How Hydraulic Properties of Organic Matter Control Effective Liquid Permeability of Mudrocks

  • Kuldeep SinghEmail author


In organic-rich Mudrocks, porous organic matter embedded within mineral matrix along with inorganic pores forms a dual porosity–permeability (ϕk) system. How hydraulic properties of organic matter embedded in the mineral matrix contribute to bulk liquid flow however is not well understood. Using computational methods, Navier–Stokes equations are coupled with Brinkman equations for dual (ϕk) mineral matrix–organic matter domains obtained from a focused ion beam–scanning electron microscope (FIB-SEM) image set of an organic-rich Murdock and a series of idealized two-dimensional (2D) pore–organic matrix domains. Results of sensitivity analysis show that variations in organic matter permeability cause variations in effective permeability, which follow ‘S-shaped’ characteristics curve on log–log scale. Hydraulic coupling between the dual (ϕk) domains shows magnification of the coupled flow behavior when permeability of organic matter is on the same order as the permeability of the connected inorganic pores. The effect of coupled flow becomes negligible when the permeability of organic matter is 102 higher or lower than the permeability of the connected inorganic pores. The fraction of maximum change in magnitude of effective permeability (Im) is found to be exponentially dependent on organic matter–pore channel fraction (f), i.e., Ime0.77f, for 0 < f < 5. The maximum contribution of organic matter on bulk liquid flow and a large variation in fluid flow velocities are found to be dependent on both the proportion of organic matter and length scale of investigation, indicating that the µm-scale FIB-SEM domains are far from the scale of representative elementary volume (REV). This study, however, describes how the hydrodynamic coupling of dual ϕk porous media contributes to emergent bulk liquid flow in organic-rich Mudrocks, and likely in similar dual ϕk porous media encountered within engineered systems to the ones found in nature.


Dual porosity Mudrock permeability Navier Stokes Brinkman organic matter kerogen Upscaling 



Author thanks the ConocoPhillips Company, Houston, TX, for providing the FIB-SEM image stack of an organic-rich Mudrock. Author also thanks the second reviewer for their valuable comments in regard to expected ‘S-shaped’ curve behavior as end-member scenario outcome of the Brinkman equation.


  1. Angot, P.: On the well-posed coupling between free fluid and porous viscous flows. Appl. Math. Lett. 24(6), 803–810 (2011)CrossRefGoogle Scholar
  2. Backeberg, N.R., Iacoviello, F., Rittner, M., Mitchell, T.M., Jones, A.P., Day, R., Wheeler, J., Shearing, P.R., Vermeesch, P., Striolo, A.: Quantifying the anisotropy and tortuosity of permeable pathways in clay-rich mudstones using models based on X-ray tomography. Sci Rep-Uk 7 (2017)Google Scholar
  3. Bear, J.: Dynamics of Fluids in Porous Media, p. 764. American Elsevier, New York (1972)Google Scholar
  4. Bhandari, A.R., Flemings, P.B., Polito, P.J., Cronin, M.B., Bryant, S.L.: Anisotropy and stress dependence of permeability in the barnett shale. Transp. Porous Med. 108(2), 393–411 (2015)CrossRefGoogle Scholar
  5. Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013). CrossRefGoogle Scholar
  6. Cao, G.H., Lin, M.A., Jiang, W.B., Li, H.S., Yi, Z.X., Wu, C.J.: A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale. Fuel 204, 129–143 (2017)CrossRefGoogle Scholar
  7. Chandesris, M., Jamet, D.: Boundary conditions at a planar fluid-porous interface for a Poiseuille flow. Int. J. Heat Mass Transf. 49(13–14), 2137–2150 (2006)CrossRefGoogle Scholar
  8. Chen, L., Zhang, L., Kang, Q.J., Viswanathan, H.S., Yao, J., Tao, W.Q.: Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity. Sci Rep-Uk 5 (2015)Google Scholar
  9. Civan, F.: Effective correlation of apparent gas permeability in tight porous media. Transp. Porous Med 82(2), 375–384 (2010). CrossRefGoogle Scholar
  10. Curtis, M.E., Sondergeld, C.H., Ambrose, R.J., Rai, C.S.: Microstructural investigation of gas shales in two and three dimensions using nanometer-scale resolution imaging. AAPG Bull. 96(4), 665–677 (2012)CrossRefGoogle Scholar
  11. Daigle, H., Reece, J.S.: Permeability of two-component granular materials. Transp. Porous Med 106(3), 523–544 (2015). CrossRefGoogle Scholar
  12. de Vries, E.T., Raoof, A., van Genuchten, M.T.: Multiscale modelling of dual-porosity porous media; a computational pore-scale study for flow and solute transport. Adv. Water Resour. 105, 82–95 (2017)CrossRefGoogle Scholar
  13. Dehghanpour, H., Lan, Q., Saeed, Y., Fei, H., Qi, Z.: Spontaneous imbibition of brine and oil in gas shales: effect of water adsorption and resulting microfractures. Energ Fuel 27(6), 3039–3049 (2013). CrossRefGoogle Scholar
  14. Deng, W., Cardenas, M.B., Kirk, M.F., Altman, S.J., Bennett, P.C.: Effect of permeable biofilm on micro- and macro-scale flow and transport in bioclogged pores. Environ. Sci. Technol. 47(19), 11092–11098 (2013)CrossRefGoogle Scholar
  15. Discacciati, M., Quarteroni, A.: Navier–Stokes/Darcy coupling: modeling, analysis, and numerical approximation. Rev. Mat. Complut 22(2), 315–426 (2009)CrossRefGoogle Scholar
  16. Gerke, H.H., Vangenuchten, M.T.: A dual-porosity model for simulating the preferential movement of water and solutes in structured porous-media. Water Resour. Res. 29(2), 305–319 (1993)CrossRefGoogle Scholar
  17. Ghanizadeh, A., Amann-Hildenbrand, A., Gasparik, M., Gensterblum, Y., Krooss, B.M., Littke, R.: Experimental study of fluid transport processes in the matrix system of the European organic-rich shales: II. Posidonia Shale (Lower Toarcian, northern Germany). Int J Coal Geol 123, 20-33 (2014a).
  18. Ghanizadeh, A., Gasparik, M., Amann-Hildenbrand, A., Gensterblum, Y., Krooss, B.M.: Experimental study of fluid transport processes in the matrix system of the European organic-rich shales: I. Scandinavian Alum Shale. Mar. Pet. Geol. 51, 79–99 (2014b)CrossRefGoogle Scholar
  19. Grathoff, G.H., Peltz, M., Enzmann, F., Kaufhold, S.: Porosity and permeability determination of organic-rich Posidonia shales based on 3-D analyses by FIB-SEM microscopy. Solid Earth 7(4), 1145–1156 (2016)CrossRefGoogle Scholar
  20. Heller, R., Vermylen, J., Zoback, M.: Experimental investigation of matrix permeability of gas shales. AAPG Bull. 98(5), 975–995 (2014)CrossRefGoogle Scholar
  21. Javadpour, F., McClure, M., Naraghi, M.E.: Slip-corrected liquid permeability and its effect on hydraulic fracturing and fluid loss in shale. Fuel 160, 549–559 (2015)CrossRefGoogle Scholar
  22. Jiang, W.B., Lin, M., Yi, Z.X., Li, H.S., Wu, S.T.: Parameter determination using 3D FIB-SEM images for development of effective model of shale gas flow in nanoscale pore clusters. Transp. Porous Med. 117(1), 5–25 (2017)CrossRefGoogle Scholar
  23. Josh, M., Esteban, L., Delle Piane, C., Sarout, J., Dewhurst, D.N., Clennell, M.B.: Laboratory characterisation of shale properties. J. Petrol. Sci. Eng. 88–89, 107–124 (2012). CrossRefGoogle Scholar
  24. Kelly, S., El-Sobky, H., Torres-Verdin, C., Balhoff, M.T.: Assessing the utility of FIB-SEM images for shale digital rock physics. Adv. Water Resour. 95, 302–316 (2016)CrossRefGoogle Scholar
  25. King, H.E., Eberle, A.P.R., Walters, C.C., Kliewer, C.E., Ertas, D., Huynh, C.: Pore architecture and connectivity in gas shale. Energy Fuel 29(3), 1375–1390 (2015)CrossRefGoogle Scholar
  26. Landry, C.J., Prodanovic, M., Eichhubl, P.: Direct simulation of supercritical gas flow in complex nanoporous media and prediction of apparent permeability. Int. J. Coal Geol. 159, 120–134 (2016)CrossRefGoogle Scholar
  27. Leu, L., Georgiadis, A., Blunt, M.J., Busch, A., Bertier, P., Schweinar, K., Liebi, M., Menzel, A., Ott, H.: Multiscale Description of Shale Pore Systems by Scanning SAXS and WAXS Microscopy. Energy Fuel 30(12), 10282–10297 (2016). CrossRefGoogle Scholar
  28. Liu, B., Schieber, J., Mastalerz, M.: Combined SEM and reflected light petrography of organic matter in the New Albany Shale (Devonian-Mississippian) in the Illinois Basin: a perspective on organic pore development with thermal maturation. Int. J. Coal Geol. 184, 57–72 (2017)CrossRefGoogle Scholar
  29. Loucks, R.G., Reed, R.M., Ruppel, S.C., Jarvie, D.M.: Morphology, genesis, and distribution of nanometer-scale pores in siliceous mudstones of the Mississippian barnett shale. J. Sediment. Res. 79(11–12), 848–861 (2009)CrossRefGoogle Scholar
  30. Loucks, R.G., Reed, R.M., Ruppel, S.C., Hammes, U.: Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-related mudrock pores. AAPG Bull. 96(6), 1071–1098 (2012)CrossRefGoogle Scholar
  31. Loucks, R.G., Ruppel, S.C., Wang, X.Z., Ko, L., Peng, S., Zhang, T.W., Rowe, H.D., Smith, P.: Pore types, pore-network analysis, and pore quantification of the lacustrine shale-hydrocarbon system in the Late Triassic Yanchang Formation in the southeastern Ordos Basin, China. Interpretation-J Sub 5(2), Sf63-Sf79 (2017)Google Scholar
  32. Mastalerz, M., Schimmelmann, A., Drobniak, A., Chen, Y.Y.: Porosity of Devonian and Mississippian New Albany Shale across a maturation gradient: insights from organic petrology, gas adsorption, and mercury intrusion. AAPG Bull. 97(10), 1621–1643 (2013)CrossRefGoogle Scholar
  33. Mehmani, A., Prodanovic, M.: The effect of microporosity on transport properties in porous media. Adv. Water Resour. 63, 104–119 (2014)CrossRefGoogle Scholar
  34. Mehmani, A., Prodanovic, M., Javadpour, F.: Multiscale, multiphysics network modeling of shale matrix gas flows. Transp. Porous Med 99(2), 377–390 (2013)CrossRefGoogle Scholar
  35. Milliken, K.L., Rudnicki, M., Awwiller, D.N., Zhang, T.W.: Organic matter-hosted pore system, Marcellus Formation (Devonian), Pennsylvania. AAPG Bull. 97(2), 177–200 (2013)CrossRefGoogle Scholar
  36. Mokhtari, M., Tutuncu, A.N.: Characterization of anisotropy in the permeability of organic-rich shales. J. Petrol. Sci. Eng. 133, 496–506 (2015)CrossRefGoogle Scholar
  37. Naraghi, M.E., Javadpour, F.: A stochastic permeability model for the shale-gas systems. Int. J. Coal Geol. 140, 111–124 (2015)CrossRefGoogle Scholar
  38. Neale, G., Nader, W.: Practical significance of brinkman’s extension of darcy’s law: coupled parallel flows within a channel and a bounding porous medium. Can. J. Chem. Eng. 52(4), 475–478 (1974). CrossRefGoogle Scholar
  39. Peng, S., Yang, J.J., Xiao, X.H., Loucks, B., Ruppel, S.C., Zhang, T.W.: An Integrated method for upscaling pore-network characterization and permeability estimation: example from the mississippian barnett shale. Transp. Porous Med. 109(2), 359–376 (2015)CrossRefGoogle Scholar
  40. Saif, T., Lin, Q.Y., Butcher, A.R., Bijeljic, B., Blunt, M.J.: Multi-scale multi-dimensional microstructure imaging of oil shale pyrolysis using X-ray micro-tomography, automated ultra-high resolution SEM. MAPS Mineral. FIB-SEM. Appl. Energy 202, 628–647 (2017)Google Scholar
  41. Salama, A., El Amin, M.F., Kumar, K., Sun, S.Y.: Flow and Transport in Tight and Shale Formations: A Review. Geofluids (2017)Google Scholar
  42. Scheibe, T.D., Perkins, W.A., Richmond, M.C., McKinley, M.I., Romero-Gomez, P.D.J., Oostrom, M., Wietsma, T.W., Serkowski, J.A., Zachara, J.M.: Pore-scale and multiscale numerical simulation of flow and transport in a laboratory-scale column. Water Resour. Res. 51(2), 1023–1035 (2015)CrossRefGoogle Scholar
  43. Singh, H., Javadpour, F., Ettehadtavakkol, A., Darabi, H.: Nonempirical apparent permeability of shale. Spe Reserv. Eval. Eng, 17(3), 414–424 (2014)CrossRefGoogle Scholar
  44. Sinn, C.J.A., Klaver, J., Fink, R., Jiang, M., Schmatz, J., Littke, R., Urai, J.L.: Using BIB-SEM Imaging for Permeability Prediction in Heterogeneous Shales. Geofluids (2017)Google Scholar
  45. Slatt, R.M., O’Brien, N.R.: Pore types in the Barnett and Woodford gas shales: contribution to understanding gas storage and migration pathways in fine-grained rocks. AAPG Bull. 95(12), 2017–2030 (2011). CrossRefGoogle Scholar
  46. Soulaine, C., Creux, P., Tchelepi, H.A.: Micro-continuum framework for pore-scale multiphase fluid transport in shale formations. Transp. Porous Med. 127(1), 85–112 (2019). CrossRefGoogle Scholar
  47. Soulaine, C., Gjetvaj, F., Garing, C., Roman, S., Russian, A., Gouze, P., Tchelepi, H.A.: The impact of sub-resolution porosity of x-ray microtomography images on the permeability. Transp. Porous Med. 113(1), 227–243 (2016)CrossRefGoogle Scholar
  48. Sun, H.F., Tao, G., Vega, S., Al-Suwaidi, A.: Simulation of gas flow in organic-rich mudrocks using digital rock physics. J. Nat. Gas Sci. Eng. 41, 17–29 (2017)CrossRefGoogle Scholar
  49. Tahmasebi, P., Javadpour, F., Sahimi, M.: Multiscale and multiresolution modeling of shales and their flow and morphological properties. Sci Rep-Uk 5 (2015)Google Scholar
  50. Travis, K.P., Todd, B.D., Evans, D.J.: Departure from Navier–Stokes hydrodynamics in confined liquids. Phys. Rev. E 55(4), 4288–4295 (1997)CrossRefGoogle Scholar
  51. Wang, L., Wang, S.H., Zhang, R.L., Wang, C., Xiong, Y., Zheng, X.S., Li, S.R., Jin, K., Rui, Z.H.: Review of multi-scale and multi-physical simulation technologies for shale and tight gas reservoirs. J. Nat. Gas Sci. Eng. 37, 560–578 (2017)CrossRefGoogle Scholar
  52. Wasaki, A., Akkutlu, I.Y.: Permeability of Organic-Rich Shale. Spe J. 20(6), 1384–1396 (2015)CrossRefGoogle Scholar
  53. Wildenschild, D., Jensen, K.H., Villholth, K., Illangasekare, T.H.: A laboratory analysis of the effect of macropores on solute transport. Ground Water 32(3), 381–389 (1994). CrossRefGoogle Scholar
  54. Wu, T.H., Li, X., Zhao, J.L., Zhang, D.X.: Multiscale pore structure and its effect on gas transport in organic-rich shale. Water Resour. Res. 53(7), 5438–5450 (2017)CrossRefGoogle Scholar
  55. Yan, B.C., Wang, Y.H., Killough, J.E.: Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs. Comput. Geosci. 20(1), 69–91 (2016)CrossRefGoogle Scholar
  56. Zhang, Q., Su, Y.L., Wang, W.D., Lu, M.J., Sheng, G.L.: Apparent permeability for liquid transport in nanopores of shale reservoirs: coupling flow enhancement and near wall flow. Int. J. Heat Mass Transf. 115, 224–234 (2017)CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of GeologyKent State UniversityKentUSA

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