Calibration and prediction improvement of imperfect subsurface flow models

Abstract

In this thesis, problems related to calibration of imperfect reservoir models, biased parameter estimation and prediction reliability have been addressed. The main objective of this thesis is to avoid overconfident, inaccurate and unreliable predictions while accounting for model-error during the calibration process. Accounting for reservoir model-error in calibration (history matching) can correct/reduce the bias in parameter estimation and improves the prediction of the subsurface flow model. In this thesis, several approaches and algorithms have been developed and investigated which could be applied at different conditions depending on the modelling assumptions. In the first approach, the parameter estimation problem is formulated as a joint estimation of the imperfect model parameters and the error-model parameters. The prior distributions of the error-model parameters are evaluated before calibration through analysis of leading sources of the modelling errors using pairs of high-fidelity and low-fidelity simulation models. A Bayesian framework is adopted for solving the inverse problem, where the ensemble smoother with multiple data assimilation (ES-MDA) is utilized as a calibration algorithm. In the second approach, two new algorithms to account for model-error during calibration are developed which are the variants of the first approach and existing algorithms. The main aim is to develop flexible algorithms that can handle strong serially correlated outputs of the physical model, variable boundary conditions (i.e. variable well open/shut schedules and rate/pressure controls) and structured model-errors (i.e. strong correlation in time). In the third approach, the model-error during calibration is accounted for without knowing any prior statistics of model-discrepancy. For this purpose, a flexible ensemble-based algorithm is developed which can reduce bias in parameter estimation after calibration of imperfect models in order to improve the prediction capacity/reliability of the calibrated physical model. The flexible ensemble-based algorithm is quite general and has the capability to capture unknown model-error uncertainty by relaxing many of the assumptions commonly introduced in the literature.