Fractional diffusion: Performance of fractured wells

Adopting a flux law that is non-local and temporal, a physically consistent approach to better understand transport in tight rocks is proposed. The fundamental solution to the diffusion equation is obtained and used to derive pressure distributions for fractured wells. The most important issue pertaining to the current understanding of fractured wells in tight reservoirs, namely the long linear trends in the production response, is noted, and the potential of new methods to evaluate such reservoirs is discussed. The solution given here also serves as a building block for more complex situations. The concepts proposed may be incorporated into the existing framework with a minimum of effort.