Rheology of High-Capillary Number Two-Phase Flow in Porous Media

Sinha, Santanu; Gjennestad, Magnus Aa.; Vassvik, Morten; Winkler, Mathias; Hansen, Alex; Flekkøy, Eirik Grude

doi:10.3389/fphy.2019.00065

Cited by 8 publications

(10 citation statements)

References 24 publications

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“…From the figure, however, it is evident that these surfaces are not overly sensitive to M , at least not for S w around 0.5. Each constant-M surface reaches values close to 1 at the highest values of Π, in agreement with the findings of Sinha et al [16] for the high-Ca limit.…”

Section: Average Flow Velocity and Mobilitysupporting

confidence: 92%

“…Instead, the fluids exhibit a large degree of mixing at high capillary numbers. This was observed also by Sinha et al [16], both in pore network model and lattice-Boltzmann simulations. Disconnected non-wetting droplets were also observed at high capillary numbers in the experiments by Avraam and Payatakes [6], and were found to contribute significantly to the total flow rate, although connected pathways were also present.…”

Section: Relative Permeabilitiessupporting

confidence: 81%

“…and are discussed together here for reasons that will become apparent below. Sinha et al [16] studied the high-Ca limit of two-phase porous media flow. They found that, at high capillary numbers, the average flow velocity followed a Darcy-type equation,…”

Section: Average Flow Velocity and Mobilitymentioning

confidence: 99%

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Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

2020

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We perform more than 6000 steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. However, while other studies find that relative permeabilities converge to straight lines at high capillary numbers we find that this is not the case when viscosity ratios are different from 1. Our conclusion is that departure from straight lines occurs when fluids mix rather than form decoupled flow channels. Another consequence of the mixing is that computed fractional flow curves, plotted against saturation, lie closer to the diagonal than they would otherwise do. At lower capillary numbers, fractional flow curves have a classical S-shape. Ratios of average mobility to their high-capillary number limit values are also considered. These vary, roughly, between 0 and 1, although values larger than 1 are also observed. For a given saturation and viscosity ratio, the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a reduction in average mobility may occur.

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Section: Average Flow Velocity and Mobilitysupporting

confidence: 92%

Section: Relative Permeabilitiessupporting

confidence: 81%

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Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

2020

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“…It is straight forward to demonstrate that if either two of the three wetting saturations S A w , S B w or S C w , coincide, then the third must also have the same value. If this is the case, we have v w = v n and dv/dS w = 0, so that the two immiscible fluids behave as if they were miscible [38]. We will use our theory to identify the wetting saturation at which this coincidence occurs for the network model we study in section 8 and then verify numerically that this is indeed so.…”

Section: Cross Pointsmentioning

confidence: 87%

Relations Between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media

et al. 2018

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Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.

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“…These "democratic" rules are symmetric in terms of the wetting and the non-wetting fluids. Therefore when the surface tension is set to zero, the capillary forces will disappear and one should obtain [68],…”

Section: Interface_creatementioning

confidence: 99%

A Dynamic Network Simulator for Immiscible Two-Phase Flow in Porous Media

Sinha¹,

Gjennestad²,

Vassvik³

et al. 2019

Preprint

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We present in detail a set of algorithms to carry out fluid displacements in a dynamic pore-network model of immiscible two-phase flow in porous media. The algorithms are general and applicable to regular and irregular pore networks in two and three dimensions with different boundary conditions. Implementing these sets of algorithms, we describe a dynamic pore-network model and reproduce some of the fundamental properties of both the transient and steady-state two-phase flow. During drainage displacements, we show that the model can reproduce the flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by altering the capillary number and the viscosity ratio. In steady-state flow, the model verifies the linear to non-linear transition of the effective rheological properties and satisfy the relations between the seepage velocities of two-phase flow in porous media.

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Rheology of High-Capillary Number Two-Phase Flow in Porous Media

Cited by 8 publications

References 24 publications

Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

Relations Between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media

A Dynamic Network Simulator for Immiscible Two-Phase Flow in Porous Media

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