Managed Pressure Drilling (MPD) is one of the most advanced technologies of well drilling in challenging hydrogeological conditions. Pressure should be maintained within a fairly narrow range during MPD to prevent formation fluid inflow into the open hole or lost circulation. The control process is normally accompanied by pressure waves in the pipe and annulus. Pressure waves as surge and swab effects can also result from tripping operations, semisubmersible drilling platform heaving, etc.

The paper presents a mathematical model, numerical method and examples of pressure fluctuationt calculations in a hole. The model accounts for the mud compressibility, the elasticity of drillstring and the wellbore walls, and the string longitudinal vibrations. Non-Newtonian fluid model with temperature and pressure dependent parameters is used as a rheological model. The drag calculations account not only for viscous friction, but for local pressure losses associated with variations of the string, BHA, bit and wellbore cross sections, existence of tool joints, eccentricity of the string in the well, etc. Drillstring tripping speed variations, top string end oscillations associated with floating rig heaving during offshore drilling, and formation fluid inflow or mud outflow are used as disturbing parameters and fluid flow rate into the pipe and backpressure at the well head in the annulus are used as control parameters.

Original equations of fluid flow in the pipe and in the well are converted into divergent form through special transformation, which enables using more efficient numerical methods for their solution.

The paper presents examples of calculations of pressure fluctuation in the well and string affected by the driving disturbances and during tripping. The steady-state dynamic solution is verified by comparison with the static (hydraulic) solution. The paper presents results of modeling of various operations for one of the wells at Yurubcheno-Takhomskoye oil/gas/condensate field.

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