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Zhangxin Chen - One of the best experts on this subject based on the ideXlab platform.

  • pre darcy flow in porous media
    Water Resources Research, 2017
    Co-Authors: Morteza Dejam, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of Fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a Fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a Slightly Compressible Fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of Fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

  • effect of fracture pressure depletion regimes on the dual porosity shape factor for flow of Compressible Fluids in fractured porous media
    Advances in Water Resources, 2011
    Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    A precise value of the matrix-fracture transfer shape factor is essential for modeling Fluid flow in fractured porous media by a dual-porosity approach. The Slightly Compressible Fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a Compressible Fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a Compressible Fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a Compressible Fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a Compressible Fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of Slightly Compressible Fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of Compressible Fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of Fluid flow in fractured porous media.

  • effect of fracture pressure depletion regimes on the dual porosity shape factor for flow of Compressible Fluids in fractured porous media
    Advances in Water Resources, 2011
    Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    A precise value of the matrix-fracture transfer shape factor is essential for modeling Fluid flow in fractured porous media by a dual-porosity approach. The Slightly Compressible Fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a Compressible Fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a Compressible Fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a Compressible Fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a Compressible Fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of Slightly Compressible Fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of Compressible Fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of Fluid flow in fractured porous media.

Ehsan Ranjbar - One of the best experts on this subject based on the ideXlab platform.

  • effect of fracture pressure depletion regimes on the dual porosity shape factor for flow of Compressible Fluids in fractured porous media
    Advances in Water Resources, 2011
    Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    A precise value of the matrix-fracture transfer shape factor is essential for modeling Fluid flow in fractured porous media by a dual-porosity approach. The Slightly Compressible Fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a Compressible Fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a Compressible Fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a Compressible Fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a Compressible Fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of Slightly Compressible Fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of Compressible Fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of Fluid flow in fractured porous media.

  • effect of fracture pressure depletion regimes on the dual porosity shape factor for flow of Compressible Fluids in fractured porous media
    Advances in Water Resources, 2011
    Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    A precise value of the matrix-fracture transfer shape factor is essential for modeling Fluid flow in fractured porous media by a dual-porosity approach. The Slightly Compressible Fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a Compressible Fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a Compressible Fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a Compressible Fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a Compressible Fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of Slightly Compressible Fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of Compressible Fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of Fluid flow in fractured porous media.

Hassan Hassanzadeh - One of the best experts on this subject based on the ideXlab platform.

  • pre darcy flow in porous media
    Water Resources Research, 2017
    Co-Authors: Morteza Dejam, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of Fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a Fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre-Darcy flow. In this paper, the unsteady flow regimes of a Slightly Compressible Fluid under the linear and radial pre-Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre-Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of Fluid flow in low-permeability media such as shale and tight formations, where pre-Darcy is the dominant flow regime.

  • effect of fracture pressure depletion regimes on the dual porosity shape factor for flow of Compressible Fluids in fractured porous media
    Advances in Water Resources, 2011
    Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    A precise value of the matrix-fracture transfer shape factor is essential for modeling Fluid flow in fractured porous media by a dual-porosity approach. The Slightly Compressible Fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a Compressible Fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a Compressible Fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a Compressible Fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a Compressible Fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of Slightly Compressible Fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of Compressible Fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of Fluid flow in fractured porous media.

  • effect of fracture pressure depletion regimes on the dual porosity shape factor for flow of Compressible Fluids in fractured porous media
    Advances in Water Resources, 2011
    Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    A precise value of the matrix-fracture transfer shape factor is essential for modeling Fluid flow in fractured porous media by a dual-porosity approach. The Slightly Compressible Fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a Compressible Fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a Compressible Fluid in dual-porosity media. Adv Water Res 2011;34(5):627–39. doi:10.1016/j.advwatres.2011.02.012]. However, for a Compressible Fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a Compressible Fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of Slightly Compressible Fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of Compressible Fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of Fluid flow in fractured porous media.

P M Adler - One of the best experts on this subject based on the ideXlab platform.

  • barometric pumping of a fractured porous medium
    Geophysical Research Letters, 2014
    Co-Authors: V V Mourzenko, Clement Varloteaux, S Guillon, J F Thovert, Eric Pili, P M Adler
    Abstract:

    Barometric pumping plays a crucial role in the release of trace gases from fractured porous media to the atmosphere, and it requires a rigorous and complete modeling in order to go beyond the approximate schemes available in the literature. Therefore, a coupled set of convection and convection-diffusion equations for a Slightly Compressible Fluid in unsteady conditions should be solved. The numerical methodology is presented, and it is applied to conditions close to the ones of the Roselend Natural Laboratory (France). The precision of the code is assessed and the mechanism of barometric pumping is explained. The usual schematization by simple vertical fractures is shown to be only qualitative. Finally, barometric pumping is shown to be efficient in a narrow range of parameter values; its efficiency is a decreasing function of the matrix porosity and of the fracture density.

Salah Naili - One of the best experts on this subject based on the ideXlab platform.

  • homogenization of the Fluid structure interaction in acoustics of porous media perfused by viscous Fluid
    Zeitschrift für Angewandte Mathematik und Physik, 2020
    Co-Authors: Eduard Rohan, Salah Naili
    Abstract:

    This paper aims to clarify the homogenization results of the Fluid–structure interaction in porous structures under the quasi-static and dynamic loading regimes. In the latter case, the acoustic fluctuations yield naturally a linear model which can be introduced in the configuration deformed as the consequence of the steady permanent flow. We consider a Newtonian Slightly Compressible Fluid under the barotropic acoustic approximation. In contrast with usual simplifications, the advection phenomenon of the Navier–Stokes equations is accounted for. The homogenization results are based on the periodic unfolding method combined with the asymptotic expansion technique which provide a straight procedure leading the local problems for corrector functions yielding the effective model parameters and the macroscopic model. We show that the local problems for the solid and Fluid parts are decoupled even in the dynamic interactions including the wall shear stress on the periodic interfaces. The dynamic permeability depends on the Fluid flow properties including the advection effects associated with an assumed stationary perfusion of the porous structure.

  • three scale model of single bone osteon modelled as double porous Fluid saturated body study of influence of micro meso structure
    Applied and Computational Mechanics, 2014
    Co-Authors: Jana Turjanicova, Eduard Rohan, Salah Naili
    Abstract:

    This paper deals with the multiscale description of a single osteon of cortical bones. The cortical bone tissue is modeled as a double-porous medium decomposed into the solid matrix and the Fluid saturated canals. The resulting homogenized model describes deformation of such medium in response to a static loading by external forces and to an injection of Slightly Compressible Fluid. Three numerical examples are presented, showing the influence of selected lower-scales geometrical features on the macroscopic body behavior.

  • Three-scale model of single bone osteon modelled as double-porous Fluid saturated body: Study of influence of micro/meso-structure
    Applied and Computational Mechanics, 2014
    Co-Authors: Jana Turjanicova, Eduard Rohan, Salah Naili
    Abstract:

    This paper deals with the multiscale description of a single osteon of cortical bones. The cortical bone tissue is modeled as a double-porous medium decomposed into the solid matrix and the Fluid saturated canals. The resulting homogenized model describes deformation of such medium in response to a static loading by external forces and to an injection of Slightly Compressible Fluid. Three numerical examples are presented, showing the influence of selected lower-scales geometrical features on the macroscopic body behavior.