Empirical determination of the effective solid modulus in organic-rich shales

Abstract

Calculating the change in the saturated bulk modulus of a saturated rock with new fluid properties requires a priori selection of an effective bulk modulus of the solid constituents. When the rock constituents have similar mineral moduli, the theoretical bounds on the solid modulus are close to each other. However, when solid properties vary greatly, as in organic-rich shales, the actual effective solid modulus of a physical rock may vary significantly between the bounds which results in uncertainty in the predicted change in the saturated bulk modulus of the rock. We use a semi-empirical rock physics model utilizing the Brown–Korringa equation for mineralogically heterogenous rocks and introduce three parameters to estimate the pore space compressibility, the dry frame compressibility, and the fractional position of the effective solid modulus relative to the Reuss and Voigt bounds. We optimize for these three parameters in seven organic shale formations and find that the Reuss bound for the effective solid material modulus best fits the data when organic content is high. Furthermore, we use this model to fluid substitute to 100% brine saturation and find Gassmann’s equation using the Hill average predicts similar saturated moduli to the semi-empirical Brown–Korringa rock physics model when volume fraction of solid organic matter is less than 5%. However, at higher organic contents, we find that the error using the Gassmann–Hill approach increases, and the semi-empirical Brown–Korringa model better fits the data.