SPE 109975 Estimation of Initial Fluid Contacts by Assimilation of Production Data With EnKF

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. Introduction The ensemble Kalman filter (EnKF), introduced by Evensen1, has been used extensively for forecasts of dynamic variables in meteorological and oceanographic systems. Since its introduction into the petroleum engineering literature as a method for real-time assisted history matching by Nævdal et al.2,3,4 for estimation or stochastic simulation of both reservoir model parameters and reservoir simulator primary variables, it has been a focus of much research activity in the reservoir engineering literature5,6,7,8,9,10,11,12. A discussion of the combined parameter and state estimation problem can be found in Evensen13. In the reservoir engineering literature, EnKF has been primarily used to estimate or stochastically simulate gridblock permeabilities and porosities. However, it can conceptually be extended to include other parameters such as depths of fluid contacts and fault transmissibilities14 or the location of boundaries between facies7. As noted above, most EnKF history matching implementations have focused on the estimation or simulation of gridblock permeabilities and porosities, properties that are easy to update sequentially in reservoir simulators. In this case, all reservoir parameters not included in the estimation, and that in reality are not perfectly known, are assumed to be correct during the history matching phase. This can result in tuning of the wrong parameters to compensate for the model error introduced by an incorrect parameter. In particular, the depths of the initial fluid contacts are often not known accurately but have a large impact on oil in place and the production of hydrocarbons as well as water. Very recently, Evensen14 presented the results of a field history match in which he was able to use EnKF to successfully match data by updating gridblock permeabilities and porosities, fault transmissibilities and the locations of initial fluid contacts together with the dynamic variables. Our objective, here, is to investigate the reliability of EnKF for updating both the depths of the initial fluid contacts and the rock property fields for a reservoir model where the truth is known exactly. Specifically, we apply EnKF to the PUNQS3 model15 to update both contact depths and simulator gridblock rock properties given prior Gaussian probability density functions where the best prior estimates of contact depths (the prior means) differ significantly from the depths of the true case. We compare reservoir performance predictions obtained with this process with those obtained by updating only rock property fields with (i) the contact depths set equal to their prior means, and (ii) the case where the location of fluid