Common approaches in kick modeling are based on the assumption of a more or less single “gas bubble” present in the annulus and slowly migrating upwards after shut-in. While this assumption satisfies straightforward volumetric well control aspects, it ignores species transport and chemical reaction kinetics leading to drill string corrosion. Especially when dealing with sour gas influxes, the assessment of corrosive damage to high-strength drill string components caused by sulfide stress cracking becomes essential. Therefore a better insight on the flow morphology and associated mechanisms during a kick event is needed to assess the associated corrosive risk. The aim of the work presented in this thesis is to provide a better understanding of the two-phase flow situation resulting from selected kick scenarios. A Computational Fluid Dynamics (CFD) approach was chosen to simulate the dissolution and distribution of influx gas. The selection of a two-phase flow model within CFD is usually based on the expected flow pattern. Since a gas-kick is a fundamentally transient event accompanied by many unknowns the intention was not to make any a-priory assumptions regarding the evolving flow field. Consequently the focus was put on a spatially highly resolved computational model combined with the application of the Volume of Fluid Method. Thereby no restriction on specific flow patterns was active and two-phase interactions could be observed at a close-up view. However the involved computational costs demanded a limitation in model size to the near bottom-hole section of the wellbore. This section shows certain characteristics that are dominated by the inflow conditions of the gas as well as by the configuration of the mud stream entering the annulus. Several inflow scenarios are investigated and methodologies are described to characterize flow aspects that are of potential interest to corrosion engineers. One of the major difficulties in modeling the corrosive risk to the drill string during a gas-kick is the determination of liquid-gas phase interface. As mass transfer and significant chemical reactions are related to the size of the phase interface area, a sound estimate of the same is of utmost importance. Simulation results illustrate two-phase flow morphology and associated specific phase interface area, as well as local mass transfer coefficients and the distribution of dissolved gas. The transient and spatial change of flow patterns in a wellbore during a kick event is discussed. It is explained how the flow pattern is affected by gas expansion and how it may be influenced by gas dissolution. Finally based on the findings of the detailed simulation studies, a coarser full scale kick modeling approach covering the entire well bore is suggested.