ABSTRACT

Laboratory measurement of P- and S-wave velocities (VP and VS, respectively) under confining pressure indicates that with an increase in confining pressure, VP and VS will increase. The trend is exponential at low pressures, transitioning to linear above a critical pressure. However, the trend of the velocity-pressure curve for each rock specimen may be determined knowing the coefficients of this curve. We first studied how the coefficients of the velocity-pressure curve were expected to be functions of elastic moduli. Then, four empirical equations were used to estimate four coefficients of the velocity-pressure curve, using the rock density and VP and VS at atmospheric pressure (unconfined conditions). This analysis was carried out based on laboratory experiments on 285 rock specimens of different lithology from around the world, namely the United States, China, Germany, Iran, and deep-sea-drilling projects. For each rock specimen, VP and VS were measured at different confining stress levels, rendering more than 4000 data points. The accuracy of the estimated wave velocities was on the order of 2%–3% of the measured values on average. This methodology is especially valuable for prediction and analysis of the rock behavior at deep well conditions. This is applicable for predicting geophysical properties of the earth’s crust at depth, geomechanical study of hydrocarbon and geothermal reservoirs, wellbore stability analysis, and in situ stress determination.

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