Reports: DNI1056474-DNI10: Direct Microstructure Quantification and Property Prediction of Porous Materials from X-ray Tomography Data

Yang Jiao, PhD, Arizona State University

1. Executive Summary

In this report period, the main focus of the project is to systematically investigate the information content of limited x-ray tomography data sets (i.e., the tomographic radiographs or projections) of bi-phase porous materials (containing a single solid phase and a pore phase). This is achieved by utilizing such data set as input for stochastic microstructure reconstructions and subsequently quantifying the reconstruction errors. Next, a novel procedure is devised to directly compute the lower-order spatial correlation functions of interest including standard two-point correlation function, surface correlation function and cluster function from limited x-ray tomographic data (including both lab-scale and APS synchrotron data sets). These research activities have led to two manuscripts, one accepted by Transport in Porous Media and the other submitted to Materials Characterization. The detailed research efforts are described below.

2. Porous Material Reconstruction via Stochastic Fusion of Bi-modal Imaging Data

In order to investigate the information content of limited x-ray tomographic data, we have developed a procedure that generalizes the Yeong-Torquato framework for accurate reconstruction of porous materials by stochastically fusing limited bimodal microstructural data including limited-angle x-ray tomographic radiographs and 2D optical micrographs. The key microstructural information contained in the micrographs is statistically extracted and represented using certain lower-order spatial correlation functions associated with the pore phase. And a probabilistic interpretation of the attenuated intensity in the tomographic radiographs is presented. Moreover, we systematically investigate the information content of the complementary bimodal microstructural data using a 2D model system. We show that combining the standard two-point correlation functions and a small of tomographic radiographs can lead to a highly accurate reconstruction of the original system, implying the morphological information contained in such distinct types of data is complementary and can be efficiently utilized by our reconstruction method. Our procedure is subsequently applied to accurately reconstruct a variety of 3D binary sandstone microstructures (i.e., monomineral rocks) with a wide range of porosities from limited X-ray tomographic radiographs and 2D optical micrographs.

We have reconstructed sandstone samples with porosity φ = 0.0598, 0.0933, 0.0950 and 0.1610, with a diversity of pore-space morphology and connectivity. We found that the reconstructed structures via fusing bimodal structural data possesses the highest accuracy for all samples. These results suggest that by fusing the complementary morphological information contained in S2 and limited tomographic projections, the pore clusters are nucleated in desired positions and the overall phase morphology can be nicely resolved in the reconstruction.

3. Direct Microstructure Quantification from Limited X-ray Tomographic Radiographs

We have also developed a novel procedure that allows one to directly extract key structural information in forms of spatial correlation functions from limited x-ray tomography data. The key component of our procedure is the computation of a “probability map”, which provides the probability of an arbitrary point in the material system belonging to specific phase. Such a probability map can be computed via inverse superposition of the properly scaled attenuation intensities available in the tomography projections. The correlation functions of interest are then readily computed from the probability map, based on their probability interpretations. The utility of our procedure is illustrated by obtaining lower-order correlation functions (including both the standard n-point correlation functions and non-standard cluster and surface functions) for a binary porous material (i.e., a sandstone sample). Such a microstructure is representative of typical geological materials commonly seen in petroleum engineering yet the two phases (i.e., solid and pore) possess large absorption contrast for high quality imaging. Both parallel-beam (synchrotron) and cone-beam (lab-scale) x-ray tomography projection data sets are used to compute the correlation functions. Our procedure directly transforms the key morphological information contained in limited x-ray tomography projections to a more understandable and usable form and opens new avenues for utilizing limited tomography data.