Improved Estimation and Forecast Through Model Error Estimation – Norne Field Example

Abstract

The ensemble based methods (especially various forms of iterative ensemble smoothers) have been proven to be effective in calibrating multiple reservoir models, so that they are consistent with historical production data. However, due to the complex nature of hydrocarbon reservoirs, the model calibration is never perfect, it is always a simplified version of reality with coarse representation and unmodeled physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when ‘perfect’ model parameters are used as model input is known as ‘model error’. Assimilation of data without accounting for this model error can result in incorrect adjustment to model parameters, underestimation of prediction uncertainties and bias in forecasts. In this paper, we investigate the benefit of recognising and accounting for model error when an iterative ensemble smoother is used to assimilate production data. The correlated ‘total error’ (combination of model error and observation error) are estimated from the data residual after a standard history matching using Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). This total error is then used in further data assimilations to improve the model prediction and uncertain quantification from the final updated model ensemble. We first illustrate the method using a synthetic 2D five spot case, where some model errors are deliberately introduced, and the results are closely examined against the known ‘true’ model. Then the Norne field case is used to further evaluate the method. The Norne model has previously been history matched using the LM-EnRML (Chen and Oliver, 2014), where cell-by-cell properties (permeability, porosity, net-to-gross, vertical transmissibility) and parameters related to fault transmissibility, depths of water-oil contacts and relative permeability function are adjusted to honour historical data. In this previous study, the authors highlighted the importance of including large amounts of model parameters, proper use of localization, and adjustment of data noise to account for modelling error. In the current study, we further improve the aspect regarding the quantification of model error. The results showed promising benefit of a systematic procedure of model diagnostics, model improvement and model error quantification during data assimilations.