Hostname: page-component-669899f699-8p65j Total loading time: 0 Render date: 2025-04-25T20:42:40.846Z Has data issue: false hasContentIssue false
  • English
  • Français

Bistability in the unstable flow of polymer solutions through pore constriction arrays

Published online by Cambridge University Press:  02 March 2020

Christopher A. Browne Open the ORCID record for Christopher A. Browne [Opens in a new window] ,
Audrey Shih Open the ORCID record for Audrey Shih [Opens in a new window]  and
Sujit S. Datta Open the ORCID record for Sujit S. Datta [Opens in a new window]
Christopher A. Browne
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Audrey Shih
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Sujit S. Datta*
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Polymer solutions are often injected in porous media for applications such as oil recovery and groundwater remediation. As the fluid navigates the tortuous pore space, elastic stresses build up, causing the flow to become unstable at sufficiently large injection rates. However, it is poorly understood how the spatial and temporal characteristics of this unstable flow depend on pore space geometry, which can vary widely between different porous media. We investigate this dependence by systematically varying the spacing between pore constrictions in a one-dimensional ordered array. We find that when the pore spacing is large, unstable eddies form upstream of each constriction, similar to observations of an isolated constriction. By contrast, when the pore spacing is sufficiently small, the flow in the different pores exhibits a surprising bistability, stochastically switching between two distinct unstable flow states. We hypothesize that this unusual behaviour arises from the interplay between elongation and relaxation of polymers as they are advected through the pore space. Consistent with this idea, we find that the flow state in a given pore persists for long times; moreover, flow states are strongly correlated between neighbouring pores. Thus, the characteristics of unstable flow are not determined just by injection conditions and the geometry of the individual pores, but also depend on the spacing between pores. Ultimately, these results help to elucidate the rich array of behaviours that can arise in polymer solution flow through porous media.

JFM classification

Non-Newtonian Flows: Polymers Non-Newtonian Flows: Viscoelasticity Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ali, M. Z., Wingreen, N. S. & Mukhopadhyay, R. 2018 Hidden long evolutionary memory in a model biochemical network. Phys. Rev. E 97 (4), 040401.Google Scholar
Aramideh, S., Vlachos, P. P. & Ardekani, A. M. 2019 Nanoparticle dispersion in porous media in viscoelastic polymer solutions. J. Non-Newtonian Fluid Mech. 268, 75–80.CrossRefGoogle Scholar
Arora, K., Sureshkumar, R. & Khomami, B. 2002 Experimental investigation of purely elastic instabilities in periodic flows. J. Non-Newtonian Fluid Mech. 108 (1-3), 209–226.CrossRefGoogle Scholar
Avgousti, M. & Beris, A. N. 1993 Non-axisymmetric modes in viscoelastic Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 50 (2-3), 225–251.CrossRefGoogle Scholar
Babayekhorasani, F., Dunstan, D. E., Krishnamoorti, R. & Conrad, J. C. 2016 Nanoparticle dispersion in disordered porous media with and without polymer additives. Soft Matt. 12 (26), 5676–5683.CrossRefGoogle ScholarPubMed
Balkovsky, E., Fouxon, A. & Lebedev, V. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84 (20), 4765–4768.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1971 The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J Fluid Mech. 46 (4), 813–829.CrossRefGoogle Scholar
Bernabe, Y. 1991 Pore geometry and pressure dependence of the transport properties in sandstones. Geophysics 56 (4), 424–576.CrossRefGoogle Scholar
Blunt, M. J. 2017 Multiphase Flow in Permeable Media: A Pore-Scale Perspective. Cambridge University Press.CrossRefGoogle Scholar
Boger, D. V. 1987 Viscoelastic flows through contractions. Annu. Rev. Fluid Mech. 19 (1), 157–182.CrossRefGoogle Scholar
Browne, C. A., Shih, A. & Datta, S. S. 2019 Pore-scale flow characterization of polymer solutions in microfluidic porous media. Small 2019, 1903944.Google Scholar
Chauveteau, G. & Moan, M. 1981 The onset of dilatant behaviour in non-inertial flow of dilute polymer solutions through channels with varying cross-sections. J. Phys. Lett. 42 (10), 201–204.CrossRefGoogle Scholar
Chauveteau, G., Moan, M. & Magueur, A. 1984 Thickening behaviour of dilute polymer solutions in non-inertial elongational flows. J. Non-Newtonian Fluid Mech. 16 (3), 315–327.CrossRefGoogle Scholar
Chertkov, M. 2000 Polymer stretching by turbulence. Phys. Rev. Lett. 84 (20), 4761.CrossRefGoogle ScholarPubMed
Clarke, A., Howe, A. M., Mitchell, J., Staniland, J. & Hawkes, L. A. 2016 How viscoelastic-polymer flooding enhances displacement efficiency. SPE J. 21 (03), 675–687.Google Scholar
Clasen, C., Plog, J. P., Kulicke, W.-M., Owens, M., Macosko, C., Scriven, L. E., Verani, M. & McKinley, G. H. 2006 How dilute are dilute solutions in extensional flows? J. Rheol. 50, 849–881.CrossRefGoogle Scholar
Datta, S. S., Chiang, H., Ramakrishnan, T. S. & Weitz, D. A. 2013 Spatial fluctuations of fluid velocities in flow through a three-dimensional porous medium. Phys. Rev. Lett. 111 (6), 064501.CrossRefGoogle ScholarPubMed
Datta, S. S., Dupin, J.-B. & Weitz, D. A. 2014a Fluid breakup during simultaneous two-phase flow through a three-dimensional porous medium. Phys. Fluids 26 (6), 062004.CrossRefGoogle Scholar
Datta, S. S., Ramakrishnan, T. S. & Weitz, D. A. 2014b Mobilization of a trapped non-wetting fluid from a three-dimensional porous medium. Phys. Fluids 26 (2), 022002.CrossRefGoogle Scholar
De, S., Koesen, S. P., Maitri, R. V., Golombok, M., Padding, J. T. & van Santvoort, J. F. M. 2018a Flow of viscoelastic surfactants through porous media. AIChE J. 64 (2), 773–781.CrossRefGoogle Scholar
De, S., Krishnan, P., van der Schaaf, J., Kuipers, J. A. M., Peters, E. A. J. F. & Padding, J. T. 2018b Viscoelastic effects on residual oil distribution in flows through pillared microchannels. J. Colloid Interface Sci. 510, 262–271.CrossRefGoogle Scholar
De, S., Kuipers, J. A. M., Peters, E. A. J. F. & Padding, J. T. 2017a Viscoelastic flow simulations in model porous media. Phys. Rev. Fluids 2 (5), 053303.CrossRefGoogle Scholar
De, S., Kuipers, J. A. M., Peters, E. A. J. F. & Padding, J. T. 2017b Viscoelastic flow simulations in random porous media. J. Non-Newtonian Fluid Mech. 248, 50–61.CrossRefGoogle Scholar
De, S., Kuipers, J. A. M., Peters, E. A. J. F. & Padding, J. T. 2017c Viscoelastic flow past mono-and bidisperse random arrays of cylinders: flow resistance, topology and normal stress distribution. Soft Matt. 13 (48), 9138–9146.CrossRefGoogle Scholar
De, S., van der Schaaf, J., Deen, N. G., Kuipers, J. A. M., Peters, E. A. J. F. & Padding, J. T. 2017d Lane change in flows through pillared micro channels. Phys. Fluids 29, 113102.CrossRefGoogle Scholar
Doyen, P. M. 1988 Permeability, conductivity, and pore geometry of sandstone. J. Geophys. Res. 93 (B7), 7729–7740.CrossRefGoogle Scholar
Durst, F. R. B. U., Haas, R. & Kaczmar, B. U. 1981 Flows of dilute hydrolyzed polyacrylamide solutions in porous media under various solvent conditions. J. Appl. Polym. Sci. 26 (9), 3125–3149.CrossRefGoogle Scholar
Fang, L., Hu, H. & Larson, R. G. 2005 DNA configurations and concentration in shearing flow near a glass surface in a microchannel. J. Rheol. 49 (1), 127–138.CrossRefGoogle Scholar
Fielding, S. M. 2007 Complex dynamics of shear banded flows. Soft Matt. 3 (10), 1262–1279.CrossRefGoogle Scholar
François, N., Amarouchene, Y., Lounis, B. & Kellay, H. 2009 Polymer conformations and hysteretic stresses in nonstationary flows of polymer solutions. Europhys. Lett. 86 (3), 34002.CrossRefGoogle Scholar
Galindo-Rosales, F. J., Campo-Deaño, L., Pinho, F. T., Van Bokhorst, E., Hamersma, P. J., Oliveira, M. S. N. & Alves, M. A. 2012 Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media. Microfluid. Nanofluid. 12 (1-4), 485–498.CrossRefGoogle Scholar
Galindo-Rosales, F. J., Campo-Deaño, L., Sousa, P. C., Ribeiro, V. M., Oliveira, M. S. N., Alves, M. A. & Pinho, F. T. 2014 Viscoelastic instabilities in micro-scale flows. Exp. Therm. Fluid Sci. 59, 128–139.Google Scholar
Gerashchenko, S., Chevallard, C. & Steinberg, V. 2005 Single-polymer dynamics: coil-stretch transition in a random flow. Europhys. Lett. 71 (2), 221.CrossRefGoogle Scholar
Grattoni, C. A., Luckham, P. F., Jing, X. D., Norman, L. & Zimmerman, R. W. 2004 Polymers as relative permeability modifiers: adsorption and the dynamic formation of thick polyacrylamide layers. J. Petrol. Sci. Engng 45 (3-4), 233–245.CrossRefGoogle Scholar
Grilli, M., Vázquez-Quesada, A. & Ellero, M. 2013 Transition to turbulence and mixing in a viscoelastic fluid flowing inside a channel with a periodic array of cylindrical obstacles. Phys. Rev. Lett. 110 (17), 174501.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405 (6782), 53.CrossRefGoogle Scholar
Gulati, S., Muller, S. J. & Liepmann, D. 2015 Flow of DNA solutions in a microfluidic gradual contraction. Biomicrofluidics 9 (5), 054102.CrossRefGoogle Scholar
Gupta, V. K., Sureshkumar, R. & Khomami, B. 2004 Polymer chain dynamics in Newtonian and viscoelastic turbulent channel flows. Phys. Fluids 16 (5), 1546–1566.CrossRefGoogle Scholar
Harnett, J. P. & Irvine, T. F. 1979 Advances in Heat Transfer. Elsevier Science.Google Scholar
Haward, S. J., McKinley, G. H. & Shen, A. Q. 2016 Elastic instabilities in planar elongational flow of monodisperse polymer solutions. Sci. Rep. 6, 33029.Google ScholarPubMed
Haward, S. J. & Odell, J. A. 2003 Viscosity enhancement in non-Newtonian flow of dilute polymer solutions through crystallographic porous media. Rheol. Acta 42 (6), 516–526.CrossRefGoogle Scholar
Haward, S. J., Toda-Peters, K. & Shen, A. Q. 2018 Steady viscoelastic flow around high-aspect-ratio, low-blockage-ratio microfluidic cylinders. J. Non-Newtonian Fluid Mech. 254, 23–35.CrossRefGoogle Scholar
Howe, A. M., Clarke, A. & Giernalczyk, D. 2015 Flow of concentrated viscoelastic polymer solutions in porous media: effect of MW and concentration on elastic turbulence onset in various geometries. Soft Matt. 11 (32), 6419–6431.CrossRefGoogle Scholar
Huh, C., Pope, G. A. et al. 2008 Residual oil saturation from polymer floods: laboratory measurements and theoretical interpretation. In SPE Symposium on Improved Oil Recovery. Society of Petroleum Engineers.Google Scholar
Ioannidis, M. A. & Chatzis, I. 1993 Network modelling of pore structure and transport properties of porous media. Chem. Engng Sci. 48 (5), 951–972.CrossRefGoogle Scholar
Kang, P. K., de Anna, P., Nunes, J. P., Bijeljic, B., Blunt, M. J. & Juanes, R. 2014 Pore-scale intermittent velocity structure underpinning anomalous transport through 3D porous media. Geophys. Res. Lett. 41 (17), 6184–6190.CrossRefGoogle Scholar
Kawale, D., Bouwman, G., Sachdev, S., Zitha, P. L. J., Kreutzer, M. T., Rossen, W. R. & Boukany, P. E. 2017a Polymer conformation during flow in porous media. Soft Matt. 13 (46), 8745–8755.CrossRefGoogle Scholar
Kawale, D., Marques, E., Zitha, P. L. J., Kreutzer, M. T., Rossen, W. R. & Boukany, P. E. 2017b Elastic instabilities during the flow of hydrolyzed polyacrylamide solution in porous media: effect of pore-shape and salt. Soft Matt. 13 (4), 765–775.CrossRefGoogle Scholar
Kekre, R., Butler, J. E. & Ladd, A. J. C. 2010 Comparison of lattice-Boltzmann and Brownian-dynamics simulations of polymer migration in confined flows. Phys. Rev. E 82 (1), 011802.Google ScholarPubMed
Kenney, S., Poper, K., Chapagain, G. & Christopher, G. F. 2013 Large Deborah number flows around confined microfluidic cylinders. Rheol. Acta 52 (5), 485–497.CrossRefGoogle Scholar
Khomami, B. & Moreno, L. D. 1997 Stability of viscoelastic flow around periodic arrays of cylinders. Rheol. Acta 36 (4), 367–383.CrossRefGoogle Scholar
Koelling, K. W. & Prud’homme, R. K. 1991 Instabilities in multi-hole converging flow of viscoelastic fluids. Rheol. Acta 30 (6), 511–522.CrossRefGoogle Scholar
Kwiecien, M. J., Macdonald, I. F. & Dullien, F. A. L. 1990 Three dimensional reconstruction of porous media from serial section data. J. Microsc. 159 (3), 343–359.CrossRefGoogle Scholar
Lanzaro, A., Corbett, D. & Yuan, X.-F. 2017 Non-linear dynamics of semi-dilute PAAm solutions in a microfluidic 3D cross-slot flow geometry. J. Non-Newtonian Fluid Mech. 242, 57–65.CrossRefGoogle Scholar
Lanzaro, A., Li, Z. & Yuan, X.-F. 2015 Quantitative characterization of high molecular weight polymer solutions in microfluidic hyperbolic contraction flow. Microfluid. Nanofluid. 18 (5-6), 819–828.CrossRefGoogle Scholar
Lanzaro, A. & Yuan, X.-F. 2011 Effects of contraction ratio on non-linear dynamics of semi-dilute, highly polydisperse PAAm solutions in microfluidics. J. Non-Newtonian Fluid Mech. 166 (17-18), 1064–1075.CrossRefGoogle Scholar
Larson, R. G. 1992 Flow-induced mixing, demixing, and phase transitions in polymeric fluids. Rheol. Acta 31 (6), 497–520.CrossRefGoogle Scholar
Ma, H. & Graham, M. D. 2005 Theory of shear-induced migration in dilute polymer solutions near solid boundaries. Phys. Fluids 17 (8), 083103.CrossRefGoogle Scholar
McKinley, G. H., Pakdel, P. & Öztekin, A. 1996 Rheological and geometric scaling of purely elastic flow instabilities. J. Non-Newtonian Fluid Mech. 67, 19–47.CrossRefGoogle Scholar
Mitchell, J., Lyons, K., Howe, A. M. & Clarke, A. 2016 Viscoelastic polymer flows and elastic turbulence in three-dimensional porous structures. Soft Matt. 12 (2), 460–468.CrossRefGoogle ScholarPubMed
Mongruel, A. & Cloitre, M. 1995 Extensional flow of semidilute suspensions of rod-like particles through an orifice. Phys. Fluids 7 (11), 2546–2552.CrossRefGoogle Scholar
Mongruel, A. & Cloitre, M. 2003 Axisymmetric orifice flow for measuring the elongational viscosity of semi-rigid polymer solutions. J. Non-Newtonian Fluid Mech. 110 (1), 27–43.CrossRefGoogle Scholar
Obey, T. M. & Griffiths, P. C. 1999 Polymer adsorption: fundamentals. In Principles of Polymer Science and Technology in Cosmetic and Personal Care (ed. Goddard, E. D. & Gruber, J. V.), pp. 51–72. Marcel Dekker.Google Scholar
O’Connell, M. G., Lu, N. B., Browne, C. A. & Datta, S. S. 2019 Cooperative size sorting of deformable particles in porous media. Soft Matt. 15, 3620.CrossRefGoogle ScholarPubMed
Odell, J. A. & Haward, S. J. 2006 Viscosity enhancement in non-Newtonian flow of dilute aqueous polymer solutions through crystallographic and random porous media. Rheol. Acta 45 (6), 853–863.CrossRefGoogle Scholar
Olmsted, P. D. 2008 Perspectives on shear banding in complex fluids. Rheol. Acta 47 (3), 283–300.CrossRefGoogle Scholar
Pak, T., Butler, I. B., Geiger, S., van Dijke, M. I. J. & Sorbie, K. S. 2015 Droplet fragmentation: 3D imaging of a previously unidentified pore-scale process during multiphase flow in porous media. Proc. Natl Acad. Sci. USA 112 (7), 1947–1952.CrossRefGoogle ScholarPubMed
Pakdel, P. & McKinley, G. H. 1996 Elastic instability and curved streamlines. Phys. Rev. Lett. 77 (12), 2459.CrossRefGoogle ScholarPubMed
Pan, L., Morozov, A., Wagner, C. & Arratia, P. E. 2013 Nonlinear elastic instability in channel flows at low Reynolds numbers. Phys. Rev. Lett. 110 (17), 174502.CrossRefGoogle ScholarPubMed
Pearson, J. R. A. 1976 Instability in non-Newtonian flow. Annu. Rev. Fluid Mech. 8 (1), 163–181.CrossRefGoogle Scholar
Pilitsis, S. & Beris, A. N. 1989 Calculations of steady-state viscoelastic flow in an undulating tube. J. Non-Newtonian Fluid Mech. 31 (3), 231–287.CrossRefGoogle Scholar
Pilitsis, S. & Beris, A. N. 1991 Viscoelastic flow in an undulating tube. Part II. Effects of high elasticity, large amplitude of undulation and inertia. J. Non-Newtonian Fluid Mech. 39 (3), 375–405.CrossRefGoogle Scholar
Pitts, M. J., Campbell, T. A., Surkalo, H., Wyatt, K. et al. 1995 Polymer flood of the Rapdan pool, Saskatchewan, Canada. SPE Res. Engng 10 (03), 183–186.Google Scholar
Qin, B. & Arratia, P. E. 2017 Characterizing elastic turbulence in channel flows at low Reynolds number. Phys. Rev. Fluids 2 (8), 083302.CrossRefGoogle Scholar
Qin, B., Salipante, P. F., Hudson, S. D. & Arratia, P. E. 2019 Upstream vortex and elastic wave in the viscoelastic flow around a confined cylinder. J Fluid Mech. 864, R2.CrossRefGoogle ScholarPubMed
Ribeiro, V. M., Coelho, P. M., Pinho, F. T. & Alves, M. A. 2014 Viscoelastic fluid flow past a confined cylinder: three-dimensional effects and stability. Chem. Engng Sci. 111, 364–380.CrossRefGoogle Scholar
Rodd, L. E., Cooper-White, J. J., Boger, D. V. & McKinley, G. H. 2007 Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries. J. Non-Newtonian Fluid Mech. 143 (2-3), 170–191.CrossRefGoogle Scholar
Roote, D. S.1998 In situ flushing. Technology Status Report. Ground Water Remediation Technology Analysis Center; available at http://www.gwrtac.org.Google Scholar
Rubinstein, M. & Colby, R. H. 2003 Polymer Physics. Oxford University Press.Google Scholar
Sadanandan, B. & Sureshkumar, R. 2004 Global linear stability analysis of viscoelastic flow through a periodic channel. J. Non-Newtonian Fluid Mech. 122 (1-3), 55–67.CrossRefGoogle Scholar
Sandiford, B. B. et al. 1964 Laboratory and field studies of water floods using polymer solutions to increase oil recoveries. J. Petrol. Tech. 16 (08), 917–922.CrossRefGoogle Scholar
Schroeder, C. M., Babcock, H. P., Shaqfeh, E. S. G. & Chu, S. 2003 Observation of polymer conformation hysteresis in extensional flow. Science 301 (5639), 1515–1519.CrossRefGoogle ScholarPubMed
Shi, X. & Christopher, G. F. 2016 Growth of viscoelastic instabilities around linear cylinder arrays. Phys. Fluids 28 (12), 124102.CrossRefGoogle Scholar
Shi, X., Kenney, S., Chapagain, G. & Christopher, G. F. 2015 Mechanisms of onset for moderate mach number instabilities of viscoelastic flows around confined cylinders. Rheol. Acta 54 (9-10), 805–815.CrossRefGoogle Scholar
Son, Y. 2007 Determination of shear viscosity and shear rate from pressure drop and flow rate relationship in a rectangular channel. Polymer 48 (2), 632–637.CrossRefGoogle Scholar
Sorbie, K. S. 2013 Polymer-Improved Oil Recovery. Springer.Google Scholar
Sousa, P. C., Pinho, F. T., Oliveira, M. S. N. & Alves, M. A. 2015 Purely elastic flow instabilities in microscale cross-slot devices. Soft Matt. 11 (45), 8856–8862.CrossRefGoogle ScholarPubMed
Sureshkumar, R., Beris, A. N. & Avgousti, M. 1994 Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow. Proc. R. Soc. Lond. A 447 (1929), 135–153.Google Scholar
Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9 (3), 743–755.CrossRefGoogle Scholar
Talwar, K. K. & Khomami, B. 1995 Flow of viscoelastic fluids past periodic square arrays of cylinders: inertial and shear thinning viscosity and elasticity effects. J. Non-Newtonian Fluid Mech. 57 (2-3), 177–202.CrossRefGoogle Scholar
Terrapon, V. E., Dubief, Y., Moin, P., Shaqfeh, E. S. G. & Lele, S. K. 2004 Simulated polymer stretch in a turbulent flow using Brownian dynamics. J. Fluid Mech. 504, 61–71.CrossRefGoogle Scholar
Vanapalli, S. A., Ceccio, S. L. & Solomon, M. J. 2006 Universal scaling for polymer chain scission in turbulence. Proc. Natl Acad. Sci. USA 103 (45), 16660–16665.CrossRefGoogle ScholarPubMed
Varshney, A. & Steinberg, V. 2017 Elastic wake instabilities in a creeping flow between two obstacles. Phys. Rev. Fluids 2 (5), 051301.CrossRefGoogle Scholar
Vázquez-Quesada, A. & Ellero, M. 2012 SPH simulations of a viscoelastic flow around a periodic array of cylinders confined in a channel. J. Non-Newtonian Fluid Mech. 167, 1–8.CrossRefGoogle Scholar
Vermolen, E. C. M., Van Haasterecht, M. J. T., Masalmeh, S. K. et al. 2014 A systematic study of the polymer visco-elastic effect on residual oil saturation by core flooding. In SPE EOR Conference at Oil and Gas West Asia. Society of Petroleum Engineers.Google Scholar
Walkama, D. M., Waisbord, N. & Guasto, J. S.2019 Disorder suppresses chaos in viscoelastic flows. arXiv:1906.11868.Google Scholar
Wang, D., Wang, G., Xia, H. et al. 2011a Large scale high visco-elastic fluid flooding in the field achieves high recoveries. In SPE Enhanced Oil Recovery Conference. Society of Petroleum Engineers.Google Scholar
Wang, S.-Q., Ravindranath, S. & Boukany, P. E. 2011b Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple-shear rheometry: a roadmap of nonlinear rheology. Macromolecules 44 (2), 183–190.CrossRefGoogle Scholar
Wei, B., Romero-Zerón, L. & Rodrigue, D. 2014 Oil displacement mechanisms of viscoelastic polymers in enhanced oil recovery (EOR): a review. J. Petrol. Explor. Prod. Technol. 4 (2), 113–121.CrossRefGoogle Scholar
Zaitoun, A., Bertin, H., Lasseux, D. et al. 1998 Two-phase flow property modifications by polymer adsorption. In SPE/DOE Improved Oil Recovery Symposium. Society of Petroleum Engineers.Google Scholar
Zaitoun, A, Kohler, N et al. 1988 Two-phase flow through porous media: effect of an adsorbed polymer layer. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.Google Scholar
Zami-Pierre, F., De Loubens, R., Quintard, M. & Davit, Y. 2016 Transition in the flow of power-law fluids through isotropic porous media. Phys. Rev. Lett. 117 (7), 074502.CrossRefGoogle ScholarPubMed
Zilz, J., Poole, R. J., Alves, M. A., Bartolo, D., Levaché, B. & Lindner, A. 2012 Geometric scaling of a purely elastic flow instability in serpentine channels. J. Fluid Mech. 712, 203–218.CrossRefGoogle Scholar
Zitha, P., Chauveteau, G., Zaitoun, A. et al. 1995 Permeability  dependent propagation of polyacrylamides under near-wellbore flow conditions. In SPE International Symposium on Oilfield Chemistry. Society of Petroleum Engineers.Google Scholar
Zitha, P. L. J., Chauveteau, G. & Léger, L. 2001 Unsteady-state flow of flexible polymers in porous media. J. Colloid Interface Sci. 234 (2), 269–283.CrossRefGoogle ScholarPubMed