4D Seismic Modeling Integrated with the Ensemble Kalman Filter Method for History Matching of Reservoir Simulation Model

From a real Norwegian North Sea field case we show simulation results where 4D seismic data are incorporated in the history matching process of reservoir simulation models. It has been shown that the Ensemble Kalman Filter technique, a Monte Carlo type Bayesian sequential inversion method, is capable of performing this task. In addition to predicted model states, data uncertainties are provided. In fact, seismic data may not only relate to one (e.g. 3D), but to more instances in time (4D or time-lapse seismic data where their differences are of concern). Furthermore they may be investigated in different domains, depending on their sensitivity to production related changes in the reservoir. In the given case study we observe an emerging fluid contact due to gas injection and corresponding travel-time shifts of seismic events on the real data. We model these effects by generating synthetic seismic sections, but in an environment which allows to incorporate Eclipse simulated variables, namely fluid saturations, densities and pressures. The Compound model builder, an interface shared by geophysical and reservoir engineering data represents our environment for integrated seismic and geologic modeling. The basic reservoir variables to be updated in this study are the static variables porosity and permeability and the dynamic variables pressures and saturations. These variables are optimized by minimizing a joint misfit function consisting of production data, such as oil-production rate, water-cut and gas-oil ratio and seismic data, which is stacked amplitude data. The benefit of including seismic data lies in a better overall reservoir description especially in areas not sampled by observations of production data.