Steady-State Two-Phase Flow in Porous Media: Statistics and Transport Properties

Tallakstad, Ken Tore; Knudsen, Henning Arendt; Ramstad, T.A.; Løvoll, Grunde; Måløy, Knut Jørgen; Toussaint, Renaud; Flekkøy, Eirik Grude

doi:10.1103/physrevlett.102.074502

Cited by 143 publications

(193 citation statements)

References 27 publications

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“…For example, one observes flow regimes such as two-phase flow in rigid porous media [40][41][42][43][44], capillary fracturing, stick-slip bubbles, and labyrinth patterns [31][32][33][34][35][36][37][38][39]. In the opposite case, during liquid injection into dry granular media [45], for a given imposed flux, the flow behavior goes from stable invasion toward saturated granular fingers for increasing flow rate and viscosity of the invading fluid.…”

Section: Introductionmentioning

confidence: 99%

“…Further, during air injection into liquid saturated granular media and suspensions, the characteristics of emerging patterns and behavior of the media depend on injection rate and the competition between mobilized friction and surface forces [31][32][33][34][35][36][37][38][39][40][41][42][43][44]. For example, one observes flow regimes such as two-phase flow in rigid porous media [40][41][42][43][44], capillary fracturing, stick-slip bubbles, and labyrinth patterns [31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

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Pneumatic fractures in confined granular media

et al. 2017

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We perform experiments where air is injected at a constant overpressure P in , ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for P in below 10 kPa, to large thick channels formed by erosion and fingers merging for high P in around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d) ∝ d β , where β = 0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvaturee., more rounded tips rather than pointy cusps, as they would be for the case β > 1. For increasing P in , the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v 0 is found to scale with injection pressure as v 0 ∝ P 3 2 in , while at a critical time t c there is a cross-over to the behavior v(t) ∝ t −α , where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate P in around 100-150 kPa, we find that the box-counting dimensions lie within the range D B ∈ [1.53,1.62], similar to viscous fingering fractals in porous media.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pneumatic fractures in confined granular media

et al. 2017

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“…Here, q i , µ i , ρ i and P i are flux, viscosity, density and pressure of phase i flowing through porous media of permeability k. While this multi-phase flow equation is widely used due to its simplicity, it is known to break down at high capillary numbers (the network is fluid) [3], unstable flow [4], high viscosity ratio (due to viscous coupling between the mobile phases) [5], and three-phase flow (the network for the intermediate phase depends on the other two phases) [6].…”

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“…The change in permeability is parameterized by the relative permeability, k ri , that is assumed to be a function of the saturation of the phase, S i (the local volume fraction of the pore space filled by the phase i). Mathematically this is expressed through the Darcy-Buckingham equation [1].Here, q i , µ i , ρ i and P i are flux, viscosity, density and pressure of phase i flowing through porous media of permeability k. While this multi-phase flow equation is widely used due to its simplicity, it is known to break down at high capillary numbers (the network is fluid) [3], unstable flow [4], high viscosity ratio (due to viscous coupling between the mobile phases) [5], and three-phase flow (the network for the intermediate phase depends on the other two phases) [6].Here we concentrate on the combined effects of threephase flow and viscous coupling. Three-phase flow occurs when three mobile fluid phases co-exist in a porous media; typically water is the most wetting phase and oil the intermediate wetting phase.…”

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Flow coupling during three-phase gravity drainage

et al. 2011

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We measure the three-phase oil relative permeability kro by conducting unsteady-state drainage experiments in a 0.8m water-wet sandpack. We find that when starting from capillary-trapped oil, kro shows a strong dependence on both the flow of water and the water saturation and a weak dependence on oil saturation, contrary to most models. The observed flow coupling between water and oil is stronger in three-phase flow than two-phase flow, and cannot be observed in steadystate measurements. The results suggest that the oil is transported through moving gas/oil/water interfaces (form drag) or momentum transport across stationary interfaces (friction drag). We present a simple model of friction drag which compares favorably to the experimental data.When the single-phase Darcy equation is generalized to multi-phase flow in porous media, it is assumed that each phase flows due to the pressure gradient within that phase, albeit with a reduced permeability [1,2]. Conceptually, each phase flows in a capillary-stable reduced network compared to single phase flow. The change in permeability is parameterized by the relative permeability, k ri , that is assumed to be a function of the saturation of the phase, S i (the local volume fraction of the pore space filled by the phase i). Mathematically this is expressed through the Darcy-Buckingham equation [1].Here, q i , µ i , ρ i and P i are flux, viscosity, density and pressure of phase i flowing through porous media of permeability k. While this multi-phase flow equation is widely used due to its simplicity, it is known to break down at high capillary numbers (the network is fluid) [3], unstable flow [4], high viscosity ratio (due to viscous coupling between the mobile phases) [5], and three-phase flow (the network for the intermediate phase depends on the other two phases) [6].Here we concentrate on the combined effects of threephase flow and viscous coupling. Three-phase flow occurs when three mobile fluid phases co-exist in a porous media; typically water is the most wetting phase and oil the intermediate wetting phase. Three-phase relative permeability has been measured using steady state experiments [6], and many empirical models of the oil relative permeability k ro have been introduced [7]. These models have a dependence on both saturations, k ro (S o , S w ), based on the idea that the connected oil network depends on the amount of water. From observations in micromodels [8,9] and capillary stability arguments based on geometry [10] and thermodynamics [11] various three-phase pore level fluid configurations and flow mechanisms have been recognized. These mechanisms have been incorporated into network models to predict three-phase relative permeability and saturations path [12][13][14], under the ansatz of each phase flowing independently in its own network. * dicarlo@mail.utexas.edu Viscous coupling, where the pressure gradient of a particular phase affects the flow of the other phase, has been investigated for two-phase flow through experiments [15][16][17], analytical...

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“…(6) Desenvolvimentos recentes em dinâmica de fluidos em micro canais podem ser encontradas em diversas aplicações como em micro-reatores (Kashid e Agar(7); Kashid et al (8)), em processos de extração líquido-líquido (Kashid et al (9)), em transporte de emulsões em meios porosos, que são relevantes em diversas aplicações como ciência ambiental (Ouyang et al(10); Allan et al (11)), bioengenharia, armazenamento de gases do efeito estufa, recuperação deóleo, entre outros (Hofman e Stein(12); Tallaskstad et al (13); Idowu e Blunt (14)). Além disso, o escoamento de emulsões tambémé utilizado como modelo para escoamentos na escala de poros (Roca(3)).…”

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Escoamento De Duas Gotas Através De Um Micro Capilar Reto

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Azevedo, Bruno Nieckele; Carvalho, Márcio da Silveira (Advisor). Flow of two drops through a straight microcapillary. Rio de Janeiro, 2014. 68p. MSc. Dissertation -Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro.Emulsions can be used as mobility control agent in enhanced oil recovery methods in order to achieve a more efficient sweep of the reservoir. The application of such technique requires full understanding of how emulsions flow in a porous material. The macroscopic flow behavior can be determined based on the pore scale flow, at which emulsions cannot be treated as a single phase non Newtonian liquid, since the drop diameters are in the same order of magnitude of the pore throats. Experiments by Cobos et al.(1) of flow of emulsions through constricted micro capillaries, wich served as a model to the geometry of a pore throat connecting two adjacent pore bodies, have shown the effect of the dispersed phase on the pressure drop for different flow conditions and emulsions characteristics. In order to widen the range of capillary number and drop size explored in the experiments and to determine the effect of interfacial tension, viscosity ratio, capillary geometry and determine the characteristics of the flow with more the one drop, we study the flow of a drops suspended in a continuous phase flowing through a constricted micro capillary. The evolution of the drop interface is determined by the level set method which is incorporated to a fully coupled implicit Navier Stokes solver based finite element method. We investigate the effect of an initial distance between the two drops, as well as the effects of the interfacial tension on the drops speed. The results provide a more detailed description of the flow of emulsions through pore throats.

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Steady-State Two-Phase Flow in Porous Media: Statistics and Transport Properties

Cited by 143 publications

References 27 publications

Pneumatic fractures in confined granular media

Pneumatic fractures in confined granular media

Flow coupling during three-phase gravity drainage

Escoamento De Duas Gotas Através De Um Micro Capilar Reto

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