A Comparative Study of Steady-state Effective Permeability Calculation Methods in Naturally Fractured Reservoir

Jiyu Wang

Research output: ThesisMaster's Thesis

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This thesis presents ways to estimate the effective permeability of naturally fractured reservoir under Discrete Fracture and Matrix Model (DFM). A Simple homogenous, steady state model, that contains an injection well and a production well at a certain distance, is firstly introduced. The pressure of the injection well can be estimated by analytical solution or numerical solution. The analytical solution is based on Darcy’s law combined with the principle of superposition and used to interpret pressure and rate response by applying reservoir homogenization. The numerical solution is based on the Finite Element Method (FEM), as implemented in CSMP++. FEM model is used to get pressure and rate response in the case where analytical model does not exist, but this response is interpreted in terms of analytical models to estimate equivalent permeability. The pressure response estimated from analytical solution and numerical solution is compared. After comparison, models with varied fracture properties (geometry, intensity, size) are run with CSMP++. For radial flow, spherical flow and linear flow, the effective permeability is estimated by converted Darcy’s law equation, once the pressure of injection well solved by CSMP++. But this can only be done for the homogeneous case, because the only case for which an analytical solution has been found previously. The injector-producer pair of wells in all models is with arbitrary completion length, because the height of the formation is not known. This pairs of wells have been operated long enough at a constant rate, so that a steady-state flow exists. The tasks accomplished by this thesis are (a). Use of homogeneous model verifies numerical method with analytical method. The difference between them is no more than 5% for models without fractures. Only with the numerical method, we can solve The permeability in complex DFM models, so that look for the equivalent k of DFM. (b). Through FEM analysis, the influence of fracture properties on the effective permeability is measured. Fracture size distribution and fracture orientation also play an important role for effective permeability. (c). The effective permeability estimated in linear flow is used as benchmark. Both radial and spherical flow interpretations result in an overestimated effective permeability. (d). The appropriate value of maximum element size is balancing simulation time and accuracy is analyzed as well. (e). Circumscribed triangle well in numerical models represents circular well in analytical methods. From the DFM simulations, it is found the parameters of power law distribution contribute to mean fracture size distribution.
Translated title of the contributionEine vergleichende Studie der Steady-State effektive Permeabilität Berechnungsmethoden im natürlich gekluefteten Reservoir
Original languageEnglish
Awarding Institution
  • Montanuniversität
  • Lang, Philipp, Co-Supervisor (internal)
  • Matthäi, Stephan, Supervisor (internal)
Award date14 Dec 2012
Publication statusPublished - 2012

Bibliographical note

embargoed until null


  • Effective Permeability
  • DFM
  • Analytical Solution
  • Numerical Solution
  • Principle of Superposition

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