Multiphase flow phenomena are encountered in all disciplines of petroleum engineering industry; drilling, production, reservoir, processes, and transportation operation. Since the crude oil production pipelines follow normal hilly terrain variations including horizontal, uphill, and downhill sections, it is possible to find several types of flow regimes at the same time at different position along the pipeline. Most of the possible flow regimes are not dangerous except slug flow. In this study, the fluid dynamics of gas liquid slug flows in horizontal, inclined, and hilly terrain pipelines are modeled using multi-dimensional Computational Fluid Dynamics codes. The Volume of Fluid Model as an interface tracking technique, is developed to predict, visualize and monitor the flow regime. The first part of the thesis is consisting of a study the flow regimes in small diameter pipelines and their characteristics. Therefore, a set of simulation runs was performed to compute flow patterns in horizontal and inclined gas-liquid pipelines. The first set of runs was done using a horizontal pipe and the results were verified against experimental work. The study covers a wide range of fluid flow rates. The slug flow characteristics have been calculated, and new relations between the superficial liquid velocity and liquid hold up have been derived. The second set of runs was conducted for a pipeline with inclination angels +5°. The effect of pipe inclination on the flow regime was studied and the flow patterns, liquid holdup and pressure drop have been computed. The second part of the work dealt with the complex and multi-dimensional nature of slug flow. It includes simulation of a full scale field pipeline from OMV-Austria By CFD-VOF technique. The transient flow behaviour occurring in a pipeline with two different diameters has been simulated. Since the pipeline under consideration is nearly 2 Km long, the corresponding computational model would involve grid cells with very large aspect ratios which invariably would lead to solution instabilities in the CFD analysis. To overcome this problem, the pipeline was sub-divided into different sections, and each section was investigated separately. Then, the whole length was simulated and complete investigations have been presented in terms of slug flow characteristics (Slug Velocity, Pressure drop, slug frequency, and holdup). The ultimate aim of this research work was to gain a deeper understanding of multiphase flow phenomena in pipelines and to guidelines to improve the design of pipelines and downstream facilities.