Elasticity of high‐porosity sandstones: Theory for two North Sea datasets

Abstract

We analyze two laboratory datasets obtained on high-porosity rock samples from the North Sea. The first set is from the Oseberg field and represents slightly cemented quartz sands. The second set represents unconsolidated and almost uncemented sands from the Troll field. We find that dry-rock ultrasonic velocities in the Oseberg samples can be well modeled by the cementation theory where the grains mechanically interact through quartz cement. In the Troll samples contact cement is almost absent and grains are held together primarily by confining pressure. In this case velocities can be modeled by a combination of the Hertz-Mindlin contact theory (interaction of two smooth uncemented spheres) and the modified Reuss average (an isostress model for suspensions). The latter approach allows us to introduce pressure dependence in the velocity model. This theoretical model generally underestimates the observed Troll velocity values. For dry rock at high pressure the error may be as large as 15 percent. This error reduces to 10 percent in saturated rock. An important result is that this Hertz-Mindlin-Reuss model can accurately predict the high Poisson`s ratios generally observed in saturated loose sediments. Both theoretical methods have analytical expressions and are ready for practical use.