A Mathematical Model for Determining Oil Migration Characteristics in Low-Permeability Porous Media Based on Fractal Theory

Oil migration processes are crucially important for determining oil reserve levels and distributions in low-permeability reservoirs. Previous researches have proved that the macroscopic parameters of oil migration processes are controlled by microscopic pore properties in low-permeability media. To analyze the relationship between pore-scale parameters and the oil migration process in low-permeability formations, a mathematical model combining the capillary bundle model and fractal theory is developed in this work. The accuracy of the proposed model is validated via comparisons with three well-designed oil charging experiments using natural core samples. Based on the validated model, the influence of four factors (pore fractal dimension, tortuosity fractal dimension, the wettability of the rock surface, and the formation water viscosity) on oil migration processes in low-permeability media is analyzed. Oil saturation and effective permeability are used as the output parameters for reflecting changes in the oil migration process. The calculation results indicate that oil saturation decreases as pore fractal dimension, tortuosity fractal dimension, the hydrophilicity of the rock surface, and brine viscosity increase. On the other hand, effective permeability decreases as tortuosity fractal dimension and formation water viscosity increase, but increases with pore fractal dimension. Moreover, the wettability dependence of effective permeability is relatively weak.