Rock physics model-based investigation on the relationship between static and dynamic Biot's coefficients in carbonate rocks

Abstract

Biot's coefficient is an essential factor for estimating reliable-effective stress and an efficient tool in understanding the rock's response to pressure and stress changes. This coefficient is normally considered as a crucial parameter for reservoir geomechanics studies, such as wellbore stability, improving production rate, and hydraulic fracturing of reservoirs. However, its measurement and modeling methods, especially in carbonate rocks, have not been sufficiently studied. The scope of this study is to investigate the relationship between static and dynamic Biot's coefficients for a carbonate oilfield in the southwest of Iran. In this study, 13 core-plug samples were measured from a carbonate oilfield under static and dynamic conditions. Static Biot's coefficient was calculated using stress loading tests and volumetric strain measurements by changing confining and pore pressures. Dynamic Biot's coefficient calculated using ultrasonic measurements under ambient conditions and applying rock physics modeling. We used two workflows based on carbonate rock physics models for two separate pore type models calculation; the first one uses the usual form of Gassmann's theory, and the second one uses its simplified form with a defined C-factor exponent. Then, two dynamic Biot's coefficients were modeled from these pore models along with the calculated grain bulk modulus and the obtained dry bulk modulus. We showed that the dynamic Biot's coefficient in the second approach follows a better agreement with the static Biot's coefficient due to the higher accuracy of the estimated porosity model. Our results also show that static and dynamic Biot's coefficients depend on the pore geometry. As a result, the increasing volume fraction of stiff (moldic and vuggy) pores decreases Biot's coefficient compared to soft (crack) pores. In addition, we used the C-factor parameter calculated from the simplified form of Gassmann's equation to investigate this relationship with the pore geometry. The results showed that C-factor gives a good accuracy for converting dynamic to the static Biot's coefficient based on the pore structure. This, furthermore, was confirmed by the pore model stiffness study. The results of this study can provide the necessary information and relationships for modeling the static Biot's coefficient as an essential parameter in geomechanical studies for exploration and development programs.