Mudstone Geophysical Properties for Pressure Prediction

Mudstones are nearly ubiquitous in sedimentary basins yet mudstones remain perhaps the most poorly understood lithology from a geophysical perspective. In particular, density and neutron logging measurements of mudstone porosity conflate the mechanically distinct porosities of both immoveable (bound) water, and moveable (pore space) water. Immoveable water is mechanically part of the crystalline structure of the mudstone and contributes to both the bulk modulus and shear modulus of the rock. Moveable water in the pore spaces contributes to the bulk modulus of the saturated rock, but not to the shear modulus.

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.