Probabilistic Decline Curve Analysis: State-of-the-Art Review

Abstract

The decline curve analysis (DCA) technique is the simplest, fastest, least computationally demanding, and least data-required reservoir forecasting method. Assuming that the decline rate of the initial production data will continue in the future, the estimated ultimate recovery (EUR) can be determined at the end of the well/reservoir lifetime based on the declining mode. Many empirical DCA models have been developed to match different types of reservoirs as the decline rate varies from one well/reservoir to another. In addition to the uncertainties related to each DCA model’s performance, structure, and reliability, any of them can be used to estimate one deterministic value of the EUR, which, therefore, might be misleading with a bias of over- and/or under-estimation. To reduce the uncertainties related to the DCA, the EUR could be assumed to be within a certain range, with different levels of confidence. Probabilistic decline curve analysis (pDCA) is the method used to generate these confidence intervals (CIs), and many pDCA approaches have been introduced to reduce the uncertainties that come with the deterministic DCA. The selected probabilistic type of analysis (i.e., frequentist or Bayesian), the used DCA model(s), the type and the number of wells, the sampling technique of the data or the model’s parameters, and the parameters themselves undergo a probability distribution, and these are the main differences among all of these approaches and the factors that determine how each approach can quantify the uncertainties and mitigate them. In this work, the Bayesian and frequentist approaches are deeply discussed. In addition, the uncertainties of DCA are briefly discussed. Further, the bases of the different probabilistic analyses are explained. After that, 15 pDCA approaches are reviewed and summarized, and the differences among them are stated. The study concludes that Bayesian analysis is generally more effective than frequentist analysis, though with narrower CIs. However, the choice of DCA model and sampling algorithm can also affect the bounds of the CIs and the calculation of the EUR. Moreover, the pDCA approach is recommended for quantifying uncertainties in DCA, with narrower CIs that indicate greater effectiveness. However, the computational time and the number of iterations in sampling are also considered critical factors. That is why various assumptions and modifications have been made in the pDCA approaches, including the assumption of a certain probability distribution for the sampled parameters to improve their reliability of reserve estimation. The motivation behind this research was to present a full state-of-the-art review of the pDCA and the latest developments in this area of research.