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28-05-2021 | Paper

Predicting water flow in fully and partially saturated porous media: a new fractal-based permeability model

Authors: Nguyen Van Nghia A., Damien Jougnot, Luong Duy Thanh, Phan Van Do, Tran Thi Chung Thuy, Dang Thi Minh Hue, Nguyen Manh Hung

Published in: Hydrogeology Journal | Issue 6/2021

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Abstract

Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many models have been proposed in the literature to estimate the permeability from properties of the porous media such as porosity, grain size or pore size. This study develops a model of the permeability for porous media saturated by one or two fluid phases with all physically based parameters using a fractal upscaling technique. The model is related to microstructural properties of porous media such as fractal dimension for pore space, fractal dimension for tortuosity, porosity, maximum radius, ratio of minimum pore radius and maximum pore radius, water saturation and irreducible water saturation. The model is favorably compared to existing and widely used models from the literature. Then, comparison with published experimental data for both unconsolidated and consolidated samples shows that the proposed model estimates the permeability from the medium properties very well.

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Abbireddy COR, Clayton CRI (2009) A review of modern particle sizing methods. Geotech Eng 162:193–201

Abeykoon T, Udukumburage R, Gallage C, Uchimura T (2017) Comparison of direct and indirect measured soil-water characteristic curves for a silty sand. Int J GEOMATE 13:9–16CrossRef

Andreola F, Leonelli C, Romagnoli M, Miselli P (2000) Techniques used to determine porosity. Am Ceramic Soc Bull 79:49–52

Archie GE (1942) The electrical resistivity log as an aid in determining some reservoir characteristics. Petroleum Trans AIME 146:54–62CrossRef

Bear J (1972) Dynamics of fluids in porous media. Dover, New York

Benzi R, Succi S, Vergassola M (1992) The lattice Boltzmann equation: theory and applications. Phys Rep 222:145–197

Biella G, Lozej A, Tabacco I (1983) Experimental study of some hydrogeophysical properties of unconsolidated porous media. Groundwater 21:741–751

Bolève A, Crespy A, Revil A, Janod F, Mattiuzzo JL (2007) Streaming potentials of granular media. Influence of the Dukhin and Reynolds numbers. J Geophys Res B08204

Boulin PF, Bretonnier P, Gland N, Lombard JM (2012) Contribution of the steady state method to water permeability measurement in very low permeability porous media. Oil Gas Sci Technol 67:387–401

Brooks R, Corey A (1964) Hydraulic properties of porous media and their relation to drainage design. Trans ASAE 7:28–28

Bryant S, Blunt M (1992) Prediction of relative permeability in simple porous media. Phys Rev A 46(4):2004–2011

Buckingham E (1907) Studies on the movement of soil moisture. US Department of Agriculture, Bureau of Soils no. 38, USDA, Washington, DC, 61 pp

Burdine N (1953) Relative permeability calculations from pore size distribution data: Journal of Petroleum Technology 5:71–78

Cai JC, Hu XY, Standnes DC, You LJ (2012a) An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids Surf A: Physicochem Eng Aspects 414:228–233

Cai JC, You LJ, Hu XY, Wang J, Peng RH (2012b) Prediction of effective permeability in porous media based on spontaneous imbibition effect. Int J Modern Phys C 23. https://doi.org/10.1142/S0129183112500544

Cai J, Boming Y (2011) A discussion of the effect of tortuosity on the capillary imbibition in porous media. Transp Porous Media 89:251–263CrossRef

Carles BA, Sanchez-Vila X, Freixa A, Romaní AM, Rubol S, Garcia DF (2017) A mechanistic model (BCC-PSSICO) to predict changes in the hydraulic properties for bio-amended variably saturated soils. Water Resour Res 53:93–109CrossRef

Carman P (1938) Determination of the specific surface of powders, part II. J Soc Chem Industry 57:225–234

Carsel RF, Parrish RS (1988) Developing joint probability distributions of soil water retention characteristics. Water Resour Res 24:755–769CrossRef

Cerepi A, Cherubini A, Garcia B, Deschamps H, Revil A (2017) Streaming potential coupling coefficient in unsaturated carbonate rocks. Geophys J Int 210:291–302CrossRef

Chauveteau G, Zaitoun A (1981) Basic rheological behavior of xanthan polysaccharide solutions in porous media: effect of pore size and polymer concentration. Proc. of the third European Symposium on Enhanced Oil Recovery, Bournemouth, UK, September 1981, pp 197–212

Chen H, Chen K, Yang M, Xu P (2020) A fractal capillary model for multiphase flow in porous media with hysteresis effect. Int J Multiphase Flow 125:103208CrossRef

Chen X, Yao G (2017) An improved model for permeability estimation in low permeable porous media based on fractal geometry and modified Hagen-Poiseuille flow. Fuel 210:748–757CrossRef

Chilindar GV (1964) Relationship between porosity, permeability and grain size distribution of sands and sandstones: deltaic and shallow marine deposits, vol I. Elsevier, Amsterdam, pp 71–75

Coates GR, Peveraro R, Hardwick A, Roberts D (1991) The magnetic resonance imaging log characterized by comparison with petrophysical properties and laboratory core data. Society of Petroleum Engineers, Richardson, TX

Daigle H (2016) Application of critical path analysis for permeability prediction in natural porous media. Adv Water Resour 96:43–54CrossRef

Darcy H (1856) Les fontaines publiques de la ville de Dijon [The public fountains of the village of Dijon]. Dalmont, Paris

De Vries E, Raoof A, Genuchten M (2017) Multiscale modelling of dual-porosity porous media: a computational pore-scale study for flow and solute transport. Adv Water Resour 105:82–95CrossRef

Doussan C, Ruy S (2009) Prediction of unsaturated soil hydraulic conductivity with electrical conductivity. Water Resour Res 45

Doyen PM (1988) Permeability, conductivity, and pore geometry of sandstone. J Geophys Res: Solid Earth 93:7729–7740CrossRef

Dullien FAL (1992) Porous media: fluid transport and pore structure. Academic, San Diego

Fan Y, Grant G, Anderson SP (2019) Water within, moving through, and shaping the earth’s surface: introducing a special issue on water in the critical zone. Hydrol Processes 33:3146–3151CrossRef

Feder J, Aharony A (1989) Fractals in physics: essays in Honour of Benoit B. Mandelbrot. North Holland, Amsterdam

Feng YJ, Yu BM, Zou MQ, Zhang DM (2004) A generalized model for the effective thermal conductivity of porous media based on self-similarity. J Phys D Appl Phys 37:3030–3040CrossRef

Feng Y, Boming Y (2007) Fractal dimension for tortuous streamtubes in porous media. Fractals 15(04):385–390. https://doi.org/10.1142/S0218348X07003654

Ghanbarian B (2020a) Applications of critical path analysis to uniform grain packings with narrow conductance distributions: I single-phase permeability. Adv Water Res 137:103529CrossRef

Ghanbarian B (2020b) Applications of critical path analysis to uniform grain packings with narrow conductance distributions: II water relative permeability. Adv Water Res 137:103524CrossRef

Ghanbarian B, Ioannidis MA, Hunt AG (2017a) Theoretical insight into the empirical tortuosity-connectivity factor in the Burdine-Brooks-Corey water relative permeability model. Water Res Res 53(12):10395–10410. https://doi.org/10.1002/2017WR021753

Ghanbarian B, Allen H, Todd S, Nicholas J (2017b) Upscaling soil saturated hydraulic conductivity from pore throat characteristics. Adv Water Resour 104:105–113CrossRef

Glover P, Zadjali II, Frew KA (2006) Permeability prediction from MICP and NMR data using an electrokinetic approach. Geophysics 71:F49–F60

Glover PWJ, Dery N (2010) Streaming potential coupling coefficient of quartz glass bead packs: dependence on grain diameter, pore size, and pore throat radius. Geophysics 75:F225–F241CrossRef

Glover PWJ, Walker E (2009) Grain-size to effective pore-size transformation derived from electrokinetic theory. Geophysics 74(1):E17–E29CrossRef

Guarracino L (2007) Estimation of saturated hydraulic conductivity Ks from the Van Genuchten shape parameter. Water Resour Res 43, W11502

Guarracino L, Jougnot D (2018) A physically based analytical model to describe effective excess charge for streaming potential generation in water saturated porous media. J Geophys Res: Solid Earth 123:52–65CrossRef

Guarracino L, Rotting T, Carrera J (2014) A fractal model to describe the evolution of multiphase flow properties during mineral dissolution. Adv Water Resour 67:78–86CrossRef

Hidajat I, Singh M, Cooper J, Mohanty KK (2002) Permeability of porous media from simulated NMR response. Transp Porous Media 48:225–247CrossRef

Hu X, Hu S, Jin F, Huang S (2017) Physics of petroleum reservoirs. Springer, HeidelbergCrossRef

Hunt A (2001) Applications of percolation theory to porous media with distributed local conductances. Adv Water Resour 24:279–307CrossRef

Ioannidis MA, Chatzis I, Lemaire C, Perunarkilli R (2006) Unsaturated hydraulic conductivity from nuclear magnetic resonance measurements. Water Resour Res 42(7). https://doi.org/10.1029/2006WR004955

Johnson DL, Plona TJ, Kojima H (1986) Probing porous media with 1st sound, 2nd sound, 4th sound and 3rd sound: physics and chemistry of porous media, vol II. AIP Conf Proceed 154:243. https://doi.org/10.1063/1.36398

Jougnot D, Revil A, Lu N, Wayllace A (2010) Transport properties of the Callovo Oxfordian clay rock under partially saturated conditions. Water Resour Res 46, W08514

Jougnot D, Linde N, Revil A, Doussan C (2012) Derivation of soil-specific streaming potential electrical parameters from hydrodynamic characteristics of partially saturated soils. Vadose Zone J 11:272–286CrossRef

Jouniaux L, Bernard ML, Zamora M, Pozzi JP (2000) Streaming potential in volcanic rocks from Mount Pelee. J Geophys Res B 105:8391–8401CrossRef

Jurin J (1719) II. An account of some experiments shown before the royal society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes. Philos Trans R Soc Lond 30:739–747

Katz AJ, Thompson AH (1985) Fractal sandstone pores: implications for conductivity and pore formation: Phys. Rev Lett 54(12):1325–1328CrossRef

Katz AJ, Thompson AH (1986) Quantitative prediction of permeability in porous rock. Phys Rev B 34(11):8179–8181CrossRef

Kimura M (2018) Prediction of tortuosity, permeability, and pore radius of water-saturated unconsolidated glass beads and sands. J Acoustical Soc Am 141:3154–3168CrossRef

Koch K, Revil A, Holliger K (2012) Relating the permeability of quartz sands to their grain size and spectral induced polarization characteristics. Geophys J Int 190:230–242CrossRef

Kostek S, Schwartz LM, Johnson DL (1992) Fluid permeability in porous media: comparison of electrical estimates with hydrodynamical calculations. Phys Rev B 45(1):186–195CrossRef

Kozeny J (1927) Uber kapillare Leitung des Wassers im Boden Aufsteigversikeung und Anwendung auf die Bemasserung. Math-naturw 136, Sitzber. Akad. Wiss., Vienna, pp 271–306

Li K, Horne RN (2004) Universal capillary pressure and relative permeability model from fractal characterization of rock. Proceedings, twenty-ninth workshop on geothermal reservoir engineering, Stanford University, Stanford, CA

Li K, Horne RN (2006a) Fractal modeling of capillary pressure curves for the geysers rocks. Geothermics 35:198–207CrossRef

Li K, Horne RN (2006b) Comparison of methods to calculate relative permeability from capillary pressure in consolidated water-wet porous media. Water Resour Res 42(6). https://doi.org/10.1029/2005WR004482

Li M, Wilkinson D, Patchigolla K (2005) Comparison of particle size distributions measured using different techniques. Particulate Sci Technol 23:265–284CrossRef

Liang M, Yang S, Yu B (2014) A fractal streaming current model for charged microscale porous media. J Electrost 72(6):441–446

Liang M, Yang S, Miao T, Yu B (2015) Analysis of electroosmotic characters in fractal porous media. Chem Eng Sci 127:202–209

Lis SA (2019) Petrophysical rock typing and permeability prediction in tight sand stone reservoir. Acta Geophysica 67:1895–1911

Lourenço S, Gallipoli D, Toll D, Evans F, Medero G (2007) Determination of the soil water retention curve with tensiometers. In: Schanz T (eds) Experimental unsaturated soil mechanics. Springer Proceedings in Physics 112. Springer, Heidelberg. https://doi.org/10.1007/3-540-69873-6_9

Mahiya GF (1999) Experimental measurement of steam-water relative permeability. MSc Thesis, Stanford University, Stanford, CA

Maineult A, Jougnot D, Revil A (2018) Variations of petrophysical properties and spectral induced polarization in response to drainage and imbibition: a study on a correlated random tube network. Geophys J Int 212:1398–1411CrossRef

Mandelbrot BB (1982) The fractal geometry of nature. Freeman, New York

Meng H, Shi Q, Liu T, Liu F, Chen P (2019) The percolation properties of electrical conductivity and permeability for fractal porous media. Energies 12:1085CrossRef

Moghadasi J, Muller Steinhagen H, Jamialahmadi M, Sharif A (2004) Theoretical and experimental study of particle movement and deposition in porous media during water injection. J Pet Sci Eng 43:163–181CrossRef

Ngo N, Tamma K (2001) Microscale permeability predictions of porous fibrous media. Int J Heat Mass Transf 44:3135–3145CrossRef

Nnaemeka Ezekwe (2010) Petroleum reservoir engineering practice. Prentice Hall, Upper Saddle River

Othman M, Helwani Z, Martunus (2010) Simulated fractal permeability for porousmembranes. Appl Math Model 34:2452–2464CrossRef

Rahimi H (1977) Comparison of direct and indirect methods for determining the coefficient of permeability of clays. PhD Thesis, Oklahoma State University, Stillwater, OK

Revil A, Cathles LM III (1999) Permeability of shaly sands. Water Resour Res 3:651–662CrossRef

Revil A, Florsch N (2010) Determination of permeability from spectral induced polarization in granular media. Geophys J Int 181:1480–1498

Revil A, Kessouri P, Torres-Verdin C (2014) Electrical conductivity, induced polarization, and permeability of the Fontainebleau sandstone. Geophysics 79:D301–D318CrossRef

Richesson S, Sahimi M (2019) Hertz-Mindlin theory of contacting grains and the effective-medium approximation for the permeability of deforming porous media. Geophys Res Lett 46:8039–8045CrossRef

Rosenzweig R, Shavit U, Furman A (2009) The influence of biofilm spatial distribution scenarios on hydraulic conductivity of unsaturated soils. Vadose Zone J 8:1080–1084CrossRef

Sander R, Pan Z, Connell LD (2017) Laboratory measurement of low permeability unconventional gas reservoir rocks: a review of experimental methods. J Natural Gas Sci Eng 37:248–279CrossRef

Samsó R, Garcia J, Molle P, Forquet N (2016) Modelling bioclogging in variably saturated porous media and the interactions between surface/subsurface flows: application. J Environ Manag 165:271–279

Sen P, Scala C, Cohen MH (1981) A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. J Soil Mech Found Division 46:781–795

Soldi M, Guarracino L, Jougnot D (2017) A simple hysteretic constitutive model for unsaturated flow. Transp Porous Media 120:271–285CrossRef

Soldi M, Guarracino L, Jougnot D (2019) An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow. Geophys J Int 216:380–394

Soldi M, Guarracino L, Jougnot D (2020) An effective excess charge model to describe hysteresis effects on streaming potential. J Hydrol 588, 124949

Swanson BF (1981) A simple correlation between permeabilities and mercury capillary pressures. J Petrol Technol 33(12):2498–2504

Thanh LD, Jougnot D, Van Do P, Van Nghia AN (2019) A physically based model for the electrical conductivity of water-saturated porous media. Geophys J Int 219:866–876CrossRef

Thanh L, Jougnot D, Do P, Ca N, Hien N (2020a) A physically based model for the streaming potential coupling coefficient in partially saturated porous media. Water 12:1588CrossRef

Thanh L, Jougnot D, Do P, Mendieta M, Ca N, Hoa V, Hien N (2020b) Electroosmotic coupling in porous media, a new model based on a fractal upscaling procedure. Transp Porous Media 134:249–274CrossRef

Thanh LD, Jougnot D, Van Do P, Van Nghia AN, Tuyen VP, Ca NX, Hien NT (2020c) A physically-based model for the electrical conductivity of partially saturated porous media. Geophys J Int 223(3):993–1006

Thanh LD, Van Do P, Van Nghia N, Ca NX (2018) A fractal model for streaming potential coefficient in porous media. Geophys Prospect 66:753–766CrossRef

Vinogradov J, Jaafar MZ, Jackson MD (2010) Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity. J Geophys Res 115. https://doi.org/10.1029/2010JB007593

Wei W, Cai J, Hu X, Han Q (2015) An electrical conductivity model for fractal porous media. Geophys Res Lett 42:4833–4840CrossRef

Xiao B, Zhang X, Wang W, Long G, Chen H, Kang H, Ren W (2018) A fractal model for water flow through unsaturated porous rocks. Fractals 26:1840015CrossRef

Xu P, Yu B (2008) Developing a new form of permeability and Kozeny-Carman constant for homogeneous porous media by means of fractal geometry. Adv Water Resour 31:74–81CrossRef

Yu B, Cheng P (2002) A fractal permeability model for bi-dispersed porous media. Int J Heat Mass Transf 45:2983–2993CrossRef

Yu B, Liu W (2004) Fractal analysis of permeabilities for porous media. AICHE J 50:46–57CrossRef

Zainaldin SA, Glover PWJ, Lorinczi P (2017) Synthetic fractal modelling of heterogeneous and anisotropic reservoirs for use in simulation studies: implications on their hydrocarbon recovery prediction. Transp Porous Med 116:181–212

Title: Predicting water flow in fully and partially saturated porous media: a new fractal-based permeability model
Authors: Nguyen Van Nghia A.
Damien Jougnot
Luong Duy Thanh
Phan Van Do
Tran Thi Chung Thuy
Dang Thi Minh Hue
Nguyen Manh Hung
Publication date: 28-05-2021
Publisher: Springer Berlin Heidelberg
Published in: Hydrogeology Journal / Issue 6/2021
Print ISSN: 1431-2174
Electronic ISSN: 1435-0157
DOI: https://doi.org/10.1007/s10040-021-02364-6

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