Abstract
Knowledge of porous media structure is an essential part of the hydrodynamic investigation of fluid flow in porous media. To study soil behavior (as a granular porous media) and water and contaminant movement in the vadose zone, appropriate estimation of soil water retention curve (SWRC) and soil hydraulic conductivity curve (SHCC) has a pivotal role and is one of the most challenging topics for researchers and engineers in soil and water science. The SWCR can be approximated using an accurate particle size distribution (PSD) function. In this study by applying the random close packing (RCP) method as an encouraging method for predicting and studying particle configuration, an optimal particle size distribution is developed for coarse-grained soils (0.025 mm < PSD < 3.35 mm). The mentioned RCP is generated using a heuristic algorithm with merging applicable equations of soil science. For porous media modeling, MATLAB software is used and the predicted results by the optimal model for the parameters of porosity, pressure drop, and saturated hydraulic conductivity are compared with laboratory measurements. Experimental design is conducted by MINITAB and predicted coarse-grained soil structure by the model is compared with four sifted soils. The results of the sensitivity analysis showed that the porosity obtained from the model is strongly sensitive to the resolution factor and should be chosen with a sufficiently large amount (higher than 250). Results showed good consistency (up to 95%) between predicted porosity and only a 10% difference in pressure drop and permeability with observed measurements.
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Abbreviations
- RCP:
-
Random close packing
- PNM:
-
Pore network modeling
- SWRC:
-
Soil water retention curve
- SHCC:
-
Soil hydraulic conductivity curve
- PSD:
-
Particle size distribution
- PoSD:
-
Pore size distribution
- d :
-
Diameter (m)
- D p :
-
Equivalent grain diameter (m)
- f :
-
Mass percent
- g :
-
Gravity acceleration (m.s−2)
- h :
-
Matric suction (m)
- k :
-
Permeability of porous media (m2)
- K s :
-
Saturated hydraulic conductivity (m.s−1)
- L :
-
Length (m)
- L c :
-
Cube edge length (m)
- L m :
-
Mesh grid (m)
- m :
-
Number of sublayers
- n :
-
Number of particles
- n i :
-
Number of particles in a specific diameter range
- RF:
-
Resolution factor
- t cal :
-
Calculations time
- v s :
-
Superficial velocity (m.s−1)
- x, y, z :
-
Nodes coordination (m,m,m)
- ΔP :
-
Pressure drop (Kg.m−1.s−2)
- ε:
-
Porosity
- θ :
-
Volumetric water content (m3.m-3)
- λ :
-
Scale parameters
- μ :
-
Dynamic viscosity (Kg.m−1.s−1)
- ρ :
-
Density (Kg.m−3)
- σ :
-
Variance of grain size distribution
- φ s :
-
Sphericity factor
- i, j, k :
-
Counter
- c :
-
Cube
- g :
-
Grain
- p :
-
Particle
- s :
-
Saturated
References
Al-Dhahli ARS, Geiger S, van Dijke MIJ (2013) Three-phase pore-network modeling for reservoirs with arbitrary wettability. SPE J 18:285–295. https://doi.org/10.2118/147991-PA
Anikeenko AV, Medvedev NN, Aste T (2008) Structural and entropic insights into the nature of the random-close-packing limit. Phys Rev E 77:1–9. https://doi.org/10.1103/PhysRevE.77.031101
Arya LM, Paris JF (1981) A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data. Soil Sci Soc Am J 45:1023–1030. https://doi.org/10.2136/sssaj1981.03615995004500060004x
Assouline S, Rouault Y (1997) Modeling the relationships between particle and pore size distributions in multicomponent sphere packs: application to the water retention curve. Colloids Surf A Physicochem Eng Asp 127:201–210. https://doi.org/10.1016/S0927-7757(97)00144-1
Baranau V, Tallarek U (2014) Random-close packing limits for monodisperse and polydisperse hard spheres. Soft Matter 10:3826–3841. https://doi.org/10.1039/c3sm52959b
Bargmann S, Klusemann B, Markmann J, Schnabel JE, Schneider K, Soyarslan C, Wilmers J (2018) Generation of 3D representative volume elements for heterogeneous materials: a review. Progress Mater Sci 96:322–384
Benabbou A, Borouchaki H, Laug P, Lu J (2010) Numerical modeling of nanostructured materials. Finite Elem Anal Des 46:165–180. https://doi.org/10.1016/j.finel.2009.06.030
Braddock RD, Parlange J-Y, Lee H (2001) Application of a soil water hysteresis model to simple water retention curves. Transp Porous Media 44:407–420. https://doi.org/10.1023/A:1010792008870
Ch NK, Foteinopoulou K, Laso M (2013) Spontaneous crystallization in athermal polymer packings. Int J Mol Sci 14:332–358. https://doi.org/10.3390/ijms14010332
Chen R-P, Liu P, Liu X-M, Wang P-F, Kang X (2019) Pore-scale model for estimating the bimodal soil–water characteristic curve and hydraulic conductivity of compacted soils with different initial densities. Eng Geol 260:105199. https://doi.org/10.1016/j.enggeo.2019.105199
Daneyko A, Höltzel A, Khirevich S, Tallarek U (2011) Influence of the particle size distribution on hydraulic permeability and eddy dispersion in bulk packings. Anal Chem 83:3903–3910. https://doi.org/10.1021/ac200424p
Dorai F, Rolland M, Wachs A, Marcoux M, Climent E (2012) Packing fixed bed reactors with cylinders: influence of particle length distribution. Procedia Eng 42:1335–1345. https://doi.org/10.1016/j.proeng.2012.07.525
Esmaeelnejad L, Siavashi F, Seyedmohammadi J, Shabanpour M (2016) The best mathematical models describing particle size distribution of soils. Model Earth Syst Environ 2:166. https://doi.org/10.1007/s40808-016-0220-9
Farr RS, Groot RD (2009) Close packing density of polydisperse hard spheres. J Chem Phys. https://doi.org/10.1063/1.3276799
Fredlund DG, Xing A, Huang S (1994) Predicting the permeability function for unsaturated soils using the soil-water characteristic curve. Can Geotech J 31:533–546
He D, Ekere NN, Cai L (1999) Computer simulation of random packing of unequal particles. Phys Rev E 60:7098–7104. https://doi.org/10.1103/PhysRevE.60.7098
Hitti K, Bernacki M (2013) Optimized dropping and rolling (ODR) method for packing of poly-disperse spheres. Appl Math Model 37:5715–5722. https://doi.org/10.1016/j.apm.2012.11.018
Irani CF, Callis RR (1963) Particle size: measurement, interpretation and application, 1st Ed. (No. 531.36 I7), John Wiley and Sons, University of Michigan
Kansal AR, Torquato S, Stillinger FH (2002) Computer generation of dense polydisperse sphere packings. J Chem Phys 117:8212–8218. https://doi.org/10.1063/1.1511510
Kyrylyuk AV, Wouterse A, Philipse AP (2009) Random packings of rod-sphere mixtures simulated by mechanical contraction. AIP Conf Proc 1145:211–214. https://doi.org/10.1063/1.3179895
Leong E-C (2019) Soil-water characteristic curves—determination, estimation and application. Jpn Geotech Soc Spec Publ 7:21–30. https://doi.org/10.3208/jgssp.v07.003
Li SX, Zhao J, Lu P, Xie Y (2010) Maximum packing densities of basic 3D objects. Chinese Sci Bull 55:114–119. https://doi.org/10.1007/s11434-009-0650-0
Loll P, Moldrup P, Schjønning P, Riley H (1999) Predicting saturated hydraulic conductivity from air permeability: application in stochastic water infiltration modeling. Water Resour Res 35:2387–2400. https://doi.org/10.1029/1999WR900137
Rhodes M (2008) Introduction to particle technology, 2nd edn. Wiley
Santiso E, Müller EA (2002) Dense packing of binary and polydisperse hard spheres. Mol Phys 100:2461–2469. https://doi.org/10.1080/00268970210125313
Shirazi MA, Boersma L (1984) A unifying quantitative analysis of soil texture. Soil Sci Soc Am J 48:142–147. https://doi.org/10.2136/sssaj1984.03615995004800010026x
Tobochnik J, Chapin PM (1988) Monte Carlo simulation of hard spheres near random closest packing using spherical boundary conditions. J Chem Phys 88:5824–5830. https://doi.org/10.1063/1.454542
Tong F, Jing L, Bin T (2012) A water retention curve model for the simulation of coupled thermo-hydro-mechanical processes in geological porous media. Transp Porous Media 91:509–530. https://doi.org/10.1007/s11242-011-9857-z
Visscher WM, Bolsterli M (1972) Random packing of equal and unequal spheres in two and three dimensions. Nature 239:504–507. https://doi.org/10.1038/239504a0
Wen T, Shao L, Guo X, Zhao Y (2020) Experimental investigations of the soil water retention curve under multiple drying–wetting cycles. Acta Geotech 15:3321–3326. https://doi.org/10.1007/s11440-020-00964-2
Wen T, Wang P, Shao L, Guo X (2021) Experimental investigations of soil shrinkage characteristics and their effects on the soil water characteristic curve. Eng Geol 284:106035. https://doi.org/10.1016/j.enggeo.2021.106035
Williams SR, Philipse AP (2003) Random packings of spheres and spherocylinders simulated by mechanical contraction. Phys Rev E 67:9. https://doi.org/10.1103/PhysRevE.67.051301
Wu Y, Zhou W, Wang B, Yang F (2010) Modeling and characterization of two-phase composites by Voronoi diagram in the Laguerre geometry based on random close packing of spheres. Comput Mater Sci 47:951–961. https://doi.org/10.1016/j.commatsci.2009.11.028
Wu H, Leung SCH, Si YW, Zhang D, Lin A (2017) Three-stage heuristic algorithm for three-dimensional irregular packing problem. Appl Math Model 41:431–444. https://doi.org/10.1016/j.apm.2016.09.018
Xiong Q, Baychev TG, Jivkov AP (2016) Review of pore network modelling of porous media: experimental characterisations, network constructions and applications to reactive transport. J Contam Hydrol 192:101–117. https://doi.org/10.1016/j.jconhyd.2016.07.002
Zhai Q, Rahardjo H, Satyanaga A, Dai G (2020) Estimation of the soil-water characteristic curve from the grain size distribution of coarse-grained soils. Eng Geol 267:105502. https://doi.org/10.1016/j.enggeo.2020.105502
Zhou J, Zhang Y, Chen JK (2009) Numerical simulation of random packing of spherical particles for powder-based additive manufacturing. J Manuf Sci Eng 131:031004. https://doi.org/10.1115/1.3123324
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Bezaatpour, J., Fatehifar, E. & Rasoulzadeh, A. Coarse-grained geological porous media structure modeling using heuristic algorithm and evaluation of porosity, hydraulic conductivity, and pressure drop with experimental results. Environ Earth Sci 80, 482 (2021). https://doi.org/10.1007/s12665-021-09699-z
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DOI: https://doi.org/10.1007/s12665-021-09699-z