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Papers by kokou dadzie

arXiv (Cornell University), Sep 9, 2019

Classical Navier-Stokes equations fail to describe some flows in both the compressible and incomp... more Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes fail.

Physical review, Sep 29, 2021

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

arXiv (Cornell University), Jul 17, 2009

We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model.... more We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model. In reference [1], a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a massdensity diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves", rather than the pressure waves of the continuum regime.

arXiv (Cornell University), Jun 30, 2021

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

Micromachines

Continuum description of flows in micro- and nano-systems requires ad hoc addition of effects suc... more Continuum description of flows in micro- and nano-systems requires ad hoc addition of effects such as slip at walls, surface diffusion, Knudsen diffusion and others. While all these effects are derived from various phenomenological formulations, a sound theoretical ground unifying these effects and observations is still lacking. In this paper, adopting the definition and existence of various type of flow velocities beyond that of the standard mass velocity, we suggest derivation of model boundary conditions that may systematically justify various diffusion process occurring in micro- and nano-flows where the classical continuum model breaks down. Using these boundary conditions in conjunction with the classical continuum flow equations we present a unified derivation of various expressions of mass flow rates and flow profiles in micro- and nano-channels that fit experimental data and provide new insights into these flow profiles. The methodology is consistent with recasting the Navi...

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as non-negativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

Shock Waves, 2020

Classical Navier–Stokes equations fail to predict shock wave profiles accurately. In this paper, ... more Classical Navier–Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier–Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the recast Navier–Stokes equations display physics not initially included in the classical form of the equations. We then analyze the stationary shock structure problem in a monatomic gas by solving both the classical and the recast Navier–Stokes equations numerically using a finite difference global solution (FDGS) scheme. The numerical results are presented for different upstream Mach numbers ranging from supersonic to hypersonic flows. We found that the recast Navier–Stokes equations show better agreement with the experimentally measured density and reciprocal shock thickness profiles.

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019, 2020

Classical Navier-Stokes equations are known to be inadequate in describing some flows in both the... more Classical Navier-Stokes equations are known to be inadequate in describing some flows in both the compressible and incompressible configurations. A ubiquitous simple example of the failure is the description of shock wave structure. A new compressible hydrodynamic set of equations is here developed using a velocity transformation technique similar in nature to Lorentz transformation and termed "re-casted Navier-Stokes equations". We found that results with the re-casted Navier-Stokes equations fit better the experimental data.

Advances in Fluid Dynamics with emphasis on Multiphase and Complex Flow, 2021

Over the past two decades, several researchers have presented experimental data from pressure-dri... more Over the past two decades, several researchers have presented experimental data from pressure-driven water flow through carbon nanotubes quoting mass flow rates which are four to five orders of magnitude higher than those predicted by the Navier-Stokes equations with no-slip condition. The current work examines the development of an OpenFOAM solver for creeping flows that better accounts for some micro-and nano-scale diffusion processes. It is based on the observation that a change of velocity variable within the classical Navier-Stokes equations leads to a form of flow model with additional diffusive terms which become apparent at the micro-and nano-scale. Numerical simulations from the new solver compare well with associated analytical solutions that match the experimental flow enhancement observed in cylindrical tubes. This lays the foundations for further investigations of liquid flows in more complex nano-sized geometries, such as those obtained from pore-scale imaging.

Journal of Physics Communications, 2019

Over the past two decades, several researchers have presented experimental data from pressure-dri... more Over the past two decades, several researchers have presented experimental data from pressure-driven liquid flows through nanotubes. They quote flow velocities which are four to five orders of magnitude higher than those predicted by the classical theory. Thus far, attempts to explain these enhanced mass flow rates at the nanoscale have focused mainly on introducing wall-slip boundary conditions on the fluid mass velocity. In this paper, we present a different theory. A change of variable on the velocity field within the classical Navier–Stokes equations is adopted to transform the equations into physically different equations. The resulting equations, termed re-casted Navier–Stokes equations, contain additional diffusion terms whose expressions depend upon the driving mechanism. The new equations are then solved for the pressure driven flow in a long nano-channel. Analogous to previous studies of gas flows in micro- and nano-channels, a perturbation expansion in the aspect ratio al...

This article deals with the calculations of the temperature jump at the wall for gas flows in the... more This article deals with the calculations of the temperature jump at the wall for gas flows in the slip regime. The analytical calculations are based on kinetic boundary conditions developed especially for polyatomic molecules. When compared to an expression previously obtained for unstructured molecules, the polyatomic molecule temperature jump reveals supplementary terms of bulk viscosity type due to the internal mode excitation. These terms may be important in high speed flows or in gas flows displaying significant relative density variation at the wall.

Physical Review E, 2021

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

Journal of Natural Gas Science and Engineering, 2017

The oil and gas reservoir pressure response to the changes in the fluid production rate has been ... more The oil and gas reservoir pressure response to the changes in the fluid production rate has been traditionally used to estimate the reservoir properties. Numerous analytical and numerical models have been developed to describe the transient pressure in and around a production well so as to interpret the in-well pressure measurements. Pressure Transient Analysis (PTA) is routinely used by Production and Reservoir Engineers at various stages in a wells life; initially for reservoir characterisation and, later, for well performance monitoring and (wider) reservoir surveillance. The recent application of high precision, downhole, temperature sensors has resulted in PTA being complemented by Temperature Transient Analysis (TTA). Recent TTA research has shown that comprehensive information on the state of the near-wellbore zone and fluid flow rates and composition can potentially be derived from such measurements. However, the derivation of useable TTA solutions describing the mass and energy transfer in porous media is challenging since it is necessary to simultaneously account for both the thermodynamic and the transient transfer effects. This paper reports a step in the development of a novel Temperature Transient Analysis (TTA) workflow. This is the first publication, to our knowledge, where the gas production TTA solutions, properly accounting for the compressible gas nature, are presented and discussed. A numerical model for determining sandface tran

arXiv (Cornell University), Feb 14, 2012

In reference [1], a kinetic equation for gas flows was proposed that leads to a set of four macro... more In reference [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation arises due to local spatial random molecular behavior, which has been described as a volume or mass diffusion process. In this present paper, we describe a procedure to construct a Gibbs-type equation and a second-law associated with these kinetic and continuum models. We also point out the close link between the kinetic equation in [1] and that proposed previously by Klimontovich, and we discuss some of their compatibilities with classical mechanical principles. Finally, a dimensional analysis highlights the nature of volume/mass diffusion: it is a non-conventional diffusive process, with some similarities to the 'ghost effect', which cannot be obtained from a fluid mechanical derivation that neglects non-local-equilibrium structures, as the conventional Navier-Stokes-Fourier model does.

Journal of Physics Communications, 2019

Classical Navier–Stokes equations fail to describe some flows in both the compressible and incomp... more Classical Navier–Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier–Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier–Stokes equations. The new models unlike the conventional Navier–Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering...

AIP Conference Proceedings, 2005

AIP Conference Proceedings, 2008

In this paper we discuss the mass-density of gas media as represented in kinetic theory. It is ar... more In this paper we discuss the mass-density of gas media as represented in kinetic theory. It is argued that conventional representations of this variable in gas kinetic theory contradict a macroscopic field variable and thermodynamic property in classical thermodynamics. We show that in cases where mass-density variations exist throughout the medium, introducing the mass-density as a macroscopic field variable leads to a restructuring of the diffusive/convective fluxes and implies some modifications to the hydrodynamic equations describing gas flows and heat transfer. As an illustration, we consider the prediction of mass-density profiles in a simple heat conduction problem between parallel plates maintained at different temperatures.

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels, 2008

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equa... more In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscos...

AIP Conference Proceedings, 2011

In this paper we investigate the problem of isothermal pressure driven gas flow through a channel... more In this paper we investigate the problem of isothermal pressure driven gas flow through a channel using a continuum equations set with a mass diffusion correction to the mass-density equation. The additional term is invoked as a way of releasing the local-equilibrium assumption in the presence of strong local gradients. Then the dissipative mass flux is proportional to local density/pressure gradient which is constant in a cross section and results in a correction to the velocity profile. Subsequently, better mass-flow rate predictions are obtained than those obtained using Maxwell-type first order slip boundary conditions. Results indicate that the mass diffusion correction captures the "Knudsen paradox" and change in curvature of the streamwise pressure profile without the need for setting higher order slip boundary conditions.

arXiv (Cornell University), Sep 9, 2019

Classical Navier-Stokes equations fail to describe some flows in both the compressible and incomp... more Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes fail.

Physical review, Sep 29, 2021

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

arXiv (Cornell University), Jul 17, 2009

We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model.... more We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model. In reference [1], a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a massdensity diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves", rather than the pressure waves of the continuum regime.

arXiv (Cornell University), Jun 30, 2021

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

Micromachines

Continuum description of flows in micro- and nano-systems requires ad hoc addition of effects suc... more Continuum description of flows in micro- and nano-systems requires ad hoc addition of effects such as slip at walls, surface diffusion, Knudsen diffusion and others. While all these effects are derived from various phenomenological formulations, a sound theoretical ground unifying these effects and observations is still lacking. In this paper, adopting the definition and existence of various type of flow velocities beyond that of the standard mass velocity, we suggest derivation of model boundary conditions that may systematically justify various diffusion process occurring in micro- and nano-flows where the classical continuum model breaks down. Using these boundary conditions in conjunction with the classical continuum flow equations we present a unified derivation of various expressions of mass flow rates and flow profiles in micro- and nano-channels that fit experimental data and provide new insights into these flow profiles. The methodology is consistent with recasting the Navi...

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as non-negativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

Shock Waves, 2020

Classical Navier–Stokes equations fail to predict shock wave profiles accurately. In this paper, ... more Classical Navier–Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier–Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the recast Navier–Stokes equations display physics not initially included in the classical form of the equations. We then analyze the stationary shock structure problem in a monatomic gas by solving both the classical and the recast Navier–Stokes equations numerically using a finite difference global solution (FDGS) scheme. The numerical results are presented for different upstream Mach numbers ranging from supersonic to hypersonic flows. We found that the recast Navier–Stokes equations show better agreement with the experimentally measured density and reciprocal shock thickness profiles.

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019, 2020

Classical Navier-Stokes equations are known to be inadequate in describing some flows in both the... more Classical Navier-Stokes equations are known to be inadequate in describing some flows in both the compressible and incompressible configurations. A ubiquitous simple example of the failure is the description of shock wave structure. A new compressible hydrodynamic set of equations is here developed using a velocity transformation technique similar in nature to Lorentz transformation and termed "re-casted Navier-Stokes equations". We found that results with the re-casted Navier-Stokes equations fit better the experimental data.

Advances in Fluid Dynamics with emphasis on Multiphase and Complex Flow, 2021

Over the past two decades, several researchers have presented experimental data from pressure-dri... more Over the past two decades, several researchers have presented experimental data from pressure-driven water flow through carbon nanotubes quoting mass flow rates which are four to five orders of magnitude higher than those predicted by the Navier-Stokes equations with no-slip condition. The current work examines the development of an OpenFOAM solver for creeping flows that better accounts for some micro-and nano-scale diffusion processes. It is based on the observation that a change of velocity variable within the classical Navier-Stokes equations leads to a form of flow model with additional diffusive terms which become apparent at the micro-and nano-scale. Numerical simulations from the new solver compare well with associated analytical solutions that match the experimental flow enhancement observed in cylindrical tubes. This lays the foundations for further investigations of liquid flows in more complex nano-sized geometries, such as those obtained from pore-scale imaging.

Journal of Physics Communications, 2019

Over the past two decades, several researchers have presented experimental data from pressure-dri... more Over the past two decades, several researchers have presented experimental data from pressure-driven liquid flows through nanotubes. They quote flow velocities which are four to five orders of magnitude higher than those predicted by the classical theory. Thus far, attempts to explain these enhanced mass flow rates at the nanoscale have focused mainly on introducing wall-slip boundary conditions on the fluid mass velocity. In this paper, we present a different theory. A change of variable on the velocity field within the classical Navier–Stokes equations is adopted to transform the equations into physically different equations. The resulting equations, termed re-casted Navier–Stokes equations, contain additional diffusion terms whose expressions depend upon the driving mechanism. The new equations are then solved for the pressure driven flow in a long nano-channel. Analogous to previous studies of gas flows in micro- and nano-channels, a perturbation expansion in the aspect ratio al...

This article deals with the calculations of the temperature jump at the wall for gas flows in the... more This article deals with the calculations of the temperature jump at the wall for gas flows in the slip regime. The analytical calculations are based on kinetic boundary conditions developed especially for polyatomic molecules. When compared to an expression previously obtained for unstructured molecules, the polyatomic molecule temperature jump reveals supplementary terms of bulk viscosity type due to the internal mode excitation. These terms may be important in high speed flows or in gas flows displaying significant relative density variation at the wall.

Physical Review E, 2021

We present a full investigation into shock wave profile description using hydrodynamics models. W... more We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

Journal of Natural Gas Science and Engineering, 2017

The oil and gas reservoir pressure response to the changes in the fluid production rate has been ... more The oil and gas reservoir pressure response to the changes in the fluid production rate has been traditionally used to estimate the reservoir properties. Numerous analytical and numerical models have been developed to describe the transient pressure in and around a production well so as to interpret the in-well pressure measurements. Pressure Transient Analysis (PTA) is routinely used by Production and Reservoir Engineers at various stages in a wells life; initially for reservoir characterisation and, later, for well performance monitoring and (wider) reservoir surveillance. The recent application of high precision, downhole, temperature sensors has resulted in PTA being complemented by Temperature Transient Analysis (TTA). Recent TTA research has shown that comprehensive information on the state of the near-wellbore zone and fluid flow rates and composition can potentially be derived from such measurements. However, the derivation of useable TTA solutions describing the mass and energy transfer in porous media is challenging since it is necessary to simultaneously account for both the thermodynamic and the transient transfer effects. This paper reports a step in the development of a novel Temperature Transient Analysis (TTA) workflow. This is the first publication, to our knowledge, where the gas production TTA solutions, properly accounting for the compressible gas nature, are presented and discussed. A numerical model for determining sandface tran

arXiv (Cornell University), Feb 14, 2012

In reference [1], a kinetic equation for gas flows was proposed that leads to a set of four macro... more In reference [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation arises due to local spatial random molecular behavior, which has been described as a volume or mass diffusion process. In this present paper, we describe a procedure to construct a Gibbs-type equation and a second-law associated with these kinetic and continuum models. We also point out the close link between the kinetic equation in [1] and that proposed previously by Klimontovich, and we discuss some of their compatibilities with classical mechanical principles. Finally, a dimensional analysis highlights the nature of volume/mass diffusion: it is a non-conventional diffusive process, with some similarities to the 'ghost effect', which cannot be obtained from a fluid mechanical derivation that neglects non-local-equilibrium structures, as the conventional Navier-Stokes-Fourier model does.

Journal of Physics Communications, 2019

Classical Navier–Stokes equations fail to describe some flows in both the compressible and incomp... more Classical Navier–Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier–Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier–Stokes equations. The new models unlike the conventional Navier–Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering...

AIP Conference Proceedings, 2005

AIP Conference Proceedings, 2008

In this paper we discuss the mass-density of gas media as represented in kinetic theory. It is ar... more In this paper we discuss the mass-density of gas media as represented in kinetic theory. It is argued that conventional representations of this variable in gas kinetic theory contradict a macroscopic field variable and thermodynamic property in classical thermodynamics. We show that in cases where mass-density variations exist throughout the medium, introducing the mass-density as a macroscopic field variable leads to a restructuring of the diffusive/convective fluxes and implies some modifications to the hydrodynamic equations describing gas flows and heat transfer. As an illustration, we consider the prediction of mass-density profiles in a simple heat conduction problem between parallel plates maintained at different temperatures.

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels, 2008

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equa... more In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscos...

AIP Conference Proceedings, 2011

In this paper we investigate the problem of isothermal pressure driven gas flow through a channel... more In this paper we investigate the problem of isothermal pressure driven gas flow through a channel using a continuum equations set with a mass diffusion correction to the mass-density equation. The additional term is invoked as a way of releasing the local-equilibrium assumption in the presence of strong local gradients. Then the dissipative mass flux is proportional to local density/pressure gradient which is constant in a cross section and results in a correction to the velocity profile. Subsequently, better mass-flow rate predictions are obtained than those obtained using Maxwell-type first order slip boundary conditions. Results indicate that the mass diffusion correction captures the "Knudsen paradox" and change in curvature of the streamwise pressure profile without the need for setting higher order slip boundary conditions.