## 2k 3k 4k 5k

Normal Stress (Compressive)

Figure 9-34. The composite failure envelope showing a family of Mohr stress circles tangent at point A and one Mohr stress circle tangent at each of points B and C. (From Secor.4i Courtesy Am. J. Science.)

Figure 9-35. A failure envelope diagram showing the effect of an incremental increase of fluid pressure on the position of the Mohr stress circle, assuming the total principal stresses remain constant. (From Secor.41 Courtesy Am. J. Science.)

Lithostatic Pressure

Lithostatic Pressure

5 10 15 20 25 30 Depth in Thousands of Feet

Figure 9-36. A graph for the case a! vertical showing the maximum depth in the earth where open fractures can occur for a variety of tensile strengths. The bulk specific gravity of the rock is 2.3. K is the tensile strength in 10s lb/ft2.1 x 10s lb per square foot = 694 psi = 49 kg/cm2. (From Secor41 Courtesy Am. J. Science.)

### 5 10 15 20 25 30 Depth in Thousands of Feet

Figure 9-36. A graph for the case a! vertical showing the maximum depth in the earth where open fractures can occur for a variety of tensile strengths. The bulk specific gravity of the rock is 2.3. K is the tensile strength in 10s lb/ft2.1 x 10s lb per square foot = 694 psi = 49 kg/cm2. (From Secor41 Courtesy Am. J. Science.)

In a drilling well the mud pressure, pm, normally exceeds pjand therefore if an open fracture is encountered, mud is certain to be lost until pm is reduced below Pr by the same mechanisms that limit the extension of induced fractures

### Openings With Structural Strength

When no tensile stresses exist in subsurface formations, voids can only exist if they have structural strength great enough to withstand the earth's compressive forces. Examples of such voids are:

1. Solution channels caused by water percolating through carbonate formations for millions of years. These channels may range in size from pinholes to caverns. Limestones often contain vugs (small cavities) interconnected by solution channels. The structural strength of cavities decreases with their size, so large caverns are only found at shallow depths.

### 2. Coarse granular beds such as gravels.

3. Natural fractures which have been closed by subsequent compressive forces but which retain some permeability because they are propped by irregularities or crystal growths on their sides, or by loose rock fragments. Such fractures may be anywhere from a few microns to several millimeters in width. Some otherwise impermeable formations have appreciable fracture permeability because of the presence of multiple microfractures.

Circulation will be lost into any opening as long as pm exceeds pf unless the drilling fluid contains particles large enough to bridge the opening. Openings in a compressive field are distinguished from tensile open fractures in that they do not enlarge unless pw exceeds pfmc.

### Lost Circulation Materials

An enormous variety of materials have been used at one time or another in attempts to cure lost circulation. They may be divided into four categories:

1. Fibrous materials, such as shredded sugar cane stalks (bagasse), cotton fibers, hoghair, shredded automobile tires, wood fibers, sawdust, and paper pulp. These materials have relatively little rigidity, and tend to be forced into large openings. If large amounts of mud containing a high concentration of the fibrous material are pumped into the formation, sufficient fric-tional resistance may develop to effect a seal. If the openings are too small for the fibers to enter, a bulky external filter cake forms on the walls of the hole, and is knocked off when the well is cleaned out.

2. Flaky materials, such as shredded cellophane, mica flakes, plastic laminate and wood chips. These materials are believed to lie flat across the face

The principle underlying diesel oil-bentonite (DOB) slurries is that large amounts of bentonite—300 lb/bbl (850 kg/m3)—can be readily mixed with diesel

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