Incident reviews of oil spill events (both large and small) suggest that human error is a contributor to 50% of well control incidents (primarily kicks). The purpose of this study was to examine operator situation awareness (SA) and associated physiological load, using heart rate and heart rate variability (HRV), during different simulated offshore well control scenarios (drilling and tripping) and criticality levels (failure presented or not). Ten trained participants completed four scenarios (tripping non-failure, tripping failure, drilling non-failure, and drilling-failure) in an experimental session, lasting similar to 6 h. Measures were obtained for each scenario, including speed and accuracy of the task performance, composite scores obtained from the Situational Awareness Rating Technique (SART), and operator heart rate and heart rate variability measures. Greater errors were found in kick-related failure events, and drilling scenarios were associated with longer reaction times. Participants perceived lower SA levels during drilling scenarios, and the was observed for lowest SA during drilling failure scenarios. Finally, while physiological responses did not differ significantly for any of the four scenarios, elevated heart rate was observed with drilling and failure-related scenarios. High variability in participant covert and overt responses may increase the challenges associated with classifying high-risk well control scenarios. It is critical that scenario planners understand and recognize the variability in driller situation awareness and associated physiological load when planning for alternative future scenarios.