Abstract: A method is described for producing an amended realization of a geostatistical model of a hydrocarbon reservoir using the Karhunen-Loève (KL) expansion. The KL expansion may be used to produce amended realizations for history matching and is widely used. However, it is necessary in order to use the KL expansion to perform singular value decomposition of the covariance matrix of the model to provide eigenvectors and eigen values for use in the expansion. In a typical geostatistical model, the covariance matrix is too large for singular value decomposition to be performed. Prior solutions to this problem involved reducing the resolution of the model so as to reduce the size of the covariance matrix. In the method described, a plurality of random realizations are generated and an approximation of the covariance matrix is constructed from the realizations, the approximation matrix having smaller dimensions than the true covariance matrix.

Abstract: A method is described for producing an amended realization of a geostatistical model of a hydrocarbon reservoir using the Karhunen-Loève (KL) expansion. The KL expansion may be used to produce amended realizations for history matching and is widely used. However, it is necessary in order to use the KL expansion to perform singular value decomposition of the covariance matrix of the model to provide eigenvectors and eigen values for use in the expansion. In a typical geostatistical model, the covariance matrix is too large for singular value decomposition to be performed. Prior solutions to this problem involved reducing the resolution of the model so as to reduce the size of the covariance matrix. In the method described, a plurality of random realizations are generated and an approximation of the covariance matrix is constructed from the realizations, the approximation matrix having smaller dimensions than the true covariance matrix.