Assimilating time-lapse seismic data in the presence of significant spatially correlated model errors

Time-lapse seismic data is becoming a common information source in reservoir model calibration workflows to improve production forecasts. The standard process compares a forward model's results with the observed data to update the model's parameters from the existing deviations. Ensemble-based methods are popular choices for this process. However, the so-called forward model is always a simplification of the real phenomena. These simplifications may significatively influence the relation between simulated and observed data and possibly yield inconsistent updates of the parameters and uncertainty underestimation. In the conventional approach for this problem, the so-called strong-constraint formulation neglects the model's limitations, causing unphysical updates of the parameters to reduce the distance between simulated and observed data. In this work, we propose a methodology to apply a weak-constraint formulation to the time-lapse seismic data assimilation to mitigate the above problem. We consider the forward model error with an additive term and update it during the data assimilation workflow. By adopting this approach, we reduce the impact of the model errors in the calibrated parameters. Also, the proposed methodology handles model bias as a type of general model error. The inclusion of the additive term weakens the updates of the model due to the time-lapse seismic data. We show that this procedure significantly benefits the data assimilation results when there are substantial spatially correlated model errors, and it has a minor impact when applied to a low-error case. We apply the proposed method to assimilate time-lapse seismic data using the Ensemble Smoother with Multiple Data Assimilations in a simple 2D case and in a realistic benchmark synthetic case based on a real offshore reservoir. In the former case, we consider model error related to the pressure sensitivity in the petroelastic model. In the latter, we consider a realistic synthetic time-lapse seismic and the correlated errors result from seismic modeling and inversion. Moreover, in the latter, we also assimilate well data. The results indicate that our methodology improved the reservoir characterization and the production forecast using relatively low-resolution time-lapse seismic data.