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Computational topology-based characterization of pore space changes due to chemical dissolution of rocks. (English) Zbl 1481.74543

Summary: In this paper, we present an algorithm for the numerical simulation of reactive transport at the pore scale to facilitate observation of pore space and rock matrix evolution. Moreover, simulation at the pore scale opens up the possibility of estimating changes in the transport properties of rocks, such as permeability and tortuosity. To quantitatively analyze pore space evolution, we developed a numerical algorithm that can be used to construct persistence diagrams of the connectivity components for pore space and the rock matrix, which characterize the topology evolution during rock matrix dissolution. Introducing the “bottle-neck” metric in the space of the persistence diagrams, we cluster the numerical experiments in terms of similarities in topology evolution. We demonstrate that the application of this metric to the persistence diagrams allowed us to distinguish topologically different dissolution scenarios, for instance, the formation of a dissolution front near the inlet, homogeneous dissolution of the matrix inside the core sample, and formation of wormholes. We illustrate that the differences in topology evolution lead to cross-correlations among the transport properties of rocks (porosity-permeability-tortuosity).

MSC:

74L10 Soil and rock mechanics
86A60 Geological problems

Software:

CrunchFlow
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Full Text: DOI

References:

[1] Ghommem, M.; Zhao, W.; Dyer, S.; Qiu, X.; Brady, D., Carbonate acidizing: modeling, analysis, and characterization of wormhole formation and propagation, J. Pet. Sci. Eng., 131, 18-33 (2015)
[2] Miller, K.; Vanorio, T.; Keehm, Y., Evolution of permeability and microstructure of tight carbonates due to numerical simulation of calcite dissolution, J. Geophys. Res.: Solid Earth, 122, 6, 4460-4474 (2017)
[3] Dadda, A.; Geindreau, C.; Emeriault, F.; Roscoat, S. R.d.; Garandet, A.; Sapin, L.; Filet, A. E., Characterization of microstructural and physical properties changes in biocemented sand using 3d x-ray microtomography, Acta Geotech., 12, 5, 955-970 (2017)
[4] Alizadeh, A. H.; Akbarabadi, M.; Barsotti, E.; Piri, M.; Fishman, N.; Nagarajan, N., Salt precipitation in ultratight porous media and its impact on pore connectivity and hydraulic conductivity, Water Resour. Res., 54, 4, 2768-2780 (2018)
[5] Kaya, E.; Zarrouk, S. J., Reinjection of greenhouse gases into geothermal reservoirs, Int. J. Greenhouse Gas Control, 67, 111-129 (2017)
[6] Lebedev, M.; Zhang, Y.; Sarmadivaleh, M.; Barifcani, A.; Al-Khdheeawi, E.; Iglauer, S., Carbon geosequestration in limestone: pore-scale dissolution and geomechanical weakening, Int. J. Greenhouse Gas Control, 66, 106-119 (2017)
[7] Steefel, C. I.; Appelo, C. A.J.; Arora, B.; Jacques, D.; Kalbacher, T.; Kolditz, O.; Lagneau, V.; Lichtner, P. C.; Mayer, K. U.; Meeussen, J. C.L.; Molins, S.; Moulton, D.; Shao, H.; Šimøunek, J.; Spycher, N.; Yabusaki, S. B.; Yeh, G. T., Reactive transport codes for subsurface environmental simulation, Comput. Geosci., 19, 3, 445-478 (2015) · Zbl 1323.86002
[8] Costa, T. B.; Kennedy, K.; Peszynska, M., Hybrid three-scale model for evolving pore-scale geometries, Comput. Geosci., 22, 3, 925-950 (2018) · Zbl 1405.76050
[9] Molins, S.; Trebotich, D.; Yang, L.; Ajo-Franklin, J. B.; Ligocki, T. J.; Shen, C.; Steefel, C. I., Pore-scale controls on calcite dissolution rates from flow-through laboratory and numerical experiments, Environ. Sci. Technol., 48, 13, 7453-7460 (2014)
[10] Yang, G.; Li, Y.; Atrens, A.; Liu, D.; Wang, Y.; Jia, L.; Lu, Y., Reactive transport modeling of long-term co2 sequestration mechanisms at the shenhua ccs demonstration project, china, J. Earth Sci., 28, 3, 457-472 (2017)
[11] Kang, Q.; Chen, L.; Valocchi, A. J.; Viswanathan, H. S., Pore-scale study of dissolution-induced changes in permeability and porosity of porous media, J. Hydrol. (Amst.), 517, 1049-1055 (2014)
[12] Yoon, H.; Valocchi, A. J.; Werth, C. J.; Dewers, T., Pore-scale simulation of mixing-induced calcium carbonate precipitation and dissolution in a microfluidic pore network, Water Resour. Res., 48, 2, W02524 (2012)
[13] Osher, S.; Fedkiw, R. P., Level set methods: an overview and some recent results, J. Comput. Phys., 169, 2, 463-502 (2001) · Zbl 0988.65093
[14] Xu, Z.; Meakin, P., Phase-field modeling of solute precipitation and dissolution, J. Chem. Phys., 129, 1, 014705 (2008)
[15] Peskin, C. S., Flow patterns around heart valves: a numerical method, J. Comput. Phys., 10, 252-271 (1972) · Zbl 0244.92002
[16] Sotiropoulos, F.; Yang, X., Immersed boundary methods for simulating fluid-structure interaction, Prog. Aerosp. Sci., 65, 1-21 (2014)
[17] Edelsbrunner, H.; Harer, J., Computational topology, an introduction, Amer. Math. Soc. (2010) · Zbl 1193.55001
[18] Kong, T. Y.; Rosenfeld, A., Digital topology: introduction and survey, computer vision, Gr. Image Process., 48, 3, 357-393 (1989)
[19] Turner, K.; Mileyko, Y.; Mukherjee, S.; Harer, J., Frechet means for distributions of persistence diagrams, Discret. Comput. Geometry, 52, 1, 44-70 (2014) · Zbl 1296.68182
[20] Bazaikin, Y.; Gurevich, B.; Iglauer, S.; Khachkova, T.; Kolyukhin, D.; Lebedev, M.; Lisitsa, V.; Reshetova, G., Effect of ct image size and resolution on the accuracy of rock property estimates, J. Geophys. Res.: Solid Earth, 122, 5, 3635-3647 (2017)
[21] Bouchelaghem, F.; Pusch, R., Fluid flow and effective conductivity calculations on numerical images of bentonite microstructure, Appl. Clay Sci., 144, 9-18 (2017)
[22] Gerke, K. M.; Karsanina, M. V.; Katsman, R., Calculation of tensorial flow properties on pore level: exploring the influence of boundary conditions on the permeability of three-dimensional stochastic reconstructions, Phys. Rev. E, 100, 5, 053312 (2019)
[23] Gibou, F.; Fedkiw, R.; Osher, S., A review of level-set methods and some recent applications, J. Comput Phys, 353, 82-109 (2018) · Zbl 1380.65196
[24] Andra, H.; Combaret, N.; Dvorkin, J.; Glatt, E.; Han, J.; Kabel, M.; Keehm, Y.; Krzikalla, F.; Lee, M.; Madonna, C.; Marsh, M.; Mukerji, T.; Saenger, E. H.; Sain, R.; Saxena, N.; Ricker, S.; Wiegmann, A.; Zhan, X., Digital rock physics benchmarks - part i: imaging and segmentation, Comput. Geosci., 50, 0, 25-32 (2013)
[25] Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid Mech., 37, 1, 239-261 (2005) · Zbl 1117.76049
[26] Fedkiw, R. P.; Aslam, T.; Merriman, B.; Osher, S., A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys., 152, 2, 457-492 (1999) · Zbl 0957.76052
[27] Cohen-Steiner, D.; Edelsbrunner, H. H., Stability of persistence diagrams, J. Discret. Comput. Geom., 37, 103-120 (2007) · Zbl 1117.54027
[28] Hyman, J. D.; Winter, C. L., Stochastic generation of explicit pore structures by thresholding Gaussian random fields, J. Comput. Phys., 277, 16-31 (2014) · Zbl 1349.76817
[29] Lisitsa, V.; Bazaikin, Y.; Khachkova, T., Barcodes of rock matrix during chemical dissolution, Mendeley Data (2020)
[30] Amikiya, A. E.; Banda, M. K., Modelling and simulation of reactive transport phenomena, J. Comput. Sci., 28, 155-167 (2018)
[31] Biot, M. A., Theory of propagation of elastic waves in fluid-saturated porous solid. i. low-frequency range, J. Acoust. Soc. Am., 28, 168-178 (1956)
[32] Caspari, E.; Novikov, M.; Lisitsa, V.; Barbosa, N. D.; Quintal, B.; Rubino, J. G.; Holliger, K., Attenuation mechanisms in fractured fluid-saturated porous rocks: a numerical modelling study, Geophys. Prospect., 67, 4, 935-955 (2019)
[33] 036319, pRE
[34] Zhang, D.; Zhang, R.; Chen, S.; Soll, W. E., Pore scale study of flow in porous media: scale dependency, rev, and statistical rev, Geophys. Res. Lett., 27, 8, 1195-1198 (2000)
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