Transport in Porous Media

, Volume 95, Issue 1, pp 239–268 | Cite as

Transient Pressure Behavior of Reservoirs with Discrete Conductive Faults and Fractures

  • Denis Biryukov
  • Fikri J. KuchukEmail author
Open Access


Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior.


Discretely fractured reservoirs Discretely faulted reservoirs Pressure diffusion in fractured porous media Uniform-pressure boundary condition Pressure transient well testing 

List of symbols





Gegenbauer polynomials

E1, E2

Exponential integrals


Error function


Fracture conductivity


Formation thickness


Heaviside step function


Modified Bessel Function of the second kind




Fracture/fault half-length




Flow rate or flux density


Radius or radial coordinate


Laplace transform variable


Chebyshev polynomial








Vertical coordinate




The Dirac delta functional


Diffusivity for pressure






Dummy variable


Dummy variable







Initial or original




Laplace transform



The authors are grateful to Schlumberger for permission to publish this article, and would like to thank Dr. Jacob Bear, Technion-Israel Institute of Technology, and Dr. Atilla Aydin, Stanford University, California, for valuable discussions of fractured media. We also thank Amine Ennaifer, Kirsty Morton, and Richard Booth, Schlumberger, for valuable discussions of naturally fractured reservoirs.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.SchlumbergerClamart CedexFrance

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