Pwpfkxspj94

pw includes the hydrostatic pressure of the mud column, pm, plus the pressure loss in the rising column if the well is being circulated, plus any transient pressures such as surge pressures when pipe is being run into the hole.

A distinction must be made between the pressure required to initiate a fracture and that required to extend it. As discussed in Chapter 8, there is a concentration of hoop stresses around the borehole. The value of these stresses depends on the ratio between the two principal horizontal stresses, a2 and ct3, and they may not be distributed evenly round the circumference of the borehole.33 In order to initiate a fracture, pw - pf must be greater than the minimum hoop stress, and in order to extend it beyond the hoop stress zone, it must be greater than ct3. The minimum hoop stress may vary from zero to twice a3, so the initiation pressure may be greater or smaller than the extension pressure, as shown in Figure 9-29.

In a drilling well, mud density must be kept great enough to control formation fluids, but not so great as to induce a fracture. In a normally pressured formation, an ample margin of safety ensures that no problem arises. In geopressured zones, however, the difference between the fracture pressure and the formation fluid pressure becomes very small as the geopressuring increases. Ability to predict formation and fracture pressures then becomes important so that mud and casing programs may be planned to minimize the risks.

Formation pore pressures may be determined from shale resistivity logs, or from acoustic logs in nearby wells. Shale bulk density is directly related to shale resistivity and to a function of shale transit time.34 Thus a plot of either shale resistivity or a function of transit time reveals anomalies in bulk density (see Figure 9-30) which are related to pore fluid pressures. The precise relationship depends on the geologic region, and must be determined empirically by measurement of formation fluid pressures in interbedded sand lenses. Figure 9-31 shows an example of fluid pressure gradient versus a shale acoustic parameter. Once such a relationship is established, it may be used to predict formation fluid pressures in future wells.

A less accurate but more convenient method depends on plotting drilling rate versus depth.35 Drilling rate is related to pm — pf, as shown in the previous see-

Figure 9-30. Shale travel time and bulk density versus burial depth. (From Hoffman and Johnson.34 Copyright 1965 by SPE-AIME.)

Pore pressures may also be determined from gamma ray logs.36b These logs reflect the degree of shaliness of a formation; consequently, there is a regional correlation between gamma ray curves and shale compaction. As discussed above, shale density can be correlated by experience with pore pressure. Therefore, gamma ray curves can be similarly correlated, and any departure from the normal regional gamma ray-depth curve can be related to a change in pore pressure. The gamma ray values can be measured while drilling (MWD) and thus provide real time information.

Fracture pressure at any depth of interest may be predicted by substituting pore pressures, determined as outlined above, in Equation 9-4, provided that the regional value of kx is known. Methods for determining kx empirically have been published by Eaton37 and Matthews and Kelly.38 Although their rationales differ, both methods are based essentially on the degree of compaction of shales, as

Drilling and Completion Fluids 0.400

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