Hysteresis and dynamic effects in the relationship between capillary pressure, saturation, and air-water interfacial area in porous media.

Abstract

Air-water interfacial areas (A) were measured for multiple drainages (primary, secondary, and scanning) using a newly developed method, along hysteretic Pc-S curves representing natural drying/wetting processes. The measurement was conducted under a condition with relatively constant interfacial tension throughout experiments, making use of an isomerically pure anionic surfactant as interfacial tracer. Langmuir and Gibbs adsorption equations were applied in area calculations. A 3D Pc-S-A relationship established for a fine sand shows a hysteretic nature, based on the observation that neither A is a unique function of Pc and S nor Pc is a unique function of S and A. It was also found that A increases monotonically with decreasing saturation, with higher A values observed for secondary and scanning drainages than primary drainage, and also for finer media than coarser media at a particular saturation. In an area measurement specifically designed to study the influence of surfactant-induced interfacial tension variations, approximately two times more interfacial area was observed for a 25 mN/m interfacial tension change, in comparison with a system with relatively constant interfacial tension. Environmental implications of the results found here are discussed.

The apparent dynamic coefficient (tau*), a measure of combined dynamic effects, was measured for various porous media ranging from sand to silt for different drying/wetting paths. Relative permeability (krw) and the dynamic capillary coefficient (tau), which measure relative permeability effects and dynamic capillary effects, respectively, were calculated from tau* with the application of Darcy's law and Brooks-Corey equations for unsaturated flow. In general, it was found that tau*, tau, and krw are hysteretic throughout the hysteretic Pc-S relationship, and vary as a function of saturation. It was further found that at a particular saturation, tau* and tau of different porous media are inversely proportional to the saturated conductivity. Results also show that for each drainage or imbibition process, the unsaturated flow is dominated by relative permeability effects at low saturations, and by dynamic capillary effects at high saturations.

This work experimentally examines two unsaturated phenomena of porous media that influence the transport and distribution of contaminants in the subsurface. The first is dynamic effects in the response of porous media to pressure changes. Dynamic effects discussed here include both relative permeability effects which control the speed of unsaturated flow, and dynamic capillary effects which influence the hysteretic capillary pressure-saturation (Pc-S) relationship under dynamic conditions. The second unsaturated phenomenon studied here is the influence of hysteretic Pc-S relationships on the magnitude of interfacial area (A) between two immiscible fluids, a critical parameter controlling contaminant distribution, transport and mass transfer in unsaturated environments.