A fractal reservoir may be thought of as having a spatial dimension that falls between the Eucledian space dimensions 1, 2 and 3. This concept may be unfamiliar to many. The objective of this study is to show that a model based on a fractal concept may be a useful complement to conventional models. To this end we investigate the productvity of wells in fractal reservoirs. The productivity index has a clear economic significance. Unfamiliar ways of characterizing rock properties are discussed by use of simplified models.

For clarity, we discuss steady state flow in a naturally fractured reservoir. A steady state condition depends on a constant pressure outer boundary. We investigate analytical solutions. These include the conventional ones as special cases. The application of the proposed solutions will be in well testing, estimation of natural flow, economic modelling and reservoir characterization.

The fractal model leads to rock properties of powerlaw dependence on the spatial variable. We find that this description may reflect the length scale of the elementary volume, REV. Fracture architecture; changing flow area and stress sensitivity may also contribute to powerlaw dependency. The analytical solutions obtained are valid for any reservoir that may be characterized by simple powerlaw expressions whether fractal or not.

We find that equation for the flow efficiency of a fractal reservoir depends on three dimensionless parameters. The flow efficiency is sensitive to a parameter (the difference between the fractal dimension and the conductivity index), dimensionless distance and skin.

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