Quantification of Nonlinear Multiphase Flow in Porous Media

Zhang, Yihuai; Bijeljic, Branko; Gao, Ying; Lin, Qingyang; Blunt, Martin J.

doi:10.1029/2020gl090477

Cited by 44 publications

(71 citation statements)

References 36 publications

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“…We now turn to the average velocity v p . As described in the Introduction, there is a regime over an interval of pressure gradients where the flow rate is proportional to the pressure gradient to a power [23][24][25][26][27][28]. This regime is clearly visible in our dynamic pore network model [29,36].…”

Section: P As a Function Of S W And ∆P/lmentioning

confidence: 77%

“…to produce a closed set of equations that together with the proper boundary and initial values solves the immiscible two-phase flow problem in the continuum limit. We note that the non-linear constitutive equation that can be constructed for v p from the observations in [23][24][25][26][27][28], is easily combined with this approach.…”

Section: Closed Set Of Equationsmentioning

confidence: 99%

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Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

2020

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We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two-and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.

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Section: P As a Function Of S W And ∆P/lmentioning

confidence: 77%

Section: Closed Set Of Equationsmentioning

confidence: 99%

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

2020

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“…In this case, the volumetric flow rate scales nonlinearly with the pressure drop due to the fact that increasing the pressure drop by a small amount creates new connecting paths in addition to increase the flow in the previously connected paths. Earlier works (Roy et al 2019;Sinha et al 2021;Tallakstad et al 2009a;Rassi et al 2011;Tallakstad et al 2009b;Aursjø et al 2014;Gao et al 2020a;Zhang et al 2021) have provided experimental, theoretical and numerical evidences for this phenomena in porous media under uniform wetting conditions. Instead of assuming uniform wetting conditions, we here investigate the same phenomena using non-uniform wetting conditions, theoretically and numerically.…”

Section: Introductionmentioning

confidence: 92%

Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

et al. 2021

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Immiscible two-phase flow in porous media with mixed wet conditions was examined using a capillary fiber bundle model, which is analytically solvable, and a dynamic pore network model. The mixed wettability was implemented in the models by allowing each tube or link to have a different wetting angle chosen randomly from a given distribution. Both models showed that mixed wettability can have significant influence on the rheology in terms of the dependence of the global volumetric flow rate on the global pressure drop. In the capillary fiber bundle model, for small pressure drops when only a small fraction of the tubes were open, it was found that the volumetric flow rate depended on the excess pressure drop as a power law with an exponent equal to 3/2 or 2 depending on the minimum pressure drop necessary for flow. When all the tubes were open due to a high pressure drop, the volumetric flow rate depended linearly on the pressure drop, independent of the wettability. In the transition region in between where most of the tubes opened, the volumetric flow depended more sensitively on the wetting angle distribution function and was in general not a simple power law. The dynamic pore network model results also showed a linear dependence of the flow rate on the pressure drop when the pressure drop is large. However, out of this limit the dynamic pore network model demonstrated a more complicated behavior that depended on the mixed wettability condition and the saturation. In particular, the exponent relating volumetric flow rate to the excess pressure drop could take on values anywhere between 1.0 and 1.8. The values of the exponent were highest for saturations approaching 0.5, also, the exponent generally increased when the difference in wettability of the two fluids were larger and when this difference was present for a larger fraction of the porous network.

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“…No threshold pressure was considered in that study while analyzing the results. A recent experimental study (Zhang et al, 2021) explores the variation of β and the crossover point as a function of fractional flow, F w = Q w /Q. By balancing the surface energy to create fluid meniscus to the injection energy, they developed a theory that can predict the crossover point between the two regimes they have studied.…”

Section: Effect Of S Wmentioning

confidence: 99%

“…They also reported a regime with linear Darcy type behavior at lower capillary numbers where the conductance does not change significantly. Further experiments by Zhang et al (2021) explore the dependence of the exponent on fractional flow and reported values in the range of 1.35 (≈ 1/0.74) to 2.27 (≈ 1/0.44). They presented a theory that can predict the boundary between the linear regime and the non-linear intermittent flow regime.…”

Section: Introductionmentioning

confidence: 99%

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

Roy¹,

Sinha²,

Hansen³

2021

Front. Water

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Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.

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Quantification of Nonlinear Multiphase Flow in Porous Media

Cited by 44 publications

References 36 publications

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

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