Dynamic Pore Network Study of Immiscible Two-Phase Flow in Porous Media

Abstract

Porous media research has widespread applications in a variety of fields including biology, medicine, and geology. Notably, it can be used to mitigate the effects of climate change through methods of carbon capture and storage. Fundamental to all disciplines of porous media research is understanding how fluids move through pores under different conditions. In many cases, it involves the movement of multiple fluids rather than a single fluid. An example is the displacement of brine in aquifers with carbon dioxide during carbon sequestration processes. When fluids are immiscible, that is when they do not form a homogeneous mixture, various phenomena arise that can influence the flow. For example, the interfaces between the fluids create capillary pressure barriers that depend on the interfacial tensions, the radii of the pores, and the wetting angles. Due to these barriers, different amount of force is needed to push through different pores. A porous medium can have varying radii and wettability and hence varying capillary pressure barriers along its body. As a result, when being subjected to an externally applied pressure, depending on the magnitude of the pressure, certain regions of the porous medium might become active while others remain dormant. This effect can cause the volumetric flow rate as a function of the applied pressure to deviate from the linear Darcy’s law in certain pressure regimes. There are various ways to model immiscible fluid flow in porous media. The models can range from a simple capillary tube to a bundle of capillary tubes to a network of interconnected tubes. One way to model a dynamic pore network is through tracking and moving the interfaces. The procedure at every time step involves calculating the pressure field and thereafter the flow rates and moving the interfaces accordingly while abiding by a set of rules that makes that system more realistic. The work in this thesis aims to contribute to a better understanding of immiscible two-phase flow in rigid porous media. The main body of work consists of 4 research papers that mostly use a numerical dynamic pore network model, and also capillary tube models. A focus was placed on steady-state non-linear dynamics in terms of the volumetric flow rate as a function of the global pressure difference. Other topics considered in this work include local statistics of porous media, critical phenomena in porous media, and the effects of compressibility.