## Solution Of Problems On

To" ""9 b" i 6 ; * 3RILL CO.LtR 0.0 - INCHES

Fig. 9.8(A). Sample solution for example problems.

To" ""9 b" i 6 ; * 3RILL CO.LtR 0.0 - INCHES

Fig. 9.8(A). Sample solution for example problems.

Example 9.6

Collar OD, in. Weight, lb Hole size, in. Hole inclination, Formation dip, °

Solution:

Established data 7

Problem data ?

90,000 12 10 30

This problem cannot be directly solved. It is necessary to try a few collar sizes and proceed for each of them as in Example 9.4.

Example 9.7

Collar OD, in. Weight, lb Hole size, in. Hole inclination, Formation dip, °

Established data 7

13,500 9 5

Problem data 11

90,000

Solution:

This problem cannot be directly solved. It is necessary to try a few hole inclinations and proceed for each of them as in Example 9.4.

Established data 7

13,500 9 5

Problem data 11

90,000 12

Example 9.8

Collar OD, in. Weight, lb Hole size, in. Hole inclination, ° Formation dip, °

Solution:

Using established data, construct rectangle A iB XC iD i as in Example 9.1 or 9.4. Similarly, using problem data, construct rectangle A 2C 2D 2, then locate points and draw lines as follows: Points E1 and Ei (located on the reference line and on the same curves as Di and Z)2, respectively); F1 (45° and 5° hole inclination): Gi (intersection of lines through E1 and F1);

G2 (located on the same curve as G, and a line through E2); F2 (10° hole inclination).

The individual effect of changing one of the variables may be studied by solving a series of problems similar to the examples just shown. Figures 9.4 and 9.5 were prepared in this manner. Numerous papers have pointed out other specific applications of these principles to actual field problems.10-12

G2 (located on the same curve as G, and a line through E2); F2 (10° hole inclination).

The individual effect of changing one of the variables may be studied by solving a series of problems similar to the examples just shown. Figures 9.4 and 9.5 were prepared in this manner. Numerous papers have pointed out other specific applications of these principles to actual field problems.10-12

### The Use of Stabilizers

Stabilizers are used as a means of controlling the location of the contact point between the hole and drill collars. The potential benefit of such action may be visualized from Figure 9.9. Part (A) shows the normal position of the drill string in an inclined hole, as previously described. If a stabilizer is used as indicated in parts (B) and (C), the effective contact point is moved up the hole; this increases the hole-straightening force imposed by the pendulum weight. Whether the optimum stabilizer location is as shown in 9.9 (B) or (C) depends on drill collar and hole size, hole inclination, and the weight on bit.8 Qualitatively, it may be surmised that for a given hole deviation, the use of a single, properly located stabilizer will allow a higher weight on bit.

### Multiple Stabilizers

The effect of using several closely spaced stabilizers near the bit has also been studied. In practice, this effect has also been attained by welding continuous steel strips outside the drill collars. This procedure may be analyzed as though the diameter were decreased by the same amount. Figure 9.5 shows that very small clearances reduce the allowed bit loading for a given equilibrium deviation angle. Therefore continuous stabilization (very low clearance) will result in a large equilibrium hole inclination; the rate of angle buildup is, however, quite slow. Consequently, this technique may be used to:

• 1) prevent sudden changes in deviation (dog-legs)
• 2) drill relatively short sections of extremely crooked hole formations; this means that although the
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