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Title: The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media

Abstract

Empirical or theoretical extensions of Darcy’s law for immiscible two-phase flow have shown significant limitations in properly modeling the flow at the continuum scale. We tackle this problem by proposing a set of upscaled equations based on pore-scale flow regimes, that is, the topology of flowing phases. The incompressible Navier-Stokes equation is upscaled by means of multiple-scale expansions and its closures derived from the mechanical energy balance for different flow regimes at the pore scale. We also derive the applicability conditions of the upscaled equations based on the order of magnitude of relevant dimensionless numbers, that is, Eotvos, Reynolds, capillary, Froude numbers, and the viscosity and density ratio of the system, as well as a set of closures valid for the basic flow regimes of low Eotvos number systems, that is, core-annular and plug and drop traffic flows. We provide analytical expressions for the relative permeability of the wetting and nonwetting phases in different flow regimes and demonstrate that the effect of the flowing-phases topology on the relative permeabilities is significant. Finally, we show that the classical two-phase Darcy law is recovered for a limited range of operative conditions, while specific terms accounting for interfacial and wall interactions should bemore » incorporated to accurately model ganglia or drop traffic flow.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Stanford Univ., CA (United States)
Publication Date:
Research Org.:
San Diego State Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1539769
Alternate Identifier(s):
OSTI ID: 1472183
Grant/Contract Number:  
[SC0014227]
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
[ Journal Volume: 54; Journal Issue: 9]; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; Environmental Sciences & Ecology; Marine & Freshwater Biology; Water Resources

Citation Formats

Picchi, D., and Battiato, I. The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media. United States: N. p., 2018. Web. doi:10.1029/2018wr023172.
Picchi, D., & Battiato, I. The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media. United States. doi:10.1029/2018wr023172.
Picchi, D., and Battiato, I. Mon . "The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media". United States. doi:10.1029/2018wr023172. https://www.osti.gov/servlets/purl/1539769.
@article{osti_1539769,
title = {The Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media},
author = {Picchi, D. and Battiato, I.},
abstractNote = {Empirical or theoretical extensions of Darcy’s law for immiscible two-phase flow have shown significant limitations in properly modeling the flow at the continuum scale. We tackle this problem by proposing a set of upscaled equations based on pore-scale flow regimes, that is, the topology of flowing phases. The incompressible Navier-Stokes equation is upscaled by means of multiple-scale expansions and its closures derived from the mechanical energy balance for different flow regimes at the pore scale. We also derive the applicability conditions of the upscaled equations based on the order of magnitude of relevant dimensionless numbers, that is, Eotvos, Reynolds, capillary, Froude numbers, and the viscosity and density ratio of the system, as well as a set of closures valid for the basic flow regimes of low Eotvos number systems, that is, core-annular and plug and drop traffic flows. We provide analytical expressions for the relative permeability of the wetting and nonwetting phases in different flow regimes and demonstrate that the effect of the flowing-phases topology on the relative permeabilities is significant. Finally, we show that the classical two-phase Darcy law is recovered for a limited range of operative conditions, while specific terms accounting for interfacial and wall interactions should be incorporated to accurately model ganglia or drop traffic flow.},
doi = {10.1029/2018wr023172},
journal = {Water Resources Research},
number = [9],
volume = [54],
place = {United States},
year = {2018},
month = {8}
}

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Works referenced in this record:

Characterization of two- and three-phase relative permeability of water-wet porous media through X-Ray saturation measurements
journal, September 2016

  • Moghadasi, Leili; Guadagnini, Alberto; Inzoli, Fabio
  • Journal of Petroleum Science and Engineering, Vol. 145
  • DOI: 10.1016/j.petrol.2016.05.031

3D image-based characterization of fluid displacement in a Berea core
journal, February 2007


Two-phase flow through porous media
journal, May 1970


X-ray Microtomography of Intermittency in Multiphase Flow at Steady State Using a Differential Imaging Method: FLOW INTERMITTENCY AT STEADY STATE
journal, December 2017

  • Gao, Ying; Lin, Qingyang; Bijeljic, Branko
  • Water Resources Research, Vol. 53, Issue 12
  • DOI: 10.1002/2017WR021736

Modeling of Two-Phase Slug Flow
journal, January 1992


Closure Relations for the Shear Stress in Two-Fluid Models for Core-Annular flow
journal, January 2004


Mechanisms of the displacement of one fluid by another in a network of capillary ducts
journal, October 1983


Experimental investigations of non-Newtonian/Newtonian liquid-liquid flows in microchannels
journal, March 2017

  • Roumpea, Evangelia; Chinaud, Maxime; Angeli, Panagiota
  • AIChE Journal, Vol. 63, Issue 8
  • DOI: 10.1002/aic.15704

Hybrid models of reactive transport in porous and fractured media
journal, September 2011


A model for two-phase flow in porous media including fluid-fluid interfacial area: TWO-PHASE FLOW IN POROUS MEDIA
journal, August 2008

  • Niessner, J.; Hassanizadeh, S. M.
  • Water Resources Research, Vol. 44, Issue 8
  • DOI: 10.1029/2007WR006721

Effect of channel size on liquid-liquid plug flow in small channels
journal, September 2015

  • Tsaoulidis, Dimitrios; Angeli, Panagiota
  • AIChE Journal, Vol. 62, Issue 1
  • DOI: 10.1002/aic.15026

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow
journal, June 2009


The derivation of a nonlinear filtration law including the inertia effects via homogenization
journal, September 2000

  • Marušić-Paloka, Eduard; Mikelić, Andro
  • Nonlinear Analysis: Theory, Methods & Applications, Vol. 42, Issue 1
  • DOI: 10.1016/S0362-546X(98)00346-0

Characteristics of stratified flows of Newtonian/non-Newtonian shear-thinning fluids
journal, December 2017


Modeling of core-annular and plug flows of Newtonian/non-Newtonian shear-thinning fluids in pipes and capillary tubes
journal, June 2018


On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media
journal, January 1982


Interfacial viscous coupling: a myth or reality?
journal, May 1999


Physics-based hybrid method for multiscale transport in porous media
journal, September 2017


Sequential Homogenization of Reactive Transport in Polydisperse Porous Media
journal, January 2016

  • Korneev, Svyatoslav; Battiato, Ilenia
  • Multiscale Modeling & Simulation, Vol. 14, Issue 4
  • DOI: 10.1137/16M1074278

Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics
journal, October 2006


Flow pattern transition, pressure gradient, hold-up predictions in gas/non-Newtonian power-law fluid stratified flow
journal, July 2014


Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries
journal, December 1990


Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems
journal, September 2016


Dynamics of two immiscible fluids flowing through deformable porous media
journal, April 1989

  • Auriault, J. -L.; Lebaigue, O.; Bonnet, G.
  • Transport in Porous Media, Vol. 4, Issue 2
  • DOI: 10.1007/BF00134993

Linking pore-scale interfacial curvature to column-scale capillary pressure
journal, September 2012


Modeling two-fluid-phase flow and species transport in porous media
journal, February 2015


Homogenizability conditions for multicomponent reactive transport
journal, December 2013


Imaging of oil layers, curvature and contact angle in a mixed-wet and a water-wet carbonate rock: IMAGING OF OIL LAYERS, CURVATURE AND CONTACT ANGLE
journal, March 2016

  • Singh, Kamaljit; Bijeljic, Branko; Blunt, Martin J.
  • Water Resources Research, Vol. 52, Issue 3
  • DOI: 10.1002/2015WR018072

The Prediction of flow Pattern maps in Minichannels
journal, January 2007


Nonsaturated deformable porous media: Quasistatics
journal, February 1987


Micromodel study of two-phase flow under transient conditions: Quantifying effects of specific interfacial area
journal, October 2014

  • Karadimitriou, N. K.; Hassanizadeh, S. M.; Joekar-Niasar, V.
  • Water Resources Research, Vol. 50, Issue 10
  • DOI: 10.1002/2014WR015388

The effect of saturation path on three‐phase relative permeability
journal, November 2015

  • Kianinejad, Amir; Chen, Xiongyu; DiCarlo, David A.
  • Water Resources Research, Vol. 51, Issue 11
  • DOI: 10.1002/2015WR017185

Noise in Algorithm Refinement Methods
journal, May 2005

  • Alexander, F. J.; Tartakovsky, D. M.; Garcia, A. L.
  • Computing in Science and Engineering, Vol. 7, Issue 3
  • DOI: 10.1109/MCSE.2005.56

On Veracity of Macroscopic Lithium-Ion Battery Models
journal, January 2015

  • Arunachalam, Harikesh; Onori, Simona; Battiato, Ilenia
  • Journal of The Electrochemical Society, Vol. 162, Issue 10
  • DOI: 10.1149/2.0771509jes

Interpretation of macroscale variables in Darcy's law: MACROSCALE VARIABLES IN DARCY'S LAW
journal, August 2007

  • Nordbotten, J. M.; Celia, M. A.; Dahle, H. K.
  • Water Resources Research, Vol. 43, Issue 8
  • DOI: 10.1029/2006WR005018

Carbon dioxide sequestration in saline formations: Part 2—Review of multiphase flow modeling
journal, December 2014


Multiphase viscoelastic flow through porous media
journal, January 1968


Generalized relative permeability coefficients during steady-state two-phase flow in porous media, and correlation with the flow mechanisms
journal, August 1995

  • Avraam, D. G.; Payatakes, A. C.
  • Transport in Porous Media, Vol. 20, Issue 1-2
  • DOI: 10.1007/BF00616928

Liquid–liquid slug flow: Hydrodynamics and pressure drop
journal, January 2011

  • Jovanović, Jovan; Zhou, Wenya; Rebrov, Evgeny V.
  • Chemical Engineering Science, Vol. 66, Issue 1
  • DOI: 10.1016/j.ces.2010.09.040

Taylor dispersion in porous media: Analysis by multiple scale expansions
journal, January 1995


From connected pathway flow to ganglion dynamics
journal, May 2015

  • Rücker, M.; Berg, S.; Armstrong, R. T.
  • Geophysical Research Letters, Vol. 42, Issue 10
  • DOI: 10.1002/2015GL064007

Hybrid Multiscale Finite Volume method for two-phase flow in porous media
journal, October 2013


Flow in porous media II: The governing equations for immiscible, two-phase flow
journal, January 1986


Two-Phase Flow in Porous Media with Slip Boundary Condition
journal, January 2008


Progress in carbon dioxide separation and capture: A review
journal, January 2008


Direct measurement of relative permeability in rocks from unsteady-state saturation profiles
journal, August 2016


Flow patterns of immiscible liquid-liquid flow in a rectangular microchannel with T-junction
journal, November 2016

  • Yagodnitsyna, Anna A.; Kovalev, Alexander V.; Bilsky, Artur V.
  • Chemical Engineering Journal, Vol. 303
  • DOI: 10.1016/j.cej.2016.06.023

The effect of weak inertia on flow through a porous medium
journal, January 1991


Multiscale level-set method for accurate modeling of immiscible two-phase flow with deposited thin films on solid surfaces
journal, March 2017

  • Abu-Al-Saud, Moataz O.; Riaz, Amir; Tchelepi, Hamdi A.
  • Journal of Computational Physics, Vol. 333
  • DOI: 10.1016/j.jcp.2016.12.038

Macroscopic equations of motion for two-phase flow in porous media
journal, August 1998


An experimental investigation and two-fluid model validation for dilute viscous oil in water dispersed pipe flow
journal, January 2015


Spatial distribution of void fraction within a liquid slug and some other related slug parameters
journal, November 1992


The motion of long bubbles in tubes
journal, March 1961


Pore-scale imaging and modelling
journal, January 2013


Homogenization of two fluid flow in porous media
journal, April 2015

  • Daly, K. R.; Roose, T.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, Issue 2176
  • DOI: 10.1098/rspa.2014.0564

Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow
journal, October 2016


Comparison of Two-Phase Darcy’s Law with a Thermodynamically Consistent Approach
journal, February 2011

  • Niessner, Jennifer; Berg, Steffen; Hassanizadeh, S. Majid
  • Transport in Porous Media, Vol. 88, Issue 1
  • DOI: 10.1007/s11242-011-9730-0

Tracking interface and common curve dynamics for two-fluid flow in porous media
journal, April 2016

  • McClure, J. E.; Berrill, M. A.; Gray, W. G.
  • Journal of Fluid Mechanics, Vol. 796
  • DOI: 10.1017/jfm.2016.212

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model
journal, May 2008

  • Lasseux, Didier; Ahmadi, Azita; Arani, Ali Akbar Abbasian
  • Transport in Porous Media, Vol. 75, Issue 3
  • DOI: 10.1007/s11242-008-9231-y

Subsecond pore-scale displacement processes and relaxation dynamics in multiphase flow
journal, December 2014

  • Armstrong, Ryan T.; Ott, Holger; Georgiadis, Apostolos
  • Water Resources Research, Vol. 50, Issue 12
  • DOI: 10.1002/2014WR015858

Geometric state function for two-fluid flow in porous media
journal, August 2018


Pore-scale capillary pressure analysis using multi-scale X-ray micromotography
journal, June 2017


Flow regimes and relative permeabilities during steady-state two-phase flow in porous media
journal, June 1995


On the dynamics and kinematics of two‐fluid‐phase flow in porous media
journal, July 2015

  • Gray, W. G.; Dye, A. L.; McClure, J. E.
  • Water Resources Research, Vol. 51, Issue 7
  • DOI: 10.1002/2015WR016921

Modeling of three-phase heavy oil–water–gas bubbly flow in upward vertical pipes
journal, June 2010


On the relations between two-phase flows under reduced gravity and earth experiment
journal, May 1990


A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface
journal, December 1987

  • Kalaydjian, Fran�ois
  • Transport in Porous Media, Vol. 2, Issue 6
  • DOI: 10.1007/BF00192154

Modeling variability in porescale multiphase flow experiments
journal, July 2017


The Flow of Gas‐Liquid Mixtures Through Unconsolidated Sands
journal, September 1936


General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow
journal, March 1980


Gas/shear-thinning liquid flows through pipes: Modeling and experiments
journal, July 2015


Toward an improved description of the physics of two-phase flow
journal, January 1993


Dynamic fluid connectivity during steady-state multiphase flow in a sandstone
journal, July 2017

  • Reynolds, Catriona A.; Menke, Hannah; Andrew, Matthew
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 31
  • DOI: 10.1073/pnas.1702834114

Steady-state supercritical CO 2 and brine relative permeability in Berea sandstone at different temperature and pressure conditions : SC-CO
journal, July 2017

  • Chen, Xiongyu; Gao, Shuang; Kianinejad, Amir
  • Water Resources Research, Vol. 53, Issue 7
  • DOI: 10.1002/2017WR020810

Macroscopic capillarity and hysteresis for flow in porous media
journal, January 2006


Closure relations for the shear stresses in two-fluid models for laminar stratified flow
journal, July 2004


Fluid breakup during simultaneous two-phase flow through a three-dimensional porous medium
journal, June 2014

  • Datta, Sujit S.; Dupin, Jean-Baptiste; Weitz, David A.
  • Physics of Fluids, Vol. 26, Issue 6
  • DOI: 10.1063/1.4884955

Influence of Viscous Fingering on Dynamic Saturation–Pressure Curves in Porous Media
journal, August 2010


Applicability regimes for macroscopic models of reactive transport in porous media
journal, March 2011


On the definition of macroscale pressure for multiphase flow in porous media: MACROSCALE PRESSURE FOR MULTIPHASE FLOW
journal, June 2008

  • Nordbotten, J. M.; Celia, M. A.; Dahle, H. K.
  • Water Resources Research, Vol. 44, Issue 6
  • DOI: 10.1029/2006WR005715

Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel
journal, September 2002


Hydrodynamics of liquid–liquid slug flow capillary microreactor: Flow regimes, slug size and pressure drop
journal, July 2007


Thermodynamic basis of capillary pressure in porous media
journal, October 1993

  • Hassanizadeh, S. Majid; Gray, William G.
  • Water Resources Research, Vol. 29, Issue 10
  • DOI: 10.1029/93WR01495

The motion of a viscous drop through a cylindrical tube
journal, January 1999


Non-Darcy behavior of two-phase channel flow
journal, August 2014


Two phase liquid–liquid flows in pipes of small diameters
journal, August 2006