This paper reports a general hydrodynamics theory of steady-state isothermal flow of non-linear viscoplastic drilling muds through the annular space of the well. The theory has been developed to fit an optimal circulation program design for conditions of high probability of circulation losses and/or formation fluid kickings. Mud compressibility problems are discussed as well as the adequacy of different rheological models to the behaviour of various mud types.

There are briefly stated fundamentals of the engineering procedure used to design optimized rheohydraulics programs for drilling wells. The said procedure with the corresponding computer program has been successfully used for drilling in deep thick abnormal pressure reservoirs of several Soviet oil and gas fields (Tengiz and others).

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