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http://hdl.handle.net/10985/9976
Analysis of the role of structural disorder on the inertial correction to Darcy’s Law
LASSEUX, Didier; AHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar
This work focuses on the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates leading to a non-linear relationship between the filtration velocity and the pressure gradient. A numerical analysis of the non linear -inertialcorrection to Darcy's law is carried out for model periodic structures made of arrays of square-section cylinders. The global aim is to determine and analyze the effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/99762010-01-01T00:00:00ZLASSEUX, DidierAHMADI-SENICHAULT, AzitaABBASIAN ARANI, Ali AkbarThis work focuses on the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates leading to a non-linear relationship between the filtration velocity and the pressure gradient. A numerical analysis of the non linear -inertialcorrection to Darcy's law is carried out for model periodic structures made of arrays of square-section cylinders. The global aim is to determine and analyze the effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scaleTwo-phase non-Darcy flow in heterogeneous porous media: A numerical investigation
http://hdl.handle.net/10985/9724
Two-phase non-Darcy flow in heterogeneous porous media: A numerical investigation
AHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier
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 In these cases, the classical description of two-phase flow in porous media by the generalized Darcy's law is no longer valid.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, this study is based on a generalized Darcy-Forchheimer approach for modelling two-phase incompressible non-stationary inertial flow in porous media. In this model, the momentum conservation equation for each phase, , has a quadratic correction to generalized Darcy’s law and is expressed as: (=”w” for water or “o” for oil): (1) This equation is completed with the mass conservation equation for each phase given by (2) and the capillary pressure and saturation relationships (3) (4) 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 clarity, results are presented in 1D and 2D configurations only. For 1D flow in a homogeneous porous medium, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the “Buckley-Leverett” model extended to take into account inertia. 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.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/97242010-01-01T00:00:00ZAHMADI-SENICHAULT, AzitaABBASIAN ARANI, Ali AkbarLASSEUX, DidierSignificant 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, this study is based on a generalized Darcy-Forchheimer approach for modelling two-phase incompressible non-stationary inertial flow in porous media. In this model, the momentum conservation equation for each phase, , has a quadratic correction to generalized Darcy’s law and is expressed as: (=”w” for water or “o” for oil): (1) This equation is completed with the mass conservation equation for each phase given by (2) and the capillary pressure and saturation relationships (3) (4) 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 clarity, results are presented in 1D and 2D configurations only. For 1D flow in a homogeneous porous medium, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the “Buckley-Leverett” model extended to take into account inertia. 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.One-phase flow in porous media: is the Forchheimer correction relevant?
http://hdl.handle.net/10985/9889
One-phase flow in porous media: is the Forchheimer correction relevant?
LASSEUX, Didier; AHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar
Our interest in this work is dedicated to the dependence upon the filtration velocity (or Reynolds number) of the inertial correction to Darcy's law for one-phase flow in homogeneous porous media. The starting point of our analysis is the averaged flow model operating at Darcy's scale. It shows that the inertial correction to Darcy's law involves a second order tensor that can be determined from the solution of the associated closure problem requiring the microscopic (pore-scale) velocity field. Numerical solutions achieved on 2D model structures are presented. The accent is laid upon the role of the Reynolds number, pressure gradient orientation and structural parameters such as porosity and structural disorder. The Forchheimer type of correction, exhibiting a quadratic dependence upon the filtration velocity, is discussed in different situations.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/98892012-01-01T00:00:00ZLASSEUX, DidierAHMADI-SENICHAULT, AzitaABBASIAN ARANI, Ali AkbarOur interest in this work is dedicated to the dependence upon the filtration velocity (or Reynolds number) of the inertial correction to Darcy's law for one-phase flow in homogeneous porous media. The starting point of our analysis is the averaged flow model operating at Darcy's scale. It shows that the inertial correction to Darcy's law involves a second order tensor that can be determined from the solution of the associated closure problem requiring the microscopic (pore-scale) velocity field. Numerical solutions achieved on 2D model structures are presented. The accent is laid upon the role of the Reynolds number, pressure gradient orientation and structural parameters such as porosity and structural disorder. The Forchheimer type of correction, exhibiting a quadratic dependence upon the filtration velocity, is discussed in different situations.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.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; AHMADI-SENICHAULT, Azita; LASSEUX, Didier
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 AkbarAHMADI-SENICHAULT, AzitaLASSEUX, DidierSignificant 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.On 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.Origin of the inertial deviation from Darcy's law: An investigation from a microscopic flow analysis on two-dimensional model structures
http://hdl.handle.net/10985/12154
Origin of the inertial deviation from Darcy's law: An investigation from a microscopic flow analysis on two-dimensional model structures
AGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, 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-SENICHAULT, 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.A numerical analysis of the inertial correction to Darcy's law
http://hdl.handle.net/10985/9980
A numerical analysis of the inertial correction to Darcy's law
ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; AHMADI-SENICHAULT, Azita
Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates so that the relationship between the filtration velocity and the pressure gradient is no longer linear. The non linear -inertial- correction to Darcy's law is investigated from a numerical point of view on model periodic structures made of regular arrays of cylinders. The starting point of the analysis is the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale. Identification of the macroscopic properties in this model is made by first solving the microscopic flow as well as the closure problem resulting from the upscaling. From these solutions, the inertial correction is computed and analyzed with respect to the Reynolds number and the pressure gradient orientation relative to the principal axes of the periodic unit cell.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/99802009-01-01T00:00:00ZABBASIAN ARANI, Ali AkbarLASSEUX, DidierAHMADI-SENICHAULT, AzitaOur interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates so that the relationship between the filtration velocity and the pressure gradient is no longer linear. The non linear -inertial- correction to Darcy's law is investigated from a numerical point of view on model periodic structures made of regular arrays of cylinders. The starting point of the analysis is the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale. Identification of the macroscopic properties in this model is made by first solving the microscopic flow as well as the closure problem resulting from the upscaling. From these solutions, the inertial correction is computed and analyzed with respect to the Reynolds number and the pressure gradient orientation relative to the principal axes of the periodic unit cell.In vitro cartilage culture: flow, transport and reaction in fibrous porous media
http://hdl.handle.net/10985/9753
In vitro cartilage culture: flow, transport and reaction in fibrous porous media
AHMADI-SENICHAULT, Azita; LASSEUX, Didier; LETELLIER, Samuel
Flow and transport in fibrous media are encountered in a wide variety of domains ranging from biotechnology to filtration in chemical engineering. The context of this work is the in vitro cartilage cell culture on a fibrous biodegradable polymer scaffold placed in a bioreactor. A seeding process using a liquid containing cells (chondrocytes) initiates the culture and an imposed continuous flow through the scaffold allows both the transport of nutrients necessary for cell-growth and of metabolic waste products. This work will attempt to contribute to the study of the hydrodynamics and transport through the fibrous scaffold at different stages of growth, both having a key role in the process of cell growth and on the final quality of the cultured cartilage. The hydrodynamics in the scaffold and in particular the relationship between macroscopic experimentally accessible properties such as the permeability and the porosity have first been studied. For this purpose, the formalism of volume averaging is employed and the associated closure problem is solved numerically with an artificial compressibility algorithm on the basis of a finite volume scheme on a Marker and Cell type of grid. Fibrous media with different microscopic structures are studied. Through a theoretical study, assuming local mass equilibrium, a macroscopic one-equation model describing the reactive transport (advection/diffusion/reaction) of the two species in a three-phase system composed of the cell-phase, a fluid phase and a solid phase is proposed. The volume averaging method is used to develop macroscopic transport equations and associated closure problems. Resolution of the latter over a unit cell representative of a pseudo-periodic medium allows the determination of effective macroscopic properties without any adjustable parameters. The dimensionless form of the closure problems involving advective, diffusive and reactive terms are numerically solved for any 3D geometrical configuration using a finite volume formulation using appropriate schemes. The velocity field input to the model is obtained by the resolution of the Navier-Stokes problem using a modified QUICK scheme and an Artificial Compressibility algorithm. The numerical tool is then validated by comparing its results to those presented in the literature for 2-D unit cells and under-classes of our model (namely, diffusion, diffusion/reaction and diffusion/advection problems). The complete problem involving convection, diffusion and reaction in the three phase system is then studied for different parameters. More precisely, the influence of a cell Peclet number and the solid and cell volume fractions on the dispersion tensor has been studied.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10985/97532007-01-01T00:00:00ZAHMADI-SENICHAULT, AzitaLASSEUX, DidierLETELLIER, SamuelFlow and transport in fibrous media are encountered in a wide variety of domains ranging from biotechnology to filtration in chemical engineering. The context of this work is the in vitro cartilage cell culture on a fibrous biodegradable polymer scaffold placed in a bioreactor. A seeding process using a liquid containing cells (chondrocytes) initiates the culture and an imposed continuous flow through the scaffold allows both the transport of nutrients necessary for cell-growth and of metabolic waste products. This work will attempt to contribute to the study of the hydrodynamics and transport through the fibrous scaffold at different stages of growth, both having a key role in the process of cell growth and on the final quality of the cultured cartilage. The hydrodynamics in the scaffold and in particular the relationship between macroscopic experimentally accessible properties such as the permeability and the porosity have first been studied. For this purpose, the formalism of volume averaging is employed and the associated closure problem is solved numerically with an artificial compressibility algorithm on the basis of a finite volume scheme on a Marker and Cell type of grid. Fibrous media with different microscopic structures are studied. Through a theoretical study, assuming local mass equilibrium, a macroscopic one-equation model describing the reactive transport (advection/diffusion/reaction) of the two species in a three-phase system composed of the cell-phase, a fluid phase and a solid phase is proposed. The volume averaging method is used to develop macroscopic transport equations and associated closure problems. Resolution of the latter over a unit cell representative of a pseudo-periodic medium allows the determination of effective macroscopic properties without any adjustable parameters. The dimensionless form of the closure problems involving advective, diffusive and reactive terms are numerically solved for any 3D geometrical configuration using a finite volume formulation using appropriate schemes. The velocity field input to the model is obtained by the resolution of the Navier-Stokes problem using a modified QUICK scheme and an Artificial Compressibility algorithm. The numerical tool is then validated by comparing its results to those presented in the literature for 2-D unit cells and under-classes of our model (namely, diffusion, diffusion/reaction and diffusion/advection problems). The complete problem involving convection, diffusion and reaction in the three phase system is then studied for different parameters. More precisely, the influence of a cell Peclet number and the solid and cell volume fractions on the dispersion tensor has been studied.