Insights Into Estimation of Sand Permeability: From Empirical Relations to Microstructure-based Methods

• Autorzy: Bodak Bartłomiej , Sobótka Maciej

Identyfikatory

DOI

10.2478/sgem-2024-0001

• Języki publikacji: EN

Abstrakty

EN

This study evaluates various methods for estimating soil permeability using microtomographyderived data and compares them to the conventional laboratory approaches. Different methods, including measurement in custom-designed permeameter at micro- CT-compatible scale, empirical equations, simulated sifting, semi-theoretical equations, pore-network modeling, and lattice-Boltzmann simulations, were applied to samples of sandy soils with distinct microstructural properties. The empirical equations showed varied results, highly dependent on the method chosen. The simulated sifting method was able to adequately estimate the granulometric properties of the soil, allowing the use of empirical permeability formulations for substantially small samples. Semi-theoretical equations based on the microstructural properties presented reasonable agreement for some samples. The pore-network modeling approach demonstrated computational efficiency but lacked accuracy. The lattice-Boltzmann method required significant computational resources but did not provide substantially closer alignment with the measured hydraulic properties of some samples. None of the simulations was able to properly determine the permeability of silty and organically contaminated sand. The study highlights the complexity of permeability estimation, emphasizing the need for choosing volumes of interest, resolution of micro-CT scans, and methods that match specific soil characteristics and available computational resources.

Słowa kluczowe

EN

microtomography; permeability; conductivity; computational fluid dynamics; Kozeny–Carman equation

• Wydawca: De Gruyter
• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2024
• Tom: Vol. 46, nr 1
• Strony: 1--20
• Opis fizyczny: Bibliogr. 37 poz., rys., tab.

Twórcy

autor

Bodak Bartłomiej

• Wrocław University of Science and Technology, Faculty of Civil Engineering

autor

Sobótka Maciej

• Wrocław University of Science and Technology, Faculty of Civil Engineering

Bibliografia

• [1] Ahrens, J., Geveci, B., & Law, C. (2005). ParaView: An End-User Tool for Large-Data Visualization. In Visualization Handbook (pp. 717–731). Elsevier. https://doi.org/10.1016/B978-012387582-2/50038-1
• [2] Beyer, W. (1964). Zur Bestimmung der Wasserdurchlässigkeit von Kiesen und Sanden aus der Kornverteilungskurve. Wasserwirtschaft Wassertechnik, 14(6), 165–168.
• [3] Blott, S. J., & Pye, K. (2007). Particle shape: A review and new methods of characterization and classification. Sedimentology, 55, 31–63. https://doi.org/10.1111/j.1365-3091.2007.00892.x
• [4] Blunt, M. J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., & Pentland, C. (2013). Pore-scale imaging and modelling. Advances in Water Resources, 51, 197–216. https://doi.org/10.1016/j.advwatres.2012.03.003
• [5] Carman, P. C. (1937). Fluid Flow through Granular Beds. AIChE, 15.
• [6] Carman, P. C. (1956). Flow of Gases through Porous Media. Academic Press Inc.
• [7] Carrier, W. D. (2003). Goodbye, Hazen; Hello, Kozeny-Carman. Journal of Geotechnical and Geoenvironmental Engineering, 129(11), 1054–1056. https://doi.org/10.1061/(ASCE)1090- 0241(2003)129:11(1054)
• [8] Chapuis, R. P., Dallaire, V., Marcotte, D., Chouteau, M., Acevedo, N., & Gagnon, F. (2005). Evaluating the hydraulic conductivity at three different scales within an unconfined sand aquifer at Lachenaie, Quebec. Canadian Geotechnical Journal, 42(4), 1212–1220. https://doi.org/10.1139/t05-045
• [9] Dong, H., & Blunt, M. J. (2009). Pore-network extraction from micro-computerized-tomography images. Physical Review E, 80(3), 036307. https://doi.org/10.1103/PhysRevE.80.036307
• [10] Dullien, F. A. L. (1979). Single-Phase Transport Phenomena in Porous Media. In Porous Media (pp. 157–234). Elsevier. https:// doi.org/10.1016/B978-0-12-223650-1.50009-7
• [11] Fatt, I. (1956). The Network Model of Porous Media. Transactions of the AIME, 207(01), 144–181. https://doi. org/10.2118/574-G
• [12] Feldkamp, L. A., Davis, L. C., & Kress, J. W. (1984). Practical
• [13] Feng, J., Teng, Q., He, X., Qing, L., & Li, Y. (2018). Reconstruction of three-dimensional heterogeneous media from a single two-dimensional section via co-occurrence correlation function. Computational Materials Science, 144, 181–192. https://doi.org/10.1016/j.commatsci.2017.11.030
• [14] Frisch, U., Hasslacher, B., & Pomeau, Y. (1986). Lattice-Gas Automata for the Navier-Stokes Equation. Physical Review Letters, 56(14), 1505–1508. https://doi.org/10.1103/ PhysRevLett.56.1505
• [15] Gostick, J. (2017). Versatile and efficient pore network extraction method using marker-based watershed segmentation. Physical Review E, 96(2), 023307. https://doi.org/10.1103/PhysRevE.96.023307
• [16] Gostick, J., Aghighi, M., Hinebaugh, J., Tranter, T., Hoeh, M. A., Day, H., Spellacy, B., Sharqawy, M. H., Bazylak, A., Burns, A., Lehnert, W., & Putz, A. (2016). OpenPNM: A Pore Network Modeling Package. Computing in Science & Engineering, 18(4), 60–74. https://doi.org/10.1109/MCSE.2016.49
• [17] Gostick, J., Khan, Z., Tranter, T., Kok, M., Agnaou, M., Sadeghi, M., & Jervis, R. (2019). PoreSpy: A Python Toolkit for Quantitative Analysis of Porous Media Images. Journal of Open Source Software, 4(37), 1296. https://doi.org/10.21105/joss.01296
• [18] Hazen, A. (1911). Discussion: Dams on sand foundations.Transactions, American Society of Civil Engineers, 73(11).
• [19] Hu, Y., Li, T.-M., Anderson, L., Ragan-Kelley, J., & Durand, F. (2019). Taichi: A language for high-performance computation on spatially sparse data structures. ACM Transactions on Graphics, 38(6), 201:1-201:16. https://doi.org/10.1145/3355089.3356506
• [20] Hussain, F., & Nabi, G. (2016). Empirical Formulae Evaluation for Hydraulic Conductivity Determination Based on Grain Size Analysis. Pyrex Journal of Research in Environmental Studies, 3, 26–32.
• [21] Kaviany, M. (1995). Principles of Heat Transfer in Porous Media. Springer New York. https://doi.org/10.1007/978-1-4612-4254-3
• [22] Kelokaski, M., Siitari-Kauppi, M., Sardini, P., Möri, A., & Hellmuth, K.-H. (2006). Characterisation of pore space geometry by 14C-PMMA impregnation—Development work for in situ studies. Journal of Geochemical Exploration, 90(1–2), 45–52. https://doi.org/10.1016/j.gexplo.2005.09.005
• [23] Kozeny, J. (1927). Ueber kapillare Leitung des Wassers im Boden. Sitzungsber Akad. Wiss., 136(2a), 271–306.
• [24] Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., & Viggen, E. M. (2017). The Lattice Boltzmann Method: Principles and Practice. Springer International Publishing. https://doi.org/10.1007/978-3-319-44649-3
• [25] Lindquist, W. B., & Venkatarangan, A. (1999). Investigating 3D geometry of porous media from high resolution images. Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 24(7), 593–599. https://doi.org/10.1016/S1464- 1895(99)00085-X
• [26] OpenCV 4.6.0. (n.d.). https://docs.opencv.org/4.6.0/
• [27] Pap, M., & Mahler, A. (2018). Comparison of Different Empirical Correlations to Estimate Permeability Coefficient of Quaternary Danube Soils. Periodica Polytechnica Civil Engineering. https://doi.org/10.3311/PPci.13108
• [28] Říha, J., Petrula, L., Hala, M., & Alhasan, Z. (2018). Assessment of empirical formulae for determining the hydraulic conductivity of glass beads. Journal of Hydrology and Hydromechanics, 66(3), 337–347. https://doi.org/10.2478/ johh-2018-0021
• [29] Sauerbrey, I. I. (1932). On the Problem and Determination of the Permeability Coefficient. Proceedings VNIIG, 3–5.
• [30] Seelheim, F. (1880). Methoden zur Bestimmung der Durchlässigkeit des Bodens. Zeitschrift Fur Analytische Chemie, 19(1), 387–418. https://doi.org/10.1007/BF01341054
• [31] Tranter, T. G., Kok, M. D. R., Lam, M., & Gostick, J. (2019). pytrax: A simple and efficient random walk implementation for calculating the directional tortuosity of images. SoftwareX, 10, 100277. https://doi.org/10.1016/j.softx.2019.100277
• [32] Valsecchi, A., Damas, S., Tubilleja, C., & Arechalde, J. (2020). Stochastic reconstruction of 3D porous media from 2D images using generative adversarial networks. Neurocomputing, 399, 227–236. https://doi.org/10.1016/j.neucom.2019.12.040
• [33] Verruijt, A. (1970). Theory of Groundwater Flow. Macmillan Education UK. https://doi.org/10.1007/978-1-349-00175-0
• [34] Vukovic, M., & Soro, A. (1992). Determination of Hydraulic Conductivity of Porous Media from Grain-size Composition. Water Resources Publications. https://books.google.pl/ books?id=q_FOAQAAIAAJ
• [35] Wyllie, M. R. J., & Rose, W. D. (1950). Application of the Kozeny Equation to Consolidated Porous Media. Nature, 165(4207), 972972.https://doi.org/10.1038/165972a0
• [36] Yang, J., Xu, Y., & Yang, L. (2022). Taichi-LBM3D: A Single-Phase and Multiphase Lattice Boltzmann Solver on Cross-Platform Multicore CPU/GPUs. Fluids, 7(8), Article 8. https://doi. org/10.3390/fluids7080270
• [37] Živković, P., Burečić Šafran, M., & Kovačević Zelić, B. (2021). Comparison of measured and estimated permeability for artificially prepared coarse-grained soil samples. Rudarsko-Geološko-Naftni Zbornik, 36(3), 167–178. https://doi.org/10.17794/rgn.2021.3.12