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 physics to interpret fractally fractured reservoirs. However, their solutions cannot 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 applicable to whole spatio-temporal ranges, is derived using the Fox H-function. Sensitivity analyses were carried out for various cases. The solution developed here permits the use of early production data. By combining early and late time data, it is possible to determine the two fractal dimensions separately. From the intrinsic property of the Fox H-function, this model makes it possible to capture the history and nonlocality of transport. Therefore, the model provides a general methodology for characterizing the pressure behavior of fractally fractured reservoirs.