Abstract: A method for controlling formation pressure during the drilling of a borehole through a subterranean formation includes selectively pumping a drilling fluid through a drill string extended into a borehole, out a drill bit at the bottom end of the drill string, and into an annular space between drill string and the borehole. The drilling fluid is discharged from the borehole to a reservoir to clean the drilling fluid for reuse. An annular space fluid pressure is selectively increased to maintain a selected fluid pressure proximate the bottom of the borehole by applying fluid pressure to the annular space. The selective increasing includes controlling an aperture of an orifice operatively coupled between the annular space and the reservoir. A formation fluid pressure is predicted at a depth below a lowermost depth to which the borehole is drilled and the aperture is adjusted to maintain a selected pressure in the borehole in response to the predicted formation fluid pressure.