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http://hdl.handle.net/10985/12154
Origin of the Inertial Deviation from Darcy's Law: an 2 Investigation from a Microscopic Flow Analysis on 2D Model
AGNAOU, Mehrez; LASSEUX, Didier; AHMADI, Azita
Inertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy’s law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy’s law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy’s law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical ustification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy’s law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/121542017-01-01T00:00:00ZAGNAOU, MehrezLASSEUX, DidierAHMADI, AzitaInertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy’s law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy’s law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy’s law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical ustification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy’s law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.Numerical Simulation of Yield Stress Fluid Flow in Capillary Bundles: Influence of the Form and the Axial Variation in the Cross Section
http://hdl.handle.net/10985/12237
Numerical Simulation of Yield Stress Fluid Flow in Capillary Bundles: Influence of the Form and the Axial Variation in the Cross Section
MALVAULT, Guillaume; AHMADI, Azita; OMARI, Aziz
In this paper, we investigate possible improvements that can be made to the bundle of capillaries model in order to better represent the flow of yield stress fluids through porous media. This was examined by performing extensive and progressive numerical simulations and by introducing the non-circularity of channels’ cross section and/or its variability along the channels’ axis. It is shown that if only the non-circularity of channels’ cross section is taken into account, a moderate influence is observed on both critical pressure gradient for the flow onset and the flow rate/pressure gradient Q(∇P) relationship. However, the axial variation in capillaries’ cross section has proved to be more impacting the computed flow rate/pressure gradient data. We show hence that when available pore throat and pore body size distributions are used to construct the bundle of axially varying capillaries, the obtained Q(∇P) data do fit well experimental results corresponding to the flow of a Bingham-like fluid through a bed of randomly packed mono-sized spheres.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/122372017-01-01T00:00:00ZMALVAULT, GuillaumeAHMADI, AzitaOMARI, AzizIn this paper, we investigate possible improvements that can be made to the bundle of capillaries model in order to better represent the flow of yield stress fluids through porous media. This was examined by performing extensive and progressive numerical simulations and by introducing the non-circularity of channels’ cross section and/or its variability along the channels’ axis. It is shown that if only the non-circularity of channels’ cross section is taken into account, a moderate influence is observed on both critical pressure gradient for the flow onset and the flow rate/pressure gradient Q(∇P) relationship. However, the axial variation in capillaries’ cross section has proved to be more impacting the computed flow rate/pressure gradient data. We show hence that when available pore throat and pore body size distributions are used to construct the bundle of axially varying capillaries, the obtained Q(∇P) data do fit well experimental results corresponding to the flow of a Bingham-like fluid through a bed of randomly packed mono-sized spheres.What can be learnt about dispersivity from transport experiments in unsaturated double-porosity soils?
http://hdl.handle.net/10985/12137
What can be learnt about dispersivity from transport experiments in unsaturated double-porosity soils?
TRAN NGOC, T.D.; AHMADI, Azita; BERTIN, Henri
Dispersivity is assumed to be an intrinsic property which characterizes the heterogeneity scale of porous media. When the medium is unsaturated by two fluid phases (water and air), dispersivity depends strongly on the saturation. “Double-porosity” medium concept can be attributed to a class of heterogeneous soils and rocks in which a strong contrast in local pore size characteristics is observed. In this work, we revisited the intrinsicity of the dispersivity of a double-porosity soil with different saturations, by performing a series of one-dimensional experiments of chloride tracer dispersion under different boundary conditions. The physical double-porosity model was composed of solidified clayey balls, distributed periodically in a more permeable sandy matrix. The dependence of the dispersivity on the saturation in the double-porosity soil was established and compared with the trends obtained for the single-porosity soils in previous studies. RÉSUMÉ Il est généralement admis que la dispersivité est une propriété intrinsèque qui caractérise l'échelle d'hétérogénéité des milieux poreux. Lorsque le milieu est saturé par deux phases fluides (eau et air), elle dépend fortement de la saturation. Le concept du milieu à « double-porosité » peut être attribué à une classe de sols et de roches hétérogènes dans lesquels on observe un fort contraste de tailles caractéristiques locales de pores. Dans ce travail, nous avons revisité la nature intrinsèque de dispersivité d'un sol à double porosité avec des saturations différentes, en effectuant une série d'expériences unidimensionnelles de la dispersion d’un traceur, pour différentes conditions aux limites. Le modèle physique à double porosité a été composé de sphères argileuses solidifiées, réparties périodiquement dans une matrice de sable plus perméable. La dépendance de la dispersivité de la saturation dans le sol à double porosité a été établie et comparée avec les tendances obtenues pour les sols à simple-porosité dans des études antérieures.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/121372017-01-01T00:00:00ZTRAN NGOC, T.D.AHMADI, AzitaBERTIN, HenriDispersivity is assumed to be an intrinsic property which characterizes the heterogeneity scale of porous media. When the medium is unsaturated by two fluid phases (water and air), dispersivity depends strongly on the saturation. “Double-porosity” medium concept can be attributed to a class of heterogeneous soils and rocks in which a strong contrast in local pore size characteristics is observed. In this work, we revisited the intrinsicity of the dispersivity of a double-porosity soil with different saturations, by performing a series of one-dimensional experiments of chloride tracer dispersion under different boundary conditions. The physical double-porosity model was composed of solidified clayey balls, distributed periodically in a more permeable sandy matrix. The dependence of the dispersivity on the saturation in the double-porosity soil was established and compared with the trends obtained for the single-porosity soils in previous studies. RÉSUMÉ Il est généralement admis que la dispersivité est une propriété intrinsèque qui caractérise l'échelle d'hétérogénéité des milieux poreux. Lorsque le milieu est saturé par deux phases fluides (eau et air), elle dépend fortement de la saturation. Le concept du milieu à « double-porosité » peut être attribué à une classe de sols et de roches hétérogènes dans lesquels on observe un fort contraste de tailles caractéristiques locales de pores. Dans ce travail, nous avons revisité la nature intrinsèque de dispersivité d'un sol à double porosité avec des saturations différentes, en effectuant une série d'expériences unidimensionnelles de la dispersion d’un traceur, pour différentes conditions aux limites. Le modèle physique à double porosité a été composé de sphères argileuses solidifiées, réparties périodiquement dans une matrice de sable plus perméable. La dépendance de la dispersivité de la saturation dans le sol à double porosité a été établie et comparée avec les tendances obtenues pour les sols à simple-porosité dans des études antérieures.Colloidal Particle Deposition in Porous Media Under Flow: A Numerical Approach
http://hdl.handle.net/10985/12155
Colloidal Particle Deposition in Porous Media Under Flow: A Numerical Approach
LI, Yajie; SARISHVILI, Otar; OMARI, Aziz; AHMADI, Azita; PU, Hongting
The objective of this study is to simulate the transport and deposition of colloidal particles at the pore scale by means of computational fluid dynamics simulations (CFD). This consists in the three-dimensional numerical modeling of the process of transport and deposition of colloidal particles in a porous medium idealized as a bundle of capillaries of circular cross section. The velocity field obtained by solving the Stokes and continuity equations is superimposed to particles diffusion and particles are let to adsorb when they closely approach the solid wall. Once a particle is adsorbed the flow velocity field is updated before a new particle is injected. Our results show that both adsorption probability and surface coverage are decreasing functions of the particle’s Péclet number. At low Péclet number values when diffusion is dominant the surface coverage is shown to approach the Random Sequential Adsorption value while it drops noticeably for high Péclet number values. Obtained data were also used to calculate the loss of porosity and permeability.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/121552017-01-01T00:00:00ZLI, YajieSARISHVILI, OtarOMARI, AzizAHMADI, AzitaPU, HongtingThe objective of this study is to simulate the transport and deposition of colloidal particles at the pore scale by means of computational fluid dynamics simulations (CFD). This consists in the three-dimensional numerical modeling of the process of transport and deposition of colloidal particles in a porous medium idealized as a bundle of capillaries of circular cross section. The velocity field obtained by solving the Stokes and continuity equations is superimposed to particles diffusion and particles are let to adsorb when they closely approach the solid wall. Once a particle is adsorbed the flow velocity field is updated before a new particle is injected. Our results show that both adsorption probability and surface coverage are decreasing functions of the particle’s Péclet number. At low Péclet number values when diffusion is dominant the surface coverage is shown to approach the Random Sequential Adsorption value while it drops noticeably for high Péclet number values. Obtained data were also used to calculate the loss of porosity and permeability.Flow of yied stress fluids through porous media : simulations, experiments and applications
http://hdl.handle.net/10985/12156
Flow of yied stress fluids through porous media : simulations, experiments and applications
AHMADI, Azita; RODRIGUEZ DE CASTRO, Antonio; MALVAULT, Guillaume; OMARI, Aziz
A Yield Stress fluids injection porosimetry Method (YSM) has recently been developed as a simple potential alternative to the extensively used Mercury Intrusion Porosimetry (MIP). Its main advantage is the use of a nontoxic fluid instead of mercury used in MIP. Using this method, the Pore Size Distribution (PSD) of a porous medium is obtained by measuring the flow rate / pressure gradient relationship obtained by injecting a yield stress fluid in the porous medium. The principle of the method and some experimental results obtained using this technique will be presented and will be compared to those obtained by Mercury Intrusion Porosimetry (MIP). In the Yield Stress fluid injection porosimetry method, the main assumption is that the porous medium is described as a bundle of straight capillaries of circular cross-section following a given pore size distribution. This simple model is revisited by introducing both non-circular and axially varying cross-sections. Two key points are tackled using numerical simulations: the flow onset at minimal pressure drop and the variation of the flow rate vs the pressure gradient. These results are finally used to show that the flow rate / pressure gradient relationship of a yield stress fluid through a porous medium can be more closely predicted using a bundle of capillaries of irregular cross-sections rather than using the classical bundle of straight circular capillaries.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/121562016-01-01T00:00:00ZAHMADI, AzitaRODRIGUEZ DE CASTRO, AntonioMALVAULT, GuillaumeOMARI, AzizA Yield Stress fluids injection porosimetry Method (YSM) has recently been developed as a simple potential alternative to the extensively used Mercury Intrusion Porosimetry (MIP). Its main advantage is the use of a nontoxic fluid instead of mercury used in MIP. Using this method, the Pore Size Distribution (PSD) of a porous medium is obtained by measuring the flow rate / pressure gradient relationship obtained by injecting a yield stress fluid in the porous medium. The principle of the method and some experimental results obtained using this technique will be presented and will be compared to those obtained by Mercury Intrusion Porosimetry (MIP). In the Yield Stress fluid injection porosimetry method, the main assumption is that the porous medium is described as a bundle of straight capillaries of circular cross-section following a given pore size distribution. This simple model is revisited by introducing both non-circular and axially varying cross-sections. Two key points are tackled using numerical simulations: the flow onset at minimal pressure drop and the variation of the flow rate vs the pressure gradient. These results are finally used to show that the flow rate / pressure gradient relationship of a yield stress fluid through a porous medium can be more closely predicted using a bundle of capillaries of irregular cross-sections rather than using the classical bundle of straight circular capillaries.Colloidal Particle Deposition in Porous Media Under Flow: A Numerical Approach
http://hdl.handle.net/10985/12235
Colloidal Particle Deposition in Porous Media Under Flow: A Numerical Approach
LI, Yajie; SARISHVILI, Otar; OMARI, Aziz; AHMADI, Azita; PU, Hongting
The objective of this study is to simulate the transport and deposition of colloidal particles at the pore scale by means of computational fluid dynamics simulations (CFD). This consists in the three-dimensional numerical modeling of the process of transport and deposition of colloidal particles in a porous medium idealized as a bundle of capillaries of circular cross section. The velocity field obtained by solving the Stokes and continuity equations is superimposed to particles diffusion and particles are let to adsorb when they closely approach the solid wall. Once a particle is adsorbed the flow velocity field is updated before a new particle is injected. Our results show that both adsorption probability and surface coverage are decreasing functions of the particle’s Péclet number. At low Péclet number values when diffusion is dominant the surface coverage is shown to approach the Random Sequential Adsorption value while it drops noticeably for high Péclet number values. Obtained data were also used to calculate the loss of porosity and permeability.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/122352017-01-01T00:00:00ZLI, YajieSARISHVILI, OtarOMARI, AzizAHMADI, AzitaPU, HongtingThe objective of this study is to simulate the transport and deposition of colloidal particles at the pore scale by means of computational fluid dynamics simulations (CFD). This consists in the three-dimensional numerical modeling of the process of transport and deposition of colloidal particles in a porous medium idealized as a bundle of capillaries of circular cross section. The velocity field obtained by solving the Stokes and continuity equations is superimposed to particles diffusion and particles are let to adsorb when they closely approach the solid wall. Once a particle is adsorbed the flow velocity field is updated before a new particle is injected. Our results show that both adsorption probability and surface coverage are decreasing functions of the particle’s Péclet number. At low Péclet number values when diffusion is dominant the surface coverage is shown to approach the Random Sequential Adsorption value while it drops noticeably for high Péclet number values. Obtained data were also used to calculate the loss of porosity and permeability.On the Inertial Single Phase Flow in 2D Model Porous Media: Role of Microscopic Structural Disorder
http://hdl.handle.net/10985/15755
On the Inertial Single Phase Flow in 2D Model Porous Media: Role of Microscopic Structural Disorder
WANG, Yibiao; AHMADI, Azita; LASSEUX, Didier
In this work, single-phase incompressible laminar flow in 2D model porous media is studied and the influence of microscopic structural disorder on the flow is thoroughly investigated. Emphasis is laid upon the onset of the deviation from Darcy’s law and the identification of different inertia regimes observed before the flow becomes unsteady. For this purpose, six globally disordered pore structures were generated and the values of the critical Reynolds number at which the flow becomes unsteady corresponding to the first Hopf bifurcation were determined. Numerical simulations of steady laminar single-phase flow were then carried out to investigate the effects of the microstructures on the inertial correction to Darcy’s law. Different flow regimes, namely weak inertia, strong inertia and the regime beyond strong inertia, are identified. Comparisons are made with results presented in the literature which were restricted to ordered and locally disordered structures. The critical Reynolds number decreases and inertia intensity increases as more disorder is introduced into the pore structure. Results on flow inertia widely extend some previous studies on the subject and show that it is mainly influenced by the shape of the obstacles (either circular or square), slightly affected by the inclination of the square cylinders and hardly disturbed by the size distribution of the obstacles.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/157552019-01-01T00:00:00ZWANG, YibiaoAHMADI, AzitaLASSEUX, DidierIn this work, single-phase incompressible laminar flow in 2D model porous media is studied and the influence of microscopic structural disorder on the flow is thoroughly investigated. Emphasis is laid upon the onset of the deviation from Darcy’s law and the identification of different inertia regimes observed before the flow becomes unsteady. For this purpose, six globally disordered pore structures were generated and the values of the critical Reynolds number at which the flow becomes unsteady corresponding to the first Hopf bifurcation were determined. Numerical simulations of steady laminar single-phase flow were then carried out to investigate the effects of the microstructures on the inertial correction to Darcy’s law. Different flow regimes, namely weak inertia, strong inertia and the regime beyond strong inertia, are identified. Comparisons are made with results presented in the literature which were restricted to ordered and locally disordered structures. The critical Reynolds number decreases and inertia intensity increases as more disorder is introduced into the pore structure. Results on flow inertia widely extend some previous studies on the subject and show that it is mainly influenced by the shape of the obstacles (either circular or square), slightly affected by the inclination of the square cylinders and hardly disturbed by the size distribution of the obstacles.Three-dimensional microscale simulation of colloidal particle transport and deposition in model porous media with converging/diverging geometries
http://hdl.handle.net/10985/15655
Three-dimensional microscale simulation of colloidal particle transport and deposition in model porous media with converging/diverging geometries
LI, Yajie; AHMADI, Azita; OMARI, Aziz; PU, Hongting
The microscale simulation of colloidal particle transport and deposition in porous media was achieved with a novel colloidal particle tracking model, called 3D-PTPO (Three-Dimensional Particle Tracking model by Python® and OpenFOAM®), using a Lagrangian method. Simulations were performed by considering the elementary pore structure as a capillary tube with converging/diverging geometries (tapered pipe and venturi tube). The particles are considered as a mass point during transport in the flow and their volume is reconstructed when they are deposited. The main feature of this novel model is to renew the flow field by reconstructing the pore structure by taking the volume of the deposited particles into account. The influence of the particle Péclet number (Pe) and the pore shape on the particle deposition therein is investigated. The results are analyzed in terms of deposition probability and dimensionless surface coverage as a function of the number of injected particles for a vast range of Péclet numbers thus allowing distinguishing the behavior in diffusion dominant and advection dominant regimes. Finally, the maximum dimensionless surface coverage Γfinal/ΓRSA is studied as a function of Pe. The declining trend observed for high Pe is in good agreement with experimental and simulation results found in the literature.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/156552018-01-01T00:00:00ZLI, YajieAHMADI, AzitaOMARI, AzizPU, HongtingThe microscale simulation of colloidal particle transport and deposition in porous media was achieved with a novel colloidal particle tracking model, called 3D-PTPO (Three-Dimensional Particle Tracking model by Python® and OpenFOAM®), using a Lagrangian method. Simulations were performed by considering the elementary pore structure as a capillary tube with converging/diverging geometries (tapered pipe and venturi tube). The particles are considered as a mass point during transport in the flow and their volume is reconstructed when they are deposited. The main feature of this novel model is to renew the flow field by reconstructing the pore structure by taking the volume of the deposited particles into account. The influence of the particle Péclet number (Pe) and the pore shape on the particle deposition therein is investigated. The results are analyzed in terms of deposition probability and dimensionless surface coverage as a function of the number of injected particles for a vast range of Péclet numbers thus allowing distinguishing the behavior in diffusion dominant and advection dominant regimes. Finally, the maximum dimensionless surface coverage Γfinal/ΓRSA is studied as a function of Pe. The declining trend observed for high Pe is in good agreement with experimental and simulation results found in the literature.