This study deals with the dissolution of a NAPL trapped in a water saturated heterogeneous porous... more 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 correlati...
In this work, we make use of numerical experiments to explore our original theoretical analysis o... more In this work, we make use of numerical experiments to explore our original theoretical analysis of two-phase flow in heterogeneous porous media (Quintard and Whitaker, 1988). The calculations were carried out with a two-region model of a stratified system, and the parameters were chosen be consistent with practical problems associated with groundwater flows and petroleum reservoir recovery processes. The comparison between theory (the large-scaled averaged equations) and experiment (numerical solution of the local volume averaged equations) has allowed us to identify conditions for which the quasi-static theory is acceptable and conditions for which a dynamic theory must be used. Byquasi-static we mean the following: (1) The local capillary pressure,everywhere in the averaging volume, can be set equal to the large-scale capillary pressure evaluated at the centroid of the averaging volume and (2) the large-scale capillary pressure is given by the difference between the large-scale pressures in the two immiscible phases, and is therefore independent of gravitational effects, flow effects and transient effects. Bydynamic, we simply mean a significant departure from the quasi-static condition, thus dynamic effects can be associated with gravitational effects, flow effects and transient effects. To be more precise about the quasi-static condition we need to refer to the relation between the local capillary pressure and the large-scale capillary pressure derived in Part I (Quintard and Whitaker, 1990). \(\begin{gathered} p_c \left| {_y = \left\{ {p_c } \right\}^c } \right|_x + \left( {\rho _\gamma - \rho _\beta } \right)g \cdot \left( {y - \left\{ y \right\}^c } \right) + \Omega _\gamma \cdot [\left( {y + b_\gamma } \right) - \left\{ {y + b_\gamma } \right\}^c ] - \Omega _\beta \cdot [\left( {y + b_\beta } \right) - \left\{ {y + b_\beta } \right\}^c ] + \\ + \tfrac{1}{2}\nabla \Omega _\gamma :[\left( {yy + D_\gamma } \right) - \left\{ {yy + D_\gamma } \right\}^c ] - \tfrac{1}{2}\nabla \Omega _\beta :[\left( {yy + D_\beta } \right) - \left\{ {yy + D_\beta } \right\}^c ] + \\ + [\left( {\mu _\gamma A_\gamma - \mu _\beta A_\beta } \right) - \left\{ {\mu _\gamma A_\gamma - \mu _\beta A_\beta } \right\}^c ]\frac{{\partial \left\{ { \in _\beta } \right\}*}}{{\partial t}} + \\ + [\left( {\mu _\gamma c_\gamma - \mu _\beta c_\beta } \right) - \left\{ {\mu _\gamma c_\gamma - \mu _\beta c_\beta } \right\}^c ] \cdot \nabla \frac{{\partial \left\{ { \in _\beta } \right\}*}}{{\partial t}} + \\ + \mu _\gamma (E_\gamma - \left\{ {E_\gamma } \right\}^c ):\nabla \Phi _\gamma - \mu _\beta (E_\beta - \left\{ {E_\beta } \right\}^c ):\nabla \Phi _{\beta \cdot } \\ \end{gathered} \) Herep c ¦y represents the local capillary pressure evaluated at a positiony relative to the centroid of the large-scale averaging volume, and {p c }¦x represents the large-scale capillary pressure evaluated at the centroid. In addition to{p c } c being evaluated at the centroid, all averaged terms on the right-hand side of Equation (1) are evaluated at the centroid. We can now write the equations describing the quasi-static condition as \(\left\{ {p_c } \right\}^c = \left\{ {\left\langle {p_\gamma } \right\rangle ^\gamma } \right\}^\gamma - \left\{ {\left\langle {p_\beta } \right\rangle ^\beta } \right\}^\beta ,\) , \(p_c \left| {_y = \left\{ {p_c } \right\}^c } \right|_{x \cdot } \) , This means that the fluids within an averaging volume are distributed according to the capillary pressure-saturation relationwith the capillary pressure held constant. It also means that the large-scale capillary pressure is devoid of any dynamic effects. Both of these conditions represent approximations (see Section 6 in Part I) and one of our main objectives in this paper is to learn something about the efficacy of these approximations. As a secondary objective we want to explore the influence of dynamic effects in terms of our original theory. In that development only the first four terms on the right hand side of Equation (1) appeared in the representation for the local capillary pressure. However, those terms will provide an indication of the influence of dynamic effects on the large-scale capillary pressure and the large-scale permeability tensor, and that information provides valuable guidance for future studies based on the theory presented in Part I.
The Canadian Journal of Chemical Engineering, 2015
ABSTRACT RésuméNotre travail présente une étude expérimentale du dépôt de particules colloïdales ... more ABSTRACT RésuméNotre travail présente une étude expérimentale du dépôt de particules colloïdales dans un milieu poreux consolidé, homogène et initialement saturé en eau. La phase fluide injectée dans le milieu poreux est une suspension de particules de latex dont la dimension est connue. L'influence de la force ionique de la suspension colloïdale et du débit d'injection sur le dépôt de particules est étudiée. On observe que le recouvrement de surface (θ) croît avec la force ionique alors que le recouvrement de surface (θ) décroît quand le nombre de Péclet augmente. Des mesures locales, par atténuation d'un rayonnement γ, mettent en évidence la réduction de porosité due au dépôt de particules. La réduction de la perméabilité, mesurée en fin d'expérience. This article is protected by copyright. All rights reserved
This study deals with the dissolution of a NAPL trapped in a water saturated heterogeneous porous... more 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
Proceedings of SPE International Symposium on Oilfield Chemistry, 2001
... 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 PV injected Tracer front Polymer front : 1st injection Polymer ... more ... 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 PV injected Tracer front Polymer front : 1st injection Polymer front : 2nd injection Page 8. 8 PH. ELMKIES, H. BERTIN, D. LASSEUX, M. MURRAY, AND A. ZAITOUN SPE 64986 TABLE 3 End Point data before and after polymer ...
The complex processes of water flow and solute transport occurring in subsurface environment have... more The complex processes of water flow and solute transport occurring in subsurface environment have to be well modeled in order to be able to protect the water aquifers against contamination, for security of nuclear waste depositories or CO2 sequestration, in the problem of extraction of geothermal energy. Since natural geological formations are often heterogeneous at different scales, it leads to
... Patrick Barreau,* Henri Bertin, SPE, and Didier Lasseux, U. of Bordeaux; Philippe Gl??nat, SP... more ... Patrick Barreau,* Henri Bertin, SPE, and Didier Lasseux, U. of Bordeaux; Philippe Gl??nat, SPE, Total; and Alan Zaitoun, SPE, Inst. ... 18. Chauveteau, G., Tirell, M., and Omari, A.: ???Concentration Depen-dence of the Effective Viscosity of Polymer Solutions in Small Pores with ...
Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy, 1997
Dispersion and the mass transfer coefficients involved in the transport equation of a pollutant p... more Dispersion and the mass transfer coefficients involved in the transport equation of a pollutant partially miscible with water saturating a porous media are estimated by a direct approach requiring the numerical solution of several local problems on representative unit cells of the porous media. An experimental set-up was used to study by gamma-ray attenuation the dissolution of toluene in a
SPE/EAGE Reservoir Characterization and Simulation Conference, 2007
Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 20... more Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 2007 SPE/EAGE Reservoir Characterization and Simulation Conference held in Abu Dhabi, UAE, 2831 October 2007. This paper was selected for presentation by an SPE ...
SPE Annual Technical Conference and Exhibition, 2006
Abstract Sequestration of carbon dioxide in geological formations is an alternative way to manage... more Abstract Sequestration of carbon dioxide in geological formations is an alternative way to manage the carbon emitted by combustion of fossil fuels. Results of an experimental and numerical modeling study aiming to investigate the important aspects of injection of CO 2 ...
This study deals with the dissolution of a NAPL trapped in a water saturated heterogeneous porous... more 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 correlati...
In this work, we make use of numerical experiments to explore our original theoretical analysis o... more In this work, we make use of numerical experiments to explore our original theoretical analysis of two-phase flow in heterogeneous porous media (Quintard and Whitaker, 1988). The calculations were carried out with a two-region model of a stratified system, and the parameters were chosen be consistent with practical problems associated with groundwater flows and petroleum reservoir recovery processes. The comparison between theory (the large-scaled averaged equations) and experiment (numerical solution of the local volume averaged equations) has allowed us to identify conditions for which the quasi-static theory is acceptable and conditions for which a dynamic theory must be used. Byquasi-static we mean the following: (1) The local capillary pressure,everywhere in the averaging volume, can be set equal to the large-scale capillary pressure evaluated at the centroid of the averaging volume and (2) the large-scale capillary pressure is given by the difference between the large-scale pressures in the two immiscible phases, and is therefore independent of gravitational effects, flow effects and transient effects. Bydynamic, we simply mean a significant departure from the quasi-static condition, thus dynamic effects can be associated with gravitational effects, flow effects and transient effects. To be more precise about the quasi-static condition we need to refer to the relation between the local capillary pressure and the large-scale capillary pressure derived in Part I (Quintard and Whitaker, 1990). \(\begin{gathered} p_c \left| {_y = \left\{ {p_c } \right\}^c } \right|_x + \left( {\rho _\gamma - \rho _\beta } \right)g \cdot \left( {y - \left\{ y \right\}^c } \right) + \Omega _\gamma \cdot [\left( {y + b_\gamma } \right) - \left\{ {y + b_\gamma } \right\}^c ] - \Omega _\beta \cdot [\left( {y + b_\beta } \right) - \left\{ {y + b_\beta } \right\}^c ] + \\ + \tfrac{1}{2}\nabla \Omega _\gamma :[\left( {yy + D_\gamma } \right) - \left\{ {yy + D_\gamma } \right\}^c ] - \tfrac{1}{2}\nabla \Omega _\beta :[\left( {yy + D_\beta } \right) - \left\{ {yy + D_\beta } \right\}^c ] + \\ + [\left( {\mu _\gamma A_\gamma - \mu _\beta A_\beta } \right) - \left\{ {\mu _\gamma A_\gamma - \mu _\beta A_\beta } \right\}^c ]\frac{{\partial \left\{ { \in _\beta } \right\}*}}{{\partial t}} + \\ + [\left( {\mu _\gamma c_\gamma - \mu _\beta c_\beta } \right) - \left\{ {\mu _\gamma c_\gamma - \mu _\beta c_\beta } \right\}^c ] \cdot \nabla \frac{{\partial \left\{ { \in _\beta } \right\}*}}{{\partial t}} + \\ + \mu _\gamma (E_\gamma - \left\{ {E_\gamma } \right\}^c ):\nabla \Phi _\gamma - \mu _\beta (E_\beta - \left\{ {E_\beta } \right\}^c ):\nabla \Phi _{\beta \cdot } \\ \end{gathered} \) Herep c ¦y represents the local capillary pressure evaluated at a positiony relative to the centroid of the large-scale averaging volume, and {p c }¦x represents the large-scale capillary pressure evaluated at the centroid. In addition to{p c } c being evaluated at the centroid, all averaged terms on the right-hand side of Equation (1) are evaluated at the centroid. We can now write the equations describing the quasi-static condition as \(\left\{ {p_c } \right\}^c = \left\{ {\left\langle {p_\gamma } \right\rangle ^\gamma } \right\}^\gamma - \left\{ {\left\langle {p_\beta } \right\rangle ^\beta } \right\}^\beta ,\) , \(p_c \left| {_y = \left\{ {p_c } \right\}^c } \right|_{x \cdot } \) , This means that the fluids within an averaging volume are distributed according to the capillary pressure-saturation relationwith the capillary pressure held constant. It also means that the large-scale capillary pressure is devoid of any dynamic effects. Both of these conditions represent approximations (see Section 6 in Part I) and one of our main objectives in this paper is to learn something about the efficacy of these approximations. As a secondary objective we want to explore the influence of dynamic effects in terms of our original theory. In that development only the first four terms on the right hand side of Equation (1) appeared in the representation for the local capillary pressure. However, those terms will provide an indication of the influence of dynamic effects on the large-scale capillary pressure and the large-scale permeability tensor, and that information provides valuable guidance for future studies based on the theory presented in Part I.
The Canadian Journal of Chemical Engineering, 2015
ABSTRACT RésuméNotre travail présente une étude expérimentale du dépôt de particules colloïdales ... more ABSTRACT RésuméNotre travail présente une étude expérimentale du dépôt de particules colloïdales dans un milieu poreux consolidé, homogène et initialement saturé en eau. La phase fluide injectée dans le milieu poreux est une suspension de particules de latex dont la dimension est connue. L'influence de la force ionique de la suspension colloïdale et du débit d'injection sur le dépôt de particules est étudiée. On observe que le recouvrement de surface (θ) croît avec la force ionique alors que le recouvrement de surface (θ) décroît quand le nombre de Péclet augmente. Des mesures locales, par atténuation d'un rayonnement γ, mettent en évidence la réduction de porosité due au dépôt de particules. La réduction de la perméabilité, mesurée en fin d'expérience. This article is protected by copyright. All rights reserved
This study deals with the dissolution of a NAPL trapped in a water saturated heterogeneous porous... more 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
Proceedings of SPE International Symposium on Oilfield Chemistry, 2001
... 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 PV injected Tracer front Polymer front : 1st injection Polymer ... more ... 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 PV injected Tracer front Polymer front : 1st injection Polymer front : 2nd injection Page 8. 8 PH. ELMKIES, H. BERTIN, D. LASSEUX, M. MURRAY, AND A. ZAITOUN SPE 64986 TABLE 3 End Point data before and after polymer ...
The complex processes of water flow and solute transport occurring in subsurface environment have... more The complex processes of water flow and solute transport occurring in subsurface environment have to be well modeled in order to be able to protect the water aquifers against contamination, for security of nuclear waste depositories or CO2 sequestration, in the problem of extraction of geothermal energy. Since natural geological formations are often heterogeneous at different scales, it leads to
... Patrick Barreau,* Henri Bertin, SPE, and Didier Lasseux, U. of Bordeaux; Philippe Gl??nat, SP... more ... Patrick Barreau,* Henri Bertin, SPE, and Didier Lasseux, U. of Bordeaux; Philippe Gl??nat, SPE, Total; and Alan Zaitoun, SPE, Inst. ... 18. Chauveteau, G., Tirell, M., and Omari, A.: ???Concentration Depen-dence of the Effective Viscosity of Polymer Solutions in Small Pores with ...
Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy, 1997
Dispersion and the mass transfer coefficients involved in the transport equation of a pollutant p... more Dispersion and the mass transfer coefficients involved in the transport equation of a pollutant partially miscible with water saturating a porous media are estimated by a direct approach requiring the numerical solution of several local problems on representative unit cells of the porous media. An experimental set-up was used to study by gamma-ray attenuation the dissolution of toluene in a
SPE/EAGE Reservoir Characterization and Simulation Conference, 2007
Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 20... more Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 2007 SPE/EAGE Reservoir Characterization and Simulation Conference held in Abu Dhabi, UAE, 2831 October 2007. This paper was selected for presentation by an SPE ...
SPE Annual Technical Conference and Exhibition, 2006
Abstract Sequestration of carbon dioxide in geological formations is an alternative way to manage... more Abstract Sequestration of carbon dioxide in geological formations is an alternative way to manage the carbon emitted by combustion of fossil fuels. Results of an experimental and numerical modeling study aiming to investigate the important aspects of injection of CO 2 ...
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