* From Mondshine.1 From Oil and Gas J.

t Concentration in lb/bbl except for diesel oil which is given in bbl/bbl. X Mud A—15 g bentonite in 350 ml water; Mud B—15 g bentonite, 60 g Glen Rose shale, 3 i lignos,ulfonate. 0.5 g caustic soda in 350 ml water.

The effect of mud composition on wear and friction between tool joints and casing has been investigated by Bol.3b He found that small-scale lubricity testers, such as the API tester, do not represent casing/tool joint contact conditions. He therefore developed a full-scale tester, using tool joints and oilfield casing. Tests with this instrument showed that wear was very high with bentonite suspensions, but decreased with the addition of barite. Additions of 0.5-2% of commercial lubricants all reduced wear by about the same amount.

Coefficients of friction were calculated from the test data. The results may be summarized as follows: oil emulsion muds, 0.15; unweighted water base muds, 0.35-0.5; weighted water base muds, 0.25-0.35. Polymeric additives, diesel oil, and glass beads had no effect. Results with lubricants were erratic, but, in general, they reduced the coefficient of friction of unweighted and low density muds to about 0.25.

In assessing Bol's results, bear in mind that they do not necessarily apply to torque and drag in the open hole. In that case, the determining factor is the friction between the pipe and the mud cake in which the additives are incorporated.

Differential Sticking of the Drill String Mechanism of Differential Sticking

Stuck pipe is one of the commonest hazards encountered in drilling operations. Sometimes the problem is caused by running or pulling the pipe into an undergauge section of the hole, or into a key seat or a bridge of cavings. In such cases, the driller is usually able to work the pipe free. A more intractable form of stuck pipe, known as differential sticking, characteristically occurs after circulation and rotation have been temporarily suspended, as when making a connection. The phenomenon was first recognized by Hay ward4 in 1937, and the mechanism was demonstrated by Helmick and Longley5 in the laboratory in 1957.

The mechanism of differential sticking, stated briefly, is as follows: a portion of the drill string lies against the low side of a deviated hole. While the pipe is being rotated, it is lubricated by a film of mud, and the pressure on all sides of the pipe is equal. When rotation of the pipe is stopped, however, the portion of the pipe in contact with the filter cake is isolated from the mud column, and the differential pressure between the two sides of the pipe causes drag when an attempt is made to pull the pipe. If the drag exceeds the pulling power of the rig, the pipe is stuck. Thus, increasing drag when pipe is being pulled warns that the pipe is liable to differential sticking.

Outmans6 has made a rigorous analysis of the mechanism of differential sticking which may be summarized as follows:

The weight distribution of the drill string is such that the drill collars will always lie against the low side of the hole, and, therefore, differential sticking will always occur in the drill-collar section of the hole. When the pipe is rotating, the collars bear against the side of the hole with a pressure equal to the component of the weight of the collars normal to the sides of the hole. Thus, the depth the collars penetrate into the cake depends on the deviation of the hole, and on the rate of mechanical erosion beneath the collars relative to the rate of hydrodynamic erosion by the mud stream over the rest of the hole. Unless the hole is badly deviated, or the rate of rotation very high, the collars will penetrate only a short distance into the cake, as shown in Figure 9-3a.

When rotation is stopped, the weight of the pipe compresses the isolated mud cake zone, forcing its pore water out into the formation. As explained in the section on cake thickness in Chapter 6, the effective stress in a mud cake increases with decrease in local pore pressure. The effective stress therefore increases as pore water is forced out of the cake, and the friction thereby created between the pipe and the cake is the fundamental cause of differential sticking. After very long set times the pore pressure in the cake becomes equal to the pore pressure in the formation and the effective stress is then equal to the difference between the pressure of the mud in the hole and the formation pore pressure, i.e., pm — pf. The force required to pull the pipe is then aiven by:

where F is the force; A is the contact area, and u is the coefficient of friction between the collars and the cake. Because the ultimate value of F is not reached under normal field conditions, Outmans computed the value of F!, which he defined as half the ultimate value of F. He found that as well as increasing with u, (pm - Pf), and A, Fl increased with the compressibility and thickness of the filter cake, the hole deviation and the diameter of the drill collars. It decreased with increase in diameter of the hole.

In the drilling well, the pull-out force also increases with set time because filtration continues under static conditions. Thus, a static cake builds up around the collars, thereby increasing the angle of contact between the cake and the collars (see Figure 9-3b).

Courteille and Zurdo6a investigated pipe-sticking phenomena in the apparatus shown in Figure 9-4. Among other things, they measured fluid pressures at the cake/mud interface and at various points in the cake and filter media. They found that:

I. The major pressure drop occurred across the internal mud cake (see Figure

2. With a thin filter cake (2 mm API) there was no change in pore pressure at the cake/pipe interface during or after embedment (see Figure 9-5).

3. With thicker filter cakes (4 to 6 mm) the pressure at the cake/pipe interface fell with time after maximum embedment, but never reached the value in the pores of the uncontaminated porous medium (see Figure 9-6).

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