The relationship of P- and S-wave velocities, density, and P-wave velocity provides a physical basis for the interpretation, inversion, and prediction of the well-logging and geophysical data of the carbonate reservoir, which is of great significance for deep geothermal exploration and exploitation. This paper takes the carbonate karst geothermal reservoir in the Niutuozhen geothermal field in North China as the research object, based on the physical property parameters such as P-wave velocity, S-wave velocity, and density obtained by petrophysical experiment and the geophysical exploration data of two-dimensional seismic and well-logging. The change rule of P- and S-wave velocities with temperature and pressure increases in carbonate rock is studied using mathematical statistics. The results show that the P-wave velocity of carbonate rocks increases with the increase in temperature below 50 °C, decreases with the rise in temperature above 50 °C, and tends to be stable above 100 °C. The change rule of S-wave velocity with temperature increasing is not apparent. Both P- and S-wave velocities increase with the increase in surrounding pressure, with the most extensive increase range of 10–15 MPa. At the same time, mathematical models of the P-S wave velocity relation and density-P-wave velocity relation applicable to the study area were also established. The density of the Wumishan formation of the Jixian System in borehole D15 was predicted under the constraint of well-logging. The results were in good agreement with the measured data, which proved the applicability of the constructed petrophysical model in the study area. It helps improve the accuracy and reliability of geophysical exploration data interpretation and reservoir prediction, and it has important practical application and theoretical value.
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