Determining equations of two-phase flows through anisotropic porous media

Dmitriev, N. M.; Maksimov, V. M.

doi:10.1007/bf02698706

Cited by 13 publications

(14 citation statements)

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“…It was shown in [6] that the relation written in this form is not universal because symmetries of the tensors and coincide for this case. The most general relation, taking into account all possible properties of symmetry, was formulated in the same work and has the following form: (2) where are the components of a fourth rank tensor of relative phase permeability.…”

Section: Introductionmentioning

confidence: 94%

“…Further, we shall enumerate briefly the expressions for the components of the phase permeability ten sor which are stated in [6,7]. The symmetry of the tensors and is assumed to be the same.…”

Section: Forms Of a Tensor Of Absolute And Phase Permeabilitiesmentioning

confidence: 99%

“…Relation (2) was derived in the explicit form in [6][7][8] for different types of anisotropy. In particular, it has been shown that even in the case when the absolute permeability tensor is isotropic, the phase per meability tensor, generally speaking, may be anisotropic.…”

Section: Forms Of a Tensor Of Absolute And Phase Permeabilitiesmentioning

confidence: 99%

“…Two phase filtration flows in anisotropic media with different types of symmetry are considered in [6][7][8] using the group theory methods. The similar analysis of the representations of the hydrodynamical dis persion tensor is performed in numerous publications [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…The generalization of the relation (1) for the case of an anisotropic medium is typically [19] written down as However, many analytical [6,20] and numerical [13] studies as well as experiments [21,22], demonstrated that a relationship between the phase and absolute permeabilities is of a tensor nature. This circumstance was explained in [20] and in some later works [13,14,[22][23][24] by capillary effects that may be substantial, especially when small scale samples are considered.…”

Section: Introductionmentioning

confidence: 99%

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The study of relative phase-permeability functions for anisotropic media

Pergament

Tomin

2012

Math Models Comput Simul

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Properties of relative phase permeability functions for different characteristic configura tions of a medium with anisotropic filtration properties are studied using the numerical analytical method. The anisotropy may be related to fracturing created, e.g., as a result of a brittle rupture. Cor relations between tensors of the phase and absolute permeabilities are analyzed on the assumption of capillary equilibrium. Examples of relative phase permeability functions are obtained for media with orthotropic and monoclinic symmetry of filtration properties. The influence of the property of con nectivity on the found functions is shown, and the dependence of the position of the principal axes of the phase permeability tensor on saturation is also investigated. Thereby, the misalignment of the ten sors of the phase and absolute permeabilities is shown. The results qualitatively agree with the experi mental data.

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Section: Introductionmentioning

confidence: 94%

Section: Forms Of a Tensor Of Absolute And Phase Permeabilitiesmentioning

confidence: 99%

Section: Forms Of a Tensor Of Absolute And Phase Permeabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The study of relative phase-permeability functions for anisotropic media

Pergament

Tomin

2012

Math Models Comput Simul

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An adaptive multiscale approach for modeling two-phase flow in porous media including capillary pressure

2013

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[2] Many important applications in porous media require the large-scale simulation of complex physical processes. Due to the limitations of computational resources, huge model domains often have to be simulated on relatively coarse grids. However, depending on the application, a high spatial resolution may be necessary to capture important effects, for example due to small-scale heterogeneities. One solution strategy is multiscale modeling. The idea is to decrease the number of global degrees of freedom while preserving important fine-scale features. In this work, we present a multiscale approach for modeling two-phase flow in porous media, which is applicable in a wide range of flow regimes, but especially if the influence of capillary pressure is significant. In this case, many existing upscaling or multiscale techniques, originally developed and successfully used for advection-dominated systems, fail or are not able to yield sufficiently accurate results. We combine an adaptive grid method based on multipoint flux approximation with various local upscaling techniques. In particular, the numerical method has to be able to treat complex effective parameters like anisotropic phase permeabilities. A crucial point is the development of suitable grid-adaptation strategies to account correctly for important effects. The method is tested and proven to work for various examples including varying heterogeneous parameter fields and different flow regimes.

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Representation of the Functions of the Relative Phase Permeabilities for Anisotropic Porous Media

Dmitriev¹,

Dmitriev²,

Maksimov³

2005

Fluid Dyn

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The most general representation of the functions of the relative phase permeabilities for porous media is written explicitly. The relations proposed for the relative phase permeabilities generalize those obtained earlier for media with transversely-isotropic and orthotropic percolation properties [1,2] which can now be obtained as a particular case. A laboratory measurement technique for finding the percolation properties and determining the absolute and phase permeabilities for media with different types of anisotropy is discussed.

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Determining equations of two-phase flows through anisotropic porous media

Cited by 13 publications

References 1 publication

The study of relative phase-permeability functions for anisotropic media

The study of relative phase-permeability functions for anisotropic media

An adaptive multiscale approach for modeling two-phase flow in porous media including capillary pressure

Representation of the Functions of the Relative Phase Permeabilities for Anisotropic Porous Media

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