Loic Courtois

Quantifying and minimising systematic and random errors in X-ray micro-tomography based volume measurements

X-ray micro-tomography (XMT) is increasingly used for the quantitative analysis of the volumes of features within the 3D images. As with any measurement, there will be error and uncertainty associated with these measurements. In this paper a method for quantifying both the systematic and random components of this error in the measured volume is presented. The systematic error is the offset between the actual and measured volume which is consistent between different measurements and can therefore be eliminated by appropriate calibration. In XMT measurements this is often caused by an inappropriate threshold value. The random error is not associated with any systematic offset in the measured volume and could be caused, for instance, by variations in the location of the specific object relative to the voxel grid. It can be eliminated by repeated measurements. It was found that both the systematic and random components of the error are a strong function of the size of the object measured relative to the voxel size. The relative error in the volume was found to follow approximately a power law relationship with the volume of the object, but with an exponent that implied, unexpectedly, that the relative error was proportional to the radius of the object for small objects, though the exponent did imply that the relative error was approximately proportional to the surface area of the object for larger objects. In an example application involving the size of mineral grains in an ore sample, the uncertainty associated with the random error in the volume is larger than the object itself for objects smaller than about 8 voxels and is greater than 10% for any object smaller than about 260 voxels. A methodology is presented for reducing the random error by combining the results from either multiple scans of the same object or scans of multiple similar objects, with an uncertainty of less than 5% requiring 12 objects of 100 voxels or 600 objects of 4 voxels. As the systematic error in a measurement cannot be eliminated by combining the results from multiple measurements, this paper introduces a procedure for using volume standards to reduce the systematic error, especially for smaller objects where the relative error is larger. Methodology for quantifying random and systematic errors in microCT images presented.Unexpected power law scaling for error in small particle volume as threshold changes.Random component of error in volume insensitive to threshold value.

Synchrotron tomographic quantification of strain and fracture during simulated thermal maturation of an organic‐rich shale, UK Kimmeridge Clay

Analyzing the development of fracture networks in shale is important to understand both hydrocarbon migration pathways within and from source rocks and the effectiveness of hydraulic stimulation upon shale reservoirs. Here we use time-resolved synchrotron X-ray tomography to quantify in four dimensions (3-D plus time) the development of fractures during the accelerated maturation of an organic-rich mudstone (the UK Kimmeridge Clay), with the aim of determining the nature and timing of crack initiation. Electron microscopy (EM, both scanning backscattered and energy dispersive) was used to correlatively characterize the microstructure of the sample preheating and postheating. The tomographic data were analyzed by using digital volume correlation (DVC) to measure the three-dimensional displacements between subsequent time/heating steps allowing the strain fields surrounding each crack to be calculated, enabling crack opening modes to be determined. Quantification of the strain eigenvectors just before crack propagation suggests that the main mode driving crack initiation is the opening displacement perpendicular to the bedding, mode I. Further, detailed investigation of the DVC measured strain evolution revealed the complex interaction of the laminar clay matrix and the maximum principal strain on incipient crack nucleation. Full field DVC also allowed accurate calculation of the coefficients of thermal expansion (8 × 10−5/°C perpendicular and 6.2 × 10−5/°C parallel to the bedding plane). These results demonstrate how correlative imaging (using synchrotron tomography, DVC, and EM) can be used to elucidate the influence of shale microstructure on its anisotropic mechanical behavior.

Correlative multi-scale imaging of shales: a review and future perspectives

Abstract As the fastest growing energy sector globally, shale and shale reservoirs have attracted the attention of both industry and scholars. However, the strong heterogeneity at different scales and the extremely fine-grained nature of shales makes macroscopic and microscopic characterization highly challenging. Recent advances in imaging techniques have provided many novel characterization opportunities of shale components and microstructures at multiple scales. Correlative imaging, where multiple techniques are combined, is playing an increasingly important role in the imaging and quantification of shale microstructures (e.g. one can combine optical microscopy, scanning electron microscopy/transmission electron microscopy and X-ray radiography in 2D, or X-ray computed tomography and electron microscopy in 3D). Combined utilization of these techniques can characterize the heterogeneity of shale microstructures over a large range of scales, from macroscale to nanoscale (c. 100–10−9 m). Other chemical and physical measurements can be correlated to imaging techniques to provide complementary information for minerals, organic matter and pores. These imaging techniques and subsequent quantification methods are critically reviewed to provide an overview of the correlative imaging workflow. Applications of the above techniques for imaging particular features in different shales are demonstrated, and key limitations and benefits summarized. Current challenges and future perspectives in shale imaging techniques and their applications are discussed.