We seek to establish through laboratory experiments the extent of size and pressure-rate effects on hydraulic fracturing breakdown pressure under zero far-field stresses. We conclude, based on an extensive study of a granite and a limestone, that size and rate effects can be significant. However, such effects appear to be insignificant within the common ranges of borehole diameters and pumping rates used in field practice. In addition, laboratory tests in boreholes that are at least 20 mm in dia. yield breakdown pressures that are essentially unaffected by borehole diameter size and are directly usable in interpretation of field data.
The in situ state of stress is a crucial rock parameter required in tectonophysics and earthquake research, in rational design of underground engineering structures, and in planning effective ways of extracting minerals from the earth. The most commonly used method for the estimation of the principal horizontal in situ stresses (SH and Sh) at great depths is hydraulic fracturing. With this method, a segment of a vertical borehole is hydraulically pressurized until a critical value is reached (Pc) at which a vertical fracture is typically induced indicating rock tensile failure (breakdown). The directions of SH and Sh are evaluated from the orientation of the vertical fracture (assumed perpendicular to Sh). Further pressurization of the fractured interval followed by pump shut off results in another critical pressure (the shut-in pressure Ps obtained when the induced fracture closes back). The magnitude of Sh is expected to be approximately equal to Ps. SH can be estimated by using a hydraulic fracturing criterion relating the breakdown pressure Pc to the principal horizontal stresses based on the most appropriate material mechanical behavior and failure mode. Several hydraulic fracturing criteria have been developed including the linear elastic (LE) model (Hubbert and Willis, 1957), the poroelastic (PE) model (Haimson and Fairhurst, 1967), the linear elastic fracture mechanics (LEFM) model (Rummel, 1987), and the point stress (PS) model (Ito and Hayashi, 1990). An integral part of all these criteria, regardless of their assumptions, is the parameter Pco (the 'zero breakdown pressure' or the breakdown pressure under zero initial pore pressure and zero far-field stresses). In the LE and PE models Pco (which in the LE model is identical to Thf or the hydraulic fracturing tensile strength), should be a constant rock mechanical property. The LEFM and the PS models require that P00 be size-dependent, and some experimental evidence shows that in fact it does vary with borehole diameter length, and rate of loading (Haimson, 1968; Ratigan, 1981). If the field zero breakdown pressure could be determined unambiguously, die ability to estimate SH would be greatly improved provided the appropriate breakdown criterion were used. The objective of our research is to study the characteristics of the zero breakdown pressure through controlled laboratory tests. Specifically, we seek to establish whether there are size and loading rate effects, and if so how can laboratory test results be related to hydraulic fracturing field tests.
