Probabilistic decline curve analysis in unconventional reservoirs using Bayesian and approximate Bayesian inference

Abstract

In this work, a probabilistic methodology for Decline Curve Analysis (DCA) in unconventional reservoirs is presented using a combination of Bayesian statistical methods and deterministic models. Accurate reserve estimation and uncertainty quantification are the primary objectives of this study. The Bayesian inferencing techniques described in this work utilizes three sampling mechanisms, namely the Gibbs Sampling (implemented in OpenBUGS), the Metropolis Algorithm, and Approximate Bayesian Computation (ABC) to sample parameter values from their posterior distributions. These different sampling mechanisms are applied in conjunction with DCA models like Arps, Power Law Exponential (PLE), Stretched Exponential Production Decline (SEPD), Duong and Logistic Growth Analysis (LGA) to estimate prediction intervals. Production is forecasted, and uncertainty bounds are established using these prediction intervals. A complete workflow and the summary steps for each of the sampling techniques are provided to permit readers to replicate results. To examine the reliability, the methodology was tested over 74 oil and gas wells located in the three main sub plays of the Permian Basin, namely, the Delaware play, the Central Basin Platform, and the Midland play. Results show that the examined DCA-Bayesian models are successful in providing a high coverage rate, low production prediction errors and narrow uncertainty bounds for the production history data sets. The methodology was also successfully applied to unconventional reservoirs with as low as 6 months of available production history. Depending on the amount of production history available, the combined deterministic-stochastic model that provides the best fit can vary. It is therefore recommended that all possible combinations of the deterministic and stochastic models be applied to the available production history data. This is in order to obtain more confidence in the conclusions related to the reserve estimates and uncertainty bounds. The novelty of this methodology relies in using multiple combinations of DCA-Bayesian models to achieve accurate reserve estimates and narrow uncertainty bounds. The paper can help assess shale plays as most of the shale plays are in the early stages of production when the reserve estimations are carried out.