Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
Summary
We report detailed procedures for compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus coupled with synchrotron X-radiation. Such experiments allow quantification of the stress distribution within samples, that ultimately sheds light on compaction processes in geomaterials.
Abstract
We report detailed procedures for performing compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus (D-DIA) coupled with synchrotron X-radiation. A cube-shaped sample assembly is prepared and compressed, at room temperature, by a set of four X-ray transparent sintered diamond anvils and two tungsten carbide anvils, in the lateral and the vertical planes, respectively. All six anvils are housed within a 250-ton hydraulic press and driven inward simultaneously by two wedged guide blocks. A horizontal energy dispersive X-ray beam is projected through and diffracted by the sample assembly. The beam is commonly in the mode of either white or monochromatic X-ray. In the case of white X-ray, the diffracted X-rays are detected by a solid-state detector array that collects the resulting energy dispersive diffraction pattern. In the case of monochromatic X-ray, the diffracted pattern is recorded using a two-dimensional (2-D) detector, such as an imaging plate or a charge-coupled device (CCD) detector. The 2-D diffraction patterns are analyzed to derive lattice spacings. The elastic strains of the sample are derived from the atomic lattice spacing within grains. The stress is then calculated using the predetermined elastic modulus and the elastic strain. Furthermore, the stress distribution in two-dimensions allow for understanding how stress is distributed in different orientations. In addition, a scintillator in the X-ray path yields a visible light image of the sample environment, which allows for the precise measurement of sample length changes during the experiment, yielding a direct measurement of volume strain on the sample. This type of experiment can quantify the stress distribution within geomaterials, which can ultimately shed light on the mechanism responsible for compaction. Such knowledge has the potential to significantly improve our understanding of key processes in rock mechanics, geotechnical engineering, mineral physics, and material science applications where compactive processes are important.
Introduction
The rationale behind the method presented in this article is to quantify the stress distribution within rock and mineral aggregate samples during compression and subsequent compaction. Understanding the compaction in rocks and mineral aggregates is of great importance to reservoir and geotechnical engineering8,17,18,19,20,28,33. Compaction acts to reduce porosity, and therefore, leads to an increase in pore pressure. Any such increase in pore pressure leads to a decrease in effective pressure35. The consequence is that it will significantly weaken the reservoir rock, and can therefore be subjected to premature failure at lower stress. Some examples of the resulting consequences of inelastic deformation in the subsurface include: failure in sustaining long term production in oil and gas reservoirs28,33, surface subsidence8,18,19,20, and alteration of fluid flow patterns17. Therefore, a comprehensive knowledge of compaction processes in rocks and mineral aggregates could aid in reducing the possibility of such potentially negative consequences.
The great advantage of using the method highlighted here is that it provides a means to quantify stress distribution internally within a geomaterial5,6 with respect to the globally-averaged externally applied pressure12,22. Moreover, as an in situ experiment, the evolution of the stress distribution is time-resolved. The externally applied pressures considered range from relatively low values (tens of megapascals) to high values (several gigapascals). The stress within the sample is measured indirectly by using the atomic lattice spacing within individual mineral grains as a measure of the local elastic strain5,6. The atomic lattice spacing is determined with the aid of X-radiation, commonly in either the mode of white or monochromatic X-ray. For the white X-ray mode (e.g., DDIA at 6BM-B beamline of the Advanced Photon Source (APS), Argonne National Laboratory), the intensity of the diffracted beam X-ray beam is determined by not just one, but by an array of 10-element Ge detectors (Figure 1) distributed along a fixed circle at azimuthal angles of 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, 180°, 270°. For the monochromatic X-ray mode, the diffracted pattern is recorded using a CCD detector (e.g., DDIA-30 at 13-ID-D beamline of the GSECARS, APS, Argonne National Laboratory)18,23. Both X-ray modes allow quantification on how the stress varies in different orientations. This approach is fundamentally different from all previous studies of compaction in geomaterials.
In typical compaction studies, a cylindrical sample is compressed by an axial force that is applied across the cross-sectional area by the actuator25. Under such conditions, the magnitude of the applied stress magnitude is generally calculated by simply dividing the axial force (measured by a load cell) by the initial cross-sectional area of the sample. It should be noted that this applied stress magnitude is merely an average, bulk value and, as such, does not realistically represent how the local stress state varies, or is distributed, within a complex, heterogeneous, granular material. Detrital sedimentary rocks, which are examples of complex granular materials, are formed by aggregation of mineral grains that are subsequently compacted and cemented through depositional and diagenetic processes1,7,21,30,31. These aggregates naturally inherit pores that comprise the void spaces between grains, which are intrinsic from the geometry of grain packing modified by secondary dissolution. Hence, any applied stress is expected to be supported by and concentrated at grain-to-grain contacts, and to vanish at grain-pore interfaces.
In addition to the complexity of stress variation within a granular material, other factors further complicate studying compaction in these scenarios. First, the local stress field is vulnerable to any changes due to microstructural artifacts (e.g., grain shape, preexisting fractures) that are inevitably present within any detrital sedimentary rock. Second, although the magnitude of the applied stress acting upon the sample surfaces can be fully quantified, the distribution of stresses within the sample body remained poorly constrained. An end effect32 — a boundary effect whereby the average stress is concentrated near the contact between the loading rams and the samples due to interface friction — is well known to be exhibited in cylindrical samples loaded in compression. As an example, Peng26 demonstrated strain heterogeneity within uniaxially compressed granite samples subjected to a variety of end conditions. Hence, to accurately compute the local stress distribution in granular material, we present the following detailed protocol for performing X-ray diffraction (XRD) experiments on rocks and mineral aggregates, using a multi-anvil deformation apparatus at beamline 6-BM-B of the APS at Argonne National Laboratory.
Protocol
Representative Results
Discussion
We present the detailed procedure for carrying out XRD experiments using the multi-anvil cell at 6-BM-B. Perhaps the most critical, and yet most challenging, steps in the above protocol involve optimizing the quality of the sample. Such importance on sample quality applies to almost all rock and mineral deformation experiments. Firstly, it is critical for the end surface of the rock cores to be flat, with both ends parallel to each other and at the same time, perpendicular to the cylindrical surface. That will ensure the…
Divulgazioni
The authors have nothing to disclose.
Acknowledgements
The authors would like to gratefully acknowledge two anonymous peer reviewers and JoVE senior review editor Dr. Alisha DSouza for their invaluable comments. This research was performed at 6-BM-B of the Advanced Photon Source (APS) at Argonne National Laboratory. The use of this facility has been supported by Consortium for Materials Properties Research in Earth Sciences (COMPRES) under National Science Foundation (NSF) cooperative agreement EAR 11-57758, EAR 1661511 and by the Mineral Physics Institute, Stony Brook University. The authors acknowledge NSF for research funding for this program through EAR 1361463, EAR 1045629, and EAR 1141895. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract DEAC02-06CH11357. The cell assemblies are under COMPRES multi-anvil cell assembly development project. All the data files are available from the authors upon request (scheung9@wisc.edu). The samples and data are archived at Mineral Physics Institute at Stony Brook University.
Materials
| Rotatory Tool Workstation Drill Press Work Station with Wrench | Dremel | 220-01 | |
| MultiPro Keyless Chuck | Dremel | 4486 | |
| Variable-Speed Rotatory Tool | Dremel | 4000-6/50 | |
| Super small Diamond Core Drill – 2.5 mm | Dad's Rock Shop | SDCD | |
| Coolant | NBK | JK-A-NBK-000-020 | Grinding Fluid Concentrate US 5 gal / 20 L |
| commercial software package and codes for instrument control and data acquisition | IDL EPICS and SPEC | installed on the computer at the beamline | |
| CCD Camera | Allied Vision | Prosilica GT | installed at the beamline |
Riferimenti
- Bjørlykke, K. Relationships between depositional environments, burial history and rock properties. Some principal aspects of diagenetic processes in sedimentary basins. Sedimentary Geology. , 1-14 (2014).
- Burnley, P. C., Zhang, D. Interpreting in situ X-ray diffraction data from high pressure deformation experiments using elastic-plastic self-consistent models: An experiment using quartz. J. Phys. Condens. Matter Solid Earth. 20 (28), 285201 (2008).
- Burnley, P. C. Elastic plastic self-consistent (EPSC) modeling of plastic deformation of fayalite olivine. American Mineralogist. 100 (7), 1424-1433 (2015).
- Chen, J., Li, L., Weidner, D. J., Vaughan, M. T. Deformation experiments using synchrotron X-rays: in situ stress and strain measurements at high pressure and temperature. Phys. of the Earth and Planetary Interiors. 143, 347-356 (2004).
- Cheung, S. N. C. . Experimental deformation in sandstone, carbonates, and quartz aggregate. , (2015).
- Cheung, S. N. C., et al. Stress distribution during cold compression of a quartz aggregate using synchrotron X-ray diffraction: observed yielding, damage, and grain crushing. J. Geophys. Res. Solid Earth. 122, 2724-2735 (2017).
- Croizé, D., Ehrenberg, S. N., Bjørlykke, K., Renard, F., Jahren, J. Petrophysical properties of bioclastic platform carbonates: implications for porosity controls during burial. Marine and Petroleum Geology. 27 (8), 1765-1774 (2010).
- Doornhof, D., Kristiansen, T. G., Nagel, N. B., Pattillo, P. D., Sayers, C. Compaction and subsidence. Oilfield rev. 18 (3), 50-68 (2006).
- Durham, W. B., Weidner, D. J., Karato, S. New developments in deformation experiments at high pressure. Rev. Mineral. Geochem. 51 (1), 22-49 (2002).
- Fyfe, W. S. The evolution of the Earth’s crust: modern plate tectonics to ancient hot spot tectonics. Chemical Geology. (1-4), 89-114 (1978).
- Gerward, L., Mo, S., Topso, H. Particle size and strain broadening in energy-dispersive -ray powder patters. J. Appl. Phys. 47 (3), 822-825 (1976).
- Heap, M. J., Farquharson, J. I., Baud, P., Lavallée, Y., Reuschlé, T. Fracture and compaction of andesite in a volcanic edifice. Bulletin of volcanology. 77 (6), 55 (2015).
- Lavina, B., Dera, P., Downs, R. T. Modern X-ray diffraction methods in mineralogy and geosci. Reviews in Mineralogy and Geochemistry. 78 (1), 1-31 (2014).
- Leinenweber, K. D., et al. Cell assemblies for reproducible multi-anvil experiments (the COMPRES assemblies). American Mineralogist. 97 (2-3), 353-368 (2012).
- Li, L., Weidner, D. J., Raterron, P., Chen, J., Vaughan, M. T. Stress measurements of deforming olivine at high pressure. Phys. of the Earth and Planetary Interiors. 143, 357-367 (2004).
- Li, L., Weidner, D. J., Chen, J., Vaughan, M. T., Davis, M., Durham, W. B. X-ray strain analysis at high pressure: Effect of plastic deformation in MgO. J. App. Phys. 95 (12), 8357-8365 (2004).
- Minkoff, S. E., Stone, C. M., Bryant, S., Peszynska, M., Wheeler, M. F. Coupled fluid flow and geomechanical deformation modeling. J. Petroleum Sci. and Engineering. 38 (1), 37-56 (2003).
- Miyagi, L., et al. Deformation and texture development in CalrO 3 post-perovskite phase up to 6 GPa and 1300 K. Earth and Planetary. 268 (3), 515-525 (2008).
- Morton, R. A., Bernier, J. C., Barras, J. A. Evidence of regional subsidence and associated interior wetland loss induced by hydrocarbon production, Gulf Coast region, USA. Environmental Geology. 50 (2), 261 (2006).
- Nagel, N. B. Compaction and subsidence issues within the petroleum industry: From Wilmington to Ekofisk and beyond. Phys. And Chem. of the Earth, Part A: Solid Earth and Geodesy. 26 (1-2), 3-14 (2001).
- Nichols, G. . Sedimentology and Stratigraphy. , (2009).
- Nicolas, A., Fortin, J., Regnet, J. B., Dimanov, A., Guéguen, Y. Brittle and semi-brittle behaviours of a carbonate rock: influence of water and temperature. Geophysical Journal International. 206 (1), 438-456 (2016).
- Nishiyama, N., Wang, Y., Sanehira, T., Irifune, T., Rivers, M. L. Development of the multi-anvil assembly 6-6 for DIA and DDIA type high-pressure apparatuses. High Pressure Research. 28 (3), 307-314 (2008).
- Nur, A., Walder, J. Time-dependent hydraulics of the Earth’s crust. The role of fluids in crustal processes. , 113-127 (1990).
- Paterson, M. S. Rock deformation experimentation. The brittle-ductile transition in rocks. The Heard Volume. The American Geophysical Union, Geophys. Monograph. 56, 187-194 (1990).
- Peng, S. D. Stresses within elastic circular cylinders loaded uniaxially and triaxially. Int. J. Rock Mech. Min. Sci. Geomech. Abst. 78 (1), 399-432 (1971).
- Raterron, P., Merkel, S., Holyoke, C. W. Axial temperature and gradient and stress measurements in the deformation D-DIA cell using alumina pistons. Rev. of Sci. Instr. 84 (4), 043906 (2013).
- Raghavan, R., Chin, L. Y. Productivity changes in reservoirs with stress-dependent permeability. SPE Annual Technical Conference and Exhibition. , (2002).
- Reynolds, C. A., Menke, H., Andrew, M., Blunt, M. J., Samuel, K. Dynamic fluid connectivity during steady-state multiphase flow in a sandstone. Proceedings of National Academy of Sci. 114 (31), 8187-8192 (2017).
- Scholle, P. A. . A color illustrated guide to constituents, textures, cements, and porosities of sandstones and associated rocks. , (1979).
- Scholle, P. A., Ulmer-Scholle, D. S. . A Color Guide to the Petrography of Carbonate Rocks: Grains, Textures, Porosity, Diagenesis. , (2003).
- Scholz, C. H. Experimental study of the fracturing process in brittle rock. J. Geophys. Res. 73 (4), 1447-1454 (1968).
- Schutjens, P. M. T. M., et al. Compaction-induced porosity/permeability reduction in sandstone reservoirs: Data and model for elasticity-dominated deformation. SPE Reservoir Evaluation & Engineering. 7 (3), 202-216 (2004).
- Simmons, G., Wang, H. . Single Crystal Elastic Constants and Calculated Aggregate Properties. , 135-160 (1971).
- Singh, A. K., Balasingh, C., Mao, H. K., Hemley, R. J., Shu, J. Analysis of lattice strains measured under nonhydrostatic pressure. J. Applied physics. 83 (12), 7567-7575 (1998).
- Terzaghi, K. V. Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spanningsercheinungen. Sitzungsberichte der Akademie der Wissenschften in Wein. Mathematisch-Naturwissenschaftliche Klasse. Abteilung lla. 132, 125-138 (1923).
- Wang, Y., Durham, W. B., Getting, I. C., Weidner, D. J. The deformation D-DIA: a new apparatus for high temperature triaxial deformation to pressures up to 15 GPa. Rev. Sci. Instrum. 74 (6), 3002-3011 (2003).
- Wang, Y., Hilairet, N., Dera, P. Recent advances in high pressure and temperature rheological studies. J. Earth Sci. 21 (5), 495-516 (2010).
- Weidner, D. J., et al. Characterisation of Stress, Pressure, and Temperature in SAM85, a DIA Type High Pressure Apparatus. Geophys. Monogr. Ser. AGU. , 13-17 (1992).
- Weidner, D. J., Wang, Y., Vaughan, M. T. Strength of diamond. Sci. 266 (5184), 419-422 (1994).
- Weidner, D. J. Rheological studies at high pressure. Rev. in Mineralogy and Geochemistry. 37 (1), 493-524 (1998).
- Weidner, D. J., Wang, Y., Chen, G., Vaughan, M. T. Rheology measurements at high pressure and temperature. Properties of Earth and Planetary Materials at High Pressure and Temperature. AGU. , 473-482 (1998).
- Weidner, D. J., Vaughan, M. T., Wang, L., Long, H., Li, L., Dixon, N. A., Durham, W. B. Precise stress measurements with white synchrotron x rays. Rev. of Sci. Instrum. 81 (1), 013903 (2010).
- Weidner, D. J., Li, L., Whitaker, M., Triplett, R. Ultrasonic Acoustic Velocities During Partial Melting of a Mantle Peridotite KLB-1. J. Geophys. Res: Solid Earth. , (2018).
- Whitaker, M. L., Baldwin, K. J., Huebsch, W. R. DIASCoPE: Directly integrated acoustic system combined with pressure experiments-A new method for fast acoustic velocity measurements at high pressure. Rev. Sci. Instrum. 88 (3), 034901 (2017).
