Efficient Data Assimilation Tool For Real Time CO2 Reservoir Monitoring and Characterization

Monday, 15 December 2014: 1:40 PM
Judith Yue Li1, Sivaram Ambikasaran2, Amalia Kokkinaki1, Eric F Darve3,4 and Peter K Kitanidis1,3, (1)Stanford University, Civil and Environmental Engineering, Stanford, CA, United States, (2)Courant Institute of Mathematical Sciences, NEW YORK, NY, United States, (3)Stanford University, Institute for Computational and Mathematical Engineering, Stanford, CA, United States, (4)Stanford University, Mechanical Engineering, Stanford, CA, United States
Reservoir forecasting and management are increasingly relying on a data-driven approach, which involves data assimilation to calibrate and keep up to date the complex model of multi-phase flow and transport in the geologic formation and to evaluate its uncertainty using monitoring data of different types and temporal resolution. The numbers of unknowns and measurements are usually very large, which represents a major computational challenge. Kalman filter (KF), the archetypical recursive filter, provides the framework to assimilate reservoir monitoring data into a dynamic system but the cost of implementing the original algorithm to large systems is computationally prohibitive. In our work, we have developed several Kalman-filter based approaches that reduce the computational and storage cost of standard KF from O (m2) to O (m), where m is the number of unknowns, and have the potential to be applied to field-scale problems. HiKF, a linear filter based on the hierarchical matrix approach, takes advantage of the informative high-frequency data acquired quasi-continuously and uses a random-walk model in the state forecast step when the a state evolution model is unavailable. A more general-purpose nonlinear filter CSKF achieves computational efficiency by exploiting the fact that the state covariance matrix for most dynamical systems can be approximated adequately through a low-rank matrix, and it allows using a forward simulator as a black-box for nonlinear error propagation. We will demonstrate both methods using synthetic CO2 injection cases and compare with the standard ensemble Kalman filter (EnKF).