A novel construction approach for the pore structure model principally focuses on the controllable roundness of rock particles

Abstract

Pores among particles provide the main space for the storage and migration of deep underground fluids (such as oil, gas, groundwater, and unconventional natural gas). The pores form a pore structure with complex morphology which is mainly dominated by the shape and distribution of particles. Therefore, the reconstruction of the pore structure or granular porous media and the evaluation of particle roundness have become an important foundation for the study of fluid flow through deep underground rock mass. This research proposes a novel approach for the multi-scale model with angular vertexes. The fractal topology theory and Voronoi space segmentation technology are combinedly used for the reconstruction of fractal granular porous media. The angular shapes are smoothed by using a modified B-spline technique and the particles with varying degrees of roundness are generated. To validate the superiority of our approach, the roundness based on the Wadell roundness calculation method is calculated and compared with the roundness obtained from particles smoothed using the vertex rounding substitution method. Results show that the roundness of particles smoothed with the modified B-spline technique closely aligns with the corresponding set rounded level (a nondimensional variable). Conversely, the vertex rounding substitution method is limited to a single dimensionally rounded radius. This innovative approach can offer a new method for the construction of granular porous media for the fluid flow study in deep underground rock mass.

Keywords

B-spline curve / complex pore network / fractal topology / granular media / roundness / Voronoi

References

[1] Ali U, Kikumoto M, Ciantia M, Cui Y, Previtali M. Systematic effect of particle roundness/angularity on macro- and microscopic behavior of granular materials. Granular Matter. 2023; 25(3): 51.

[2] Böhm G, Galuppo P, Vesnaver A. 3D adaptive tomography using Delaunay triangles and Voronoi polygons. Geophys Prospect. 2000; 48(4): 723-744.

[3] Cai J, Huai X-L. A lattice Boltzmann model for fluid-solid coupling heat transfer in fractal porous media. Chin Phys Lett. 2009; 26(6):064401.

[4] Chen J, Li R, Mo PQ, Zhou G, Cai S, Chen D. A modified method for morphology quantification and generation of 2D granular particles. Granular Matter. 2021; 24(1): 16.

[5] Chen R-P, Liu Q-W, Wu H-N, Wang H-L, Meng F-Y. Effect of particle shape on the development of 2D soil arching. Comput Geotech. 2020; 125: 103662.

[6] Chen S, Zhang J, Yin D, Li F, Lu J, Zhu P. Visualizing experimental investigation on gas-liquid replacements in a microcleat model using the reconstruction method. Deep Undergr Sci Eng. 2023; 2(3): 295-303.

[7] Cho G-C, Dodds J, Santamarina JC. Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J Geotech Geoenviron Eng. 2006; 132(5): 591-602.

[8] Eshtehardian SA, Khodaygan S. A continuous RRT*-based path planning method for non-holonomic mobile robots using B-spline curves. J Ambient Intell Human Comput. 2023; 14(7): 8693-8702.

[9] Gadelmawla ES. Simple and efficient algorithms for roundness evaluation from the coordinate measurement data. Measurement. 2010; 43(2): 223-235.

[10] Greco FP, Lawson AB, Cocchi D, Temples T. Some interpolation estimators in environmental risk assessment for spatially misaligned health data. Environ Ecol Stat. 2005; 12(4): 379-395.

[11] Hosseini M, Arif M, Keshavarz A, Iglauer S. Neutron scattering: a subsurface application review. Earth-Sci Rev. 2021; 221: 103755.

[12] Hu S, Han Y, Lin Q, Ren D. Numerical simulation of soil heat and moisture migration containing different stones using lattice boltzmann method. J Therm Sci Eng Appl. 2023; 15(7): 071004.

[13] Jin Y, Dong J, Zhang X, Li X, Wu Y. Scale and size effects on fluid flow through self-affine rough fractures. Int J Heat Mass Transf. 2017; 105: 443-451.

[14] Jin Y, Li X, Zhao M, Liu X, Li H. A mathematical model of fluid flow in tight porous media based on fractal assumptions. Int J Heat Mass Transfer. 2017; 108: 1078-1088.

[15] Jin Y, Wang C, Liu S, Quan W, Liu X. Systematic definition of complexity assembly in fractal porous media. Fractals. 2020; 28(5): 2050079.

[16] Jin Y, Wu Y, Li H, Zhao M, Pan J. Definition of fractal topography to essential understanding of scale-invariance. Sci Rep. 2017; 7: 46672.

[17] Li B. Modeling of shale gas transport in multi-scale complex fracture networks considering fracture hits. Transp Porous Media. 2023; 149(1): 71-86

[18] Li H, Shi S, Lu J, Ye Q, Lu Y, Zhu X. Pore structure and multifractal analysis of coal subjected to microwave heating. Powder Technol. 2019; 346: 97-108.

[19] Li J, Fu G, Liu Z. Quantitative characterization of the lower limit of the physical properties of tight oil reservoirs in nano-material porous media. Integr Ferroelectr. 2022; 227: 288-303.

[20] Li L, Wang J, Yang S, Klein B, Wang Z, Liu F. Estimate of three-dimensional Wadell roundness of irregular particles using image processing and topographic analysis. Constr Build Mater. 2023; 396: 132273.

[21] Liang H, Shen Y, Xu J, Shen X. Multiscale three-dimensional morphological characterization of calcareous sand particles using spherical harmonic analysis. Front Phys. 2021; 9: 496.

[22] Liang M, Fu C, Xiao B, Luo L, Wang Z. A fractal study for the effective electrolyte diffusion through charged porous media. Int J Heat Mass Transfer. 2019; 137: 365-371.

[23] Liu G, Gao F, Liao WH. Design and optimization of a magnetorheological damper based on B-spline curves. Mech Syst Sign Process. 2022; 178: 109279.

[24] Liu X, Nie B. Fractal characteristics of coal samples utilizing image analysis and gas adsorption. Fuel. 2016; 182: 314-322.

[25] Lucarini V, Danihlik R, Kriegerova I, Speranza A. Hydrological cycle in the Danube basin in present-day and XXII century simulations by IPCCAR4 global climate models. J Geophys Res: Atmos. 2008; 113(D9): D009167.

[26] Majeed A, Abbas M, Sittar AA, Misro MY, Kamran M. Airplane designing using quadratic trigonometric B-spline with shape parameters. AIMS Math. 2021; 6(7): 7669-7683.

[27] Mandelbrot B. How long is the coast of britain? Statistical self-similarity and fractional dimension. Science. 1967; 156: 636-638.

[28] Mushtaha AM, Van Camp M, Walraevens K. Quantification of recharge and runoff from rainfall using new GIS tool: example of the gaza strip aquifer. Water. 2019; 11(1): 84.

[29] Nelson T, Boots B, Wulder MA. Techniques for accuracy assessment of tree locations extracted from remotely sensed imagery. J Environ Manage. 2005; 74(3): 265-271.

[30] Nie Z, Liang Z, Wang X, Gong J. Evaluation of granular particle roundness using digital image processing and computational geometry. Constr Build Mater. 2018; 172: 319-329.

[31] Pan J, Zhao Y, Hou Q, Jin Y. Nanoscale pores in coal related to coal rank and deformation structures. Trans Porous Media. 2015; 107(2): 543-554.

[32] Perrier E, Bird N, Rieu M. Generalizing the fractal model of soil structure: the pore-solid fractal approach. Geoderma. 1999; 88(3): 137-164.

[33] Prabhakar P, Ramasamy A. Influence of morphological features on mechanical properties of granular soils from different depositional environments. Powder Technol. 2024; 435: 119399.

[34] Ren Y, Wei J, Zhang L, Zhang J, Zhang L. A fractal permeability model for gas transport in the dual-porosity media of the coalbed methane reservoir. Trans Porous Media. 2021; 140(2): 511-534.

[35] Resentini A, AndÒ S, Garzanti E. Quantifying roundness of detrital minerals by image analysis: sediment transport, shape effects, and provenance implications. J Sediment Res. 2018; 88(2): 276-289.

[36] Richesson S, Sahimi M. Flow and transport properties of deforming porous media. I. permeability. Trans Porous Media. 2021; 138(3): 577-609.

[37] Schlicht L, Valcu M, Kempenaers B. Thiessen polygons as a model for animal territory estimation. Ibis. 2014; 156: 215-219.

[38] Tao J, Changmin Z, Jianhua Q, Rui Z, Rui Y, Jin P. Application of gravel roundness quantitative description in conglomerates reservoirs. Chem Eng Trans. 2017; 62: 457-462.

[39] Tao J, Zhang C, Guo X, Zhu R, Pan J, Tang Y. Application of quantitative roundness characterization to identify sedimentary microfacies in fan delta deposits: a case study of conglomerates in the Baikouquan Formation, Mahu Sag. Acta Sedimentol Sin. 2020; 38(5): 956-965.

[40] Thiessen AH. Precipitation averages for large areas. Mon Weather Rev. 1911; 39: 1082-1089.

[41] Vandeginste V, Ji Y, Buysschaert F, Anoyatis G. Mineralogy, microstructures and geomechanics of rock salt for underground gas storage. Deep Undergr Sci Eng. 2023; 2(2): 129-147.

[42] Wadell H. Volume, shape, and roundness of rock particles. J Geol. 1932; 40(5): 443-451.

[43] Wang B, Jin Y, Chen Q, Zheng J, Zhu Y, Zhang X. Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice Boltzmann method. Fractals. 2014; 22(3): 1440005.

[44] Wang J, Wang H, Wang X, et al. A multiphysical-geochemical coupling model for caprock sealing efficiency in CO₂ geosequestration. Deep Undergr Sci Eng. 2023; 2(2): 188-203.

[45] Wang P, Jiang Z, Ji W, et al. Heterogeneity of intergranular, intraparticle and organic pores in Longmaxi shale in Sichuan Basin, South China: evidence from SEM digital images and fractal and multifractal geometries. Marine Petrol Geol. 2016; 72: 122-138.

[46] Wentworth CK. A laboratory and field study of cobble abrasion. J Geol. 1919; 27(7): 507-521.

[47] Xiao B, Huang Q, Chen H, Chen X, Long G. A fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media. Fractals. 2021; 29(1): 2150017.

[48] Yaagoubi R, Yarmani M, Kamel A, Khemiri W. HybVOR: a Voronoi-based 3D GIS approach for camera surveillance network placement. ISPRS Int J Geo-Inform. 2015; 4: 754-782.

[49] Yan Y, Zhang L, Luo X, Liu K, Jia T, Lu Y. Influence of the grain shape and packing texture on the primary porosity of sandstone: insights from a numerical simulation. Sedimentology. 2023; 70(6): 1856-1885.

[50] Yao W, Wang E, Liu X, Zhou R. Fracture distribution in overburden strata induced by underground mining. Deep Undergr Sci Eng. 2022; 1(1): 58-64.

[51] Yao Y, Sun X, Zheng S, et al. Methods for petrological and petrophysical characterization of gas shales. Energy Fuels. 2021; 35: 11061-11088.

[52] Zhang K, Zou A, Wang L, Cheng Y, Li W, Liu C. Multiscale morphological and topological characterization of coal microstructure: insights into the intrinsic structural difference between original and tectonic coals. Fuel. 2022; 321: 124076.

[53] Zhang Y, Zeng J, Cai J, Feng S, Feng X, Qiao J. A mathematical model for determining oil migration characteristics in low-permeability porous media based on fractal theory. Trans Porous Media. 2019; 129: 633-652.

[54] Zhao M, Jin Y, Liu X, Zheng J, Liu S. Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application. J Geophys Res: Solid Earth. 2020; 125(12): e2020JB020110.

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2025 The Author(s). Deep Underground Science and Engineering published by John Wiley & Sons Australia, Ltd on behalf of China University of Mining and Technology.