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Volume 71, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We present a new unified model for the permeability, electrical conductivity and streaming potential coupling coefficient in variably saturated fractured media. For those, we conceptualize the fractured medium as a partially saturated bundle of parallel capillary slits with varying sizes. We assume that the fracture size distribution of the corresponding medium follows a fractal scaling law, which allows us to establish a pressure head‐saturation relationship based on the Laplace equation. We first describe the flow rate, the conduction current and the electrokinetic streaming current within a single fracture. Then, we upscale these properties at the scale of an equivalent fractured media partially saturated in order to obtain the relative permeability, the electrical conductivity and the streaming potential coupling coefficient. The newly proposed model explicitly depends on pore water chemistry, interface properties, microstructural parameters of fractured media and water saturation. Model predictions are in good agreement with both experimental and simulated data and with another model from the literature. The results of this work constitute a useful framework to estimate hydraulic properties and monitor water flow in fractured media.

© 2023 European Association of Geoscientists & Engineers. © 2022 European Association of Geoscientists & Engineers.
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2023-01-20
2024-04-25

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References

  1. Aizawa, K., Ogawa, Y. & Ishido, T. (2009) Groundwater flow and hydrothermal systems within volcanic edifices: delineation by electric self‐potential and magnetotellurics. Journal of Geophysical Research, 114(B01208).
  2. Alkafeef, S.F. & Alajmi, A.F. (2006) Streaming potentials and conductivities of reservoir rock cores in aqueous and non‐aqueous liquids. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 289, 141–148.
     [Google Scholar]
  3. Binley, A., Hubbard, S.S., Huisman, J.A., Revil, A., Robinson, D.A., Singha, K. & Slater, L.D. (2015) The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales. Water Resources Research, 51(6), 3837–3866.
     [Google Scholar]
  4. Bodvarsson, G., Boyle, W., Patterson, R. & Williams, D. (1999) Overview of scientific investigations at Yucca Mountain: the potential repository for high‐level nuclear waste. Journal of Contaminant Hydrology, 38(1), 3–24.
     [Google Scholar]
  5. Bonnet, E., Bour, O., Odling, N.E., Davy, P., Main, I., Cowie, P. & Berkowitz, B. (2001) Scaling of fracture systems in geological media. Reviews of Geophysics, 39(3), 347–383.
     [Google Scholar]
  6. Bullard, J.W. & Garboczi, E.J. (2009) Capillary rise between planar surfaces. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics.79, 011604.
     [Google Scholar]
  7. Chung, C. (2010) Extrusion of polymers : Theory and practice, 2nd edition. Munich: Hanser Publications.
     [Google Scholar]
  8. Clair, J.S., Moon, S., Holbrook, W.S., Perron, J.T., Riebe, C.S., Martel, S.J., Carr, B.J., Harman, C., Singha, K. & Richter, D.D. (2015) Geophysical imaging reveals topographic stress control of bedrock weathering. Science, 350, 534–538.
     [Google Scholar]
  9. Corwin, R.F. & Hoover, D.B. (1979) The self‐potential method in geothermal exploration. Geophysics, 44(2), 226–245.
     [Google Scholar]
  10. Demirel, S., Roubinet, D., Irving, J. & Voytek, E. (2018) Characterizing near‐surface fractured‐rock aquifers: Insights provided by the numerical analysis of electrical resistivity experiments. Water, 10, 1117.
     [Google Scholar]
  11. DesRoches, A.J., Butler, K.E. & MacQuarrie, K.T. (2018) Surface self‐potential patterns related to transmissive fracture trends during a water injection test. Geophysical Journal International, 212(3), 2047–2060.
     [Google Scholar]
  12. Doussan, C., Jouniaux, L. & Thony, J.L. (2002) Variations of self‐potential and unsaturated water flow with time in sandy loam and clay loam soils. Journal of Hydrology, 267(3), 173–185.
     [Google Scholar]
  13. Erol, S., Fowler, S., Harcouët‐Menou, V. & Laenen, B. (2017) An analytical model of porosity – permeability for porous and fractured media. Transport in Porous Media, 120, 327–358.
     [Google Scholar]
  14. Fagerlund, F. & Heinson, G. (2003) Detecting sub‐surface groundwater flow in fractured rock using self‐potential (SP) methods. Environmental Geology, 43, 782–794.
     [Google Scholar]
  15. Finizola, A., Lenat, N., Macedo, O., Ramos, D., Thouret, J. & Sortino, F. (2004) Fluid circulation and structural discontinuities inside Misti volcano (Peru) inferred from self‐potential measurements. Journal of Volcanology and Geothermal Research, 135(4), 343–360.
     [Google Scholar]
  16. Ghanbarian, B., Perfect, E. & Liu, H.H. (2019) A geometrical aperture‐width relationship for rock fractures. Fractals, 27(01), 1940002.
     [Google Scholar]
  17. Grobbe, N. & Barde‐Cabusson, S. (2019) Self‐potential studies in volcanic environments: a cheap and efficient method for multiscale fluid‐flow investigations. International Journal of Geophysics, 2019, 1–19.
     [Google Scholar]
  18. Guarracino, L. (2006) A fractal constitutive model for unsaturated flow in fractured hard rocks. Journal of Hydrology, 324(1), 154–162.
     [Google Scholar]
  19. Guarracino, L. & Jougnot, D. (2022) A fractal model for effective excess charge density in variably saturated fractured rocks. Journal of Geophysical Research: Solid Earth, 127(3), e2021JB022982.
     [Google Scholar]
  20. Guichet, X., Jouniaux, L. & Pozzi, J.P. (2003) Streaming potential of a sand column in partial saturation conditions. Journal of Geophysical Research: Solid Earth, 108(B3), 2141.
     [Google Scholar]
  21. Haas, A.K., Revil, A., Karaoulis, M., Frash, L., Hampton, J., Gutierrez, M., & Mooney, M. (2013) Electric potential source localization reveals a borehole leak during hydraulic fracturing. Geophysics, 78(2), D93–D113.
     [Google Scholar]
  22. Herwanger, J., Worthington, M., Lubbe, R., Binley, A. & Khazanehdari, J. (2004) A comparison of cross‐hole electrical and seismic data in fractured rock. Geophysical Prospecting, 52(2), 109–121.
     [Google Scholar]
  23. Hu, K., Jougnot, D., Huang, Q., Looms, M.C. & Linde, N. (2020) Advancing quantitative understanding of self‐potential signatures in the critical zone through long‐term monitoring. Journal of Hydrology, 585, 124771.
     [Google Scholar]
  24. Hunter, R.J. (1981) Zeta Potential in colloid science. New York: Academic Press.
     [Google Scholar]
  25. Ishido, T. & Mizutani, H. (1981) Experimental and theoretical basis of electrokinetic phenomena in rock‐water systems and its applications to geophysics. Journal of Geophysical Research, 86, 1763–1775.
     [Google Scholar]
  26. Jardani, A., Revil, A., Boleve, A., Crespy, A., Dupont, J.P., Barrash, W. & Malama, B. (2007) Tomography of the Darcy velocity from self‐potential measurements. Geophysical Research Letters, 34(24), L24403.
     [Google Scholar]
  27. Johnson, D.L., Koplik, J. & Schwartz, L.M. (1986) New pore‐size parameter characterizing transport in porous media. Physics Review Letters, 57, 2564–2567.
     [Google Scholar]
  28. Jougnot, D., Linde, N., Haarder, E. & Looms, M. (2015) Monitoring of saline tracer movement with vertically distributed self‐potential measurements at the hobe agricultural test site, Voulund, Denmark. Journal of Hydrology, 521, 314–327.
     [Google Scholar]
  29. Jougnot, D., Revil, A., Lu, N. & Wayllace, A. (2010) Transport properties of the callovo‐oxfordian clay rock under partially saturated conditions. Water Resources Research, 46(8), W08514.
     [Google Scholar]
  30. Jougnot, D., Roubinet, D., Guarracino, L. & Maineult, A. (2020) Modeling Streaming potential in porous and fractured media, description and benefits of the effective excess charge density approach. In: Biswas A., Sharma S. (eds) Advances in modeling and interpretation in near surface geophysics. Springer Geophysics. Cham: Springer, pp. 61–96.
  31. Jouniaux, L., Pozzi, J., Berthier, J. & Masse', P. (1999) Detection of fluid flow variations at the Nankai trough by electric and magnetic measurements in boreholes or at the seafloor. Journal of Geophysical Research, 104(B12), 29293–29309.
     [Google Scholar]
  32. Klimczak, C., Schultz, R., Parashar, R. & Reeves, D. (2010) Cubic law with aperture‐length correlation: implications for network scale fluid flow. Hydrogeology Journal, 18, 851–862.
     [Google Scholar]
  33. Kormiltsev, V.V., Ratushnyak, A.N. & Shapiro, V.A. (1998) Three‐dimensional modeling of electric and magnetic fields induced by the fluid flow movement in porous media. Physics of the Earth and Planetary Interiors, 105(3), 109–118.
     [Google Scholar]
  34. Kruhl, J.H. (2013) Fractal‐geometry techniques in the quantification of complex rock structures: a special view on scaling regimes, inhomogeneity and anisotropy. Journal of Structural Geology, 46, 2–21.
     [Google Scholar]
  35. Li, X.Y. (1997) Fractured reservoir delineation using multicomponent seismic data. Geophysical Prospecting, 45(1), 39–64.
     [Google Scholar]
  36. Liu, H.H. & Bodvarsson, G.S. (2001) Constitutive relations for unsaturated flow in a fracture network. Journal of Hydrology, 252(1), 116–125.
     [Google Scholar]
  37. Maineult, A., Thomas, B., Nussbaum, C., Wieczorek, K., Gibert, D., Lavielle, B., Kergosien, B., Nicollin, F., Mahiouz, K. & Lesparre, N. (2013) Anomalies of noble gases and self‐potential associated with fractures and fluid dynamics in a horizontal borehole, Mont Terri Underground Rock Laboratory. Engineering Geology, 156, 46–57.
     [Google Scholar]
  38. Majumdar, A. & Bhushan, B. (1990) Role of fractal geometry in roughness characterization and contact mechanics of surfaces. Journal of Tribology, 112(2), 205–216.
     [Google Scholar]
  39. Martinez‐Pagan, P., Jardani, A., Revil, A. & Haas, A. (2010) Self‐potential monitoring of a salt plume. Geophysics, 75(4), WA17–WA25.
     [Google Scholar]
  40. Mauri, G., Williams‐Jones, G. & Saracco, G. (2010) Depth determinations of shallow hydrothermal systems by self‐potential and multi‐scale wavelet tomography. Journal of Volcanology and Geothermal Research, 191(3–4), 233–244.
     [Google Scholar]
  41. Medici, G., West, L. & Banwart, S. (2019) Groundwater flow velocities in a fractured carbonate aquifer‐type: implications for contaminant transport. Journal of Contaminant Hydrology, 222, 1–16.
     [Google Scholar]
  42. Miao, T., Chen, A., Xu, Y., Cheng, S. & Yu, B. (2019) A fractal permeability model for porous‐fracture media with the transfer of fluids from porous matrix to fracture. Fractals, 27(6), 1950121.
     [Google Scholar]
  43. Miao, T., Yu, B., Duan, Y. & Fang, Q. (2015) A fractal analysis of permeability for fractured rocks. International Journal of Heat and Mass Transfer, 81, 75–80.
     [Google Scholar]
  44. Moore, J.R. & Glaser, S.D. (2007) Self‐potential observations during hydraulic fracturing. Journal of Geophysical Research: Solid Earth, 112(B2), B02204.
     [Google Scholar]
  45. Morgan, F.D., Williams, E.R. & Madden, T.R. (1989) Streaming potential properties of westerly granite with applications. Journal of Geophysical Research, 94(B9), 12.449–12.461.
     [Google Scholar]
  46. Murphy, H.D., Tester, J.W., Grigsby, C.O. & Potter, R.M. (1981) Energy extraction from fractured geothermal reservoirs in low‐permeability crystalline rock. Journal of Geophysical Research: Solid Earth, 86(B8), 7145–7158.
     [Google Scholar]
  47. Naudet, V., Revil, A., Bottero, J.Y. & Bégassat, P. (2003) Relationship between self‐potential (SP) signals and redox conditions in contaminated groundwater. Geophysical Research Letters, 30(21), 2091.
     [Google Scholar]
  48. Neuman, S. (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeology Journal, 13, 124–147.
     [Google Scholar]
  49. Neuzil, C.E. & Tracy, J.V. (1981) Flow through fractures. Water Resources Research, 17(1), 191–199.
     [Google Scholar]
  50. Okubo, P.G. & Aki, K. (1987) Fractal geometry in the San Andreas Fault system. Journal of Geophysical Research: Solid Earth, 92(B1), 345–355.
     [Google Scholar]
  51. Osiptsov, A.A. (2017) Fluid mechanics of hydraulic fracturing: a review. Journal of Petroleum Science and Engineering, 156, 513–535.
     [Google Scholar]
  52. Overbeek, J. (1952) Electrochemistry of the double layer. In: Kruyt, H.R. (Ed.) Colloid science, irreversible systems. Houston, TX: Elsevier, 194–24.
     [Google Scholar]
  53. Parsekian, A.D., Singha, K., Minsley, B.J., Holbrook, W.S. & Slater, L. (2015) Multiscale geophysical imaging of the critical zone. Reviews of Geophysics, 53(1), 1–26.
     [Google Scholar]
  54. Patterson, J.R., Cardiff, M. & Feigl, K.L. (2020) Optimizing geothermal production in fractured rock reservoirs under uncertainty. Geothermics, 88, 101906.
     [Google Scholar]
  55. Peshcherenko, A., Bekerov, I., Chuprakov, D. & Abdrazakov, D. (2022) Fast‐running model for high‐volume hydraulic fracturing. Journal of Petroleum Science and Engineering, 213, 110430.
     [Google Scholar]
  56. Pride, S. (1994) Governing equations for the coupled electromagnetics and acoustics of porous media. Physical Review B, 50(21), 15678–15696.
     [Google Scholar]
  57. Ren, F., Ma, G., Wang, Y., Fan, L. & Zhu, H. (2017) Two‐phase flow pipe network method for simulation of co2 sequestration in fractured saline aquifers. International Journal of Rock Mechanics and Mining Sciences, 98, 39–53.
     [Google Scholar]
  58. Revil, A. & Cerepi, A. (2004) Streaming potentials in two‐phase flow conditions. Geophysical Research Letters, 31(11), L11605.
     [Google Scholar]
  59. Revil, A. & Glover, P. W.J. (1998) Nature of surface electrical conductivity in natural sands, sandstones, and clays. Geophysical Research Letters, 25(5), 691–694.
     [Google Scholar]
  60. Revil, A. & Jardani, A. (2013) The Self‐potential method: Theory and applications in environmental geosciences. Cambridge, UK: Cambridge University Press.
     [Google Scholar]
  61. Revil, A., Karaoulis, M., Johnson, T. & Kemna, A. (2012) Review: Some low‐frequency electrical methods for subsurface characterization and monitoring in hydrogeology. Hydrogeology Journal, 20, 617–658.
     [Google Scholar]
  62. Revil, A. & Leroy, P. (2004) Constitutive equations for ionic transport in porous shales. Journal of Geophysical Research: Solid Earth, 109(B3), B03208.
     [Google Scholar]
  63. Rice, C. & Whitehead, R. (1965) Electrokinetic flow in a narrow cylindrical capillary. Journal of Physics and Chemistry, 69(11), 4017–4024.
     [Google Scholar]
  64. Rod, K.A., Um, W., Colby, S.M., Rockhold, M.L., Strickland, C.E., Han, S., & Kuprat, A.P. (2019) Relative permeability for water and gas through fractures in cement. PLoS ONE, 14(1), 1–17.
     [Google Scholar]
  65. Roubinet, D. & Irving, J. (2014) Discrete‐dual‐porosity model for electric current flow in fractured rock. Journal of Geophysical Research: Solid Earth, 119(2), 767–786.
     [Google Scholar]
  66. Roubinet, D., Irving, J. & Pezard, P. (2018) Relating topological and electrical properties of fractured porous media: Insights into the characterization of rock fracturing. Minerals, 8, 14.
     [Google Scholar]
  67. Roubinet, D., Linde, N., Jougnot, D. & Irving, J. (2016) Streaming potential modeling in fractured rock: insights into the identification of hydraulically active fractures. Geophysical Research Letters, 43(10), 4937–4944.
     [Google Scholar]
  68. Roy, A., Perfect, E., Dunne, W.M. & McKay, L.D. (2007) Fractal characterization of fracture networks: an improved box‐counting technique. Journal of Geophysical Research: Solid Earth, 112(B12), B12201.
     [Google Scholar]
  69. Roy, I.G. (2022) Subchapter 3.1 ‐ self‐potential: a low‐cost geophysical method in investigating groundwater and contaminant plume. In A.Moitra, J.Kayal, B.Mukerji, J.Bhattacharya, & A.Das (Eds.) Innovative exploration methods for minerals, oil, gas, and groundwater for sustainable development . Amsterdam, The Netherlands: Elsevier, pp. 193–211.
     [Google Scholar]
  70. Sen, P.N. & Goode, P.A. (1992) Influence of temperature on electrical conductivity on shaly sands. Geophysics, 57(1), 89–96.
     [Google Scholar]
  71. Shen, J., Su, B. & Guo, N. (2009) Anisotropic characteristics of electrical responses of fractured reservoir with multiple sets of fractures. Petroleum Science, 6, 127–138.
     [Google Scholar]
  72. Smoluchowski, M. (1903) Contribution à la théorie de l'endosmose électrique et de quelques phénomènes corrélatifs. Bulletin international de l'Académie des Sciences de Cracovie, 8, 182–200.
     [Google Scholar]
  73. Soueid Ahmed, A., Revil, A., Byrdina, S., Coperey, A., Gailler, L., Grobbe, N., Viveiros, F., Silva, C., Jougnot, D., Ghorbani, A., Hogg, C., Kiyan, D., Rath, V., Heap, M.J., Grandis, H. & Humaida, H. (2018) 3D electrical conductivity tomography of volcanoes. Journal of Volcanology and Geothermal Research, 356, 243–263.
     [Google Scholar]
  74. Stesky, R.M. (1986) Electrical conductivity of brine‐saturated fractured rock. Geophysics, 51(8), 1585–1593.
     [Google Scholar]
  75. Straface, S., Rizzo, E. & Chidichimo, F. (2010) Estimation of hydraulic conductivity and water table map in a large‐scale laboratory model by means of the self‐potential method. Journal of Geophysical Research, 115, B06105.
     [Google Scholar]
  76. Thanh, L.D., Jougnot, D., Do, P.V., Hue, D. T.M., Thuy, T. T.C. & Tuyen, V.P. (2021) Predicting electrokinetic coupling and electrical conductivity in fractured media using a fractal distribution of tortuous capillary fractures. Applied Sciences, 11(11), 5121.
     [Google Scholar]
  77. Thanh, L.D., Jougnot, D., Van Do, P. & Van Nghia A, N. (2019) A physically based model for the electrical conductivity of water‐saturated porous media. Geophysical Journal International, 219(2), 866–876.
     [Google Scholar]
  78. Thanh, L.D., Jougnot, D., Van Do, P., Van Nghia A, N., Tuyen, V.P., Ca, N.X. & Hien, N.T. (2020) A physically‐based model for the electrical conductivity of partially saturated porous media. Geophysical Journal International.
  79. Thanh, L.D. & Sprik, R. (2016) Permeability dependence of streaming potential coefficient in porous media. Geophysical Prospecting, 64(3), 714–725.
     [Google Scholar]
  80. Titov, K., Revil, A., Konosavsky, P., Straface, S. & Troisi, S. (2005) Numerical modelling of self‐potential signals associated with a pumping test experiment. Geophysical Journal International, 162(2), 641–650.
     [Google Scholar]
  81. Torabi, A. & Berg, S.S. (2011) Scaling of fault attributes: a review. Marine and Petroleum Geology, 28(8), 1444–1460.
     [Google Scholar]
  82. Tyler, S.W. & Wheatcraft, S.W. (1990) Fractal processes in soil water retention. Water Resources Research, 26(5), 1047–1054.
     [Google Scholar]
  83. Vinogradov, J., Hidayat, M., Kumar, Y., Healy, D. & Comte, J.C. (2022) Laboratory measurements of zeta potential in fractured Lewisian gneiss: implications for the characterization of flow in fractured crystalline bedrock. Applied Sciences, 12(1), 180.
     [Google Scholar]
  84. Vinogradov, J., Hidayat, M., Sarmadivaleh, M., Derksen, J., Vega‐Maza, D., Iglauer, S., Jougnot, D., Azaroual, M. & Leroy, P. (2022) Predictive surface complexation model of the calcite‐aqueous solution interface: the impact of high concentration and complex composition of brines. Journal of Colloid and Interface Science, 609, 852–867.
     [Google Scholar]
  85. Vinogradov, J. & Jackson, M.D. (2011) Multiphase streaming potential in sandstones saturated with gas/brine and oil/brine during drainage and imbibition. Geophysical Research Letters, 38(1), L01301.
     [Google Scholar]
  86. Violay, M., Pezard, P.A., Ildefonse, B., Belghoul, A. & Laverne, C. (2010) Petrophysical properties of the root zone of sheeted dikes in the ocean crust: a case study from HOLE ODP/IODP 1256D, Eastern Equatorial Pacific. Tectonophysics, 493(1), 139–152.
     [Google Scholar]
  87. Voytek, E.B., Barnard, H.R., Jougnot, D. & Singha, K. (2019) Transpiration‐ and precipitation‐induced subsurface water flow observed using the self‐potential method. Hydrological Processes, 33(13), 1784–1801.
     [Google Scholar]
  88. Walsh, J. & Watterson, J. (1993) Fractal analysis of fracture patterns using the standard box‐counting technique: valid and invalid methodologies. Journal of Structural Geology, 15(12), 1509–1512.
     [Google Scholar]
  89. Wang, J.S.Y. & Hudson, J.A. (2015) Fracture flow and underground research laboratories for nuclear waste disposal and physics experiments. In: Faybishenko, B., Benson, S.M., Gale, J.E. (Eds.) Fluid dynamics in complex fractured‐porous systems. Washington, DC: American Geophysical Union, chapter 2 (pp. 19–41).
     [Google Scholar]
  90. Wang, S., Xu, Y., Zhang, Y., Yu, Q. & Wang, L. (2022) Evaluating the influence of fracture roughness and tortuosity on fluid seepage based on fluid seepage experiments. Applied Sciences, 12(15), 7661.
     [Google Scholar]
  91. Wishart, D.N., Slater, L.D. & Gates, A.E. (2006) Self potential improves characterization of hydraulically‐active fractures from azimuthal geoelectrical measurements. Geophysical Research Letters, 33(17), L17314.
     [Google Scholar]
  92. Zhang, C.L. (2013) Sealing of fractures in claystone. Journal of Rock Mechanics and Geotechnical Engineering, 5(3), 214–220.
     [Google Scholar]
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A unified model for the permeability, electrical conductivity and streaming potential coupling coefficient in variably saturated fractured media
Geophysical Prospecting 71, 279 (2023); https://doi.org/10.1111/1365-2478.13295
/content/journals/10.1111/1365-2478.13295
/content/journals/10.1111/1365-2478.13295
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  • Article Type: Research Article
Keyword(s): Mathematical formulation; Petrophysics; Reservoir geophysics

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