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.

To prevent CO2 leakage and ensure the safety of long-term CO2 storage, it is essential to investigate the flow mechanism of CO2 in complex pore structures at the pore scale. This study focuses on reviewing the experimental, theoretical, and numerical simulation studies on the microscopic flow of CO2 in complex pore structures during the last decade. For example, advanced imaging techniques, such as X-ray computed tomography (CT) and nuclear magnetic resonance (NMR), are used to reconstruct the complex pore structures of rocks. Mathematical methods, such as Darcy's law, Young–Laplace’s law, and the Navier-Stokes equation, are used to describe the microscopic flow of CO2. Numerical methods, such as the lattice Boltzmann method (LBM) and pore network (PN) model, are used for numerical simulation. The application of these experimental and theoretical models and numerical simulation studies is discussed, considering the effect of complex pore structures. Finally, future research is suggested to focus on: (1) Conducting real-time CT scanning experiments of CO2 displacement combined with the developed real-time CT scanning clamping device to realize real-time visualization and provide quantitative description of the flow behavior of CO2 in complex pore structures; (2) The effect of pore structures change on the CO2 flow mechanism caused by the chemical reaction between CO2 and the pore surface, the flow theory of CO2 considering wettability and damage theory in a complex pore structures; (3) The flow mechanism of multi-phase CO2 in complex pore structures; (4) The flow mechanism of CO2 in the pore structures at multiscale and the scale upgrade from microscopic to mesoscopic to macroscopic. Generally, this study focuses on reviewing the research progress of CO2 flow mechanisms in complex pore structures at the pore scale and affords an overview of potential advanced developments to enhance the current understanding of CO2 microscopic flow mechanisms.