Experimental investigation of dynamic effects in capillary pressure: Grain size dependency and upscaling

The macroscopic flow equations used to predict two-phase flow typically utilizes a capillary pressure-saturation relationship determined under equilibrium conditions. Theoretical reasoning, experimental evidence, and numerical modeling results have indicated that when one fluid phase replaces another fluid, this relationship may not be unique but may depend on the rate at which the phase saturations change in response to changes in phase pressures. This nonuniqueness likely depends on a variety of factors including soil-fluid properties and possibly physical scale. To quantify this dependency experimentally, direct measurements of equilibrium and dynamic capillary pressure-saturation relationships were developed for two Ottawa sands with different grain sizes using a 20 cm long column. A number of replicate air-water experiments were conducted to facilitate statistical comparison of capillary pressure-saturation relationships. Water and air pressures and phase saturations were measured at three different vertical locations in the sand column under different desaturation rates (1) to measure local capillary pressure-saturation relationships (static and dynamic); (2) to quantify the dynamic coefficient tau, a measure of the magnitude of observed dynamic effects, as a function of water saturation for different grain sizes and desaturation rates; (3) to investigate the importance of grain size on measured dynamic effects; and (4) to assess the importance of sample scale on the magnitude of dynamic effects in capillary pressure. A comparison of the static and dynamic P-c-S-w relationships showed that at a given water saturation, capillary pressure measured under transient water drainage conditions is statistically larger than capillary pressure measured under equilibrium or static conditions, consistent with thermodynamic theory. The dynamic coefficient iota, used in the expression relating the static and dynamic capillary pressures to the desaturation rate was dependant on porous media mean grain size but not on the desaturation rate. Results also suggest that the magnitude of the dynamic coefficient did not increase with the increased averaging volume considered in this study, as has been reported in the literature. This work suggests that dynamic effects in capillary pressure should be included in numerical models used to predict multiphase flow in systems when saturations change rapidly, particularly in fine-grained soil systems (e. g., CO2 sequestration, enhanced oil recovery, air sparging for remediation).