(Pm - Pt) - Differential Pressure - psi tures, the width of which is initially very small. If the fluid does not flow in fast enough, a vacuum is created under the chips, while the full weight of the mud column acts on top of the chip.

The magnitude of the dynamic chip hold-down pressure depends on the rpm of the bit, the permeability of the rock, and the type of bit.17 For a given rock and bit, the dynamic CHDP increases—and the rate of penetration decreases—as the rpm increases, until a full vacuum is pulled under the chips, and then remains constant with further increase in rpm. The maximum dynamic CHDP is thus one atmosphere plus the pressure of the mud column, pm. Figure 9-18 shows the rate of penetration of various bits versus rpm when drilling in Belgian limestone, permeability 0.5 md. The differences in the performance of the various bit types are related to the velocity of the mud across the hole bottom (note, for instance, the superior performance of jet bits) which suggests that the filtration characteristics of the mud influence dynamic CHDP, presumably because they control rate of penetration of fluid into the cracks.

Bottom-Hole Balling

If the drill cuttings are not removed from beneath the bit as fast as they are generated, they will be reground, and a layer of broken rock will build up between the bit and the true hole bottom. From data obtained in the field, Speer21 showed that a plot of penetration rate versus weight was linear up to a certain bit weight, and then fell off rather rapidly. Since the decrease in rate was less at higher bit hydraulic horse power (see Figure 9-19). Speer concluded that the

Reduction factor for penetration rate

Rotary speed

Figure 9-18. Dynamic hold-down versus rotary speed. (From van Lingen.u Copyright 1962 by SPE-AIME.)

Rotary speed

Figure 9-18. Dynamic hold-down versus rotary speed. (From van Lingen.u Copyright 1962 by SPE-AIME.)

Figure 9-19. Influence of lack of hydraulic horsepower on "balling up" and penetration rate. (From Speer:21 Courtesy of Oil and Gas J.)

Weight on Bit - Thousand Pounds

Weight on Bit - Thousand Pounds

Figure 9-19. Influence of lack of hydraulic horsepower on "balling up" and penetration rate. (From Speer:21 Courtesy of Oil and Gas J.)

phenomenon was caused by inadequate scavenging of the cuttings from beneath the bit. In laboratory tests at high bit weights, a layer of crushed rock mixed with mud solids was noticed on the bottom of the hole at the conclusion of the tests.15 The importance of bottom hole cleaning has been shown by Maurer.18 He deduced that under conditions of perfect cleaning, the rate of penetration would be given by:


where R is the rate of penetration; C, a drillability constant; N, the bit rpm. W. the weight on the bit; D, the diameter of the bit; and S, the drillability strength of the rock. In laboratory experiments with full scale bits and near perfect cleaning conditions—atmospheric pressure, water as the drilling fluid, and impermeable Beeksmantown dolomite—he found this formula to be valid, except that the R/N ratio was not linear at rotary speeds greater than 300 rpm—obviously because of dynamic CHDP. On the other hand, when drilling with a mud pressure equivalent to a mud column of 3,000 feet (914 meters), all other conditions being the same, he obtained R/N and R/W curves very different from the theoretical, as shown in Figure 9-20. Since most drilling in the field is done with bit weights as shown from c to d on the curves, it is evident that inadequate bottom hole scavenging is a major factor restricting penetration rates in the field.

Bit Weight (A)

Rotary Speed

Figure 9-20. Rate/weight/speed relationships for imperfect cleaning. (From Maurer,18 Copyright 1962 by SPE-AIME.)

Bit Bailing

Like bottom balling, bit balling occurs at high bit weights. In hard formations the teeth become partially clogged with cuttings. How far such clogging restricts penetration rate is obscure because the effect is indistinguishable from bottom balling. Garnier and van Lingen16 postulated that when the cuttings are pressed against the bit surfaces, they adhere because of the difference between pore pres-

sure in the cuttings and the mud pressure. Thus they are held by a mechanism similar to differential sticking of drill pipe. Eventually the cuttings are released because filtration neutralizes the pressure differential.

A much worse type of bit balling occurs in soft shales, particularly gumbo shales and swelling shales that adsorb water from the mud. In this case, a ball of compacted shale may build up and cover the whole bit, preventing further drilling progress. The driller must then either try to spud the ball off, or pull a green bit. To avoid bit balling, gumbo shales are often drilled with less weight than would otherwise be optimum.

The severity of bit balling in soft shales is caused by two factors: (1) the differential pressures postulated by Gamier and van Lingen are magnified by the hydrational forces of compressed subsurface shales (see section on hydration of the borehole, in Chapter 8), and (2) adhesive forces become significant because the ductile shales deform, and are forced into intimate contact with the bit surfaces. As discussed in the section on surface free energy, in Chapter 7, short range attractive forces become effective when contact between solids is intimate. In addition, soft shales—or shales that become soft on contact with aqueous drilling fluids—have low internal cohesion and, as already mentioned, adhesion depends on the difference between the adhesive and cohesive forces.

The mechanism of adhesion in the case of bit balling is probably hydrogen bonding, extending from the molecular layers of water adsorbed on the shale surfaces to the layer of water adhering to the steel surface. Chesser and Perri-cone22 recommend the use of an aluminum lignosulfonate chelate* to prevent bit balling. This complex is adsorbed on the surface of the shale through linkages between the aluminum and the oxygen atoms in the silicate layer on the shale surface. These linkages thereby disrupt the hydrogen bonding. Because the aluminum is chelated, the concentration of aluminum ions in the aqueous phase is very low, so the mud is not flocculated.

The Effect of Mud Properties on Drilling Rate

Density is the most important mud property affecting penetration rate. For any given formation pressure, the higher the density, the greater will be the differential pressure, and, consequently, the greater the static chip hold down, and likelihood of bottom-hole and bit balling. Figure 9-21 summarizes the effect of pressure differential on drilling rate as observed in the laboratory by the various investigators discussed above; Figure 9-22 shows similar results obtained by Vidrine and Benit23 in a controlled field study. Note that in both figures, drilling rate decreased by over 70% when the differential pressure increased from 0 to 1,000 psi (70 kg/cm2). In addition, decreasing mud density decreases dynamic chip hold down, permitting faster

* A chelate is a heterocyclic ring of organic molecules having coordinate bonds with a metal ion.

to establish a filter cake on unconsolidated sands (100 to 200 psi). Note that, for a constant mud density and formation pressure gradient, the differential pressure increases with depth. For example, a 10 lb/gal mud would exert a differential pressure of 70 psi at 1,000 feet, and 700 psi at 10,000 feet if the formation pressure gradient remained unchanged at 0.45 psi per foot. In geopressured formations, safety of the well must be the first consideration, but do not increase the mud density unnecessarily; for instance, do not increase the density because of gas swabbed into the hole on a trip—reduce the gel strength or lower the hoisting speeds instead. Lower differential pressures can be carried if the mud returns are continuously monitored for gas, or if drill string telemetry is installed.

Viscosity is another mud property that materially influences penetration rate. Low viscosity promotes fast rates mainly because of good scavenging of cuttings from under the bit. The relevant viscosity is the effective viscosity at the shear rate prevailing under the bit, not the plastic or funnel viscosity. The determination of viscosity at high shear rates was discussed in the section on the generalized power law, in Chapter 5. Eckel24 obtained a rather good correlation between kinematic viscosity (viscosity/density) and drilling rate as shown in Figure 9-23 Note, however, that worthwhile increases in drilling rate were only obtained at viscosities less than 10 cs. The tests were made in a micro bit drilling machine with a wide variety of liquids: water, salt solutions, glycerine, oils, water-base and oil base muds. Viscosities were measured at the shear rates prevailing in the bit nozzies.

Low viscosities are particularly important at high rotational speeds because of lower dynamic chip hold down. When the bit tooth strikes, the fractures are at first exceedingly small and the viscosity of the filtrate is probably the relevant factor, but as the chips move out, the viscosity of the mud becomes relevant.

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