Permeability Inference From 3D Grayscale Images Using Deep Learning: How a Large-Scale Data Set Can Contribute to Model Generalization

<ns0:p>In this study, we initially gathered a set of 50 mini-plugs, each measuring 1 cm in diameter and 2 cm in length, extracted from nine distinct sandstone rock types (RTs) characterized by porosities and permeabilities spanning 12 to 23% and 150 to 6,000 md, respectively. Utilizing a synchrotron facility, we obtained three-dimensional (3D) X-ray microcomputed tomography (μCT) images at a resolution of 5.82 μm and 1,100 × 1,100 × 2,800 voxels in size. These images were employed to conduct direct velocity field simulations using a parallelized two-relaxation times lattice Boltzmann method. To maximize the data set size, a 3D convolutional operator was applied to the velocity field, resulting in a 3D permeability map consisting of 135 billion data points for each of the 50 samples, serving as the ground truth. For this investigation, a data set comprising 6 million randomly sampled pairs (1003 voxel subvolume, permeability) from six different RTs was created. Two distinct 3D convolutional neural networks (CNN) were trained, representing a shallow plain architecture (SP3D) and a deeper residual network (R3D_18). Training involved the use of either gray-level or binary segmented 3D images. The trained models were then employed to predict permeability for various RTs, with the R2 coefficient serving as a metric for predicting performance. Our results demonstrated that the R3D_18 model consistently outperformed other models in terms of accuracy and generalization, achieving impressive R2 scores on both seen and unseen rock types. Additionally, we observed that utilizing gray-level images enhanced the accuracy of the R3D_18 model, while it had mixed effects on the performance of the SP3D model.</ns0:p>