Bayesian inversion for rock composition and petrophysical endpoints in multimineral analysis

Multimineral analysis that quantifies the volume fractions of minerals and fluids from a set of well logs has been used for reservoir characterization in complex geological settings. However, due to the data errors and the similarity between petrophysical endpoints, the solutions of multimineral analysis are non-unique. Furthermore, defining the petrophysical endpoints is challenging in complex geological settings because standard endpoint values may not be optimal. All the uncertainties must be evaluated but cannot be achieved by standard linear solvers. Stochastic Bayesian inversion methods have been developed to assess the uncertainties, but the high computational time and the need for detailed prior information hinder their practical use. We employ a Markov chain Monte Carlo with ensemble samplers (MCMCES) in the Bayesian framework, which is more efficient in convergence than the conventional random walk methods in high dimensional problems. We apply the new method in two different applications. First, we evaluate the uncertainty of constituent volume fractions resulting from the data errors and the similarity of endpoints on a conventional carbonate reservoir. In our second implementation of MCMCES, we assess the uncertainty of key endpoints that are difficult to estimate and optimize multimineral analysis using a synthetic dataset and field data from the Bakken Formation. Our proposed method provides different realizations in volume fractions or in petrophysical endpoints for interpreters to better evaluate multimineral results.