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Keysight Technologies Measuring Stress-Strain Curves for Shale Rock by Dynamic Instrumented Indentation Application Note
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2015 |
| Abstract | Three samples of shale rock, two from the Eagle Ford play, and one from the Haynesville play, were successfully tested by instrumented indentation. Results were remarkably repeatable, and hardness and Young's modulus were independent of force for test forces above 300 mN. For the two samples from the Eagle Ford play, the reduced moduli were 54.3 GPa and 40.6 GPa, and the hardness values were 1.55 GPa and 1.12 GPa. For the Haynesville sample, the modulus was 22.5 GPa and the hardness was 0.51 GPa. By assuming a Poisson's ratio of 0.25 and negligible work hardening, stress-strain curves were deduced from these indentation measurements. Finite-element simulations of indentation experiments were conducted wherein the simulated materials were assigned the deduced stress-strain curves. Simulated force-displacement curves matched experimental force-displacement curves reasonably well, thus lending credibility to the material model and to the indentation method of determining constitutive properties. Shale formations host vast natural gas and oil reserves which are accessed by hydraulic fracturing. Experts in the oil and gas industry have analytical tools at their disposal for optimizing fractures to maximize the productivity of a well, and these analytical tools require knowing the stress-strain curve for the shale, as well as other mechanical properties. The simplest elastic-plastic constitutive model is illustrated schematically in Figure 1 as a bi-linear stress-strain curve. Materials for which this model is appropriate experience elastic deformation so long as the principle stress remains below the yield stress, Y. The primary characterization of the elasticity of the material is the Young's modulus, E, which is the slope of the stress-strain curve prior to the onset of plasticity. For isotropic materials, elasticity is fully described by the Young's modulus and the Poisson's ratio, v. For stresses above the yield stress, the material deforms plastically, exhibiting large strains for relatively small increases in stress. If the material has a capacity for work-hardening, then the stress-strain curve has a positive slope, F, beyond the yield point. If the material has no capacity for work-hardening, then the stress-strain curve is flat beyond the yield point (F = 0). In summary, such materials are mechanically described by only four parameters: Young's modulus (E), Poisson's ratio (v), yield stress (Y), and hardening slope (F). Figure 1. Idealized bi-linear stress-strain curve which requires four material constants for full definition: E, v, Y, F. Introduction Indeed, shale is a complex composite of clay, minerals, and organic material. Yet there are reasons to hope that at large scales, relative to the microstructure, shale might succumb to a simple mechanical model like that illustrated in Figure 1, and that further, instrumented indentation might be used to obtain essential mechanical properties. Thus, an obvious question arises: If instrumented indentation is used to measure the mechanical properties, how large must the indentations be in order to measure properties which are relevant and representative of the bulk material? In the present work, we develop a methodology by which this question may be answered generally, and we apply that methodology to three specific shale samples. Finally, we verify both the constitutive model and the properties obtained by indentation using finite-element analysis, by comparing experimental and simulated force-displacement data. From this comparison between simulation and experiment, we speculate about how the constitutive model might be improved to more closely represent the true mechanical behavior of the shale. Review of Instrumented Indentation Theory For two smooth, isotropic, axisymmetric bodies in elastic contact, the reduced elastic modulus (Er), contact stiffness (S), and contact area (A) are related as [1, 2] |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://literature.cdn.keysight.com/litweb/pdf/5991-4754EN.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
