Mudstone Geophysical Properties for Pressure Prediction
Models of mudstones should be consistent with all known geophysically measurable properties of mudstones. Some obvious geophysical properties to start with are total porosity (or equivalently, density), P-wave velocity, and S-wave velocity. Earlier work modeling mudstones has utilized the Hashin-Shtrikman lower and upper bounds (Holt et al., 2004). Holt was able to produce P-wave and S-wave velocities from his model that replicated his shale laboratory measurements. Nevertheless, his model leaves a bit to be desired. Holt's mathematical model assumes spherically concentric distribution of elastic materials for constituent particles, which is not consistent with tabular clay minerals which can be described as platelets.
I propose an alternative mathematical model described by Reuss (1929) which assumes flat plates. This is more consistent with the repeated unit cell geometries that characterize individual clay platelets. Total porosities from the literature (Velde, 1996) are used as bounding constraints on the model, and the model separates the moveable and immoveable porosities based upon observations of clay compaction behavior. P-wave and S-wave velocities from this new model compare favorably with field and laboratory measurements (Hamilton, 1972, and Gregory, 1976). Better modeling of mudstones should ultimately lead to fewer surprises in practical pressure prediction as the mudstone-effective stress relationship becomes better understood.