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Abstract

Popularity of application of the ensemble Kalman filter (EnKF) and other ensemble methods to history matching of reservoir models has been growing for a number of years. Recent applications demonstrated that ensemble based methods are efficient for producing models with a good match of the history. However, they don’t necessarily keep consistency of the resulting models with the initial geostatistical description. One of the causes of this problem is an imperfection of the estimation of the model state error covariance from ensembles of a finite size. First we illustrate a spurious stochastic behaviour of the covariance when applying the EnKF to a simple "well-test like" synthetic example. Experimental covariance estimated from the ensemble of a practical size of about a hundred members is clearly quite different from one that can be expected from an analytical solution. When the size of the ensemble is increased by an order of magnitude the covariance function becomes significantly smoother. Nevertheless, in all the cases it is not difficult to see that the main disturbance of the covariance happens beyond the area of the pressure front propagation. Thus, results of the EnKF potentially can be improved by application of a flow based covariance localisation. Then we show an application of the EnKF with a streamline based covariance localisation (Devegowda et al. 2007) to a real field problem. The forward model is solved by a conventional finite-difference reservoir simulator and at every update step streamlines are traced using a separate routine (Jimenez et al. 2007). Traced streamlines are used for determination of an influence zone for each well and covariance of the production data from each well and model parameters is localised accordingly. We compare the results in case of localisation based on the zones determined by the full length of the streamlines and in case of localisation zones limited by the flow fronts propagation. In both cases there is an improvement of the production data match and less disturbance of the initial geostatistical realisations compared to the EnKF without localisation.

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/content/papers/10.3997/2214-4609.20146414
2008-09-08
2020-09-30
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20146414
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