DOI: https://doi.org/10.26089/NumMet.v21r104

Use of the computational topology to analyze the pore space changes during chemical dissolution

Authors

  • T.S. Khachkova
  • Ya.V. Bazaikin
  • V.V. Lisitsa

Keywords:

persistence homology
chemical dissolution

Abstract

A new algorithm for constructing the persistence diagrams to estimate the changes in the rock matrix topology during the chemical fluid-solid interaction. In the space of the persistence diagrams, a metric is introduced, which allows one to clusterize the diagrams in order to estimate their dissimilarities in the topology changes. This clusterization shows that the main parameters affecting the topology of the rock matrix are the reaction rate and the diffusion coefficient, whereas the fluid flow rate makes a smaller effect on the topology.


Published

2020-01-30

Issue

Section

Section 1. Numerical methods and applications

Author Biographies

T.S. Khachkova

Ya.V. Bazaikin

V.V. Lisitsa


References

  1. Ya. V. Bazaikin, Lectures on Computational Topology (Novosib. Gos. Univ., Novosibirsk, 2017) [in Russian].
  2. K. A. Gadylshina, T. S. Khachkova, and V. V. Lisitsa, “Numerical Modeling of Chemical Interaction between a Fluid and Rocks,” Vychisl. Metody Programm. 20, 457-470 (2019).
  3. M. A. Novikov, Ya. V. Bazaikin, V. V. Lisitsa, and A. A. Kozyaev, “Numerical Modeling of Wave Propagation in Fractured Porous Fluid-Saturated Media,” Vychisl. Metody Programm. 19, 235-252 (2018).
  4. M. A. Novikov, V. V. Lisitsa, and A. A. Kozyaev, “Numerical Modeling of Wave Processes in Fractured Porous Fluid-Saturated Media,” Vychisl. Metody Programm. 19, 130-149 (2018).
  5. Y. Al-Khulaifi, Q. Lin, M. J. Blunt, and B. Bijeljic, “Pore-Scale Dissolution by CO_2 Saturated Brine in a Multimineral Carbonate at Reservoir Conditions: Impact of Physical and Chemical Heterogeneity,” Water Resour. Res. 55 (4), 3171-3193 (2019).
  6. A. E. Amikiya and M. K. Banda, “Modelling and Simulation of Reactive Transport Phenomena,” J. Comput. Sci. 28, 155-167 (2018).
  7. C. Arson and T. Vanorio, “Chemomechanical Evolution of Pore Space in Carbonate Microstructures upon Dissolution: Linking Pore Geometry to Bulk Elasticity,” J. Geophys. Res.: Solid Earth 120 (10), 6878-6894 (2015).
  8. Y. Bazaikin, B. Gurevich, S. Iglauer, et al., “Effect of CT Image Size and Resolution on the Accuracy of Rock Property Estimates,” J. Geophys. Res.: Solid Earth 122 (5), 3635-3647 (2017).
  9. M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range,” J. Acoust. Soc. Am. 28 (2), 168-178 (1956).
  10. M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range,” J. Acoust. Soc. Am. 28 (2), 179-191 (1956).
  11. S. Carroll, Y. Hao, M. Smith, and Y. Sholokhova, “Development of Scaling Parameters to Describe CO_2-rock Interactions within Weyburn-Midale Carbonate Flow Units,” Int. J. Greenh. Gas Con. 16 (Suppl. 1), S185-S193 (2013).
  12. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer, “Stability of Persistence Diagrams,” Discrete Comput. Geom. 37, 103-120 (2007).
  13. T. B. Costa, K. Kennedy, and M. Peszynska, “Hybrid Three-Scale Model for Evolving Pore-Scale Geometries,” Comput. Geosci. 22 (3), 925-950 (2018).
  14. M.-J. Cui, J.-J. Zheng, R.-J. Zhang, et al., “Influence of Cementation Level on the Strength Behaviour of Bio-Cemented Sand,” Acta Geotech. 12 (5), 971-986 (2017).
  15. H. Edelsbrunner, D. Letscher, and A. Zomorodian, “Topological Persistence and Simplification,” Discrete Comput. Geom. 28, 511-533 (2002).
  16. H. Edelsbrunner and J. L. Harer, Computational Topology: An Introduction (AMS Press, Providence, 2010).
  17. M. Ghommem, W. Zhao, S. Dyer, et al., “Carbonate Acidizing: Modeling, Analysis, and Characterization of Wormhole Formation and Propagation,” J. Petrol. Sci. Eng. 131, 18-33 (2015).
  18. F. Gibou, R. Fedkiw, and S. Osher, “A Review of Level-Set Methods and Some Recent Applications,” J. Comput. Phys. 353, 82-109 (2018).
  19. P. Gouze and L. Luquot, “X-ray Microtomography Characterization of Porosity, Permeability and Reactive Surface Changes during Dissolution,” J. Contam. Hydrol. 120-121}, 45-55 (2011).
  20. D. Guérillot and J. Bruyelle, “Compositional Dual Mesh Method for Single Phase Flow in Heterogeneous Porous Media - Application to CO_2 Storage,” Comput. Geosci. 21 (5-6), 949-961 (2017).
  21. Y. Hao, M. Smith, Y. Sholokhova, and S. Carroll, “CO_2-Induced Dissolution of Low Permeability Carbonates. Part II: Numerical Modeling of Experiments,” Adv. Water Resour. 62 (Part C), 388-408 (2013).
  22. F. Huang, P. Bergmann, C. Juhlin, et al., “The First Post-Injection Seismic Monitor Survey at the Ketzin Pilot CO_2 Storage Site: Results from Time-Lapse Analysis,” Geophys. Prospect. 66 (1), 62-84 (2018).
  23. Q. Kang, L. Chen, A. J. Valocchi, and H. S. Viswanathan, “Pore-Scale Study of Dissolution-Induced Changes in Permeability and Porosity of Porous Media,” J. Hydrol. 517, 1049-1055 (2014).
  24. T. Y. Kong and A. Rosenfeld, “Digital Topology: Introduction and Survey,” Comput. Vision Gr. Image Process. 48 (3), 357-393 (1989).
  25. M. Lebedev, Y. Zhang, M. Sarmadivaleh, et al., “Carbon Geosequestration in Limestone: Pore-Scale Dissolution and Geomechanical Weakening,” Int. J. Greenh. Gas Con. 66, 106-119 (2017).
  26. X. Li, H. Huang, and P. Meakin, “Level Set Simulation of Coupled Advection-Diffusion and Pore Structure Evolution Due to Mineral Precipitation in Porous Media,” Water Resour. Res. 44 (2008).
    doi 10.1029/2007WR006742
  27. X. Li, H. Huang, and P. Meakin, “A Three-Dimensional Level Set Simulation of Coupled Reactive Transport and Precipitation/Dissolution,” Int. J. Heat Mass Transf. 53 (13-14), 2908-2923 (2010).
  28. H. O. McLeod, “Matrix Acidizing,” J. Petroleum Technol. 36 (12), 2055-2069 (1984)
  29. A. Meirmanov, N. Omarov, V. Tcheverda, and A. Zhumaly, “Mesoscopic Dynamics of Solid-Liquid Interfaces. A General Mathematical Model,” Sib. Elektron. Mat. Izv. 12, 884-900 (2015).
  30. H. P. Menke, C. A. Reynolds, M. G. Andrew, et al., “4D Multi-Scale Imaging of Reactive Flow in Carbonates: Assessing the Impact of Heterogeneity on Dissolution Regimes Using Streamlines at Multiple Length Scales,” Chem. Geol. 481, 27-37 (2018).
  31. R. Mittal and G. Iaccarino, “Immersed Boundary Methods,” Ann. Rev. Fluid. Mech. 37 (1), 239-261 (2005).
  32. S. Molins, D. Trebotich, C. I. Steefel, and C. Shen, “An Investigation of the Effect of Pore Scale Flow on Average Geochemical Reaction Rates Using Direct Numerical Simulation,” Water Resour. Res. 48 (2012).
    doi 10.1029/2011WR011404
  33. S. Molins, D. Trebotich, L. Yang, et al., “Pore-Scale Controls on Calcite Dissolution Rates from Flow-through Laboratory and Numerical Experiments,” Environ. Sci. Technol. 48 (13), 7453-7460 (2014).
  34. N. Nishiyama and T. Yokoyama, “Permeability of Porous Media: Role of the Critical Pore Size,” J. Geophys. Res.: Solid Earth 122 (9), 6955-6971 (2017).
  35. C. Noiriel, L. Luquot, B. Madé, et al., “Changes in Reactive Surface Area during Limestone Dissolution: An Experimental and Modelling Study,” Chem. Geol. 265 (1-2), 160-170 (2009).
  36. S. Osher and R. Fedkiw, “Level Set Methods: An Overview and Some Recent Results,” J. Comput. Phys. 169 (2), 463-502 (2001).
  37. A. Safari, M. M. Dowlatabad, A. Hassani, and F. Rashidi, “Numerical Simulation and X-ray Imaging Validation of Wormhole Propagation during Acid Core-Flood Experiments in a Carbonate Gas Reservoir,” J. Nat. Gas Sci. Eng. 30, 539-547 (2016).
  38. M. M. Smith, Y. Hao, H. E. Mason, and S. A. Carroll, “Experiments and Modeling of Variably Permeable Carbonate Reservoir Samples in Contact with CO_2-Acidified Brines,” Energy Procedia 63, 3126-3137 (2014).
  39. F. Sotiropoulos and X. Yang, “Immersed Boundary Methods for Simulating Fluid-Structure Interaction,” Prog. Aerosp. Sci. 65, 1-21 (2014).
  40. C. I. Steefel, C. A. J. Appelo, B. Arora, et al., “Reactive Transport Codes for Subsurface Environmental Simulation,” Comput. Geosci. 19 (3), 445-478 (2015).
  41. T. Vanorio, G. Mavko, S. Vialle, and K. Spratt, “The Rock Physics Basis for 4D Seismic Monitoring of CO_2 Fate: Are We There Yet?,” Lead. Edge 29 (2), 113-240 (2010).
  42. A. Verri, C. Uras, P. Frosini, and M. Ferri, “On the Use of Size Functions for Shape Analysis,” Biol. Cybern. 70 (2), 99-107 (1993).
  43. G. Yang, Y. Li, A. Atrens, et al., “Reactive Transport Modeling of Long-Term CO_2 Sequestration Mechanisms at the Shenhua CCS Demonstration Project, China,” J. Earth Sci. 28 (3), 457-472 (2017).
  44. W. Zhu and G. Hirth, “A Network Model for Permeability in Partially Molten Rocks,” Earth Planet. Sci. Lett. 212 (3-4), 407-416 (2003).
  45. A. Zomorodian and G. Carlsson, “Computing Persistent Homology,” Discrete Comput. Geom. 33 (2), 249-274 (2005).
  46. L. Zuo, J. B. Ajo-Franklin, M. Voltolini, et al., “Pore-Scale Multiphase Flow Modeling and Imaging of CO_2 Exsolution in Sandstone,” J. Petrol. Sci. Eng. 155, 63-77 (2017).