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The fractal geometry is used to model of a naturally fractured reservoir and the concept of
fractional derivative is applied to the diffusion equation to incorporate the history of fluid
flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD)
equation is solved analytically in the Laplace space for three outer boundary conditions.
The analytical solutions are used to analyze the response of a naturally fractured reservoir
considering the anomalous behavior of oil production. Several synthetic examples are
provided to illustrate the methodology proposed in this work and to explain the diffusion
process in fractally fractured systems.
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