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Non-monotonic effect of compaction on longitudinal dispersion coefficient of porous media

Published online by Cambridge University Press:  04 June 2024

Yang Liu ,
Wenbo Gong ,
Han Xiao  and
Moran Wang Open the ORCID record for Moran Wang [Opens in a new window]
Yang Liu
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Wenbo Gong
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Han Xiao
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Moran Wang*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: moralwang@jhu.edu
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Abstract

Utilizing the discrete element method and the pore network model, we numerically investigate the impact of compaction on the longitudinal dispersion coefficient of porous media. Notably, the dispersion coefficient exhibits a non-monotonic dependence on the degree of compaction, which is distinguished by the presence of three distinct regimes in the variation of dispersion coefficient. The non-monotonic variation of dispersion coefficient is attributed to the disparate effect of compaction on dispersion mechanisms. Specifically, the porous medium tightens with an increasing pressure load, reducing the effect of molecular diffusion that primarily governs at small Péclet numbers. On the other hand, heightened pressure loads enhance the heterogeneity of pore structures, resulting in increased disorder and a higher proportion of stagnant zones within porous media flow. These enhancements further strengthen mechanical dispersion and hold-up dispersion, respectively, both acting at higher Péclet numbers. It is crucial to highlight that hold-up dispersion is induced by the low-velocity regions in porous media flow, which differ fundamentally from zero-velocity regions (such as dead-ends or the interior of permeable grains) as described by the classical theory of dispersion. The competition between weakened molecular diffusion and enhanced hold-up dispersion and mechanical dispersion, together with the shift in the dominance of dispersion mechanisms across various Péclet numbers, results in multiple regimes in the variation of dispersion coefficients. Our study provides unique insights into structural design and modulation of the dispersion coefficient of porous materials.

JFM classification

Low-Reynolds-number flows: Porous media Mass Transport: Dispersion
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 988 , 10 June 2024 , R2
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Amooie, M.A., Soltanian, M.R. & Moortgat, J. 2018 Solutal convection in porous media: comparison between boundary conditions of constant concentration and constant flux. Phys. Rev. E 98 (3), 033118.CrossRefGoogle Scholar
Bijeljic, B., Mostaghimi, P. & Blunt, M.J. 2011 Signature of non-Fickian solute transport in complex heterogeneous porous media. Phys. Rev. Lett. 107 (20), 204502.CrossRefGoogle ScholarPubMed
Bijeljic, B., Muggeridge, A.H. & Blunt, M.J. 2004 Pore-scale modeling of longitudinal dispersion. Water Resour. Res. 40 (11), W11501.CrossRefGoogle Scholar
Bolster, D. 2014 The fluid mechanics of dissolution trapping in geologic storage of CO2. J. Fluid Mech. 740, 1–4.CrossRefGoogle Scholar
Boon, M., Bijeljic, B. & Krevor, S. 2017 Observations of the impact of rock heterogeneity on solute spreading and mixing. Water Resour. Res. 53 (6), 4624–4642.CrossRefGoogle Scholar
Bordoloi, A.D., Scheidweiler, D., Dentz, M., Bouabdellaoui, M., Abbarchi, M. & de Anna, P. 2022 Structure induced laminar vortices control anomalous dispersion in porous media. Nat. Commun. 13 (1), 3820.CrossRefGoogle ScholarPubMed
Borgne, T.L., Dentz, M., Bolster, D., Carrera, J., de Dreuzy, J.-R. & Davy, P. 2010 Non-fickian mixing: temporal evolution of the scalar dissipation rate in heterogeneous porous media. Adv. Water Resour. 33 (12), 1468–1475.CrossRefGoogle Scholar
Bruderer, C. & Bernabé, Y. 2001 Network modeling of dispersion: transition from taylor dispersion in homogeneous networks to mechanical dispersion in very heterogeneous ones. Water Resour. Res. 37 (4), 897–908.CrossRefGoogle Scholar
Charlaix, E., Hulin, J.P. & Plona, T.J. 1987 Experimental study of tracer dispersion in sintered glass porous materials of variable compaction. Phys. Fluids 30 (6), 1690–1698.CrossRefGoogle Scholar
Chen, Z., Jin, X. & Wang, M. 2018 A new thermo-mechanical coupled dem model with non-spherical grains for thermally induced damage of rocks. J. Mech. Phys. Solids 116, 54–69.CrossRefGoogle Scholar
Cundall, P.A. & Strack, O.D. 1979 A discrete numerical model for granular assemblies. Geotechnique 29 (1), 47–65.CrossRefGoogle Scholar
Dentz, M., Creppy, A., Douarche, C., Clément, E. & Auradou, H. 2022 Dispersion of motile bacteria in a porous medium. J. Fluid Mech. 946, A33.CrossRefGoogle Scholar
Dentz, M., Hidalgo, J.J. & Lester, D. 2023 Mixing in porous media: concepts and approaches across scales. Transp. Porous Media 146 (1-2), 5–53.CrossRefGoogle Scholar
Dentz, M., Icardi, M. & Hidalgo, J.J. 2018 Mechanisms of dispersion in a porous medium. J. Fluid Mech. 841, 851–882.CrossRefGoogle Scholar
Dong, H. & Blunt, M.J. 2009 Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E 80 (3), 036307.CrossRefGoogle ScholarPubMed
Fatt, I. 1956 The network model of porous media. Trans. AIME 207 (01), 144–181.CrossRefGoogle Scholar
Goldobin, D.S. 2011 Scaling of transport coefficients of porous media under compaction. Europhys. Lett. 95 (6), 64004.CrossRefGoogle Scholar
Hamamoto, S., Perera, M.S.A., Resurreccion, A., Kawamoto, K., Hasegawa, S., Komatsu, T. & Moldrup, P. 2009 The solute diffusion coefficient in variably compacted, unsaturated volcanic ash soils. Vadose Zone J. 8 (4), 942–952.CrossRefGoogle Scholar
Han, N.W., Bhakta, J. & Carbonell, R.G. 1985 Longitudinal and lateral dispersion in packed beds: effect of column length and particle size distribution. AlChE J. 31 (2), 277–288.CrossRefGoogle Scholar
Huh, J.P., Charlaix, E. & Plona, T.J. 1988 Tracer dispersion in sintered glass beads with a bidisperse size distribution. AlChE J. 34 (4), 610–617.Google Scholar
Jurtz, N., Kraume, M. & Wehinger, G.D. 2019 Advances in fixed-bed reactor modeling using particle-resolved computational fluid dynamics (CFD). Rev. Chem. Engng 35 (2), 139–190.CrossRefGoogle Scholar
Kang, P.K., Lei, Q., Dentz, M. & Juanes, R. 2019 Stress-induced anomalous transport in natural fracture networks. Water Resour. Res. 55 (5), 4163–4185.CrossRefGoogle Scholar
Koch, D.L. & Brady, J.F. 1985 Dispersion in fixed beds. J. Fluid Mech. 154, 399–427.CrossRefGoogle Scholar
Kumar, A., Jaiswal, D.K. & Kumar, N. 2009 Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain. J. Earth Syst. Sci. 118, 539–549.CrossRefGoogle Scholar
Kuncoro, P.H., Koga, K., Satta, N. & Muto, Y. 2014 A study on the effect of compaction on transport properties of soil gas and water I: relative gas diffusivity, air permeability, and saturated hydraulic conductivity. Soil Tillage Res. 143, 172–179.CrossRefGoogle Scholar
Lindquist, W.B., Lee, S.M., Coker, D.A., Jones, K.W. & Spanne, P. 1996 Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J. Geophys. Res.: Solid Earth 101 (B4), 8297–8310.CrossRefGoogle Scholar
Liu, Y., Gong, W., Xiao, H. & Wang, M. 2024 A pore-scale numerical framework for solute transport and dispersion in porous media. Adv. Water Resour. 183, 104602.CrossRefGoogle Scholar
Liu, Y., Gong, W., Zhao, Y., Jin, X. & Wang, M. 2022 A pore-throat segmentation method based on local hydraulic resistance equivalence for pore-network modeling. Water Resour. Res. 58 (12), e2022WR033142.CrossRefGoogle Scholar
Liu, F. & Wang, M. 2022 Trapping patterns during capillary displacements in disordered media. J. Fluid Mech. 933, A52.CrossRefGoogle Scholar
Mehmani, Y. & Balhoff, M.T. 2015 Eulerian network modeling of longitudinal dispersion. Water Resour. Res. 51 (10), 8586–8606.CrossRefGoogle Scholar
Morris, J.P., Hao, Y., Foxall, W. & McNab, W. 2011 A study of injection-induced mechanical deformation at the in salah CO2 storage project. Intl J. Greenh. Gas Control 5 (2), 270–280.CrossRefGoogle Scholar
Östergren, K.C.E. & Trägårdh, C. 2000 Characterization of hydrodynamic dispersion in a chromatographic column under compression. Chem. Engng J. 79 (2), 103–111.CrossRefGoogle Scholar
Peters, G.P. & Smith, D.W. 2002 Solute transport through a deforming porous medium. Intl J. Numer. Anal. Meth. Geomech. 26 (7), 683–717.CrossRefGoogle Scholar
Potyondy, D.O. & Cundall, P. 2004 A bonded-particle model for rock. Intl J. Rock Mech. Min. Sci. 41 (8), 1329–1364.CrossRefGoogle Scholar
Puyguiraud, A., Gouze, P. & Dentz, M. 2021 Pore-scale mixing and the evolution of hydrodynamic dispersion in porous media. Phys. Rev. Lett. 126 (16), 164501.CrossRefGoogle ScholarPubMed
Qiu, J., Chen, X. & Tong, J. 2022 Fully transient analytical solution for solute transport in 1D deforming saturated porous media considering nonlinear compressibility and permeability. Appl. Math. Model. 108, 122–141.CrossRefGoogle Scholar
Ranjith, P. & Perera, M. 2011 A new triaxial apparatus to study the mechanical and fluid flow aspects of carbon dioxide sequestration in geological formations. Fuel 90 (8), 2751–2759.CrossRefGoogle Scholar
Reynolds, S.V.R.A.M. & Harral, B.B. 2000 Flow and dispersion through a close-packed fixed bed of spheres. Phys. Rev. E 62 (3), 3632.CrossRefGoogle ScholarPubMed
Ringrose, P., Mathieson, A., Wright, I., Selama, F., Hansen, O., Bissell, R., Saoula, N. & Midgley, J. 2013 The in salah CO2 storage project: lessons learned and knowledge transfer. Energy Procedia 37, 6226–6236.CrossRefGoogle Scholar
Saffman, P.G. 1959 A theory of dispersion in a porous medium. J. Fluid Mech. 6 (3), 321–349.CrossRefGoogle Scholar
Sahimi, M., Hughes, B.D., Scriven, L.E. & Davis, H.T. 1986 Dispersion in flow through porous media–I. One-phase flow. Chem. Engng Sci. 41 (8), 2103–2122.CrossRefGoogle Scholar
Šmilauer, V., Catalano, E., Chareyre, B., Dorofeenko, S., Duriez, J., Dyck, N., Elias, J., Er, B., Eulitz, A. & Gladky, A. 2015 Yade documentation 2nd ed. The yade project. Transp. Porous Media.Google Scholar
Smith, D.W. 2000 One-dimensional contaminant transport through a deforming porous medium: theory and a solution for a quasi-steady-state problem. Intl J. Numer. Anal. Meth. Geomech. 24 (8), 693–722.3.0.CO;2-E>CrossRefGoogle Scholar
Souzy, M., Lhuissier, H., Méheust, Y., Le Borgne, T. & Metzger, B. 2020 Velocity distributions, dispersion and stretching in three-dimensional porous media. J. Fluid Mech. 891, A16.CrossRefGoogle Scholar
Tian, Z., Zhang, D., Zhou, G., Zhang, S. & Wang, M. 2023 Compaction and sintering effects on scaling law of permeability-porosity relation of powder materials. Intl J. Mech. Sci. 256, 108511.CrossRefGoogle Scholar