Many topics of driller’s method have been taught on the drillingformulas.com and I would like to summarize about advantages and disadvantages of driller’s method.
Advantages of Driller’s Method
• Circulation can be established right away so the bottom hole pressure will not increase much due to gas migration.
• Influx can be removed out of the well even though the rig does not have sufficient amount of weighting agent.
• Gas migration is minimized.
• Operation is quite simple when compared to weight and weight method.
• Calculation is simple and drill pipe pressure schedule is not required.
Disadvantages of Driller’s Method
• There will be more time for circulation because the driller’s method requires 2 times of circulation. The first circulation is to remove influx and the second circulation is to kill the well.
• It will generate higher surface pressure and shoe pressure than wait and weight method.
Reference book: 
Well Control Books
