A two-phase liquid-liquid system is generally defined as a system in which two immiscible liquids, for instance water and oil, flow together and have a shared interface. When the two liquids flow through the pores and fractures in the subsurface rock, we deal with two-phase liquid-liquid systems in porous and fractured media. Such liquid-liquid flow systems are studied for applications in petroleum reservoir engineering and hydrocarbon exploration, and more and more for applications in soil and aquifer remediation techniques in the context of environmental engineering. However, the concept of liquid-liquid systems can be generalised by considering only one liquid, for instance water, and to consider the water in the pores of the blocks of intact rock as one phase-the 'rockwater' phase-and the water in the fractures as the other phase-the 'fracturewater' phase. The distinction between the phases 'rockwater' and 'fracturewater' can further be justified by the fact that the rockwater entrapped in the almost impermeable rock, has a chemical composition with concentrations of dissolved matter that differ from the composition and concentrations in the relatively fast moving fracturewater. Such types of miscible liquid-liquid flow systems are studied in the context of groundwater flow and transport of dissolved matter in porous and fractured rock. Liquid-liquid flow and transport in heterogeneous porous and fractured natural media can be studied from the point of view of many spatio-temporal scales. The microscopic spatial scale is the scale of the pores and fractures. On the scale of a block of intact porous rock, the average flow is governed by Darcy's law. On that scale one of the most prominent parameter for flow is the permeability of the intact rock. For flow on the scale of a naturally fractured rock reservoir, the composite permeability is the most dominant parameter describing the averaged flow through the pores in the intact rock and through the fractures. The derivation of large-scale composite parameters from fine-scale parameters is generally called homogenisation or upscaling. Homogenisation is a key item in practical studies on liquid-liquid two-phase flow systems.
