Which of the following is NOT part of the first circulation process in the Driller's Method?

The process of the first circulation in the Driller's Method is primarily focused on controlling the well after a kick has been detected, often following a series of essential steps to ensure safety and stability. One crucial component of this process is shutting the well in after the kick is detected, which helps contain pressure and prevent further influx of formation fluids.

Another critical step during this initial phase is maintaining constant drill pipe pressure. This is vital for preventing further inflow of formation fluids and ensuring that the system remains stable while mitigating risks associated with well control.

Circulating out the influx is also a fundamental action taken during this method as it involves using the drilling mud to push the gas or liquid that has entered the wellbore back to the surface. This step is necessary to eliminate the kick, allowing for better control of the situation.

Pumping kill mud immediately, however, is not part of the first circulation process and is considered more of a subsequent action in well control. The initial steps focus on containing the situation and stabilizing conditions rather than immediately changing the fluid in the wellbore. This is why the option referencing the immediate pumping of kill mud is not part of the first circulation process outlined in the Driller's Method.