A Micromechanics Model for Solute Diffusion Coefficient in Unsaturated Granular Materials

详细信息    查看全文

• 作者：Rongwei Yang ; Eric Lemarchand ; Teddy Fen-Chong
• 关键词：Unsaturated ; Diffusion coefficient ; Micromechanics ; Eshelby problem ; Granular material ; Liquid layer
• 刊名：Transport in Porous Media
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：111
• 期：2
• 页码：347-368
• 全文大小：1,639 KB
• 参考文献：Archie, G.: The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME 146(99), 54–62 (1942)CrossRef
  Bayuk, I., Chesnokov, E.: Correlation between elastic and transport properties of porous cracked anisotropic media. Phys. Chem. Earth. 23(3), 361–366 (1998)CrossRef
  Blunt, M.J., Jackson, M.D., Piri, M., Valvatne, P.H.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water. Resour. 25(8), 1069–1089 (2002)CrossRef
  Bourg, I., Sposito, G., Bourg, A.: Modeling cation diffusion in compacted water saturated sodium bentonite at low ionic strength. Environ. Sci. Technol. 41(23), 8118–8122 (2007)CrossRef
  Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media. Colorado State University (March), Hydrology Papers (1964)
  Bryant, S., Johnson, A.: Wetting phase connectivity and irreducible saturation in simple granular media. J. Colloid Interface Sci. 263(2), 572–579 (2003)CrossRef
  Conca, J., Wright, J.: Diffusion and flow in gravel, soil, and whole rock. Hydrogeo J 1(1), 5–24 (1992)CrossRef
  De Kuijper, A., Sandor, R.K., Hofman, J., Koelman, J., Hofstra, P., De Waal, J.: Electrical conductivities in oil-bearing shaly sand accurately described with the satori saturation model. In: SPWLA 36th annual logging symposium, society of petrophysicists and well-log analysts (1995)
  Deng, F., Van Vliet, K.J.: Prediction of elastic properties for polymerparticle nanocomposites exhibiting an interphase. Nanotechnology 22(16), 165703 (2011)CrossRef
  Dormieux, L., Kondo, D., Ulm, F.: Microporomechanics. Wiley, New York (2006)CrossRef
  Dormieux, L., Jeannin, L., Gland, N.: Homogenized models of stress-sensitive reservoir rocks. Int. J. Eng. Sci. 49(5), 386–396 (2011)CrossRef
  Dullien, F.A., Zarcone, C., Macdonald, I.F., Collins, A., Bochard, R.D.: The effects of surface roughness on the capillary pressure curves and the heights of capillary rise in glass bead packs. J. Colloid Interfece Sci. 127(2), 362372 (1989)
  Fenaux, M., Reyes Pozo, E., Moragues Terrades, A., Gálvez Ruź, J.: Modelling of chloride transport in non-saturated concrete: from microscale to macroscale (2013)
  Fredlund, D.G., Xing, A.: Equations for the soil–water characteristic curve. Can. Geotech. J. 31(4), 521–532 (1994)CrossRef
  Genty, A., Pot, V.: Numerical calculation of effective diffusion in unsaturated porous media by the TRT lattice Boltzmann method. Transp. Porous Med. 105(2), 391–410 (2014)CrossRef
  Go, J., Bortone, I., Muggeridge, A., Smalley, C.: Predicting vertical flow barriers using tracer diffusion in partially saturated, layered porous media. Transp. Porous Med. 105(2), 255–276 (2014)CrossRef
  Grathwohl, P.: Diffusion in Natural Porous Media. Kluwer, Boston (2002)
  Gueguen, Y., Dienes, J.: Transport properties of rocks from statistics and percolation. Math. Geol. 21(1), 1–13 (1989)CrossRef
  Hamamoto, S., Moldrup, P., Kawamoto, K., Komatsu, T.: Excluded-volume expansion of Archies law for gas and solute diffusivities and electrical and thermal conductivities in variably saturated porous media. Water Resour. Res. 46(6), W06514 (2010)
  Han, M., Youssef, S., Rosenberg, E., Fleury, M., Levitz, P.: Deviation from Archie law in partially saturated porous media: wetting film versus disconnectedness of the conducting phase. Phys. Rev. E 79(3), 031127 (2009)CrossRef
  Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)CrossRef
  Herring, A.L., Harper, E.J., Andersson, L., Sheppard, A., Bay, B.K., Wildenschild, D.: Effect of fluid topology on residual nonwetting phase trapping: implications for geologic \(CO_2\) sequestration. Adv. Water Resour. 62, 47–58 (2013)CrossRef
  Hill, R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13(4), 213–222 (1965)CrossRef
  Hu, Q., Wang, J.: Aqueous-phase diffusion in unsaturated geologic media: a review. Taylor & Francis, New York (2003)
  Hu, Q., Kneafsey, T.J., Roberts, J.J., Tomutsa, L., Wang, J.S.: Characterizing unsaturated diffusion in porous tuff gravel. Vadose Zone J. 3(4), 1425–1438 (2004)CrossRef
  Hunt, A., Ewing, R.: Percolation Theory for Flow in Porous Media, vol. 771. Springer, Berlin (2009)
  Kibbey, T.C.: The configuration of water on rough natural surfaces: implications for understanding air-water interfacial area, film thickness, and imaging resolution. Water. Resour. Res. 49(8), 4765–4774 (2013)CrossRef
  Kim, T.W., Tokunaga, T.K., Shuman, D.B., Sutton, S.R., Newville, M., Lanzirotti, A.: Thickness measurements of nanoscale brine films on silica surfaces under geologic \(CO_2\) sequestration conditions using synchrotron X-ray fluorescence. Water Resour. Res. 48(9), W09558 (2012)
  Kleinfelter-Domelle, N., Cushman, J.: The role of connectivity in the theory of saturated/unsaturated flow through swelling media. Water Resour Res 48(1) (2012)
  Knudby, C., Carrera, J., Bumgardner, J.D., Fogg, G.E.: Binary upscaling—the role of connectivity and a new formula. Adv. Water Resour. 29(4), 590–604 (2006)CrossRef
  Koelman, J., De Kuijper, A.: An effective medium model for the electric conductivity of an N-component anisotropic and percolating mixture. Phys. A 247(1), 10–22 (1997)CrossRef
  Kroner, E.: Self-consistent scheme and graded disorder in polycrystal elasticity. J. Phys. F Met. Phys. 8(11), 2261 (1978)CrossRef
  Lemarchand, E.: Contribution de la micromécanique á l’ étude des phénoménes de transport et de couplage poromécanique dans les milieux poreux: Application aux phénomènes de gonflement des géomatériaux. PhD thesis, Ecole des Ponts ParisTech (2001)
  Lemarchand, E., Davy, C.A., Dormieux, L., Chen, W., Skoczylas, F.: Micromechanics contribution to coupled transport and mechanical properties of fractured geomaterials. Transp. Porous Media 79(3), 335358 (2009)CrossRef
  Lemarchand, E., Davy, C.A., Dormieux, L., Skoczylas, F.: Tortuosity effects in coupled advective transport and mechanical properties of fractured geomaterials. Transp. Porous Med. 84(1), 119 (2010)
  Lim, P., Barbour, S., Fredlund, D.: The influence of degree of saturation on the coefficient of aqueous diffusion. Can. Geotech. J. 35(5), 811827 (1998)
  Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metal. 21(5), 571–574 (1973)CrossRef
  Neithalath, N., Weiss, J., Olek, J.: Characterizing enhanced porosity concrete using electrical impedance to predict acoustic and hydraulic performance. Cem. Concr. Res. 36(11), 2074–2085 (2006)CrossRef
  Or, D., Tuller, M.: Flow in unsaturated fractured porous media: hydraulic conductivity of rough surfaces. Water Resour. Res. 36(5), 11651177 (2000)
  Raoof, A., Hassanizadeh, S.: Saturation-dependent solute dispersivity in porous media: pore-scale processes. Water Resour. Res. 49(4), 1943–1951 (2013)CrossRef
  Romkens, M., Bruce, R.: Nitrate diffusivity in relation to moisture content of non-adsorbing porous media. Soil Sci. 98(5), 332–337 (1964)CrossRef
  Tokunaga, T.: Hydraulic properties of adsorbed water films in unsaturated porous media. Water Resour. Res. 45(6), W06415 (2009)
  Tokunaga, T.: Physicochemical controls on adsorbed water film thickness in unsaturated geological media. Water Resour. Res. 47(8), W08514 (2011)
  Tsakiroglou, C.D., Fleury, M.: Resistivity index of fractional wettability porous media. J. Petrol. Sci. Eng. 22(4), 253–274 (1999)CrossRef
  Van Schaik, J., Kemper, W., Olsen, S.: Contribution of adsorbed cations to diffusion in clay-water systems. Soil Sci. Soc. Am. J. 30(1), 17–22 (1966)CrossRef
  Yang, R.W.: Contributions to micromechanical modelling of transport and freezing phenomena within unsaturated porous media. Ph.D. thesis, Université Paris-Est (2013)
  Zhang, M., Xu, K., He, Y., Jivkov, A.P.: Pore-scale modelling of 3d moisture distribution and critical saturation in cementitious materials. Constr. Build. Mater. 64, 222–230 (2014)CrossRef
  
• 作者单位：Rongwei Yang (1)
  Eric Lemarchand (1)
  Teddy Fen-Chong (1) (2)
  
  1. Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, Université Paris-Est, 77420, Marne-la-Vallée, France
  2. MAST, FM2D, IFSTTAR, Université Paris-Est, 77447, Marne-la-Vallée, France
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geotechnical Engineering
  Industrial Chemistry and Chemical Engineering
  Civil Engineering
  Hydrogeology
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Netherlands
• ISSN：1573-1634

文摘

A new micromechanics analysis of solute diffusion in unsaturated granular materials is put forward. This permits predicting the percolation effect. To do so, the pore water is divided up into four phases that account for the different spatial distributions and diffusion properties: interconnected capillary water, isolated capillary water, wetting layer and water film. A parameter denoted as connectivity ratio is introduced to account for the connectivity of the capillary pore water. Our model agrees well with experimental results on unsaturated sands and glass beads from literature. It also permits interpreting the physical meaning of the saturation exponent of Archie’s law: The latter is found to be correlated with the connectivity ratio of the unsaturated granular materials. Keywords Unsaturated Diffusion coefficient Micromechanics Eshelby problem Granular material Liquid layer