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).     

Coupled Effects of Ionic Strength,Particle Size,and Flow Velocity on Transport and Deposition of Suspended Particles in Saturated Porous Media

In this study, the coupled effect of ionic strength, particle size, and flow velocity on transport and deposition of suspended particles (SP) in saturated sand was undertaken. Three polydispersive SP populations (silt particles with the median of 3.5, 9.5 and 18.3 \(\upmu \)m) were investigated using a pulse injection technique. High ionic strengths were used and vary from 0 to 600 mM (NaCl). Two high velocities were tested: 0.15 and 0.30 cm/s. Suspended particles recovery and deposition kinetics were strongly dependent on the solution chemistry, the hydrodynamics, and the suspended particles size, with greater deposition occurring for increasing ionic strength, lower flow velocity, and larger ratios of the median diameter of the SP to the median sand grain diameter. A shift between the extended Derjaguin–Landau–Verwey–Overbeek theory prediction (the particles and sand grain surfaces are considered chemically and topographically homogeneous) and the experimental results for certain ionic strength was observed. So, as reported in recent literature, effects of surface heterogeneities should be considered. The residence time of the non-captured particles is dependent on ionic strength and hydrodynamic. A relationship between the deposition kinetics, particle and grain sizes, flow velocity, and ionic strength is proposed.     

A Two-Dimensional Network Model to Simulate Permeability Decrease Under Hydrodynamic Effect of Particle Release and Capture

A model was developed to simulate permeability decrease induced by hydrodynamic effects when injecting a fluid in a reservoir with respect to particle release and capture mechanisms and the parameters of the fluid–rock system. The kinetics of particle release and capture were integrated after computing the initial permeability of the porous medium with a square lattice of a two–dimensional network model. The rate of particle release is related to the difference between a microscopic velocity of the fluid and a critical velocity. The permeability decrease shows a direct link to the reduction of pore throat radii by three mechanisms of particle capture: straining and particle accumulation through direct interception or diffusion. Comparison between the simulations and the experimental results shows that the model reproduces the physics of the permeability decrease phenomenon, although the values are overestimated. The difference between the two sets of results can be explained by the fact that the simulations are realized at constant pressure whereas the experiments are realized at constant flow rate, and that re–entrainment of the trapped particles was not taken into account in the model.     

The effect of pH,ionic strength,and temperature on the rheology and stability of aqueous clay suspensions

The effect of pH level, ionic strength, and temperature on the theology and stability of aqueous suspensions of attapulgite clay was systematically investigated. A Rheometrics Mechanical Spectrometer with cone and plate fixtures was used to measure the steady shear viscosity of the system. The edge charges of the clay particles can be adjusted by changing the pH level of the suspending medium so as to influence the flocculation state and, consequently, the rheological behavior of the suspension. This pH effect may be counteracted by the ionic strength effect at both very high and very low pH levels where the ionic strength is high enough to cause flocculation of the electrostatically stabilized suspension. The temperature effect study indicates that the relative contribution of Brownian motion and shear flow to the viscosity is dependent on the flocculation state of the suspension.     

Experimental Investigation and Modelling of Colloidal Release in Porous Media

Gas production from underground storage reservoirs is sometimes associated with solid particles eroded from the rock matrix. This phenomenon often called sand production can cause damage to the storage equipments, leading the operator to choke the wells and prevent them from producing at full capacity. Colloid release is often associated as a precursor of larger solid production. Indeed, in sandstone storage sites, clay release induced by the presence of condensed water associated with the gas production in the near-wellbore region can be a forecast of intergranular cement erosion. The objective of this work is twofold: firstly to experimentally investigate colloidal particle detachment through ionic strength reduction (absence of salinity of the condensed water) in porous media and secondly to determine its evolution with time and to model it. Laboratory experiments with model systems are developed to reproduce the particle generation and their transport in porous media. The model porous medium is a packed column of two powders: silicon carbide particles of 50 μm and silica particles of 0.5 μm (3% by weight) initially mixed together. Brine flows at different concentrations are imposed through the porous sample and, at very low salt concentration, colloid silica particles are massively released from the medium. Experimental evolutions of the particle concentration with time are compared to solutions of the advection–dispersion equation including first-order source terms for colloid release. The dispersion coefficients of the porous medium have been determined with tracer tests. The experimental results exhibit a different behaviour at short- and long-time intervals and a model has been built to predict the colloid production evolution with the introduction of two different time scales for the eroded rate. The model can be used in a core test to evaluate the amount of detachable fines and the rate of erosion.     

Numerical modeling of deposition-release mechanisms in long-term filtration: validation from experimental data

A numerical phenomenological filtration model based on the combination of existing modeling approaches for simulating the transport of suspended particles in saturated porous medium is presented. The model accounts for the decreased physical straining with the distance from the inlet and the amount of deposited particles in the deposition kinetics. The particle release flux is a function of the local shear stress exerted by the flow on the pore surfaces. The proposed model is validated by interpreting a series of experimental data, realized in a laboratory sand column. The results show that the present model allows simulating the presence of a plateau in the breakthrough curves in the light of the shear stress conditions, and the spatial profile of deposited particles in the porous medium in the light of the straining profile.     

Lateral migration mechanisms in capillary hydrodynamic chromatography

In all chromatographic systems that achieve separation of colloidal particles based on the particles' hydrodynamic behavior, there are partitioning mechanisms that promote lateral migration of particles across solvent streamlines. In this work, solvent inertia and particle electrostatics are incorporated in Brenner & Gaydos' general diffusive transport theory for particles and solvent flowing in a capillary, yielding the mean axial velocity of particles as a function of particle size. A comparison is made with capillary hydrodynamic chromatography results. The lateral migration of small particles is primarily due to diffusion, while large particles are focused by the inertial force at one equilibrium radial position, as observed in “tubular pinch” experiments. The transition from diffusion- to inertia-controlled lateral migration can be tuned to specific particle size ranges through variation of solvent ionic strength, flowrate and capillary radius. Poor prediction of the separation behavior of large particles is attributed to inaccuracy in the calculation of the inertial radial velocity, suggesting the need for further theoretical analysis and experimental study of inertial migration.     

Experimental and mechanistic study of dispersed micrometer-sized particle resuspension in a square straight duct with rough walls

The resuspension of graphite dust is an important phenomenon in the release of radioactivity and the safety of nuclear reactors during severe accidents. In this study, a visualization experimental platform is constructed to study effects of particle size, flow velocity, and wall roughness on the resuspension characteristics of graphite particles. A statistical model of particle resuspension applicable to monolayer dispersed particles is developed based on the moment equilibrium of the particles and the flow field characteristics, as calculated by the large-eddy simulation framework. The results show that particle resuspension can be divided into short- and long-term resuspension stages. Most particle resuspension occurs during the short-term stage. With increases in flow velocity and particle diameter, the aerodynamic or adhesion force acting on the particles increases, and corresponding particle resuspension fraction increases. The influence of rough walls on particle resuspension is related to both the force on the particles and the arm ratio between the wall morphology and the particle diameter. A comparison with the experimental results demonstrates that the particle resuspension model developed in this study accurately predicts the impact of flow velocity, particle size, and wall roughness on particle resuspension.     

A model for tracking inertial particles in a lattice Boltzmann turbulent flow simulation

A computationally inexpensive model for tracking inertial particles through a turbulent flow is presented and applied to the turbulent flow through a square duct having a friction Reynolds number of Re_τ = 300. Prior to introducing particles into the model, the flow is simulated using a lattice Boltzmann computation, which is allowed to evolve until a steady state turbulent flow is achieved. A snapshot of the flow is then stored, and the trajectories of particles are computed through the flow domain under the influence of this static probability field. Although the flow is not computationally evolving during the particle tracking simulation, the local velocity is obtained stochastically from the local probability function, thus allowing the dynamics of the turbulent flow to be resolved from the point of view of the suspended particles. Particle inertia is modeled by using a relaxation parameter based on the particle Stokes number that allows for a particle velocity history to be incorporated during each time step. Wall deposition rates and deposition patterns are obtained and exhibit a high level of agreement with previously obtained DNS computational results and experimental results for a wide range of particle inertia. These results suggest that accurate particle tracking through complex turbulent flows may be feasible given a suitable probability field, such as one obtained from a lattice Boltzmann simulation. This in turn presents a new paradigm for the rapid acquisition of particle transport statistics without the need for concurrent computations of fluid flow evolution.     

Numerical simulation of particle migration in asymmetric bifurcation channel

In this work we provide numerical validation of the particle migration during flow of concentrated suspension in asymmetric T-junction bifurcation channel observed in a recent experiment [1]. The mathematical models developed to explain particle migration phenomenon basically fall into two categories, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, many processes often involve flow in complex 3D geometries. In this work we have carried out numerical simulation of concentrated suspension flow in 3D bifurcation geometry using the diffusive flux model. The simulation method was validated with available experimental and theoretical results for channel flow. After validation of the method we have applied the simulation technique to study the flow of concentrated suspensions through an asymmetric T-junction bifurcation composed of rectangular channels. It is observed that in the span-wise direction inhomogeneous concentration distribution that develops upstream persists throughout the inlet and downstream channels. Due to the migration of particles near the bifurcation section there is almost equal partitioning of flow in the two downstream branches. The detailed comparison of numerical simulation results is made with the experimental data.     

Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon, in order to promote the versatility of gas/oil reservoirs. A numerical simulation of proppants transport at both hydraulic fracture (HF) and natural fracture (NF) intersection is performed to provide a better understanding of key factors which cause, or contribute to proppants transport in HF–NF intersection. Computational fluid dynamics (CFD) in association with discrete element method (DEM) is used to model the complex interactions between proppant particles, host fluid medium and fractured walls. The effect of non-spherical geometry of particles is considered in this model, using the multi-sphere method. All interaction forces between fluid flow and particles are considered in the computational model. Moreover, the interactions of particle–particle and particle–wall are taken into account via Hertz–Mindlin model. The results of the CFD-DEM simulations are compared to the experimental data. It is found that the CFD-DEM simulation is capable of predicting proppant transport and deposition quality at intersections which are in agreement with experimental data. The results indicate that the HF–NF intersection type, fluid velocity and NF aperture affect the quality of blockage occurrence, presenting a new index, called the blockage coefficient which indicates the severity of the blockage.     

Shear and squeeze rheometry of suspensions of magnetic polymerized chains

We present the first experimental results on the magnetorheology of suspensions of non-Brownian magnetic ellipsoidal particles. These particles are made of spherical iron particles linked by polymers and are called polymerized chains. Steady shear, oscillatory shear, and oscillatory squeeze rheological tests have been performed. The rheological properties of the suspension of polymerized chains have been compared with those of the suspension of spherical iron particles. In shear flow, both suspensions develop nearly the same yield stress, while in squeeze flow, the yield stress is several times higher for the suspension of polymerized chains. We show that the squeezing force of a suspension of spherical particles is an increasing function of the magnetic field intensity at low magnetic fields but decreases dramatically at higher fields. Surprisingly, this phenomenon, attributed to cavitation or air entrainment, does not occur in the suspension of polymerized chains.     

Effective Solution through the Streamline Technique and HT-Splitting for the 3D Dynamic Analysis of the Compositional Flows in Oil Reservoirs

In this article we suggest a new phenomenological mathematical model for the groundwater transport of colloid particles through porous media which is able to describe some significant effects experimentally observed but not captured within the framework of the classic approach. Our basic idea is to consider both the pure water and the colloid suspension as two thermodynamic phases. Using the network models of porous media, we simulated numerically the transport process at the pore-scale. By averaging the result derived, we have obtained the relative permeabilities for both phases, the percolation threshold for suspension flow, and the effective suspension viscosity. Due to specific laws of colloid particles repartition between various classes of pores, the relative permeability of suspension happens to be a highly nonlinear function of saturation, very far from the diagonal straight line. This determines a difference between the macroscale phase velocities. The suspension velocity is shown to be higher than that of water in major cases, only if the colloid particles are not too large. The suggested model predicts and describes in a closed form the effect of colloid transport facilitation observed experimentally.     

Effects of Particle Size Non-Uniformity on Transport and Retention in Saturated Porous Media

Short-pulse injection experiments are investigated to study the effects of particle size non-uniformity on the transport and retention in saturated porous media. Monodisperse particles (3, 10, and 16 \(\upmu \hbox {m}\) latex microspheres) and polydisperse particles (containing 3, 10, and 16 latex microspheres) were explored. The obtained results suggest considering not only the particle sizes but also their polydispersivity (particle size non-uniformity) in transport and retention. Although, the density of the suspended particles is close to that of water, results reveal a slow transport of particles compared to the dissolved tracer whatever their size and flow velocity. The recovered particles in the mixture experiments show that the retention of large particles (10 and 16 \(\upmu \hbox {m}\)) enhances the retention of small ones (3 \(\upmu \hbox {m}\)). However, the straining of 10 and 16 \(\upmu \hbox {m}\) particles in “mixture experiments” is smaller than their straining in “monodisperse experiments”. A linear relationship summarizing the simultaneous effect of particle sizes and flow velocity on deposition kinetics coefficient is proposed.     

On the deposition of particles in liquid metals onto vertical ceramic walls

The deposition of non-metallic particles in liquid-metal flows is a serious industrial problem because the build-up of particles on ceramic walls clogs the flow path and interrupts the production, and this leads to large economic losses. This paper is an effort to extend the current state-of-the-art knowledge of particle deposition in air in order to predict particle deposition rates in liquid-metal flows using an improved Eulerian deposition model and considering Brownian and turbulent diffusion, turbophoresis and thermophoresis as transportation mechanisms. The model was used to predict the rate of deposition of particles in an air flow, and the predictions were compared to published measurements to demonstrate its performance. The model was then modified to take into account the differences in properties between air and liquid metals and thereafter applied to liquid-metal flows. Effects on the deposition rate of parameters such as steel flow rate, particle diameter, particle density, wall roughness and temperature gradient near the wall were investigated. It is shown that the steel flow rate has a very important influence on the rate of deposition of large particles, for which turbophoresis is the main deposition mechanism. For small particles, both wall roughness and thermophoresis have a significant influence on the particle deposition rate. Particle deposition rates under various conditions were successfully predicted.     

Verification of a model to predict the influence of particle inertia and gravity on a decaying turbulent particle-laden flow

In an earlier publication some of the authors presented a theoretical model for the calculation of the influence of particle inertia and gravity on the turbulence in a stationary particle-laden flow. In the present publication the model is extended for application to a decaying suspension. Also a comparison is given between predictions made with the model and experimental data (own data and data reported in the literature) on a decaying turbulent flow with particles in a water tunnel or in a wind tunnel. For most of the experiments a prediction with reasonable accuracy and an interpretation is possible by means of the model.     

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.     

Mechanisms of Particle Transport Acceleration in Porous Media

Experimental data show that the groundwater transport of radionuclides in porous media is frequently facilitated when accompanied with colloid particles. This is usually explained by the size exclusion mechanism which implies that the particles move through the largest pores where the flow velocity is higher. We call attention to three other mechanisms which influence the colloid particle motion, while determining both the probable transport facilitation and retardation. First of all, it is shown that the transport facilitation may be significantly reduced and even transformed into a retardation due to the growth of the effective suspension viscosity (a friction-limited facilitation). Secondly, we will show that the transport of particles through the largest pores can be retarded due to a reduced connectivity of the large-pore cluster (a percolation-breakup retardation). Thirdly, we highlight the Fermi mechanism of acceleration known in statistical physics which is based on the elastic collisions between particles. All three effects are analyzed in terms of the velocity enhancement factor, by using statistical models of porous media in the form of a capillary bundle and a 3D capillary network. Optimal and critical regimes of velocity enhancement are quantified. Estimations show that for realistic parameters, the maximal facilitation of colloid transport is close to the experimentally observed data.     

Multi-fluid model of suspension filtration in a porous medium

In the framework of a three-fluid approach, a new model of suspension filtration in a porous medium is constructed with account for the formation of a dense packing of trapped particles with finite permeability and porosity. The following three continua are considered: the carrier fluid, the suspended particles, and the deposited particles. For a one-dimensional transient flow of suspension, a system of equations for the concentrations of the suspended and deposited particles, the suspension velocity, and the pressure is constructed. Two cases of the flow in a porous medium are considered: plane and radial. Numerical solution is found using a finite-difference method. Numerical calculations are shown to be in agreement with an analytical solution for the simplest case of filtration with a constant velocity and constant porosity and permeability. A comparison is performed with the classic filtration models for five sets of experimental data on the contamination of a porous sample. It is shown that near the inlet boundary, where an intense deposition of particles takes place, the new model describes the concentration profile of the deposited particles more accurately than the classical model.