Effect of Scale Dependent Data Correlations in an Integrated History Matching Loop Combining Production Data and 4D Seismic Data

Abstract

Abstract The 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 history-matching 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. The data seems to contain information about distribution of gas and oil not recovered by history matching to production data only. However, it turned out to be difficult to obtain a good match to the time-lapse seismic data in the regression. It is not clear whether this is due to large uncertainties in the data, incorrect petroelastic model, or incorrect parameterization. This should be investigated in future work. Introduction When building reservoir models, the coherence with respect to all the available data is the main way to improve the reliability of the model and, then, the reliability of the predictions. Traditionally, model properties like porosity and permeability have been conditioned to static and dynamic well data only, and considering the very small parts of the reservoir covered, this conditioning problem often becomes ill-conditioned. Recently, time-lapse, or 4D, seismic data have become available as an additional set of dynamic data. These data add a new dimension to history matching since they contain information of fluid movement and pressure changes between and beyond the wells. During the past few years several papers have considered the use of real 4D data in history matching. Most of these, however, incorporate the information qualitatively, e.g., by manipulating fault barriers to match observed flow paths, see for instance Ref. 1. Huang et al.2 have presented a case study where calibrating a dry-gas reservoir model by minimizing the misfit between 4D amplitudes and synthesized amplitude based on simulation results has improved the reliability of the model predictions. Production data are included in the matching, but there is a lack of documentation about the exact definition of seismic and production terms, while the use of amplitudes in a more general framework for history matching is questionable. Waggoner et al.3,4 have maximized the similarity between acoustic impedance variations from 4D and impedance synthesized using pressure and saturations computed by a numerical simulator. The iterative process has been run using a global greedy optimization algorithm, with an initial calibration of the static model to make it consistent with the trend shown by the base monitor data. This approach has improved the reliability of the prediction for a simple condensate gas reservoir.