Advertisement

Applied Mathematics and Mechanics

, Volume 37, Issue 5, pp 611–626 | Cite as

Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

  • Yizhao Wan
  • Yuewu LiuEmail author
  • Weiping Ouyang
  • Guofeng Han
  • Wenchao Liu
Article

Abstract

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed. Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model (DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density. The pressure propagation is slower in the direction of larger fracture density.

Key words

dual-porosity model (DPM) discrete-fracture model fracture network finite-element method upscaling numerical well test 

Chinese Library Classification

O242.21 O357.3 

2010 Mathematics Subject Classification

76S05 74S05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Barenblatt, G. I., Zheltov, I. P., and Kochina, I. N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]. Journal of Applied Mathematics and Mechanics, 24(5), 1286–1303 (1960)CrossRefzbMATHGoogle Scholar
  2. [2]
    Warren, J. E. and Root, P. J. The behavior of naturally fractured reservoirs. Society of Petroleum Engineers Journal, 3(3), 245–255 (1963)CrossRefGoogle Scholar
  3. [3]
    Kazemi, H. Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Society of Petroleum Engineers Journal, 9(4), 451–462 (1969)CrossRefGoogle Scholar
  4. [4.
    De Swaan, O. A. Analytic solutions for determining naturally fractured reservoir properties by well testing. Society of Petroleum Engineers Journal, 16(3), 117–122 (1976)CrossRefGoogle Scholar
  5. [5]
    Kazemi, H. and Gilman, J. R. Multiphase flow in fractured petroleum reservoirs. Flow and Contaminant Transport in Fractured Rock, 31(91), 267–323 (1993)CrossRefGoogle Scholar
  6. [6]
    Thomas, L. K., Dixon, T. N., and Pierson, R. G. Fractured reservoir simulation. Society of Petroleum Engineers Journal, 23(1), 42–54 (1983)CrossRefGoogle Scholar
  7. [7]
    Coats, K. H. Implicit compositional simulation of single-porosity and dual porosity reservoirs. SPE Symposium on Reservoir Simulation, Society of Petroleum Engineers, Houston (1989)Google Scholar
  8. [8]
    Ueda, Y., Murata, S., Watanabe, Y., and Fanatsu, K. Investigation of the shape factor used in the dual-porosity reservoir simulator. SPE Asia-Pacific Conference, Society of Petroleum Engineers, Sydney (1989)Google Scholar
  9. [9]
    Zimmerman, R. W., Chen, G., Hadgu, T., and Bodvarsson, G. S. A numerical dual-porosity model with semi-analytical treatment of fracture/matrix flow. Water Resources Research, 29(7), 2127–2137 (1993)CrossRefGoogle Scholar
  10. [10]
    Chang, M. M. Analytical Solution to Single and Two-Phase Flow Problems of Naturally Fractured Reservoirs: Theoretical Shape Factor and Transfer Functions, Ph. D. dissertation, University of Tulsa (1995)Google Scholar
  11. [11]
    Quintard, M. and Whitaker, S. Transport in chemically and mechanically heterogeneous porous media I: theoretical development of region-averaged equations for slightly compressible singlephase flow. Advances in Water Resources, 19(1), 29–47 (1996)CrossRefGoogle Scholar
  12. [12]
    Ranjbar, E. and Hassanzadeh, H. Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Advances in Water Resources, 34(1), 627–639 (2011)CrossRefGoogle Scholar
  13. [13]
    Hassanzadeh, H. and Pooladi-Darvish, M. Effects of fracture boundary conditions on matrixfracture transfer shape factor. Transport in Porous Media, 64(1), 51–71 (2006)MathSciNetCrossRefGoogle Scholar
  14. [14]
    Noorishad, J. and Mehran, M. An upstream finite element method for solution of transient transport equation in fractured porous media. Water Resources Research, 3(18), 588–596 (1982)CrossRefGoogle Scholar
  15. [15]
    Baca, R. G., Arnett, R. C., and Langford, D. W. Modeling fluid flow in fractured-porous rock masses by finite-element techniques. International Journal of Methods in Fluids, 4(4), 337–348 (1984)CrossRefzbMATHGoogle Scholar
  16. [16]
    Kim, J. G. and Deo, M. D. Comparison of the performance of a discrete fracture multiphase model with those using conventional methods. SPE Symposium on Reservoir Simulation, Society of Petroleum Engineers, Houston (1999)Google Scholar
  17. [17]
    Hoteit, H. and Firoozabadi, A. Compositional modeling by the combined discontinuous Galerkin and mixed methods. Society of Petroleum Engineers Journal, 11(1), 19–24 (2006)Google Scholar
  18. [18]
    Zhang, D. M., Cai, C. X., Zhang, K. B., Zhan, J. M., and Huang, H. Computational Fluid Mechanics (in Chinese), Sun Yat-sen University Press, Guangzhou (1991)Google Scholar
  19. [19]
    Cinco-Ley, H. and Samaniego-V, F. Fractured reservoir simulation. Society of Petroleum Engineers Journal, 33(09), 1749–1766 (1981)Google Scholar
  20. [20]
    Noetinger, B. and Estebenet, T. Up-scaling of double porosity fractured media using continuoustime random walks methods. Transport in Porous Media, 39(1), 315–337 (2000)CrossRefGoogle Scholar
  21. [21]
    Bourdet, D. Well Test Analysis: The Use of Advanced Interpretation Models, Elsevier, Amaterdam, 63–65 (2002)Google Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yizhao Wan
    • 1
  • Yuewu Liu
    • 1
    Email author
  • Weiping Ouyang
    • 2
  • Guofeng Han
    • 1
  • Wenchao Liu
    • 1
  1. 1.Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.Changqing Downhole Technology Company, Chuanqing Drilling Engineering Company LimitedChina National Petroleum CorporationXianChina

Personalised recommendations