Uncertainty quantification analysis in porous media using differential evolution McMC method with selection (DESk)

Resumo

Reservoir rocks display high spatial variability hydraulic properties. In general, this variability can not be deterministically described, and therefore, geostatistical methods come into place to approach the problem from a stochastic perspective. In particular, Markov chain Monte Carlo methods are often used on those applications. The most significant difficulty in using McMC methods for flow problems in porous media is related to the large stochastic dimension of the fields, which leads to low acceptance rates. Adaptive McMC methods have been a strong ally on this matter. Among them, differential evolution-based Markov chain Monte Carlo methods showed promising results. These methods exchange information among multiple chains running in parallel. Thus, improving its acceptance rate is not something as well explored in the literature. Additionally, to reduce the stochastic dimension of the problem, neural network techniques have become pretty popular as an alternative to using classical Karhunen-Loève expansion (KLE) to generate permeability fields. This work generates the proposed fields through variational autoencoders (VAE). A novel differential evolution Markov chain Monte Carlo with selection mechanisms (DESk) is proposed for solving a Bayesian inference problem involving a single fluid flow in a heterogeneous media. The scheme combines the faster convergence characteristic from the DE, which is improved by selection steps. The results showed that DESk performed better than the standard DE strategy for different selection pressures.