Spontaneous Imbibition Dynamics of Liquids in Partially-Wet Nanoporous Media: Experiment and Theory

Abstract

Nanoscale spontaneous imbibition is a common process in nanoporous soil and unconventional reservoirs. Due to the complexity of these natural nanoporous media, the relevant spontaneous imbibition dynamics are still unclear. Thus, this paper studies spontaneous imbibition dynamics of liquids into a nanoporous carbon scaffold (NCS, with controllable wettability and pore geometry). The effects of evaporation and surfactant on spontaneous imbibition are also examined. For low-volatility liquids, a linear relationship between spontaneous imbibition height ( $$H$$ ) and square root of time ( $$\sqrt{t}$$ ) is observed. A modified Lucas–Washburn (L–W) equation is developed to describe the corresponding dynamics and to predict the NCS effective radius and the advancing water contact angle. A dimensionless time function is presented, which includes the properties of solid and liquid and their interactions, and can be used for upscaling spontaneous imbibition data in nanoporous media from laboratory to reservoir scales. Both a larger NCS pore diameter and pore throat diameter cause faster imbibition. The addition of surfactant into an aqueous solution increases the imbibition rate, although this influence is suppressed with pore size decrease. In contrast, for high-volatility liquids, a significant deviation from the linear relationship between $$H$$ and $$\sqrt{t}$$ is found at late times. The modified L–W equation is further developed to include evaporation effect. This study thus provides fundamental understanding of spontaneous imbibition dynamics at nanoscales. The developed theoretical models are expected to be applicable to important problems such as water infiltration into soil, fracturing fluid loss in unconventional reservoirs, and electrolyte migration in electrochemical devices.