Estimation of Initial Fluid Contacts by Assimilation of Production Data with EnKF

Abstract

Abstract Much recent work on automatic history matching and data assimilation has focused on the adjustment of simulator gridblock permeabilities and porosities. Here, we show that when production data are assimilated into reservoir models with the ensemble Kalman filter, it is relatively easy to account for uncertainty in the depths of the initial fluid contacts and provide estimates of these depths in addition to the traditional estimates of rock properties fields. The contact depths strongly affect the initial oil in place and cumulative oil production. We demonstrate that if one uses fixed, but incorrect fluid contacts when assimilating data with EnKF, reasonable matches of production data are obtained, but future performance predictions are inaccurate and severely biased. Considering these same inaccurate contact depths as the means of probability density functions for the two depths and including both the contact depths and rock property fields in the EnKF state vector, we obtain improved performance predictions compared with the case where incorrect depths are assumed to be correct. With uncertain initial fluid contacts, the estimates of the location (depths) of the contacts obtained by matching production data are more accurate than the prior estimates, but unfortunately, do not always provide an improved estimate of the thickness of the oil column. However, this is reflected in a larger estimated uncertainty in the predictions. In the reservoir engineering community, there exists some uncertainty about whether performance prediction runs with a reservoir simulator should be made by predicting forward from the end of data assimilation or by rerunning the reservoir simulator from time zero using the final ensemble of reservoir parameters obtained at the final data assimilation step. We show that if the model error is negligible and the relation between data and the combined state vector is linear, then both procedures give the same predictions. We demonstrate, that for the nonlinear examples considered here the two procedures give reasonably consistent results, although rerunning from time zero tends to give slightly larger estimates of uncertainty in the predictions.