Smoothing-based Compressed State Kalman Filter (sCSKF) for Real-time State-parameter Estimation: CO2 Reservoir Monitoring and Characterization

Abstract:

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. The predictions of such models can be greatly improved by data assimilation techniques. Kalman-type techniques sequentially assimilate monitoring data in real-time to update model predictions. Essentially, this update constitutes a nonlinear optimization, which is solved by linearizing an objective function around the model forecast and applying a linear correction to the predictions. However, if model parameters are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. This effect can be reduced by smoothing-based filters, in which current observations are used to correct the state and parameters one step back in time. We propose the smoothing-based Compressed State Kalman filter (sCSKF), an algorithm that combines smoothing-based filtering to tackle nonlinearity effects, with an accurate covariance compression scheme that reduces the computational cost by exploring the high-dimensional state and parameter space more efficiently. The latter feature is crucial for large-scale applications with a large number of unknowns. Our numerical experiments for a CO₂ sequestration application show that the sCSKF gives more accurate model and parameter estimates than its non-smoothing variant for large assimilation intervals or highly uncertain model parameters. As such conditions are often true in real field applications, the sCSKF presents a reliable and practical method for large-scale joint state-parameter estimation problems with strong non-linearity. Finally, in our experiments the sCSKF provides similar accuracy at an equal or lower computational cost than the iterative Kalman Filter, a more conventional approach for reducing nonlinearity effects.