Effective Relative Permeabilities and Capillary Pressure for 1D Heterogeneous Media

Dale, Magnar; Ekrann, S.; Mykkeltveit, Johannes; Virnovsky, G.A.

doi:10.3997/2214-4609.201411163

Cited by 26 publications

(32 citation statements)

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“…First, for a very small Reynolds number of 2.46 × 10 −5 , the saturation profiles (Fig. 4) show similar behavior as those reported in the literature (Chang and Yortsos 1989;Dale et al 1997) for cases in the Darcy regime. Indeed, a downward peak is observed when liquid flows from a more permeable zone to a less permeable one (ηω interface), and the contrary happens when the order is reversed (ωη interface).…”

Section: One-dimensional Configurationssupporting

confidence: 81%

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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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Section: One-dimensional Configurationssupporting

confidence: 81%

“…Here, in Eq. 39 inspired by the definition proposed by Chang and Yortsos (1989) or Dale et al (1997), higher Ca corresponds to the dominance of capillary effects. While cases with Re = 2.46 × 10 −3 can be considered as an intermediate case, for the two higher Re, capillary effects are definitely negligible (Table 2).…”

Section: One-dimensional Configurationsmentioning

confidence: 99%

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

2009

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“…Steady-state methods may still be used, but are more difficult to apply. For example Dale et al (1997) consider steady-state upscaling for 1D heterogeneous media, with a range of viscous and capillary forces. Also, an intermediate viscous-capillary steadystate method was developed by Stephen and Pickup (2000), which can capture capillary trapping more accurately in a flood with an intermediate force balance.…”

Section: Intermediate Balance Of Forcesmentioning

confidence: 99%

Multi-Stage Upscaling: Selection of Suitable Methods

Pickup

Stephen

et al. 2005

Transp Porous Med

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Reservoirs are often composed of an assortment of rock types giving rise to permeability heterogeneities at a variety of length-scales. To predict fluid flow at the fullfield scale, it is necessary to be aware of these different types of heterogeneity, to recognise which are likely to have important effects on fluid flow, and to capture them by upscaling. In fact, we may require a series of stages of upscaling to go from small-scales (mm or cm) to a full-field model. When there are two (or more) phases present, we also need to know how these heterogeneities interact with fluid forces (capillary, viscous and gravity). We discuss how these effects may be taken into account by upscaling. This study focusses on the effects of steady-state upscaling for viscous-dominated floods and tests carried out on a range of 2D models are described. Upscaling errors are shown to be reduced slightly by the increase in numerical dispersion at the coarse scale. We select a combination of three different upscaling methods, and apply this approach to a model of a North Sea oil reservoir in a deep marine environment. Six different genetic units (rock types) were identified, including channel sandstone and inter-bedded sandstone and mudstone. These units were modelled using different approaches, depending on the nature of the heterogeneities. Our results show that the importance of small-scale heterogeneity depends on the large-scale distribution of the rock types. Upscaling may not be worthwhile in sparsely distributed genetic units. However, it is important in the dominant rock type, especially if there is good connectivity through the unit between the injector wells (or aquifer) and the producer wells.

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“…Any single-phase upscaling technique can then be used to calculate the upscaled relative permeability and capillary pressure curves (Dale et al 1997;Ekrann and Aasen 2000). Steady-state approaches are based on the assumption that either capillary (Capillary limit, CL) or viscous (Viscous limit, VL) forces control the distribution of fluids within the averaging volume (such as a coarse grid-block) (Smith 1991;Lemouzy et al 1993;Dale et al 1997;Ekrann and Aasen 2000;Virnovsky et al 2004). These methods are simple and reproducible and, in principle, make upscaling from the smallest lengthscale feasible .…”

Section: Introductionmentioning

confidence: 99%

New criteria for the validity of steady-state upscaling

Jonoud

Jackson

2007

Transp Porous Med

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We present new dimensionless criteria to determine the validity of steadystate upscaling techniques in the limit that capillary (capillary limit, CL) or viscous (viscous limit, VL) forces dominate flow in a simple, layered geological system. We begin by identifying a suit of dimensionless groups which characterize the balance of capillary and viscous forces, then use numerical experiments to determine empirically the threshold values of these dimensionless groups for which each upscaling method is valid. Our criteria capture the effects of capillary trapping and are valid regardless of fluid mobility, wettability, or end-point saturation. They can be used to determine the reservoir conditions for which each upscaling method is valid. Previous studies have used a single dimensionless number to characterize the balance of forces, so have failed to properly identify the range of validity. We apply our new criteria to explain cases when the upscaling methods have been observed to do unexpectedly well or poorly. We also demonstrate that the CL method can be valid for a wider range of reservoir conditions than previously thought, particularly in mixed-and oil-wet systems where capillary trapping is minimal.

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Effective Relative Permeabilities and Capillary Pressure for 1D Heterogeneous Media

Cited by 26 publications

References 0 publications

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

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

Multi-Stage Upscaling: Selection of Suitable Methods

New criteria for the validity of steady-state upscaling

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