Combining Physics, Statistics, and Heuristics in the Decline-Curve Analysis of Large Data Sets In Unconventional Reservoirs
- Rafael Wanderley de Holanda (Texas A&M University) | Eduardo Gildin (Texas A&M University) | Peter P. Valko (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2018
- Document Type
- Journal Paper
- 683 - 702
- 2018.Society of Petroleum Engineers
- Bayesian estimation, legal data, automatic decline curve analysis, unconventional reservoirs, Jacobi theta functions
- 4 in the last 30 days
- 601 since 2007
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Analytical single-well models have been particularly useful in forecasting production rates and estimated ultimate recovery (EUR) for the massive number of wells in unconventional reservoirs. In this work, a physics-based decline-curve model accounting for linear flow and material balance in horizontal multistage-hydraulically-fractured wells is introduced. The main characteristics of pressure diffusion in the porous media and the fact that the reservoir is a limited resource are embedded in the functional form, such that there is a transition from transient to boundary-dominated flow and the EUR is always finite. Analogously to the frequently used Arps (1945) hyperbolic model, the new model has only three parameters, where two of them define the decline profile and the third one is a multiplier.
This model is applied to a large data set in a work flow that incorporates heuristic knowledge into the history matching and uncertainty quantification by assigning weights to rate measurements. The heuristic rules aim to lessen the effects of nonreservoir-related variations in the production data (e.g., temporary shut-in caused by fracturing in a neighboring well) and emphasize the reservoir dynamics to perform reliable predictions. However, there are additional degrees of freedom in the way these rules define the values of the weights; therefore, a criterion is established that “calibrates” the uncertainty in the probabilistic models by adjusting the parameters in the heuristic rules. Uncertainty quantification and calibration are performed using a Bayesian approach with hindcasts. This methodology is implemented in an automated framework and applied to 992 gas wells from the Barnett Shale. A comparison with the Arps (1945) hyperbolic model, the Duong (2011) model, and stretched exponential model for this data set shows that the new model is the most conservative in terms of estimated reserves.
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Al-Hussainy, R., Ramey, H. Jr., and Crawford, P. 1966. The Flow of Real Gases Through Porous Media. J Pet Technol, 18 (5): 624–636. SPE-1243-APA. https://doi.org/10.2118/1243-A-PA.
Arps, J. J. 1945. Analysis of Decline Curves. Trans. AIME 160 (1): 228–247. SPE-945228-G. https://doi.org/10.2118/945228-G.
Bello, R. O. 2009. Rate Transient Analysis in Shale Gas Reservoirs With Transient Linear Behavior. PhD dissertation, Texas A&M University, College Station, Texas.
Bello, R. O. and Wattenbarger, R. A. 2008. Rate Transient Analysis in Naturally Fractured Shale Gas Reservoirs. Presented at the CIPC/SPE Gas Technology Symposium 2008 Joint Conference, Calgary, 16–19 June. SPE-114591-MS. https://doi.org/10.2118/114591-MS.
Browning, J., Ikonnikova, S., Gülen, G. et al. 2013. Barnett Shale Production Outlook. SPE Econ & Mgmt 5 (3): 89–104. SPE-165585-PA. https://doi.org/10.2118/165585-PA.
Burnham, K. P. and Anderson, D. R. 2002. Model Selection and Multimodel Inference. New York City: Springer.
Camacho-Velázquez, R. G. 1987. Well Performance Under Solution Gas Drive. PhD dissertation, University of Tulsa, Tulsa.
Camacho-Velázquez, R. G. and Raghavan, R. 1989. Boundary-Dominated Flow in Solutions-Gas-Drive Reservoirs. SPE Res Eval & Eng 4 (4): 503–512. SPE-18562-PA. https://doi.org/10.2118/18562-PA.
Carslaw, H. S. and Jaeger, J. C. 1959. Conduction of Heat in Solids, second edition. Oxford, UK: Clarendon Press.
Castineira, D., Mondal, A., and Matringe, S. 2014. A New Approach for Fast Evaluations of Large Portfolios of Oil and Gas Fields. Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. SPE-170989-MS. https://doi.org/10.2118/170989-MS.
Chang, C.-P. and Lin, Z.-S. 1999. Stochastic Analysis of Production Decline Data for Production Prediction and Reserves Estimation. J. Pet. Sci. Eng. 23 (3–4): 149–160. https://doi.org/10.1016/S0920-4105(99)00013-3.
Chaudhary, N. L. and Lee, W. J. 2016. Detecting and Removing Outliers in Production Data to Enhance Production Forecasting. Presented at the SPE/IAEE Hydrocarbon Economics and Evaluation Symposium, Houston, 17–18 May. SPE-179958-MS. https://doi.org/10.2118/179958-MS.
Cheng, Y., Lee, W. J., and McVay, D. A. 2008. Quantification of Uncertainty in Reserve Estimation From Decline Curve Analysis of Production Data for Unconventional Reservoirs. J. Energy Resour. Technol. 130 (4): 043201-1–043201-6. https://doi.org/10.1115/1.3000096.
Chouikha, A. R. 2005. On Properties of Elliptic Jacobi Functions and Applications. J. Nonlin. Math. Phys. 12 (2): 162–169. https://doi.org/10.2991/jnmp.2005.12.2.2.
Clarkson, C. R., Behmanesh, H., and Chorney, L. 2013. Production-Data and Pressure-Transient Analysis of Horseshoe Canyon Coalbed-Methane Wells, Part II: Accounting for Dynamic Skin. J Can Pet Technol 52 (1): 41–53. SPE-148994-PA. https://doi.org/10.2118/148994-PA.
Cronquist, C. 1991. Reserves and Probabilities: Synergism or Anachronism? J Pet Technol 43 (10): 1258–1264. SPE-23586-PA. https://doi.org/10.2118/23586-PA.
D’Ambroise, J. 2010. Applications of Elliptic and Theta Functions to Friedmann-Robertson-Lemaitre-Walker Cosmology With Cosmological Constant. In A Window Into Zeta and Modular Physics, ed. K. Kirsten and F. L. Williams, Vol. 57, 279–294. New York City: Cambridge University Press. Drillinginfo. DI Desktop, 1998–2017, 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. https://doi.org/10.2118/137748-PA.
Easley, T. G. 2012. A Nonpressure Dependent Method for Forecasting Rate and Reserves in Linear Flowing Conventional and Unconventional Wells. Presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Calgary, 24–25 September. SPE-159391-MS. https://doi.org/10.2118/159391-MS.
Fetkovich, M. 1980. Decline Curve Analysis Using Type Curves. J Pet Technol 32 (6): 1065–1077. SPE-4629-PA. https://doi.org/10.2118/4629-PA.
Fuentes-Cruz, G. and Valkó, P. P. 2015. Revisiting the Dual-Porosity/Dual-Permeability Modeling of Unconventional Reservoirs: The Induced-Interporosity Flow Field. SPE J. 20 (1): 124–141. SPE-173895-PA. https://doi.org/10.2118/173895-PA.
Fulford, D. S. and Blasingame, T. A. 2013. Evaluation of Time-Rate Performance of Shale Wells Using the Transient Hyperbolic Relation. Presented at the SPE Unconventional Resources Conference Canada, Calgary, 5–7 November. SPE-167242-MS. https://doi.org/10.2118/167242-MS.
Fulford, D. S., Bowie, B., Berry, M. E. et al. 2016. Machine Learning as a Reliable Technology for Evaluating Time/Rate Performance of Unconventional Wells. SPE Econ & Mgmt 8 (1): 23–39. SPE-174784-PA. https://doi.org/10.2118/174784-PA.
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.
Hashmi, G., Kabir, C. S., and Hasan, A. R. 2014. Interpretation of Cleanup Data in Gas-Well Testing From Derived Rates. Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. SPE-170603-MS. https://doi.org/10.2118/170603-MS.
Igor, M. 2007. Theta Function of Four Types, MathWorks, Inc., http://www.mathworks.com/matlabcentral/fileexchange/18140-theta-function-of-fourtypes (accessed 13 January 2017).
Johansson, F. et al. 2013. mpmath: A Python Library for Arbitrary-Precision Floating-Point Arithmetic, Version 0.18, http://mpmath.org (accessed 18 February 2017).
Kuchuk, F., Morton, K., and Biryukov, D. 2016. Rate-Transient Analysis for Multistage Fractured Horizontal Wells in Conventional and Un-Conventional Homogeneous and Naturally Fractured Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Dubai, 26–28 September. SPE-181488-MS. https://doi.org/10.2118/181488-MS.
Larsen, L. and Kviljo, K. 1990. Variable-Skin and Cleanup Effects in Well-Test Data. SPE Form Eval 5 (3): 272–276. SPE-15581-PA. https://doi.org/10.2118/15581-PA.
Lee, W. J. and Sidle, R. 2010. Gas-Reserves Estimation in Resource Plays. SPE Econ & Mgmt 2 (2): 86–91. SPE-130102-PA. https://doi.org/10.2118/130102-PA.
Ogunyomi, B. A., Patzek, T. W., Lake, L. W. et al. 2016. History Matching and Rate Forecasting in Unconventional Oil Reservoirs With an Approximate Analytical Solution to the Double-Porosity Model. SPE Res Eval & Eng 19 (1): 70–82. SPE-171031-PA. https://doi.org/10.2118/171031-PA.
Oliver, D. S., Reynolds, A. C., and Liu, N. 2008. Inverse Theory for Petroleum Reservoir Characterization and History Matching. New York City: Cambridge University Press.
Parshall, J. 2008. Barnett Shale Showcases Tight-Gas Development. J Pet Technol 60 (9): 48–55. SPE-0908-0048-JPT. https://doi.org/10.2118/0908-0048-JPT.
Purvis, D. C. and Kuzma, H. 2016. Evolution of Uncertainty Methods in Decline Curve Analysis. Presented at the SPE/IAEE Hydrocarbon Economics and Evaluation Symposium, Houston, 17–18 May. SPE-179980-MS. https://doi.org/10.2118/179980-MS.
Robertson, S. 1988. Generalized Hyperbolic Equation. SPE-18731-MS.
Shahamat, M. S., Mattar, L., and Aguilera, R. 2015. A Physics-Based Method To Forecast Production From Tight and Shale Petroleum Reservoirs by Use of Succession of Pseudosteady States. SPE Res Eval & Eng 18 (4): 508–522. SPE-167686-PA. https://doi.org/10.2118/167686-PA.
Sidle, R. E. and Lee, W. J. 2010. The Demonstration of a “Reliable Technology” for Estimating Oil and Gas Reserves. Presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, 8–9 March. SPE-129689-MS. https://doi.org/10.2118/129689-MS.
Sidle, R. E. and Lee, W. J. 2016. An Update on Demonstrating “Reliable Technology”—Where are We Now? Presented at the SPE/IAEE Hydrocarbon Economics and Evaluation Symposium, Houston, 17–18 May. SPE-179991-MS. https://doi.org/10.2118/179991-MS.
Tyurin, A. 2002. Quantization, Classical and Quantum Field Theory and Theta Functions. Washington, DC: American Mathematical Society
Valkó, P. P. 2009. Assigning Value to Stimulation in the Barnett Shale: A Simultaneous Analysis of 7000 Plus Production Histories and Well Completion Records. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19–21 January. SPE-119369-MS. https://doi.org/10.2118/119369-MS.
Valkó , 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.
Warren, J. E. and Root, P. J. 1963. The Behavior of Naturally Fractured Reservoirs. SPE J. 3 (3): 245–255. SPE-426-PA. https://doi.org/10.2118/426-PA.
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, 5–8 April. SPE-39931-MS. https://doi.org/10.2118/39931-MS.
Weijermars, R., Sorek, N., Sen, D. et al. 2017. Eagle Ford Shale Play Economics: US versus Mexico. J. Nat. Gas Sci. Eng. 38 (February): 345–372. https://doi.org/10.1016/j.jngse.2016.12.009.
Wolfram Research, Inc. 1988. EllipticTheta, http://reference.wolfram.com/language/ref/EllipticTheta.html (accessed 13 January 2017).
Wolfram Research, Inc. 2015. Mathematica, Version 10.3, Champaign, IL: Wolfram Research.
Yu, W., Tan, X., Zuo, L. et al. 2016. A New Probabilistic Approach for Uncertainty Quantification in Well Performance of Shale Gas Reservoirs. SPE J. 21 (6): 2,038–2,048. SPE-183651-PA. https://doi.org/10.2118/183651-PA.
Zhao, Y.-L., Zhang, L.-H., Zhao, J.-Z. et al. 2013. “Triple Porosity” Modeling of Transient Well Test and Rate Decline Analysis for Multi-Fractured Horizontal Well in Shale Gas Reservoirs. J. Pet. Sci. Eng. 110 (October): 253–262. https://doi.org/10.1016/j.petrol.2013.09.006.