HR: 09:30h
AN: SF11A-07    [Abstracts]
TI: An Efficient Data Assimilation Technique Using the Karhunen-Loeve Kalman Filter
AU: * Lu, Z
EM: zhiming@lanl.gov
AF: Hydrology, Geochemistry, and Geology Group, Los Alamos National Laboratory, MS T003, Los Alamos, NM 87545 United States
AU: Zhang, D
EM: donzhang@ou.edu
AF: Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma, 100 East Boyd, SEC T301, Norman, OK 73019 United States
AB: The Kalman filter has been widely applied for assimilating new measurements to continuously update the estimate of state variables. The standard Kalman filtering scheme requires computing and storing the covariance matrix of state variables, which is computationally expensive for large-scale problems with millions of grid nodes. In the ensemble Kalman filter, this problem is alleviated with sampling from a limited number of realizations and computing the required subset of the covariance matrix at each update. However, the goodness of the (ensemble) covariance approximated from the limited ensemble depends on the number of realizations used. In this study, we propose a new Kalman filtering scheme based on Karhunen-Loeve or other orthogonal polynomial decompositions of the state vector. We consider flow in heterogeneous reservoirs with spatial variability in permeability. The pressure is measured at some locations at various time intervals. The aim is to characterize the permeability field and to predict the mean pressure and its uncertainty at a future time. In our scheme, the covariance of the permeability is approximated by a small set of eigenvalues and eigenfunctions using the Karhunen-Loeve (KL) decomposition, and reconstruction of this covariance from the KL decomposition can be done whenever needed. In each update, the forward problem is solved using the KL-based moment method, giving a set of functions from which the mean and covariance of the state variables can be constructed, when needed. The statistics of both the permeability field and the pressure field are then updated with the available measurements at this time using the auto-covariance of the pressure and the cross-covariance between the head and permeability from the forward problem. We illustrated our algorithm for a synthetic heterogeneous reservoir and results are compared with those from the exiting methods.
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3260 Inverse theory
DE: 1829 Groundwater hydrology
DE: 1869 Stochastic processes
SC: Special Focus: Advances in Data Acquisition, Management, Analysis and Display [SF]
MN: 2004 AGU Fall Meeting