Fractional derivatives: Application to transient flow

Concepts of classical diffusion are generalized through fractional derivatives to explain features of anomalous diffusion that are sometimes evident on transient tests. A constitutive equation based on concepts used to model a continuous time random walk (CTRW) is described. This model does not assume Darcy-like flux behavior for the evolution of the pressure distribution and is global in character. Although the starting point is quite different, fractional derivatives have been used to study transport in fractal structures. Consequently, we link with solutions in the literature for fractal systems and provide perspectives that are perhaps informative.

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► We extend concepts of analysis of pressure tests based on classical diffusion.
► A new model to analyze transients with anomalous features is outlined.
► A model is based on CTRW concepts is presented