Quantification of prediction uncertainty using imperfect subsurface models with model error estimation

摘要

Subsurface reservoirs are far more heterogeneous and complex than the simulation models in terms of scale, assumptions and description. In this work, we address the issue of prediction reliability while calibrating imperfect/low-fidelity reservoir models. The main goal is to avoid over-confident and inaccurate predictions by including a model for the bias terms (i.e. error-model of a predefined form) during the history matching process. Our aim is to obtain unbiased posterior distributions of the physical model parameters and thus improving the prediction capacity of the calibrated low-fidelity reservoir models. We formulate the parameter estimation problem as a joint estimation of the imperfect model parameters and the error-model parameters. The structure of the error-model and the prior distributions of the error-model parameters are evaluated before calibration through analysis of leading sources of the modeling errors. We adopt a Bayesian framework for solving the inverse problem, where we utilize the ensemble smoother with multiple data assimilation (ES-MDA) as a practical history matching algorithm.