Approximate Bayesian Computation for Probabilistic Decline-Curve Analysis in Unconventional Reservoirs
- Mohit Paryani (University of Alaska, Fairbanks) | Obadare O. Awoleke (University of Alaska, Fairbanks) | Mohabbat Ahmadi (University of Alaska, Fairbanks) | Catherine Hanks (University of Alaska, Fairbanks) | Ronald Barry (University of Alaska, Fairbanks)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2017
- Document Type
- Journal Paper
- 478 - 485
- 2017.Society of Petroleum Engineers
- Unconventional Reservoirs, Probabilistic Decline Curve Analysis, Uncertainty Quantification, Bayesian inference , Reserves estimates
- 5 in the last 30 days
- 463 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
In this work, we developed a methodology that integrates decline curve-analysis (DCA) models with an approximate Bayesian probabilistic method that is based on rejection sampling to quantify the uncertainty associated with DCA models. This methodology does not require the estimation of the likelihood, which simplifies the Bayesian inference greatly.
In approximate Bayesian computation (ABC) with rejection sampling, the posterior distribution is approximated by substituting different values of the decline-equation parameters into the Arps’ DCA model and generating a large number of production-profile realizations. Summary statistics (mean, standard deviation) between the simulated and observed production data are then compared. On the basis of some optimum threshold value, the rejection-sampling technique is applied to either accept or discard the simulated production data. The resulting distribution is used to approximate the posterior. The 10th, 50th, and the 90th percentiles of the accepted data sets provide the P90, P50, and P10 estimates for reserves, respectively.
History matching was performed to test the proposed Bayesian model and to check how well the simulation results match with the observed production data. Chosen for analysis were 57 gas wells from Johnson County (Barnett Shale) and 21 oil wells from Karnes County (Eagle Ford Shale) with production history of 90 and 45 months, respectively. Best-fit (deterministic) curves were computed with the least-squares regression method. Only two-thirds of available history was used for modeling, and the remaining one third of the history was used for validating the methodology.
The P50 history match trended well with the best-fit curve for majority of wells. The ABC P90–P50–P10 average cumulative production interval for wells in Johnson County was 1,263–1,410–1,528 MMcf, whereas the true average cumulative production per well was 1,425 MMcf. Similarly, for Karnes County, the ABC P90–P50–P10 average interval per well was 170,000/184,000/204,000 STB, whereas the true average cumulative production per well was 183,000 STB. This implies that the ABC bounds bracket the true reserve well. Approximately 42 and 98% of wells’ true cumulative production at the end of hindcast were greater than their P50 and P90 estimates, respectively. This implies that the P50 and P90 estimates were quite accurate even with short production history (approximately 2 years). The P10 estimates were less accurate but still acceptable with only 4% of wells’ true production higher than their P10 estimate. Therefore, estimates from the ABC methodology are well-calibrated.
The proposed ABC methodology combined with rejection sampling provides a procedure that not only produces probabilistic forecasts but also quantifies reserves uncertainty in shale plays quickly and consistently. The ABC methodology can be coupled with any other deterministic DCA model.
|File Size||807 KB||Number of Pages||8|
Agrawal, A., Wei, Y., and Holditch, S. 2012. A Technical and Economic Study of Completion Techniques in Five Emerging US Gas Shales: A Woodford Shale Example. SPE Drill & Compl 27 (1): 39–49. SPE-135396-PA. https://doi.org/10.2118/135396-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. https://doi.org/10.2118/95974-PA.
Clark, A. J., Lake, L. W., and Patzek, T. W. 2011. Production Forecasting With Logistic Growth Models. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE 144790-MS. https://doi.org/10.2118/144790-MS.
Dossary, M. and McVay, D. A. 2012. The Value of Assessing Uncertainty. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8–10 October. SPE-160189-MS. https://doi.org/10.2118/160189-MS.
Gong, X., Gonzalez, R., McVay, D. A. et al. 2014. Bayesian Probabilistic Decline-Curve Analysis Reliably Quantifies Uncertainty in Shale-Well-Production Forecasts. SPE J. 19 (6): 1047–1057. SPE-147588-PA. https://doi.org/10.2118/147588-PA.
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, 6–9 October. SPE-36633-MS. https://doi.org/10.2118/36633-MS.
Kanfar, M. and Wattenbarger, R. 2012. Comparison of Empirical Decline Curve Methods for Shale Wells. Presented at the SPE Canadian Unconventional Resources Conference, Calgary, 30 October–1 November. SPE-162648-MS. https://doi.org/10.2118/162648-MS.
Kruschke, J. K. 2011. Doing Bayesian Data Analysis: A Tutorial With R and BUGS. Burlington, Massachusetts: Academic Press.
Suliman, B., Meek, R., Hull, R. et al. 2013. Variable Stimulated Reservoir Volume (SRV) Simulation: Eagle Ford Shale Case Study. Presented at the SPE Unconventional Resources Technology Conference, Denver, 12–14 August. SPE-168832-MS. https://doi.org/10.1190/URTEC2013-057.
Turner, B. M. and Van Zandt, T. 2012. A Tutorial on Approximate Bayesian Computation. Journal of Mathematical Psychology 56 (2): 69–85. ISSN 0022-2496. https://doi.org/10.1016/j.jmp.2012.02.005.
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. https://doi.org/10.2118/134231-MS.