The climate change agreements require large investments in renewable energies. However, with the increasing demand for energy, immediately stopping the production and use of fossil fuels is not realistic. Natural gas is twice as clean as coal and hence could be considered as a transition fuel, which can help to find a balance between the requirements of fighting climate change and producing more and cleaner energy.The high-pressure, underground reservoirs supply natural gas which is usually wetted with liquid hydrocarbons and water. Natural gas is lifted through a production tubing to the surface, with a relatively high velocity and the drag between the gas and liquid will also bring the oil (or condensate) and water to the surface. However, over time the gas supply from the reservoirs will deplete, which gives a decreasing gas velocity, until liquid starts to fall. This is known as liquid loading, which can finally lead to the killing of the gas production. One of the solutions to operate such aging reservoirs is to reduce the cross-sectional area of the production tubing through making use of an annulus (which actually is the space in between an outer pipe and an inner pipe).Liquid loading is noticed to occur when the flow regime changes from annular flow to churn flow. A good understanding of this multiphase flow behaviour in an annulus is desired. Therefore, this Master Thesis project was devoted to obtaining new experimental data and to develop a model for upward gas-liquid flow in a vertical annulus. Experiments with air and water were carried out in the small-scale flow loop of TNO in Delft. The air and water throughputs were varied, and both concentric and eccentric pipe-in-pipe configurations were measured. Both the pressure drop and liquid holdup were measured. The model is able to predict the pressure gradient and holdup for a range of superficial gas and liquid velocities, using different eccentricities in the annulus configuration. The model predicted the pressure gradient within 10% of the experimental values at high superficial liquid velocities (>0.5 cm/s). However, for a superficial liquid velocity of 0.5 cm/s, the model was overpredicting the pressure drop by 100%, which could be attributed to the partial dry-out on the tube walls. To determine the superficial gas velocity, for a given pressure drop and holdup, a modified version of the Wallis correlation was used for the interfacial friction factor. The gas velocity was predicted within 5 to 10% at low holdups (< 0.075). For higher holdups the gas velocity was overpredicted by about 40%. The primary modifications made to the model for the eccentric cases are based on applying a number of grid cells in circular direction allowing for the inclusion of a closure for the variation of the circular film thickness both at the inner and at the outer pipe wall. A verification of the closure of the amplitude or of the closure of the film thickness variation is required to confirm the dependency between this parameter, the eccentricity and the holdup. However, with the applied closure of the amplitude the pressure gradient with respect to the holdup was predicted within 6% accuracy for the eccentric cases.