Bullheading is a well control technique where heavy kill fluid is pumped down a wellbore to force a gas influx back into the formation, but poor estimation of the required injection pressure has historically led to failed interventions, most notably during the Macondo/Deepwater Horizon blowout. This study numerically simulates bullheading operations in a deepwater reservoir setting using the Petrel E&P platform, focusing on bottomhole pressure (BHP) behavior and the injection pressure needed to displace an influx. A vertical-well grid model representative of deepwater turbidite reservoirs was built, and a sensitivity analysis was performed across five reservoir/operational parameters, namely horizontal permeability, vertical permeability, porosity, net-to-gross (NTG) ratio, rock compressibility, and injection rate, using thirty-nine simulation cases. Horizontal permeability and NTG ratio were found to have the greatest influence on injection pressure, followed by porosity and rock compressibility, while vertical permeability showed no measurable effect. Injection rate, the only field-controllable variable, showed a strong direct relationship with both BHP and injection pressure. A subsequent uncertainty and cluster analysis using horizontal permeability and NTG ratio identified representative low, mid, and high pressure scenarios. These results indicate that reservoir characterization, particularly of horizontal permeability and NTG is critical to accurately predicting injection pressure for safe bullheading design in deepwater wells, and that simulation outputs should be validated against downhole pressure gauge data to reduce estimation uncertainty.