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In efforts to reduce uncertainties about effects of minor changes in the pore structure of porous media on dynamic nonequilibrium effects (DNEs), we monitored water saturation-capillary pressure relationships in both dynamic flow and static states in stepwise drainage processes of a sandy medium. The acquired data were used to detect DNE and their changes with time in each drainage step and construct new parameters to characterize DNE. Effects of factors affecting water flow-including capillary number, water saturation, rate of change of water saturation with time (Delta S-w/Delta t), and the maximum value of this rate (RSMAX)-on the magnitude of the DNE were then determined. Results show that entry pressures are considerably larger under dynamic flow conditions than under static flow conditions, and DNE only occurs when the water saturation exceeds a threshold value in a drainage process. During either a smooth drainage or drainage step, the maximum capillary pressure (PMAX) is reached before the minimum water saturation (SMIN). Moreover, in drainage steps RSMAX occurs before the maximum difference between the capillary pressures associated with the static and dynamic states (DPMAX), except when they start from the saturated state. Accordingly, DNEs in a drainage step are mainly reflected in the time between PMAX and SMIN (Delta t), DPMAX, the average sum of the squares of the difference between capillary pressures of the static and dynamic states (DPAVE), and the dynamic coefficient tau (which is often used to characterize DNE). Furthermore, our results indicate that the water saturation and its rate of change with time are more important parameters than the capillary number for modeling DNE in a drainage process, and we detected no clear correlation between either maximum or minimum values of and the timing of the most significant DNE during drainages. tau appears to characterize DNE effectively in smooth drainage processes, while Delta t, DPAVE, and DPMAX constitute meaningful supplementary parameters for the characterization of DNE in a drainage step of a stepwise drainage.

Plain Language Summary We investigated both smooth and stepwise drainage processes, and the influences of the (i) capillary number, (ii) water saturation, and (iii) rate of change of water saturation with time on the magnitude of DNE were determined. We found that entry pressures are considerably larger under dynamic flow conditions than under static flow conditions, and DNE only occurs when the water saturation exceeds a threshold value in a drainage process. During either a smooth drainage or drainage step, the maximum capillary pressure (PMAX) reaches earlier than the minimum water saturation (SMIN). The magnitude of the DNE is more correlated with the water saturation and its change ratio with respect to time, rather than with the capillary number. DNE in a drainage step is mainly reflected in the time between PMAX and SMIN (Delta t), DPMAX, the average sum of the squares of the difference between capillary pressures of the static and dynamic states (DPAVE), and the dynamic coefficient tau. We also detected that tau appears to characterize DNE effectively in smooth drainage processes, while Delta t, DPAVE, and DPMAX constitute meaningful supplementary parameters for the characterization of DNE in a drainage step of a stepwise drainage.