Computational Geosciences

, Volume 22, Issue 1, pp 413–421 | Cite as

Analytical solution and Bayesian inference for interference pumping tests in fractal dual-porosity media

  • Mohamed Hayek
  • Anis Younes
  • Jabran Zouali
  • Noura Fajraoui
  • Marwan Fahs
Original Paper


A new analytical solution is developed for interference hydraulic pumping tests in fractal fractured porous media using the dual-porosity concept. Heterogeneous fractured reservoirs are considered with hydrodynamic parameters assumed to follow power-law functions in radial distance. The developed analytical solution is verified by comparison against a finite volume numerical solution. The comparison shows that the numerical solution converges toward the analytical one when the size of the time step decreases. The applicability of the fractal dual-porosity model is then assessed by investigating the identifiability of the parameters from a synthetic interference pumping test with a set of noisy data using Bayesian parameter inference. The results show that if the storage coefficient in the matrix is fixed, the rest of the parameters can be appropriately inferred; otherwise, the identification of the parameters is faced with convergence problems because of equifinality issues.


Fractured porous media Interference pumping test Dual porosity Fractal media Bayesian inversion 


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This work was partially supported by the GdR MoMaS (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN), France, and by the French National Research Agency (ANR) through the program AAP Blanc - SIMI 6 project RESAIN (no. ANR-12-BS06-0010-02).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mohamed Hayek
    • 1
  • Anis Younes
    • 2
    • 3
    • 4
  • Jabran Zouali
    • 2
  • Noura Fajraoui
    • 5
  • Marwan Fahs
    • 2
  1. 1.INTERA IncorporatedAustin (USA)WettingenSwitzerland
  2. 2.LHyGeS, UMR-CNRS 7517Université de Strasbourg/EOST/ ENGEESStrasbourgFrance
  3. 3.IRD UMR LISAHMontpellierFrance
  4. 4.LMHEEcole Nationale d’Ingénieurs de TunisTunisTunisia
  5. 5.ETH ZurichZurichSwitzerland

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