Pressure dynamics of asymmetrically fractured wells in arbitrary shaped reservoir

  • Yu-long Zhao (赵玉龙)Email author
  • Bao-chao Shan (单保超)
  • Lie-hui Zhang (张烈辉)


A numerical model was established and solved by boundary element method and coupled boundary/finite element method to analyze pressure dynamics of an asymmetrically fractured well in an arbitrary shaped reservoir. The model was derived and solved in Laplace domain, with different flow regimes divided considering wellbore storage and skin effects or not. Parameters sensitivity analyses, i.e. asymmetry factor, fracture conductivity, outer boundary shape, boundary size and well location, were conducted. Model accuracy was validated by comparing it with two simplified cases and a field case study. The study is helpful for well testing interpretation and hydraulic fracturing design.

Key words

fractured well finite conductivity fracture pressure dynamics numerical method arbitrary drainage area 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Wang H., Guo J., Zhang L., A semi–analytical model for multilateral horizontal wells in low–permeability naturally fractured reservoirs [J]. J Petrol Sci Eng, 2017, 149:564–578CrossRefGoogle Scholar
  2. [2]
    Ding D., Wu Y., Jeannin L. Efficient simulation of hydraulic fractured wells in unconventional reservoirs [J]. J Petrol Sci Eng, 2014, 122: 631–642CrossRefGoogle Scholar
  3. [3]
    Yuan B., David A. Wood, Production analysis and performance forecasting for natural gas reservoirs: Theory and practice (2011–2015) [J]. J Nat Gas Sci Eng, 2015, 26: 1433–1438CrossRefGoogle Scholar
  4. [4]
    Zhang L., Guo J., Liu Q. A new well test model for stress–sensitive and radially heterogeneous dual–porosity reservoirs with non–uniform thicknesses, Journal of Hydrodynamics, Ser. B [J]. 2011, 23(6):759–766.Google Scholar
  5. [5]
    Huang Y., Cheng S., Yu H., He Y., Lin B., Feng N., A semianalytical approach to estimate fracture closure and formation damage of vertically fractured wells in tight gas reservoir [J]. J Petrol Sci Eng, 2017, 150: 85–90CrossRefGoogle Scholar
  6. [6]
    Chen Z., Liao X., Zhao X., Dou X., Zhu L., A semi–analytical mathematical model for transient pressure behavior of multiple fractured vertical well in coal reservoirs incorporating with diffusion, adsorption, and stress–sensitivity [J]. J Nat Gas Sci Eng, 2016,29: 570–582Google Scholar
  7. [7]
    Zhao Y., Zhang L., Liu Y., Hu S., Liu Q. Transient pressure analysis of fractured well in bi–zonal gas reservoirs [J]. J Hydrol, 2015, 524: 89–99CrossRefGoogle Scholar
  8. [8]
    Kambi. Razminia, Abolhassan Razminia, Delfim F.M. Torres, Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure [J]. Applied Mathematics and Computation, 2015, 257: 374–380MathSciNetCrossRefGoogle Scholar
  9. [9]
    Li D., Zhang L., John Y. Wang, Lu D., Du J., Effect of adsorption and permeability correction on transient pressures in organic rich gas reservoirs: Vertical and hydraulically fractured horizontal wells [J]. J Nat Gas Sci Eng, 2016, 31: 214–225CrossRefGoogle Scholar
  10. [10]
    Zhang Z., He S., Liu G., Guo X., Mo S. Pressure buildup behavior of vertically fractured wells with stress–sensitive conductivity [J]. J Petrol Sci Eng, 2014, 122: 48–55CrossRefGoogle Scholar
  11. [11]
    Ibrahim S.N., Pressure–transient analysis of infinite–conductivity fractured gas wells producing at high–flow rates [J]. J Petrol Sci Eng, 2008, 63(1–4,): 73–83Google Scholar
  12. [12]
    Zhao, Y.L., Zhang, L.H., Xiong, Y., et al. Pressure response and production performance for multi–fractured horizontal wells with complex seepage mechanism in box–shaped shale gas reservoir [J]. Journal of Natural Gas Science and Engineering, 2016, 32: 66–80.CrossRefGoogle Scholar
  13. [13]
    Ibrahim Sami Nashawi, Constant–pressure well test analysis of finite–conductivity hydraulically fractured gas wells influenced by non–Darcy flow effects [J]. J Petrol Sci Eng, 2006, 53(3–4): 225–238.Google Scholar
  14. [14]
    Ibrahim Sami Nashawi, Adel H. Malallah, Well test analysis of finite–conductivity fractured wells producing at constant bottomhole pressure [J]. J Petrol Sci Eng, 2007, 57(3–4):303–320.Google Scholar
  15. [15]
    Yan X., Huang Z., Yao J., Song W., Li Y., Gong L., Theoretical analysis of fracture conductivity created by the channel fracturing technique [J]. J Nat Gas Sci Eng, 2016, 31:320–330.CrossRefGoogle Scholar
  16. [16]
    Zhao Y.L., Zhang, L.H., Shan, B.C. Mathematical model of fractured horizontal well in shale gas reservoir with rectangular stimulated reservoir volume [J]. Journal of Natural Gas Science and Engineering, 2018, 59:67–79CrossRefGoogle Scholar
  17. [17]
    Bennet, C. O. Influence of fracture heterogeneity and wing length on the response of vertically fractured wells [J]. SPE J., 1983, 23: 219–230.Google Scholar
  18. [18]
    Fernando, R. Cinco–Ley, H. Evaluation of fracture asymmetry of finite conductivity fractured wells[J]. SPE production Evaluation, 1992, 7(2): 233–239.CrossRefGoogle Scholar
  19. [19]
    Resurreicão, C. E. S., Fernando, R. Transient rate behavior of finite–conductivity asymmetrically fractured wells producing at constant pressure [C]. Proceedings SPE Annual Technical Conference and Exhibition, Dallas, TX, 1991.Google Scholar
  20. [20]
    Wang L, Wang X. Type curves analysis for asymmetrically fractured wells [J]. ASME J. Energy Resour. Technol.2013, 136(2): 023101.Google Scholar
  21. [21]
    Wang L., Wang X., Li J., and Wang J. Simulation of pressure transient behavior for asymmetrically finite–conductivity fractured wells [J]. Transp Porous Med, 2013, 97: 353–372.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Yu-long Zhao (赵玉龙)
    • 1
    Email author
  • Bao-chao Shan (单保超)
    • 1
    • 2
  • Lie-hui Zhang (张烈辉)
    • 1
  1. 1.State Key Laboratory of Oil and Gas Reservoir Geology and ExploitationSouthwest Petroleum UniversityChengduChina
  2. 2.State Key Laboratory of Coal CombustionHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations