A Refined Model Considering Entrance Resistance for Two-Phase Spontaneous Imbibition in Nanopores

Spontaneous imbibition is an important process in enhanced oil recovery, yet its accurate prediction in nanoscale pores remains a significant challenge due to the breakdown of continuum assumptions at the nanoscale. The classical Lucas-Washburn (L-W) equation, which suggests that imbibition length is proportional to the square root of time, fails to capture the complex early-time dynamics in nanopores. Therefore, in this work, coarse-grained molecular dynamics simulations were employed to systematically investigate two-phase imbibition across a range of pore sizes (1.85–7 nm), fluid types (C4–C20 alkanes), and wettability conditions. The results reveal a distinct transition from continuum-dominated to molecularly dominated flow as pore size decreases, with anomalous kinetics that originate from molecular-scale interactions in sub-2-nm pores. A refined imbibition model is proposed that explicitly incorporates an entrance resistance term in addition to the capillary and viscous forces. This new model successfully resolves the overestimated initial velocity by the L-W equation, revealing a dual-regime physics, including an early-time, almost linear regime influenced by entrance resistance, followed by the classical late-time L-W regime. The model demonstrates excellent agreement with molecular dynamics data for mesoscopic nanopores (r ≥ 3.5 nm), validating its physical basis. Although the proposed model is still not predictive due to the implicit inclusion of imbibition rate in the derivision, the findings provide a robust theoretical foundation for describing imbibition in nanopores and highlight the critical need for molecular-scale approaches in extreme nanoconfinement.