Sub-core permeability inversion using positron emission tomography data-Ensemble Kalman Filter performance comparison and ensemble generation using an advanced convolutional neural network

Multiscale permeability parameterization in geologic cores is key for quantifying multiphase flow and conservative, reactive, and colloidal transport processes in geologic systems. Despite its importance in controlling flow and transport processes, permeability measurement methods often suffer from low spatial resolution, high computational cost, or lack of generalizability. This study leverages positron emission tomography (PET) experimental data to record time-lapse radiotracer concentration distributions at millimeter -scale resolution in geologic cores. Through iterative forward simulations, an Ensemble Kalman Filter (EnKF) is employed to assimilate the input transport data and an ensemble of possible permeability distributions to determine the corresponding three-dimensional permeability map for a given geologic core sample. A second approach, specifically a convolutional neural network (CNN) with new hierarchical modifications, is also used for permeability inversion. This data -driven CNN eliminates the need for numerically defining and iteratively running a forward operator once the training is completed. The EnKF and CNN methods are separately evaluated for permeability inversion with a combination of synthetically generated data and PET imaging data. Inverted 3-D sub -core scale permeability maps are used to parameterize forward numerical models for direct comparison with the PET measurements for accuracy evaluation on experimental data. The trained CNN produces more robust inversion results with orders of magnitude improvement in computational efficiency compared with the EnKF. Finally, we propose an improved EnKF inversion workflow where the initial ensemble is generated by adding perturbations to the CNN permeability map prediction. The results indicate that the hybrid EnKF-CNN workflow achieves improvements in inversion accuracy in nearly all core samples but at the expense of computational efficiency relative to the CNN alone. Overall, this combination of experimental, numerical, and deep -learning methodologies considerably advances the speed and reliability of 3-D multiscale permeability characterization in geologic core samples.