A comparative study of the stress-dependence of dynamic and static moduli for sandstones

Understanding the differences between the static and dynamic elastic moduli of reservoir rocks is essential for the successful exploration and production of hydrocarbon reservoirs. However, the controlling factors on the dynamic-static discrepancy for sandstones remain ambiguous. Consequently, we have purposely selected three outcrop sandstone samples with large porosity contrast to investigate the effects of the stress state, magnitude, and load-unload history on the dynamic and static moduli through laboratory measurements. The results suggest that the dynamic moduli are systematically larger than the static moduli at almost any hydrostatic or deviatoric stress magnitude. In contrast, the static moduli are much more sensitive to the stress variations than the dynamic ones, leading to the decreasing dynamic-static difference upon hydrostatic loading and the increasing dynamic-static difference upon deviatoric loading. When the maximum stress in a cycle is initially reversed, the dynamic-static ratio tends to approach one, whatever the bulk modulus under hydrostatic pressure condition or the Young's modulus under triaxial stress condition. Under the subsequent unloading process, the static bulk modulus is always higher than that derived during loading. However, the unloading static Young's modulus is larger than the loading Young's modulus only at a relatively high deviatoric stress magnitude greater than 30 MPa, while showing an opposite trend at a low-stress condition of less than 25 MPa. From the microstructural viewpoint, it is believed that the static tests accumulate the elastic, viscoelastic, and nonelastic properties within a certain stress or strain range. In contrast to the dynamic modulus, the static modulus exhibits greater sensitivity to the pressure or stress changes under hydrostatic and deviatoric stress conditions. The strong stress dependence makes it important to consider the in situ stress conditions when establishing dynamic-static modulus relations.