The objective of this project is to conduct a quantitative study of dynamic capillary effects throughout the hysteretic capillary pressure-saturation relationship using a combination of experimental techniques. The hypothesis is that dynamic capillary effects vary with saturation, wetting/drying path, and fluid and porous media properties, and that the relationships are dictated by the magnitude of the response of the ratio between capillary and viscous forces to changing velocity. This hypothesis will be evaluated through direct measurement of the dynamic capillary pressure coefficient, ô, throughout the hysteretic capillary pressure-saturation (Pc - S) relationship. Experiments will make use of custom-designed membrane-based fluid-selective pore pressure micro-sensors, coupled with a method for rapid measurement of hysteretic (Pc - S) relationships. A collaborative modeling effort using the CompSim 3-D multiphase flow model will use the results of experimental measurements to explore the potential impacts of dynamic effects in large-scale systems.
Capillary forces are forces present between immiscible fluids (e.g., air and water) in porous media. Conventional theory suggests phenomena controlled by capillary forces should not depend on the rate that fluids enter or leave a porous medium. However, many experimental measurements reported over the past five decades have shown evidence that some phenomena governed by capillary forces may, in fact, depend on rate. Apparent rate effects in capillary phenomena have come to be referred to as dynamic capillary effects. One of the most commonly-reported dynamic capillary effects has been an observed rate dependence in the capillary pressure-saturation (Pc-S) relationship – a relationship describing the pressure difference between fluids in a porous medium as a function of saturation. Dynamic capillary effects may have significant implications for a range of hydrologic problems. However, reported experimental studies examining their magnitude and dependencies have been highly contradictory. The purpose of this project was to use a range of sophisticated experimental techniques to develop a new quantitative understanding of the nature of dynamic effects. The objective was to provide a quantitative picture of dynamic capillary effects that could both explain the range of published results, and guide development of future flow models. Work on the project has resulted in three published journal papers to date, with two additional papers currently in preparation. Work has strongly suggested that a range of previously-underappreciated experimental artifacts may have dominated experimental measurements of dynamic effects in the Pc-S relationship. Experiments in small volume soil cells found that correction for sensor response rate and internal gas pressure gradients could virtually eliminate apparent dynamic effects in the Pc-S relationship for three different systems. The results found that calculation of the dynamic capillary coefficient, a parameter often used to describe the magnitude of dynamic capillary effects in porous media, is extremely sensitive to small differences in sensor response, so seemingly minimal errors are amplified in its calculation. A second set of experiments explored the effect of drainage rate on apparent residual saturation (the minimum water saturation achieved in a medium after drainage). Results found relationships between porous medium and fluid properties and the sensitivity of apparent residual saturation to drainage rate. Complementary imaging studies were unable to identify differences in average fluid configurations that led to the different residual saturations. However, simulations conducted using a dynamic pore network model suggest that the phenomenon is likely the result of pore scale flow patterns, coupled with water continuity effects produced by the presence of a boundary. Multiphase flow simulations were conducted to explore how fluid properties influence the measurement of dynamic capillary effects through inducing unavoidable saturation averaging. Because sensors for detecting water content have a finite spatial range, they do not measure point saturation values, but rather measure saturation over some spatial distance. As such, the calculation of rate of saturation change from sensors is sensitive to the shape of the fluid front in the medium. As a result, fluids that produce sharper fronts (higher viscosity fluids) tend to induce more spatial averaging in rate of saturation change, leading to amplification of any measured apparent dynamic capillary effect. Finally, an extensive set of experiments was conducted to explore gas pressure gradients in porous media, and results were simulated in an accompanying multiphase flow modeling effort. Results found that gas pressure gradients are substantial near moving fluid fronts in many systems, and can mimic dynamic effects. The fact that gas pressure gradients area greatest in magnitude within a few cm of a front means that column vents do not necessarily prevent internal gas pressure gradients. This result was verified and observed in experimental studies. Effects of inlet and outlet system resistances on internal gas pressure gradients were also quantified.
