We began this research by asking "Can we use Bayes' theorem to supplement available decline models and improve the accuracy of our estimates of ultimate recovery?" This study focuses on the Eagle Ford Shale, and in particular, on oil wells in the Greater Core Eagle Ford Area. Our goal was to develop a method based on a probabilistic approach to identify, characterize, and better model well production based on standard decline models
To attempt to answer this question, we first obtained data for 68 wells in the Greater Core of the Eagle Ford Shale, Texas. As process, we eliminated the wells that did not have enough production data, wells that did not show a production decline and wells that had too much data noise, leaving eight wells. We then performed decline curve analysis (DCA) using the Modified Hyperbolic (MH) and Power-Law Exponential (PLE) models (the two most common DCA models), consisting in user-guided analysis software. Then, the Bayesian paradigm was implemented to calibrate the same two models on the same set of wells.
The primary focus of the research was the implementation of the Bayesian paradigm on the eight-well data set. We first performed a "best fit" parameter estimation using least squares optimization, which provided an optimized set of parameters for the two decline models. This was followed by using the Markov Chain Monte Carlo (MCMC) integration of the Bayesian posterior function for each model, which provided a full probabilistic description of its parameters. This allowed for the simulation of a number of likely realizations of the decline curves, from which first order statistics were computed to provide a confidence metric on the calibration of each model as applied to the production data of each well.
Results showed variation on the calibration of the MH and PLE models. The forward models (MH and PLE) overestimated the ultimate recovery in the majority of the wells compared with the Bayesian calibrations, proving that the Bayesian paradigm was able to capture a more accurate trend of the data and thus able to determine more accurate estimates of reserves.
In industry, the same decline models are used for unconventional wells as for conventional wells, even though we know that the same models may not apply. Based on the proposed results, we believe that Bayesian inference yields more accurate estimates of ultimate recovery for unconventional reservoirs than deterministic DCA methods. Moreover, it provides a measure of confidence on the prediction of production as a function of varying data and varying decline models.