Focusing on the non-Gaussian distribution of the field and the nonlinearity between the production data and the reservoir model of the fluvial channel reservoir, the HIEnKF method with discrete cosine transform was used to study the fluvial channel reservoir model by automatic history matching method. The non-Gaussian permeability field is transformed to nearly Gaussian distributed DCT coefficient by discrete cosine transform. DCT exhibits excellent energy compaction for highly correlated images. The estimated permeability field is smooth if the low frequency DCT coefficients are retained. The non-Gaussian problem of the fluvial channel reservoir can be solved by the discrete cosine transform. The HIEnKF method can solve the nonlinearity of the production data and the reservoir model. The equivalence of the HIEnKF to EnRML is proved theoretically. The results of standard EnKF, standard EnKF coupling with DCT and HIEnKF coupling with DCT were compared. The effects of retained mode and the number of retained DCT coefficients were discussed. The results show that fewer DCT coefficients need to be retained to capture the geological structure when the triangular area mode was used to truncate the coefficients. The estimated results can get the main geological structure of the fluvial channel reservoir when only 2.5% DCT coefficients were retained.
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