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A Semi-analytical Model for Pressure-Dependent Permeability of Tight Sandstone Reservoirs

Abstract

In tight gas reservoirs, permeability is pressure dependent owing to pore pressure reduction during the life of the reservoir. Empirical models are commonly used to describe pressure-dependent permeability. In this paper, it was discussed a number of issues which centered around tight sandstone pressure-dependent permeability experiment, first to apply core aging on permeability test and then to develop a new semi-analytical model to predict permeability. In tight sandstone permeability test experiment, the microinterstice between core and sleeves resulted in over estimation of dependency of permeability on pressure. Then, a new semi-analytical model was developed to identify the relation between permeability and fluid pressure in tight sandstone, which indicates there is a linear relation between pore pressure changes and the inverse of permeability to a constant power. Pressure-dependent permeability of 8 tight sandstone core samples from Ordos Basin, China, was obtained using the modified procedure, and results were perfectly matched with the proposed model. Meanwhile, the semi-analytical model was also verified by pressure-dependent permeability of 16 cores in the literature and experiment results of these 24 cores were matched by empirical models and the semi-analytical model. Compared with regression result of commonly used empirical models, the semi-analytical model outperforms the current empirical models on 8 cores from our experiment and 16 cores from the literature. The model verification also indicates that the semi-theoretical model can match the pressure-dependent permeability of different rock types. In addition, the permeability performance under reservoir condition is discussed, which is divided into two stages. In most tight gas reservoirs, the permeability performance during production is located in stage II. The evaluation result with proposed experiment procedure and the stress condition in stage II will reduce permeability sensitivity to stress.

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References

  1. Abass, H.H., Ortiz, I., Khan, M.R., Beresky, J.K., Sierra, L.: Understanding stress dependant permeability of matrix natural fractures and hydraulic fractures in carbonate formations. In: SPE Saudi Arabia Section Technical Symposium. SPE-110973-MS, SPE Saudi Arabia Section Technical Symposium, 7–8 May, Dhahran, Saudi Arabia (2007)

  2. Aguilera, R.: Recovery factors and reserves in naturally fractured reservoirs. J. Can. Pet. Technol. 38(7), 15–18 (1999)

  3. Aguilera, R.: Incorporating capillary pressure, pore throat aperture radii, height above free water table, and Winland R35 values on Pickett plots. AAPG Bull. 86, 605–624 (2002)

  4. Beijing Chemical Industrial Company Inc.: Cryogenic Handbook, pp. 216 – 217, Beijing (1979)

  5. Bernabe, Y.: The effective pressure law for permeability in Chelmsford granite and barre granite. In: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, vol. 23, no. 3, pp. 267–275 (1986)

  6. Bernabe, Y.: The effective pressure law for permeability during pore pressure and confining pressure cycling of several crystalline rocks. J. Geophys. Res. Solid Earth 92(B1), 649–657 (1987)

  7. Bernabe, Y.: Comparison of the effective pressure law for permeability and resistivity formation factor in Chelmsford granite. Pure Appl. Geophys. 127(4), 607–625 (1988)

  8. Bhandari, A.R., Flemings, P.B., Polito, P.J., Cronin, M.B., Bryant, S.L.: Erratum to: anisotropy and stress dependence of permeability in the Barnett shale. Transp. Porous Media 108(3), 393–411 (2015)

  9. Boosari, S.S.H., Aybar, U., Eshkalak, M.O.: Unconventional resource’s production under desorption-induced effects. Petroleum 2(2), 148–155 (2016)

  10. Caulk, R.A., Ghazanfari, E., Perdrial, J.N., Perdrial, N.: Experimental investigation of fracture aperture and permeability change within enhanced geothermal systems. Geothermics 62, 12–21 (2016)

  11. Chen, M., Bai, M.: Modeling stress-dependent permeability for anisotropic fractured porous rocks. Int J Rock Mech Min Sci 35(8), 1113–1119 (1998)

  12. Chen, Y., Liu, D., Yao, Y., Cai, Y., Chen, L.: Dynamic permeability change during coalbed methane production and its controlling factors. J Nat Gas Sci Eng 25, 335–346 (2015)

  13. Cho, Y., Ozkan, E., Apaydin, O.G.: Pressure-dependent natural-fracture permeability in shale and its effect on shale-gas well production. SPE Reserv. Eval. Eng. 16(2), 216–228 (2012)

  14. David, C., Wong, T.F., Zhu, W., Zhang, J.: Laboratory measurement of compaction-induced permeability change in porous rocks: implications for the generation and maintenance of pore pressure excess in the crust. Pure Appl. Geophys. 143(1), 425–456 (1994)

  15. Dong, J.J., Hsu, J.Y., Wu, W.J., Shimamoto, T., Hung, J.H., Yeh, E.C., et al.: Stress-dependence of the permeability and porosity of sandstone and shale from TCDP hole-A. Int. J. Rock Mech. Min. Sci. 47(7), 1141–1157 (2010)

  16. Dou, X., Liao, X., Zhao, X., Wang, H., Lv, S.: Quantification of permeability stress-sensitivity in tight gas reservoir based on straight-line analysis. J. Nat. Gas Sci. Eng. 22, 598–608 (2015)

  17. Duan, Z., Davy, C.A., Agostini, F., Jeannin, L., Troadec, D., Skoczylas, F.: Gas recovery potential of sandstones from tight gas reservoirs. Int. J. Rock Mech. Min. Sci. 65(1), 75–85 (2014)

  18. Feng, R., Harpalani, S., Pandey, R.: Laboratory measurement of stress-dependent coal permeability using pulse-decay technique and flow modeling with gas depletion. Fuel 177, 76–86 (2016)

  19. Gangi, A.F.: Variation of whole and fractured porous rock permeability with confining pressure. In: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, vol. 15, no. 05, pp. 249–257 (1978)

  20. Guo, P., Cheng, Y., Jin, K., Li, W., Tu, Q., Liu, H.: Impact of effective stress and matrix deformation on the coal fracture permeability. Transp. Porous Media 103(1), 99–115 (2014)

  21. Hall, H.N.: Compressibility of reservoir rocks. J. Pet. Technol. 5(1), 17–19 (1953)

  22. Heid, J.G., McMahon, J.J., Nielsen, R.F., Yuster, S.T.: Study of the permeability of rocks to homogenous fluids. In: Drilling and Production, Practice, API-50-230, pp. 230–246. API, New York (1950)

  23. Huo, D., Benson, S.M.: Experimental investigation of stress-dependency of relative permeability in rock fractures. Transp. Porous Media 113(3), 567–590 (2016)

  24. Jaeger, J.C., Cook, N.G., Zimmerman, R.: Fundamentals of Rock Mechanics. Wiley, New York (2009)

  25. Jiao, C., He, S.L., Xie, Q., Gu, D.H., Zhu, H.Y., Sun, L., Liu, H.X.: An experimental study on stress-dependent sensitivity of ultra-low permeability sandstone reservoirs. Acta Pet. Sin. 32(3), 489–494 (2011)

  26. Jones, F.O., Owens, W.W.: A laboratory study of low-permeability gas sands. J. Pet. Technol. 32(9), 1631–1640 (1980)

  27. Karacan, C.Ö.: Prediction of porosity and permeability of caved zone in longwall gobs. Transp. Porous Media 82(2), 413–439 (2010)

  28. Li, M., Bernabé, Y., Xiao, W.I., Chen, Z.Y., Liu, Z.Q.: Effective pressure law for permeability of E-Bei sandstones. J. Geophys. Res. Solid Earth 114(B7), 223–223 (2009)

  29. Li, M., Xiao, W., Bernabé, Y., Zhao, J.: Nonlinear effective pressure law for permeability. J. Geophys. Res. Solid Earth 119(1), 302–318 (2014)

  30. Lorenz, J.C.: Stress-sensitive reservoirs. J. Pet. Technol. 51(01), 61–63 (1999)

  31. Lv, Z., Li, S., Liu, G., Zhang, Z., Guo, X.: Factors affecting the productivity of a multifractured horizontal well. Pet. Sci. Technol. 31(22), 2325–2334 (2013)

  32. Ma, F., He, S., Zhu, H., Xie, Q., Jiao, C.: The effect of stress and pore pressure on formation permeability of ultra-low-permeability reservoir. Pet. Sci. Technol. 30(12), 1221–1231 (2012)

  33. Mbia, E.N., Fabricius, I.L., Oji, C.O.: Equivalent pore radius and velocity of elastic waves in shale Skjold Flank-1 Well, Danish North Sea. J. Pet. Sci. Eng. 109, 280–290 (2013)

  34. Mbia, E.N., Fabricius, I.L., Krogsboll, A., Frykman, P., Dalhoff, F.: Permeability, compressibility and porosity of Jurassic shale from the norwegian-danish basin. Pet. Geosci. 20(3), 257–281 (2014)

  35. McKee, C.R., Bumb, A.C., Koenig, R.A.: Stress-dependent permeability and porosity of coal and other geologic formations. SPE Form. Eval. 3(01), 81–91 (1988)

  36. Nojabaei, B., Siripatrachai, N., Johns, R.T., Ertekin, T.: Effect of large gas-oil capillary pressure on production: a compositionally-extended black oil formulation. J. Pet. Sci. Eng. 147, 317–329 (2016)

  37. Ostad, M.N., Asghari, O., Emery, X., Azizzadeh, M., Khoshbakht, F.: Fracture network modeling using petrophysical data, an approach based on geostatistical concepts. J. Nat. Gas Sci. Eng. 31, 758–768 (2016)

  38. Ostensen, R.W.: The effect of stress-dependent permeability on gas production and well testing. SPE Form. Eval. 1(03), 227–235 (1986)

  39. Pengpeng, G., Wei, S., Ruimin, G.: A study of stress sensitivity on the effective development of low-permeability gas reservoirs in the Sulige gas field. Pet. Sci. Technol. 32(17), 2068–2074 (2014)

  40. Rashid, F., Glover, P.W.J., Lorinczi, P., Hussein, D., Collier, R., Lawrence, J.: Permeability prediction in tight carbonate rocks using capillary pressure measurements. Mar. Pet. Geol. 68, 536–550 (2015)

  41. Sander, R., Pan, Z., Connell, L.D.: Laboratory measurement of low permeability unconventional gas reservoir rocks: a review of experimental methods. J. Nat. Gas Sci. Eng. 37(3), 248–279 (2016)

  42. Schutjens, P.M.T.M., Hanssen, T.H., Hettema, M.H.H., Merour, J., De Bree, P., Coremans, J.W.A., Helliesen, G.: Compaction-induced porosity/permeability reduction in sandstone reservoirs: Data and model for elasticity-dominated deformation. SPE Reserv. Eval. Eng. 7(03), 202–216 (2004)

  43. Schmitt, M., Fernandes, C.P., Wolf, F.G., Neto, J.A.B.D.C., Rahner, C.P.: Characterization of Brazilian tight gas sandstones relating permeability and angstrom-to micron-scale pore structures. J. Nat. Gas Sci. Eng. 27, 785–807 (2015)

  44. Sigal, R.F.: The pressure dependence of permeability. Soc. Petrophys. Well-Log Anal. 43(2), 92–102 (2002)

  45. Shi, J.Q., Durucan, S.: Drawdown induced changes in permeability of coalbeds: a new interpretation of the reservoir response to primary recovery. Transp. Porous Media 56(1), 1–16 (2004)

  46. Sun, H.D.: Study on productivity evaluation and performance prediction method of overpressured, stress-sensitive gas reservoirs. Phys. Chem. Chem. Phys. 9(15), 1764–73 (2007)

  47. Sun, L., Song, W., Jiang, T.: Experimental research on reservoir sensitivity to stress and impacts on productivity in Kela 2 gas field. Sci. China 47(z2), 159–166 (2004)

  48. Tiab, D., Donaldson, E.C.: Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties. Gulf professional publishing, Houston (2015)

  49. Tian, X., Cheng, L., Cao, R., Wang, Y., Zhao, W., Yan, Y., et al.: A new approach to calculate permeability stress sensitivity in tight sandstone oil reservoirs considering micro-pore-throat structure. J. Pet. Sci. Eng. 133, 576–588 (2015)

  50. Vairogs, J., Hearn, C.L., Dareing, D.W., Rhoades, V.W.: Effect of rock stress on gas production from low-permeability reservoirs. J. Pet. Technol. 23(09), 1161–1167 (1971)

  51. Walsh, J.B.: Effect of pore pressure and confining pressure on fracture permeability. In: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, vol. 18, no. 5, pp. 429–435 (1981)

  52. Warpinski, N.R., Teufel, L.W.: In-situ stresses in low-permeability, nonmarine rocks. J. Pet. Technol. 41(4), 405–414 (1989)

  53. Xiao, W., Tao, L.I., Min, L.I., Zhao, J., Zheng, L., Ling, L.I.: Evaluation of the stress sensitivity in tight reservoirs. Pet. Explor. Dev. Online 43(1), 115–123 (2016)

  54. Zhang, H., Liu, H., Luan, G., He, S., Gu, D., Mo, S., et al.: A novel quantitative petrophysical model for the stress sensitivity of tight sandstones. J. Pet. Sci. Eng. 122, 657–666 (2014)

  55. Zhang, R., Ning, Z., Yang, F., Wang, X., Zhao, H., Wang, Q.: Impacts of nanopore structure and elastic properties on stress-dependent permeability of gas shales. J. Nat. Gas Sci. Eng. 26, 1663–1672 (2015)

  56. Zhao, J., Xiao, W., Li, M., Xiang, Z., Li, L., Wang, J.: The effective pressure law for permeability of clay-rich sandstones. Pet. Sci. 08(2), 194–199 (2011)

  57. Ziarani, A.S., Aguilera, R.: Pore-throat radius and tortuosity estimation from formation resistivity data for tight-gas sandstone reservoirs. J. Appl. Geophys. 83(6), 65–73 (2012)

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Acknowledgements

This paper is financially supported by National Natural Science Foundation of China (51474179) and China Major Science and Technique Project (2016ZX05054), which is acknowledged. Meanwhile, this research is also supported by China Scholar Council (CSC No. 201708510122). In addition, we would also like to thank the editor and anonymous reviewers for their constructive comments.

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Correspondence to Zhi-Min Du.

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Zhu, S., Du, Z., Li, C. et al. A Semi-analytical Model for Pressure-Dependent Permeability of Tight Sandstone Reservoirs. Transp Porous Med 122, 235–252 (2018). https://doi.org/10.1007/s11242-018-1001-x

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Keywords

  • Tight gas
  • Pressure-dependent permeability
  • Reservoir condition
  • Microinterstice
  • Stress sensitivity