Doctoral dissertation on data assimilation in oil reservoir modeling

Dr. Alexandra Seiler has very successfully defended her Ph.D. thesis ”Reservoir Structural Model Updating Using the Ensemble Kalman Filter” at the Faculty of Science at University of Bergen. The work has been performed at the Nansen Center and Statoil ASA, within the Research Council of Norway eVita project coordinated by the Nansen Center. The opponents were Professor Peter van del Leeuwen, University of Reading and Professor Ramus Hanea, Delft University of Technoogy.

In reservoir characterization, a large emphasis is placed on risk management and uncertainty assessment, and the dangers of basing decisions on a single base-case reservoir model are widely recognized. In the last years, statistical methods for assisted history matching have gained popularity for providing integrated models with quantified uncertainty, conditioned on all available data.

Structural modelling is the first step in a reservoir modelling workflow and consists in defining the geometrical framework of the reservoir, based on the information from seismic surveys and well data. Large uncertainties are typically associated with the processing and interpretation of seismic data. However, the structural model is often fixed to a single interpretation in history-matching workflows due to the complexity of updating the structural model and related reservoir grid.

This thesis present a method that allows to account for the uncertainties in the structural model and continuously update the model and related uncertainties by assimilation of production data using the Ensemble Kalman Filter (EnKF). We consider uncertainties in the depth of the reservoir horizons and in the fault geometry, and assimilate production data, such as oil production rate, gas-oil ratio and water-cut.

In the EnKF model-updating workflow, an ensemble of reservoir models, expressing explicitly the model uncertainty, is created. We present a parameterization that allows to generate different realizations of the structural model to account for the uncertainties in faults and horizons and that maintains the consistency throughout the reservoir characterization project, from the structural model to the prediction of production profiles.
The uncertainty in the depth of the horizons is parameterized as simulated depth surfaces, the fault position as a displacement vector and the fault throw as a throw-scaling factor.

In the EnKF, the model parameters and state variables are updated sequentially in time, as new measurements become available. Updates in the structural model impact the reservoir grid, and when the grid architecture is modified, all the cell-referenced and grid-region parameters need to be updated as well. The entire reservoir modelling workflow, from structural modelling to flow simulation, needs to be rerun, and thus, automated. Furthermore, a major constraint is that the current EnKF implementation considers a fixed dimension of the state vector, which implies a constant number of active cells in the reservoir grid. The requirements of an automated workflow and a fixed grid architecture leads to the proposed method, where the geometry of the base-case grid, representing the most likely interpretation, is deformed to match the different realizations of the structural model. In this project, grid deformation algorithms for updating the geometry of a corner-point grid have been developed and integrated in the EnKF model-updating workflow.

The proposed method for updating the structural-model uncertainties has been applied to synthetic cases and is implemented on real field cases. The result is an updated ensemble of structural models, conditioned to all production data, and with reduced and quantified uncertainty. The updated ensemble of structures provides a more reliable characterization of the reservoir architecture, including the top and bottom horizons and the fault geometry, and a better estimate of the field oil-in-place.

Picture; Alexandra and her happy parents after the dissertation.

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