资源环境科技发展态势分析平台

The operation of most engineered hydrogeological systems relies on simulating physical processes using numerical models with uncertain parameters and initial conditions. Predictions by such uncertain models can be greatly improved by Kalman-filter techniques that sequentially assimilate monitoring data. Each assimilation constitutes a nonlinear optimization, which is solved by linearizing an objective function about the model prediction and applying a linear correction to this prediction. However, if model parameters and initial conditions are uncertain, the optimization problem becomes strongly nonlinear and a linear correction may yield unphysical results. In this paper, we investigate the utility of one-step ahead smoothing, a variant of the traditional filtering process, to eliminate nonphysical results and reduce estimation artifacts caused by nonlinearities. We present the smoothing-based compressed state Kalman filter (sCSKF), an algorithm that combines one step ahead smoothing, in which current observations are used to correct the state and parameters one step back in time, with a nonensemble covariance compression scheme, that reduces the computational cost by efficiently exploring the high-dimensional state and parameter space. Numerical experiments show that when model parameters are uncertain and the states exhibit hyperbolic behavior with sharp fronts, as in CO2 storage applications, one-step ahead smoothing reduces overshooting errors and, by design, gives physically consistent state and parameter estimates. We compared sCSKF with commonly used data assimilation methods and showed that for the same computational cost, combining one step ahead smoothing and nonensemble compression is advantageous for real-time characterization and monitoring of large-scale hydrogeological systems with sharp moving fronts.

Plain Language Summary Geologic CO2 storage is a promising technology to reduce the CO2 in the atmosphere by injecting them into the deep saline reservoir for permanent storage. To assure safe operations and effective containment of CO2, numerical models are developed to accurately predict the CO2 behaviors underground in order to make informed decisions, such as adjusting the volume and rate of injection to prevent fracturing the surrounding rock. However, because of our limited knowledge about the reservoir properties, often the numerical model is highly uncertain. Statistical techniques like Kalman filtering use sensor data to reduce the prediction uncertainty in the numerical model by correcting the unknown reservoir properties recursively in time when data becomes available. The amount of correction is determined by solving an optimization problem. However, it is computationally intractable to find feasible solutions to such problems if reservoir properties to be estimated are high dimensional. Moreover, when the optimization problem is nonlinear, Kalman-type approaches can give unphysical results. By improving the way information is extracted from the sensor data, we present a new Kalman-type approach that can solve this optimization problem with better accuracy and reduced uncertainty.