Scale-Corrected Ensemble Kalman Filtering Applied to Production-History Conditioning in Reservoir Evaluation
- Ole P. Lodoen (StatoilHydro) | Henning Omre (Norwegian University of Science and Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2008
- Document Type
- Journal Paper
- 177 - 194
- 2008. Society of Petroleum Engineers
- 2.2.2 Perforating, 5.5.3 Scaling Methods, 5.1.1 Exploration, Development, Structural Geology, 3.3 Well & Reservoir Surveillance and Monitoring, 5.5.8 History Matching, 4.3.4 Scale, 5.1.5 Geologic Modeling, 5.6.1 Open hole/cased hole log analysis, 3 Production and Well Operations, 5.5 Reservoir Simulation, 5.6.9 Production Forecasting
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In reservoir evaluation problems, the reservoir properties are largely unknown. To infer these properties from observations of the reservoir production is referred to as history matching or production history conditioning. Traditionally, this is done by repeated fluid-flow simulations, where all the available production data are used simultaneously to arrive at a set of history-matched reservoir models. In recent years, the amount of data continuously collected from a reservoir under production has been on the increase. Hence, the need for automatic, continuous model updating is apparent. The ensemble Kalman filter has been shown to be suitable for this purpose. However, large reservoir evaluation problems require upscaling reservoir properties to perform the necessary number of fluid-flow simulations. Traditional ensemble Kalman filtering is shown to give bias in the production history conditioned reservoir representations. The loss in accuracy and precision introduced by performing fluid-flow simulations on a coarser scale should be accounted for, but this is rarely or never done. We introduce the scale-corrected ensemble Kalman filter approach in order to quantify the loss in accuracy and precision. A reference scale is defined and all uncertainty quantifications are made relative to this scale, although the fluid flow simulations are made on a coarser scale. The production history conditioned reservoir representation will be accurate with realistic precision measures on this reference scale. The methodology is demonstrated on a large case study inspired by the characteristics of the Troll field in the North Sea.
One of the objectives of reservoir evaluation is to find the optimal well configuration and well-operating conditions for a given reservoir. Forecasts of hydrocarbon production for a given recovery strategy can be used to determine this. Quantification of the uncertainty both in the prediction of the reservoir properties and in the forecast of the production properties should be an integral part of the evaluation process.
The assessment of the uncertainty in the production forecasts requires repeated fluid-flow simulations. This is done by using a reservoir production simulator. The reservoir conditions needed as input to this simulator are in practice largely unknown, however. Therefore, the uncertainty in the reservoir properties must be described by a stochastic reservoir model, taking all the available data into account. Prior to starting production, the available data are static data. After the reservoir has been in production for a while, an observed production history is also available. The observed production history should be used to update the reservoir model, and thereby improve the production forecasts. In petroleum-related literature this is referred to as "history matching."
Traditionally, production history conditioning is performed through repeated fluid-flow simulations, where the reservoir properties are tuned to the production history, either manually or automatically by minimizing an objective function involving the mismatch between simulated and observed production. There are two problems with this methodology. The first problem is the computational cost of repeated fluid-flow simulations, which severely restricts the size of the reservoir models to which the production history conditioning can be applied. The second problem is that the reservoir models are updated using all the available production data simultaneously. This means that when new production data become available, the entire production history conditioning process must be repeated. In recent years, the use of permanent sensors for monitoring dynamic production properties has increased, requiring more frequent updating of the reservoir models.
Ideally, the observations should be included in the model sequentially as they become available. This approach requires continuous or sequential production history-conditioning techniques. The Kalman filter has been widely used for this type of time series problem. However, the Kalman filter is most appropriate when the number of variables in the model is low and the observations are linearly related to the model. This is not the case in spatio-temporal reservoir evaluation problems, where the number of model parameters is typically very high, and the relation between the reservoir model and the production observations, represented by a fluid-flow simulator, is highly nonlinear.
Several extensions to the Kalman filter techniques have been suggested, among these the ensemble Kalman filter, developed by Evensen (1994). The ensemble Kalman filter is used to update both the reservoir properties and the production properties. The computations are based on an ensemble of realizations of the reservoir and production properties, from which relevant statistics concerning the model uncertainty can be estimated. At times where new observations become available, all ensemble members are updated to honor these observations. Consequently, the realizations are always kept up to date with the latest observations. The ensemble Kalman filter methodology has been applied to numerous cases in various fields, such as weather forecasting (Evensen 1994; Houtekamer and Mitchell 1998), ground water hydrology (Reichle et al. 2002), and petroleum engineering (Nævdal et al. 2002, 2005; Gu and Oliver 2005; Wen and Chen 2006; Haugen et al. 2006). For a review of recent progress see Evensen (2007).
The ensemble Kalman filter is shown to perform well with an ensemble size of around 100 members. In practice, however, the computational demands by fluid-flow simulation on large reservoir models prohibit ensembles of this size. This problem is typically overcome by performing fluid-flow simulations on a coarser-scale representation of the reservoir variables. This upscaling is known to introduce bias in the production forecasts, however, which should be accounted for. For notational convenience, we will refer to this as coarse-scale fluid flow simulation contrary to fine-scale fluid flow simulation on the preferable fine-scale representation of the reservoir variables. Let us emphasize that the same fluid-flow simulator is used; it is only the gridding of the input variables which vary. In this paper we use the general ensemble Kalman filtering framework of Evensen (1994), and extend it to correct for the effect of using coarse-scale fluid flow simulators, using the approach of Omre and Lødøen (2004). The basic idea of Omre and Lødøen is to use coarse-scale fluid flow simulation to predict the results from fine-scale fluid-flow simulation, and to assess the associated prediction uncertainty. The fine-scale representation is termed the reference scale. This correction is feasible if the coarse-scale fluid flow simulations capture the most important features of the fine-scale fluid-flow simulations. We coin our approach scale-corrected ensemble Kalman filter.
This paper proceeds as follows: We start by defining the notation and describing the ensemble Kalman filter methodology. Then we motivate and present our model extensions. We proceed by presenting a case study, which is inspired by the characteristics of the Troll field in the North Sea. Further, we present and discuss the results from our simulation studies, and finally we draw some conclusions.
|File Size||6 MB||Number of Pages||18|
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