Numerical investigation of 1D anomalous diffusion in fractured nanoporous reservoirs
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This dissertation presents a numerical anomalous-diffusion model for well performance analysis in unconventional wells and investigates its applicability to actual field data. Motivation for this research arises from the limitations of current modeling approaches to properly capture the production characteristics observed in complex nanoporous formations. First, a linear (1D) anomalous-diffusion model for single-phase slightly compressible flow is developed. To do so, Darcy’s Law is replaced by a more general fractional flux law incorporating long-range spatial and temporal pressure dependencies. ...