A locally conservative multiphase level set method for capillary-controlled displacements in porous media

Jettestuen, Espen; Friis, Helmer André; Helland, Johan Olav

doi:10.1016/j.jcp.2020.109965

Cited by 26 publications

(55 citation statements)

References 47 publications

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“…Here, we introduce the phase-specific Helmholtz free energy, F α , which models the energy contribution from phase α to the fluid/fluid and fluid/solid interfacial free energies. This splitting strategy borrows ideas from pore-scale modeling of three-phase displacement where interfacial properties, like interfacial tension and contact angle, are formulated as the sum of individual phase contributions (Helland & Jettestuen, 2016;Helland et al, 2019;Jettestuen et al, 2021). We also assume this Helmholtz energy is a function of its own phase volume only, that is,…”

Section: Methodsmentioning

confidence: 99%

“…Displacement behavior vary significantly with immiscible and near-miscible fluid systems, the spreading behavior of oils on gas/water interfaces, and different wetting orders of the three phases (Alhosani et al, 2019;Hui & Blunt, 2000;Keller et al, 1997;Khishvand et al, 2016;Scanziani et al, 2020; van Dijke & Sorbie, 2002). At the pore scale, double displacements (Helland & Jettestuen, 2016;Helland et al, 2019;Keller et al, 1997;Khishvand et al, 2016;Øren & Pinczewski, 1995), where a continuous phase displaces a second isolated phase that displaces a third continuous phase, and multiple displacement chains (Jettestuen et al, 2021;Scanziani et al, 2020; van Dijke & Sorbie, 2003), where the continuous phases displace a chain of several isolated fluid ganglia, make three-phase flow different to two-phase flow. Further, three-phase experiments are time-consuming and challenging, while three-phase pore-scale simulations are computationally demanding (Helland et al, 2019;Jettestuen et al, 2021).…”

mentioning

confidence: 99%

“…At the pore scale, double displacements (Helland & Jettestuen, 2016;Helland et al, 2019;Keller et al, 1997;Khishvand et al, 2016;Øren & Pinczewski, 1995), where a continuous phase displaces a second isolated phase that displaces a third continuous phase, and multiple displacement chains (Jettestuen et al, 2021;Scanziani et al, 2020; van Dijke & Sorbie, 2003), where the continuous phases displace a chain of several isolated fluid ganglia, make three-phase flow different to two-phase flow. Further, three-phase experiments are time-consuming and challenging, while three-phase pore-scale simulations are computationally demanding (Helland et al, 2019;Jettestuen et al, 2021). They both rely on having established the relevant two-phase saturation history prior to the investigation.…”

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confidence: 99%

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A discrete-domain approach to three-phase hysteresis in porous media

Helland

Jettestuen

Friis

2021

Preprint

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An inherent challenge with multiphase flow processes in porous media, such as water-alternate-gas invasions for oil recovery or CO 2 injection for geologic storage, is that fluid displacements are irreversible, that is, they are history-dependent and exhibit hysteresis (Spiteri & Juanes, 2006). Hysteresis can be rate-dependent or rate-independent. Here, we examine rate-independent hysteresis in three-phase systems based on an energy landscape exhibiting metastability and barriers. Thus, we approach fluid displacements quasi-statically as a series of small changes of pressure or saturation. This is a reasonable approximation for slow displacement at pore scale where capillary forces typically dominate over viscous forces and gravity (Hilfer & Øren, 1996). At darcy (or, core) scale, hysteresis in two-phase systems emerges as the difference between drainage and imbibition capillary pressure curves (P αβ (S β )-curves), where capillary pressure is the difference in phase pressures p between nonwetting (α) and wetting (β) phases (i.e., P αβ = p α − p β ), and S β is wetting-phase saturation. Collectively, the shape of P αβ (S β )-curves depends on porous structure, pore-scale fluid displacements, saturation history, and wetting state. Morrow (1970) interpreted P αβ (S β )-curves thermodynamically as a sequence of reversible and irreversible pore-scale fluid displacements, termed "isons" and "rheons," respectively, that describe transitions between capillary equilibrium states (i.e., local energy

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Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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A discrete-domain approach to three-phase hysteresis in porous media

Helland

Jettestuen

Friis

2021

Preprint

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“…Displacement behavior vary significantly with immiscible and near‐miscible fluid systems, the spreading behavior of oils on gas/water interfaces, and different wetting orders of the three phases (Alhosani et al., 2019; Hui & Blunt, 2000; Keller et al., 1997; Khishvand et al., 2016; Scanziani et al., 2020; van Dijke & Sorbie, 2002). At the pore scale, double displacements (Helland & Jettestuen, 2016; Helland et al., 2019; Keller et al., 1997; Khishvand et al., 2016; Øren & Pinczewski, 1995), where a continuous phase displaces a second isolated phase that displaces a third continuous phase, and multiple displacement chains (Jettestuen et al., 2021; Scanziani et al., 2020; van Dijke & Sorbie, 2003), where the continuous phases displace a chain of several isolated fluid ganglia, make three‐phase flow different to two‐phase flow. Further, three‐phase experiments are time‐consuming and challenging, while three‐phase pore‐scale simulations are computationally demanding (Helland et al., 2019; Jettestuen et al., 2021).…”

Section: Introductionmentioning

confidence: 99%

“…At the pore scale, double displacements (Helland & Jettestuen, 2016; Helland et al., 2019; Keller et al., 1997; Khishvand et al., 2016; Øren & Pinczewski, 1995), where a continuous phase displaces a second isolated phase that displaces a third continuous phase, and multiple displacement chains (Jettestuen et al., 2021; Scanziani et al., 2020; van Dijke & Sorbie, 2003), where the continuous phases displace a chain of several isolated fluid ganglia, make three‐phase flow different to two‐phase flow. Further, three‐phase experiments are time‐consuming and challenging, while three‐phase pore‐scale simulations are computationally demanding (Helland et al., 2019; Jettestuen et al., 2021). They both rely on having established the relevant two‐phase saturation history prior to the investigation.…”

Section: Introductionmentioning

confidence: 99%

A Discrete‐Domain Approach to Three‐Phase Hysteresis in Porous Media

Helland

Jettestuen

Friis

2021

Water Resources Research

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We present a discrete‐domain approach to three‐phase displacements and hysteresis in porous media. In this method, constrained energy minimization leads to evolution equations for local saturations that describe a wide range of three‐phase displacements, including pressure‐ and saturation‐controlled displacement with or without preservation of one of the defending phases. Under action of global saturation constraints, irreversible displacements lead to significant fluid redistribution, as well as abrupt fluctuations of both the three‐phase saturation paths and the corresponding capillary pressures. These features are a consequence of Haines jumps with cooperative behavior that occur at pore scale in three‐phase systems. The method is a fast and convenient way to investigate hysteresis behavior of three‐phase displacement in porous media. As free energy is an extensive property, the framework links pore and core scales and provide a means to achieve upscaled three‐phase displacements for higher‐order hysteresis loops, which rarely is obtained in time‐consuming three‐phase measurements or pore‐scale simulations.

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