Bayesian Optimization With Transfer Learning: A Study on Spatial Variability of Rock Properties Using NMR Relaxometry

Abstract

Nuclear magnetic resonance measurements of sedimentary rocks are used to extract various transport properties including hydraulic conductivity and water retention curves. These estimates are controlled by intrinsic physical quantities like surface relaxivities, and effective relaxation time and restricted self-diffusion coefficient of water in clay. Sampling these properties on a set of core plugs presents a series of inverse problems where some of the extracted parameters are expected to be similar. To leverage such valuable information, we extend a previously developed single-task inverse solution workflow (ISW) to the multi-task case, transferring the knowledge gained from previous optimization tasks. Two multi-task kernels: intrinsic model of coregionalization (ICM) and linear model of coregionalization are compared to capture the underlying correlations. We consider three micro-CT images of Bentheimer sandstone from two different blocks imaged at different resolutions, following different segmentation pathways, and demonstrate our approach for the case of low and high task similarity. In both scenarios the multi-task ISW finds lower fitting residuals and uses only one-third to one-half of the function evaluations required by the single-task ISW. The scalability of the multi-task ISW is demonstrated by transferring knowledge of two completed optimization tasks to a third task, which outperforms the single-task ISW, with ICM showing faster convergence. The observed 4% difference for the values identified for samples from the same block and around 28% difference across blocks indicates significant spatial variability in surface relaxivity of the main mineral component, while effective clay parameters show a significantly higher variability. LI ET AL.