Directional drilling is costly. Roundtrips of the entire drillstring is often required to implement directional corrections. The directional driller is a specialist using numerical simulators for analysis. To simplify this, work was undertaken to derive simple analytical equations that would replace the simulators, and, to gain further insight into the controlling mechanisms.

The first part of the paper investigate the minimum weight and length of the BHA. Performing a force balance, including torque and drag (Coulomb friction), minimum BHA length are obtained both for rotating and sliding mode.

The second part of the paper is based on indeterminate beam theory. Explicit equations are derived to model the two key mechanisms; weight (gravity) and geometry (BHA deflection). The equations clearly shows that the build-rate depends on wellbore inclination. Using the insight from the models it is shown that a catenary (minimum friction) wellpath can be approximated by proper stabilizer placement, and can be drilled without altering the BHA, that is, no correction trips are required.

Several practical examples are provided, including a well drilled to 110 degrees inclination. It is shown that buckling defines the maximum bit force, and also shown is the design of such an operation, including optimal placement of stabilizers and drillcollars.

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