ORPHEE 3D is a three-dimensional mathematical model of bottomhole assemblies (BHAs) behavior. A new release of this model is presented in the paper. It can predict both build/drop rate and walk rate for BHAs now including any elements with knee, like bent sub, bent housing, downhole motor, DTU… The static equilibrium position of the ΒΉΑ in the borehole is computed by the finite element method. This method allows us to model any type of BHAs.

The first part of the paper describes the modification in the finite element method to treat bent subs and to compute lateral side forces at the bit. An original method to compute the build/drop and walk rates is presented. It allows to solve the problem of the coupling between inclination and azimuthal side forces due to the bent sub knee.

Then, the main results of a parameter analysis are pointed out. The behavior of classical bent sub BHAs, qualitatively known by the directional drillers, are explained and quantified by the model. Moreover, original and unexpected results arise from this analysis. One of the most interesting is the optimum which can be found for the distance between bit and bent sub knee.

Finally, the model predictions are compared with field results. This work shows that the model can now predict the directional response of BHAs including elements with knee, by adjustment on the downhole motor flexural rigidity.

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