Abstract
The solid system in deformable porous media undergoes deformation with the flow of fluid. In this paper, in order to study the micro-mechanism of the deformation, the solid system in the porous media is represented by a pack of spherical particles and simulated by discrete element method. The fluid system in the porous media is also simulated by computational fluid dynamics. To consider the fluid–particle interactions in the porous media, the above techniques are coupled and applied for simulating the solid deformation and fluid flow. Different models consisting of different particle sizes are studied in dry (without the presence of fluid) and wet states (with the flow of fluid). The results show that with the decrease in the particle size, the solid deformation declines, which imitates the actual deformation in the porous media. More importantly, the comparison between the dry and wet models indicates that the effect of the fluid on the particle system is diminishing with the smaller packed particles. The solid deformation tendency is quantified by the reduction in the values of some micro-mechanical properties, such as permeability (absolute and relative), porosity and pore-size distribution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aslannejad, H., Hassanizadeh, S.M.: Study of hydraulic properties of uncoated paper: image analysis and pore-scale modeling. Transp. Porous Media 120, 67–81 (2017). https://doi.org/10.1007/s11242-017-0909-x
Aslannejad, H., Hassanizadeh, S.M., Raoof, A., de Winter, D.A.M., Tomozeiu, N., van Genuchten, M.T.: Characterizing the hydraulic properties of paper coating layer using FIB-SEM tomography and 3D pore-scale modeling. Chem. Eng. Sci. 160, 275–280 (2017). https://doi.org/10.1016/j.ces.2016.11.021
Ballarini, E., Graupner, B., Bauer, S.: Thermal–hydraulic–mechanical behavior of bentonite and sand-bentonite materials as seal for a nuclear waste repository: numerical simulation of column experiments. Appl. Clay Sci. 135, 289–299 (2017). https://doi.org/10.1016/j.clay.2016.10.007
Bertrand, F., Leclaire, L.-A., Levecque, G.: DEM-based models for the mixing of granular materials. Chem. Eng. Sci. 60, 2517–2531 (2005). https://doi.org/10.1016/j.ces.2004.11.048
Biot, M.A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941). https://doi.org/10.1063/1.1712886
Biot, M.A.: Theory of Deformation of a Porous Viscoelastic Anisotropic Solid. J. Appl. Phys. 27, 459–467 (1956). https://doi.org/10.1063/1.1722402
Boutt, D.F., Cook, B.K., McPherson, B.J.O.L., Williams, J.R.: Direct simulation of fluid-solid mechanics in porous media using the discrete element and lattice-Boltzmann methods. J. Geophys. Res. Solid Earth (2007). https://doi.org/10.1029/2004jb003213
Brahimi, F., Ouibrahim, A.: Blade dynamical response based on aeroelastic analysis of fluid structure interaction in turbomachinery. Energy. 115, 986–995 (2016). https://doi.org/10.1016/j.energy.2016.09.071
Carbone, A., Chiaia, B.M., Frigo, B., Türk, C.: Snow metamorphism: a fractal approach. Phys. Rev. E 82, 036103 (2010). https://doi.org/10.1103/PhysRevE.82.036103
Carlos Varas, A.E., Peters, E.A.J.F., Kuipers, J.A.M.: Computational fluid dynamics–discrete element method (CFD-DEM) study of mass-transfer mechanisms in riser flow. Ind. Eng. Chem. Res. 56, 5558–5572 (2017). https://doi.org/10.1021/acs.iecr.7b00366
Chen, F., Drumm, E.C., Guiochon, G.: Prediction/verification of particle motion in one dimension with the discrete-element method. Int. J. Geomech. 7, 344–352 (2007). https://doi.org/10.1061/(asce)1532-3641(2007)7:5(344)
Chen, S., Adepu, M., Emady, H., Jiao, Y., Gel, A.: Enhancing the physical modeling capability of open-source MFIX-DEM software for handling particle size polydispersity: implementation and validation. Powder Technol. 317, 117–125 (2017). https://doi.org/10.1016/J.POWTEC.2017.04.055
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique. 29, 47–65 (1979). https://doi.org/10.1680/geot.1979.29.1.47
Dong, H., Blunt, M. J.: Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E. 80, 036307 (2009). https://doi.org/10.1103/PhysRevE.80.036307
Dumitriu, R.P., Oprea, A.M., Vasile, C.: Kinetics of swelling and drug release from PNIPAAm/alginate stimuli responsive hydrogels. Solid State Phenom. 154, 17–22 (2009). https://doi.org/10.4028/www.scientific.net/SSP.154.17
Eringen, A.C.: A continuum theory of swelling porous elastic soils. Int. J. Eng. Sci. 32, 1337–1349 (1994). https://doi.org/10.1016/0020-7225(94)90042-6
Fagbemi, S., Tahmasebi, P., Piri, M.: Interaction between fluid and porous media with complex geometries: a direct pore-scale study. Water Resour. Res. (2018a). https://doi.org/10.1029/2017wr022242
Fagbemi, S., Tahmasebi, P., Piri, M.: Pore-scale modeling of multiphase flow through porous media under triaxial stress. Adv. Water Resour. 122, 206–216 (2018b). https://doi.org/10.1016/j.advwatres.2018.10.018
Garg, R., Galvin, J., Li, T., Pannala, S.: Open-source MFIX-DEM software for gas–solids flows: part I—verification studies. Powder Technol. 220, 122–137 (2012). https://doi.org/10.1016/j.powtec.2011.09.019
Ghassemzadeh, J., Sahimi, M.: Pore network simulation of fluid imbibition into paper during coating—III: modelling of the two-phase flow. Chem. Eng. Sci. 59, 2281–2296 (2004). https://doi.org/10.1016/J.CES.2004.01.058
Gopalakrishnan, P., Tafti, D.: Development of parallel DEM for the open source code MFIX. Powder Technol. 235, 33–41 (2013). https://doi.org/10.1016/j.powtec.2012.09.006
Han, Y., Cundall, P.A.: LBM–DEM modeling of fluid–solid interaction in porous media. Int. J. Numer. Anal. Methods Geomech. 37, 1391–1407 (2013). https://doi.org/10.1002/nag.2096
Hilton, J.E., Mason, L.R., Cleary, P.W.: Dynamics of gas–solid fluidised beds with non-spherical particle geometry. Chem. Eng. Sci. 65, 1584–1596 (2010). https://doi.org/10.1016/j.ces.2009.10.028
Hu, H.H.: Direct simulation of flows of solid-liquid mixtures. Int. J. Multiph. Flow 22, 335–352 (1996). https://doi.org/10.1016/0301-9322(95)00068-2
Hutzler, S., Péron, N., Weaire, D., Drenckhan, W.: The foam/emulsion analogy in structure and drainage. Eur. Phys. J. E 14, 381–386 (2004). https://doi.org/10.1140/epje/i2003-10152-1
Iritani, E., Katagiri, N., Yamaguchi, K., Cho, J.-H.: Compression-permeability properties of compressed bed of superabsorbent hydrogel particles. Dry Technol. 24, 1243–1249 (2006). https://doi.org/10.1080/07373930600840252
Jiang, M., Shen, Z., Zhou, W., Arroyo, M., Zhang, W.: Coupled CFD–DEM method for undrained biaxial shear test of methane hydrate bearing sediments. Granul. Matter. 20, 63 (2018). https://doi.org/10.1007/s10035-018-0826-x
Jing, L., Tsang, C.F., Stephansson, O.: DECOVALEX-An international co-operative research project on mathematical models of coupled THM processes for safety analysis of radioactive waste repositories. Int. J. Rock Mech. Min. Sci. 32, 389–398 (1995). https://doi.org/10.1016/0148-9062(95)00031-B
Kafui, K.D., Thornton, C., Adams, M.J.: Discrete particle-continuum fluid modelling of gas–solid fluidised beds. Chem. Eng. Sci. 57, 2395–2410 (2002). https://doi.org/10.1016/S0009-2509(02)00140-9
Karada, E., Kundakci, S., Üzüm, Ö.B.: Investigation of swelling/sorption characteristics of highly swollen AAm/AMPS hydrogels and semi IPNS with PEG as biopotential sorbent. J. Encapsul. Adsorpt. Sci. 01, 7–22 (2011). https://doi.org/10.4236/jeas.2011.11002
Kawamoto, R., Andò, E., Viggiani, G., Andrade, J.E.: Level set discrete element method for three-dimensional computations with triaxial case study. J. Mech. Phys. Solids 91, 1–13 (2016). https://doi.org/10.1016/j.jmps.2016.02.021
Khalili, N., Habte, M.A., Zargarbashi, S.: A fully coupled flow deformation model for cyclic analysis of unsaturated soils including hydraulic and mechanical hystereses. Comput. Geotech. 35, 872–889 (2008). https://doi.org/10.1016/j.compgeo.2008.08.003
Knauss, K.G., Johnson, J.W., Steefel, C.I.: Evaluation of the impact of CO2, co-contaminant gas, aqueous fluid and reservoir rock interactions on the geologic sequestration of CO2. Chem. Geol. 217, 339–350 (2005). https://doi.org/10.1016/j.chemgeo.2004.12.017
Koch, D.L., Brady, J.F.: Dispersion in fixed beds. J. Fluid Mech. 154, 399 (1985). https://doi.org/10.1017/S0022112085001598
Koehler, S.A., Hilgenfeldt, S., Stone, H.A.: A generalized view of foam drainage: experiment and theory. Langmuir 1, 1 (2000). https://doi.org/10.1021/la9913147
Lim, K.-W., Andrade, J.E.: Granular element method for three-dimensional discrete element calculations. Int. J. Numer. Anal. Methods Geomech. 38, 167–188 (2014). https://doi.org/10.1002/nag.2203
Lorenceau, E., Louvet, N., Rouyer, F., Pitois, O.: Permeability of aqueous foams. Eur. Phys. J. E 28, 293–304 (2009). https://doi.org/10.1140/epje/i2008-10411-7
Masoodi, R., Pillai, K.M.: Darcy’s law-based model for wicking in paper-like swelling porous media. AIChE J. (2010). https://doi.org/10.1002/aic.12163
Osei-Bonsu, K., Grassia, P., Shokri, N.: Effects of pore geometry on flowing foam dynamics in 3D-printed porous media. Transp. Porous Media (2018). https://doi.org/10.1007/s11242-018-1103-5
Pandey, S.N., Chaudhuri, A., Kelkar, S.: A coupled thermo-hydro-mechanical modeling of fracture aperture alteration and reservoir deformation during heat extraction from a geothermal reservoir. Geothermics 65, 17–31 (2017). https://doi.org/10.1016/j.geothermics.2016.08.006
Pitois, O., Lorenceau, E., Louvet, N., Rouyer, F.: Specific surface area model for foam permeability. Langmuir 25, 97–100 (2009). https://doi.org/10.1021/la8029616
Rutqvist, J., Birkholzer, J., Cappa, F., Tsang, C.F.: Estimating maximum sustainable injection pressure during geological sequestration of CO2 using coupled fluid flow and geomechanical fault-slip analysis. Energy Convers. Manag. 48, 1798–1807 (2007). https://doi.org/10.1016/j.enconman.2007.01.021
Sahimi, M.: Flow and Transport in Porous Media and Fractured Rock. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim (2011)
Sahimi, M., Imdakm, A.O.: Hydrodynamics of particulate motion in porous media. Phys. Rev. Lett. 66, 1169–1172 (1991)
Salimi, H., Pourjavadi, A., Seidi, F., Jahromi, P.E., Soleyman, R.: New smart carrageenan-based superabsorbent hydrogel hybrid: investigation of swelling rate and environmental responsiveness. J. Appl. Polym. Sci. 11, 7 (2010). https://doi.org/10.1002/app.32210
Savoji, M.T., Pourjavadi, A.: Partially hydrolyzed kappa carrageenan—polyacrylonitrile as a novel biopolymer-based superabsorbent hydrogel: synthesis, characterization, and swelling behaviors. Polym. Eng. Sci. 46, 1778–1786 (2006). https://doi.org/10.1002/pen.20646
Sweijen, T., Hassanizadeh, S., Aslannejad, H., Leszczynski, S.: Grain-scale modelling of swelling granular materials using the discrete element method and the multi-sphere approximation In: Poromechanics VI, pp. 329–336. Paris (2017)
Syamlal, M.: MFIX documentation numerical technique, National energy technology laboratory, Department of Energy, Technical Note No. DOE/MC31346-5824, United States (1998)
Tabib, M.V., Johansen, S.T., Amini, S.: A 3D CFD-DEM methodology for simulating industrial scale packed bed chemical looping combustion reactors. Ind. Eng. Chem. Res. 52, 12041–12058 (2013). https://doi.org/10.1021/ie302028s
Taghipour, F., Ellis, N., Wong, C.: Experimental and computational study of gas–solid fluidized bed hydrodynamics. Chem. Eng. Sci. 60, 6857–6867 (2005). https://doi.org/10.1016/j.ces.2005.05.044
Tahmasebi, P.: HYPPS: a hybrid geostatistical modeling algorithm for subsurface modeling. Water Resour. Res. 53, 5980–5997 (2017). https://doi.org/10.1002/2017WR021078
Tahmasebi, P.: Multiple point statistics: a review. In: Daya Sagar, B.S., Cheng, Q., Agterberg, F. (eds.) Handbook of Mathematical Geosciences, pp. 613–643. Springer, Cham (2018a)
Tahmasebi, P.: Packing of discrete and irregular particles. Comput. Geotech. 100, 52–61 (2018b). https://doi.org/10.1016/j.compgeo.2018.03.011
Tahmasebi, P.: Accurate modeling and evaluation of microstructures in complex materials. Phys. Rev. E 97, 023307 (2018c). https://doi.org/10.1103/physreve.97.023307
Tahmasebi, P., Kamrava, S.: Rapid multiscale modeling of flow in porous media. Phys. Rev. E 98, 052901 (2018). https://doi.org/10.1103/PhysRevE.98.052901
Tahmasebi, P., Kamrava, S.: A pore-scale mathematical modeling of fluid–particle interactions: thermo-hydro-mechanical coupling. Int. J. Greenh. Gas Control 1, 1 (2019). https://doi.org/10.1016/j.ijggc.2018.12.014
Taron, J., Elsworth, D.: Thermal–hydrologic–mechanical–chemical processes in the evolution of engineered geothermal reservoirs. Int. J. Rock Mech. Min. Sci. 46, 855–864 (2009). https://doi.org/10.1016/j.ijrmms.2009.01.007
Taron, J., Elsworth, D., Min, K.-B.: Numerical simulation of thermal-hydrologic-mechanical-chemical processes in deformable, fractured porous media. Int. J. Rock Mech. Min. Sci. 46, 842–854 (2009). https://doi.org/10.1016/j.ijrmms.2009.01.008
Tsuji, Y., Tanaka, T., Ishida, T.: Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250 (1992). https://doi.org/10.1016/0032-5910(92)88030-L
Vilarrasa, V., Bolster, D., Olivella, S., Carrera, J.: Coupled hydromechanical modeling of CO2 sequestration in deep saline aquifers. Int. J. Greenh. Gas Control. 4, 910–919 (2010). https://doi.org/10.1016/j.ijggc.2010.06.006
Wei, C., Muraleetharan, K.K.: A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity. Int. J. Eng. Sci. 40, 1807–1833 (2002). https://doi.org/10.1016/S0020-7225(02)00068-X
Williams, J.R., O’Connor, R.: Discrete element simulation and the contact problem. Arch. Comput. Methods Eng. 6, 279–304 (1999). https://doi.org/10.1007/BF02818917
Wu, Q., Andreopoulos, Y., Xanthos, S., Weinbaum, S.: Dynamic compression of highly compressible porous media with application to snow compaction. J. Fluid Mech. 542, 281 (2005). https://doi.org/10.1017/S0022112005006294
Xu, B.H., Yu, A.B.: Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chem. Eng. Sci. 52, 2785–2809 (1997). https://doi.org/10.1016/S0009-2509(97)00081-X
Yang, S., Luo, K., Fang, M., Zhang, K., Fan, J.: Parallel CFD–DEM modeling of the hydrodynamics in a lab-scale double slot-rectangular spouted bed with a partition plate. Chem. Eng. J. 236, 158–170 (2014). https://doi.org/10.1016/j.cej.2013.09.082
Yin, S., Dusseault, M.B., Rothenburg, L.: Coupled THMC modeling of CO2 injection by finite element methods. J. Pet. Sci. Eng. 80, 53–60 (2011). https://doi.org/10.1016/j.petrol.2011.10.008
Yu, A.B., Xu, B.H.: Particle-scale modelling of gas–solid flow in fluidisation. J. Chem. Technol. Biotechnol. 78, 111–121 (2003). https://doi.org/10.1002/jctb.788
Yuan, C.: Pore-scale modeling and hydromechanics of partially saturated granular materials, Ph.D. thesis, Université Grenoble Alpes (2016)
Zeghal, M., El Shamy, U.: A continuum-discrete hydromechanical analysis of granular deposit liquefaction. Int. J. Numer. Anal. Methods Geomech. 28, 1361–1383 (2004). https://doi.org/10.1002/nag.390
Zeng, J., Li, H., Zhang, D.: Numerical simulation of proppant transport in hydraulic fracture with the upscaling CFD-DEM method. J. Nat. Gas Sci. Eng. 33, 264–277 (2016). https://doi.org/10.1016/j.jngse.2016.05.030
Zhang, G., Li, M., Gutierrez, M.: Simulation of the transport and placement of multi-sized proppant in hydraulic fractures using a coupled CFD-DEM approach. Adv. Powder Technol. 28, 1704–1718 (2017). https://doi.org/10.1016/j.apt.2017.04.008
Zhang, X., Tahmasebi, P.: Micromechanical evaluation of rock and fluid interactions. Int. J. Greenh. Gas Control. 76, 266–277 (2018). https://doi.org/10.1016/J.IJGGC.2018.07.018
Zhao, J., Shan, T.: Coupled CFD–DEM simulation of fluid–particle interaction in geomechanics. Powder Technol. 239, 248–258 (2013). https://doi.org/10.1016/j.powtec.2013.02.003
Zheng, C., Liu, Y., Wang, H., Zhu, H., Liu, Z., Ji, R., Shen, Y.: Structural optimization of downhole fracturing tool using turbulent flow CFD simulation. J. Pet. Sci. Eng. 133, 218–225 (2015). https://doi.org/10.1016/j.petrol.2015.06.006
Zhong, W.-Q., Zhang, Y., Jin, B.-S., Zhang, M.-Y.: Discrete element method simulation of cylinder-shaped particle flow in a gas-solid fluidized bed. Chem. Eng. Technol. 32, 386–391 (2009). https://doi.org/10.1002/ceat.200800516
Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B.: Discrete particle simulation of particulate systems: theoretical developments. Chem. Eng. Sci. 62, 3378–3396 (2007). https://doi.org/10.1016/j.ces.2006.12.089
Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B.: Discrete particle simulation of particulate systems: a review of major applications and findings. Chem. Eng. Sci. 63, 5728–5770 (2008). https://doi.org/10.1016/j.ces.2008.08.006
Zhu, Q.J., He, Y.F., Yin, Y.: Finite element analysis of deformation mechanism for porous materials under fluid-solid interaction. Mater. Res. Innov. 18, 22–27 (2014). https://doi.org/10.1179/1432891714Z.000000000519
Acknowledgements
The financial support from the University of Wyoming for this research is greatly acknowledged.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhang, X., Tahmasebi, P. Effects of Grain Size on Deformation in Porous Media. Transp Porous Med 129, 321–341 (2019). https://doi.org/10.1007/s11242-019-01291-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-019-01291-1