Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction

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 engineering^{8,17,18,19,20,28,33}. 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 reservoirs^28,33, surface subsidence^8,18,19,20, 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 geomaterial^5,6 with respect to the globally-averaged externally applied pressure^12,22. 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 strain^5,6. 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 processes^1,7,21,30,31. 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.