http://hdl.handle.net/10985/13598 Sun, 05 Apr 2026 17:33:54 GMT 2026-04-05T17:33:54Z https://sam.ensam.eu:443/bitstream/id/42a111ce-810d-4394-96b3-ed87ede31e31/ http://hdl.handle.net/10985/13598 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 GMT http://hdl.handle.net/10985/9981 2009-01-01T00:00:00Z 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. 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 GMT http://hdl.handle.net/10985/9982 2009-01-01T00:00:00Z 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. 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 GMT http://hdl.handle.net/10985/9980 2009-01-01T00:00:00Z 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. http://hdl.handle.net/10985/10029 Résolution numérique de l’écoulement diphasique en milieu poreux hétérogène incluant les effets inertiels ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; AHMADI, Azita La mise en place d'un outil numérique 3D de simulation d'écoulement diphasique hors régime de Darcy basé sur le modèle de Darcy-Forchheimer généralisé est présentée. L'outil est tout d’abord validé à l’aide d'une solution semi analytique 1D de type Buckley-Leverett. Des résultats obtenus dans différentes configurations homogène et hétérogènes 1D et 2D mettent en évidence l'importance des termes inertiels en fonction d'un nombre de Reynolds de l'écoulement. Mon, 01 Jan 2007 00:00:00 GMT http://hdl.handle.net/10985/10029 2007-01-01T00:00:00Z ABBASIAN ARANI, Ali Akbar LASSEUX, Didier AHMADI, Azita La mise en place d'un outil numérique 3D de simulation d'écoulement diphasique hors régime de Darcy basé sur le modèle de Darcy-Forchheimer généralisé est présentée. L'outil est tout d’abord validé à l’aide d'une solution semi analytique 1D de type Buckley-Leverett. Des résultats obtenus dans différentes configurations homogène et hétérogènes 1D et 2D mettent en évidence l'importance des termes inertiels en fonction d'un nombre de Reynolds de l'écoulement. http://hdl.handle.net/10985/25627 Unlocking the power of LiOH: Key to next-generation ultra-compact thermal energy storage systems ACHCHAQ, Fouzia; MOON, S.-C.; LEGROS, P. This study explores the potential of untapped lithium hydroxide (LiOH) as a phase change material for thermal energy storage. By overcoming the challenges associated with the liquid LiOH leakage, we successfully thermal-cycled LiOH in a laboratory scale experimentation, and observed its stability (>500 thermal cycles), without chemical decomposition. This step has never been performed to date. Its solid-to-liquid reversible transitions temperatures and related solidification/melting enthalpies values have been verified. Then, the first experimental characterization of LiOH's thermal properties shows unexpected values for its heat capacity, thermal conductivity and diffusivity, in contradiction with the few ones available in literature. This opens avenues for LiOH's applications for the storage of sensible and latent heat, as shown through the increased cycle efficiency potential of a thermal energy storage system if based on its energy storage capacity; up to six times more volumetric energy density compared to traditional Solar Salt-based systems used in the solar tower plant (4.5 GJ/m3 vs. 0.76 GJ/m3 over 1000 thermal cycles). Additionally, we observed a softening phenomenon that occurs inconsistently during heating, but which may account for its excellent melting properties and the interplay with other raw chemicals. This new insight contributes certainly to the underlying mechanisms in the synthesis of another promising heat storage material in development: the peritectic compound Li4Br(OH)3. This pioneering work suggests LiOH as a promising ultra-compact thermal energy storage material for filling the intermediary gap from current to next-generation solar power plants, although its large-scale application requires further investigation to achieve economic viability. Mon, 01 Jul 2024 00:00:00 GMT http://hdl.handle.net/10985/25627 2024-07-01T00:00:00Z ACHCHAQ, Fouzia MOON, S.-C. LEGROS, P. This study explores the potential of untapped lithium hydroxide (LiOH) as a phase change material for thermal energy storage. By overcoming the challenges associated with the liquid LiOH leakage, we successfully thermal-cycled LiOH in a laboratory scale experimentation, and observed its stability (>500 thermal cycles), without chemical decomposition. This step has never been performed to date. Its solid-to-liquid reversible transitions temperatures and related solidification/melting enthalpies values have been verified. Then, the first experimental characterization of LiOH's thermal properties shows unexpected values for its heat capacity, thermal conductivity and diffusivity, in contradiction with the few ones available in literature. This opens avenues for LiOH's applications for the storage of sensible and latent heat, as shown through the increased cycle efficiency potential of a thermal energy storage system if based on its energy storage capacity; up to six times more volumetric energy density compared to traditional Solar Salt-based systems used in the solar tower plant (4.5 GJ/m3 vs. 0.76 GJ/m3 over 1000 thermal cycles). Additionally, we observed a softening phenomenon that occurs inconsistently during heating, but which may account for its excellent melting properties and the interplay with other raw chemicals. This new insight contributes certainly to the underlying mechanisms in the synthesis of another promising heat storage material in development: the peritectic compound Li4Br(OH)3. This pioneering work suggests LiOH as a promising ultra-compact thermal energy storage material for filling the intermediary gap from current to next-generation solar power plants, although its large-scale application requires further investigation to achieve economic viability. http://hdl.handle.net/10985/7497 High cycle multiaxial fatigue crack initiation : experimental observations and microstructure simulations AGBESSI, Komlan; SAINTIER, Nicolas; PALIN-LUC, Thierry This study provides an analysis of high cycle multiaxial fatigue crack initiation modes based on SEM observations.The statistical study of crack initiation preferential sites shows that grains with multiple slip have a high probability of crack initiation. The application of Dang Van criterion at the grain scale using finite element analysis (cubic elasticity with / or without crystal plasticity) on 3D synthetic semi-periodic microstructures shows a strong heterogeneity of both the hydrostatic stress and shear. The evolution of this heterogeneity introduced by the material behavior is discussed. Finally, a method based on the extreme values statistics is proposed and applied to the fatigue indicative parameter associated to the Dang Van criterion. The effects of free surface and constitutive material model were analyzed. Tue, 01 Jan 2013 00:00:00 GMT http://hdl.handle.net/10985/7497 2013-01-01T00:00:00Z AGBESSI, Komlan SAINTIER, Nicolas PALIN-LUC, Thierry This study provides an analysis of high cycle multiaxial fatigue crack initiation modes based on SEM observations.The statistical study of crack initiation preferential sites shows that grains with multiple slip have a high probability of crack initiation. The application of Dang Van criterion at the grain scale using finite element analysis (cubic elasticity with / or without crystal plasticity) on 3D synthetic semi-periodic microstructures shows a strong heterogeneity of both the hydrostatic stress and shear. The evolution of this heterogeneity introduced by the material behavior is discussed. Finally, a method based on the extreme values statistics is proposed and applied to the fatigue indicative parameter associated to the Dang Van criterion. The effects of free surface and constitutive material model were analyzed. http://hdl.handle.net/10985/16561 Microstructure-based study of the crack initaition mechanisms in pure copper under high cycle multiaxial fatigue loading conditions AGBESSI, Komlan; SAINTIER, Nicolas; PALIN-LUC, Thierry This paper aims to contribute in understanding the fatigue crack initiation mechanisms in metallic materials under high cycle multiaxial fatigue loadings. It addresses proportional and non-proportional multiaxial loading conditions with the analysis and observation of the cyclic plasticity development (mainly persistent slip band) until crack initiation (especially short cracks) on a pure oxygen-free high conductivity (OFHC) polycristalline copper. Observation and analysis techniques are based mainly on optical microscopy and scanning electron microscopy (SEM). It has been observed that the plastic slip multiplicity in grains seems more important for multiaxial loadings at a stress level corresponding to the same median fatigue strength at 106 cycles of the material. A multiaxial loading induces an additional multiplicity of the plastic slip in grains compared to uniaxial loading condition. For all the loading conditions investigated, although most of the grains exhibits single slip activated, analysis of the preferential crack initiation sites and modes show a higher probability of intragranular microcrack initiation in the multiple slip grains (with more than two slip systems activated). Most multiple slip grains and higher probability of crack initiation in these grains were observed especially for non-proportional multiaxial loadings. Finally, the effects of the biaxiality ratio and the phase shift on the fatigue crack initiation was highlighted. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/10985/16561 2016-01-01T00:00:00Z AGBESSI, Komlan SAINTIER, Nicolas PALIN-LUC, Thierry This paper aims to contribute in understanding the fatigue crack initiation mechanisms in metallic materials under high cycle multiaxial fatigue loadings. It addresses proportional and non-proportional multiaxial loading conditions with the analysis and observation of the cyclic plasticity development (mainly persistent slip band) until crack initiation (especially short cracks) on a pure oxygen-free high conductivity (OFHC) polycristalline copper. Observation and analysis techniques are based mainly on optical microscopy and scanning electron microscopy (SEM). It has been observed that the plastic slip multiplicity in grains seems more important for multiaxial loadings at a stress level corresponding to the same median fatigue strength at 106 cycles of the material. A multiaxial loading induces an additional multiplicity of the plastic slip in grains compared to uniaxial loading condition. For all the loading conditions investigated, although most of the grains exhibits single slip activated, analysis of the preferential crack initiation sites and modes show a higher probability of intragranular microcrack initiation in the multiple slip grains (with more than two slip systems activated). Most multiple slip grains and higher probability of crack initiation in these grains were observed especially for non-proportional multiaxial loadings. Finally, the effects of the biaxiality ratio and the phase shift on the fatigue crack initiation was highlighted. 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 GMT http://hdl.handle.net/10985/10895 2016-01-01T00:00:00Z 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. http://hdl.handle.net/10985/9888 Inertial flow in porous media: A numerical investigation on model structures AGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, Azita The aim of this work is to study the correction to Darcy's law for inertial flow in porous media. In many situations encountered in industrial applications such as flow in column reactors, gas flow near wells for hydrocarbon recovery and CO2 sequestration, flow in filters... , Reynolds numbers are large enough to lead to a non-linear relationship between the filtration velocity and the pressure gradient. In this work, a numerical analysis of the non linear -inertial- correction to Darcy's law is carried out for the stationary inertial flow of a one-phase Newtonian incompressible fluid on model 2D and 3D structures. Effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale are determined using the microscopic flow fields and solving the closure problems resulting from up-scaling. From the numerical simulations, the dependence of the correction to Darcy's law on the geometrical properties of the 3D structure is studied. These properties are the shape of the solid grains which may be cubic or spherical and the degree of disorder in their arrangement in the domain. Weak disorder corresponds to a random placement of the grains of identical shape and size within each cell of a regular 3D lattice, while for strong disorder, grain size is also randomly distributed. Tue, 01 Jan 2013 00:00:00 GMT http://hdl.handle.net/10985/9888 2013-01-01T00:00:00Z AGNAOU, Mehrez LASSEUX, Didier AHMADI-SENICHAULT, Azita The aim of this work is to study the correction to Darcy's law for inertial flow in porous media. In many situations encountered in industrial applications such as flow in column reactors, gas flow near wells for hydrocarbon recovery and CO2 sequestration, flow in filters... , Reynolds numbers are large enough to lead to a non-linear relationship between the filtration velocity and the pressure gradient. In this work, a numerical analysis of the non linear -inertial- correction to Darcy's law is carried out for the stationary inertial flow of a one-phase Newtonian incompressible fluid on model 2D and 3D structures. Effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale are determined using the microscopic flow fields and solving the closure problems resulting from up-scaling. From the numerical simulations, the dependence of the correction to Darcy's law on the geometrical properties of the 3D structure is studied. These properties are the shape of the solid grains which may be cubic or spherical and the degree of disorder in their arrangement in the domain. Weak disorder corresponds to a random placement of the grains of identical shape and size within each cell of a regular 3D lattice, while for strong disorder, grain size is also randomly distributed. 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 GMT http://hdl.handle.net/10985/12154 2017-01-01T00:00:00Z 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.