Simultaneous imbibition–heat convection process in a non-Darcian porous medium

Sánchez, Mario; Luna, E. Reyes de; Medina, A.; Méndez, F.

doi:10.1016/j.jcis.2005.03.016

Cited by 4 publications

(7 citation statements)

References 9 publications

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“…Therefore, for the estimation of the convective time scale, we use directly a comparison or an energy balance between the transported thermal energy by the motion of the liquid and the accumulation energy term. A similar argument was used in [12]. In the present case, the comparison yields a direct relationship between the first and second term of the left-hand side of Eq.…”

Section: Theoretical Modelmentioning

confidence: 67%

“…We assume that the temperature of the front is maintained at temperature T 0 . This approximation was proved in [12] based on the fact of that the characteristic imbibitions time is larger than the corresponding thermal time. The origin of coordinates is located at the base of the sheet.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…He proved that oil production by imbibition can be driven by injecting a hot water vapor. Other interesting study of combined effects was considered by Sánchez et al [12] to analyze the convective heat transfer process conducted by the imbibitions in a non-Darcian porous medium.…”

Section: Introductionmentioning

confidence: 99%

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Thermal dispersion driven by the spontaneous imbibition process

Bautista¹,

Méndez

Bautista³

2010

Applied Mathematical Modelling

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a b s t r a c tIn this work, we have theoretically analyzed the thermal dispersion process under the influence of the spontaneous imbibition of a liquid trapped in a capillary element, considering the presence of a uniform temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature T 0 and pressure P 0 . Suddenly, the lower part of the porous medium touches a liquid reservoir at temperature T l and pressure P 0 . This contact between both phases, in turn causes spontaneously the imbibition process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and Nusselt numbers. The above results are shown by taking into account the influence of three dimensionless parameters: the ratio of the characteristic thermal time to the characteristic imbibition time, b, the ratio of the hydrostatic head of the imbibed liquid to the characteristic pressure difference for the imbibition front, a, and the ratio of the dispersive thermal diffusivity to the effective thermal diffusivity of the medium, X. The predictions show that temperature profiles and the heat transfer process are strongly dependent on thermal dispersion effects, indicating a clear deviation in comparison with the case of X = 0 that represents the absence of the thermal dispersion.

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Section: Theoretical Modelmentioning

confidence: 67%

Section: Theoretical Modelmentioning

confidence: 99%

See 1 more Smart Citation

Thermal dispersion driven by the spontaneous imbibition process

Bautista¹,

Méndez

Bautista³

2010

Applied Mathematical Modelling

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“…He proved that the oil production by the wicking process can be driven by injecting a hot water vapor. Other interesting study of combined effects was considered by Sánchez et al [4] to analyze the convective heat transfer process conducted by the imbibition in a non-Darcian porous medium.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Wicking-Convection Heat Transfer Process with Non-Newtonian Power-Law Fluid

Bautista¹,

Méndez

Bautista³

2010

DDF

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In this work, we have theoretically analyzed the heat convection process in a porous medium under the influence of spontaneous wicking of a non-Newtonian power-law fluid, trapped in a capillary element, considering the presence of a temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature and pressure . Suddenly the lower part of the porous medium touches a reservoir with a non-Newtonian fluid with temperature and pressure . This contact between both phases, in turn causes spontaneously the wicking process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibitions front as well as the dimensionless temperature profiles and Nusselt number. The above results are shown by considering the physical influence of two nondimensional parameters: the ratio of the characteristic thermal time to the characteristic wicking time, , the ratio of the hydrostatic head of the imbibed fluid to the characteristic pressure difference between the wicking front and the dry zone of the porous medium, , and the power-law index, n, for the non-Newtonian fluid. The predictions show that the wicking and heat transfer process are strongly dependent on the above nondimensional parameters, indicating a clear deviation in comparison with and n = 1, that represents the classical Lucas-Washburn solution.

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“…So far, very few studies addressing this issue have been reported in contrast to inertial one-phase flow that has concentrated more significant efforts from both theoretical and numerical points of view (Mei and Auriault 1991;Whitaker 1996;Kim and Park 1999;Fourar et al 2005;Mazaheri et al 2005;Khashan et al 2006). Moreover, in most existing numerical investigations, special cases such as steady-state flow without capillary pressure in a cylindrical configuration (Jamiolahmady et al 2006) or 1D frontal displacement based on Muskat's model assuming piston-like displacement coupled with heat transfer (Sanchez et al 2005) are considered. In this study, two-phase, incompressible, non-stationary flow in a non-deformable heterogeneous porous media is considered with Reynolds numbers high enough to justify the use of a model including inertial terms.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Two-Phase Inertial Flow in Heterogeneous Porous Media

2009

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In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a finite volume formulation, although for clarity, results are presented in 1D and 2D configurations only. Since a formalized theoretical model confirmed by experimental data is still lacking, our study is based on the widely used generalized Darcy-Forchheimer model. First, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the Buckley-Leverett model extended to take into account inertia. Second, we highlight the importance of inertial terms on the evolution of saturation fronts as a function of a suitable Reynolds number. Saturation fields are shown to have a structure markedly different from the classical case without inertia, especially for heterogeneous media, thereby, emphasizing the necessity of a more complete model than the classical generalized Darcy's one when inertial effects are not negligible.

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Simultaneous imbibition–heat convection process in a non-Darcian porous medium

Cited by 4 publications

References 9 publications

Thermal dispersion driven by the spontaneous imbibition process

Thermal dispersion driven by the spontaneous imbibition process

Simultaneous Wicking-Convection Heat Transfer Process with Non-Newtonian Power-Law Fluid

Numerical Simulation of Two-Phase Inertial Flow in Heterogeneous Porous Media

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