Abstract
SUMMARY This paper presents pressure transient behavior in reservoirs with stochastic fractal geometry patterns. When a fractal object is embedded in an Euclidean porous medium, permeability and porosity variations in the medium are power functions of radial distance from wells. A three-region composite model, where the middle region is fractal, is proposed for these systems and an analytical solution for pressure transients is derived. A field pressure buildup test from a reservoir with deep damage problems is analyzed by this composite fractal model. Pressure transients in 1-D heterogeneous reservoirs with statistical fractal correlation functions of fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) are also studied, using a radially multicomposite model. Well test-derived effective permeabilities of multiple heterogeneity realizations are found to be close to the harmonic average of permeability distributions.
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