The effects of dynamic capillary pressure on the two-phase flow and blob mobilization in porous media

Studies have shown that, in porous media, contact angles can be vary due to contact angle hysteresis, and capillary pressure could be dynamic during the processes of drainage and imbibition. The research presented here examined the effect of contact angle hysteresis and dynamic capillary pressure on multiscale two-phase flow in porous media. This dissertation is composed of three essays: "Pore-scale analysis of the effects of contact angle hysteresis on blob mobilization in a pore doublet," "Theoretical and experimental study of resonance of blobs in porous media," and "Incorporation of dynamic capillary pressure into the Green-Ampt model for infiltration.";The first essay focuses on the Jamin effect which is the main barrier to the mobilization of residual blobs in porous media. Experiments performed within a model pore doublet showed that the Jamin effect on a blob can be explained entirely through contact angle hysteresis. A blob is able to sustain pressure gradients by changing its interfacial shape and contact angles while maintaining its contact line position. The sustained pressure gradient was not only directly measured with pressure transducers but also well predicted by the theory. We also developed methods to measure contact angles and mean interfacial curvatures in three dimensions.;In the second essay, we propose a theoretical model supported by experimental data describing the frequency response of blobs in porous media subjected to an oscillatory pressure difference. The simple model pore system consists of a blob in a capillary tube and accounts for frequency-dependent viscous pressure drops in the blob and in the surrounding liquid. In this model, the capillary pressure is variable due to contact line pinning. Using the planar laser-induced fluorescence technique, the dynamic response of blobs in porous media was visualized in a series of two-dimensional cross-sectional images. In a capillary tube, both air and liquid blobs exhibited resonance as predicted by the model. Furthermore, for the first time, the experimental results showed that a liquid blob in a sphere-packing medium exhibits resonance.;The third essay proposes a modified Green-Ampt model to account for a capillary pressure that depends on the flow velocity. A functional form for dynamic capillary pressure is postulated, based on dimensional analysis and physical considerations. In this form, the nonequilibrium capillary pressure is assumed to depend on the capillary number according to a power law. This model for dynamic capillary pressure describes previously published measurements of capillary pressure versus Darcy velocity. In addition, by using dimensional analysis, the three dynamic capillary pressure curves measured by Geiger and Durnford (Soil Sci. Soc. Am. J., 2000) in sand columns of different grain size are collapsed onto a single curve. The model also describes Tabuchi's capillary rise experiments (Rec. Land Reclam. Res., 1971) well. An implicit analytical solution was also derived for calculating the front velocity.