Stress measurement interpretation using the hydraulic fracture method explicitly assumes that the rocks are linear elastic materials. Because this is seldom an acceptable assumption in high porosity or fractured materials, we present a non-linear elastic model that more closely describes real rock behavior. The analytical model demonstrates that fracture initiation pressure ( FIP) depends on the material stiffness, which is stress-dependent. Also, we will show that FIP depends on the Poisson's ratio of the non-linear material. Focusing only on Poisson's ratio, we demonstrate that, compared to a linear elastic model, a higher FIP is expected for rocks with a Poisson's ratio greater than certain value, and a lower FIP is expected for rocks with a Poisson's ratio less than the value. Our calculated results demonstrate that the conventional interpretation of FIP for stress measurements may be significantly in error, particularly for high porosity strata. The new equations developed may help in interpretation of fracturing data.
Although this has been widely accepted in petroleum engineering and geomechanics, many unsatisfactory results are known in practice. Assuming hydrostatic loading, Wang and Dusseault[ 1991a,b] show that no information of in situ stress can be obtained from fracture breakdown analysis in a boreholes surrounded by plastic yielded material. 1986]. Thus, in this paper we investigate the effect of a stress-dependent Young's modulus on the stress distributions around a wellboreand analyze the consequences on in situ stress measurements. Haimson and Fairhurst[1969] conducted experimental confining stress determination interpreting results with the linear elastic model. They observed that predicted breakdown pressures (B P) were always higher than measured BP for impermeable media. Whereas part of this disparity may be the result of poor estimates for To, the larger part is likely the result of an inadequate constitutive model. Although BP is related to the pressure which initiates tensile parting (fracture initiation pressure, FIP), the former is larger than the latter, and specifies the pressure at which a fracture suddenly propagates in a temporarily unstable manner through the stress concentration around a borehole. The FIP is the pressure at which the local To is exceeded, and may be equal to or less than the BP. According to fracture mechanics concepts, a critical length required for unstable propagation has been invoked to explain discrepancies [Abou-sayed et al., 1978; Ishijima and Roegiers, 1983]. Boone [1989], however showed that numerical non-linear fracture analysis predictions may be 30% higher than for linear prediction. Here, we present an alternative and analytical approach to analyze fracture data, and we will argue that at least part of the discrepancies are the result of a non-linear stiffness, which causes a redistribution of the tangential stresses reducing the magnitude of the stress concentration and perhaps relocating it away from the borehole wall. This simple analysis may have limitations, but it clearly shows that hydraulic fracturing pressures are not independent of material properties, and that FIP may be much lower than BP becausec s?] max is located away from the borehole wall.
