the grout, its injection processes, and on the mechanical properties of the soil formation. During the process of pouring cement-based grouting into a porous medium, a variation with time occurs in the viscosity of grout suspension. In addition, the particle filtration phenomenon will limit the expansion of the grouted zone because cement particles are progressively stagnant within the soil matrix. In this paper, a closed-form solution was derived by implementing the mass balance equations and the generalized phenomenological filtration law, which can be used to evaluate the deposition of cement-based grout in the soil matrix. The closed-form solution relevant to a particular spherical flow was modified by a step-wise numerical calculation, considering the variable viscosity caused by a chemical reaction, and the decrease in porosity resulting from grout particle deposition in the soil pores. A series of pilot-scale chamber injection tests was performed to verify that the developed step-wise numerical calculation is able to evaluate the injectable volume of grout and the deposition of grout particles. The results of the chamber injection tests concurred well with that of the step-wise numerical calculation. Based on the filtration phenomenon, a viable approach for estimating the groutability of cement-based grout in a porous medium was also suggested, which might facilitate a new insight in the design of the grouting process. Copyright 2009 John Wiley & Sons, Ltd. [source]

    Analytical solutions for dynamic pressures of coupling fluid,porous medium,solid due to SV wave incidence

    Jin-Ting Wang
    Abstract This paper presents the results of theoretical investigation on the dynamic coupling of an ideal fluid-porous medium-elastic half-space system subjected to SV waves to study the effect of sediment on the seismic response of dams for reservoirs that are deposited with a significant amount of sediment after a long period of operation. The effects of the porous medium and the incident wave angle on dynamic pressures in the overlying ideal fluid are analyzed, and the reflection and transmission coefficients of the wave at the material interfaces are derived using an analytical solution in terms of displacement potentials. The numerical test of modeling shows that the dynamic pressures significantly depend on the properties of porous medium. The fully saturated porous medium reduces the response peaks slightly, while the partially saturated porous medium causes a considerable increase in the resonance peaks. Copyright 2009 John Wiley & Sons, Ltd. [source]

    Coupled simulation of wave propagation and water flow in soil induced by high-speed trains

    P. Kettil
    Abstract The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water-saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright 2007 John Wiley & Sons, Ltd. [source]

    Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs

    Massimiliano Ferronato
    Abstract The stress variation induced by gas/oil production may activate pre-existing regional faults. This may enhance the expected land subsidence due to the generation of mechanically weak points close to the producing field. A class of elasto-plastic interface elements (IE), specifically designed to address the mechanical behaviour of faults over a regional scale, is integrated into a finite element (FE) geomechanical model and used to investigate the role exerted by active faults in anthropogenic land subsidence. The importance of regional faults depends on a variety of factors including depth of the depleted reservoir, fault number, orientation and size, geomechanical properties of porous medium, pore pressure drawdown induced by fluid production, etc. With the aid of some representative examples, a useful indication is provided as to where and how fault activation may influence both magnitude and extent of the land subsidence bowl above producing gas/oil reservoirs, pointing to a generally limited impact on the ground surface. The simulation of a real faulted gas reservoir in a complex 3-D setting shows that the proposed IE can be simply and efficiently incorporated into a FE geomechanical model, thus improving the quality of the stress and displacement prediction. Copyright 2007 John Wiley & Sons, Ltd. [source]

    Poroelastic model for pile,soil interaction in a half-space porous medium due to seismic waves

    Jian-Fei Lu
    Abstract In this paper, frequency domain dynamic response of a pile embedded in a half-space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half-space and a fictitious pile. The extended porous half-space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1-D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half-space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half-space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile,half-space system. Significant differences between conventional single-phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright 2007 John Wiley & Sons, Ltd. [source]

    Analytical solution of the harmonic waves diffraction by a cylindrical lined cavity in poroelastic saturated medium

    Y. S. Karinski
    Abstract This paper presents a model for the analysis of plane waves diffraction at a cavity in an infinite homogeneous poroelastic saturated medium, lined by a lining composed of four equal segments. An elastic boundary layer is placed between the cavity lining and the infinite porous medium. The boundary layer is simulated by ,elastic boundary conditions' in which the bulk matrix stress is proportional to the relative displacement between the lining and the surrounding medium matrix boundary. In addition, fluid impermeability through the intermediate layer is assumed. For the frequencies, that differ from the pseudoresonanse frequencies, the problem was reduced to the problem of an ideal elastic medium. A closed-form analytical solution of the problem was obtained using Fourier,Bessel series, the convergence of which was proven. It was shown that the number of series terms required to obtain a desired level of accuracy can be determined in advance. The influence of the medium porosity on the medium dynamic stress concentration was studied. Copyright 2006 John Wiley & Sons, Ltd. [source]

    Modelling of cement suspension flow in granular porous media

    Z. Saada
    Abstract A theoretical model of cement suspensions flow in granular porous media considering particle filtration is presented in this paper. Two phenomenological laws have been retained for the filtration rate and the intrinsic permeability evolution. A linear evolution with respect to the volume fraction of cement in the grout has been retained for the filtration rate. The intrinsic permeability of the porous medium is looked for in the form of a hyperbolic function of the porosity change. The model depends on two phenomenological parameters only. The equations of this model are solved analytically in the one-dimensional case. Besides, a numerical resolution based on the finite element method is also presented. It could be implemented easily in situations where no analytical solution is available. Finally, the predictions of the model are compared to the results of a grout injection test on a long column of sand. Copyright 2005 John Wiley & Sons, Ltd. [source]

    About Darcy's law in non-Galilean frame

    C. Geindreau
    Abstract This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall,Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek,1 is ,,(1). These variations are estimated to be less than 5% if Ek,1<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright 2004 John Wiley & Sons, Ltd. [source]

    Response of saturated porous media to cyclic thermal loading

    E. Blond
    Abstract The response of a semi-infinite saturated porous medium subjected to a harmonic thermal loading on its free face is studied herein. The pressure diffusion equation that governs the fluctuation of the interstitial pressure is established. It allows us to obtain prevalent parameters, i.e. the thermal and fluid mass diffusivities and the coefficient of relative bulk variation. Closed-form solutions of the maximum fluid pressure Pmax and its location xcr are derived. It is shown that the location xcr of Pmax is localized and depends on the diffusivity ratio and the frequency of the thermal loading while the magnitude of Pmax depends on the diffusivity ratio and the thermal amplitude. Master curves for xcr and Pmax versus diffusivity ratio are built. It follows that three regimes can be distinguished: namely, thin spalling, thick spalling or in-depth cracking and no cracking. Copyright 2003 John Wiley & Sons, Ltd. [source]

    Solute transport through a deforming porous medium

    Glen P. Peters
    Abstract Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co-ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non-linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers. Copyright 2002 John Wiley & Sons, Ltd. [source]

    Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

    A. Giraud
    Abstract In this article we present closed-form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr,Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non-associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short-term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed-form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright 2002 John Wiley & Sons, Ltd. [source]

    Numerical modelling of fluid flow in microscopic images of granular materials

    E. Masad
    Abstract A program for the simulation of two-dimensional (2-D) fluid flow at the microstructural level of a saturated anisotropic granular medium is presented. The program provides a numerical solution to the complete set of Navier,Stokes equations without a priori assumptions on the viscous or convection components. This is especially suited for the simulation of the flow of fluids with different density and viscosity values and for a wide range of granular material porosity. The analytical solution for fluid flow in a simple microstructure of porous medium is used to verify the computer program. Subsequently, the flow field is computed within microscopic images of granular material that differ in porosity, particle size and particle shape. The computed flow fields are shown to follow certain paths depending on air void size and connectivity. The permeability tensor coefficients are derived from the flow fields, and their values are shown to compare well with laboratory experimental data on glass beads, Ottawa sand and silica sands. The directional distribution of permeability is expressed in a functional form and its anisotropy is quantified. Permeability anisotropy is found to be more pronounced in the silica sand medium that consists of elongated particles. Copyright 2001 John Wiley & Sons, Ltd. [source]

    Real-scale miscible grout injection experiment and performance of advection,dispersion,filtration model

    F. Bouchelaghem
    Abstract A model was developed, to describe miscible grout propagation in a saturated deformable porous medium, based on Bear's statistical model with spatial volume averaging. In a previous paper, the model was first successfully confronted to one-dimensional laboratory experiments. In the present paper, the numerical model is used to simulate practical grouting operation in a cylindrical injection model. The cylindrical injection model lends itself to study main flow and propagation character istics for a dispersed suspension-type grout, under axisymmetric conditions close to real scale conditions. Comparison between numerical solutions and experimental results is essential to confirm the validity and accuracy of the proposed model from a phenomenological standpoint. The numerical model performances show that the underlying mathematical model constitutes a realistic predictive model reproducing most prominent features during injection of a suspension-type grout into a deformable porous medium. The basic mechanism by which injected miscible grout permeates a soil mass is discussed in detail. Such a tool leads to quality control criteria for grouting on a theoretical basis, which complements existing criteria acquired through engineering practice. Copyright 2001 John Wiley & Sons, Ltd. [source]