Horizontal wells are better producers than vertical ones as they can be extended for a long distance in the producing zone. However, experiences have shown that the actual production rate is often significantly less than the forecasted one. There are a number of reasons for the discrepancy of predicted to produced production rates. Often, the problem lies in the drilling of horizontal section. Operators try to maintain a predetermined, constant hole inclination in the pay zone. Unfortunately, drilling sinusoidal wells are more common and only a fraction of total length produces from the pay zone. Consequently, in such a case lower production rates are inevitable.

The stability in the borehole inclination can be maintained by keeping formation dip angle and near-bit BHA inclination parallel at zero bit side force which are the two major factors contributing responsible from hole inclination. Therefore it is crucial to forecast the inclination of BHA axis near the bit, as well as the bit side force at various BHA arrangements and bit weights.

The finite elements methods (FEM) can be used to determine the bit side force and the bit tilt simultaneously. The FEM is superior to current analytical techniques because of following three reasons. One, it can accommodate more independent parameters in assessing the bit side force. Two, it predicts the inclination of the axis of BHA. Three, it can test the stability of a given BHA under given loading condition. A buckled BHA yields different results than a stable one.

A FEM is presented to estimate the bit side force and the BHA axis and compared with an analytical method.


BHA is the part of drill string that affects the trajectory of borehole by bit side force and tilt1. The bit side force is the controlling factor for hard formations (i.e., drilling rates 1 to 1o ft/hr). For formations soft to medium hard, the side force is not the only component that will influence the inclination and direction of the bit. Bit tilt becomes influential as well. Because of the curvature of the BHA near the bit, the bit is canted or tilted in some resultant direction and inclination, somewhat like the bent housing and bent sub1. Side force becomes controlling factor once again for very soft formations (i.e., drilling rates in excess of 100 ft/hr).

For a given BHA, the bit side force and tilt depends on a number of parameters. These parameters are hole, drill collar and stabilizer sizes, BHA material properties, mud weight, stabilizer locations, borehole inclination, direction, contact length and location between pipe and hole and finally, weight on bit. Unfortunately, analytical techniques derived to estimate bit side force ignores some of these parameters for the sake of practicality. For example, the analytical method developed based on "Three Moment Equation" ignores the effect of pipe to wall contact as well as hole curvature2,3.

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