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A unified theory for sharp dissolution front propagation in chemical dissolution of fluid-saturated porous rocks

  • ChongBin ZhaoEmail author
  • Bruce Hobbs
  • Alison Ord
Article
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Abstract

This paper presents a unified theory to deal with when, why and how a sharp acidization dissolution front (ADF), which is represented by the porosity distribution curve, can take place in an acidization dissolution system composed of fluid-saturated porous rocks. The theory contains the following main points: (1) A reaction rate of infinity alone can lead to a sharp ADF of the Stefan-type in the acidization dissolution system. This sharp front is unstable when permeability in the downstream region is smaller than that in the upstream region. (2) For a finite reaction rate, when the acid dissolution capacity number approaches zero, the ADF can have a sharp profile of the Stefan-type either on a much smaller time scale or on a much larger time scale than the dissolution time scale. In the former case, the ADF may become unstable on a much larger time scale than the transport time scale, while in the latter case, it may become unstable if the growth rate of a small perturbation is greater than zero. (3) On the dissolution time scale, even if both the reaction rate is finite and the acid dissolution capacity number approaches zero, the profile of an ADF may not be sharp because it is in a transient state. In this case, not only can an ADF change its profile with time, but also its morphology can grow if the growth rate of a small perturbation is greater than zero. Due to the involvement of both the change rate and the growth rate of the ADF profile, it is necessary to conduct a transient linear stability analysis for determining whether or not a time-dependent ADF is stable in the acidization dissolution system.

Keywords

sharp dissolution front stationary/steady state transient state acid dissolution capacity acidization dissolution porous rocks 

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References

  1. 1.
    Gow P A, Upton P, Zhao C, et al. Copper-gold mineralisation in New Guinea: Numerical modelling of collision, fluid flow and intrusionrelated hydrothermal systems. Aust J Earth Sci, 2002, 49: 753–771CrossRefGoogle Scholar
  2. 2.
    Schaubs P M, Zhao C. Numerical models of gold-deposit formation in the Bendigo-Ballarat Zone, Victoria. Aust J Earth Sci, 2002, 49: 1077–1096CrossRefGoogle Scholar
  3. 3.
    Sorjonen-Ward P, Zhang Y, Zhao C. Numerical modelling of orogenic processes and gold mineralisation in the southeastern part of the Yilgarn Craton, Western Australia. Aust J Earth Sci, 2002, 49: 935–964CrossRefGoogle Scholar
  4. 4.
    Ju M, Zhao C, Dai T, et al. Finite element modeling of pore-fluid flow in the Dachang ore district, Guangxi, China: Implications for hydrothermal mineralization. Geosci Front, 2011, 2: 463–474CrossRefGoogle Scholar
  5. 5.
    Liu Y, Dai T. Numerical modeling of pore-fluid flow and heat transfer in the Fushan iron ore district, Hebei, China: Implications for hydrothermal mineralization. J Geochem Explor, 2014, 144: 115–127CrossRefGoogle Scholar
  6. 6.
    Chadam J, Hoff D, Merino E, et al. Reactive infiltration instabilities. IMA J Appl Math, 1986, 36: 207–221MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chadam J, Ortoleva P, Sen A. A weakly nonlinear stability analysis of the reactive infiltration interface. IAM J Appl Math, 1988, 48: 1362–1378MathSciNetzbMATHGoogle Scholar
  8. 8.
    Ormond A, Ortoleva P. Numerical modeling of reaction-induced cavities in a porous rock. J Geophys Res, 2000, 105: 16737–16747CrossRefGoogle Scholar
  9. 9.
    Ortoleva P, Chadam J, Merino E, et al. Geochemical self-organization II: The reactive-infiltration instability. Am J Sci, 1987, 287: 1008–1040Google Scholar
  10. 10.
    Chen J S, Liu C W. Numerical simulation of the evolution of aquifer porosity and species concentrations during reactive transport. Comput Geosci, 2002, 28: 485–499CrossRefGoogle Scholar
  11. 11.
    Chen J S, Liu C W. Interaction of reactive fronts during transport in a homogeneous porous medium with initial small non-uniformity. J Contam Hydrol, 2004, 72: 47–66CrossRefGoogle Scholar
  12. 12.
    Zhao C, Hobbs B E, Hornby P, et al. Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. Int J Numer Anal Meth Geomech, 2008, 32: 1107–1130CrossRefzbMATHGoogle Scholar
  13. 13.
    Chen J S, Liu C W, Lai G X, et al. Effects of mechanical dispersion on the morphological evolution of a chemical dissolution front in a fluidsaturated porous medium. J Hydrol, 2009, 373: 96–102CrossRefGoogle Scholar
  14. 14.
    Zhao C, Hobbs B E, Ord A, et al. Effects of mineral dissolution ratios on chemical-dissolution front instability in fluid-saturated porous media. Transp Porous Media, 2010, 82: 317–335CrossRefGoogle Scholar
  15. 15.
    Sherwood J D. Stability of a plane reaction front in a porous medium. Chem Eng Sci, 1987, 42: 1823–1829CrossRefGoogle Scholar
  16. 16.
    Hinch E J, Bhatt B S. Stability of an acid front moving through porous rock. J Fluid Mech, 1990, 212: 279–288CrossRefzbMATHGoogle Scholar
  17. 17.
    Fredd C N, Fogler H S. Influence of transport and reaction on wormhole formation in porous media. Aiche J, 1998, 44: 1933–1949CrossRefGoogle Scholar
  18. 18.
    Golfier F, Zarcone C, Bazin B, et al. On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium. J Fluid Mech, 2002, 457: 213–254CrossRefzbMATHGoogle Scholar
  19. 19.
    Panga M K R, Ziauddin M, Balakotaiah V. Two-scale continuum model for simulation of wormholes in carbonate acidization. Aiche J, 2005, 51: 3231–3248CrossRefGoogle Scholar
  20. 20.
    Kalia N, Balakotaiah V. Modeling and analysis of wormhole formation in reactive dissolution of carbonate rocks. Chem Eng Sci, 2007, 62: 919–928CrossRefGoogle Scholar
  21. 21.
    Kalia N, Balakotaiah V. Effect of medium heterogeneities on reactive dissolution of carbonates. Chem Eng Sci, 2009, 64: 376–390CrossRefGoogle Scholar
  22. 22.
    Cohen C E, Ding D, Quintard M, et al. From pore scale to wellbore scale: Impact of geometry on wormhole growth in carbonate acidization. Chem Eng Sci, 2008, 63: 3088–3099CrossRefGoogle Scholar
  23. 23.
    Zhao C, Hobbs B E, Ord A. Theoretical analyses of acidization dissolution front instability in fluid-saturated carbonate rocks. Int J Numer Anal Meth Geomech, 2013, 37: 2084–2105CrossRefGoogle Scholar
  24. 24.
    Wangen M. Stability of reaction-fronts in porous media. Appl Math Model, 2013, 37: 4860–4873MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Szymczak P, Ladd A J C. Reactive-infiltration instabilities in rocks. Part 2. Dissolution of a porous matrix. J Fluid Mech, 2014, 738: 591–630zbMATHGoogle Scholar
  26. 26.
    Zhao C B, Hobbs B, Ord A. A new alternative approach for investigating acidization dissolution front propagation in fluid-saturated carbonate rocks. Sci China Tech Sci, 2017, 60: 1197–1210CrossRefGoogle Scholar
  27. 27.
    Zhao C, Hobbs B E, Ord A. Theoretical analyses of the effects of solute dispersion on chemical-dissolution front instability in fluidsaturated porous media. Transp Porous Media, 2010, 84: 629–653MathSciNetCrossRefGoogle Scholar
  28. 28.
    Carman P C. Flow of Gases Through Porous Media. New York: Academic Press, 1956zbMATHGoogle Scholar
  29. 29.
    Ortoleva P, Merino E, Moore C, et al. Geochemical self-organization I: Reaction-transport feedbacks and modeling approach. Am J Sci, 1987, 287: 979–1007Google Scholar
  30. 30.
    Lai K H, Chen J S, Liu C W, et al. Effect of permeability-porosity functions on simulated morphological evolution of a chemical dissolution front. Hydrol Process, 2014, 28: 16–24CrossRefGoogle Scholar
  31. 31.
    Lai K H, Chen J S, Liu C W, et al. Effect of medium permeability anisotropy on the morphological evolution of two non-uniformities in a geochemical dissolution system. J Hydrol, 2016, 533: 224–233CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computational Geosciences Research CentreCentral South UniversityChangshaChina
  2. 2.School of Earth and EnvironmentThe University of Western AustraliaCrawleyAustralia

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