The use of the Manage Pressure Drilling (MPD) is spreading in offshore operations. The increasing complexity in the new exploratory frontiers is demanding for new techniques to reduce costs and increase operational safety. MPD appears as an answer for that demand and sometimes it is the only viable way to drill some of the challenging wells. In that way, understanding the gas migration behavior while drilling in PMCD mode allows an optimized well design concerning cost and operational safety. The present study validates a mathematical model capable of simulating a scenario where loss of drilling fluid in the bottom of the well is present while having an influx from the same reservoir and observing gas migration to the surface in a PMCD operation. A Drift Flux Two Phase Flow Model is used in association with the Advection Upstream Splitting Method (AUSMV). Before the presentation and discussion of the complete PMCD scenario, two simple cases were simulated and the results were compared to the ones from a computer application considered as a reference to the industry, validating the proposed model. The results of the simulations can be used as a base for the elaboration of operational procedures to monitor gas behavior and optimize bullhead in PMCD scenarios.