Determination of intrinsic physical properties of porous media by applying Bayesian Optimization to inverse problems in Laplace NMR relaxometry

Abstract

Nuclear magnetic resonance (NMR) longitudinal (T1) and transverse (T2) relaxation time distributions are widely used for the characterization of porous media. Subject to simplifying assumptions predictions about pore size, permeability and fluid content can be made. Numerical forward models based on high-resolution images are employed to naturally incorporate structural heterogeneity and diffusive motion without limiting assumptions, offering alternate interpretation approaches. Extracting the required multiple intrinsic parameters of the system poses an ill-conditioned inverse problem where multiple scales are covered by the underlying microstructure. Three general and robust inverse solution workflows (ISW) utilizing Bayesian optimization for the inverse problem of estimation of intrinsic physical quantities from the integration of pore-scale forward modeling and experimental measurements of macroscopic system responses are developed. A single-task ISW identifies multiple intrinsic properties for a single core by minimization of the deviation between simulated and measured T2 distributions. A multi-task ISW efficiently identifies the same set of unknown quantities for different cores by leveraging information from completed tasks using transfer learning. Finally, a dual-task ISW inspired by the multi-task ISW incorporates transfer learning for the simultaneous statistical modeling of T1 and T2 distributions, providing robust estimates of T1 and T2 intrinsic properties. A multi-modal search strategy comprising the multi-start L-BFGS-B optimizer and the social-learning particle swarm optimizer, and a multi-modal solution analysis procedure are applied in these workflows for the identification of non-unique solution sets. The performance of the single-task ISW is demonstrated on T2 relaxation responses of a Bentheimer sandstone, extracting three physical parameters simultaneously, and the results facilitate the multi-task ISW to study the spatial variability of the three physical quantities of three Bentheimer sandstone cored from two different blocks. The performance of the dual-task ISW is demonstrated on the identification of the five physical quantities with two extra T1 related unknowns. The effect of SNR on the identified parameter values is demonstrated. Inverse solution workflows enable the use of classical interpretation techniques and local analysis of responses based on numerical simulation