New method of XRF/XRD based mineralogy for estimating matrix-modulus, Biot’s-coefficient and effective-stress using VRH and HS bounds of rock physics principles
Abstract:
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. Effective stress is also useful in any triaxial core testing in the laboratory for calibrating log-based estimations. Effective stress (Image) is expressed as difference between total stress (Image) applied and existing pore pressure (Image) multiplied by Biot’s coefficient, Image. The ‘Image 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 ‘Image’ is much smaller than unity. Traditionally, ‘Image’ is expressed in terms of bulk modulus (Kb) and matrix bulk modulus (Kma) as in Image The Kb is estimated by acoustic logs as well as measured by triaxial test in the laboratory with due care to distinguish between pore- and bulk compressibility and stress path used. However, Kma is difficult to measure, especially in low porosity or low permeable formation. The common practice is to estimate it theoretically; for example, limestone is assumed to have a Kma ~ 75GPa, sandstone with Kma ~ 36GPa.
Current advancement in hardware and software used in Mud-logging or Surface-logging at the rig-site has enabled use of portable X-ray fluorescence (XRF) and X-Ray diffraction (XRD) tools which are low cost and results obtained from them are fast. These tools and their analysis have been used in geomechanical analysis first time to get inorganic elements and successively the mineralogy for estimating Kma. The XRF/XRD analysis obtained from two different wells located in different parts of the world were analyzed and investigated. The mineralogy obtained from XRF are compared with that obtained from XRD and compared from laboratory-based core testing. The well-known rock-physics principles of upper-bound Voigt (1910), lower-bound Reuss (1929), and an average of two, Hill (1963) models as well as upper and lower Hashin-Shtrikman (1963) bounds were compared. Finally, the Biot’s coefficient obtained from Voigt, Reuss, Hill and Hashin-Shtrikman bounds were compared with porosity-based estimations and compared with laboratory testing. The effective stress obtained from above gives a great confidence in modeling and simulation of sub-surface integrity evaluation, calibrating horizontal stresses for both geothermal, unconventional, and hydraulic fracture design applications. The effective stress could also help determine the decline characteristics of porosity, permeability and production history reliably in the field.
