- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Reactive convective dissolution with differential diffusivities: Nonlinear simulations of onset times and asymptotic fluxes

M. Jotkar*, L. Rongy†, and A. De Wit‡

  • Université libre de Bruxelles, Nonlinear Physical Chemistry Unit, Faculté des Sciences, Campus Plaine, C.P. 231, 1050 Brussels, Belgium

  • *mjotkar@ulb.ac.be
  • †lrongy@ulb.ac.be
  • ‡adewit@ulb.ac.be
PDF

Phys. Rev. Fluids 5, 104502 – Published 19 October, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.104502

Abstract

Convection can develop upon dissolution of a given species A in a host phase when dissolution leads to a buoyantly unstable density stratification. If A reacts with a solute B present in the host solution according to a bimolecular A+B→C reaction, convective dissolution can be enhanced or slowed down depending on the relative contribution to density of each chemical species. We study numerically the influence of differential diffusion on such reactive convective dissolution in the nonlinear regime. In particular we compute the temporal evolution of the dissolution flux, its asymptotic value and the onset time of convection as a function of the ratio of the diffusion coefficients. We find that, when B diffuses faster than C, the density profiles can exhibit a local minimum below the reaction front where a double-diffusive instability develops. This has a destabilizing effect and leads to enhanced mixing, earlier onset of convection, and increased asymptotic fluxes. On the other hand, when B diffuses slower than C, the density profiles can contain a local minimum at the reaction front followed by a local maximum below, which gives rise to two convection zones with a diffusive-layer convection instability occurring below the reaction front. The overall dynamics is stabilizing with delayed onset of convection and with smaller asymptotic fluxes. When B and C diffuse at an equal rate but differently from A, differential diffusion can accelerate or slow down convection.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. Intergovernmental Panel on Climate Change (IPCC) special report on Carbon Dioxide Capture and Storage (Cambridge University Press, New York, 2005).
  2. G. S. Pau, J. B. Bell, K. Pruess, A. S. Almgren, M. J. Lijewski, and K. Zhang, High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers, Adv. Water Resour. 33, 443 (2010).
  3. M. T. Elenius and K. Johannsen, On the time scales of nonlinear instability in miscible displacement porous media flow, Comput. Geosci. 16, 901 (2012).
  4. A. C. Slim, M. M. Bandi, J. C. Miller, and L. Mahadevan, Dissolution-driven convection in a Hele-Shaw cell, Phys. Fluids 25, 024101 (2013).
  5. A. C. Slim, Solutal-convection regimes in a two-dimensional porous medium, J. Fluid Mech. 741, 461 (2014).
  6. H. E. Huppert and J. A. Neufeld, The fluid mechanics of carbon dioxide sequestration, Annu. Rev. Fluid Mech. 46, 255 (2014).
  7. H. Emami-Meybodi, H. Hassanzadeh, C. P. Green, and J. Ennis-King, Convective dissolution of CO2 in saline aquifers: Progress in modeling and experiments, Int. J. Greenhouse Gas Control 40, 238 (2015).
  8. A. De Wit, Chemo-hydrodynamic patterns in porous media, Phil. Trans. R. Soc. A 374, 20150419 (2016).
  9. C. Thomas, S. Dehaeck, and A. De Wit, Convective dissolution of CO2 in water and salt solutions, Int. J. Greenhouse Gas Control 72, 105 (2018).
  10. J. Ennis-King and L. Paterson, Coupling of geochemical reactions and convective mixing in the long-term geological storage of carbon dioxide, Int. J. Greenhouse Gas Control 1, 86 (2007).
  11. M. A. Budroni, L. A. Riolfo, L. Lemaigre, F. Rossi, M. Rustici, and A. De Wit, Chemical control of hydrodynamic instabilities in partially miscible two-layer systems, J. Phys. Chem. Lett. 5, 875 (2014).
  12. V. Loodts, C. Thomas, L. Rongy, and A. De Wit, Control of Convective Dissolution by Chemical Reactions: General Classification and Application to CO2 Dissolution in Reactive Aqueous Solutions, Phys. Rev. Lett. 113, 114501 (2014).
  13. C. Wylock, A. Rednikov, B. Haut, and P. Colinet, Nonmonotonic Raleigh-Taylor instabilities driven by gas-liquid CO2 chemisorption, J. Phys. Chem. B 118, 11323 (2014).
  14. S. S. S. Cardoso and J. T. H. Andres, Geochemistry of silicate-rich rocks can curtail spreading of carbon dioxide in subsurface aquifers, Nat. Commun. 5, 5743 (2014).
  15. V. Loodts, L. Rongy, and A. De Wit, Chemical control of dissolution-driven convection in partially miscible systems: Theoretical classification, Phys. Chem. Chem. Phys. 17, 29814 (2015).
  16. V. Loodts, P. M. J. Trevelyan, L. Rongy, and A. De Wit, Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification, Phys. Rev. E 94, 043115 (2016).
  17. C. Thomas, V. Loodts, L. Rongy, and A. De Wit, Convective dissolution of CO2 in reactive alkaline solutions: Active role of spectator ions, Int. J. Greenhouse Gas Control 53, 230 (2016).
  18. I. Cherezov and S. S. S. Cardoso, Acceleration of convective dissolution by chemical reaction in a Hele-Shaw cell, Phys. Chem. Chem. Phys. 18, 23727 (2016).
  19. V. Loodts, Influence of chemical reactions on convective dissolution: a theoretical study, Ph.D. thesis, Université libre de Bruxelles, Brussels, Belgium, 2016.
  20. V. Loodts, B. Knaepen, L. Rongy, and A. De Wit, Enhanced steady-state dissolution flux in reactive convective dissolution, Phys. Chem. Chem. Phys. 19, 18565 (2017).
  21. P. Ghoshal, M. C. Kim, and S. S. S. Cardoso, Reactive-convective dissolution in a porous medium: The storage of carbon dioxide in saline aquifers, Phys. Chem. Chem. Phys. 19, 644 (2017).
  22. C. Wylock, A. Rednikov, P. Colinet, and B. Haut, Experimental and numerical analysis of buoyancy-induced instability during CO2 absorption in NaHCO3−Na2CO3 aqueous solutions, Chem. Eng. Sc. 157, 232 (2017).
  23. M. A. Budroni, C. Thomas, and A. De Wit, Chemical control of dissolution-driven convection in partially miscible systems: Nonlinear simulations and experiments, Phys. Chem. Chem. Phys. 19, 7936 (2017).
  24. V. Loodts, H. Saghou, B. Knaepen, L. Rongy, and A. De Wit, Differential diffusivity effects in reactive convective dissolution, Fluids 3, 83 (2018).
  25. M. C. Kim and S. S. S. Cardoso, Diffusivity ratio effect on the onset of the buoyancy-driven instability of an A+B→C chemical reaction system in a Hele-Shaw cell: Asymptotic and linear stability analyses, Phys. Fluids 30, 094102 (2018).
  26. M. Jotkar, A. De Wit, and L. Rongy, Enhanced convective dissolution due to an A+B→C reaction: Control of the nonlinear dynamics via solutal density contributions, Phys. Chem. Chem. Phys. 21, 6432 (2019).
  27. T. Lei and K. H. Luo, Pore-scale study of dissolution-driven density instability with reaction A + B → C in porous media, Phys. Rev. Fluids 4, 063907 (2019).
  28. A. De Wit, Chemo-hydrodynamic patterns and instabilities, Annu. Rev. Fluid Mech. 52, 531 (2020).
  29. R. W. Griffiths, Layered double-diffusive convection in porous media, J. Fluid Mech. 102, 221 (1981).
  30. H. E. Huppert and J. S. Turner, Double-diffusive convection, J. Fluid Mech. 106, 299 (1981).
  31. P. M. J. Trevelyan, C. Almarcha, and A. De Wit, Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells, J. Fluid Mech. 670, 38 (2011).
  32. J. Carballido-Landeira, P. M. J. Trevelyan, C. Almarcha, and A. De Wit, Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes, Phys. Fluids 25, 024107 (2013).
  33. S. M. J. Raad, H. Hassanzadeh, and J. Ennis-King, On the dynamics of two-component convective dissolution in porous media, Water Resourc. 55, 4030 (2019).
  34. M. C. Kim and S. S. S. Cardoso, Diffusivity ratio effect on the onset of the buoyancy-driven instability of an A+B→C chemical reaction system in a Hele-Shaw cell: Numerical simulations and comparison with experiments, Phys. Fluids 31, 084101 (2019).
  35. T. Lei and K. H. Luo, Differential diffusion effects on density-driven instability of reactive flows in porous media, Phys. Rev. Fluids 5, 033903 (2020).
  36. M. Bestehorn and A. Firoozabadi, Effect of fluctuations on the onset of density-driven convection in porous media, Phys. Fluids 24, 114102 (2012).
  37. N. Tilton, D. Daniel, and A. Riaz, The initial transient period of gravitionally unstable diffusive boundary layers developing in porous media, Phys. Fluids 25, 092107 (2013).
  38. M. Jotkar, L. Rongy, and A. De Wit, Chemically-driven convective dissolution, Phys. Chem. Chem. Phys. 21, 19054 (2019).
  39. V. Moureau, P. Domingo, L. Vervisch, and A. Riaz, Design of a massively parallel CFD code for complex geometries, C. R. Mech. 339, 141 (2011).

Outline

Information

Phys. Rev. Fluids 5, 104502– Published 19 October, 2020
  • Received 28 May 2020
  • Accepted 28 September 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation