The concept of ‘effective stress’ is the foundation of any subsurface investigations which controls the deformation, fracture, failure, and production decline characteristics including dynamic acoustic wave propagation or specifying confining pressures in laboratory testing. Effective stress (σ′) is the difference between total stress (σ) and existing pore pressure (Pp) multiplied by Biot's coefficient, α. The ‘α′ is expressed in terms of bulk modulus (Kb) and matrix bulk modulus (Kma) as in 1 − Kb/Kma. The Kb is estimated by acoustic logs as well as measured by triaxial test. However, Kma is difficult to measure, especially in low porosity or low permeable shale/caprock or crystalline rocks. Current advancement in hardware and software enabled use of portable X-ray fluorescence (XRF) and X-Ray diffraction (XRD) tools to get inorganic elements and successively mineralogy for estimating Kma and further constrain α using rock-physics models (VRH or HS) for better confidence in modeling and simulation.
In any civil, mining, or petroleum application the concept of stress (or strain) under the influence of load or displacement is the foundation of geomechanical investigations. However, since the subsurface geological formation consists of pore, voids and fluid pressure, it is the ‘effective stress’ and not the ‘total stress’ which controls the deformation, fracture, failure, and production decline characteristics including dynamic acoustic wave propagation in rock formations.
Fig 1 shows the elastic behavior of volumetric strain change for dry and saturated sandstone under laboratory testing environment while changing the confining and pore pressure (Pp). While ignoring the Pp, change in elastic behavior is not explained, by using the concept of Terzaghi (1934) effective stress the response in elastic behavior is better explained. However, while incorporating the concept of Biot (1941), full elastic behavior is best explained [modified after Nur, 1971].
Effective stress is also useful in any triaxial core testing in the laboratory for calibrating log-based estimations. Effective stress (σ′) is expressed as difference between total stress (σ) applied and existing pore pressure (Pp) multiplied by Biot's coefficient, α as postulated by Terzaghi, (1934) and Biot (1941), Eq. (1). The ‘α′ for highly porous rocks is unity where load applied is counteracted equally by grain-matrix and pore-pressure. However, for low porosity and low permeable tight rocks as encountered in unconventional reservoirs, CCUS cap-rocks, or geothermal crystalline rocks, only a fraction of load is shared by pore fluid and the ‘α’ is much smaller than unity.
