Abstract
There are several issues to consider when we use ensemble smoothers to condition reservoir models on rate data. The values in a time series of rate data contain redundant information that may lead to poorly conditioned inversions and thereby influence the stability of the numerical computation of the update. A time series of rate data typically has correlated measurement errors in time, and negligence of the correlations leads to a too strong impact from conditioning on the rate data and possible ensemble collapse. The total number of rate data included in the smoother update will typically exceed the ensemble size, and special care needs to be taken to ensure numerically stable results. We force the reservoir model with production rate data derived from the observed production, and the further conditioning on the same rate data implies that we use the data twice. This paper discusses strategies for conditioning reservoir models on rate data using ensemble smoothers. In particular, a significant redundancy in the rate data makes it possible to subsample the rate data. The alternative to subsampling is to model the unknown measurement error correlations and specify the full measurement error covariance matrix. We demonstrate the proposed strategies using different ensemble smoothers with the Norne full-field reservoir model.
Highlights
Ensemble methods for data assimilation and parameter estimation are well established in the reservoir-engineering community for history matching reservoir models
Following the first application of Ensemble Kalman Filter (EnKF) with reservoir simulation models by [25], there is a large number of publications that address the estimation of parameters in reservoir simulation models using EnKF, and we refer to the review by [1] and references therein for an overview
We have pointed out that rate data include a dependency in time, i.e., the measurements have errors correlated in time
Summary
Ensemble methods for data assimilation and parameter estimation (see, e.g., [9, 12, 13]) are well established in the reservoir-engineering community for history matching reservoir models. – The number of measurements used in the computation of the update may become very large since all data are conditioned on simultaneously, whereas in EnKF they are processed recursively in time. One would include a term constraining the deviation from the prior estimate of the parameters In this formulation, it is not crucial to include time correlations and avoid redundancy in the rate data, since adding more data does not necessarily lead to a stronger update. When introducing EnKF and ensemble smoothers for solving the history-matching problem, we have continued to use the rate data as done traditionally. For the history-matching problem, the state vector x contains all the uncertain parameters and augments the predicted measurements, which represents a simulation of the model to produce the observed well rates. It is important to understand the difference between dependent and redundant measurements
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