Direct Quantification of Dynamic Effects in Capillary Pressure for Drainage–Wetting Cycles

The constitutive relationship between capillary pressure ( P c) and wetting fluid saturation ( S w), or retention curve, is needed to model multiphase flow in porous media. This relationship is usually measured under static conditions; however, transient flow is governed by a dynamic relationship between the P c and S w. Differences in P c measured under static and dynamic conditions are due to dynamic effects typically defined as a product of a dynamic coefficient (τ) and the rate of change in S w. To date, relatively few experimental studies have been conducted to directly quantify the magnitude of this effect. In this study, the magnitude of τ was quantified by measuring both static and dynamic retention curves in repeated drainage and wetting experiments using a field sand. The 95% confidence intervals for the static retention curves showed that the dynamic retention curves were statistically different. The measured τ for primary drainage generally increased with decreasing S w. The measured τ values were also compared with those estimated using a different approach based on redistribution time. The measured and estimated τ were in close agreement when the redistribution times were 146 s for the wetting cycle and 509 s for primary and main drainage cycles. The shape of the τ– S w relationship was largely controlled by the slope of the static retention curve. Numerical modeling demonstrated that a log-linear model relating τ and S w yielded the best match to experimental outflow results.