19 20 21 22 23

Figure 8-1. Composite overburden load. For all normally compacted Gulf Coast formations. (From Eaton.1 Copyright 1969 by SPE-AIME.)

Overburden Load-psi/ft.

Figure 8-1. Composite overburden load. For all normally compacted Gulf Coast formations. (From Eaton.1 Copyright 1969 by SPE-AIME.)

where a is the intergranular stress between the grains, and pf is the pressure exerted by the column of fluid within the pores, commonly referred to as the formation pressure or the pore pressure. pf increases with depth and the density of the fluid so that:

where p/is the density of the pore fluid. The pore fluid in the Mid-Continent region is fresh water, so pf/Z = 0.433 psi/ft (0.1 kg/cm2/m.)3 In the Gulf Coast region, the salinity of the pore water is around 80,000 ppm and p//Z - 0.465 psi/ ft (0.107 kg/cm2/m).4 In the Williston Basin, N. Dakota, the salinity is about 366,000 ppm, and pf= 0.512 psi/ft (0.118 kg/cm2/m).5

Abnormal or Geopressured Gradients

Abnormal pressures occur when fluids expelled by a compacting sediment cannot migrate freely to the surface.4 This condition typically occurs in a thick argillaceous series, because clays develop very low permeabilities when com pacted. For example, bentonite has a permeability of about 2 x 10 ~6 md when compacted at a pressure 8,500 psi (600 kg/cm2), corresponding to a depth of burial of 8,500 ft (2,600 m).6 The permeabilities of shales are of the same order of magnitude. Sandstones are mostly in the range 1 to 103 md.

When a clay formation is in contact with a sand layer that provides a permeable path to the surface, water is at first freely expelled from the clay as the clay compacts. However, a layer of low-permeability compacted clay develops adjacent to the sand, restricting flow from the remainder of the clay body. Thus, in a thick clay formation, the rate of expulsion is not able to keep pace with the rate of compaction, and the pore pressure therefore increases above that normal for the depth of burial. Such shales are said to be geopressured,1 or abnormally pressured. Any sand body, either interbedded in, or contiguous with the shale will also be geopressured if it is isolated from the surface either by pinch-out or faulting (see Figure 8-2). Geopressures will, in the course of geologic time, decline to normal pressures, but the thicker the shale, the longer the time required.

Geopressures may have any value up to the total weight of the overburden, and the density of the mud must be increased accordingly. Thus, densities greater than 19.2 lb/gal (2.3 SG) may be required to control formation fluids— oil, gas, or water—in geopressured formations.

Figure 8-3 shows typical subsurface pressures and stresses in the Gulf Coast region.

Because of the abnormally high water content of geopressured shales, a plot of bulk density versus depth will identify geopressured zones and indicate their magnitude, as shown in Figure 8-4.

Geopressures may be encountered at quite shallow depths, e.g., at about 4,000 feet (1,200 m) in the Forties Field, North Sea,8 but highly geopressured formations are only found at considerable depths, and the geopressuring is usually associated with the diagenesis of montmorillonite to illite. Illite contains much less water of hydration than montmorillonite, so the diagenesis is accompanied by the expulsion of water from the clay crystal, thereby increasing the geopressure. It has been established beyond doubt that the geopressures found in the Gulf Coast at depths of about 10,000 feet (3,000 m) are associated with diagenesis.9,10'11,12 It is known that the conversion of montmorillonite to illite takes place under pressure at temperatures of about 200°F (94 °C), if the electrochemical environment is suitable. The requisite conditions are present in the Gulf Coast from about 10,000 feet down. Furthermore, some experiments with artificial diagenesis, in which sediments from Gulf Coast wells were heated with simulated sea water in pressure bombs, checked well with field data.13 Finally, montmorillonite is the dominant clay mineral found in cores down to 10,000 feet, but decreases thereunder, and is almost completely replaced by illite at 14,000 feet (4,300 m).

Abnormally high pressures may also be found in formerly normally pressured formations that have been elevated above sea level by tectonic forces, and some

Figure 8-2. Types of reservoir seals necessary to preserve abnormal pressures. (From Dickinson.* Courtesy AAPG.)

surface layers then eroded. Isolated sand bodies within such formations will then have high pore pressures relative to their depth below the surface.

The Behavior of Rocks Under Stress

The behavior of rocks under stress may be studied in a triaxial tester, such as that shown in Figure 8-5. A cylindrical specimen is enclosed in a flexible jacket, an axial load is applied by a piston, and an external confining pressure is exerted by a liquid surrounding the jacket. An internal pore pressure may also be applied.

a. Oil Creek Sandstone b. Green River Shale

c. Hockley Rock Salt

Figure 8-6. Stress/strain relationships for a sandstone, a shale, and a rock salt from triaxial tests of jacketed specimens. (From Handin and Hager. Courtesy Shell Development Co.)

c. Hockley Rock Salt

Figure 8-6. Stress/strain relationships for a sandstone, a shale, and a rock salt from triaxial tests of jacketed specimens. (From Handin and Hager. Courtesy Shell Development Co.)

The shear stress at this point is called the yield stress. Above the yield stress two types of deformation may occur:

1. Brittle failure: the rock shatters suddenly. This type of failure is exhibited by hard, indurated rocks, such as sandstones, as shown in Figure 8-6a.

2. Plastic deformation: rapidly increasing strain with little increase in stress, or a decrease in stress, until the specimen eventually shatters. This type of failure is exhibited by ductile rocks, such as rock salt and shales, as shown in Figures 8-6b and 6c.

Note particularly the difference between the ultimate strength, the ultimate strain, and failure. Ultimate strength is defined as the maximum stress on the stress/strain curve. Failure occurs when the ultimate strain is reached, and the rock shatters. In the case of brittle failure, the ultimate strength and the ultimate strain are reached at virtually the same stress. With both brittle and ductile rocks, the ultimate strength and the ductility increase with increase in confining pressure. Therefore, the strength and ductility of rocks in the earth's subsurface increase with depth of burial.

The Subsurface Stress Field

As already mentioned, a subsurface rock must bear the weight of the overburden, i.e., the solid matrix plus interstitial fluids. Equation 8-2 shows that the effective stress gradient resulting from this load is;

Since rocks are viscoelastic, the vertical stress generates horizontal components. According to Eaton,1 the horizontal components are equilateral, and may be determined from Poisson's ratio, which is equal to unit change in transverse dimension divided by unit change in length. However, this thesis involves the assumption that the sediments are rigidly confined, so that no lateral movement takes place. That lateral movements do, in fact, take place is shown by the extensive faulting observed in the earth's crust.

Hubbert and Willis2 have pointed out that the horizontal stresses are modified by the tectonic forces that have acted throughout geologic history. They resolve the effective stresses acting on a subsurface rock into three unequal principal components acting at right angles to each other. Thus ay is the greatest principal stress, regardless of its direction; a2 is the intermediate principal stress, and a3 is the least principal stress. The three possible arrangements of these stresses are shown in Figure 8-7. When the difference between cr, and a3 exceeds the

Figure 8-7. Three possible principal stress configurations in the earth's crust.

From the geometry of the Mohr diagram it may be shown that the least principal stress at faulting is given by

1 — sin <j> I 2c cos <j> 1 + sin <f)j 1 + sin <t>

Hubbert and Willis2 showed that c for unconsolidated sand is zero, and <p is 30° (Figure 8-9), in which case Equation 8-5 reduces to cr3 = lhox, and that approximately the same relationship holds for sandstones and anhydrite. They concluded that in regions such as the Gulf Coast where tectonic forces are relaxed and tension faulting (see Figure 8-10a) is prevalent, cr3 would be horizontal and that its value would vary between V3 and V2 au depending upon the stress history. In regions where there were active compressive tectonic forces, as indicated by overthrust faulting (see Figure 8-10b), oy would be horizontal, and cr3 would be vertical. In that case, the horizontal stress might be three times as great as the vertical, and the land would be rising.

Normal faulting, tensile tectonic forces. ^ = S-pf

Normal faulting, tensile tectonic forces. ^ = S-pf

Overthrust faulting, compressive tectonic forces. <r3 = (S-pf)

Figure 8-10. Normal faulting vs. overthrust faulting.

Bear in mind that the relationships between ax and cr3 given by Hubbert and Willis are valid only for the stated values of c and <p. For rocks with substantially different values of c and <p the relation between the two stresses may be deduced from Equation 8-5. For example, with unconsolidated clays, <p is zero (see Figure 8-11), and Equation 8-5 reduces to

When a hole is drilled into a subsurface rock the horizontal stresses are relieved, and the borehole contracts until the radial stress at its walls is equal to the pressure of the mud column, pw, minus the pore pressure, pf. The load is transferred to a zone of hoop stresses that create tangential shear stresses around the

- Ccf>!ti'"ne of QofChoiii
Figure 8-13, Determination of the depth of plastic zone for stability of a bore hole through a sandstone, a shale, and a rock salt. Note: cj) and c were determined from Mohr diagrams, using data from triaxia! tests shown in Figure 8-6, (From Broms,:5 Cour-tesy Shelf Development Co.) 5

Table 8-1

Horizontal Virgin Effective Stresses, and Equivalent Depths, at Elastic Limit of Borehole Walls*

Rock aQ at

Elastic-Limit

Equivalent depths assuming:

Horizontal stress = I Vertical

Horizontal stress = Vertical x 3

Oil Creek sandstone

17,000 psi 1190 kg/cm-

94,000 ft 28,600 m

10,500 ft 3200 m

Green River shale

7160 psi 500 kg/cnr

40,000 ft 12.200 in

4400 ft 1340 m

Hockley salt

820 psi 60 kg/cm2

4550 ft 1390 m

500 ft 150 m

Assumed: Pore pressure gradient 0-46 psi/ft

Equilateral horizontal effective stresses No mud cake, fluid flow or temperature effects Air in borehole

*Data from Broms,15 courtesy Shell Development Co,

Mitchell et al27a used the finite element method to analyze borehole movements in sandstones and limestones and obtained quantitative agreement with field data. Maury and Sauzay27b modified the Mohr-Coulomb theory to allow for the various stress conditions that occur around boreholes. They postulated 8 to 10 failure parameters, but found that any given drilling problem depended only on two or three of them. The various modes of failure are shown in Figure 8-15a. The top lefthand model corresponds to the spalling observed in the model borehole (see Figure 8-24) and the top righthand model corresponds to the anisotropic failure shown in Figure 8-26.

Nordgren24 obtained expressions for oe and pc under the condition that the principal horizontal stresses are not equal, which occurs in regions of active faulting, as discussed earlier in this chapter. If the horizontal stresses are not equal , then oe is not evenly distributed around the circumference of the hole—it is greatest parallel to the least horizontal stress, and least parallel to the greatest

Table 8-2

Horizontal Virgin Effective Stresses and Equivalent Depths for Collapse of Borehole Walls*

Table 8-2

Horizontal Virgin Effective Stresses and Equivalent Depths for Collapse of Borehole Walls*

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