Abstract
Predicting the permeability of porous media in saturated and partially saturated conditions is crucial in geoengineering. The Kozeny–Carman equation is a pervasive method used for estimating the saturated hydraulic conductivity of soils. The previously reported modified Kozeny–Carman equation did not consider the influence of a wide range of particle size distribution on the saturated hydraulic conductivity. In this study, we quantified the influence of fine particle content on the saturated hydraulic conductivity and introduced the geometrical parameters to the Kozeny–Carman equation, followed by determining the range of empirical constant in the equation by the results of seepage test. Herein, a modified Kozeny–Carman equation, considering the particle size distribution of the particle system, is proposed based on particle gradation and size characteristic parameters including non-uniformity coefficient, curvature coefficient, and effective grain diameter. A laboratory test was performed to measure the saturated hydraulic conductivity values of sand–gravel mixture with different particle size distribution, using one-dimensional seepage equipment. Data from laboratory experiments performed in this study and available data from the literature were finally used to verify this proposed model. The findings of this study demonstrated the higher prediction accuracy of the proposed modified model.
This is a preview of subscription content, log in via an institution to check access.
Abbreviations
- K :
-
Permeability
- K s :
-
Saturated hydraulic conductivity
- ϕ :
-
Porosity
- d 30 :
-
30 % mass passing of a soil
- ρ w :
-
Density of water, g/cm3
- η :
-
Viscosity coefficient of water, Pa s
- e 0 :
-
Initial void ratio
- G s :
-
Specific gravity of soil
- τ :
-
Tortuosity
- S :
-
Specific surface area
- PSD:
-
Particle size distribution
- C2 :
-
Empirical constant of the modified Kozeny-Carman equation
References
Amaefule JO, Altunbay M, Tiab D, et al (1993) Enhanced reservoir description: using core and log data to identify hydraulic (flow) units and predict permeability in uncored intervals/ wells. In: Proceedings - SPE Annual Technical Conference and Exhibition
Bayles GA, Klinzing GE, Chiang S-H (1989) Fractal mathematics applied to flow in porous systems. Part Part Syst Charact 6:168–175. https://doi.org/10.1002/ppsc.19890060128
Bear J (1975) Dynamics of fluids in porous media. Soil Sci 120:162–163. https://doi.org/10.1097/00010694-197508000-00022
Behrang A, Mohammadmoradi P, Taheri S, Kantzas A (2016) A theoretical study on the permeability of tight media; effects of slippage and condensation. Fuel 181:610–617. https://doi.org/10.1016/j.fuel.2016.05.048
Cao C, Xu Z, Chai J, Li Y (2019) Radial fluid flow regime in a single fracture under high hydraulic pressure during shear process. J Hydrol 579:124142. https://doi.org/10.1016/j.jhydrol.2019.124142
Cao C, Xu Z, Chai J et al (2021) Determination method for influence zone of pumped storage underground cavern and drainage system. J Hydrol 595:126018. https://doi.org/10.1016/j.jhydrol.2021.126018
Carman PC (1939) Permeability of saturated sands, soils and clays. J Agric Sci. https://doi.org/10.1017/S0021859600051789
Chapuis RP, Aubertin M (2003) On the use of the Kozeny-Carman equation to predict the hydraulic conductivity of soils. Can Geotech J 40:616–628. https://doi.org/10.1139/t03-013
Chen Q, Liu L, He CR, Zhu FQ (2009) Criterion of pi** types for gap-graded coarse-grained soils. Yantu Lixue/Rock Soil Mech 30:2249–2253
Costa A (2006) Permeability-porosity relationship: a reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption. Geophys Res Lett 33:L02318. https://doi.org/10.1029/2005GL025134
Cui RF (2006) Study on permeability characteristic of Noneohesives soil and the meehanism of seepage-failure. Hohai university
Cui X, Zhu C, Hu M et al (2021) Permeability of porous media in coral reefs. Bull Eng Geol Environ 88:5111–5126. https://doi.org/10.1007/s10064-020-02082-5
Dashtaki SG, Homaee M, Khodaverdiloo H (2010) Derivation and validation of pedotransfer functions for estimating soil water retention curve using a variety of soil data. Soil Use Manag 26:68–74. https://doi.org/10.1111/j.1475-2743.2009.00254.x
Domenico PA, Schwartz FW (1990) Physical and chemical hydrogeology. Phys Chem Hydrogeol
Ebrahimi Khabbazi A, Ellis JS, Bazylak A (2013) Develo** a new form of the Kozeny-Carman parameter for structured porous media through lattice-Boltzmann modeling. Comput Fluids 75:35–41. https://doi.org/10.1016/j.compfluid.2013.01.008
GB/T 50123-1999 (1999) Standard for soil test method. China Plan Press
Ghorbani-Dashtaki S, Homaee M, Loiskandl W (2016) Towards using pedotransfer functions for estimating infiltration parameters. Hydrol Sci J 61:1477–1488. https://doi.org/10.1080/02626667.2015.1031763
Hu MJ, Cui X, Wang XZ et al (2019) Experimental study of the effect of fine particles on permeability of the calcareous sand. Yantu Lixue/Rock Soil Mech. https://doi.org/10.16285/j.rsm.2018.0849
Huang B, Guo C, Tang Y et al (2019) Experimental study on the permeability characteristic of fused quartz sand and mixed oil as a transparent soil. Water (Switzerland) 11. https://doi.org/10.3390/w11122514
Kaviany M (1995) Principles of heat transfer in porous media - 2nd edition
Khodaverdiloo H, Samadi A (2011) Batch equilibrium study on sorption, desorption, and immobilisation of cadmium in some semi-arid zone soils as affected by soil properties. Soil Res 49:444–454. https://doi.org/10.1071/SR10156
Le Gallo Y, Bildstein O, Brosse E (1998) Coupled reaction-flow modeling of diagenetic changes in reservoir permeability, porosity and mineral compositions. J Hydrol 209:366–388. https://doi.org/10.1016/S0022-1694(98)00183-8
Liu L (2006) Testing study on seepage property and seepage law of the coarse grain. Sichuan University
Liu YF, Jeng DS (2019) Pore scale study of the influence of particle geometry on soil permeability. Adv Water Resour 129:232–249. https://doi.org/10.1016/j.advwatres.2019.05.024
McGregor R, Peters RH (1965) The effect of rate of flow on rate of dyeing I–the diffusional boundary layer in dyeing. J Soc Dye Colour. https://doi.org/10.1111/j.1478-4408.1965.tb02675.x
Nakayama A, Kuwahara F, Sano Y (2007) Concept of equivalent diameter for heat and fluid flow in porous media. AICHE J 53:732–736. https://doi.org/10.1002/aic.11092
Nomura S, Yamamoto Y, Sakaguchi H (2018) Modified expression of Kozeny–Carman equation based on semilog–sigmoid function. Soils Found 58:1350–1357. https://doi.org/10.1016/j.sandf.2018.07.011
Ozgumus T, Mobedi M, Ozkol U (2014) Determination of Kozeny constant based on porosity and pore to throat size ratio in porous medium with rectangular rods. Eng Appl Comput Fluid Mech 8:308–318. https://doi.org/10.1080/19942060.2014.11015516
Panda MN, Lake LW (1994) Estimation of single-phase permeability from parameters of particle- size distribution. Am Assoc Pet Geol Bull.
Pisani L (2011) Simple expression for the tortuosity of porous media. Transp Porous Media 88:193–203. https://doi.org/10.1007/s11242-011-9734-9
Ren YB, Wang Y, Yang Q (2018) Effects of particle size distribution and shape on permeability of calcareous sand. Yantu Lixue/Rock Soil Mech. https://doi.org/10.16285/j.rsm.2016.0277
Rodríguez E, Giacomelli F, Vazquez A (2004) Permeability-porosity relationship in RTM for different fiberglass and natural reinforcements. J Compos Mater 38:259–268. https://doi.org/10.1177/0021998304039269
Safari M, Gholami R, Jami M et al (2021) Develo** a porosity-permeability relationship for ellipsoidal grains: a correction shape factor for Kozeny-Carman’s equation. J Pet Sci Eng 205:108896. https://doi.org/10.1016/j.petrol.2021.108896
Saxton KE, Rawls WJ, Romberger JS, Papendick RI (1986) Estimating generalized soil-water characteristics from texture. Soil Sci Soc Am J. https://doi.org/10.2136/sssaj1986.03615995005000040039x
Schulz R, Ray N, Zech S et al (2019) Beyond Kozeny–Carman: predicting the permeability in porous media. Transp Porous Media 130:487–512. https://doi.org/10.1007/s11242-019-01321-y
Su LJ, Zhang YJ, Wang TX (2014) Investigation on permeability of sands with different particle sizes. Yantu Lixue/Rock Soil Mech
Szabó NP, Kormos K, Dobróka M (2015) Evaluation of hydraulic conductivity in shallow groundwater formations: a comparative study of the Csókás’ and Kozeny–Carman model. Acta Geod Geophys 50:461–477. https://doi.org/10.1007/s40328-015-0105-9
Tang XS, Zheng YR, Dong C (2007) Prediction of seepage coefficient of coarse-grained soil by neurotic network. Yantu Lixue/Rock Soil Mech:28
Wei W, Cai J, **ao J et al (2018) Kozeny-Carman constant of porous media: Insights from fractal-capillary imbibition theory. Fuel 234:1373–1379. https://doi.org/10.1016/j.fuel.2018.08.012
Xu Z, Ye Y (2022) On the evaluation of internal stability of gap-graded soil: a status quo review. Nat Hazards. https://doi.org/10.1007/s11069-022-05317-8
Xu P, Yu B (2008) Develo** a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry. Adv Water Resour 31:74–81. https://doi.org/10.1016/j.advwatres.2007.06.003
Xu P, Mujumdar AS, Yu B (2008) Fractal theory on drying: a review. Dry Technol 26:640–650. https://doi.org/10.1080/07373930802045932
Xu G, Li Z, Li P (2013) Fractal features of soil particle-size distribution and total soil nitrogen distribution in a typical watershed in the source area of the middle Dan River, China. Catena 101:17–23. https://doi.org/10.1016/j.catena.2012.09.013
Yazdchi K, Srivastava S, Luding S (2011) On the validity of the Carman-Kozeny equation in random fibrous media. In: Particle-Based Methods II - Fundamentals and Applications. https://doi.org/10.13031/2013.8403
Yu B, Cai J, Zou M (2009) On the physical properties of apparent two-phase fractal porous media. Vadose Zo J 8:177–186. https://doi.org/10.2136/vzj2008.0015
Zheng W, Tannant DD (2017) Improved estimate of the effective diameter for use in the Kozeny-Carman equation for permeability prediction. Geotech Lett 7:1–5. https://doi.org/10.1680/jgele.16.00088
Zhu C (2005) Study on the coarse-grained soil permeability characteristic. Master thesis. North West Agriculture and Forestry University (China)
Funding
This work was supported by the National Natural Science Foundation for Excellent Young Scientists of China (51922088).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Additional information
Responsible Editor: Zeynal Abiddin Erguler
Rights and permissions
About this article
Cite this article
Ye, Y., Xu, Z., Zhu, G. et al. A modification of the Kozeny–Carman equation based on soil particle size distribution. Arab J Geosci 15, 1079 (2022). https://doi.org/10.1007/s12517-022-10224-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-022-10224-0