Unscented Importance Sampling for Parameter Calibration of Carbon Sequestration Systems

A Bayesian importance sampling method is developed to efficiently and accurately calibrate the parameters of non-linear and non-Gaussian system models. The UIS consists of two stages. The first stage uses the latest monitoring data to generate a Gaussian approximation of the true posterior distribution of the uncertain parameters and utilizes the measurement update stage of the Unscented Kalman Filter (UKF) to approximate the posterior. The second stage of UIS uses a mixture of approximate posterior computed in the first stage and a heavy tailed distribution as the proposal distribution for Bayesian importance sampling. UIS is repeated whenever new monitoring data becomes available. Two case studies were developed to study the UIS method and to compare it UKF and Importance Sampling (IS) methods: a non-linear analytical system model and synthesized CO2 injection model using a numerical multi-phase flow simulator. In analytical case study, it is shown that UIS is more accurate than both UKF and traditional IS with static proposal and the relative accuracy of the UIS over traditional IS increases with dimensionality of the parameter space. The higher accuracy of UIS compared to UKF and traditional IS with static proposal is also shown in the CO2 injection case study. It is also shown that increasing number of samples and a defensive mixture distribution with a mixture ratio between 0.1 and 0.25 enhances the performance of UIS