The mechanical response of a high-porosity, weakly-cemented sandstone from the Oseberg field, North Sea has been characterized using laboratory experiments and discrete particle modeling to determine the effects of reservoir stress path and boundary conditions on rock compressibility. Laboratory experiments simulating reservoir depletion from initial reservoir conditions show that the compressibility is dependent on stress path. Compressibilities measured under an uniaxial strain path or a K value less than uniaxial strain are more than twice the corresponding value found for hydrostatic loading. The discrete particle model used in this study captures important characteristics of the stress-path-dependent deformation behavior of weakly cemented sandstones, but the model also has limitations. The modeling results suggest that stress sensitivity is closely related to grain-scale in-elastic deformation processes caused by path-dependent development of grain-scale shear and tensile failures. However, odometer experiments carried out on disintegrated samples of the Oseberg sand show that it is difficult to define a coefficient of friction for a granular material composed of circular particles that reflects the deformation behavior of irregularly shaped particles. Two-dimensional models also tend to overestimate the volumetric strain response of dilatancy relative to compaction because of the differences in porosity in three dimensions compared to areal density in two dimensions. Accordingly, simulation of the volumetric response of rock under different stress conditions will require a three-dimensional model not restricted to spherical particles.
Rock compressibility is a fundamentally important characteristic of hydrocarbon reservoirs because it provides a measure of both reservoir volume and producibility. Laboratory measurements of rock compressibility are applied to production forecasts, reservoir pressure maintenance evaluations, and reservoir compaction and subsidence studies (Johnson et al., 1989; Ruddy et al., 1989; Teufel et al., 1991; Rhett and Teufel, 1992). A limited number of laboratory studies indicate that compressibility is dependent on the anisotropic stress state in the reservoir and that changes in compressibility are dependent on the reservoir stress path during pore pressure drawdown. The importance of stress path and reservoir boundary conditions on compressibility has been clearly demonstrated in comparisons of rock loaded under hydrostatic and uniaxial strain boundary conditions. These studies have shown, almost without exceptions and seemingly independent of lithology, that compressibility declines at increasing pressure under hydrostatic loading while remaining almost constant under uniaxial strain conditions. Zheng (1993) measured compressibility of the Berea sandstone under different stress conditions and found that the bulk compressibility as a function of mean effective stress is almost linear under uniaxial strain conditions, while nonlinear stress dependence was prominent under hydrostatic loading. Qualitatively similar observations were made by Rhett and Teufel (1992) from testing a North Sea sandstone. Recent in situ stress measurements have demonstrated that many reservoirs follow stress paths (defined as the change in effective horizontal stress divided by effective vertical stress from initial reservoir conditions) that are significantly different from either hydrostatic stress or uniaxial strain boundary conditions (Teufel and Rhett, 1992). In most reservoirs the stress path is unknown, particularly in the early stages of the reservoir's life.
