Ensemble Kalman filter for automatic history matching of geologic facies

In this paper we address two fairly difficult problems. The first is the problem of matching production data (in this case, production and injection rates) by adjustment of the locations of the geologic facies boundaries. The second is the use of a Kalman filter for updating the facies locations in the reservoir model. Traditional automatic history matching tools are not widely available for reservoirs with unknown facies boundaries, largely because of the complexity of developing software for computing the sensitivity of the data to model parameters, the lack of differentiability of facies type, and the high computational cost in generating multiple reservoir models that are conditional to given data. With careful definition of variables, the use of the ensemble Kalman filter (EnKF) minimizes those difficulties. First, the gradient does not need to be computed explicitly, the coding for the EnKF algorithm is easy and adaptable to any reservoir simulator on a plug-in basis. Second, an approximation to differentiability results from the correlation of variables. Third, the ensemble Kalman filter (EnKF) method takes one simulation run per reservoir model realization, and the simulations of the reservoir models in the ensemble are ideal for multiple-processor parallel computation. We use the truncated pluri-Gaussian model to generate random facies realizations. The geostatistical model is fully specified by the threshold truncation map and the covariance models for the two Gaussian random fields. The pluri-Gaussian model is well known but not widely used, partly because of the difficulty of generating conditional realizations. In the first example, we demonstrate the application of the EnKF to the problem of generating facies realizations conditional to observations at 18 wells on a 128 x 128 grid. In the second example, realizations of facies on a 50 x 50 grid, conditional to facies observations at the wells and to production and injection rates, are generated using the EnKF. In general, we found that application of the EnKF to the problem of adjusting facies boundaries to match production data was relatively straightforward and efficient. (c) 2005 Elsevier B.V. All rights reserved.