Dynamic non-equilibrium effects (DNEs) of imbibition processes in an air-water two-phase fine sandy medium- a...

We systematically investigated DNEs throughout imbibition processes, specifically evaluating: (1) the temporal correspondence between DNE development and changes in water saturation/capillary pressure, and (2) the dominant factors governing DNE magnitude during imbibition. The signal drift during extended testing, and the gravitational effect on both the capillary pressure and water saturation were eliminated. The results indicate that, when water saturation was below a threshold value (∼0.43), the maximum difference between static and dynamic capillary pressures (DPMAX) occurred first, followed sequentially by: the maximum rate of water saturation change over time (RSMAX), minimum capillary pressure in an imbibition step (PMIN), and maximum water saturation (SMAX). In subsequent imbibition steps, this sequence shifted to: RSMAX, DPMAX, PMIN, and SMAX. For smooth imbibition processes, the order of events was: RSMAX, SMAX, PMIN and DPMAX (occurring nearly simultaneously). The imbibition process demonstrated no systematic correlation between the extremum values of capillary pressure (PMIN), water saturation (SMAX), and their respective derivatives (DPMAX, RSMAX). Lag times between consecutive parameter pairs (DPMAX, RSMAX, PMIN, and SMAX) exhibited decreasing trends as the water saturation change rate (ΔSw/Δt) increased. Therefore, in stepwise imbibition processes, DNEs are primarily characterized by: (1) the lag time between initial response points of capillary pressure and water saturation (Δt₁), (2) the lag time between PMIN and SMAX (Δt₂), (3) DPMAX, and (4) the dynamic coefficient τ (Hassanizadeh and Gray, 1990). While Δt₁ and Δt₂ are clearly observable in both stepwise and smooth imbibition processes, they become negligible above 0.43 water saturation. Notably, the maximum dynamic effect (DPMAX) increased with increasing water saturation while τ decreased with increasing water saturation. Furthermore, results confirmed that DNE magnitudes correlated more strongly with water saturation and its rate of change (ΔSw/Δt) than with capillary number, consistent with previous findings. Lag times (Δt₁, Δt₂), τ, and DPMAX constitute meaningful quantitative parameters for characterizing DNEs in stepwise imbibition processes.