Two-phase flow in porous media: power-law scaling of effective permeability

Grøva, Morten; Hansen, Alex

doi:10.1088/1742-6596/319/1/012009

Cited by 9 publications

(8 citation statements)

References 34 publications

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“…Rather than asking for the flow rate of each of the two fluids, how does the combined flow react to a given pressure drop. It has since Tallakstad et al [22,23] did their experimental study of immiscible two-phase flow under steady-state conditions in a Hele-Shaw cell filled with fixed glass beads, become increasingly clear that there is a flow regime in which the flow rate is proportional to the pressure drop to a power different than one [24][25][26][27][28][29]. That is, the immiscible two fluids flowing at the pore scale act at the continuum scale as a single non-Newtonian fluid, or more precisely a Herschel-Bulkley fluid where the effective viscosity depends on the shear rate, and hence the flow rate, as a power law [30].…”

Section: Introductionmentioning

confidence: 99%

Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

Roy,

Sinha,

Hansen

2019

Preprint

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It is becoming increasingly clear that there is a regime in immiscible two-phase flow in porous media where the flow rate depends of the pressure drop as a power law with exponent different than one. This occurs when the capillary forces and viscous forces both influence the flow. At higher flow rates, where the viscous forces dominate, the flow rate depends linearly on the pressure drop. The question we pose here is what happens to the linear regime when the system size is increased. Based on analytical calculations using the capillary fiber bundle model and on numerical simulations using a dynamical network model, we find that the non-linear regime moves towards smaller and smaller pressure gradients as the system size grows.

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Section: Introductionmentioning

confidence: 99%

Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

Roy,

Sinha,

Hansen

2019

Preprint

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“…Backbone of the incipient infinite percolation cluster [5] in two-dimensions (2D) at the percolation threshold is a random fractal lattice whose various scaling properties are well known [6,7,8]. Several dynamical models are also studied on percolation cluster for its wide application, such as random walk on percolation cluster [9], flow in porous media [10,11], absorbing state phase transition [12], etc. In all such studies, the emergence of non-trivial results occurs due to the coupling of the fractal nature of the underlying object to the model's critical dynamics.…”

Section: Introductionmentioning

confidence: 99%

Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone

Bhaumik

Santra

2020

Physica A: Statistical Mechanics and its Applications

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Both the deterministic and stochastic sandpile models are studied on the percolation backbone, a random fractal, generated on a square lattice in 2-dimensions. In spite of the underline random structure of the backbone, the deterministic Bak Tang Wiesenfeld (BTW) model preserves its positive time auto-correlation and multifractal behaviour due to its complete toppling balance, whereas the critical properties of the stochastic sandpile model (SSM) still exhibits finite size scaling (FSS) as it exhibits on the regular lattices. Analyzing the topography of the avalanches, various scaling relations are developed. While for the SSM, the extended set of critical exponents obtained is found to obey various the scaling relation in terms of the fractal dimension d B f of the backbone, whereas the deterministic BTW model, on the other hand, does not. As the critical exponents of the SSM defined on the backbone are related to d B f , the backbone fractal dimension, they are found to be entirely different from those of the SSM defined on the regular lattice as well as on other deterministic fractals. The SSM on the percolation backbone is found to obey FSS but belongs to a new stochastic universality class.

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“…The relative permeability functions of porous rocks for a specific fluid system (gas/water, gas/oil, oil/water, gas/oil/ water) are commonly measured with special core analysis tests performed on representative rock samples under transient (Sidiq et al, 2017) or steady-state (Reynolds and Krevor, 2015) conditions. Alternatively, computational methods such as the Lattice-Boltzman technique (Ramstad et al, 2012;Zhang et al, 2016), the pore network modeling (Ramstad and Hansen, 2006;Grøva and Hansen, 2011), and the tube bundle model (Wu et al, 2016) might be used to calculate the relative permeabilities from information concerning the pore space morphology, wettability, and fluid dynamics. The steady-state two-phase flow is established by injecting two fluids through a porous medium at fixed flow rates, and has extensively be analyzed by using hierarchical simulations at pore-and network-scale (Constantinides and Payatakes, 1996;Ramstad and Hansen, 2006;Sinha and Hansen, 2012;Valavanides, 2012;Valavanides et al, 2016), and systematic experimental approaches in model porous media (Avraam and Payatakes, 1995a, 1995b, 1999Tsakiroglou et al, 2007;Gutierrez et al, 2008;Tallakstad et al, 2009aTallakstad et al, , 2009bErpelding et al, 2013;Tsakiroglou et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

The correlation of the steady-state gas/water relative permeabilities of porous media with gas and water capillary numbers

Tsakiroglou

2019

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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The steady-state gas, k rg, and water, k rw, relative permeabilities are measured with experiments of the simultaneous flow, at varying flow rates, of nitrogen and brine (aqueous solution of NaCl brine) on a homogeneous sand column. Two differential pressure transducers are used to measure the pressure drop across each phase, and six ring electrodes are used to measure the electrical resistance across five segments of the sand column. The electrical resistances are converted to water saturations with the aid of the Archie equation for resistivity index. Both k rw and k rg are regarded as power functions of water, Caw, and gas, Cag, capillary numbers, the exponents of which are estimated with non-linear fitting to the experimental datasets. An analogous power law is used to express water saturation as a function of Caw, and Cag. In agreement to earlier studies, it seems that the two-phase flow regime is dominated by connected pathway flow and disconnected ganglia dynamics for the wetting fluid (brine), and only disconnected ganglia dynamics for the non-wetting fluid (gas). The water saturation is insensitive to changes of water and gas capillary numbers. Each relative permeability is affected by both water and gas capillary numbers, with the water relative permeability being a strong function of water capillary number and gas relative permeability depending strongly on the gas capillary number. The slope of the water relative permeability curve for a gas/water system is much higher than that of an oil/water system, and the slope of the gas relative permeability is lower than that of an oil/water system.

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Two-phase flow in porous media: power-law scaling of effective permeability

Cited by 9 publications

References 34 publications

Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

Immiscible two-phase flow in porous media: Effective rheology in the continuum limit

Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone

The correlation of the steady-state gas/water relative permeabilities of porous media with gas and water capillary numbers

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