Pressure behavior of transport in fractal porous media using a fractional calculus approach

Many authors have used theories of anomalous diffusion in the field of phys ics to interpret fractally fractured reservoirs. However; their solutions c annot separate the two fractal dimensions d(f) and d(w), and their results are not valid in the early time range. In this study, a new general constant-flow-rate solution, which is applicab le to whole spatio-temporal ranges, is derived using the Fox H-function. Se nsitivity analyses were carried out for various cases. The solution develop ed here permits the use of early production data. By combining early and la te time data, it is possible to determine the two fractal dimensions separa tely. From the intrinsic property of the the Fox H-function, this model mak es it possible to capture the history and nonlocality of transport Therefor e, the model provides a general methodology for characterizing the pressure behavior of fractally fractured reservoirs.