Hydraulics play an important function in many oil field operations, in the case of drilling, with the implementation and promotion of management pressure drilling technology, the role of accurate hydraulic parameter predictions becomes vital for drilling. This paper describes a utility hydraulic calculation model for Herschel-Bulkley (H-B) rheological model.

Firstly, the explicit equation between the wall shear stress and volumetric flow rate of H-B fluid flow in pipe and annuli were obtained. Then, the accurate numerical solutions of wall shear rate and shear stress both in pipe and annuli were obtained. Secondly, we defined a new generalized flow behavior index and effective diameter for H-B fluid annular flow. The generalized effective diameter accounts for the effects both of annuli geometry and fluid rheology but which is different from that was proposed by Reed & Pilehvari. Moreover, through the effective diameter we link the H-B fluid flow both in pipe and annuli to Newtonian pipe flow. At last, a general expression of generalized Reynolds number was derived from this model in view of generalized flow index is non-constant. Then, a theoretical calculation method was proposed for the generalized flow index of both pipe and annular flow and a uniform pressure drop calculation model was obtained. The predictions of the improved hydraulic model have been compared with an extensive set of experimental data. The comparison of different fluids both in pipe and annulus show very good agreement over the entire range of flow types.

Finally, the utility model has been applied in several wells in Sichuan basin and Tarim basin for monitoring real-time hydraulics while MPD, and there is an excellent match between the model and measured data. Therefore, it can be seen that this utility method can be applied to provide more accurate estimations of hydraulic parameters in drilling engineering.

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