Application of fractal geometry to describe reservoirs with complex structures

Abstract

Abstract This study provides basic instantaneous source functions for different source-reservoir geometries in infinite fractal reservoirs (FRs) and infinite slab FRs. The concept of fractal geometry (FG) has already been adopted to analyse and model well-reservoir systems with complex structures. All these complexities have been modelled through a partial differential equation called fractal diffusivity equation (FDE). In this paper, by use of the source/Green’s function technique, we analytically solve the FDE for different boundary conditions, i.e., different source-reservoir geometries. The wellbore pressure response for horizontal wells in an infinite slab FR (synthetic example) is derived and analysed to illustrate the applications of the provided analytical source solutions and how to use these solutions.