TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe use of time-lapse data, or 4D seismic, in conjunction with production data in computer aided history matching of reservoir models requires that the various types of data are incorporated in a single objective function measuring the mismatch between the simulated and measured data. In the context of linear maximum likelihood estimation, the contribution of seismic data and production data to the objective function can be balanced on the basis of the sum of the inverse of the data and model error covariance matrices. Methods to estimate these covariance matrices for the combined set of production data and seismic impedance are presented. Generally, the seismic data will be correlated leading to a nondiagonal error covariance matrix. This matrix will also be very large, and efficient methods to invert this matrix are required. This is done using a very fast discrete convolution inverse based on multiplication of block Toeplitz matrices. It is shown that the regression may converge to a wrong solution if incorrect values for the data correlations are used.The presented methodology is applied to an actual historymatching project using data from a North Sea oil field, and a procedure for mapping the time-lapse seismic data and covariance matrix from the seismic grid to the simulation grid is presented.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe use of time-lapse data, or 4D seismic, in conjunction with production data in computer aided history matching of reservoir models requires that the various types of data are incorporated in a single objective function measuring the mismatch between the simulated and measured data. In the context of linear maximum likelihood estimation, the contribution of seismic data and production data to the objective function can be balanced on the basis of the sum of the inverse of the data and model error covariance matrices. Methods to estimate these covariance matrices for the combined set of production data and seismic impedance are presented. Generally, the seismic data will be correlated leading to a nondiagonal error covariance matrix. This matrix will also be very large, and efficient methods to invert this matrix are required. This is done using a very fast discrete convolution inverse based on multiplication of block Toeplitz matrices. It is shown that the regression may converge to a wrong solution if incorrect values for the data correlations are used.The presented methodology is applied to an actual historymatching project using data from a North Sea oil field, and a procedure for mapping the time-lapse seismic data and covariance matrix from the seismic grid to the simulation grid is presented.