Articles | Volume 26, issue 13
https://doi.org/10.5194/hess-26-3359-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/hess-26-3359-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Experimental study of non-Darcy flow characteristics in permeable stones
Zhongxia Li
School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, China
Junwei Wan
School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, China
Tao Xiong
School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, China
Hongbin Zhan
CORRESPONDING AUTHOR
Department of Geology and Geophysics, Texas A & M University,
College Station, TX 77843-3115, USA
Linqing He
Changjiang Institute of Survey Technical Research MWR, Wuhan, China
Kun Huang
CORRESPONDING AUTHOR
School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, China
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Cited articles
Alvarez, A. E., Mahmoud, E., Martin, A. E., Masad, E., and Estakhri, C.:
Stone-on-stone contact of permeable friction course mixtures, J.
Mater. Civil Eng., 22, 1129–1138,
https://doi.org/10.1061/(ASCE)MT.1943-5533.0000117, 2010.
Anovitz, L. M. and Cole, D. R.: Characterization and Analysis of Porosity
and Pore Structures, Reviews in Mineralogy and Geochemistry, 80, 61–164,
https://doi.org/10.2138/rmg.2015.80.04, 2015.
Bear, J.: Dynamics of fluids in porous media, Soil Science, 120, 162–163, https://doi.org/10.1097/00010694-197508000-00022, 1975.
Beavers, G. S., Sparrow, E., and Rodenz, D. E.: Influence of Bed Size on the
Flow Characteristics and Porosity of Randomly Packed Beds of Spheres,
J. Appl. Mech., 40, 655–660,
https://doi.org/10.1115/1.3423067, 1972.
Blick, E.: Capillary-Orifice Model for High-Speed Flow through Porous Media,
Industrial Engineering Chemistry Process Design Development, 5, 90–94,
https://doi.org/10.1021/i260017a019, 1966.
Bu, S., Yang, J., Dong, Q., and Wang, Q.: Experimental study of transition
flow in packed beds of spheres with different particle sizes based on
electrochemical microelectrodes measurement, Appl. Therm. Eng.,
73, 1525–1532,
https://doi.org/10.1016/j.applthermaleng.2014.03.063, 2014.
Darcy, H.: Recherches expérimentales relatives au mouvement de l'eau dans les tuyaux, Impr. Impériale, Paris, France, https://www.scirp.org/reference/referencespapers.aspx?referenceid=1200904 (last access: 23 June 2022), 1857.
Dejam, M., Hassanzadeh, H., and Chen, Z.: Pre-Darcy
flow in porous media, Water Resour. Res., 53, 8187–8210,
https://doi.org/10.1002/2017WR021257, 2017.
Dudgeon, C. R.: An experimental study of the flow of water through coarse
granular media, Houille Blanche, 785–801,
https://doi.org/10.1051/lhb/1966049, 1966.
Dybbs, A. and Edwards, R. V.: A New Look at Porous Media Fluid Mechanics –
Darcy to Turbulent, Springer Netherlands, 199–256,
https://doi.org/10.1007/978-94-009-6175-3_4, 1984.
Ergun, S.: Fluid flow through packed columns, Chem. Eng. Prog.,
89–94, https://doi.org/10.1016/0009-2509(53)80048-5, 1952.
Fancher, G. H. and Lewis, J. A.: Flow of simple fluids through porous
materials, Ind. Eng. Chem., 25, 1139–1147, https://doi.org/10.1021/ie50286a020, 1933.
Fetter, C. W.: Applied Hydrogeology:International Edition, Prentice Hall, Pearson, Engelwood Cliffs, 10: 0131226878, 2001.
Forchheimer, P.: Wasserbewegung durch boden, Z. Ver. Deutsch, Ing., 45,
1728–1782, 1901.
Geertsma, J.: Estimating the Coefficient of Inertial Resistance in Fluid
Flow Through Porous Media, Soc. Petrol. Eng. J., 14,
445–450, https://doi.org/10.2118/4706-PA, 1974.
Guan, X., Wang, J., and Xiao, F.: Sponge city strategy and application of
pavement materials in sponge city, J. Clean. Prod., 303, 127022, https://doi.org/10.1016/j.jclepro.2021.127022, 2021.
Hall, P. L., Mildner, D., and Borst, R. L.: Small-angle scattering studies
of the pore spaces of shaly rocks, J. Geophys. Res.-Atmos., 91, 2183–2192, https://doi.org/10.1029/JB091iB02p02183, 1986.
Han, D., Wei, L., and Zhang, J.: Experimental study on performance of
asphalt mixture designed by different method, Procedia Engineer., 137,
407–414, https://doi.org/10.1016/j.proeng.2016.01.275, 2016.
Harlan, J., Picot, D., Loll, P., and Garavito, R.: Calibration of
size-exclusion chromatography: use of a double Gaussian distribution
function to describe pore sizes, Anal. Biochem., 224, 557–563, https://doi.org/10.1006/abio.1995.1087, 1995.
He, X. and Zhang, Z.: Microscopic pore structural characteristics in coal particles, 3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME 2015), Guangzhou, China, 1907–1911, https://doi.org/10.2991/ic3me-15.2015.368, 2015.
Huang, K.: Exploration of the basic seepage equation in porous media, PhD thesis, School of Environmental Studies, China University of Geosciences, China, 95 pp., http://kns-cnki-net-s.webvpn.cug.edu.cn:8118/kns8/defaultresult/index (last access: 22 June 2022,), 2012.
Huang, K., Wan, J., Chen, C., Linqing, H., Mei, W., and Zhang, M.:
Experimental investigation on water flow in cubic arrays of spheres, J.
Hydrol., 492, 61–68, https://doi.org/10.1016/j.jhydrol.2013.03.039, 2013.
Irmay, S.: Theoretical models of flow through porous media, RILEM Symp.
Transfer of Water in porous media, 29, 37–43, 1964.
Izbash, S.: O Filtracii V Kropnozernstom Materiale, Leningrad, USSR, https://xueshu.dailyheadlines.cc/scholar?hl=zh-CN&as_sdt=0,5&q=Izbash,+S.:+O+Filtracii+V+Kropnozernstom+Materiale&btnG= (last access: 22 June 2022), 1931.
Javadi, M., Sharifzadeh, M., Shahriar, K., and Mitani, Y.: Critical Reynolds
number for nonlinear flow through rough walled fractures: The role of
shear processes, Water Resour. Res., 50, 1789–1804, https://doi.org/10.1002/2013WR014610, 2014.
Jeon, H., Cho, H., Kim, J., and Sung, B.: Non-Gaussian rotational diffusion
in heterogeneous media, Phys. Rev. E, 90, 042105, https://doi.org/10.1103/PhysRevE.90.042105, 2014.
Kadlec, R. H. and Knight, R. L.: Treatment Wetlands, Lewis Pub, Boca Raton, ISBN 9781566705264, 1996.
Kate, J. M. and Gokhale, C. S.: A simple method to estimate complete pore
size distribution of rocks, Eng. Geol., 84, 48–69, https://doi.org/10.1016/j.enggeo.2005.11.009, 2006.
Koch, D. and Ladd, A.: Moderate Reynolds number flows through periodic and
random arrays of aligned cylinders, J. Fluid Mech., 349, 31–66, https://doi.org/10.1017/S002211209700671X, 1996.
Kovács, G.: Seepage Hydraulics, Development in Water Sciences, Elsevier, New York, ISBN 9780080870014, 1981.
Latifi, M., Midoux, N., Storck, A., and Gence, J.: The use of micro-electrodes in the study of the flow regimes in a packed bed reactor with single phase liquid flow, Chem. Eng. Sci., 44, 2501–2508, https://doi.org/10.1016/0009-2509(89)85194-2, 1989.
Li, Q., Wang, F., Yu, Y., Huang, Z., Li, M., and Guan, Y. J. J. o. E. M.:
Comprehensive performance evaluation of LID practices for the sponge city
construction: a case study in Guangxi, China, J. Environ.
Manage., 231, 10–20, https://doi.org/10.1016/j.jenvman.2018.10.024, 2019.
Li, Z., Wan, J., Huang, K., Chang, W., and He, Y.: Effects of particle
diameter on flow characteristics in sand columns, Int. J. Heat Mass Tran., 104, 533–536, https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.085, 2017.
Li, Z., Wan, J., Zhan, H., Cheng, X., Chang, W., and Huang, K.: Particle
size distribution on Forchheimer flow and transition of flow regimes in
porous media, J. Hydrol., 574, 1–11, https://doi.org/10.1016/j.jhydrol.2019.04.026, 2019.
Lindquist, E.: On the flow of water through porous soil, Premier Congres des grands barrages, Stockholm, 81–101, https://xs2.dailyheadlines.cc/scholar?cluster=10665091756027963788&hl=zh-CN&as_sdt=2005&sciodt=0,5 (last access: 22 June 2022), 1933.
Lindquist, W. B., Venkatarangan, A., Dunsmuir, J., and Wong, T. F.: Pore and
throat size distributions measured from synchrotron X-ray tomographic images
of Fontainebleau sandstones, J. Geophys. Res.-Sol. Ea.,
105, 21509–21527, https://doi.org/10.1029/2000JB900208, 2000.
Maalal, O., Prat, M., Peinador, R., and Lasseux, D.: Determination of the
throat size distribution of a porous medium as an inverse optimization
problem combining pore network modeling and genetic and hill climbing
algorithms, Phys. Rev. E, 103, 023303, https://doi.org/10.1103/PhysRevE.103.023303, 2021.
Macdonald, I., El-Sayed, M., Mow, K., and Dullien, F.: Flow through porous
media-the Ergun equation revisited, Ind. Eng. Chem.
Fund., 18, 199–208, https://doi.org/10.1021/i160071a001,
1979.
Min, Z., Min, C., Zhang, S., Wang, X., and Wang, Y.: Effect of precursor on the pore structure of carbon foams, New Carbon Materials, 22, 75–79, https://doi.org/10.1016/S1872-5805(07)60009-2, 2007.
Moutsopoulos, K. N., Papaspyros, I. N., and Tsihrintzis, V. A.: Experimental
investigation of inertial flow processes in porous media, J.
Hydrol., 374, 242–254, https://doi.org/10.1016/j.jhydrol.2009.06.015, 2009.
Niranjan, H.: Non-Darcy flow through porous media, MS dissertation, ITT, Kanpur, India, https://xs2.dailyheadlines.cc/scholar?hl=zh-CN&as_sdt=0,5&q=Niranjan,+H+1973&btnG= (last access: 22 June 2022), 1973.
Panfilov, M. and Fourar, M.: Physical splitting of nonlinear effects in
high-velocity stable flow through porous media, Adv. Water Resour.,
29, 30–41, https://doi.org/10.1016/j.advwatres.2005.05.002,
2006.
Pittman, E. D.: Relationship of porosity and permeability to various
parameters derived from mercury injection-capillary pressure curves for
sandstone (1), AAPG Bull., 76, 191–198, https://doi.org/10.1306/BDFF87A4-1718-11D7-8645000102C1865D, 1992.
Prowell, B. D., Allen Cooley Jr., L., and Schreck, R. J.: Virginia's
experience with 9.5-mm nominal-maximum-aggregate-size stone matrix asphalt,
Transportation research record, Transportation research record, 1813, 133–141, https://doi.org/10.3141/1813-16, 2002.
Rezaee, R., Saeedi, A., and Clennell, B.: Tight gas sands permeability
estimation from mercury injection capillary pressure and nuclear magnetic
resonance data, J. Petrol. Sci. Eng., 88, 92–99, https://doi.org/10.1016/j.petrol.2011.12.014, 2012.
Rijfkogel, L. S., Ghanbarian, B., Hu, Q., and Liu, H. H.: Clarifying pore
diameter, pore width, and their relationship through pressure measurements:
A critical study, Mar. Petrol. Geol., 107, 142–148, https://doi.org/10.1016/j.marpetgeo.2019.05.019, 2019.
Scheidegger, A. E.: The physics of flow through porous media, Soil Sci.,
86, 355–362, https://doi.org/10.3138/9781487583750, 1958.
Scheidegger, A. E.: On the stability of displacement fronts in porous media:
a disscussion of the muskat-aronofsky model, Can. J. Phys.,
38, 153–162, https://doi.org/10.1139/p60-017, 1960.
Schmitt, M., Fernandes, C. P., da Cunha Neto, J. A., Wolf, F. G., and dos
Santos, V. S.: Characterization of pore systems in seal rocks using nitrogen
gas adsorption combined with mercury injection capillary pressure
techniques, Mar. Petrol. Geol., 39, 138–149, https://doi.org/10.1016/j.marpetgeo.2012.09.001, 2013.
Schneebeli, G.: Experiences sur la limite de validite de la loi de Darcy et
l'apparition de la turbulence dans un ecoulemant de filtration, Huille
Blanche, 2, 141–149, https://doi.org/10.1051/lhb/1955030, 1955.
Sedghi-Asl, M., Rahimi, H., and Salehi, R.: Non-Darcy Flow of Water Through
a Packed Column Test, Transport in Porous Media, 101, 215–227, https://doi.org/10.1007/s11242-013-0240-0, 2014.
Seguin, D., Montillet, A., and Comiti, J.: Experimental characterisation of
flow regimes in various porous media – I: Limit of laminar flow regime,
Chem. Eng. Sci., 53, 3751–3761, https://doi.org/10.1016/S0009-2509(98)00175-4, 1998.
Shi, W., Yang, T., and Yu, S.: Experimental Investigation on Non-Darcy Flow
Behavior of Granular Limestone with Different Porosity, J.
Hydrol. Eng., 25, 06020004, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001966, 2020.
Sidiropoulou, M. G., Moutsopoulos, K. N., and Tsihrintzis, V.: Determination
of Forchheimer equation coefficients a and b, Hydrol. Process., 21,
534–554, https://doi.org/10.1002/hyp.6264, 2007.
Skjetne, E., Hansen, A., and Gudmundsson, J.: High-velocity flow in a rough
fracture, J. Fluid Mech., 383, 1–28, https://doi.org/10.1017/S0022112098002444, 1999.
Soni, J., Islam, N., and Basak, P.: An experimental evaluation of
non-Darcian flow in porous media, J. Hydrol., 38, 231–241, https://doi.org/10.1016/0022-1694(78)90070-7, 1978.
Souto, H. P. A. and Moyne, C.: Dispersion in two-dimensional periodic porous
media. Part I. Hydrodynamics, Phys. Fluids, 9, 2243–2252, https://doi.org/10.1063/1.869365, 1997.
Suo, Z., Bao, X., Nie, L., Yan, Q., and Qi, K.: Optimization Design of Mix
Proportion of Large Stone Permeable Mixture Based on Target Air Voids,
Buildings, 11, 514, https://doi.org/10.3390/buildings11110514,
2021.
Swartzendruber, D.: Modification of Darcy's law for the flow of water in
soils, Soil Sci., 93, 22–29, https://doi.org/10.1097/00010694-196201000-00005, 1962a.
Swartzendruber, D.: Non-Darcy flow behavior in
liquid-saturated porous media, J. Geophys.
Res., 67, 5205–5213, https://doi.org/10.1029/JZ067i013p05205, 1962b.
Van Lopik, J. H., Snoeijers, R., van Dooren, T. C. G. W., Raoof, A., and
Schotting, R. J.: The Effect of Grain Size Distribution on Nonlinear Flow
Behavior in Sandy Porous Media, Transport Porous Med., 120, 1–30, https://doi.org/10.1007/s11242-017-0903-3, 2017.
Van Lopik, J. H., Zazai, L., Hartog, N., and Schotting, R.: Nonlinear Flow
Behavior in Packed Beds of Natural and Variably Graded Granular Materials,
Transport Porous Med., 131, 957–983, https://doi.org/10.1007/s11242-019-01373-0, 2019.
Wang, J., Ng, P.-L., Gong, Y., Su, H., and Du, J.: Experimental Study of Low
Temperature Performance of Porous Asphalt Mixture, Appl. Sci., 11,
4029, https://doi.org/10.3390/app11094029, 2021.
Ward, J. C.: Turbulent Flow in Porous Media, J. Hydraul.
Eng., 90, 1–12, https://doi.org/10.1016/S0301-9322(02)00051-4, 1964.
Washburn, E. W.: The Dynamics of Capillary Flow, Phys. Rev., 17,
273–283, https://doi.org/10.1103/PhysRev.17.273, 1921.
Wright, D.: Nonlinear Flow Through Granular Media, Journal of Hydraulic
Engineering, 94, 851–872, https://doi.org/10.1061/JYCEAJ.0001858, 1968.
Xie, H. and Watson, D. E.: Determining air voids content of compacted stone
matrix asphalt mixtures, Transport. Res. Rec., 1891, 203–211, https://doi.org/10.3141/1891-24, 2004.
Xu, C. and Torres-Verdín, C.: Pore System Characterization and
Petrophysical Rock Classification Using a Bimodal Gaussian Density Function,
Math. Geosci., 45, 753–771, https://doi.org/10.1007/s11004-013-9473-2, 2013.
Yang, B., Yang, T., Xu, Z., Liu, H., Yang, X., and Shi, W.: Impact of
Particle-Size Distribution on Flow Properties of a Packed Column, J.
Hydrol. Eng., 24, 04018070, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001735, 2019.
Yu, T., Liu, D., Zhang, H., and Wang, H.: Influence of pore water phase
change on service performance for permeable pavement in Sponge City, Water
Sci. Technol., 84, 3769–3779, https://doi.org/10.2166/wst.2021.459, 2021.
Zeng, Z. and Grigg, R.: A criterion for non-Darcy flow in porous media,
Transport Porous Med., 63, 57–69, https://doi.org/10.1007/s11242-005-2720-3, 2006.
Zhihong, L. I., Jihong, S., Dong, W. U., Yuhan, S., Liu, Y. I., Wenjun, S.,
and Baozhong, D.: Determination of average pore diameter of SiO2 xerogels by
small angle X-ray scattering, ACTA Phys. Sin., 49, 1312–1315, https://doi.org/10.3321/j.issn:1000-3290.2000.07.020, 2000.
Zhou, H., Fang, Y.-G., Chen, M., Gu, R.-G., and Li, W.: Experimental and
analytical study on electro-osmosis in low-permeability soil considering the
pore size effect, Geotechnique, 71, 141–152, https://doi.org/10.1680/jgeot.18.p.362, 2019.
Short summary
Four permeable rocks with different pore sizes were considered to provide experimental evidence of Forchheimer flow and the transition between different flow regimes. The mercury injection technique was used to measure the pore size distribution, which is an essential factor for determining the flow regime, for four permeable stones. Finally, the influences of porosity and particle size on the Forchheimer coefficients were discussed.
Four permeable rocks with different pore sizes were considered to provide experimental evidence...
Special issue