Reducing the model uncertainties
February 13th Kristian Fossum defended his PhD thesis on "Assessment of Sequential and Simultaneous Ensemble-based History Matching Methods for Weakly Non-linear Problems".
The ensemble Kalman filter (EnKF) has, since its introduction in 1994, gained much attention as a tool for sequential data assimilation in many scientific areas. In recent years, the EnKF has been utilized for estimating the poorly known petrophysical parameters in petroleum reservoir models. The ensemble based methodology has inspired several related methods, utilized both in data assimilation and for parameter estimation.
All these methods, including the EnKF, can be shown to converge to the correct solution in the case of a Gaussian prior model, Gaussian data error, and linear model dynamics. However, for many problems, where the methods are applied, this is not satisfied. Moreover, several numerical studies have shown that, for such cases, the different methods have different approximation error.
Via numerical modelling, Kristian investigates the difference between sequential and simultaneous assimilation on toy models and simplified reservoir problems. Utilizing realistic reservoir data, he shows that the assumption of difference in non-linearity for different data holds. Moreover, he demonstrates that, for favourable degree of nonlinearity, it is beneficial to assimilate the data ordered after ascending degree of nonlinearity.
Kristian now works as a researcher at Uni Research CIPR.
Would like to know more about Kristians work? The thesis is available at Bora