Computational Geosciences manuscript No. (will be inserted by the editor) History Matching Time-lapse Seismic Data Using the Ensemble Kalman Filter with Multiple Data Assimilations Alexandre A. Emerick · Albert C. Reynolds Received: date / Accepted: date Abstract The ensemble Kalman filter (EnKF) has be- come a popular method for history matching produc- tion and seismic data in petroleum reservoir models. However, it is known that EnKF may fail to give ac- ceptable data matches especially for highly nonlinear problems. In this paper, we introduce a procedure to improve EnKF data matches based on assimilating the same data multiple times with the covariance matrix of the measurement errors multiplied by the number of data assimilations. We prove the equivalence between single and multiple data assimilations for the linear- Gaussian case and present computational evidence that multiple data assimilations can improve EnKF estimates for the nonlinear case. The proposed procedure was tested by assimilating time-lapse seismic data in two synthetic reservoir problems and the results show signif- icant improvements compared to the standard EnKF. In addition, we review the inversion schemes used in the EnKF analysis and present a rescaling procedure to avoid loss of information during the truncation of small singular values. Keywords Ensemble Kalman filter · multiple data assimilations · time-lapse seismic A. A. Emerick Univ. of Tulsa, 800 South Tucker Drive, Tulsa, OK 74104 Tel.: +1-918-691-9138 E-mail: aemerick@gmail.com A. C. Reynolds Univ. of Tulsa, 800 South Tucker Drive, Tulsa, OK 74104 Tel.: +1-918-631-3043 E-mail: reynolds@utulsa.edu 1 Introduction Reservoir simulation plays an important role in the en- tire hydrocarbon recovery process. In a reservoir sim- ulation model, rock and fluid properties are character- ized and the physical process of fluid flow in the porous media is modeled in order to predict the reservoir’s fu- ture performance. However, the reservoir data available are typically inaccurate, inconsistent and insufficient, so that reservoir models are built with uncertain pa- rameters, which means that predictions based on these models are also uncertain. In order to improve the re- liability of reservoir predictions, the dynamic informa- tion available from historical field production data and seismic acquisitions needs to be incorporated into these reservoir models. This process is known in the oil indus- try as history matching. Bayesian statistics provides an adequate framework to incorporate field observations in reservoir simulation models in a way that allows one to describe uncertainty in the reservoir parameters and simulations predictions. The EnKF, which can be derived from Bayesian statistics [13, Chap. 9], represents an attractive method for reservoir history matching because it is easy to im- plement and computationally efficient. Aanonsen et al. [1] present a comprehensive review of EnKF applica- tions to reservoir problems. Some recent field applica- tions of EnKF can be found in [6, 39, 15, 10]. Even though the EnKF was originally proposed as an alter- native to the extended Kalman filter [13, Chap. 4] for applications in nonlinear dynamical systems, the up- date step in the EnKF is still linear. This linear update may result in a sub-optimal performance for highly non- linear problems. Although the measurement errors do not directly impact the nonlinear relation between pre- dicted data and the EnKF state vector, it is well known