Analysis of radial composite systems based on fractal theory and fractional calculus

This paper analyzes the mathematical modeling of a two-region composite reservoir using the concepts of fractal geometry and fractional calculus. Heterogeneity of the reservoir is considered based on fractal geometry. Fractional calculus is used to consider production history in fractal reservoirs. An analytical solution is derived for the pressure-transient behavior of a well in a radial composite system when wellbore storage and skin effects are significant. Some new type-curves are developed under three outer boundary conditions: infinite, closed and constant-pressure. These new type curves can be used to analyze well-tests from a variety of enhanced oil recovery projects, geothermal reservoirs and acidization projects, more accurately.