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Resonance-like dynamics in radial cyclic injection flows of immiscible fluids in homogeneous porous media

Published online by Cambridge University Press:  27 April 2017

T. F. Lins  and
J. Azaiez Open the ORCID record for J. Azaiez [Opens in a new window]
T. F. Lins
Affiliation:
Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, AB T2N 1N4, Canada
J. Azaiez*
Affiliation:
Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, AB T2N 1N4, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Interfacial instabilities of immiscible radial displacements in homogeneous porous media are analysed in the case of sinusoidal injection flows. The analysis is carried out through numerical simulations based on the immersed interface and level set methods. Investigations of the effects of the period of the sinusoidal injection flows revealed a novel resonance effect where, for a critical period, the number of fingers as well as their structures are considerably changed. The resonance in the flow development is clearly identified through the abrupt changes in the Fourier spectrum of the interface as well as quantitative characteristics of the flow in the form of the minimum and maximum radii of the interface. For the range of parameters examined in this study that correspond to instabilities dominated by viscous forces, the resonance period was found to correlate with a characteristic time of the flow and the fluids mobility ratio. This new physical phenomenon offers new perspectives for using the flow instability to determine important physical properties such as the viscosity and the surface tension of fluids.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 713 - 729
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Copyright
© 2017 Cambridge University Press 

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References

Ahmadlouydarab, M., Azaiez, J. & Chen, Z. 2015 Immiscible flow displacements with phase change in radial injection. Intl J. Multiphase Flow 72, 73–82.CrossRefGoogle Scholar
Al-Gosayir, M., Leung, J., Babadagli, T. & Al-Bahlani, A. M. M. 2013 Optimization of steam-over-solvent injection in fractured reservoirs (sos-fr) method using hybrid techniques: testing cyclic injection case. J. Petrol. Sci. Engng 110, 74–84.Google Scholar
Barrio, V. L., Schaub, G., Rohde, M., Rabe, S., Vogel, F., Cambra, J. F., Arias, P. L. & Gemez, M. B. 2007 Reactor modeling to simulate catalytic partial oxidation and steam reforming of methane. Comparison of temperature profiles and strategies for hot spot minimization. Intl J. Hydrogen Energy 32 (10), 1421–1428.Google Scholar
Bataille, J. 1968 Stabilité d’un écoulement radial non miscible. Rev. Inst. Fr. Pet. Ann. Combust. Liq. 23, 1349–1364.Google Scholar
Brailovsky, I., Babchin, A., Frankel, M. & Sivashinsky, G. 2006 Fingering instability in water–oil displacement. Trans. Porous Med. 63 (3), 363–380.Google Scholar
Cardoso, S. S. S. & Woods, A. W. 1995 The formation of drops through viscous instability. J. Fluid Mech. 289, 351–378.CrossRefGoogle Scholar
Chen, J.-D. 1987 Radial viscous fingering patterns in Hele-Shaw cells. Exp. Fluids 5, 363–371.Google Scholar
Chen, C.-Y., Huang, Y.-C., Huang, Y.-S. & Miranda, J. A. 2015 Enhanced mixing via alternating injection in radial Hele-Shaw flows. Phys. Rev. E 92, 043008.Google Scholar
Dias, E. O., Alvarez-Lacalle, E., Carvalho, M. S. & Miranda, J. A. 2012 Minimization of viscous fluid fingering: avariational scheme for optimal flow rates. Phys. Rev. Lett. 109 (4), 144502.Google Scholar
Dias, E. O. & Miranda, J. A. 2010 Control of radial fingering patterns: a weakly nonlinear approac. Phys. Rev. E 81, 016312.Google Scholar
Dias, E. O. & Miranda, J. A. 2013 Minimization of instabilities in growing interfaces: a variational approach. Phys. Rev. E 88 (6), 062404.Google Scholar
Dias, E. O., Parisio, F. & Miranda, J. A. 2010 Suppression of viscous fluid fingering: a piecewise-constant injection process. Phys. Rev. E 82 (6), 067301.Google Scholar
Gland, N. & Pisarenko, D. 2003 Controlling fingering instabilities in nonflat Hele-Shaw geometries. In Thermo-Hydro-Mechanical Coupling in Fractured Rock (ed. Kümpel, H.-J.), vol. 160, pp. 977–988. Birkhäuser.Google Scholar
Hill, S. 1952 Channeling in packed columns. Chem. Engng Sci. 1, 247–253.Google Scholar
Homsy, G. M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271–311.Google Scholar
Hornof, V. & Baig, F. U. 1995 Influence of interfacial reaction and mobility ratio on the displacement of oil in a Hele-Shaw cell. Exp. Fluids 18, 448–453.Google Scholar
Hou, T. Y., Li, Z., Osher, S. & Zhao, H. 1997 A hybrid method for moving interface problems with application to the Hele-Shaw flow. J. Comput. Phys. 134, 236–252.Google Scholar
Huang, Y. S. & Chen, C. Y. 2015 A numerical study on radial Hele-Shaw flow: influence of fluid miscibility and injection scheme. Comput. Mech. 55 (2), 407–420.Google Scholar
Kueper, B. H. & Frind, E. O. 1988 An overview of immiscible fingering in porous media. J. Contam. Hydrol. 2 (2), 95–110.Google Scholar
Leshchine, A., Thrasher, M., Mineev-Weinstein, M. B. & Swinney, H. L. 2010 Harmonic moment dynamics in laplacian growth. Phys. Rev. E 81, 016206.Google Scholar
Li, S., Lowengrub, J. S., Fontana, J. & Palffy-Muhoray, P. 2009 Control of viscous fingering patterns in a radial Hele-Shaw cell. Phys. Rev. Lett. 102 (17), 174501.Google Scholar
Lins, T. F. & Azaiez, J. 2016 Flow instabilities of time-dependent injection schemes in immiscible displacements. Can. J. Chem. Engng 94, 2061–2071.CrossRefGoogle Scholar
McCloud, K. V. & Maher, J. V. 1995 Experimental perturbations to Saffman–Taylor flow. Phys. Rep. 260 (3), 139–185.Google Scholar
Miranda, J. A. & Widom, M. 1998 Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis. Physica D 120 (3), 315–328.Google Scholar
Paterson, L. 1981 Radial fingering in a Hele-Shaw cell. J. Fluid Mech. 113, 513–529.Google Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220–252.Google Scholar
dos Reis, L. & Miranda, J. A. 2011 Controlling fingering instabilities in nonflat Hele-Shaw geometries. Phys. Rev. E 84 (6), 066313.Google Scholar
Ruith, M. & Meiburg, E. 2000 Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium. J. Fluid Mech. 420, 225–257.Google Scholar
Saffman, P. G. & Taylor, S. G. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312–329.Google Scholar
Slobod, R. L. & Caudlel, B. H. 1952 X-ray shadowgraph studies of areal sweepout efficiencies. Trans. AIME 195, 265–270.Google Scholar
Surguchev, L., Koundin, A., Melberg, O., Rolfsvg, T. A. & Menardr, W. P. 2002 Cyclic water injection: improved oil recovery at zero cost. Petrol. Geosc. 8, 89–95.Google Scholar
Tan, C. T. & Homsy, G. M. 1986 Stability of miscible displacements in porous media: rectilinear flow. Phys. Fluids 29 (11), 3549–3556.Google Scholar
Tan, C. T. & Homsy, G. M. 1987 Stability of miscible displacements in porous media: radial source flow. Phys. Fluids 30, 1239–1245.CrossRefGoogle Scholar
Tan, C. T. & Homsy, G. M. 1992 Viscous fingering with permeability heterogeneity. Phys. Fluids A 4, 1099–1101.Google Scholar
Yortsos, Y. C. 1990 Instabilities in displacement processes in porous media. J. Phys.: Condens. Matter 2 (S), SA443–SA448.Google Scholar
Yuan, Q. & Azaiez, J. 2014 Cyclic time-dependent reactive flow displacements in porous media. Chem. Engng Sci. 109, 136–146.Google Scholar
Yuan, Q. & Azaiez, J. 2015 Inertial effects in cyclic time-dependent displacement flows in homogeneous porous media. Can. J. Chem. Engng 93 (8), 1490–1499.Google Scholar
Zheng, Z., Kim, H. & Stone, H. A. 2015 Controlling viscous fingering using time-dependent strategies. Phys. Rev. Lett. 115, 174501.Google Scholar