Managed pressure drilling with rig heave compensation

A method comprising the steps of:

• pumping fluid through a drill string extended from a drilling platform into a wellbore drilled through a subsurface formation;
• measuring a flow rate of the pumped fluid;
• measuring a first fluid pressure in an annular space between the drill string and a wall of the wellbore at a position proximate a bottom of a body of water on which the drilling platform floats;
• measuring a second fluid pressure proximate a variable orifice flow restriction disposed in a fluid outlet from the annular space, the annular space arranged and designed to change length as a result of heave of the floating drilling platform;
• determining time derivatives of the first and second fluid pressures;
• and
• controlling the variable orifice flow restriction to maintain a selected pressure in the wellbore based upon at least the time derivatives of the first and second pressures.

A method comprising the steps of:

• pumping fluid at a determined flow rate into a drill string disposed in a wellbore, the drill string being suspended from a drilling platform floating on a body of water;
• measuring fluid pressure of fluid returning from the wellbore within a fluid discharge line, the fluid discharge line having a variable length portion arranged and designed to vary the length of the fluid discharge line to correspond to a change in elevation of the drilling platform above a bottom of the body of water;
• determining a wellbore pressure at a position selected from the group consisting of a selected depth position in the wellbore, a position along a drilling riser, and a position along the variable length portion of the fluid discharge line, the wellbore pressure being determined using at least one of the determined flow rate, the measured fluid pressure, a hydraulics model or rheological properties of the fluid;
• operating a backpressure system to maintain the adjusted determined wellbore pressure at a selected value by measuring a fluid pressure in the wellbore proximate a blowout preventer and measuring a fluid pressure in the fluid discharge line at a position prior to a controllable orifice choke disposed therein;
• and
• adjusting the determined wellbore pressure to account for changes in length of the fluid discharge line corresponding to changes in elevation of the drilling platform above the bottom of the body of water.