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Slip Velocity of Particle S-A

20 40 60 80

YP, Yield Point, pounds per 100 feet2

Figure 5-58. Particle slip velocity versus yield point for 0.954 in. OD sphere. (From Hopkin & Copyright 1967 by SPE-AIME.)

mental evidence on this point is contradictory. Hopkin63 found that cuttings slip velocity correlated better with yield point than with any other rheological parameter (see Figure 5-58). Field experience reported by O'Brien and Dobson69a seems to confirm Hopkin's results: they found that troublesome cavings could not be cleaned out of large diameter holes in Oklahoma unless the yield point was increased to 30-40 lb/100 ft2. They also found, when drilling in granite sections, that the size of the cuttings increased as the yield point was increased. For example, the maximum particle dimension was 0.5 in. when the yield point was 19 lb/100 ft2, 1.1 in. when it was 55, and 1.6 in. when it was 85. On the other hand, Sifferman et al64 found that muds with a yield point of about 20 lb/ 100 ft2 (102 dynes/cm2) had no better transport ratios than Newtonian oils of equivalent viscosity. In one respect, however, their experiments did not fully simulate well conditions: in their tests the mud was pumped into the base of the column by a centrifugal pump, which must have reduced the structural viscosity to very low value, as occurs at the bit. In the well, the structural viscosity rebuilds as the mud rises in the annulus, but there would have been little time for it to do so in the comparatively short experimental annulus. Hussaini and Azar643 found that the YP/PV ratio, the apparent viscosity, the yield point, and the initial gel were the controlling rheological factors (but, as previously mentioned, these factors had no significant effect at rising velocities above 120 ft/min).

It has been suggested70 that a mud with a low value of n would also be advantageous because it would have a comparatively flat velocity profile (see Figure 5-23), and therefore, low shear rates and high local viscosities would prevail over the greater part of the annular radius. There appears to be no good experimental evidence—in which n was varied and all other factors held constant—to support this theory. One would certainly expect flat profiles to be an advantage in so far as they reduce recycling action observed bv Williams and Bruce,65 but.

on the other hand, reducing n reduces the mean effective viscosity, since fie = K(y)"-1.

Inclined Holes

The behavior of cuttings in high angle deviated wells is very different from that in vertical or low angle vyells.71,72-73'74'75,75a-75b In a vertical hole, slip velocity acts parallel to the axis of the hole. In inclined holes, slip velocity has two components, an axial one and a radial one. The axial component decreases as the angle of the hole increases, and is zero in horizontal hole. On the other hand, the radial component increases with the angle of the hole. Consequently, cuttings tend to form on the low side of high angle holes. High annular mud velocities are necessary in order to limit cutting bed formation.

Extensive laboratory tests under simulated well conditions by Okrajni and Azar75 showed that:

1. In holes with inclinations up 45°, laminar flow provided better cutting transport than turbulent, whereas turbulent was better at inclinations above 55°. There was little difference between the two regimes at inclinations between 45° and 55°.

2. When laminar flow was maintained, the higher the yield value of the mud the better the cuttings transport at inclinations below 45°, but yield value had little or no effect at inclinations above 550.

3. High YP/PV ratios provided better transport at all hole inclinations.

4. The effects of yield value and YP/PV ratios are greater at low annular velocities.

5. As would be expected, the rheological properties of a mud in turbulent flow had little effect on cuttings transport.

Note that although turbulent flow would provide better cuttings transport at high hole inclinations, it could not be used in many applications because of its adverse influence on borehole enlargement. Under such conditions, the highest annular velocity that will not cause turbulent flow should be used. A mud with a high effective viscosity will increase the critical Reynolds number, and thus enable a higher annular velocity to be maintained without causing turbulent flow.

Gavignet and Sobey75a developed a model, based on a momentum balance, which may be used to calculate a critical flow rate above which a bed of cuttings will not form. Its value is dependent on pipe, hole, and particle size (see Figures 5-58a,b). The eccentricity of the drill pipe has a major effect. Even when the flow is turbulent, a bed of cuttings will form at flow rates below a critical value. Calculations based on this model are in fairly good agreement with the results of experiments with water and carbopol by Iyoho72 (see Figures 5-58a and 5-58c).

Martin et al75b investigated the influence of mud properties, flow rate, and drill string rotation in cylindrical tubes and annuli in the laboratory, and checked their results against field data. Their results showed that:

IYOHO DATA + WATER A LOW VIS MUD O CARBOPOL X HIGH VIS MUD

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