Bayesian Probabilistic Decline-Curve Analysis Reliably Quantifies Uncertainty in Shale-Well-Production Forecasts

Several analytical decline-curve models have been developed recently for shale-gas wells (Ilk et al. 2008; Anderson et al. 2010; Valko and Lee 2010). However, these authors did not quantify the uncertainty in production forecasts and reserves estimates. This is important because most shale plays are in the early stages of production and virtually any method will have large uncertainty when there are limited production data available. Jochen and Spivey (1996) and Cheng et al. (2010) developed bootstrap methods that can generate probabilistic decline forecasts and quantify reserves uncertainty. Hindcasts with the modified bootstrap method (MBM) (Cheng et al. 2010) provide good coverage of the true cumulative production. However, the authors did not show they can quantify reserves uncertainty with limited production data in unconventional plays. In this paper, we introduce a Bayesian probabilistic methodology using Markov-chain Monte Carlo (MCMC) combined with Arps' decline-curve analysis. We tested this model on two data sets: Barnett shale horizontal-well gas production with more than 7 years of history and Eagle Ford shale horizontal-well oil production with more than 1 year of history. In both cases, P50 hindcasts were very close to true cumulative production and P90 and P10 hindcasts quantified the cumulative production uncertainty reliably with as little as 6 months of production available for matching. In this Bayesian methodology, the decline-curve parameters q(i), D-i, and b are assumed to be random variables instead of parameters to be modified to obtain a best fit. A Markov chain of the decline-curve parameters is constructed by use of MCMC with the Metropolis algorithm (random walk). We developed the model by performing hindcasts with the Barnett case study consisting of 197 horizontal gas wells with more than 7 years of production. The prior distribution, proposal distribution, and likelihood function were calibrated so the probabilistic decline curves quantified the cumulative-production uncertainty reliably with as little as 6 months of data. The same model was then tested with analysis of Eagle Ford shale oil production from 536 wells; the probabilistic decline curves quantified the cumulative-production uncertainty reasonably well by changing only the prior distribution. The proposed Bayesian methodology provides a means and a workflow to generate probabilistic decline-curve forecasts and quantify reserves uncertainty in shale plays quickly and reliably. This Bayesian methodology can also be applied with other analytical decline-curve models if desired.