Inverting an Object Based geostatistical facies model with Ensemble Smoother Multiple Data assimilation technique
Résumé
During the last decade, new inversion techniques (Ensemble Kalman filters, Ensemble Smoother, ...) have emerged which can be very useful for assisted history match of complex problems. They are based on an ensemble of geo-models. These geo-models are simulated dynamically (initial state) and the mismatch regarding dynamic observations is calculated. Subsequently, the link between geo-models’ parameters and dynamic mismatch is defined with a Kalman gain matrix computation. Then geo-models underlying parameters are updated and a new state is computed. By repeating the procedure (called dynamic data assimilation), we can converge to a set of calibrated models. Concerning facies modeling, these inversion techniques are very efficient with truncated gaussian related facies models. For this kind of models, the underlying gaussian fields are updated with the Kalman gain matrix and the corresponding facies model is rebuilt from these updated underlying gaussian fields. However, for other facies models and specifically object-based facies models, the update is not so trivial and problematic. This fact strongly limits the application domain of assisted history match techniques based on Kalman gain. In the paper, an innovative method is presented to actualize an object-based facies model in the framework of these assisted history match techniques. The idea is relatively simple: each individual object of one realization is coupled with its homolog in another realization; by doing so, we can invert object coordinates and sizes (thickness and width) with the Kalman gain matrix. The tricky aspects are to preserve conditioning data and to be able to invert the model on a limited area if required. The method is applied on a synthetic five-spot example. Results are very encouraging. Conclusions and future works are proposed based on these first experimental results.