Using two point geo-statistics reservoir model parameters reduction. An algorithm has been developed to constrain gridded reservoir models that are used with assisted history matching with geo-statistical information and at the same time reduce the number of variables that are needed to describe the model. Gridded models, as used within most reservoir modelling packages, may consist of 10^5 up to 10^6 grid blocks. A covariance matrix which can be used to constrain the model with a variogram (two point statistics) would consist of 10^10 up to 10^12 coefficients and a direct principal component decomposition of is beyond the capability of current computer systems. A common way to reduce the number of variables is using the members of an ensemble of models from a geo-statistical simulation as basis vectors for a subspace. When a history match is obtained with a model that is constrained to this subspace, this model will have a decently looking continuity behaviour. There is however no guarantee that this subspace contains the directions that correspond with the eigenvectors of the covariance matrix with the largest eigenvalues. This can be demonstrated with a simple simulation and is theoretically described by the Wishart distribution. It is possible to construct a set of orthonormal basis vectors that contains the directions that correspond with the eigenvectors of the covariance matrix with the significantly large eigenvalues. The number of basis vectors may still be rather large but it is mainly determined by the size of the model and the range of the variogram. From an eigenvector decomposition of this covariance matrix, a very good approximation can be obtained of the eigenvectors with a significant large eigenvalues. As the small eigenvalues can be neglected, the number of eigenvectors needed to describe the model is approximately 10^2, which results in a significant parameter reduction.


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