Nonlinear Elasticity and Hysteresis
Nonlinear Elasticity and Hysteresis
Dynamic Pressure and Temperature Responses of Porous Sedimentary Rocks by Simultaneous Resonant Ultrasound Spectroscopy and Neutron Time-of-Flight Measurements
James A. TenCate, Timothy W. Darling, and Sven C. Vogel
1.1 Introduction and Background
Rocks are everywhere, yet there are still surprising puzzles about their peculiar dynamic elastic properties, especially their hysteresis, non-Hookean response, and rate-dependent behavior. Since before recorded history, mankind has been making dwellings, hammering out monuments, and even constructing huge buildings out of rock, for example, the famous Strasbourg Cathedral built in the Middle Ages is made almost entirely from Vosges sandstone. Nowadays, one extracts oil and gas from rocks, explores ways to store excess CO2 in them, and tries to mimic their resilience and durability with concrete. The imperfect way in which mineral grains end up cemented into rocks dictates how fluids move in oil or gas reservoirs or in aquifers. Indeed, these very fluids are often a key mechanism for that cementation. The diagenesis of rocks, their formation, and cementation history are of great geological interest as well. Hence, the dynamic elastic properties of rocks have been a topic of continuing scientific study for well over a century.
To narrow the focus of this chapter, the subject is primarily the behavior of rocks that have commercial interest. These rocks may contain oil and gas, or might be considered as a reservoir for CO2 storage. These rocks are primarily sedimentary, and the focus of this chapter will sharpen even more, dealing exclusively with sandstones. A sandstone is an imperfectly cemented collection of quartz grains, which is porous and permeable to fluids (which often play a key role in the cementation) and may contain significant amounts of clays and other materials. In the experiments described here, the rocks studied will be extremely pure and clean sandstones, 99+% pure SiO2 formed from quartz (prehistoric, 77 MYBP) Aeolian beach sand, known as Fontainebleau sandstone . Such rocks are simply composed of the grains and cementation.
How does one describe and examine such a sandstone and how is it different from man-made materials? A thin section examined under a polarizing microscope can show the crystallographic orientation and the nature of the grains, bonds, and cementation. A thin section of Fontainebleau sandstone is shown in Figure 1.1 . All the grains are roughly of the same size (about 150-200 µm), and none of the material in the section shown here has any significant polycrystalline components and very little of it is amorphous or glassy (which shows up as black under crossed polarizers). However, the reality is that a thin slice of a rock really does not give a very good representation of the porosity and permeability or even of the cementation. Care must be taken in extracting distributions of pore and grain sizes from sections, and often the cementation at grain contacts is difficult to identify. Amorphous cement, for example, can easily be missed and more advanced petrographic techniques such as cathodoluminescence or electron backscatter diffraction in an SEM must be used . Occasionally, pore casts - where an epoxy is spun into the pore space and the sand dissolved away with an acid - are made to study the three-dimensional network of pores . X-ray micro-CT images on very small samples are made as well, originally to provide an input for modeling, but similar to thin sections, they contain no information on the mechanical properties of the system. The contact network of grains, the pore space they can rotate into, and the fluids that can move around in that pore space (e.g., water, oil, and gas) all couple to the dynamics of a rock; direct measurements on the scale of these features is extremely difficult.