A non-equilibrium model of a porous medium saturated with immiscible fluids

Kondaurov, V. I.

doi:10.1016/j.jappmathmech.2009.03.004

Cited by 12 publications

(12 citation statements)

References 11 publications

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“…In the framework of Kondaurov's formalism [23], a non-equilibrium porous medium saturated by two fluids is described by a dependence of the thermodynamical potential on a number of constitutive parameters. Using the relations which guarantee a thermodynamical model consistency, it is possible to calculate the capillary pressure function and the right-hand side of the kinetic equation.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we introduce the adimensionalized non-equilibrium Kondaurov flow model proposed in [23] and then developed in [24]. More recently it was discussed in [25].…”

Section: Adimensionalized Non-equilibrium Kondaurov Modelmentioning

confidence: 99%

“…In this paper we study an immiscible non-equilibrium two-phase flow in double porosity media in the framework of the thermodynamically consistent Kondaurov model [23,24] which is, in fact, an integrodifferential one due to the fact that the mobility functions and the capillary pressure depend on Kondaurov's non-equilibrium parameter which satisfies a kinetic equation with respect to the real saturation (see Section 2 below). The detailed comparison of the Kondaurov model and Barenblatt's and Hassanizadeh's non-equilibrium flow models is done in [24,25].…”

Section: Introductionmentioning

confidence: 99%

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New non-equilibrium matrix imbibition equation for Kondaurov's double porosity model

Konyukhov,

Pankratov

2016

Preprint

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The paper deals with the global Kondaurov double porosity model describing a non-equilibrium two-phase immiscible flow in fractured-porous reservoirs when non-equilibrium phenomena occur in the matrix blocks, only. It is shown that the homogenized model can be represented as usual equations of two-phase incompressible immiscible flow, except for the addition of two source terms calculated by a solution to a local problem which is a boundary value problem for a non-equilibrium imbibition equation given in terms of the real saturation and a non-equilibrium parameter.

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Section: Discussionmentioning

confidence: 99%

“…In this section we introduce the adimensionalized non-equilibrium Kondaurov flow model proposed in [23] and then developed in [24]. More recently it was discussed in [25].…”

Section: Adimensionalized Non-equilibrium Kondaurov Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New non-equilibrium matrix imbibition equation for Kondaurov's double porosity model

Konyukhov,

Pankratov

2016

Preprint

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“…In the case of the isothermal flow of incompressible fluids in the porous media with solid skeleton, the free energy of such medium is determined by the surface energy of the phase contact and is a function of the saturation and this additional parameter. For the description of the flow in such media the thermodynamically consistent model proposed by Kondaurov in [4] can be applied. We consider the application of this approach for the description of the non-equilibrium flow in the framework of the mesoscale model.…”

Section: Introductionmentioning

confidence: 99%

The homogenized Kondaurov type non-equilibrium model of two-phase flow in multiscale non-homogeneous media

2019

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The goal of the paper is to derive a homogenized model of the incompressible two-phase flow in multiscale porous media made of disjoint non-homogeneous porous blocks surrounded by highly permeable connected porous subspace which is regarded as a fracture system. The nonhomogeneity of the porous blocks means that they contain the inclusions with contrast properties. The upscaling process is done in two steps. At the first step a Kondaurov type non-equilibrium flow model on the mesoscale level is derived. This model takes into account the capillary non-equilibrium phenomena of the flow in the blocks and fractures. Upscaling the mesoscale model, we obtain the desired macroscopic (homogenized) Kondaurovs type model. The upscaling process at the second step is justified by the numerical simulation.

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“…In our opinion, the kinetics of the transition is related not to nucleation (the formation and growth of nuclei of the new phase), but to another factor, namely, the finite time for the establishment of capillary equilibrium. 14,15 The redistribution of fluids in pore channels of different diameter in an elementary volume under the action of capillary forces is a considerably slower process than nucleation.…”

Section: Introductionmentioning

confidence: 99%