Probabilistic Decline Curve Analysis in the Permian Basin using Bayesian and Approximate Bayesian Inference

In this work, a probabilistic methodology for decline curve analysis (DCA) in unconventional reservoirs is presented using several Bayesian model-fitting algorithms and deterministic models. The deterministic models considered are the power law exponential (PLE) model, the stretched exponential production decline (SEPD) model, Duong's model, and the logistic growth analysis (LGA) model. Accurate production forecasting and uncertainty quantification were the primary objectives of this study. The Bayesian inferencing techniques described in this work utilize three sampling vehicles, namely the Gibbs sampling (implemented in OpenBUGS, an open-source software), the Metropolis-Hastings (MH) algorithm, and approximate Bayesian computation (ABC) to sample parameter values from their posterior distributions. These different sampling algorithms are applied in conjunction with DCA models to estimate DCA parameter prediction intervals. Using these prediction levels, production is forecasted, and uncertainty bounds are established. To examine its reliability, the methodology was tested on over 74 oil and gas wells located in the three main subplays 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 well calibrated, result in low production errors, and narrow uncertainty bounds for the production history data sets. Also, the LGA model is best in terms of prediction errors for all algorithms except MH. The Gibbs algorithm is nearly the best algorithm in terms of prediction error for all DCA models except the Arps model. Prediction errors are the highest in the Central Basin Platform. The methodology was also successfully applied to unconventional reservoirs with as low as six months of available production history. Depending on the amount of production history data available, the probabilistic model that provides the best fit can vary. It is therefore recommended that all possible combinations of the deterministic and Bayesian model-fitting algorithms be applied to the available production history. This is to obtain more confidence in the conclusions related to the production forecasts, reserves estimate, and uncertainty bounds. The novelty of this methodology relies on using multiple combinations of DCA-Bayesian models to achieve accurate reserves estimates and narrow uncertainty bounds. This paper can help assess shale plays because some of the shale plays are in the early stages of development when productivity estimations are carried out.