Decline curve analysis is the most commonly used technique to estimate reserves from historical production data for the evaluation of unconventional resources. Quantifying the uncertainty of reserve estimates is an important issue in decline curve analysis, particularly for unconventional resources since forecasting future performance is particularly difficult in the analysis of unconventional oil or gas wells. Probabilistic approaches are sometimes used to provide a distribution of reserve estimates with three confidence levels ($P10$, $P50$, and $P90$) and a corresponding 80% confidence interval to quantify uncertainties. Our investigation indicates that uncertainty is commonly underestimated in practice when using traditional statistical analyses. The challenge in probabilistic reserve estimation is not only how to appropriately characterize probabilistic properties of complex production data sets, but also how to determine and then improve the reliability of the uncertainty quantifications. In this paper, we present an advanced technique for the probabilistic quantification of reserve estimates using decline curve analysis. We examine the reliability of the uncertainty quantification of reserve estimates by analyzing actual oil and gas wells that have produced to near-abandonment conditions, and also show how uncertainty in reserve estimates changes with time as more data become available. We demonstrate that our method provides a more reliable probabilistic reserve estimation than other methods proposed in the literature. These results have important impacts on economic risk analysis and on reservoir management.

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