A semi-analytical model to simulate the behavior of a gas kick in an annulus was developed utilizing various concepts, including gas solubility in oil-based drilling fluids. This simulator examines critical kick indicators such as Pit Gain and Wellhead Pressure with time. It models the gas behavior using a drift-flux approach with bubble rise velocity appropriate for flow through an annulus. It also uses the Peng-Robison equation of state, van der Waals mixing rules, along with binary interaction coefficients appropriate for drilling fluids, to account for gas solubility in oil-based mud. The simulation results predict that a five-barrel (bbl) gas kick, would reach the wellhead of a 10,000 ft deep, non-circulating, vertical well in approximately 78 minutes. But it would only take 35 minutes to traverse the same well, if the well is circulating at 702 gallons per minute. The simulations also predict that if there is a constant kick influx of 1 scf/sec, the first gas bubbles would reach the wellhead of the same, non-circulating well in 4.45 hours. But only take 52 minutes when it is circulating. Incorporating gas solubility into these simulations revealed that the choice of drilling fluid volume factor (Bo) correlation affects the results significantly. It also showed that some of the existing Bo correlations fail, for drilling fluid swelling calculations, at higher pressures and temperatures. Finally, the results indicate that a gas kick would take longer to reach the wellhead when it is soluble in the mud than when it is not, regardless of the choice of Bo correlation. Most of the existing kick simulators either partially or entirely overlook the effects of solubility on gas migration. This model accounts for the gas kick's solubility in Oil-based drilling fluids, an issue that is critical for off-shore drilling. Applicability of empirical two-phase flow correlations developed for flow in cylindrical conduits, to a gas kick situation is questionable. This simulator addresses this issue by using a semi-analytical approach for modeling two-phase flow in an annulus.