Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

Duijn, C.J. van; Eichel, Hartmut; Helmig, Rainer; Pop, Sorin

doi:10.1007/s11242-006-9089-9

Cited by 34 publications

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“…Trapping of air (or non-wetting fluid in general) is also observed at larger (macroscopic) scale, where the porous medium can be considered a continuum. This can be related to the presence of material heterogeneities, such as layers or coarse inclusions or lenses (having low air-entry pressure) surrounded with finer material (having higher air-entry pressure) [22,32,39,48,52]. In this case, during capillary dominated flow the fine material outside inclusions becomes saturated with water at an elevated value of the capillary pressure, for which the water saturation in coarse material is still low.…”

Section: Introductionmentioning

confidence: 99%

Simulations of air and water flow in a model dike during overflow experiments

et al. 2018

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Flow in flood dikes, earth dams, and embankments occurs in variably saturated conditions, with pores of the earth material filled partly with water and partly with air. In routine engineering analysis, the influence of pore air is neglected and the air pressure is assumed equal to atmospheric. In some circumstances, for example, during overtopping of the dike by water, the effect of pore air on water flow and stability of the structure can be important. These features cannot be captured with the commonly used Richards equation. In this paper, we analyze earlier experiments on the overtopping of a model dike made of fine sand. During the experiments, a significant amount of air was trapped near the outer slope of the dike, which later escaped through a fracture formed in wet sand. The observations were compared with numerical simulations using the Richards equation and the two-phase immiscible flow model. The deformation and damage of the dike were not modelled, but the initial evolution of the entrapped air pressure (before damage occurred) was in a good agreement with two-phase flow simulations.

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Section: Introductionmentioning

confidence: 99%

Simulations of air and water flow in a model dike during overflow experiments

et al. 2018

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“…However, most of them assume that the pressures in both fluid phases are continuous across the material interfaces, which makes them unsuitable for the description of the trapping effects. Non-wetting phase trapping was investigated in the framework of the homogenization theory by van Duijn et al (2002van Duijn et al ( , 2007 but their work was limited to one-dimensional layered medium and horizontal incompressible flow.…”

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Two-Phase Flow in Heterogeneous Porous Media with Non-Wetting Phase Trapping

2010

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This article presents a mathematical model describing flow of two fluid phases in a heterogeneous porous medium. The medium contains disconnected inclusions embedded in the background material. The background material is characterized by higher value of the non-wetting-phase entry pressure than the inclusions, which causes non-standard behavior of the medium at the macroscopic scale. During the displacement of the non-wetting fluid by the wetting one, some portions of the non-wetting fluid become trapped in the inclusions. On the other hand, if the medium is initially saturated with the wetting phase, it starts to drain only after the capillary pressure exceeds the entry pressure of the background material. These effects cannot be represented by standard upscaling approaches based on the assumption of local equilibrium of the capillary pressure. We propose a relevant modification of the upscaled model obtained by asymptotic homogenization. The modification concerns the form of flow equations and the calculation of the effective hydraulic functions. This approach is illustrated with two numerical examples concerning oil-water and CO 2 -brine flow, respectively.

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On the homogenization of the Buckley‐Leverett equation including trapping effects at the micro scale

Pop

Schweizer

2007

Proc Appl Math and Mech

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We consider a simplified, one dimensional model for two-phase (oil/water) flow in a porous medium. The medium consist of alternating homogeneous blocks separated by interfaces, where trapping effects may occur. Two effective models are derived in [2] and [7]. In this paper we show that the two models are equivalent.We consider a simplified, one dimensional model for two-phase (oil/water) flow in a porous medium. The medium consists of alternating homogeneous (coarse and fine) layers, having high and low permeability. These layers are separated by an interface, where oil can be trapped at the transition from a coarse to a fine layer. This situation is considered in both [2] and [7], where effective equations are derived by means of homogenization techniques. The model in [2] is derived explicitly by means of formal asymptotic expansion. In the absence of mathematically rigorous convergence results, the results are sustained by numerical experiments.[7] provides the structure of an effective model, and the results there are sustained by a rigorous mathematical analysis proving the weak convergence of the multi scale saturation and flux towards their effective counterparts. In this contribution we show that the effective models derived in the papers mentioned above are equivalent.We skip the modeling details; a thorough discussion can be found in [5]. Here we adopt the simplified context in [2], [3] and [7], and refer directly to the dimensionless model. We assume also that the dimensionless numbers occurring in the adimensionalization are scaled to 1. In particular, this means that the viscous forces are dominating, a situation called capillary limit in [3]. All these papers assume that the medium consists of periodically alternating thin homogeneous layers of fixed width ε > 0, separated by interfaces located at the points {εi : i ∈ Z}. For the ease of presentation, the only varying parameter is the absolute permeability K ε , this being either K + , or K − , depending on whether the location x is inside a coarse, respectively a fine layer:where K(y) = K + if y ∈ (2i − 1, 2i),

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Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

Cited by 34 publications

References 20 publications

Simulations of air and water flow in a model dike during overflow experiments

Simulations of air and water flow in a model dike during overflow experiments

Two-Phase Flow in Heterogeneous Porous Media with Non-Wetting Phase Trapping

On the homogenization of the Buckley‐Leverett equation including trapping effects at the micro scale

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