A multifractal geometric model for estimating spontaneous imbibition in an unsaturated fractured core-scale network in a low-permeability reservoir

Several mathematical models have been established for describing the saturated seepage of fracture networks in low-permeability reservoirs, but there is still a lack of systematic research on unsaturated seepage models. Therefore, by combining these single connected fractures into the physical geometry of a parallel plate, a comprehensive spontaneous imbibition model at the fracture and core scales considering a rough wall geometry, streamline tortuosity, and heterogeneity of the fracture size distribution is derived by applying the classical cubic law describing flat flow and fractal geometry theory. Compared with existing models, our proposed model is verified by using experimental data on the spontaneous imbibition of a single fracture and fractured core available from the literature. Based on the established model, the mechanism through which various geometric elements control spontaneous imbibition is analysed at the fracture and core scales. The maximum fracture aperture plays an important role in controlling the wettability evolution behaviour at the core scale, and the fractal dimensions of fracture tortuosity and roughness are more sensitive to spontaneous imbibition in fractured cores than is the fractal dimension of the fracture size distribution. These research results are useful for evaluating the balance between reservoir damage and fracturing effects.