Bayesian Probabilistic Decline Curve Analysis Quantifies Shale Gas Reserves Uncertainty

摘要

Several analytical decline curve models have been developed recently for shale gas wells(Anderson et al.2010;Ilk et al.2008;Valko and Lee 2010).However,despite the considerable uncertainty associated with forecasting shale gas production,these authors either do not quantify the reserves uncertainty in shale gas wells or fail to demonstrate that their probabilistic forecasts are well calibrated.Jochen and Spivey(1996)and Cheng et al.(2010)developed bootstrap methods that can generate probabilistic decline forecasts and quantify reserves uncertainty.Forecasts with the Modified Bootstrap Method(Cheng et al.2010)provide good coverage of the true reserves.However,it is not time efficient because it requires hundreds of Newton iterations for each well.In this work,we introduce a Bayesian methodology for probabilistic decline curve analysis that quantifies reserves uncertainty reliably,quickly,and without modifying the historical production data.We analyzed 167 horizontal gas wells with more than 7 years of production in the Barnett shale to validate the methodology.In this Bayesian methodology,the decline curve parameters qi,Di,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 using MCMC with the Metropolis algorithm.In the test of 167 Barnett shale horizontal gas wells,we assume that the first half of production is known and the second half of production is unknown and acts as"future production."Approximately 85% of the 167 wells'"future production"falls in the range of P90 and P10 reserves generated by this Bayesian methodology,indicating the method is well calibrated,and the Bayesian method is 13 times faster than the modified bootstrap method.The proposed Bayesian methodology provides a means to generate probabilistic decline curve forecasts and quantify the reserves uncertainty in shale gas plays quickly and reliably.This Bayesian methodology can also be applied with other analytical decline curve models if desired.