Fractal model of spontaneous imbibition in low-permeability reservoirs coupled with heterogeneity of pore seepage channels and threshold pressure

Spontaneous imbibition (SI) is an important mechanism for enhancing oil recovery in low-permeability reservoirs. Due to the strong heterogeneity, and the non-Darcy flow, the construction of SI model for low-permeability reservoirs is extremely challenging. Commonly, traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure (TP) on imbibition. Therefore, in this work, based on capillary model and fractal theory, a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established. On this basis, the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil. The proposed new SI model was verified by imbibition experimental data. The study shows that for weakly heterogeneous cores with permeability of 0–1 mD, the traditional SI model can characterize the imbibition process relatively accurately, and the new imbibition model can increase the coefficient of determination by 1.05 times. However, traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10–50 mD. The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem, and the determination coefficient is increased from 0.344 to 0.922, which is increased by 2.68 times. For low-permeability reservoirs, the production of the oil in transitional pores (0.01–0.1 μm) and mesopores (0.1–1 μm) significantly affects the imbibition recovery, as the research shows that when the heterogeneity of pore seepage channels is ignored, the oil recovery in transitional pores and mesopores decreases by 7.54% and 4.26%, respectively. Sensitivity analysis shows that increasing interfacial tension, decreasing contact angle, oil–water viscosity ratio and threshold pressure will increase imbibition recovery. In addition, there are critical values for the influence of these factors on the imbibition recovery, which provides theoretical support for surfactant optimization.