Two-Stage MCMC with Surrogate Models for Efficient Uncertainty Quantification in Multiphase Flow

We present a novel two-stage Markov Chain Monte Carlo (MCMC) method that improves the efficiency of MCMC sampling while maintaining its sampling rigor. Our method employs response surfaces as surrogate models in the first stage to direct the sampling and identify promising reservoir models, replacing computationally expensive multiphase flow simulations. In the second stage, flow simulations are conducted only on proposals that pass the first stage to calculate acceptance probability, and the surrogate model is updated regularly upon adding new flow simulations. This strategy significantly increases the acceptance rate and reduces computational costs compared to conventional MCMC sampling, without sacrificing accuracy. To demonstrate the efficacy and efficiency of our approach, we apply it to a field example involving three-phase flow and the integration of historical reservoir production data, generating multiple reservoir models and assessing uncertainty in production forecasts.