Using internal standards in time-resolved X-ray micro-computed tomography to quantify grain-scale developments in solid-state mineral reactions

X-ray computed tomography has established itself as a crucial tool in the analysis of rock materials, providing the ability to visualise intricate 3D microstructures and capture quantitative information about internal phenomena such as structural damage, mineral reactions, and fluid–rock interactions. The efficacy of this tool, however, depends significantly on the precision of image segmentation, a process that has seen varied results across different methodologies, ranging from simple histogram thresholding to more complex machine learning and deep-learning strategies. The irregularity in these segmentation outcomes raises concerns about the reproducibility of the results, a challenge that we aim to address in this work. In our study, we employ the mass balance of a metamorphic reaction as an internal standard to verify segmentation accuracy and shed light on the advantages of deep-learning approaches, particularly their capacity to efficiently process expansive datasets. Our methodology utilises deep learning to achieve accurate segmentation of time-resolved volumetric images of the gypsum dehydration reaction, a process that traditional segmentation techniques have struggled with due to poor contrast between reactants and products. We utilise a 2D U-net architecture for segmentation and introduce machine-learning-obtained labelled data (specifically, from random forest classification) as an innovative solution to the limitations of training data obtained from imaging. The deep-learning algorithm we developed has demonstrated remarkable resilience, consistently segmenting volume phases across all experiments. Furthermore, our trained neural network exhibits impressively short run times on a standard workstation equipped with a graphic processing unit (GPU). To evaluate the precision of our workflow, we compared the theoretical and measured molar evolution of gypsum to bassanite during dehydration. The errors between the predicted and segmented volumes in all time series experiments fell within the 2 % confidence intervals of the theoretical curves, affirming the accuracy of our methodology. We also compared the results obtained by the proposed method with standard segmentation methods and found a significant improvement in precision and accuracy of segmented volumes. This makes the segmented computed tomography images suited for extracting quantitative data, such as variations in mineral growth rate and pore size during the reaction. In this work, we introduce a distinctive approach by using an internal standard to validate the accuracy of a segmentation model, demonstrating its potential as a robust and reliable method for image segmentation in this field. This ability to measure the volumetric evolution during a reaction with precision paves the way for advanced modelling and verification of the physical properties of rock materials, particularly those involved in tectono-metamorphic processes. Our work underscores the promise of deep-learning approaches in elevating the quality and reproducibility of research in the geosciences.