Improved triple porosity model for calculating porosity exponent of fractured-vuggy reservoirs based on Maxwell-Garnett mixing rule and anisotropic conductivity analysis

Abstract

Porosity exponent (m) is a key parameter for calculating reservoir oil and gas saturation and evaluating reservoir effectiveness; the development of matrix pores, vug pores, and fractures makes the m response regularity of fractured-vuggy reservoirs unclear, which makes the accurate calculation of saturation difficult. By applying Maxwell-Garnett mixing rule to vuggy reservoirs and conductivity tensor analysis to fractured reservoirs, an improved Triple Porosity Model considering fracture dip angle is established. The newly improved Triple Porosity Model clarifies the response regularity of m to the matrix pores, vug pores, fracture pores, and fracture angles. Based on the improved Triple Porosity Model, the response regularity chart of m is further established. The findings show that: (1) m increases with the increase of fracture dip angle (θ) and the development of vugs; (2) m increases with the development of high-angle fractures and decreases with the development of low-angle fractures; (3) in fractured reservoirs, the fracture dip angle of 33° is the critical dip angle that determines the relationship between m and matrix porosity exponent (mb); (4) an increase in matrix porosity will weaken the influence of vugs, fractures, and fracture dip angle on m, which will eventually make m converge to mb. The field application of fractured-vuggy reservoirs shows that the water saturation calculated by the improved Triple Porosity Model is better in agreement with the core analysis results.