Elasticity of high-porosity sandstones: Theory for two North Sea data sets

We have analyzed two laboratory data sets obtained on high-porosity rock samples from the North Sea. The velocities observed are unusual in that they seem to disagree with some simple models based on porosity. On the other hand, the rocks are unusually poorly-cemented (for laboratory studies, at least), and we investigate the likelihood that this is the cause of the disagreement. One set of rocks, from the Oseberg Field, is made of slightly cemented quartz sands. We find that we can model their dry-rock velocities using a cementation theory where the grains mechanically interact through cement at the grain boundaries. This model does not allow for pressure dependence. The other set of rocks, from the Troll Field, is almost completely uncemented. The grains are held together by the applied confining pressure. In this case, a lower bound for the velocities can be found by using the Hertz-Mindlin contact theory (interaction of uncemented spheres) to predict velocities at a critical porosity, combined with the modified Hashin-Strikman lower bound for other porosities. This model, which allows for pressure-dependence, also predicts fairly large Poisson's ratios for saturated rocks, such as those observed in the measurements. The usefulness of these theories may be in estimating the nature of cement in rocks from measurements such as sonic logs. The theories could help indicate sand strength in poorly consolidated formations and predict the likelihood of sand production. Both theoretical methods have analytical expressions and are ready for practical use.