4D Seismic History Matching Using the Ensemble Kalman Filter (EnKF): Possibilities and Challenges
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This research endeavor presents a 4D seismic history matching work flow based on the ensemble Kalman filter (EnKF) methodology. The objective of this work is to investigate the sensitivity of different combinations of production and seismic data on EnKF model updating. In particular, we are interested to quantify the performance of EnKF-based model updating experiments with respect to production and seismic data matching as well as to estimate uncertain reservoir parameters, e.g., porosity and permeability. The reservoir-seismic model system used consists of a commercial reservoir simulator coupled to an implemented rock physics model and a forward seismic modeling tool based on 1D convolution with weak contrast reflectivity approximation. One of the challenging issues of using 4D seismic data into reservoir history matching is to compare the measured data to the model data in a consistent way. Based on our realistic synthetic reservoir characterization case, time-difference impedance data generally performed better than time-difference amplitude data, and the matching of seismic data mostly improved with the inclusion of seismic data. In estimating posterior porosity and permeability, seismic difference data provided better estimate than using only production data, especially in aquifer region and also in areas that might be considered for in-fill wells. We experienced that the integration of seismic data in the elastic domain mostly provided better results than using seismic data at the amplitude level. This may be due to the measurement error used, and hence, further investigations are suggested to ascertain the appropriate level of seismic data integration. The reservoir simulation model used is a sector model based on a full field North sea reservoir. The prior ensemble used consists of 100 model realizations. For computational efficiency, wehave used efficient subspacebased EnKF implementations to handle the effects of large data sets such as 4D seismic. It may be difficult to assimilate 4D seismic data since it is related to the model variable at two or more time instances. Hence, we have used a combination of the EnKF and the ensemble Kalman smoother (EnKS) to condition the reservoir with seismic data. We performed a thorough study on the effects of using large number of measurements in EnKF by considering a single update of a very simple linear model. The sensitivity of EnKF update for several parameters, e.g., model dimension, correlation length, and measurement error variance also presented. We investigated the accuracy of the traditional covariance estimate with a large number of measurements. We demonstrated that the ensemble size has to be much larger than the number of measurements in order to obtain an accurate solution, and that the problem becomes more severe when the measurement uncertainty decreases, indicating that some kind of localization may have to be applied more often than previously believed. In the real field case study, we have focused on matching the inverted acoustic impedance ratio (monitor survey/base survey) data between two time steps of several years of production. Note that for this real field case, there is a long period of production before the seismic data was assimilated. Hence, the porosity and permeability fields had a large influence induced by production data before they were actually updated with seismic data. Global and local analysis schemes assimilate production data and seismic data respectively. In our implementation of local analysis, we used three significant regions and seismic data within a given local analysis region is influenced by only variables in the same region. The posterior ensemble of models showed good match to both production data and seismic data. In most of the cases of reservoir characterization, the combined use of 4D seismic with production data improved history matching for the wells and also improved posterior impedance ratio data matching. In addition, 4D seismic data provided more information related to permeability update in the aquifer and in-fill areas. The results indicate that the local analysis reduced the amount of spurious correlations and tendencies to ensemble collapse seen with global analysis.
Paper A: Fahimuddin, A.; Aanonsen, S.; Skjervheim, J.-A., Ensemble Based 4D Seismic History Matching: Integration of Different Levels and Types of Seismic Data, SPE 131453. In: Proceeding of the 72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010, Barcelona, Spain, 14-17 June 2010. Copyright Society of Petroleum Engineers. Full text not available in BORA due to publisher restrictions.Paper B: Fahimuddin, A.; Aanonsen, S.; Skjervheim, J.-A., 4D Seismic History Matching of a Real Field Case with EnKF: Use of Local Analysis for Model Updating, SPE 134894. In: Proceedings of the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22 September 2010. Copyright Society of Petroleum Engineers. Full text not available in BORA due to publisher restrictions.Paper C: Fahimuddin, A.; Aanonsen, S.; Mannseth, T., Effect of Large Number of Measurements on the Performance of EnKF Model Updating. In: Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, Bergen, Norway, 8-11 September 2008. Copyright the authors. Reproduced with permission. Published version.Report 1: Fahimuddin, A., Petro-elastic Modeling of a North Sea Reservoir: Rock Physics Recipe and ECLIPSE Simulator. CIPR-PETROMAKS Project Report, 2009. Copyright the author. Reproduced with permission.Report 2: Fahimuddin, A., Forward Seismic Modeling Using 1D Convolution with Weak Contrast Approximation of Reflectivity. CIPR-PETROMAKS Project Report, 2009. Copyright the author. Reproduced with permission.