History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations

Abstract

The ensemble Kalman filter (EnKF) has become a popular method for history matching production and seismic data in petroleum reservoir models. However, it is known that EnKF may fail to give acceptable 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 linearGaussian 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 significant 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.

Conditioning Multiple-Point Geostatistical Facies Simulation on Nonlinear Flow Data Using Pilot Points Method

“…In our implementation, the ES simultaneously applies a damped version of the EnKF update to a long vector containing the stacked state forecast vectors for all timesteps. We also consider a variant of the ES, known as ES-MDA, that was proposed by Emerick and Reynolds (2012). In ES-MDA, the forecast and update steps are repeated multiple times, each time using the updated models from the previous iteration.…”

“…As an example, the ensemble Kalman filter (EnKF) (Evensen 1994, Evensen 2004) has received significant attention in subsurface flow model calibration, see (Aanonsen et al 2009) for a review. In this study, for updating the facies types at the pilot points, we use a variant of the ensemble smoother (ES) (Van Leeuwen and Evensen 1996) with multiple data assimilation (ES-MDA) (Emerick and Reynolds 2012), which is briefly discussed in the Methodology Section.…”

Synergizing Crosswell Seismic and Electromagnetic Techniques for Enhancing Reservoir Characterization

“…The previous discussed time-lapse surface seismic techniques were considerably applied for reservoir-monitoring purposes to determine waterflooding and to provide more-accurate geological descriptions (Lumley 2001;Emerick and Reynolds 2012). These techniques encounter different challenges such as limited resolution, not being applicable in certain environments (e.g., close to buildings) (Yukon Corporation Seismic Imaging Report 2006), and facing processing challenges, such as imaging beneath salt layers (Hoversten et al 1998;Leveille et al 2011).…”

Enhanced heavy oil recovery for carbonate reservoirs integrating cross-well seismic – A synthetic Wafra case study

“…Hiebert et al (2014) presented a history matching study for determining the size, shape, and growth of the steam chamber in a SAGD project, showing that the incorporation of 4D seismic surveys assists in improving the categorization of the reservoir and the evolution of the steam chamber. The development of 4D seismic has led to increased interest in the integration of geophysical data into history matching and several studies on the integration of 4D time lapse seismic data attributes were conducted (Gosselin and Aanonsen, 2001;Kazemi et al, 2011;Emerick and Reynolds, 2012;Skjervheim et al, 2007). With the growing necessity to obtain a detailed understanding of the interwell regions in reservoirs, cross-well seismic tomography has been considered as a viable technique for overcoming the resolution limits of surface seismic techniques.…”