Abstract: A method for controlling entry of hydrocarbon into a wellbore from a subsurface formation includes determining whether hydrocarbon is entering the wellbore. Whether a rate of hydrocarbon entry into the wellbore is slowing is then determined Control of discharge from the wellbore is then switched from maintaining a selected wellbore pressure to controlling a rate of discharge of fluid from the wellbore to be substantially constant if the hydrocarbon entry rate is slowing. Control of discharge from the wellbore is returned to maintaining the selected wellbore pressure when the hydrocarbon stops entering the wellbore.

Abstract: A system for controlling wellbore annulus pressure during the drilling of a subterranean formation includes a drill string extending into a wellbore. A primary pump is configured for selectively pumping a drilling fluid through the drill string and into an annular space created between the drill string and the wellbore. A fluid discharge conduit is in fluid communication with the annular space for discharging the drilling fluid to a reservoir. A fluid back pressure system is connected to the fluid discharge conduit configured to selectively maintain pressure therein. The fluid back pressure system includes a fluid choke, a back pressure source and an accumulator hydraulically coupled between the back pressure source and the discharge conduit.