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.