The availability of effective and reliable monitoring is recognized as a requirement for the acceptance of geologic sequestration of CO2. The focus of this project is research that develops ultra fast computational methods for the real-time monitoring of CO2 plumes and the evaluation of risks of leakage. The ultimate objective is the development of computational tools for data assimilation and uncertainty quantification based on sound fundamentals and numerical methods but adapted to specific problems.
The emphasis of this exploratory research is on demonstrating the potential of these methods through specific examples. Over the last seven months, we developed and implemented algorithms that can process large data sets and estimate large number of unknowns, which will be of prime importance in real-time monitoring and optimal control at CO2 sequestration sites. The methods assimilate data and also quantify uncertainty, which is important in weighing data of different types and in taking decisions that minimize the probability of failure. The algorithms speed up the time taken to solve large scale problems by orders of magnitude compared to conventional methods. These algorithms have been applied and tested for synthetic data sets. These algorithms are becoming part of two software packages, under development, to enable solving inverse problems in real time. The first package implements two fast direct solvers for a class of linear systems, which is relevant to linear inversion problems, with complexity O (N log2N) and O (N log N) as opposed to conventional direct solvers with complexity O (N3). This means that, as the size of the problem, N, increases, the above mentioned methods become much faster than conventional methods. The second package implements a novel algorithm that couples the fast multipole method with the sparsity (zero fill-ins) of the underlying measurement operator.
We have been developing a Fast Kalman Filter for the sequential processing of data in time and have been comparing its speed and performance to traditional Kalman Filter (KF) and Ensemble Kalman Filter (EnKF) for the linear dynamic case. As can be shown from synthetic cases, the traditional KF that is the optimal filter is computationally very expensive to apply, particularly in updating covariance matrix at each time step. The EnKF reduces the cost of updating large covariance matrices by using sample covariance to approximate the true state error covariance; however, the its performance is suboptimal. The method under development in this project has the potential to be less expensive than KF while more accurate and versatile than
EnKF. Among other research in progress is a Kalman Smoother (KS) for assimilating both seismic difference data and well measurements to improve estimation of pressure or saturation.