Carbonate rocks are of global importance as they contain about 50% of the world’s remaining hydrocarbon reserves and are also a major host to the world’s groundwater resources. Therefore, understanding and modelling the fluid flow processes in carbonates are of great importance. A critical problem is that, unlike homogenous media (such as sandstones), carbonates often show features, including porosity, that span across a wide spatial range, from sub-micron porosity to fractures of meters length-scale. In this study X-ray computed micro-tomography (μCT) has been utilised as a tool to monitor two phase (oil-brine) flow in porous carbonate (dolomite) plugs at ambient temperature and pressures smaller than 690 kPa. A simple, low-cost and highly X-ray transparent core-holder was utilised for which the design is introduced. Capillary end effects were recognised and avoided in data analysis. Displacement processes that occur in the dolomite under water-wet, oil-wet, and partially mixed-wet states were investigated. The experiments consisted of a series of drainage and imbibition processes occurring under capillary and viscous dominated flow regimes. Pore-scale mechanisms of piston-like displacement and snap-off (or at least clear results of them), that were previously observed in sandstones and 2D micro-models, were observed in the dolomite under study. In addition, a new pore-scale mechanism was identified which occurred at high capillary numbers, referred to as droplet-fragmentation. This new pore-scale mechanism may provide an explanation to the capillary-desaturation process for heterogeneous media. In the experiments performed on the oil-wet plug formation of a stable water in oil emulsion was observed which appears to be the first 3D observation of in situ emulsion formation made using μCT. Direct visualisation of the oil-brine-rock configurations and measurement of the contact angles are presented. A comparison was made for the contact angle distributions measured for the water-wet and oil-wet conditions. Observation of fluid displacement processes as well as oil-brine-rock contact angle distributions demonstrate that pore-scale imaging provides a promising tool for wettability characterisation on both pore and core scales. Such detailed wettability data can also be used in pore-scale flow models. For the dolomite under study multiple-scale pore network models were constructed by integrating single-scale networks extracted from μCT images acquired at different length-scales. Mercury injection capillary pressure laboratory measurements were used to evaluate the capillary pressure (vs. saturation) curves calculated using single, two-scale, and three-scale network models of this dolomite. The integrated networks displayed an improved match to the laboratory measurements in comparison with the single-scale network model. The three-scale network provided the closest simulated curve, this result confirms that a more representative model displays closer properties. While simulated capillary pressure curves are close (converging) for the integrated networks the calculated relative permeability curves show variability for different multiple-scale networks. The present work demonstrates that the pore-scale fluid displacement processes occurring in heterogeneous porous media are more complex than those occurring in homogeneous media. In addition, successful fluid flow simulations require construction of multiple-scale models as well as consideration of the pore-scale processes (such as droplet-fragmentation) that are specific to such complex pore systems.