Analytical solution for anomalous diffusion in fractured nano-porous reservoirs
This dissertation presents an analytical fluid flow model for multi-fractured horizontal wells in unconventional naturally fractured reservoirs. The solution builds on anomalous diffusion concept and fractional calculus to account for non-uniform velocity in highly disordered porous media. The mathematical model is derived for an isothermal, single phase and slightly compressible fluid. The model computes the transient bottomhole pressure solution for the well and is referred to as Tri-Linear Anomalous Diffusion and Dual-Porosity (TADDP) model. In this work, a time-dependent flux incorporating ...