The effect of injection-fluid flow through the borehole wall on hydraulic fracture breakdown pressure was studied theoretically and in the laboratory, for both low and high permeability rocks, under initially dry or saturated (under pore pressure) conditions. The results indicate that the conventional Hubbert and Willis equation developed for fluids that do not infiltrate rock does not apply, and suggest that the poroelastic model with appropriately derived Biot parameter and Poisson's ratio is more realistic. Fortunately, the difference between the two approaches is not significant under typical in situ stresses at shallow depths. However, at great depths (say over 1–2 km) use of the proper stress-pressure relation is critical if a more realistic maximum horizontal stress magnitude is to be determined.
Wells deeper than ever before are being drilled for oil production, for hot dry rock geothermal energy, for waste disposal, and for scientific purposes. The Kola Peninsula scientific well in the Soviet Union has reached the unprecedented depth of over 12 km, and ultra deep scientific borings are underway in Germany, Sweden, and elsewhere. However, most of our hydraulic fracturing (HF) stress measurements have been limited to shallower depths. Outside of the Michigan Deep-Well tests (Haimson, 1978) in which measurements were conducted to a depth of 5 km, hydraulic fracturing has so far been confined to the top 2 km below the surface. A major problem with deeper wells is that rock stresses tend to become larger, affecting the stability of the borehole with respect to both compressive failure as expressed in the form of breakouts, and tensile failure when subjected to internal pressurization as in hydraulic fracturing. At the University of Wisconsin, we have been investigating in the laboratory the mechanical conditions under which wellbore breakouts occur (Haimson and Herrick, 1986, 1989), and hydraulic fractures are induced (Haimson and Edl, 1972; Edl, 1973; Haimson and Huang, 1988; Huang, 1989), for in situ stresses ranging to levels encountered in ultra deep holes. This contribution summarizes our findings related to the stress-pressure relation in deep-well HF stress measurements.
The conventional elastic (E) model used to calculate in situ stresses from HF pressures assumes that the rock surrounding the wellbore is linearly elastic, isotropic, and impermeable to the fluid injected into the borehole (Hubbert and Willis, 1957). They used the known solutions of the "hole in a plate" and the "hollow thick cylinder" problems in linear elasticity to establish the relation between the tangential stress at the wellbore wall St, the injection-fluid pressure and the far-field minimum and maximum horizontal stresses Sh and Sh. They asserted that hydraulic fracturing is initiated when St becomes so small, as a result of increasing injection-fluid pressure, that tensile failure occurs. The criterion used was Steff- -T (where T is the tensile strength of the rock, and Steff- St - Po; Po is the pore pressure, and Steff is the effective minimum tangential stress at the wellbore wall, related to St by Terzaghi's effective stress law).
