Spontaneous imbibition is a capillary-driven flow phenomenon that exists widely in nature and is important for several industries. Recently, Tolman length has been introduced to improve the classical Lucas-Washburn imbibition model, in order to alleviate the deviations in calculating the capillary pressure. However, imbibition experiments to measure Tolman length have been scarce. In addition, the fluid-wall friction has a considerable impact on the imbibition process, while it is often ignored. In this work, imbibition experiments under specific conditions are carried out to measure the values of Tolman length, and the fluid-wall friction is taken into consideration in the equilibrium equation. The water uptake model in fractures is adopted to make corrections to the rise of water level. The experimental results show that Tolman length decreases first and then rises with the increasing curvature radius of liquid-gas interface. The data reveal that the Tolman length-based model can better describe the real imbibition processes than the classical Lucas-Washburn model.

In this work the problem of displacing a ganglion of a fluid by another immiscible one in capillaries is investigated. A modeling approach is developed to predict the location of the ganglion with time. The model describes two patterns; namely, when the ganglion totally exists inside the tube, and when the advancing interface of the ganglion has broken through the exit of the tube. The model is valid for the case in which the ganglion is wetting as well as when it is nonwetting to the wall of the tube. It also considers the situation in which both the advancing and the receding interfaces assume, generally, different contact angles. For the special case when the displacement process is quasistatic, both the receding and the advancing contact angles may be considered the same. Under these conditions, interfacial tension force plays no role and the ganglion moves as a plug inside the tube with a constant velocity. When the viscosity ratio between the invading fluid and the ganglion is one (i.e., both phases are having the same viscosity) the motion reduces to the Hagen-Poiseuille flow in pipes. Once the advancing interface breaks through the exit of the tube, interfacial tension starts to take part in the displacement process and the ganglion starts to accelerate or decelerate according to the viscosity ratio. When the ganglion is nonwetting, interfacial tension becomes in the direction of the flow and is opposite to the flow otherwise. The model accounts for external forces such as pressure and gravity in addition to capillarity. A computational fluid dynamics analysis of this system is conducted for both types of wettability scenarios and shows very good match with the results of the developed model during both the two modes of flow patterns. This builds confidence in the developed modeling approach. Other cases have also been explored to highlight the effects of other scenarios.

After fracturing operations, a large amount of fracturing fluid is retained in shale fracture network, resulting in low flowback efficiency. This has been attributed to the imbibition of fracturing fluid into matrix pores. However, it is unclear how the imbibition mechanism is involved, what are its governing laws and controling parameters in fracture networks? Based on the three-dimensional water imbibition theory of matrix blocks, a fracture network model is established, and a number of dimensionless controling parameters are proposed and analyzed for flowback efficiency. The results show that the imbibition characteristics of fracturing fluid in fracture network are mainly determined by two dimensionless numbers; namely, dimensionless imbibition time, fracture width, and imbibition capacity. The dimensionless imbibition time characterizes the contact time between the fracturing fluid and shale formation, which negatively correlates to the flowback efficiency. The dimensionless fracture width is the ratio of the fracture width to the rock length, which is inversely proportional to the flowback efficiency. Smaller value of the dimensionless fracture width corresponds to larger contact area of fracturing fluid and shale, leading to a lower flowback efficiency. The dimensionless imbibition capacity depicts the capacity of shale reservoirs to imbibe fracturing fluid, which has a negative linear correlation with flowback efficiency. In addition, dimensionless time and fracture width are related to the fracturing operations, and are enhanced by increasing the shut-in periods and proppant concentration. Therefore, the flowback efficiency can be controlled by changing fracturing operations. The predictive method of the flowback efficiency established here is of great significance for reservoir damage analysis and flowback regime optimization.