Étude expérimentale du dépôt de particules colloïdales en milieu poreux : Influence de l'hydrodynamique et de la salinité

This study deals with colloid transport in porous media which applications are found in subsurface water, petroleum engineering or civil engineering. An experimental study of colloidal polystyrene Latex particles deposition in a consolidated porous medium is presented. The influence of ionic strength of the colloid suspension and the flow rate on particle deposition is investigated. We see first that beyond a critical salt concentration, the total collector efficiency increases with the ionic strength. Moreover, such collector efficiency decreases as the flow rate increases according to theory. In other respects, using a γ ray attenuation technique allows us to measure local porosity fluctuation due to particles deposition. By this way deposition kinetics may be followed locally and precisely. Nevertheless when considering the thickness of the adsorbed layer over large scales, obtained results using the γ rays attenuation technique are found in good agreement with those obtained by means of an usual technique especially at latest stages of adsorption process. To cite this article: A. Djehiche et al., C. R. Mecanique 337 (2009).     

Structure of filtration pseudoturbulence

The problem of large-scale (pseudoturbulent) motion of a fluid in a nonuniform porous medium was formulated in [1]. Since in practice the local porosity (x) is unknown, it may be considered a continuous random point function. The difference of the local values of the porosity (x) from the mean value for the medium as a whole leads to the occurrence of random pseudoturbulent motions of the filtering fluid, which are superposed on the mean filtration flow. The characteristics of the large-scale filtration motion in a medium with this sort of random porosity were considered in detail in [1], where the formal solution is presented for the resulting equations for two-point correlations, based on the use of considerations of spatial invariance. Also presented is a qualitative discussion of the effect of pseudoturbulence of the filtering medium on the transport processes in the medium.We note that the considered problem of pseudoturbulence of a filtering fluid in a nonuniform porous medium does not have anything in common with the statistical problem of the motion of small fluid elements in a broken porous space. The latter problem is interesting in connection with the analysis of the convective diffusion processes in a porous body (both uniform and nonuniform) and, beginning with [3], has been considered in several studies, including [2].In the present study we have used a method for solving the problem which is significantly different in comparison with that of [1], based on the representation of the variation of the local porosity from point to point as a random process with independent increments. This method has the advantage that it permits expressing the required correlation functions in the form of quadratures with arbitrary values of the characteristic parameters. In the following, for simplicity we consider the axisymmetric problem under the assumption that the two-point correlation of the deviations of the local values of the porosity from the mean are representable in the form of an isotropie Gaussian function of the distance between the points. The explicit expressions for the correlations are also written in some approximation and the physical consequences resulting from these assumptions are discussed.     

Jump Condition for Diffusive and Convective Mass Transfer Between a Porous Medium and a Fluid Involving Adsorption and Chemical Reaction

In this paper, mass transfer at the fluid–porous medium boundaries is studied. The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., ), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.     

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.     

Simulation of Radon Transport through Building Materials: Influence of the Water Content on Radon Exhalation Rate

Radon transport in porous materials is strongly influenced by the presence of water. It is also necessary to be able to numerically control the effects of this parameter. The radon concentration and radon exhalation rate have been determined by simulation in various building materials containing an increasing water content. It has been proved that the presence of water does not involve the same variations in the concentration on the surface of the medium, according to its porosity. For porous media with low porosity like concrete or granite, ( < 0.2), the radon concentration and radon exhalation rate sharply increase with water until the volumetric water content becomes higher than 30%. At this point, radon emanation plays an important role, in relation to the molecular diffusion process. For materials with medium porosities (e.g., limestone, brick, cement: 0.3 < < 0.45), the concentration was observed to increase up to a volumetric water content of about 10% and then decreased from there. In this case, the molecular diffusion has a greater effect due to a greater quantity of pores in the material. For a small water content, this parameter tends to make the radon concentration decrease at the surface of the medium. These simulations have been compared with experimental analysis and are in strong accordance with the experimental results.     

Friction and forced convective heat transfer in a sintered porous channel with obstacle blocks

This work experimentally studies the flow characteristics and forced convective heat transfer in a sintered porous channel that filled with sintered copper beads of three average diameters ( 0.830, and 1.163 mm). The pressure drop and the local temperature measurements can be applied to figure out the distributions of the friction coefficient and the heat transfer coefficient. Three sintered porous channels differ in the arrangement of obstacle blocks. Model A has no obstacle. Models B and C have five obstacle blocks facing down and up, respectively, in a sintered porous channel. The range of experimental parameters, porosity, heat flux, and effect of forced convection are 0.370 ≤ ɛ ≤ 0.385, q=0.228, 0.872, 1.862 W/cm², and 200 ≤ Re _d ≤ 800. The permeability and inertia coefficient of each of the three sintered porous channels are analyzed. The results for Model A agree with those obtained by previous investigations in C _f distribution. The heat transfer of Model C exceeds that of Model A by approximately 20%. Finally, a series of empirical correlation equations were obtained for practical applications and engineering problems.     

Understanding and Modelling Turbulence Over and Inside Porous Media

To understand turbulence over porous media, a series of PIV measurements were carried out in porous-walled channel flows. The porous walls were made of three types of foamed ceramics which had the same porosity but different permeability. For turbulence inside porous media, LES studies of fully developed flows in three different model porous media were performed. Referring to these databases, a multi-scale k ? ε four equation eddy viscosity model for turbulence around and/or inside porous media was developed. Through the comparison to the experimental results, the proposed model was validated with satisfactory accuracy.     

Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects

An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter $d_{50}$ of these populations was 3.5, 9.5, and $18.3~\upmu \hbox {m}$ . To study the effect of polydispersivity, a fourth population noted “Mixture” ( $d_{50} = 17.4\; \upmu \hbox {m}$ ) obtained by mixing in equal proportion (volume) the populations 3.5 and $18.3\;\upmu \hbox {m}$ was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.     

Composite heat transfer in a variable porosity medium bounded by an infinite flat plate

Heat transfer by simultaneous radiation and convection in a variable porosity medium bounded by an infinite flat plate is determined by solving momentum and energy equations. The problem is investigated for two different cases, viz., presence of porous medium and absence of porous medium. In the presence of porous medium both variable and constant porosity situations are studied. Similarity solutions are obtained for an isothermal and impermeable wall. The Kozeny-Blake expression connecting porosity and permeability is incorporated in the analysis for unified treatment. A parameter survey is made to study the effect of optical thickness, porous parameter, albedo scattering and ratio of conduction to radiation using Runge-Kutta-Gill method. The heating and cooling cases are considered for variable porosity situation. The results show that both convective and radiative components decrease with increase in porous parameter, and the inhomogeneity of the medium enhances heat transfer rate. The increase in optical thickness leads to decrease in both convective and radiative fluxes. For a particular value of wall emissivity ( _w =0.5932116) the radiative flux is reduced to zero.

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Kombinierter Wärmeübergang in einem durch eine unendlich ausgedehnte ebene Platte begrenzten Medium variabler Porosität

Zusammenfassung Der Wärmeübergang bei gleichzeitigem Einfluß von Strahlung und Konvektion in einem Medium variabler Porosität, das durch eine unendlich ausgedehnte ebene Platte begrenzt ist, wird durch Lösung der Impuls- und Energiegleichung bestimmt (den Sonderfall, daß nur Fluid, aber kein poröses Medium vorliegt, eingeschlossen). Im allgemeinen Fall — mit porösem Medium — wird sowohl variable, wie auch konstante Porosität unterstellt. Für die isotherme und stoffundurchlässige Wand existieren Ähnlichkeitslösungen. Um eine einheitliche mathematische Behandlung zu ermöglichen, wird die (Porosität und Permeabilität verknüpfende) Beziehung nach Kozeny-Blake eingeführt. Eine Parameterstudie, durchgeführt unter Verwendung der Runge-Kutta-Gill-Methode, zeigt den Einfluß der optischen Dicke, des Porositätsparameters, der Albedo-Streuung und des Verhältnises von Leitung zu Strahlung. Die Fälle Heizung und Kühlung wurden bei variabler Porosität untersucht. Aus den Ergebnissen geht hervor, daß die Konvektions- und Strahlungsanteile mit zunehmenden Porositätsparameter abnehmen und daß der Wärmeübergang durch Inhomogenität des Mediums verbessert wird. Zunehmende optische Dicke verusacht eine Abnahme sowohl des Konvektions- wie des Strahlungsflusses. Beim Wert _w =0.5932116 des Wandemissionsverhältnisses fällt der Strahlungsfluß auf Null ab.

     

On the Theory of Local Acoustic Probing of Borehole Zones in Rocks

A theory of local probing of borehole zones in porous and permeable rocks by means of acoustic waves is developed. Acoustic signals are assumed to propagate in an annular gap between the probe body and porous permeable wall of the borehole. Quantitative characteristics and special features of wave dynamics depending on the character of inhomogeneity of the porous medium are considered, in particular, in the case with radial fractures or a poorly permeable crust around the channel. The results obtained show that permeability and porosity of rocks in some cases exert a significant effect on evolution of acoustic signals in the borehole.     

Nonlinear cellular convection and heat transport in a porous medium

Nonlinear steady cellular convection in a fluid-saturated porous medium is investigated using the technique of spectral analysis. The effect of permeability is shown to contract the cell and to damp the convection process. The influence of Prandtl number, though small, is seen only in the fourth order term. The cross-interactions of the higher modes caused by nonlinear effects are considered through the modal Rayleigh number R . The possibility of the existence of a steady solution with two self-excited modes in certain regions is predicted. A detailed discussion of the heat transport is made. The theoretical value of the Nusselt number is found to be in good agreement with the experimental results. The similarities and qualitative differences between the present analysis and that of the power integral technique are brought out.     

Sediment–Water Interface Flow with the Multiparticle Collision Dynamics

This paper presents an experimental study of particle transport in porous medium using a self-developed sand layer transportation–deposition testing system, aiming at delineating the detachment characteristics of deposited particles in porous medium. Two experimental modes, increase flow velocity and change flow direction, were adopted in this study. The tests were conducted using quartz powder as the particles and quartz sand as the porous media to study the response of detachment characteristics to changes in particle diameter (\(d_{s}\), with median diameter 18 and 41 \(\upmu \)m) and grain diameter (\(d_{p}\), with median diameter 0.36 and 1.25 mm). Breakthrough curves after the second peak were well described by a double exponential model with parameters of weight coefficient and detachment coefficient. This study shows that both modes can change the detach rate of deposited particles observably, and detach rate is affected by the value of flow velocity greatly.     

An experimental method for the investigation of droplet oscillations in a gaseous medium

An experimental method for the investigation of droplet oscillations in a gaseous medium is presented. The droplets are produced using vibrating orifice droplet generators. Experiments are carried out with droplets in the diameter range from 91 m to 288 m using propanol-2, water, and n-hexadecane; the gaseous host medium is air. Oscillatory motions of the fundamental mode n = 2 and of the first higher order mode n = 3 occur during the disintegration of the liquid jet produced by the droplet generator. The periodical production of the droplets allows the observation and evaluation of each phase of the motion under quasi-steady conditions. Surface energies are determined from the droplet shapes on photos. The periods of the oscillations are found to be very close to the prediction of the linear theory.     

Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

The measurement of velocity gradients in fluid flow by laser light scattering

The motion of the speckle pattern in the far field limit is uniquely determined by the velocity gradient of the light scattering medium. This is the basic physical effect of a non-invasive method that allows the measurement of velocity gradients with high spatial and temporal resolution down to 75 m and 1 ms, respectively. We present three different measurement schemes for the analysis of the scattered light. The experimental results refer to mean gradients obtained from measurements on turbulent channel flows.     

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (\(d_{50 }>0.39\) mm) to gravel (\(d_{50}=6.3\) mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size \((d_{50})\) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased \(C_{u}\) values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size \((d_{50})\) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal \(d_{50}\), resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of \(d_{m}-\sigma \) as characteristic pore length predicted the coefficients a and b accurately.     

A variable angle method of calibration for X-probes applied to wall-bounded turbulent shear flow

A variable angle calibration technique for hot wire and hot film X-probes incorporating a new method of interpolation is described here along with measurements in a fully developed turbulent channel flow. Results based on the new method of calibration include the mean velocity profile, Reynolds stress, and probability density distributions for fluctuating velocity components u and and for the flow angle. Also skewness and flatness factors for u and are given. Measurement data were also evaluated using the conventional method. A comparison of both techniques shows that the new method does not yield appreciable differences in statistical flow analyses but is more accurate in measuring rare flow events associated with large flow angles. An extended version of the new method of calibration allowing three dimensional measurements in turbulent flow will be discussed.     

Steady laminar flow past a heated horizontal plate embedded in a saturated porous medium

In this paper we study the boundary layer equations for steady laminar flow past a heated horizontal plate embedded in a saturated porous medium by adopting the formulation of Chandrasekhara [3], Kolar and Sastri [7]. The velocity distribution and temperature distribution are determined by using the implicit Crank-Nicolson-Predictor-Corrector method of finite difference scheme [7] and [1]. With the help of a compute the distributions are estimated at both (i+1/2)th and (i+1)th levels and they are presented in tabular form. The curves for these distributions are plotted. We calculate the shear stress and skin friction at the wall and observe that the skin-friction directly depends upon the dimensions of the plate and inversely depends upon the Reynolds numberRe. The heat flux and the Nusselt number are evaluated. Further we observe that the Nusselt number depends upon the length of the porous plate.

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Stetige laminare Strömung über eine in einem gesättigten porösen Medium eingebettete horizontale Platte

Zusammenfassung Diese Untersuchung befaßt sich mit den Grenzschichtgleichungen für eine stetige laminare Strömung über eine beheizte Platte, die in ein gesättigtes poröses Medium eingebettet ist, mittels des Formalismus von Chandrasekhara [3], Kolar und Sastri [7]. Die Geschwindigkeits- und Temperaturverteilung wurden unter Benutzung der impliziten Crank-Nicolson-Korrekturmethode des Finiten-Elemente-Schemas bestimmt. Die (i+1/2). und die (i+1). Ebene der Verteilungen wurden mit Computer-Hilfe berechnet und in Tabellenform dargestellt. Die Graphen der Temperatur- und Geschwindigkeitsverteilung wurden ausgeplottet. Die Schubspannungen und die Oberflächenreibung an der Wand wurden berechnet und es konnte festgestellt werden, daß die Oberflächenreibung direkt von der Größe der Platte abhängt und umgekehrt proportional der Reynolds-ZahlRe ist. Der Wärmestrom und die Nusselt-Zahl wurden bestimmt. Weiterhin konnte festgestellt werden, daß die Nusselt-Zahl von der Länge der porösen Platte abhängt.

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Nomenclature C _p specific heat of the convective fluid - D skin friction - k permeability of the porous medium - k _f thermal conductivity of the fluid - k _m the coefficient of thermal conductivity of the porous medium - k _s the conductivity of the solid matrix - N(x) Nusselt number - q(x) specific heat flux - Re local Reynolds number - T temperature - T ₀ temperature of the free stream - T _w temperature of the plate - u velocity in thex-direction - u ₀ velocity of the free stream - V velocity iny-direction - x coordinate axis along the plate - y coordinate axis normal to the plate Greek symbols thermal diffusivity - thickness of the velocity boundary layers in thex direction - thickness of the velocity boundary layer in they-direction - the porosity of the medium - dimensionless variable - kinematic viscosity of the fluid - density of the fluid - shear stress     

An extended theory to predict the onset of viscous instabilities for miscible displacements in porous media

Many enhanced oil recovery schemes involve the displacement of oil by a miscible fluid. Whether a displacement is stable or unstable has a profound effect on how efficiently a solvent displaces oil within a reservoir. That is, if viscous fingers are present, the displacement efficiency and, hence, the economic return of the recovery scheme is seriously impaired bacause of macroscopic bypassing of the oil. As a consequence, it is of interest to be able to predict the boundary which separates stable displacements from those which are unstable.This paper presents a dimensionless scaling group for predicting the onset of hydrodynamic instability of a miscible displacement in porous media. An existing linear perturbation analysis was extended in order to obtain the scaling group. The new scaling group differs from those obtained in previous studies because it takes into account a variable unperturbed concentration profile, both transverse dimensions of the porous medium, and both the longitudinal and the transverse dispersion coefficient.It has been shown that stability criteria derived in the literature are special cases of the general condition given here. Therefore, the stability criterion obtained in this study should be used for a displacement conducted under arbitrary conditions. The stability criterion is verified by comparing it with miscible displacement experiments carried out in a Hele-Shaw cell. Moreover, a comparison of the theory with some porous medium experiments from the literature also supports the validity of the theory.Nomenclature c solvent concentration - C _g fractional glycerine volume - D molecular diffusion coefficient, cm²/s - D _L longitudinal dispersion coefficient, cm²/s - D _T transverse dispersion coefficient, cm²/s - g gravitational acceleration, cm/s² - h distance between the plates, cm - I _sr dimensionless scaling group - k permeability, cm² - L _x width of the porous medium, cm - L _y height of the porous medium, cm - t time, s - u velocity in thex direction, cm/s - v velocity in they direction, cm/s - V displacement velocity, cm/s - w velocity in thez direction, cm/s - z length of the graded viscosity bank, cm - eigenvalue in thex direction - eigenvalue in they direction - wave number - viscosity, poise - density, g/cc - time constant, s^-1 - porosity