Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter

Abstract

Summary A method based on the ensemble Kalman filter (EnKF) for continuous model updating with respect to the combination of production data and 4D seismic data is presented. When the seismic data are given as a difference between two surveys, a combination of the ensemble Kalman filter and the ensemble Kalman smoother has to be applied. Also, special care has to be taken because of the large amount of data assimilated. Still, the method is completely recursive, with little additional cost compared to the traditional EnKF. The model system consists of a commercial reservoir simulator coupled to a rock physics and seismic modelling software. Both static variables (porosity, permeability, rock physic parameters, etc.) and dynamic variables (saturations and pressures) may be updated continuously with time based on the information contained in the assimilated measurements. The method is applied to a synthetic model and a real field case from the North Sea. In both cases, the 4D seismic data are different variations of inverted seismic. For the synthetic case, it is shown that the introduction of seismic data gives a much better estimate of reservoir permeability. For the field case, the introduction of seismic data gives a very different permeability field than using only production data, while retaining the production match. Introduction The Kalman filter was originally developed to update the states of linear systems.[1] For a presentation of this method in a probabilistic, linear least-squares setting, see e.g., Tarantola.[2] However, this method is not suitable for non-linear models, and the ensemble Kalman filter (EnKF) method was introduced in 1994 by Geir Evensen for updating non-linear ocean models.[3] It may also be applied to a combined state and parameter estimation problem.[4] Several recent investigations have shown the potential of the EnKF for continuous updating of reservoir simulation models, as an alternative to traditional history-matching.[5–10] The EnKF method is a Monte Carlo type sequential Bayesian inversion, and provides an approximate solution to the combined parameter and state estimation problem. The result is an ensemble of solutions approximating the posterior probability density function for the model input parameters (e.g., permeability and porosity), state variables (pressures and saturations), and other output data (e.g., well production history) conditioned to measured, dynamic data. Conditioning reservoir simulation models to seismic data is a difficult task.[11] In this paper we show how the ensemble Kalman filter method can be used to update a combined reservoir simulation/seismic model using the combination of production data and inverted 4D seismic data. Special challenges are involved in the assimilation of the large amount of data available with 4D seismic, and the present work is based on the work presented by Evensen,[4,12] and Evensen and van Leeuwen.[13] In the following, the combined state and parameter estimation problem is described in a Bayesian framework, and it is shown how this problem is solved using the EnKF method, with emphasis on the application to 4D seismic data. When the seismic data are given as a difference between two surveys, a combination of the ensemble Kalman filter and the ensemble Kalman smoother has to be applied. Special challenges involved when the amount of data is very large are discussed. The validity of the method is examined using a synthetic model, and finally a real case from the North Sea is presented.

Ensemble-based conditioning of reservoir models to seismic data

“…Using a Bayesian formulation, it was demonstrated by Skjervheim et al [32] that, since the simulated timelapse data at time t j depend both on the state at time t j , as well as on the state at the initial time t 0 , differences should be calculated with respect to the smoothed estimate for the state at the initial time t 0 . The smoother solution can be obtained by adding the initial state to the state vector x, and updating it at every time t i , 0 < i < j at which measurements are assimilated.…”

“…Note furthermore that, even though permeability will not affect the seismic response directly, it will generally be related to porosity by a porosity-permeability relation and should therefore also be updated for consistency. Skjervheim et al [32] recommended that the ensemble should additionally be conditioned to the initial 3D seismic data. We will present an experiment that investigates this issue.…”

“…Following the suggestion by Skjervheim et al [32] we first investigated the impact of incorporating the initial 3D seismic base survey data. Eight iterations with the EnRML were performed to obtain a match between simulated and measured seismic amplitudes consistent with the specified error statistics.…”

“…An early study which demonstrated the applicability of the method to reservoir history matching based on production data was conducted by Naevdal et al [26], while Evensen et al [11] demonstrate an application to a North Sea reservoir model. Two early applications of the EnKF to seismic history matching were presented by Dong et al [9] and Skjervheim et al [32]. The seismic attributes that have been mostly used in realistic case studies are acoustic (P-wave) impedance and Poisson ratio, which can be obtained fairly easily by applying a rock physics model to the simulator output, but which require more elaborate inversion schemes to obtain from observed seismic amplitudes.…”

Multiscale ensemble filtering for reservoir engineering applications

“…Several publications have discussed the use of EnKF with oil reservoir models: Naevdal et al [19][20][21], Gu and Oliver [10], Gao and Reynolds [8], Liu and Oliver [15], Wen and Chen [27], and Skjervheim et al [24], showing promising results and, at the same time, raising some possible drawbacks.…”