Method of Fractal Reservoir with Irregular Crack Bedrock System and Its Application for Well Test Analysis

Abstract

In this paper the fractal theory is used to derive formulas for calculating seepage velocity, permeability, and porosity for the flow of/kids in porous media with dual fractal dimensions (capillary diameter and capillary distortion fractal dimension). The dual fractal model is applicable for most limestone reservoirs. It is shown that the percolation equation of micro-compressible fluids, or the double fractal pressure diffusion equation, is a partial differential equation. The equation is solved for the pressure drop and pressure recovery conditions. The solutions for the actual wellbore consider wellbore storage and skin Wen parameters, and a model curve of an infinite reservior is drawn. Analysis of the double fractal media shows that the traditional well test analysis methods, like the pressure drop semi-log linear curve method, pressure recovery Horner method, and Gringarten-Bourdet diagram method will bring great errors, especially when the distortion fractal dimension is large. Using the established well test model, the parameters of the limestone oil reservoir and the unstable pressure data are measured, and the accurate oil reservoir effective permeability, fractal length, and fractal dimensions are calculated.