Optimizing Estimates of Probabilistic Reserves from Production Trends Using a Bayesian Approach

Abstract

The estimation of probabilistic reserves distributions is nowadays a mandatory task in the oil industry. The trade-off between speed and accuracy, coupled with the urgency of results is still making of Decline Curve Analysis (DCA) one of the most popular method to address these calculations. In a previous paper, we introduced a quick and efficient application (PREP) to estimate probabilistic reserves distribution combining the advantages of stochastic methods (Bootstrapping) and DCA. Although the proposed tool is robust and effective, one of the limitations found was reconciling the statistical uncertainty associated in the generation of the DCA parameter distributions with the observed production trends. The objective of this paper is to present a proficient procedure to reduce the uncertainties in DCA probabilistic reserves estimation via Bayesian techniques. The procedure allows the analysis of multiple decline trends taking full advantage of the self-learning capability implicit in Bayesian techniques. The usefulness of the results is maximized when coupled with proper reservoir knowledge, leading to statistically strong results. The new methodology was applied in the reserve evaluation of three (3) Colombian fields located in the Valle Superior del Magdalena Basin in Colombia, South America. The method provided a new set of declination parameters with smaller covariance, reducing the uncertainty compared to any previous reserves distribution. Introduction Decline curve analysis is still a helpful and widely used tool to estimate future reserves and predict production behavior of oil and gas wells[1,2,3]. The basic assumption in this procedure is that whatever controls the trend of a curve in the past will continue to govern its trend in the future in a uniform manner. With this assumption, future flow rates and recoveries can be forecasted. The simplicity and availability of data makes this procedure a very useful and attractive tool to reservoir engineers and managers, when quick estimates are needed. Departing from Jochen et al.[4], in a previous paper[5], we presented a quick and efficient application for estimating probabilistic distribution of reserves combining the usually available production information with the versatility of stochastic methods through the use of decline curve analysis: PREP (Probabilistic Reserves Estimation Package). The application uses the Bootstrapping technique (a Monte Carlo method) coupled with an efficient optimization algorithm to calculate the DCA parameters. The main advantage of this technique is that it does not require a priori knowledge of the parameter probability distributions. The method is founded in smart resampling, i.e., probabilistic reserves are calculated based only on rearrangements of the original production data. The sampling consists of random selections from the original production data with replacements. In this case, some points can be excluded and some can be repeated. As a consequence of this process, the set of calculated reservoir parameters can be used to obtain their own and independent probability distributions. This procedure is summarized in Figure1 and Figure 2. For a successful application of the tehcnqiue, two main assumptions are required. First, a model to predict reservoir performance should be available. Second, the available field data must be independently and identically distributed, which implies that oscillations in the data are due to measurement error, rather than normal changes in field operational conditions. This hypothesis could be seen as a weakness, but most of regression analysis methods for production data analysis make the same assumption.