Skip to main content
SpringerLink
Log in

A Model of the Fractal Fluid Loss Coefficient and its Effect on Fracture Length and Well Productivity

  • Published:
Chemistry and Technology of Fuels and Oils Aims and scope

An Erratum to this article was published on 26 July 2015

Loss of the fracturing fluid in hydraulic fracturing is a complex flow process that impacts the effectiveness of the technology, affecting such factors as fracture length and gas-well productivity. Many computational models have been constructed for the fluid loss coefficient, but the models do not account for the fractal character and tortuosity of the porous medium. This study considers these two parameters and proposes a fractal model to calculate the fluid loss coefficient. Fractal permeability is calculated based on the capillary-pressure curves of nine core samples. The permeability values based on fractal theory agree well with the measured values. The fluid loss coefficient determined by the fractal model is higher than the coefficient obtained by standard calculations because of high tortuosity of the porous medium. Predictions of fracture length and gas-well productivity, which depend on the fluid loss coefficient, are discussed and compared, and it is suggested that accurate determination of this coefficient is essential for optimizing hydraulic fracturing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. R. D. Carter, in: Appendix I of “Optimum Fluid Characteristics for Fracture Extension.” Drilling and Production Practice. G. C. Howard and C. R. Fast. American Petroleum Institute, New York (1957) pp. 261–269.

  2. G. C. Howard and C. R. Fast, in: Drilling and Production Practice. American Petroleum Institute, New York (1957), pp. 261–270.

  3. B. B. Williams, J. Petroleum Technology, 22, 882–888 (1970).

    Article  Google Scholar 

  4. A. Settari, SPE J., 20, 487–500 (1980).

    Article  Google Scholar 

  5. A. Settari and M. P. Cleary, SPE J., 36, 1177–1190 (1984).

    Google Scholar 

  6. A. Settari, SPE J., 25, 491–501 (1985).

    Article  Google Scholar 

  7. Y. C. Li et al., Petroleum Production Engineering (2nd ed.). Petroleum Engineering Press, Beijing (2009).

    Google Scholar 

  8. X. Ning, R. P. Marcinew, and T. N. Olsen, Annual Technical Meeting of the Petroleum Society of CIM. May 14–17, 1995. Banff, Alberta, Canada. Paper No. 95–43.

  9. K. Adegbola and C. Boney, SPE International Symposium and Exhibition on Formation Damage Control. February 20–21, 2002. Lafayette, Louisiana. SPE 73759.

  10. R. Gdanski, J. Weaver, B. Slabaugh, et al. SPE European Formation Damage Conference. May 25–27, 2005. Scheveningen, Netherlands. SPE 94649.

  11. H. Jiang, Z. H. Z. Yang, X. G. Li, et al., Journal of Yangtze University (Nature Science Edition) Science & Engineering, 5, No. 1, 87–89 (2008).

  12. J. Li, B. Guo, D. Gao, et al., SPE European Formation Damage Conference. June 7–10, 2011. Noordwijk, Netherlands. SPE 143304.

  13. M. J. Economides and K. G. Nolte, Reservoir Simulation (3rd ed.). John Wiley & Sons (2000).

  14. A. J. Katz and A. H. Thompson, Phys. Rev. Lett., 54, 1325–1328 (1985).

    Article  Google Scholar 

  15. M. A. Bhushan and B. Bhushan, J. Tribology, 112, 205–216 (1990).

    Article  Google Scholar 

  16. M. Sahimi, Flow and Transport in Porous Media and Fractured Rocks. VCH Verlag GmbH, Weinheim (1995), p. 13.

  17. B. M. Yu, L. J. Lee, and H. Cao, Fractals, 9, 365–372 (2001).

    Article  CAS  Google Scholar 

  18. B. M. Yu and L. J. Lee, Ibid., 9, 365–372 (2001).

    CAS  Google Scholar 

  19. B. M. Yu, Applied Mechanics Reviews, 61, pp. 050801–050820.

  20. J. Chang and Y. C. Yortsos, SPE Formation Evaluation, March, 31–38 (1990).

  21. J. A. Acuna and Y. C. Yortsos, Water Resour. Res., 31, 527–540 (1995).

    Article  Google Scholar 

  22. J. A. Acuna, I. Ershaghi, and Y. C. Yortsos, SPE Formation Evaluation, September, 173–179 (1995).

  23. B. M. Yu and P. Cheng, Int. J. Heat Mass Transfer, 45, 2983–2993 (2002).

    Article  Google Scholar 

  24. Y. Shi, J. S. Xiao, M. Pan, et al. J. Power Sources, 160, 277–283 (2006).

    Article  CAS  Google Scholar 

  25. P. Xu and B. M. Yu, Adv. Water Resour., 31, 74–81 (2008).

    Article  CAS  Google Scholar 

  26. V. M. Yu and J. H. Li, Fractals, 15, 386–390 (2007).

    Google Scholar 

  27. B. M. Yu, Chin. Phys. Lett., 1, 158–160 (2005).

    Google Scholar 

  28. Y. J. Feng and B. M. Yu, Fractals, 15, 386–390 (2007).

    Article  Google Scholar 

  29. F. A. L. Dullien, Porous Media, Fluid Transport, and Pore Structure. Academic Press, San Diego (1979).

    Google Scholar 

  30. M. R. J. Wyllie and A. R. Gregory, Ind. Eng. Chem., 47, 1379–1388 (1955).

    Article  CAS  Google Scholar 

  31. J. Comiti and M. Renaud, Chem. Eng. Sci., 44, 1539–1545 (1989).

    Article  CAS  Google Scholar 

  32. A. Koponen, M. Kataja, and J. Timonen, Phys. Rev. E, 54, 406–410 (1996).

    Article  CAS  Google Scholar 

  33. A. Koponen, M. Kataja, and J. Timonen, Ibid., 56, 3319–3325 (1997).

    CAS  Google Scholar 

  34. J. V. Westhuizen and J. P. D. Pless, J. Compos. Mater., 28, 619–637 (1994).

    Google Scholar 

  35. B. M. Yu and J. H. Li, Chin. Phys. Lett., 21, 1569–1571 (2004).

    Article  Google Scholar 

  36. A. S. Abou-Sayed and R. L. Dougherty, SPE Annual Technical Conference and Exhibition. September 16–19, 1984. Houston, Texas, U.S. SPE 13275.

  37. L. J. Harrington, N. F. Whitsitt, and R. R. Hannah, Prediction and Movement of Fluid Interfaces in the Fracture. Southwestern Petroleum Short Course. April, 1973. Texas Tech University. Lubbock, Texas. Conference Report No. CONF-7304106 – Journal ID: CODEN:PSPCD.

  38. K. G. Nolte, SPE Annual Technical Conference and Exhibition. September 23–26, 1979. Las Vegas, Nevada, U.S. SPE 8341.

  39. Sh. L. Li et al., Natural Gas Engineering. Petroleum Industry Press, Beijing (2000).

    Google Scholar 

  40. M. Tan, Zh. Zhang, X. Han, et al., Natural Gas and Oil, 31, No. 1, 54–56 (2013).

    Google Scholar 

  41. H. Cinco-Ley and V. F. Samaniego, SPE Annual Technical Conference and Exhibition. October 9–12, 1977. SPE 6752.

  42. H. Cinco-Ley and V. F. Samaniego, SPE Annual Technical Conference and Exhibition. October 5–7, 1981. San Antonio, Texas. SPE 10179.

  43. S. L. Yang, Fundamentals of Petrophysics. Petroleum Industry Press, Beijing (2011).

    Google Scholar 

Download references

This study was conducted with the support of the National Science Fund of the People’s Republic of China (Grant Nos. 51204138 and 51074134).

Author information

Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Ghengu, China

    Guofa Ji, Zhaozhong Yang, Xiaogang Li, Yanjun Lu & Dan Luo

Authors
  1. Guofa Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhaozhong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaogang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanjun Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dan Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guofa Ji.

Additional information

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, pp. 22 – 28, March– April, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ji, G., Yang, Z., Li, X. et al. A Model of the Fractal Fluid Loss Coefficient and its Effect on Fracture Length and Well Productivity. Chem Technol Fuels Oils 51, 168–180 (2015). https://doi.org/10.1007/s10553-015-0590-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10553-015-0590-0

Keywords

Search

Navigation