Dynamics of the Water–Oil Front for Two-Phase, Immiscible Flow in Heterogeneous Porous Media. 2 – Isotropic Media

Nœtinger, B.; Artus, Vincent; Ricard, Ludovic

doi:10.1023/b:tipm.0000026086.75908.ca

Cited by 26 publications

(31 citation statements)

References 27 publications

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“…Artus et al (2004) show that, for M f < 1 (stable flood), fluctuations in the front due to heterogeneities become stationary, whereas if M f > 1 (unstable flood), perturbations in the front grow. Noetinger et al (2004) show that this is also true for isotropic stochastic media. Zhang and Tchelepi (1999) show that the amount of dispersion in a correlated random model increased with the standard deviation and correlation length of the permeability field.…”

Section: Viscous-dominated Flowmentioning

confidence: 59%

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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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Section: Viscous-dominated Flowmentioning

confidence: 59%

“…See Figure 1. Artus et al (2004) and Noetinger et al (2004) take account of viscous cross-flow between high and low permeability regions in layered and isotropic models, respectively. They show that the amount of dispersion depends on the mobility ratio at the flood front, defined as:…”

Section: Viscous-dominated Flowmentioning

confidence: 99%

Multi-Stage Upscaling: Selection of Suitable Methods

Pickup

Stephen

et al. 2005

Transp Porous Med

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“…However, one must be cautious in doing this as this may not be correct for the unstable or stabilizing cases. In the unstable case viscous fingering dominates while for the stabilizing case the velocity field is no longer stationary as the velocity variance in the vicinity of the front is suppressed [e.g., Noetinger et al, 2004].…”

Section: Stochastic Modelmentioning

confidence: 99%

Effective two‐phase flow in heterogeneous media under temporal pressure fluctuations

Bolster

Dentz

Carrera

2009

Water Resources Research

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[1] We study the combined effect of spatial heterogeneity and temporal pressure fluctuations on the dispersion of the saturation of a displacing fluid during injection into an immiscible one. In a stochastic modeling framework, we define two different dispersion quantities, one which measures the front uncertainty due to temporal pressure fluctuations and another one which quantifies the actual spreading and dispersion of the saturation front in a typical medium realization. We derive an effective large-scale flow equation for the saturation of the displacing fluid that is characterized by a nonlocal dispersive flux term. From the latter we derive measures for the spread of the saturation front due to spatiotemporal fluctuations. Our analysis demonstrates that temporal fluctuations enhance the front uncertainty but not the average spreading of the saturation front. The analytical developments are complemented by numerical simulations of the full two-phase flow problem. Correct assessment of the spread of the saturation front is of importance to several applications, including the assessment of the sequestration potential of a carbon dioxide storage site, for example. Spreading enhances the surface area between the fluids, which in turn enhances the dissolution and entrapment efficiency. The latter facilitates reactions and thus the sequestration of CO 2 in stable forms. Our study provides a theoretical basis for the design of injection strategies to optimize dispersion and to minimize uncertainty of the saturation front.

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“…An important question concerning two-phase flows is the investigation of the growth of the macroscopic mixing zone for stratified and isotropic media (see References [17,18]). In this example we want to study the combined effect of gravity, mobility ratio and heterogeneity on the growth of a mixing region for the water infiltration problem in unsaturated soils.…”

Section: Front Stabilitymentioning

confidence: 99%

Numerical simulation of transient water infiltration in heterogeneous soils combining central schemes and mixed finite elements

Aquino¹,

Francisco²,

Pereira³

et al. 2006

Commun. Numer. Meth. Engng.

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SUMMARYWe present a new numerical scheme for the approximation of solutions of transient water infiltration problems in heterogeneous soils. The two-phase (water and air) flow problem is governed by a pressurevelocity equation coupled to a saturation equation. The numerical scheme combines a non-oscillatory, second-order, conservative central finite differencing scheme for the saturation equation with mixed finite elements for the pressure-velocity equation. An operator splitting technique allows for the use of distinct time steps for the solution of the equations of the governing system. One and two-dimensional numerical experiments show that the proposed scheme is able to capture accurately and efficiently sharp fronts in two-phase water-air problem. The simulations were carried out taking into account the effects of gravity and capillary diffusion forces.

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Dynamics of the Water–Oil Front for Two-Phase, Immiscible Flow in Heterogeneous Porous Media. 2 – Isotropic Media

Cited by 26 publications

References 27 publications

Multi-Stage Upscaling: Selection of Suitable Methods

Multi-Stage Upscaling: Selection of Suitable Methods

Effective two‐phase flow in heterogeneous media under temporal pressure fluctuations

Numerical simulation of transient water infiltration in heterogeneous soils combining central schemes and mixed finite elements

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