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Mixing Efficiency via Alternating Injection in a Heterogeneous Porous Medium

Published online by Cambridge University Press:  15 May 2017

J. S. Li ,
Q. Li ,
W. H. Cai ,
F. C. Li  and
C. Y. Chen
J. S. Li
Affiliation:
Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchu, Taiwan
Q. Li
Affiliation:
School of Energy Science and EngineeringHarbin Institute of TechnologyHarbin, China
W. H. Cai
Affiliation:
School of Energy Science and EngineeringHarbin Institute of TechnologyHarbin, China
F. C. Li
Affiliation:
School of Energy Science and EngineeringHarbin Institute of TechnologyHarbin, China
C. Y. Chen*
Affiliation:
Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchu, Taiwan
*
*Corresponding author (chingyao@mail.nctu.edu.tw)
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Abstract

We numerically verify better fluid mixing efficiency can be achieved by alternating injection scheme in a heterogeneous porous medium, whose permeability heterogeneity is characterized by two statistical parameters, i.e., the variance s and the correlation length l. Nevertheless, the fingering pattern is strongly affected by permeability distribution to result in similar fingering interface on each of injected layer of less viscous fluids. Instead of randomly chaotic fingering interaction in a homogeneous condition, more orderly channeling interaction occurs in a heterogeneous medium. As a result, higher Peclet number Pe (relative measure of advection and diffusion effects) generally leads to worse mixing efficiency in a heterogeneous medium, which might contradict the result found in a homogeneous case. By the same token, in the cases which strong chaotic fingering interaction already exists in homogeneous conditions, e.g., sufficiently short alternating injection interval Δt, large viscosity contrast A and high Pe, the presence of permeability heterogeneity would constrain the randomly chaotic fingering interaction and favors the more orderly channeling interaction, so that mixing efficiency is deteriorated compared with the corresponding homogeneous case.

Keywords

Heterogeneous porous mediaViscous fingeringAlternating injectionMixing efficiency
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 2 , April 2018 , pp. 167 - 176
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Saffman, P. G. and Taylor, G. I., “The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 245, pp. 312–329 (1958).Google Scholar
2. Homsy, G. M., “Viscous Fingering in Porous Media,” Annual Review of Fluid Mechanics, 19, pp. 271–311 (1987).CrossRefGoogle Scholar
3. McCloud, K. V. and Maher, J. V., “Experimental Perturbations to Saffman-Taylor flow,” Physics Reports, 260, pp. 139–185 (1995).CrossRefGoogle Scholar
4. Li, S., Lowengrub, J. S., Fontana, J. and Palffy-Muhoray, P., “Control of Viscous Fingering Patterns in a Radial Hele-Shaw Cell, Phys,” Physical Review Letters, 102, 174501 (2009).CrossRefGoogle Scholar
5. Chen, C.-Y., Huang, C.-W., Wang, L.-C. and Miranda, J., “Controlling Radial Fingering Patterns in Miscible Confined Flows,” Physical Review E, 82, 56308 (2010).CrossRefGoogle ScholarPubMed
6. Dias, E. O. and Miranda, J., “Control of Radial Fingering Patterns: A Weakly Nonlinear Approach,” Physical Review E, 8, 016312 (2010).CrossRefGoogle Scholar
7. Dias, E. O., Alvarez-Lacalle, E., Carvalho, M. S. and Miranda, J. A., “Minimization of Viscous Fluid Fingering: A Variational Scheme for Optimal Flow Rates,” Physical Review Letters, 109, 144502 (2012).CrossRefGoogle ScholarPubMed
8. Huang, Y.-S. and Chen, C.-Y., “A Numerical Study on Radial Hele-Shaw Flow: Influence of Fluid Miscibility and Injection Scheme,” Computational Mechanics, 55, pp. 407–420 (2015).CrossRefGoogle Scholar
9. Chen, C.-Y. and Yan, P.-Y., “Radial Flows in Heterogeneous Porous Media with a Linear Injection Scheme,” Computers & Fluids, 142, pp. 30–36, (2017).CrossRefGoogle Scholar
10. Stone, H. A., Stroock, A. D. and Ajdari, A., “Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip,” Annual Review of Fluid Mechanics, 36, pp. 381–411 (2004).CrossRefGoogle Scholar
11. Katija, K. and Dabiri, J. O., “A Viscosity-Enhanced Mechanism for Biogenic Ocean Mixing,” Nature, 460, pp. 624–626 (2009).CrossRefGoogle ScholarPubMed
12. Korolev, K. S., Avlund, M., Hallatschek, O. and Nelson, D. R., “Genetic Demixing and Evolution in Linear Stepping Stone Models,” Reviews of Modern Physics, 82, pp. 1691–1718 (2010).CrossRefGoogle ScholarPubMed
13. Jha, B., Cueto-Felgueroso, L. and Juanes, R., “Fluid Mixing from Viscous Fingering,” Physical Review Letters, 106, 194502 (2011).CrossRefGoogle ScholarPubMed
14. Jha, B., Cueto-Felgueroso, L. and Juanes, R., “Synergetic Fluid Mixing from Viscous Fingering and Alternating Injection,” Physical Review Letters, 111, 144501 (2013).CrossRefGoogle ScholarPubMed
15. Chen, C.-Y., Huang, Y.-C., Huang, Y.-S. and Miranda, J. A., “Enhanced Mixing via Alternating Injection in Radial Hele-Shaw Flows,” Physical Review E, 92, 043008 (2015).CrossRefGoogle ScholarPubMed
16. Tan, C. T. and Homsy, G. M., “Viscous Fingering with Permeability Heterogeneity,” Physics of Fluids A, 4, pp. 1099–1101 (1992).CrossRefGoogle Scholar
17. Chen, C.-Y. and Meiburg, E., “Miscible Porous Media Flows in the Quarter Five-Spot Configuration. Part 1: The Homogeneous Case,” Journal of Fluid Mechanics, 371, pp. 233–268 (1998).CrossRefGoogle Scholar
18. Chen, C.-Y. and Meiburg, E., “Miscible Porous Media Flows in the Quarter Five-Spot Configuration. Part 2: Effect of Heterogeneities,” Journal of Fluid Mechanics, 371, pp. 269–299 (1998).CrossRefGoogle Scholar
19. Meiburg, E. and Chen, C.-Y., “High-Accuracy Implicit Finite-Difference Simulations of Homogeneous and Heterogeneous Miscible Porous Medium Flows,” SPE Journal, 5, pp. 129–137 (2000).CrossRefGoogle Scholar
20. Chen, C.-Y. and Yan, P.-Y., “A Diffuse Interface Approach to Injection-Driven Flows of Different Miscibility in Heterogeneous Porous Media,” Physics of Fluids, 27, 083101 (2015).CrossRefGoogle Scholar
21. Chen, C.-Y., Lin, T.-S., and Miranda, J. A., “Rotationally Induced Fingering Patterns in a Two-Dimensional Heterogeneous Porous Medium,” Physical Review E, 94, 053105 (2016).CrossRefGoogle Scholar
22. Shinozuka, M. and Jan, C.-M., “Digital Simulation of Random Processes and Its Applications,” Journal of Sound and Vibration, 25, pp. 111–128 (1972).CrossRefGoogle Scholar