Figure 9-32. d exponent—differential pressure relationship, bit run data. (From Jorderr and Shirley.35 Copyright 1966 by SPE-AIME.)

For Brunei

Depths less than 10,000 ft.

where SHmin = the total minimum horizontal stress (effective stress plus pore pressure)

pf„ = the normal pore pressure, assuming a gradient of 0.465 psi/ft

Measurements of the vertical distribution of SHmin in the lower Mesa Verde formation in Colorado have been made by Warpinski et al.nb Accurate, reproducible ISIPs were obtained by conducting repeated, small volume "minifracs" through perforations. Results showed that the value of SHmin depended on the lithology. In shales the horizontal stress approached that of the vertical, and fracture gradients were greater than 1 psi/ft, whereas in sandstones the gradients were 0.85 to 0.9 psi/ft.

Theoretical values of SHmin were calculated from the equation:

where v is Poisson's ratio, which was obtained from the long space sonic logs and experimentally determined Young moduli. The calculated values deviated substantially from the values measured in shales, indicating that the shales did not behave elastically—probably because of creep.

Daines38c developed a method for predicting fracture pressures from data obtained in the first fracture test in a wildcat well. His model for horizontal stress contains two components: an expression for the compressive stress created by the pressure of the overburden; and a superimposed stress, au created by tectonic forces, if any. A fracture then occurs when:

After the first fracture test, a, is obtained by subtracting the elastic component from the fracture pressure. Poisson's ratio is obtained from the experimentally determined values shown in Table 9-5. Lithology is determined from drill cuttings, and pore pressure by the usual means, previously discussed. Assuming that the ratio o,/o\ remains constant with depth, the fracture pressure at any subsequent depth can be calculated from the lithology and pore pressure at that depth. Use of the method is limited because aJox will only be constant with depth when the formations are close to horizontal and when the structure does not change significantly with depth.

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