Session F36: Porous Media Flows: Immiscible Fluids and Multiphase Flows

High Resolution X-Ray Differential Phase Contrast for Fluid Imaging in Porous Media

X-Ray computed tomography is a common technique for determining the three-dimensional structure of solids but has found limited application for measuring the structure of liquid-liquid interfaces within porous media because the X-Ray absorption coefficients tend to be similar for most fluids. Two primary techniques, a high brightness source or added contrast agent, have previously been utilized to enable X-Ray imaging of 3D liquid-liquid interfaces. The use of a high brightness source is expensive and logistically complicated. Adding a contrast agent effects the fluid dynamics that are being observed.
We’ve developed a tool for the high resolution inspection of these 3D liquid-liquid interfaces within porous media by using differential phase contrast (DPC) X-ray imaging. This tool uses a micro-focus x-ray source, paired with a high resolution indirect x-ray detector, along with gold amplitude and phase gratings to measure the index of refraction of the fluids under interrogation along with the absorption coefficient that is normally measured in x-ray microscopy. Using this technique, we show experimental images of oil-water interfaces within porous media.   

Nonclassical Solutions for Three-Phase Flow in Porous Media

We consider a strictly hyperbolic model for three-phase flow in porous media and solutions of its associated Riemann problem. Juanes and Patzek showed that solutions of such a system, in the absence of gravity and capillarity, include rarefaction waves and shocks which satisfy the Liu entropy criterion. By incorporating capillary pressure, as given by thermodynamically constrained averaging theory (TCAT), the model gains dissipation and dispersion terms, the latter of which is rate-dependent. This extends the framework developed by Hayes and LeFloch in which the presence of shocks which do not satisfy the Liu entropy criterion can be determined with an entropy dissipation function. These shocks are undercompressive and contribute to nonclassical solutions of the Riemann problem. In this talk, we give the regularized model and discuss the implications for the catalogue of solutions of the Riemann problem.   

Universal dynamics for unsaturated flows in a confined porous layer

We study the dynamics of unsaturated flows from fluid injection into a confined porous layer. A partial differential equation of the evolution type is derived to describe the time evolution of the interface shape, defined as the location where the saturation of the injected fluid is zero. The saturation field can then be computed once the interface evolution is obtained. We provide an example calculation and demonstrate how the flow behaviour evolves from early-time unconfined to late-time confined behaviours. In particular, at early times, the influence of capillary forces indicates the existence of a new similarity solution in the unconfined limit, which is different from the gravity current solution. At late times, we obtain two new similarity solutions, a modified shock and a compound wave, in addition to the rarefaction and shock solutions in the sharp-interface limit. A regime diagram is also provided, which summarizes all possible similarity solutions and the time transitions between them for the unsaturated flows resulting from fluid injection into a confined porous layer. The influence of the dimensionless control parameters are also discussed, including the effects of viscosity ratio, pore-scale heterogeneity and relative contribution of capillary over buoyancy forces.
  

Wettability patterning for managing liquid jets striking porous substrates

Orthogonal liquid jet impingement on porous materials is important for applications such as heat transfer, filtration, and incontinence products. A desirable outcome of such situations is that the liquid does not penetrate the substrate at or near the point of jet impingement, but rather is spread over a wider area before it penetrates through. A wettability-patterning technique for altering the surface of a porous nonwoven matrix is presented in this work (Sen et al., ACS Appl. Mater. Interfaces, 2018). A water jet impinging orthogonally on such a substrate is distributed on the top surface and through the porous matrix, and is subsequently dispensed from prespecified points underneath the sample. The optimum design for uniform distribution of a liquid jet with flow rate exceeding 1 L/min with minimal or no spilling over the sample edges is identified. The effect of varying the impingement spot is also studied, and satisfactory performance even at offset impact conditions is observed.