The Influence of Pore Structure of the Core-Scale Fracture-Controlled Matrix Unit on Imbibition: Model Construction and Definition of the Fractal Coefficient

Abstract

Abstract Imbibition oil recovery plays an important role in the development of low-permeability fractured reservoirs. However, the effects of the complex pore structure of the matrix on imbibition have not been considered comprehensively at different scales in the scientific literature. This paper reports a study of the mechanisms of influence of different matrix pores on imbibition recovery ratio and defines the concept of a fractal coefficient using the method of combining numerical simulation at the core scale with mathematical methods at a pore scale. A matrix model with different pore fractal dimensions and tortuosity of the capillary was established using Python language programming. Y-type and S-type were used to characterize the fractures, and a two-dimensional fracture-controlled matrix unit core-scale numerical model with complex pore structures was established. Based on phase field theory, an oil-water two-phase imbibition numerical simulation was conducted. Comparisons of numerical simulation results and microscopic analysis indicated that imbibition recovery ratio was 39.28% and 50.94%, respectively. The imbibition law revealed by the numerical simulation results is consistent with the results of the microscopic imbibition experiment, and the imbibition effect of bifurcated fractures was better than that of simple curved fractures. As the pore fractal dimension and tortuosity of the capillary increased, the imbibition recovery ratio decreased. A comparison of results of the mathematical model demonstrated that there was a difference between the pore scale and core scale because the pore fractal dimension and capillary tortuosity changed dynamically with pore structure at the core scale. Thus, a parameter that characterizes the relative change of pore fractal dimension and tortuosity was defined and called the fractal coefficient. When the skeleton particles are 200, 400, and 500, the fractal coefficient were calculated to be 0.625 and 0.6, respectively, indicating that when the pore structure changes, the imbibition recovery ratio should be dominated by capillary tortuosity.