A multiscale model for estimating spontaneous imbibition in tight porous media considering surface effects

Spontaneous imbibition model holds significant theoretical value and application potential in hydraulic fracturing and water migration. However, due to the neglect of nanoscale surface effects in conventional theories governing water flow, existing models fail to accurately describe the spontaneous imbibition in hydrophilic mineral nanopores. To tackle this issue, this study first quantitatively revealed the impact of surface effects on fluid behavior through theoretical derivation and then proposed an improved multiscale imbibition model. The model describes and expresses the surface effect through the interaction energy between fluids and minerals and the dynamic contact angle. Compared with existing models, the applicability of this model was then verified by experimental data of silica nanochannels, Bentheim core, and porous Vycor glass. Subsequently, the theory was employed to investigate the effects of pore size, mineral composition (quartz, muscovite, and montmorillonite), and pore geometry (slit and circular) on spontaneous imbibition behavior. The research findings reveal the impact of geotechnical parameters on the imbibition process: With increasing pore size, the average effective viscosity decreases and the influence of the dynamic contact angle becomes more pronounced, under identical conditions. In addition, compared to circular pores, the attenuation of solid–liquid interfacial interactions in slit pores exhibits a more gradual decay with increasing pore size. Specifically, in circular pores with a radius of 200 nm, the interaction between the pore wall and water can be neglected; however, in slit pores, even when the pore size reaches 1000 nm, the interaction between montmorillonite and water molecules remains significant.