History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter

Abstract The problem of reservoir characterization through automatic history matching has been extensively studied in recent years. Efficient applications have, however, required either an adjoint or a gradient simulator method to compute the gradient of the objective function or a sensitivity coefficient matrix for the minimization. Both computations are expensive when the number of model parameters or the number of observation data is large. The codes for gradient-based history matching methods are also complex and time-consuming to write. This paper reports the use of the Ensemble Kalman Filter (EnKF) for automatic history matching. EnKF is a Monte Carlo method, in which an ensemble of reservoir models is used. The correlation between reservoir response (e.g. watercut and rate) and reservoir variables (e.g. permeability and porosity) can be estimated from the ensemble. An estimate of uncertainty in future reservoir performance can also be obtained from the ensemble. The methodology of EnKF consists of a forecast step and an assimilation step. A finite-difference, 3-D, 3-phase black-oil reservoir simulator is used for stepping forward the reservoir states. However, unlike the traditional history matching, the source code of the reservoir simulator is not required, which allows this method to be used with any reservoir simulator. Moreover, this forward step is well suited for parallel computation since the time evolution of ensemble reservoir models are independent, hence the ensemble of reservoir models can be advanced in time simultaneously using multiple processors. Only the data assimilation step, i.e. the computation of Kalman filter, requires communication between processors. The assimilation of the data in EnKF is done sequentially rather than simultaneously as in traditional history matching. By so doing the reservoir models are always kept up-to-date, which is important and practical when the frequency of data is fairly high as, for example, the data from permanent sensors. The PUNQ-S3 reservoir model is used to test the method in this paper. It is a small-size (19 × 28 × 5) reservoir engineering model that was developed by a group of companies, institutes and universities in the European Union to compare methods for quantifying uncertainty assessment in history matching. One conclusion is that EnKF can sometimes provide satisfactory history matching results while requiring less computation work than traditional methods.