SAM
https://sam.ensam.eu:443
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 06 Oct 2024 13:38:20 GMT2024-10-06T13:38:20ZOn the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media
http://hdl.handle.net/10985/9726
On the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media
LASSEUX, Didier; ABBASIAN ARANI, Ali Akbar; AHMADI-SENICHAULT, Azita
We report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is performed on the basis of an upscaled form of the Navier-Stokes equation requiring the solution of both the micro-scale flow and the associated closure problem. It is carried out with a special focus on the different regimes of inertia (weak and strong inertia) and the crossover between these regimes versus flow orientation and structural parameters, namely porosity and disorder. For ordered structures, it is shown that (i) the tensor involved in the expression of the correction is generally not symmetric, despite the isotropic feature of the permeability tensor. This is in accordance with the fact that the extra force due to inertia exerted on the structure is not pure drag in the general case; (ii) the Forchheimer type of correction (which strictly depends on the square of the filtration velocity) is an approximation that does not hold at all for particular orientations of the pressure gradient with respect to the axes of the structure; and (iii) the weak inertia regime always exists as predicted by theoretical developments. When structural disorder is introduced, this work shows that (i) the quadratic dependence of the correction upon the filtration velocity is very robust over a wide range of the Reynolds number in the strong inertia regime; (ii) the Reynolds number interval corresponding to weak inertia, that is always present, is strongly reduced in comparison to ordered structures. In conjunction with its relatively small magnitude, it explains why this weak inertia regime is most of the time overlooked during experiments on natural media. In all cases, the Forchheimer correction implies that the permeability is different from the intrinsic one.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/97262011-01-01T00:00:00ZLASSEUX, DidierABBASIAN ARANI, Ali AkbarAHMADI-SENICHAULT, AzitaWe report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is performed on the basis of an upscaled form of the Navier-Stokes equation requiring the solution of both the micro-scale flow and the associated closure problem. It is carried out with a special focus on the different regimes of inertia (weak and strong inertia) and the crossover between these regimes versus flow orientation and structural parameters, namely porosity and disorder. For ordered structures, it is shown that (i) the tensor involved in the expression of the correction is generally not symmetric, despite the isotropic feature of the permeability tensor. This is in accordance with the fact that the extra force due to inertia exerted on the structure is not pure drag in the general case; (ii) the Forchheimer type of correction (which strictly depends on the square of the filtration velocity) is an approximation that does not hold at all for particular orientations of the pressure gradient with respect to the axes of the structure; and (iii) the weak inertia regime always exists as predicted by theoretical developments. When structural disorder is introduced, this work shows that (i) the quadratic dependence of the correction upon the filtration velocity is very robust over a wide range of the Reynolds number in the strong inertia regime; (ii) the Reynolds number interval corresponding to weak inertia, that is always present, is strongly reduced in comparison to ordered structures. In conjunction with its relatively small magnitude, it explains why this weak inertia regime is most of the time overlooked during experiments on natural media. In all cases, the Forchheimer correction implies that the permeability is different from the intrinsic one.Measurement of the thermal diffusivity of a silica fiber bundle using a laser and an IR camera
http://hdl.handle.net/10985/10064
Measurement of the thermal diffusivity of a silica fiber bundle using a laser and an IR camera
VIGNOLES, Gérard; BRESSON, Grégory; LORRETTE, Christophe; AHMADI-SENICHAULT, Azita
We propose a lightweight method for the determination of heat diffusivity of silica fiber bundles based on the use of a laser and an IR camera. The fiber bundle is maintained in traction in a holder; exposition is made as a step function, followed by a laser shutdown. The movie obtained by the IR camera is then processed : frame averaging, backgraound computation and substraction, image smoothing, extraction of the IR signal along the fiber bundle. A 1D model has been developed. This problem admits an analytic solution that we have obtained through the use of Laplace transforms. Several identification methods are proposed and tested, and have been compared favorably with an existing method based on periodic heating. Results are in agreement with literature values.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/100642012-01-01T00:00:00ZVIGNOLES, GérardBRESSON, GrégoryLORRETTE, ChristopheAHMADI-SENICHAULT, AzitaWe propose a lightweight method for the determination of heat diffusivity of silica fiber bundles based on the use of a laser and an IR camera. The fiber bundle is maintained in traction in a holder; exposition is made as a step function, followed by a laser shutdown. The movie obtained by the IR camera is then processed : frame averaging, backgraound computation and substraction, image smoothing, extraction of the IR signal along the fiber bundle. A 1D model has been developed. This problem admits an analytic solution that we have obtained through the use of Laplace transforms. Several identification methods are proposed and tested, and have been compared favorably with an existing method based on periodic heating. Results are in agreement with literature values.From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation
http://hdl.handle.net/10985/10895
From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation
AGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, Azita
This work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide range of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/108952016-01-01T00:00:00ZAGNAOU, MehrezLASSEUX, DidierAHMADI-SENICHAULT, AzitaThis work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide range of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics.Displacement of colloidal dispersions in Porous Media: experimental & numerical approaches
http://hdl.handle.net/10985/10902
Displacement of colloidal dispersions in Porous Media: experimental & numerical approaches
CANSECO, Vladimir; SEFRIOUI-CHAIBAINOU, Nisrine; OMARI, Aziz; BERTIN, Henri; AHMADI-SENICHAULT, Azita
The main objective of this paper is to give more insight on colloids deposition and re-entrainment in presence of a rough surface. Experiments on retention and release of colloids in a porous medium are first presented. The influence of physicochemical and hydrodynamic conditions is investigated. The experimental results cannot be qualitatively interpreted using the DLVO theory and knowledges at pore scale are then needed. A 3D numerical simulation approach at the pore scale is therefore proposed where the motion of colloids is solved in presence of collector surfaces bearing various kinds of asperities and by taking into account physico-chemical interactions calculated at each time step during colloid movement. It is obviously observed that both deposition and mobilization of particles are dependent on solution chemistry and hydrodynamic conditions and are significantly affected by the form and size of the local roughness of the pore surface. Therefore, depending on solution ionic strength and surface topography, colloids may be adsorbed or not and when a particle is retained an increase of flow strength is then needed to remove it and such an increase is specific to the location of occurrence of the adsorption step. In general, simulation results allow us to explain our experimental results that show that by steeply increasing the flow strength, more and more fractions of particles retained inside the porous medium are released until all particles are removed.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/109022016-01-01T00:00:00ZCANSECO, VladimirSEFRIOUI-CHAIBAINOU, NisrineOMARI, AzizBERTIN, HenriAHMADI-SENICHAULT, AzitaThe main objective of this paper is to give more insight on colloids deposition and re-entrainment in presence of a rough surface. Experiments on retention and release of colloids in a porous medium are first presented. The influence of physicochemical and hydrodynamic conditions is investigated. The experimental results cannot be qualitatively interpreted using the DLVO theory and knowledges at pore scale are then needed. A 3D numerical simulation approach at the pore scale is therefore proposed where the motion of colloids is solved in presence of collector surfaces bearing various kinds of asperities and by taking into account physico-chemical interactions calculated at each time step during colloid movement. It is obviously observed that both deposition and mobilization of particles are dependent on solution chemistry and hydrodynamic conditions and are significantly affected by the form and size of the local roughness of the pore surface. Therefore, depending on solution ionic strength and surface topography, colloids may be adsorbed or not and when a particle is retained an increase of flow strength is then needed to remove it and such an increase is specific to the location of occurrence of the adsorption step. In general, simulation results allow us to explain our experimental results that show that by steeply increasing the flow strength, more and more fractions of particles retained inside the porous medium are released until all particles are removed.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; PU, Hongting; AHMADI-SENICHAULT, Azita
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, AzizPU, HongtingAHMADI-SENICHAULT, AzitaThe 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
MALVAULT, Guillaume; OMARI, Aziz; RODRIGUEZ DE CASTRO, Antonio; AHMADI-SENICHAULT, Azita
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/10985/121562016-01-01T00:00:00ZMALVAULT, GuillaumeOMARI, AzizRODRIGUEZ DE CASTRO, AntonioAHMADI-SENICHAULT, AzitaA 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.Displacement of Colloidal Dispersions in Porous Media: Experimental & Numerical Approaches
http://hdl.handle.net/10985/9751
Displacement of Colloidal Dispersions in Porous Media: Experimental & Numerical Approaches
OMARI, Aziz; BERTIN, Henri; AHMADI-SENICHAULT, Azita
The displacement of colloidal dispersions is of particular interest in many applications ranging from environmental issues to petroleum recovery. Natural porous media such as soils, aquifers or reservoirs contain colloidal particles of different nature (bacteria, viruses, clay, metal complexes …). Colloids can act as vehicles for micro organisms’ transport in aquifers causing danger for human health. In petroleum recovery techniques, water containing colloids is sometimes injected and their release and adsorption may alter the petrophysical properties of reservoirs causing their damage. This talk focuses on the study of colloid transport in porous media under different hydrodynamic and physicochemical conditions (pH, salinity) using both experimental and numerical approaches. Typical laboratory experiments consist in the injection of a colloidal dispersion of a given concentration in a porous column. The analysis of the effluents after brine-flushing allows investigating the kinetics of release and adsorption of colloids inside the porous medium. In-situ investigations are performed either by post-mortem destructive methods or by using more sophisticated non-destructive methods. Moreover, a first approach to model these processes consists in solving the appropriate convection-dispersion-reaction equations involving macroscopic properties. Although this gives valuable qualitative insight on the displacement mechanisms, a more detailed study at the pore-scale is needed. Numerical approaches have been used at the pore-scale to study the displacement of colloidal particles. As a first approximation, the transport of the mass center of the particles has been considered. More complete numerical methods have allowed to study the transport of a colloidal particle taking into account pore-surface roughness, hydrodynamic forces and particle/pore physicochemical interactions (DLVO forces monitored through the change of the ionic strength of the suspending fluid). An overview of our experimental and numerical studies will be presented.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/97512015-01-01T00:00:00ZOMARI, AzizBERTIN, HenriAHMADI-SENICHAULT, AzitaThe displacement of colloidal dispersions is of particular interest in many applications ranging from environmental issues to petroleum recovery. Natural porous media such as soils, aquifers or reservoirs contain colloidal particles of different nature (bacteria, viruses, clay, metal complexes …). Colloids can act as vehicles for micro organisms’ transport in aquifers causing danger for human health. In petroleum recovery techniques, water containing colloids is sometimes injected and their release and adsorption may alter the petrophysical properties of reservoirs causing their damage. This talk focuses on the study of colloid transport in porous media under different hydrodynamic and physicochemical conditions (pH, salinity) using both experimental and numerical approaches. Typical laboratory experiments consist in the injection of a colloidal dispersion of a given concentration in a porous column. The analysis of the effluents after brine-flushing allows investigating the kinetics of release and adsorption of colloids inside the porous medium. In-situ investigations are performed either by post-mortem destructive methods or by using more sophisticated non-destructive methods. Moreover, a first approach to model these processes consists in solving the appropriate convection-dispersion-reaction equations involving macroscopic properties. Although this gives valuable qualitative insight on the displacement mechanisms, a more detailed study at the pore-scale is needed. Numerical approaches have been used at the pore-scale to study the displacement of colloidal particles. As a first approximation, the transport of the mass center of the particles has been considered. More complete numerical methods have allowed to study the transport of a colloidal particle taking into account pore-surface roughness, hydrodynamic forces and particle/pore physicochemical interactions (DLVO forces monitored through the change of the ionic strength of the suspending fluid). An overview of our experimental and numerical studies will be presented.NAPL disolution in an heterogeneous porous medium: experimental and numerical study
http://hdl.handle.net/10985/10031
NAPL disolution in an heterogeneous porous medium: experimental and numerical study
YRA, Adrienne; BERTIN, Henri; AHMADI-SENICHAULT, Azita
This study deals with the dissolution of a NAPL trapped in a water saturated heterogeneous porous medium (stratified medium with flow normal to the strata). The experimental study consists in injecting pure water in a stratified porous medium made of five strata of two different porous media wherein a pollutant (TCE) has been trapped under capillary forces. Pollutant concentration in effluent water is measured using a gas chromatography device, while local saturation is measured using a gamma ray attenuation apparatus. The experimental data show a slow dissolution of the pollutant at a concentration lower than the equilibrium concentration. This typical non equilibrium is attributed to the macroscopic heterogeneity of the porous medium and to the microscopic heterogeneity of the strata. A numerical study has been performed to analyse the experimental data. The non equilibrium physical model solved numerically allows a satisfactory description of the experimental data using correlations for the mass exchange coefficient of each medium similar to those reported in the literature. The macroscopic modelisation of dissolution in the stratified formation using the “equivalent homogeneous medium” approach has been explored. Although, a very good agreement between experimental and numerical data is observed using a macroscopic non-equilibirum model with adjusted effective properties, direct estimation of these properties remains rather complex.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/100312009-01-01T00:00:00ZYRA, AdrienneBERTIN, HenriAHMADI-SENICHAULT, AzitaThis study deals with the dissolution of a NAPL trapped in a water saturated heterogeneous porous medium (stratified medium with flow normal to the strata). The experimental study consists in injecting pure water in a stratified porous medium made of five strata of two different porous media wherein a pollutant (TCE) has been trapped under capillary forces. Pollutant concentration in effluent water is measured using a gas chromatography device, while local saturation is measured using a gamma ray attenuation apparatus. The experimental data show a slow dissolution of the pollutant at a concentration lower than the equilibrium concentration. This typical non equilibrium is attributed to the macroscopic heterogeneity of the porous medium and to the microscopic heterogeneity of the strata. A numerical study has been performed to analyse the experimental data. The non equilibrium physical model solved numerically allows a satisfactory description of the experimental data using correlations for the mass exchange coefficient of each medium similar to those reported in the literature. The macroscopic modelisation of dissolution in the stratified formation using the “equivalent homogeneous medium” approach has been explored. Although, a very good agreement between experimental and numerical data is observed using a macroscopic non-equilibirum model with adjusted effective properties, direct estimation of these properties remains rather complex.A numerical approach of two-phase non-Darcy flow in heterogeneous porous media
http://hdl.handle.net/10985/9982
A numerical approach of two-phase non-Darcy flow in heterogeneous porous media
ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; AHMADI-SENICHAULT, Azita
Significant inertial effects are observed for many applications such as flow in the near-wellbore region, in very permeable reservoirs or in packed-bed reactors. In these cases, the classical description of two-phase flow in porous media by the generalized Darcy's law is no longer valid. Due to the lack of a formalized theoretical model confirmed experimentally, our study is based on a generalized Darcy-Forchheimer approach for modelling two-phase incompressible inertial flow in porous media. Using a finite volume formulation, an IMPES (IMplicit for Pressures, Explicit for Saturations) scheme and a Fixed Point method for the treatment of non-linearities caused by inertia, a 3D numerical tool has been developed. For 1D flow in a homogeneous porous medium, comparison of saturation profiles obtained numerically at different times to those obtained semi-analytically using an “Inertial Buckley-Leverett model” allows a validation of the tool. The influence of inertial effects on the saturation profiles and therefore on the breakthrough curves for homogeneous media is analysed for different Reynolds numbers, thus emphasizing the necessity of taking into account this additional energy loss when necessary. For 1D heterogeneous configurations, a thorough analysis of the saturation fronts as well as the saturation jumps at the interface between two media of contrasted properties highlights the influence of inertial effects for different Reynolds and capillary numbers. In 2D heterogeneous configurations, saturation distributions are strongly affected by inertial effects. In particular, capillary trapping of the displaced fluid observed for the Darcy regime in certain regions can completely disappears when inertial effects become dominant.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/99822009-01-01T00:00:00ZABBASIAN ARANI, Ali AkbarLASSEUX, DidierAHMADI-SENICHAULT, AzitaSignificant inertial effects are observed for many applications such as flow in the near-wellbore region, in very permeable reservoirs or in packed-bed reactors. In these cases, the classical description of two-phase flow in porous media by the generalized Darcy's law is no longer valid. Due to the lack of a formalized theoretical model confirmed experimentally, our study is based on a generalized Darcy-Forchheimer approach for modelling two-phase incompressible inertial flow in porous media. Using a finite volume formulation, an IMPES (IMplicit for Pressures, Explicit for Saturations) scheme and a Fixed Point method for the treatment of non-linearities caused by inertia, a 3D numerical tool has been developed. For 1D flow in a homogeneous porous medium, comparison of saturation profiles obtained numerically at different times to those obtained semi-analytically using an “Inertial Buckley-Leverett model” allows a validation of the tool. The influence of inertial effects on the saturation profiles and therefore on the breakthrough curves for homogeneous media is analysed for different Reynolds numbers, thus emphasizing the necessity of taking into account this additional energy loss when necessary. For 1D heterogeneous configurations, a thorough analysis of the saturation fronts as well as the saturation jumps at the interface between two media of contrasted properties highlights the influence of inertial effects for different Reynolds and capillary numbers. In 2D heterogeneous configurations, saturation distributions are strongly affected by inertial effects. In particular, capillary trapping of the displaced fluid observed for the Darcy regime in certain regions can completely disappears when inertial effects become dominant.Derivation of a macroscopic model for two-phase non-Darcy flow in homogeneous porous media using volume averaging
http://hdl.handle.net/10985/9981
Derivation of a macroscopic model for two-phase non-Darcy flow in homogeneous porous media using volume averaging
ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; AHMADI-SENICHAULT, Azita
The purpose of this work is to propose a derivation of a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. The starting point of the procedure is the pore-scale boundary value problem given by the continuity and Navier–Stokes equations in each phase β and γ along with boundary conditions at interfaces. The method of volume averaging is employed subjected to a series of constraints for the development to hold. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The development also assumes that fluctuations of the curvature of the fluid–fluid interfaces are unimportant over the unit cell representing the porous medium. Under these circumstances, the resulting macroscopic momentum equation, for the -phase (=, ) relates the gradient of the phase-averaged pressure to the filtration or Darcy velocity in a coupled nonlinear form. All tensors appearing in the macroscopic equation can be determined from closure problems that are to be solved using a spatially periodic model of a porous medium. Some indications to compute these tensors are provided.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/99812009-01-01T00:00:00ZABBASIAN ARANI, Ali AkbarLASSEUX, DidierAHMADI-SENICHAULT, AzitaThe purpose of this work is to propose a derivation of a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. The starting point of the procedure is the pore-scale boundary value problem given by the continuity and Navier–Stokes equations in each phase β and γ along with boundary conditions at interfaces. The method of volume averaging is employed subjected to a series of constraints for the development to hold. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The development also assumes that fluctuations of the curvature of the fluid–fluid interfaces are unimportant over the unit cell representing the porous medium. Under these circumstances, the resulting macroscopic momentum equation, for the -phase (=, ) relates the gradient of the phase-averaged pressure to the filtration or Darcy velocity in a coupled nonlinear form. All tensors appearing in the macroscopic equation can be determined from closure problems that are to be solved using a spatially periodic model of a porous medium. Some indications to compute these tensors are provided.