Analytical solutions are presented for the analysis of dual-porosity systems intercepted by hydraulic vertical fractures of finite conductivity. The well can be in an infinite or a bounded dual-porosity system. The outer boundary can be sealed or it can be at constant pressures. pressures. The following flow periods have been identified:

  1. A bilinear flow period typical of finite conductivity fractures. This is recognized by a quarter slope in a conventional log-log crossplot of pressure differential vs. time.

  2. A transition period due to flow from the matrix into the natural fractures.

  3. A pseudo radial flow period recognized by a straight line in a conventional semilograthmic plot.

  4. Boundary effects which can be due to a sealed boundary or an outer boundary at constant pressure.

Recognition of these flow periods allow calculation of parameters such as omega, lambda, distance between natural fractures, permeability, fracture conductivity and permeability, fracture conductivity and half-fracture length. This is illustrated with an example.


Naturally fractured reservoirs have been the object of intensive studies during the last few years. The effect of a fully penetrating vertical fracture of infinite conductivity in a homogeneous reservoir has been studied by Prats, Prats et al., Russel and Truitt, Prats, Prats et al., Russel and Truitt, van Everdingen and Meyer, and Gringarten et al.

Many times naturally fractured reservoirs are hydraulically fractured. For example, this has happened repeatedly in the Austin Chalk and the Appalachian Basin. Houze et al. studied this problem by considering an infinite problem by considering an infinite conductivity vertical fracture in an infinite acting reservoir and concluded that a log-log plot of vs. time should result in an early straight line with a 0.5 slope, followed by a transition period, and reaching pseudo radial flow when pressure in matrix and fractures reach an equilibrium.

Lancaster and Gatens have presented some practical guidelines regarding analysis methods for hydraulically fractured wells in dual-porosity reservoirs. They conclude that pre-fracture well test data are important for a proper post-fracture well test interpretation. post-fracture well test interpretation. From the pre-fracture test one can obtain natural fracture permeability, lambda and omega, critical parameters for the postfracture well test interpretation. postfracture well test interpretation. Aguilera has presented an approximate solution of linear flow in naturally fractured reservoirs.

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