A Bayesian optimization approach to the extraction of intrinsic physical parameters from T2 relaxation responses

NMR transverse relaxation responses in porous media provide a sensitive probe of the micro-structure yet are influenced by a set of factors which are not easily detangled. Low-field T2 transverse relaxation measurements can be carried out quickly and are frequently used to derive pore size distributions and determine derivate parameters like movable fluid volumes or permeability. Here we present an inverse solution workflow extracting related intrinsic physical parameters of the system by tightly fitting experiment and numerical simulation(s). We propose a Bayesian optimization approach that determines five T2 related properties associated with two values of temperature simultaneously. This concurrent optimization (CO-OPT) utilizes Gaussian process regression to determine the intrinsic physical parameters leading to a match to experiment with a minimal number of function evaluations. A multi-modal search strategy is employed to identify non-unique solution sets of the problem. The workflow is demonstrated on Bentheimer sandstone, identifying five intrinsic physical parameters simultaneously, namely the surface relaxivity of quartz and the effective diffusion and relaxation times of the clay regions at 20∘ C and 60∘ C, providing the temperature-dependent quartz surface relaxivity and effective clay parameters. Given the generality of the method, it can easily be adapted to transverse relaxation experiments, or dynamic conditions where e.g., a change in wettability is monitored by intrinsic NMR parameters.