History matching using a multiscale Ensemble Kalman Filter

History matching using a multiscale Ensemble Kalman Filter

Lawniczak, W.
Hanea, R.G.
Heemink, A.W.
McLaughlin, D.
Jansen, J.D.
TNO Bouw en Ondergrond

2008

Since the first version of Kalman Filter was introduced in 1960 it received a lot of attention in mathematical and engineering world. There are many successful successors like for example Ensemble Kalman Filter (Evensen 1996) which has been applied also for reservoir engineering problems. The method proposed in [Zhou et al. 2007] draws together the ensemble filtering ideas and an efficient covariance representation, and is expected to perform well in history matching for reservoir engineering. It is the Ensemble Multiscale Filter. The EnMSF is a different way to represent the covariance of an ensemble. The computations are done on a tree structure and are based on an ensemble of possible realizations of the states and/or parameters of interest. The ensemble consists of replicates that are the values of states per pixel. The pixels in the grid are partitioned between the nodes of the finest scale in the tree. A construction of the tree is led by the eigenvalue decomposition. Then, the state combinations with the greatest corresponding eigenvalues are kept on the higher scales. The updated states/parameters using the EnMSF are believed to keep geological structure due to localization property. It comes from the filter s characterization where the pixels from the grid (e.g. permeability field) are distributed (in groups) over the finest scale tree nodes. We present a comparison of covariance matrices obtained with different setups used in the EnMSF. This sensitivity study is necessary since there are many parameters in the algorithm which can be adjusted to the needs of an application; they are connected to the tree construction part. The study gives the idea of how to efficiently use the EnMSF. The localization property is discussed based on the example where the filter is run with a simple simulator (2D, 2 phase) and a binary ensemble is used (the pixels in the replicates of permeability have two values only). Several possible patterns for ordering the pixels are applied.

Geological Survey Netherlands
Geosciences
Energy / Geological Survey Netherlands
Covariance matrix
Eigenvalues and eigenfunctions
Forestry
Kalman filters
Parameter estimation
Petroleum reservoirs
Pixels
Covariance matrices
Eigenvalue decomposition
Ensemble Kalman Filter
Geological structures
Localization properties
Permeability fields
Reservoir engineering
Sensitivity studies
Trees (mathematics)

http://resolver.tudelft.nl/uuid:749a0375-e922-44af-ad2c-7e8ad89e01b1

493126

European Association of Geoscientists and Engineers, EAGE

11th European Conference on the Mathematics of Oil Recovery, ECMOR 2008, 8 September 2008 through 11 September 2008, Bergen

B06

Sponsors: CIPR; IFP; NR; StatoilHydro; Total

conference paper