Fractional diffusion in naturally fractured unconventional reservoirs

The objective of the research presented in this Master of Science thesis is to examine the concept of anomalous diffusion as an alternative to the conventional dual-porosity idealizations used to model the stimulated reservoir volume (SRV) around fractured horizontal wells in tight, unconventional reservoirs. The motivation is the recent skepticism about the applicability of dual-porosity models to fractured reservoirs due to the scale and discontinuity of the fractures and the complexity of the heterogeneous, nano-porous matrix and the increased awareness of the promises of fractional derivatives in representing anomalous diffusion in highly heterogeneous porous media.;A trilinear, anomalous-diffusion (TAD) model has been developed for fractured horizontal wells surrounded by an SRV in this work and compared with the existing trilinear, dual-porosity (TDP) model. The trilinear flow model is used because of its relative simplicity and availability for the dual-porosity idealization, which allows a direct comparison. The work includes the analytical solution of a general, 1D time-fractional diffusion equation for a bounded system and the implementation of the new solution in the trilinear model formulation for the fractured inner reservoir. Numerical evaluation of the solution has been performed by a computational code in Matlab. The differences, shortcomings, and advantages of both models are discussed. The application of the models to field data is also demonstrated.;A discussion of the characteristics of the pressure and derivative responses obtained from the TAD model is also provided and related to the fractal nature of fractured media. Physical interpretations are also assigned to fractional derivatives and the phenomenological coefficient of the fractional flux law. It is shown that the anomalous diffusion formulation does not require explicit references to the intrinsic properties of the matrix and fracture media and thus relaxes the stringent requirements used in dual-porosity idealizations to couple matrix and fracture flows. The trilinear anomalous-diffusion model should be useful for performance predictions and pressure- and rate-transient analysis of fractured horizontal wells in tight unconventional reservoirs.