Transport in Porous Media

, Volume 108, Issue 2, pp 393–411 | Cite as

Anisotropy and Stress Dependence of Permeability in the Barnett Shale

  • Athma R. Bhandari
  • Peter B. Flemings
  • Peter J. Polito
  • Michael B. Cronin
  • Steven L. Bryant


We document vertical permeability of \(2.3 \times 10^{-21}\, \hbox {m}^{2}\) (2.3 nd) and horizontal permeability of \(9.5 \times 10^{-20}\, \hbox {m}^{2}\) (96.3 nd) in two Barnett Shale samples. The samples are composed predominantly of quartz, calcite, and clay; have a porosity and a total organic content of \(\sim \)4 % each; and have a thermal maturity of 1.9 % vitrinite reflectance. Both samples exhibit stress-dependent permeability when the confining pressure is increased from 10.3 to 41.4 MPa. We measure a permeability anisotropy, the ratio of the horizontal to the vertical permeability, of \(\sim \)40. We find that the permeability anisotropy does not vary with effective stress. Multiscale permeability, as demonstrated by pressure dissipation, is related to millimeter-scale stratigraphic variation. We attribute the permeability anisotropy to preferential flow along more permeable layers and attribute the stress dependence to pore closure. A determination of permeability anisotropy allows us to understand flow properties in horizontal and vertical directions and assists our understanding of upscaling. Characterization of stress dependency allows us to predict permeability evolution during production.


Mudrocks Pulse-decay permeability Anisotropy Stress dependence Heterogeneity 

List of symbols

\(\alpha \)

Pressure-sensitivity factor (\(\hbox {Pa}^{-1}\))

\(\mu \)

Gas viscosity (Pa s)

\(\phi \)

Porosity of core plug


Ratio of sample pore volume to volume of upstream reservoir


Ratio of sample pore volume to volume of downstream reservoir


Klinkenberg’s gas slippage factor (Pa)


Gas compressibility (\(\hbox {Pa}^{-1}\))


Semilog slope of the differential pressure decay (at 90 % decay)

\(f (a, b)\)

\((a +b + ab) - (1/3)(a+b + 0.4132 a\,b)^{2 }+ 0.0744 (a+b + 0.0578 a\, b)^{3}\)


Apparent gas permeability (\(\hbox {m}^{2}\))


Apparent gas permeability at \(P_\mathrm{c} - P_\mathrm{p} = 0\) \((\hbox {m}^{2})\)

\(k_{\infty }\)

Absolute (Klinkenberg’s corrected) permeability


Horizontal permeability (\(\hbox {m}^{2}\))


Vertical permeability (\(\hbox {m}^{2}\))


Length of core plug (m)


Pressure in sample (Pa)


Upstream reservoir pressure (Pa)


Downstream reservoir pressure (Pa)


Confining pressure (Pa)


Dimensionless pressure


Average pore pressure (Pa)

\(\varDelta P\)

Differential (upstream – downstream) pressure at time t (Pa)

\(\varDelta P_{0}\)

Initial differential pressure (Pa)


Time elapsed (s)


Distance along the sample (m)



This research project is funded by Shell under the Shell–UT Unconventional Research (SUTUR) program. We thank Julia Reece for her help during the early stages of this research, Patrick Smith for taking the backscattered electron images, and Jessica Maisano for taking the microscale X-ray computed tomography images. Publication authorized by the Director of the Bureau of Economic Geology, The University of Texas at Austin\(^{\mathrm{TM}}\).

Supplementary material

11242_2015_482_MOESM1_ESM.docx (12 kb)
Supplementary material 1 (docx 12 KB)
11242_2015_482_MOESM2_ESM.txt (12 kb)
Supplementary material 2 (txt 12 KB)
11242_2015_482_MOESM3_ESM.txt (10 kb)
Supplementary material 3 (txt 9 KB)
11242_2015_482_MOESM4_ESM.txt (11 kb)
Supplementary material 4 (txt 10 KB)
11242_2015_482_MOESM5_ESM.txt (19 kb)
Supplementary material 5 (txt 19 KB)
11242_2015_482_MOESM6_ESM.txt (30 kb)
Supplementary material 6 (txt 30 KB)
11242_2015_482_MOESM7_ESM.txt (21 kb)
Supplementary material 7 (txt 21 KB)
11242_2015_482_MOESM8_ESM.txt (33 kb)
Supplementary material 8 (txt 33 KB)
11242_2015_482_MOESM9_ESM.txt (29 kb)
Supplementary material 9 (txt 28 KB)


  1. Adams, A.L., Germaine, J.T., Flemings, P.B., Day-Stirrat, R.J.: Stress induced permeability anisotropy of resedimented Boston Blue Clay. Water Resour. Res. 49, 1–11 (2013). doi: 10.1002/wrcr.20470 CrossRefGoogle Scholar
  2. Armitage, P.J., Faulkner, D.R., Worden, R.H., Aplin, A.C., Butcher, A.R., Iliffe, J.: Experimental measurement of, and controls on, permeability and permeability anisotropy of caprocks from the \(\text{ CO }_{2}\) storage project at the Krechba Field, Algeria. J. Geophys. Res. Solid Earth 116, B12208 (2011). doi: 10.1029/2011JB008385 CrossRefGoogle Scholar
  3. Best, M.E., Katsube, T.J.: Shale permeability and its significance in hydrocarbon exploration. Lead. Edge 14, 165–170 (1995)CrossRefGoogle Scholar
  4. Brace, W.F., Walsh, J.B., Frangos, W.T.: Permeability of granite under high pressure. J. Geophys. Res. 73(6), 2225–2236 (1968). doi: 10.1029/JB073i006p02225 CrossRefGoogle Scholar
  5. Bustin, A.M., Bustin, R.M.: Importance of rock properties on the producibility of gas shales. Int. J. Coal Geol. 103, 132–147 (2012). doi: 10.1016/j.coal.2012.04.012 CrossRefGoogle Scholar
  6. Bustin, A.M., Cui, X., Ross, D.J.K., Pathi, V.S.M.: Impact of shale properties on pore structure and storage characteristics. SPE paper 119892 presented at the SPE Shale Gas Production Conference held in Fort Worth, Texas, 16–18 November 2008. doi: 10.2118/119892-MS
  7. Chalmers, G.R.L., Ross, D.J.K., Bustin, R.M.: Geological controls on matrix permeability of Devonian gas shales in the Horn River and Liard basins, northeastern British Columbia, Canada. Int. J. Coal Geol. 103, 120–131 (2012). doi: 10.1016/j.coal.2012.05.006 CrossRefGoogle Scholar
  8. Clarkson, C.R.: Production data analysis of unconventional gas wells: review of theory and best practices. Int. J. Coal Geol. 109–110, 101–146 (2013). doi: 10.1016/j.coal.2013.01.002 CrossRefGoogle Scholar
  9. Clarkson, C.R., Nobakht, M., Kaviani, D., Ertekin, T.: Production analysis of tight-gas and shale-gas reservoirs using the dynamic-slippage concept. SPE J. 17(1), 230–242 (2012)CrossRefGoogle Scholar
  10. Clennell, M.B., Dewhurst, D.N., Brown, K.M., Westbrook, G.K.: Permeability anisotropy of consolidated clays. Geol. Soc. Lond. Spec. Publ. 158(1), 79–96 (1999). doi: 10.1144/gsl.sp.1999.158.01.07 CrossRefGoogle Scholar
  11. Comisky, J.T., Santiago, M., McCollom, B., Buddhala, A., Newsham, K. E.: Sample size effects on the application of Mercruy Intrusion Capillary Pressure for determining the storage capacity of tight gas and oil shales. CSUG/SPE paper 149432 presented at the Canadian Unconventional Resources Conference held in Calgary, Alberta, 15–17 November 2011. doi: 10.2118/149432-MS
  12. Cui, X., Bustin, A.M.M., Bustin, R.M.: Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 9(3), 208–223 (2009). doi: 10.1111/j.1468-8123.2009.00244.x CrossRefGoogle Scholar
  13. 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). doi: 10.1306/08151110188 CrossRefGoogle Scholar
  14. Daigle, H., Dugan, B.: Permeability anisotropy and fabric development: a mechanistic explanation. Water Resour. Res. 47(12), W12517 (2011). doi: 10.1029/2011WR011110 CrossRefGoogle Scholar
  15. Dicker, A.I., Smits, R.M.: A practical method for determining permeability from laboratory pressure-pulse decay measurements. SPE paper 17578 presented at the International Meeting on Petroleum Engineering held in Tianjin, China, 1–4 November 1988Google Scholar
  16. EIA (U.S. Energy Information Administration): Technically recoverable shale oil and shale gas resources: An assessment of 137 shale formations in 41 countries outside the United States, pp. 730 (2013)Google Scholar
  17. Gale, J., Holder, J.: Natural fractures in some U.S. shales and their importance for gas production. Geological Society of London, Petroleum Geology Conference, Series 7, 1131–1140 (2010). doi: 10.1144/0071131
  18. Gale, J., Reed, R.M., Holder, J.: Natural fractures in the Barnett Shale and their importance for hydraulic fracture treatments. AAPG Bull. 91(4), 603–622 (2007). doi: 10.1306/11010606061 CrossRefGoogle Scholar
  19. 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 (2014a). doi: 10.1016/j.marpetgeo.2013.10.013 CrossRefGoogle Scholar
  20. 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 (2014b). doi: 10.1016/j.coal.2013.06.009 CrossRefGoogle Scholar
  21. Handwerger, D.A., Keller, J., Vaughn, K.: Improved petrophysical core measurements on tight shale reservoirs using retort and crushed samples. SPE paper 47456 presented at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 30 October–2 November 2011. doi: 10.2118/147456-MS
  22. Heid, J.G., McMahon, J.J., Nielsen, R.F., Yuster, S.T.: Study of the Permeability of Rocks to Homogenous Fluids, pp. 230–246. API Drilling & Production Practice, New York (1950)Google Scholar
  23. Heller, R.: Multiscale Investigation of Fluid Transport in Gas Shales. PhD Thesis, Stanford University, Palo Alto, California, USA, pp. 182 (2013)Google Scholar
  24. Heller, R., Vermylen, J., Zoback, M.: Experimental investigation of matrix permeability of gas shales. AAPG Bull. 98(5), 975–995 (2014). doi: 10.1306/09231313023 CrossRefGoogle Scholar
  25. Hickey, J.J., Henk, B.: Lithofacies summary of the Mississippian Barnett Shale, Mitchell 2 T.P. Sims well, Wise County, Texas. AAPG Bull. 91(4), 437–443 (2007). doi: 10.1306/12040606053 CrossRefGoogle Scholar
  26. Hinkley, R., Gu, Z., Wong, T., Camilleri, D.: Multi-porosity simulation of unconventional reservoirs. SPE 167146 paper presented at the SPE Unconventional Resources Conference Canada held in Calgary, Alberta, Canada, 5–7 November 2013. doi: 10.2118/167146-MS
  27. Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E.: A transient laboratory method for determining the hydraulic properties of tight rocks. 1. Theory. Int. J. Rock Mech. Min. Sci. 18(3), 245–252 (1981). doi: 10.1016/0148-9062(81)90979-7 CrossRefGoogle Scholar
  28. Jones, S.C.: A technique for faster pulse-decay permeability measurements in tight rocks. SPE Form. Eval. 12(1), 19–26 (1997). doi: 10.2118/28450-PA. SPE 28450CrossRefGoogle Scholar
  29. Jones, F.O., Owens, W.W.: A laboratory study of low permeability gas sands. SPE 7551. In: Presented at the 1979 SPE Symposium on Low-Permeability Gas Reservoirs, Denver, May 20–22 (1979)Google Scholar
  30. Kamath, J., Boyer, R.E., Nakagawa, F.M.: Characterization of core-scale heterogeneities using laboratory pressure transients. SPE Form. Eval. 7(3), 219–227 (1992). SPE 20575CrossRefGoogle Scholar
  31. Kang, S.M., Fathi, E., Ambrose, R.J., Akkutlu, I.Y., Sigal, R.F.: Carbon dioxide storage capacity of organic-rich shales. SPE J. 16(4), 842–855 (2011). doi: 10.2118/134583-PA. SPE 134583CrossRefGoogle Scholar
  32. Klinkenberg, L.J.: The permeability of porous media to liquids and gases. Paper preseneted at the API 11th mid year meeting, Tulsa, Oklahoma, May 1941; in Drilling and Production Practice, pp. 200–213 (1941)Google Scholar
  33. Kwon, O., Kronenberg, A.K., Gangi, A.F., Johnson, B., Herbert, B.E.: Permeability of illite-bearing shale: 1. Anisotropy and effects of clay content and loading. J. Geophys. Res. 109, B10205 (2004). doi: 10.1029/2004jb003052 CrossRefGoogle Scholar
  34. 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). doi: 10.1306/08171111061 CrossRefGoogle Scholar
  35. 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 Mississipian Barnett shale. J. Sediment. Res. 79(12), 848–861 (2009)CrossRefGoogle Scholar
  36. Loucks, R.G., Ruppel, S.C.: Mississippian Barnett Shale: Lithofacies and depositional setting of a deep-water shale gas succession in the Fort Worth Basin, Texas. AAPG Bull. 91(4), 579–601 (2007)CrossRefGoogle Scholar
  37. Luffel, D.L., Hopkins, C.W., Holditch, S.A., Schetter, P.D.: Matrix permeability measurement of gas productive shales. SPE Annual Technical Conference and Exhibition, Houston, Texas. SPE 26633, 261–270 (1993). doi: 10.2118/26633-MS
  38. Mckernan, R.E., Rutter, E.H., Mecklenburgh, J., Taylor, K.G., Covey-Crump, S.J.: Influence of effective pressure on mudstone matrix permability: implications for shale gas production. SPE paper 167762 presented at the SPE/EAGE European Unconventional Conference and Exhibition held in Vienna, Austria, 25–27 February 2014Google Scholar
  39. Metwally, Y.M., Sondergeld, C.H.: Measuring low permeabilities of gas-sands and shales using a pressure transmission technique. Int. J. Rock Mech. Min. Sci. 48(7), 1135–1144 (2011). doi: 10.1016/j.ijrmms.2011.08.004 CrossRefGoogle Scholar
  40. Milliken, K.L., Esch, W.L., Reed, R.M., Zhang, T.W.: Grain assemblages and strong diagenetic overprinting in siliceous mudrocks, Barnett Shale (Mississippian), Fort Worth Basin, Texas. AAPG Bull. 96(8), 1553–1578 (2012). doi: 10.1306/12011111129 CrossRefGoogle Scholar
  41. Ning, X.: The Measurement of Matrix and Fracture Properties in Naturally Fractured Low Permeability Cores using a Pressure Pulse Method. PhD Thesis, Texas A&M University, College Station, Texas, USA, pp. 204 (1992)Google Scholar
  42. Ning, X., Fan, J., Holditch, S.A., Lee, W.J.: The measurement of matrix and fracture properties in naturally fractured cores. SPE paper 25898 presented at the Low Permeability Reservoirs Symposium held in Denver, Colorado, 26–28 April 1993. doi: 10.2118/25898-MS
  43. NIST (National Institute of Standards and Technology) (2014)
  44. Pathi, V.S.M.: Factors Affecting the Permeability of Gas Shales. Master’s Thesis, University of British Columbia, Vancouver, Canada, pp. 189 (2008)Google Scholar
  45. Patzek, T.W., Male, F., Marder, M.: Gas production in the Barnett Shale obeys a simple scaling theory. Proc. Natl. Acad. Sci. 110(49), 19731–19736 (2013). doi: 10.1073/pnas.1313380110 CrossRefGoogle Scholar
  46. Silin, D.B., Kneafsey, T.J.: Gas shale: from nanometer-scale observations to well modeling. SPE paper 149489 presented at the Canadian Unconventional Resources Conference held in Alberta, Canada, 15–17 November 2011. doi: 10.2118/149489-MS
  47. Soeder, D.J.: Porosity and permeability of Eastern Devonian gas shale. SPE Form. Eval. 3(1), 116–124 (1988). doi: 10.2118/15213-PA. SPE Paper 15213CrossRefGoogle Scholar
  48. Stegent, N.A., Ingram, S.R., Callard, J.G.: Hydraulic fracture stimulation design considerations and production analysis. SPE paper 139981 presented at the SPE Hydraulic Fracturing Technology Conference held in The Woodlands, Texas, USA, 24–26 January 2011. doi: 10.2118/139981-MS
  49. Suarez-Rivera, R., Chertov, M., Willberg, D.M., Green, S.J., Keller, J.: Understanding permeability measurements in tight shales promotes enhanced determination of reservoir quality. SPE paper 162816 presented at the SPE Canadian Unconventional Resources Conference held in Calgary, Alberta, Canada, 30 October–1 November 2012. doi: 10.2118/162816-MS
  50. Tinni, A., Fathi, E., Agarwal, R., Sondergeld, C., Akkutlu, Y., Rai, C.: Shale permeability measurements on plugs and crushed samples. SPE paper 162235 presented at the SPE Canadian Unconventional Resources Conference held in Calgary, Alberta, Canada, 30 October–1 November 2012. doi: 10.2118/162235-MS
  51. Vega, B., Dutta, A., Kovscek, A.: CT imaging of low-permeability, dual-porosity systems using high X-ray constrast gas. Transp. Porous Med. 101, 81–97 (2014). doi: 10.1007/s11242-013-0232-0 CrossRefGoogle Scholar
  52. Vermylen, J.P.: Geomechanical Studies of the Barnett Shale, Texas, USA. PhD Thesis, Stanford University, Palo Alto, California, pp. 143 (2011)Google Scholar
  53. Waters, G.A., Dean, B.K., Downie, R.C., Kerrihard, K.J., Austbo, L., McPherson, B.: Simultaneous hydraulic fracturing of adjacent horizontal wells in the Woodford Shale. SPE paper 119635 presented at the SPE Hydraulic Fracturing Technology Conference held in The Woodlands, Texas, 19–21 January 2009. doi: 10.2118/119635-MS
  54. Witt, K.-J., Brauns, J.: Permeability–anisotropy due to particle shape. J. Geotech. Eng. 109(9), 1181–1187 (1983)CrossRefGoogle Scholar
  55. Yang, Y.L., Aplin, A.C.: Permeability and petrophysical properties of 30 natural mudstones. J. Geophys. Res. Solid Earth 112, B03206 (2007). doi: 10.1029/2005JB004243 Google Scholar
  56. Ziarani, A.S., Aguilera, R.: Knudsen’s permeability correction for tight porous media. Transp. Porous Med. 91, 239–260 (2012). doi: 10.1007/s11242-011-9842-6 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Athma R. Bhandari
    • 1
  • Peter B. Flemings
    • 2
  • Peter J. Polito
    • 1
  • Michael B. Cronin
    • 2
  • Steven L. Bryant
    • 3
  1. 1.Bureau of Economic Geology, Jackson School of GeosciencesThe University of Texas at AustinAustinUSA
  2. 2.Jackson School of GeosciencesThe University of Texas at AustinAustinUSA
  3. 3.Schulich School of EngineeringUniversity of CalgaryCalgaryCanada

Personalised recommendations