Direct quantification of dynamic effects in capillary pressure for drainage-wetting cycles

The constitutive relationship between capillary pressure (P (sub c) ) and wetting fluid saturation (S (sub 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 (sub c) and S (sub w) . Differences in P (sub c) measured under static and dynamic conditions are due to dynamic effects typically defined as a product of a dynamic coefficient (tau ) and the rate of change in S (sub w) . To date, relatively few experimental studies have been conducted to directly quantify the magnitude of this effect. In this study, the magnitude of tau 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 tau for primary drainage generally increased with decreasing S (sub w) . The measured tau values were also compared with those estimated using a different approach based on redistribution time. The measured and estimated tau 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 tau -S (sub w) relationship was largely controlled by the slope of the static retention curve. Numerical modeling demonstrated that a log-linear model relating tau and S (sub w) yielded the best match to experimental outflow results.