Continuous Updating of a Coupled Reservoir-Seismic Model Using an Ensemble Kalman Filter Technique
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This work presents the development of a method based on the ensemble Kalman filter (EnKF) for continuous reservoir model updating with respect to the combination of production data, 3D seismic data and time-lapse seismic data. The reservoir-seismic model system consists of a commercial reservoir simulator coupled to existing rock physics and seismic modelling software. The EnKF provides an ideal-setting for real time updating and prediction in reservoir simulation models, and has been applied to synthetic models and real field cases from the North Sea. In the EnKF method, static parameters as the porosity and permeability, and dynamic variables, as fluid saturations and pressure, are updated in the reservoir model at each step data become available. In addition, we have updated a lithology parameter (clay ratio) which is linked to the rock physics model, and the fracture density in a synthetic fractured reservoir. In the EnKF experiments we have assimilated various types of production and seismic data. Gas oil ratio (GOR), water cut (WCT) and bottom-hole pressure (BHP) are used in the data assimilation. Furthermore, inverted seismic data, such as Poisson’s ratio and acoustic impedance, and seismic waveform data have been assimilated. In reservoir applications seismic data may introduce a large amount of data in the assimilation schemes, and the computational time becomes expensive. In this project efficient EnKF schemes are used to handle such large datasets, where challenging aspects such as the inversion of a large covariance matrix and potential loss of rank are considered. Time-lapse seismic data may be difficult to assimilate since they are time difference data, i.e. data which are related to the model variable at two or more time instances. Here we have presented a general sequential Bayesian formulation which incorporates time difference data, and we show that the posterior distribution includes both a filter and a smoother solution. Further, we show that when time difference data are used in the EnKF, a combination of the ensemble Kalman filter and the ensemble Kalman smoother has to be applied. However, the method is still completely recursive, with little additional cost compared to the standard EnKF. An underestimation of the uncertainty of the model variables may become a problem when few ensemble members and a large amount of data are used during the assimilation. Thus, to improve the reservoir model updating we have proposed a methodology based on a combination of a global and a local analysis scheme.