... and limitations in multi-layered field applications in particular. This paper presents a Mittag-Leffler (ML) function decline model which enhances the reliability of forecasts for multi-layered unconventional oil reservoirs by honoring anomalous diffusion physics for each layer. Many traditional decline curve...

... (2018) showed apparent radial or linear flow could exist under anomalous diffusion for heterogeneous reservoirs. In this work, we present a technique for analyzing power-law PIT data, which is typical of most horizontally fractured shale wells. This model is a unique approach to understanding flow...

... can be expressed in a relation between the mean-square displacement (MSD) of the particle, 〈 r 2 〉, and time, t , given by (1) 〈 r 2 〉 ∼ t γ . Fundamentals of anomalous diffusion concept have been discussed in many publications ( Gefen et al. 1983 , Le Mehaute and Crepy...

... Abstract This paper presents an anomalous diffusion based approach for modeling two-phase oil/water flow in fractured nanoporous media, such as that encountered in unconventional oil and gas reservoirs. Production is assumed to be from a multiply fractured horizontal well and the focus...

... Abstract Based on the premises of anomalous diffusion models in fractal porous media, an alternative to dual-porosity based formulations of flow in fractured unconventional reservoirs is presented. The new formulation is implemented in the trilinear flow idealization for a fractured horizontal...