Fractional-calculus-based formulation of the fractured wells in fractal radial composite reservoirs

摘要

This paper goes into the behavior of a vertically hydraulic fractured well in a radial composite system with complex structure. Using fractal geometry, a mathematical model of this type of reservoir is developed in terms of two important fractal parameters; i.e., fractal topological dimension (d(f)) and fractal dynamical index (theta). Moreover, the fractional derivative approach is used to model the fluid transport in porous media and explain the dynamical properties of the system. An infinitesimally thin skin at the discontinuous boundary is considered to explain the actual behavior of radial composite reservoirs. Having applied the Laplace transformation approach and making use of a rigorous method, an analytical solution for hydraulic fractured wells is attained in a closed form. The importance of having a closed form solution and its application in analyzing the pressure-transient behavior of fractured wells in composite reservoirs are shown by investigating the effects of the reservoir parameters in seven synthetic examples.