Different forms of gassmann equation and implications for the estimation of rock properties
Abstract
Three new equivalent forms of Gassmann equation are presented that are useful when the unknown parameters are the Biot- Willis coefficient, the dry bulk modulus, and/or the grain matrix bulk modulus. We apply these equations to several sets of laboratory measurements to determine the profiles of grain matrix bulk modulus and Biot-Willis coefficient as functions of applied pressure, and perform a Monte Carlo simulation to examine the effect of uncertainty and/or measurement errors on the calculated grain matrix bulk modulus and Biot-Willis coefficient. The results show that the calculated grain matrix bulk modulus is relatively constant with applied differential pressure (up to 50MPa). However, it is very sensitive to the uncertainty of dry and saturated bulk modulus values. Thus, the presented new forms of Gassmann equation can be used to effectively quantify the uncertainty of dry and saturated bulk modulus (and subsequently, the seismic velocities) in fluid identification, fluid substitution, or reservoir monitoring applications.
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