Proposing a Characteristic Length Definition for Flow Characterization in Porous Media: A Methodology for Estimating Hydraulic Radius
DOI:
https://doi.org/10.18311/jmmf/2023/43591Keywords:
Characteristic Length, Flow through Porous Media, Hydraulic Radius, Porous Media.Abstract
This study explores the complex factors influencing fluid flow and associated head loss within porous media, focusing on particle size, shape, and packing porosity. The chosen characteristic length, hydraulic radius (denoted as “r”), integrates these factors, providing a comprehensive measure for characterizing flow behavior in specific packing configurations. Crushed stones and glass spheres of varying sizes are used as porous media. Porosity, size, and shape of the media are meticulously determined to understand their impact on flow characteristics. The study’s findings offer valuable insights for researchers and designers in porous media applications, guiding the selection of appropriate characteristic length expressions. Additionally, this work contributes to a deeper understanding of porous media flow and provides a practical framework for characterizing and analyzing porous media properties, advancing the broader field of fluid dynamics in porous structures.
Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
Banerjee A, Pasupuleti S, Singh MK, Kumar GNP. A study on the Wilkins and Forchheimer equations used in coarse granular media flow. Acta Geophys 2018; 66:81-91. https:// doi.org/10.1007/s11600-017-0102-1 DOI: https://doi.org/10.1007/s11600-017-0102-1
Banerjee A, Pasupuleti S, Mondal K, Nezhad MM. Application of data driven machine learning approach for modelling of non-linear filtration through granular porous media. Int J Heat Mass Transf 2021; 179. https://doi. org/10.1016/j.ijheatmasstransfer.2021.121650 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2021.121650
Dan H-C, He L-H, Xu B. Experimental investigation on non-Darcian flow in unbound graded aggregate material of highway pavement. Transp Porous Media. 2016; 112(1):189- 206. https://doi.org/10.1007/s11242-016-0640-z DOI: https://doi.org/10.1007/s11242-016-0640-z
Dudgeon CR. Wall effects in permeameters. J Hydraul Div 1967; 93(5):137-48. https://doi.org/10.1061/ JYCEAJ.0001673 DOI: https://doi.org/10.1061/JYCEAJ.0001673
Firoozabadi A, Katz DL. An analysis of high-velocity gas flow through porous media. J Pet Technol 1979; 31(02):211- 16. https://doi.org/10.2118/6827-PA DOI: https://doi.org/10.2118/6827-PA
Hassanizadeh SM, Gray WG. High velocity flow in porous media. Transp Porous Media. 1987; 2:521-31. https://doi. org/10.1007/BF00192152 DOI: https://doi.org/10.1007/BF00192152
Curtis RP, Lawson JD. Flow over and through rockfill banks. J Hydraul Div. 1967; 93(5):1-22. https://doi.org/10.1061/ JYCEAJ.0001671 DOI: https://doi.org/10.1061/JYCEAJ.0001671
Ferdos F, Wörman A, Ekström I. Hydraulic conductivity of coarse rockfill used in hydraulic structures. Transp Porous Media. 2015; 108(2):367-91. https://doi.org/10.1007/ s11242-015-0481-1 DOI: https://doi.org/10.1007/s11242-015-0481-1
Hansen D. The behaviour of flowthrough rockfill dams; 1995.
Fang H, Zhu J. Simulation of groundwater exchange between an unconfined aquifer and a discrete fracture network with laminar and turbulent flows. J Hydrol. 2018; 562:468-76. https://doi.org/10.1016/j.jhydrol.2018.05.022 DOI: https://doi.org/10.1016/j.jhydrol.2018.05.022
Holditch S, Morse R. The effects of non-Darcy flow on the behavior of hydraulically fractured gas wells (includes associated paper 6417). J Pet Technol. 1976; 28(10):1169-179. https://doi.org/10.2118/5586-PA DOI: https://doi.org/10.2118/5586-PA
Houben GJ, Wachenhausen J, Morel CRG. Effects of ageing on the hydraulics of water wells and the influence of non-Darcy flow. Hydrogeol J. 2018; 26(4). https://doi. org/10.1007/s10040-018-1775-5 DOI: https://doi.org/10.1007/s10040-018-1775-5
Huang H, Ayoub J. Applicability of the Forchheimer equation for non-Darcy flow in porous media. Spe J. 2008; 13(01):112-22. https://doi.org/10.2118/102715-PA DOI: https://doi.org/10.2118/102715-PA
Nezhad MM, Rezania M, Baioni E. Transport in porous media with nonlinear flow condition. Transp Porous Media. 2019; 126:5-22. https://doi.org/10.1007/s11242-018-1173-4 DOI: https://doi.org/10.1007/s11242-018-1173-4
Salahi M-B, Sedghi-Asl M, Parvizi M. Nonlinear flow through a packed-column experiment. J Hydrol Eng. 2015; 20(9). https://doi.org/10.1061/(ASCE)HE.1943- 5584.0001166 DOI: https://doi.org/10.1061/(ASCE)HE.1943-5584.0001166
Banerjee A, Pasupuleti S. Effect of convergent boundaries on post laminar flow through porous media. Powder Technol. 2019; 342:288-300. https://doi.org/10.1016/j.powtec. 2018.09.085 DOI: https://doi.org/10.1016/j.powtec.2018.09.085
Reddy NP, Rao PM. Convergence effect on the flow resistance in porous media. J Inst Eng India Civ Eng Div. 2004; 85(mai):36-43.
Reddy NBP. Convergence factors effect on non-uniform flow through porous media. J Inst Eng Part CV Civ Eng Div. 2006; 86(4):133-38.
Reddy NBP. An experimental study on the effect of converging boundary on flow through porous media. ISH J Hydraul Eng. 2005; 11(2):73-89. https://doi.org/10.1080/0 9715010.2005.10514782 DOI: https://doi.org/10.1080/09715010.2005.10514782
Thiruvengadam M, Kumar GP. Validity of Forchheimer equation in radial flow through coarse granular media. J Eng Mech. 1997; 123(7):696-705. https://doi.org/10.1061/ (ASCE)0733-9399(1997)123:7(696) DOI: https://doi.org/10.1061/(ASCE)0733-9399(1997)123:7(696)
Kovacs G. Seepage through saturated and unsaturated layers. Hydrol Sci J. 1971; 16(2):27-40. https://doi. org/10.1080/02626667109493046 DOI: https://doi.org/10.1080/02626667109493046
Andrade Jr JS, Costa UMS, Almeida MP, Maske HA, Stanley HE. Inertial effects on fluid flow through disordered porous media. Phys Rev Lett. 1999; 82(26). https://doi.org/10.1103/ PhysRevLett.82.5249 DOI: https://doi.org/10.1103/PhysRevLett.82.5249
Blick E, Civan F. Porous-media momentum equation for highly accelerated flow. SPE Reserv Eng. 1988; 3(03):1048- 52. https://doi.org/10.2118/16202-PA DOI: https://doi.org/10.2118/16202-PA
Bu S, Yang J, Dong Q, Wang Q. Experimental study of transition flow in packed beds of spheres with different particle sizes based on electrochemical microelectrodes measurement. Appl Therm Eng. 2014; 73(2):1525-32. https://doi. org/10.1016/j.applthermaleng.2014.03.063 DOI: https://doi.org/10.1016/j.applthermaleng.2014.03.063
Fourar M, Radilla G, Lenormand R, Moyne C. On the nonlinear behavior of a laminar single-phase flow through two and three-dimensional porous media. Adv Water Resour. 2004; 27(6):669-77. https://doi.org/10.1016/j.advwatres. 2004.02.021 DOI: https://doi.org/10.1016/j.advwatres.2004.02.021
Green Jr L, Duwez P. Fluid flow through porous metals. J Appl Mech. 1951; 18. https://doi.org/10.1115/1.4010218 27. Horton N, Pokrajac D. Onset of turbulence in a regular porous medium: An experimental study. Phys Fluids. 2009; 21(4). https://doi.org/10.1063/1.3091944 DOI: https://doi.org/10.1063/1.3091944
Jolls K, Hanratty T. Transition to turbulence for flow through a dumped bed of spheres. Chem Eng Sci. 1966; 21(12):1185- 90. https://doi.org/10.1016/0009-2509(66)85038-8 DOI: https://doi.org/10.1016/0009-2509(66)85038-8
Latifi MA, Midoux N, Storck A, Gence JN. 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. 1989; 44(11):2501-08. https://doi.org/10.1016/0009- 2509(89)85194-2 DOI: https://doi.org/10.1016/0009-2509(89)85194-2
Lesage F, Midoux N, Latifi M. New local measurements of hydrodynamics in porous media. Exp Fluids. 2004; 37(2):257-62. https://doi.org/10.1007/s00348-004-0811-5 DOI: https://doi.org/10.1007/s00348-004-0811-5
Rode S, Midoux N, Latifi MA, Storck A, Saatdjian E. Hydrodynamics of liquid flow in packed beds: An experimental study using electrochemical shear rate sensors. Chem Eng Sci. 1994; 49(6):889-900. https://doi. org/10.1016/0009-2509(94)80025-1 DOI: https://doi.org/10.1016/0009-2509(94)80025-1
Wegner TH, Karabelas AJ, Hanratty TJ. Visual studies of flow in a regular array of spheres. Chem Eng Sci. 1971; 26(1):59- 63. https://doi.org/10.1016/0009-2509(71)86081-5 DOI: https://doi.org/10.1016/0009-2509(71)86081-5
Beavers GS, Sparrow EM. Non-Darcy flow through fibrous porous media. J Appl Mech. 1969; 36(4):711-14. https://doi. org/10.1115/1.3564760 DOI: https://doi.org/10.1115/1.3564760
Berg CF. Permeability description by characteristic length, tortuosity, constriction and porosity. Transp Porous Media. 2014; 103(3):381-400. https://doi.org/10.1007/s11242-014-0307-6 DOI: https://doi.org/10.1007/s11242-014-0307-6
Carman PC. Fluid flow through a granular bed. Trans Inst Chem Eng Lond. 1937; 15:150-6.
Ward J. Turbulent flow in porous media. J Hydraul Div. 1964; 90(5):1-12. https://doi.org/10.1061/JYCEAJ.0001096 DOI: https://doi.org/10.1061/JYCEAJ.0001096
Glover P, Zadjali I, Frew K. Permeability prediction from MICP and NMR data using an electrokinetic approach. Geophysics. 2006; 71(4):F49-60. https://doi. org/10.1190/1.2216930 DOI: https://doi.org/10.1190/1.2216930
Glover P, Walker E. Grain-size to effective poresize transformation derived from electrokinetic theory. Geophysics. 2009; 74(1):E17-29. https://doi. org/10.1190/1.3033217 DOI: https://doi.org/10.1190/1.3033217
Johnson DL, Koplik J, Schwartz LM. New pore-size parameter characterizing transport in porous media. Phys Rev Lett. 1986; 57(20). https://doi.org/10.1103/PhysRevLett.57.2564 PMid:10033799 DOI: https://doi.org/10.1103/PhysRevLett.57.2564
Johnson DL, Sen PN. Dependence of the conductivity of a porous medium on electrolyte conductivity. Phys Rev B. 1988; 37(7). https://doi.org/10.1103/PhysRevB.37.3502 PMid:9944946 DOI: https://doi.org/10.1103/PhysRevB.37.3502
Katz A, Thompson A. Prediction of rock electrical conductivity from mercury injection measurements. J Geophys Res Solid Earth. 1987; 92(B1):599-607. https://doi.org/10.1029/ JB092iB01p00599 DOI: https://doi.org/10.1029/JB092iB01p00599
Katz A, Thompson A. Quantitative prediction of permeability in porous rock. Phys Rev B. 1986; 34(11). https://doi. org/10.1103/PhysRevB.34.8179 PMid:9939522 DOI: https://doi.org/10.1103/PhysRevB.34.8179
Schwartz LM, Sen PN, Johnson DL. Influence of rough surfaces on electrolytic conduction in porous media. Phys Rev B. 1989; 40(4). https://doi.org/10.1103/PhysRevB.40.2450 PMid:9992132 DOI: https://doi.org/10.1103/PhysRevB.40.2450
Ergun S. Fluid flow through packed columns. Chem Eng Prog. 1952; 48:89-94.
Niven RK. Physical insight into the Ergun and Wen and Yu equations for fluid flow in packed and fluidised beds. Chem Eng Sci. 2002; 57(3):527-34. https://doi.org/10.1016/S0009- 2509(01)00371-2 DOI: https://doi.org/10.1016/S0009-2509(01)00371-2
Takatsu Y, Masuoka T. Transition process to turbulent flow in porous media. ASME 2005 International Mechanical Engineering Congress and Exposition. 2005 Nov 5-11, USA: Orlando FL; 2008. pp. 573-8. https://doi.org/10.1115/ IMECE2005-80690
Seguin D, Montillet A, Comiti J. Experimental characterisation of flow regimes in various porous media-I: Limit of laminar flow regime. Chem Eng Sci. 1998; 53(21):3751-61. https://doi.org/10.1016/S0009-2509(98)00175-4 DOI: https://doi.org/10.1016/S0009-2509(98)00175-4
Thauvin F, Mohanty K. Network modeling of non-Darcy flow through porous media. Transp Porous Media. 1998; 31(1):19-37. https://doi.org/10.1023/A:1006558926606 DOI: https://doi.org/10.1023/A:1006558926606
Wahyudi I, Montillet A, Khalifa AA. Darcy and post-Darcy flows within different sands. J Hydraul Res. 2002; 40(4):519- 25. https://doi.org/10.1080/00221680209499893 DOI: https://doi.org/10.1080/00221680209499893
Banerjee A, Pasupuleti S, Singh MK, Kumar GNP. An investigation of parallel post-laminar flow through coarse granular porous media with the Wilkins Equation. Energies. 2018; 11(2). https://doi.org/10.3390/ en11020320 DOI: https://doi.org/10.3390/en11020320
Banerjee A, Pasupuleti S, Singh MK, Dutta SC, Pradeep GN. Modelling of flow through porous media over the complete flow regime. Transp Porous Media. 2019; 129(1):1-23. https://doi.org/10.1007/s11242-019-01274-2 DOI: https://doi.org/10.1007/s11242-019-01274-2
Scheidegger AE. The physics of flow through porous media. University of Toronto Press: Toronto; 1960.
Kumar GP, Venkataraman P. Non-Darcy converging flow through coarse granular media. J Inst Eng India Civ Eng. 1995; 504(76):6-11.