| Physically-based theory of two-phase flow in porous media including fluid-fluid interfacial area In many natural and industrial porous media, flow of two immiscible fluids plays a major role. Examples of two-phase (or multi-phase) flow in natural porous media are the flow of oil and water in oil reservoirs, the spread of organic liquids in contaminated aquifers, or the flow of fluids in biological tissues. In industrial porous media, two-phase flow is of importance in, for example, the drying process of paper, the adsorption of liquids in diapers and similar absorbing products, fuel cells, the drying of foods, or in filters. Two-phase flow is a complex process. Yet, the current theory for the description of two-phase flow in porous media is based on a simple equation that was initially proposed by Henry Darcy in 1856. Darcy's equation was originally meant for the case of slow flow of a single-phase fluid in a porous medium. But, through the past 150 years, this equation has been "extended" in an ad-hoc manner and applied to more and more complicated systems, including the flow of two immiscible phases in porous media. But, in fact the form of the equation has not changed at all; the driving and resisting forces of flow have remained the same. In particular, interfacial forces that are present in two-phase flow systems are not taken into account. There are two very important differences between two-phase and single-phase flow. The first difference is that in two-phase flow, the phases have to share the pore space and encounter more difficulty to flow. This difference is accounted for in the traditional theory through the introduction of saturation and reducing the medium permeability by a fraction called "relative permeability". The second difference is the presence of fluid-fluid interfaces between the two immiscible fluids. The interfaces define the phase boundaries at the pore scale, and the interaction between the phases takes place through these interfaces. They play the central role in many processes and effects, such as capillarity, dissolution, adsorption of surfactants, transport of micro-organisms in the unsaturated zone, evaporation, and drying processes. But, in current theories of multiphase flow, interfacial area is completely absent. Recently, a truly-extended theory of two-phase flow theory has been developed that explicitly includes interfacial forces. In this theory, in addition to saturation, a new macroscale variable, called specific interfacial area (that is the amount of fluid-fluid interfacial area per unit volume) is introduced. This theory has received much attention internationally and has led to a wave of research aimed at trying to measure the new variable, specific interfacial area. But, so far there has been no attempt to validate the new theory. In this project, we shall develop an experimental set up where the variation of saturation and specific interfacial area in time and space will be measured and used to determine the significance of including interfacial area in two-phase flow theories. Experiments will be carried out in a so-called micormodel. Micromodels are fabricated porous media consisting of a network of pores created on a flat surface, commonly held between two glass plates. Typically, they have dimensions of about one millimetre. As they are transparent, the detailed movement of phases inside the system can be visualised by a microscope and registered with the aid of a high resolution camera. This allows quantification of interfacial area as well as saturation, and validation of the new theory. In this project, for the first time, a long micromodel, with dimensions of 1mm by 1 cm will be constructed. This allows us to mimic processes occurring in a column; we can determine the variation of average saturation and specific interfacial area in time and along the micromodel. We shall develop a numerical code two-phase flow equations based on the new theory. The code will be calibrated with the aid of results from micromodel experiments and the theory will be validated with the aid of additional experiments with the micromodel. Consequences of the new theory for modelling flow through an oil filter (involving air-oil flow) and for modelling secondary oil recovery by water injection will be investigated. |
