A Strategy for Rapid Quantification of Uncertainty in Reservoir Performance Prediction

Abstract

Abstract This paper will describe a strategy for rapid quantification of uncertainty in reservoir performance prediction. The strategy is based on a combination of streamline and conventional finite difference simulators. Our uncertainty framework uses the Neighbourhood Approximation algorithm to generate an ensemble of history match models, and has been described previously. A speedup in generating the misfit surface is essential since effective quantification of uncertainty can require thousands of reservoir model runs. Our speedup strategy for quantifying uncertainty in performance prediction involves using an approximate streamline simulator to rapidly explore the parameter space to identify good history matching regions, and to generate an approximate misfit surface. We then switch to a conventional, finite difference simulator, and selectively explore the identified parameter space regions. This paper will show results from a parallel version of the Neighbourhood Approximation algorithm on a Linux cluster, demonstrating the advantages of perfect parallelism. We show how it is possible to sample from the posterior probability distribution both to assess accuracy of the approximate misfit surface, and also to generate automatic history match models. Introduction Petroleum reservoir data is inherently uncertain. The field information is usually sparse and noisy. Part of the data is obtained from cores collected at a finite set of wells. The data may also consist of time averaged responses over large scales or derived from an incomplete knowledge of the subsurface geology. The standard procedure for reducing the uncertainty is by constraining the model to data representative of the chosen recovery scheme, i.e., dynamic data, in the form of oil, water and gas production rates, as well as pressure. In contrast to the static data (e.g., geometry and geology) obtained prior to the inception of production, these data are a direct measure of the reservoir response to the recovery process in application. The use of dynamic data in constraining the reservoir model is therefore a sound paradigm. This process of incorporating dynamic data in the generation of reservoir models is known as history matching. The history-matching problem involves determining a set of parameters such that the model output is as close to the history data as possible. What makes history matching a daunting task is the usually high dimensionality of the model parameters, and the non-linear relationship between the parameters and the model output. A second consideration is that the history-matching problem belongs to a class of mathematical problems, which are referred to as inverse and ill-posed [1]. The history match is therefore non-unique, i.e.; more than one combination of the reservoir model input parameters match the observed production data. Consequently predicting model performance is also uncertain, and this uncertainty must be quantified. The only way to quantify uncertainty in reservoir performance requires the generation of multiple model realizations, which are constrained by the dynamic data. For problems with high input-output dimensions, each run of the simulator can be very expensive in CPU time. A single run of the model can take several minutes for a relatively coarse grid to several hours for a fine grid. The fundamental task is how to rapidly generate multiple realizations by exhaustive exploration of parameter space. This is directly tied in with a second consideration, which is the need to restrict the range of investigation for the unknown parameters, thus preventing the algorithm from searching for physically unrealistic solutions. Since realistic uncertainty quantification depends on the quality of the ensemble of solutions generated, the above considerations are imperative for quantifying uncertainty in reservoir performance prediction. Two distinct approaches to exploring model parameter space have been identified in the literature namely, deterministic [2, 3, 4, 5] and stochastic [6, 7, 8] methods.