50

Time (min)

Figure 9-6. Change in pore pressure with time after embedment. Initial cake thickness was 4mm. Minimum thickness after embedment was 1mm. (From Courteille6a Copyright 1985 by SPE-AIME.)

These results indicate that the pressure differential across a stuck pipe will never reach the full value of pm —pf.

Outmans' assumption that differential sticking always occurs in the drill collar section of the drill string is not substantiated by field experience. In a study of 56 recovery logs, Adams7 found that in 31 cases the drill pipe was stuck, and in the remaining cases either the drill collars only or the drill collars and the drill pipe were stuck. These results in no way invalidate the basic mechanisms postulated by Outmans; they merely show that sticking may occur at any point in the drill string where it bears against a permeable formation with a filter cake thereon. The chances that sticking will occur in the drill collar section are increased by the weight distribution of the drill string, which ensures that the collars will always lie against the low side of the hole, but are decreased by the circumstance that the filter cake will be much thinner because of erosion caused by the high shear rates prevailing in the narrow annulus around the drill collars.

The compaction of the filter cake and its effect on the coefficient of friction postulated by Outmans was confirmed experimentally by Annis and Monaghan,8 who measured the friction between a flat steel plate and a filter cake in the apparatus shown in Figure 9-7. They found that it increased with time up to a maxi-

force involved in pulling stuck pipe, and that lubricants reduce adhesion and thus reduce pull-out force. Apparently some surfactants also reduce adhesion. For instance, when measuring friction in the apparatus shown in Figure 6-24, Wyant et a/86 observed that when a styrene butadiene block copolymer was added to an invert oil emulsion mud, the plate would not adhere to the cake. An example of the magnitude of adhesive force may be deduced from the work of Courteille and Zurdo.6a They measured the pull-out force when the pipe simulator shown in Figure 9-4 was fully embedded. Table 9-2 shows that when the mud pressure was zero, the pull-out force per unit area of pipe-to-cake contact (which may then be taken as a measure of adhesion) was almost the same—about 0.1 daNV cm2 (1.40 psi)—for all three cake thicknesses. When mud pressure was applied, the pull-out force increased with increasing cake thickness because of decreasing pore pressure at the cake/pipe interface.

Table 9-2

Pull-out force after maximum embedment. (.After Courteille and Zurdo.ta)

Table 9-2

Pull-out force after maximum embedment. (.After Courteille and Zurdo.ta)

Mud

Pull-out pressure daN/cm2 (psi) Mud pressure: zero 40 x 10s Pa (580 psi)

Low filter loss, lOcc, 2mm API Medium filter loss, 70cc, 4mm API High filter loss, 120cc, 6mm API

0.09 (1.305) 0.13 (2.45) 0.1 (1.45) 0.23 (3.33) 0.1 (1.45) .30 (4.35)

Differential sticking is particularly liable to occur when drilling high-angle holes from offshore platforms. In such circumstances, the weight component of the collars normal to the wall of the hole, and erosion under the collars, may be so high that no external filter cake can form (see Figure 9-3c). The weight of the collars is then borne by the formation, and the cake in the fillet between the collars and the formation will not be compacted when rotation ceases. The fric-tional forces acting on the collar will then derive in part from the friction between the collars and the formation, and in part from the effective stress between the cake in the fillet and the collars. In the section on inclined holes in Chapter 5, it was shown that a bed of cuttings tends to form on the low side of the hole when annular velocities are low. Evidence obtained by Wyant et aPb leads them to suggest that such cuttings will become incorporated in the filter cake, greatly increasing sticking tendencies.

Prevention of Differential Sticking

One way to prevent differential sticking is to minimize the contact area by suitable drill string design. Non-circular collars, fluted or spiraled drill collars, and driil pipe stabilizers have been used for this purpose. Long drill collar sections and oversized (packed hole) collars increase the contact area, and for that reason increase the chances of stuck pipe. This effect may be offset by drilling the hole more nearly straight.

Another approach is to maintain suitable mud properties. Outmans6 showed that the pull-out force increased with differential pressure, contact area, thickness of the filter cake, and coefficient of friction. The differential pressure may be minimized by keeping the mud density as low as possible, consistent with well safety. To minimize contact area and cake thickness, cake permeability should be kept low, and drilled solids content should be reduced by rigorous de-silting. Remember that cake thickness does not necessarily correlate with filter loss (see section on cake thickness in Chapter 6), and therefore should always be directly measured when concerned with differential sticking. The coefficient of friction of the filter cake depends on the composition of the mud. A number of papers on this subject have been published,89101,a llb but correlation between them is difficult because of differences in the testing methods and procedures. Some investigators measured the torque or pull-out force, while others measured the coefficient of friction in the lubricity tester shown in Figure 9-2. The latter tests are of doubtful value because the composition of the mud is unlikely to have the same effect on the friction between two steel surfaces as on the friction between steel and the mud filter cake. Results may be summarized as follows:

!. Oil-base muds have much lower coefficients of friction than water-base muds. Since they also lay down very thin filter cakes, they are much better muds for avoidance of differential sticking. This conclusion was strikingly confirmed in the field study by Adams,7 who found that out of 310 cases of stuck pipe in southern Louisiana, only one occurred when oil-base mud was in the hole.

2. Sufficient evidence is not available for establishing which class of waterbase muds yields filter cakes with the lowest coefficient of friction. The best (though rather limited) data were obtained by Simpson,10 who measured the torque required to free a disc embedded in a cake of standard thickness at elevated temperatures, under conditions of both static and dy namic filtration (see Figure 9-9 and Table 9-3).

3. Barite content increases the friction coefficient of all muds.

4. Emulsification of oil or the addition of friction reducers to a water base mud reduces the force required to free stuck pipe. Krol,,a compared the effect of diesel oil and various commercial additives on pull-out force in an apparatus closely simulating downhole conditions. He found that 2% diesel oil reduced the force required by 33%, and that larger amounts had no further effect. Only a few commercial additives reduced the pull-out force significantly more than 33%, and some reduced it considerably less. The amount of additive required to achieve maximum reduction depended on the amount of solids in the mud and the degree of dispersion. For example.

Table 9-3 Differential Pressure Sticking Tests*

(Filter cake deposited dynamically at 200°F [93 C] 1/32 inch (0.8 mm) thick. Differential pressure 500 psi [35 kg/cm2].)

(All muds weighted to 14 lb/gal [1.68 SG] with barite)

Torque after 30 minute set time (in—lb)

Lahoratory-prepared muds:

Fresh water chrome lignosulfonate Gyp-chrome lignosulfonate invert emulsion oil-base mud

Field muds:

Fresh water chrome lignosulfonate Gyp-chrome lignosulfonate Gyp-chrome lignosulfonate + 8% oil Chrome lignite/chrome lignosulfonate Invert emulsion oil-base mud Asphaltic oil-base mud

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