Bayesian Probabilistic Decline-Curve Analysis Reliably Quantifies Uncertainty in Shale-Well-Production Forecasts
- Xinglai Gong (Texas A&M University) | Raul Gonzalez (Texas A&M University) | Duane A. McVay (Texas A&M University) | Jeffery D. Hart (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2014
- Document Type
- Journal Paper
- 1,047 - 1,057
- 2014.Society of Petroleum Engineers
- 5.8.4 Shale Oil, 5.6.9 Production Forecasting, 5.8.2 Shale Gas
- MCMC, probabilistic decline-curve analysis, shale gas
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- 891 since 2007
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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 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 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.
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Anderson, D. M., Nobakht, M., Moghadam, S., et al. 2010. Analysis of Production Data from Fractured Shale Gas Wells. Presented at the SPE Unconventional Gas Conference, Pittsburgh, Pennsylvania, 23–25 February. SPE-131787-MS. http://dx.doi.org/10.2118/131787-MS.
Arps, J. J. 1945. Analysis of Decline Curves. Trans. AIME 160: 228–247.
Capen, E. C. 1976. The Difficulty of Assessing Uncertainty. J Pet Technol 28 (8): 843–850. SPE-5579-PA. http://dx.doi.org/10.2118/5579-PA.
Cheng, Y., Wang, Y., McVay, D., et al. 2010. Practical Application of a Probabilistic Approach to Estimate Reserves Using Production Decline Data. SPE Econ & Mgmt 2 (1): 19–31. SPE-95974-PA. http://dx.doi.org/10.2118/95974-PA.
Drillinginfo. 1998–2011. DI Desktop, http://www.hpdi.com/.
Duong, A. N. 2011. Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs. SPE Res Eval & Eng 14 (3): 377–387. SPE-137748-PA. http://dx.doi.org/10.2118/137748-PA.
Gelman, A., Carlin, J., Stern, H., et al. 2004. Bayesian Data Analysis, second edition. Boca Raton, Florida: CRC Press.
Ilk, D., Rushing, J. A., Perego, A. D., et al. 2008. Exponential Vs. Hyperbolic Decline in Tight Gas Sands–Understanding the Origin and Implications for Reserve Estimates Using Arps’ Decline Curves. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 21–24 September. SPE-116731-MS. http://dx.doi.org/10.2118/116731-MS.
Jochen, V. A. and Spivey, J. P. 1996. Probabilistic Reserves Estimation Using Decline Curve Analysis with the Bootstrap Method. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 6–9 October. SPE-36633-MS. http://dx.doi.org/10.2118/36633-MS.
Lee, W. J. and Sidle, R. 2010. Gas-Reserves Estimation in Resource Plays. SPE Econ & Mgmt 2 (2): 86–91. SPE-130102-PA. http://dx.doi.org/10.2118/130102-PA.
Liu, C. and McVay, D. A. 2009. Continuous Reservoir Simulation Model Updating and Forecasting Using a Markov Chain Monte Carlo Method. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 2–4 February. SPE-119197-MS. http://dx.doi.org/10.2118/119197-MS.
Valko, P. P. and Lee, W. J. 2010. A Better Way to Forecast Production from Unconventional Gas Wells. Presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. SPE-134231-MS. http://dx.doi.org/10.2118/134231-MS.
Wattenbarger, R. A., El-Banbi, A. H., Villegas, M. E., et al. 1998. Production Analysis of Linear Flow into Fractured Tight Gas Wells. Presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, Colorado, 5–8 April. SPE-39931-MS. http://dx.doi.org/10.2118/39931-MS.
Xie, J., Efendiev, Y., and Datta-Gupta, A. 2011. Uncertainty Quantification in History Matching of Channelized Reservoirs Using Markov Chain Level Set Approaches. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 21–23 February. SPE-141811-MS. http://dx.doi.org/10.2118/141811-MS.