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An approximate dynamic programming approachto decision making in the presence of uncertainty for surfactant-polymer flooding

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Abstract

The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data.

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References

  1. Alkhatib, A., Babaei, M., King, P.: Decision making under uncertainty: applying the least squares Monte Carlo method in surfactant flooding implementation. SPE J. (2013). doi:10.2118/154467-PA. (in press)

  2. Alkhatib, A., King, P.: Uncertainty quantification of a chemically enhanced oil recovery process: applying the probabilistic collocation method to a surfactant-polymer flood, paper SPE 164244. In: 18th Middle East Oil and Gas Show and Conference, Manama, 10–13 March 2013. doi:10.2118/164244-MS (in press)

  3. Alsofi, A., Blunt, M.: The design and optimization of polymer flooding under uncertainty, paper SPE 145110. In: SPE Enhanced Oil Recovery Conference, Kuala Lumpur, 19–21 July 2011. doi:10.2118/145110-MS

  4. Anderson, G., Delshad, M., King, C., Mohammadi, H., Pope, G.: Optimization of chemical flooding in a mixed-wet dolomite reservoir, paper SPE 100082. In: 2006 SPE/DOE Symposium on Improved Oil Recovery, Tulsa, 22–26 April 2006. doi:10.2118/100082-MS

  5. Bellman, R.: Dynamic Programming. Princeton University Press, Princeton, NJ (1957)

  6. Bratvold, R., Begg, S.: Making Good Decisions. Society of Petroleum Engineers, Richardson (2010)

  7. Brown, C., Smith, P.: The evaluation of uncertainty in surfactant EOR performance prediction, paper SPE 13237. In: 59th SPE Annual Technical Conference and Exhibition, Houston, 16–19 September 1984. doi:10.2118/13237-MS

  8. Cheng, H., Shook, G., Taimur, M., Dwarakanath, V.: Interwell tracer tests to optimize operating conditions for a surfactant field trial: design, evaluation, and implications. SPE Reserv. Eval. Eng. 15, 229–242 (2012)

    Google Scholar 

  9. Cheong, Y., Gupta, R.: Experimental design and analysis methods for assessing volumetric uncertainties. SPE J. 10(3), 324–335 (2005). doi:10.2118/80537-PA

    Article  Google Scholar 

  10. Choudhury, A., King, A., Kumar, S., Sabharwal, Y.: Optimizations in financial engineering: the least-squares Monte Carlo method of Longstaff and Schwartz, paper IEEE 4536290. In: 2008 IEEE International Symposium on Parallel and Distributed Processing, Miami, 14–18 April 2008

  11. Christie, M., Blunt, M.: Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reserv. Eng. Eval 4, 308–317 (2001)

    Google Scholar 

  12. Cortazar, G., Gravet, M., Urzua, J.: The valuation of multidimensional American real options using the LSM simulation method. Comput. Oper. Res. 35(1), 113–129 (2006). doi:10.1016/j.cor.2006.02.016

    Article  Google Scholar 

  13. Dang, C., Chen, Z., Nguyen, N., Bae, W., Phung, T.: Development of isotherm polymer/surfactant adsorption models in chemical flooding, paper SPE 147872. In: SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, 20–22 September 2011. doi:10.2118/147872-MS

  14. Dias, M.: Monte Carlo Simulation of Stochastic Processes. http://www.puc-rio.br/marco.ind/sim_stoc_proc.html (2004). Accessed 17 Jul 2012

  15. Dixit, A., Pindyck, R.: Investment under Uncertainty. Princeton University Press, Princeton (1994)

  16. ECLIPSE Reservoir Engineering Software. Schlumberger. http://www.slb.com/content/services/software/recent/ (2010). Accessed 1 January 2010

  17. ECLIPSE Technical Description, Version 2010.1. Schlumberger 2010

  18. Energy Information Agency (EIA): NYMEX Futures Price Data. http://www.eia.gov/dnav/pet/pet_pri_fut_s1_d.htm (2012). Accessed 10 July 2012

  19. Feinberg, J.: Probabilistic Collocation Method Module (polychaos). https://bitbucket.org/jonathf/polychaos (2012). Accessed 7 July 2012

  20. Field, R., Mircea, D.: Convergence properties of polynomial chaos approximations for L2 random variables, public report. Sandia National Laboratories, Albuquerque (2007)

    Book  Google Scholar 

  21. Foo, J., Xiaoliang, W., Karniadakis, G.: The multi-element probabilistic collocation method: error analysis and applications. J. Comput. Phys. 227, 9572–9595 (2008)

    Article  Google Scholar 

  22. Gamba, A.: An extension of least squares Monte Carlo simulation for multi-options problems. In: 6th Annual Real Options Conference, Paphos, Cyprus, July 4-6 (2002)

  23. Gautschi, W.: Algorithm 726: ORTHPOL—a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Softw. 20, 21–62 (1994)

    Article  Google Scholar 

  24. Gerbacia, W.: The evaluation of surfactant systems for oil recovery using statistical design principles and analysis, paper SPE 7070. In: SPE Symposium on Improved Methods of Oil Recovery, Tulsa, Oklahoma 16–17 April 1978

  25. Ghanem, R., Spanos, P.: Stochastic finite elements: a spectral approach. Springer, New York (1991)

    Book  Google Scholar 

  26. Golub, G., Welsch, J.: Calculation of Gauss quadrature rules. Math. Comput. 23, 221–230 (1969)

    Article  Google Scholar 

  27. Hankins, N., Harwell, J.: Case studies for the feasibility of sweep improvement in surfactant-assisted waterflooding. J. Pet. Sci. Eng. 17, 41–62 (1996). doi:10.1016/S0920-4105(96)00055-1

    Article  Google Scholar 

  28. Hirasaki, G., Miller, C., Puerto, M.: Recent advances in surfactant EOR. SPE J. 16, 889–907 (2011). doi:10.2118/115386-PA

    Article  Google Scholar 

  29. Jafarizadeh, B., Bratvold, R.: Taking real options into the real world: asset valuation through option simulation, paper SPE 124488. In: 2009 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana 4–7 October 2009. doi:10.2118/124488

  30. Karambeigi, M., Zabihi, R., Hekmat, Z.: Neuro-simulation modelling of chemical flooding. J. Pet. Sci. Eng. 78(2), 208–219 (2011). doi:10.1016/j.petrol.2011.07.012

    Article  Google Scholar 

  31. Kossack, C., Bilhartz, H.: The sensitivity of micellar flooding to reservoir heterogeneities, paper SPE 5808. In: SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma 22–24 March 1976. doi:10.2118/5808-MS

  32. Lake, L.W.: Enhanced oil recovery. Prentice Hall, Upper Saddle River (1989)

    Google Scholar 

  33. Li, H., Sarma, P., Zhang, D.: A comparative study of the probabilistic-collocation and experimental-design methods for petroleum-reservoir uncertainty quantification. SPE J. 16, 429–439 (2011). doi:10.2118/140738-PA

    Article  Google Scholar 

  34. Li, H., Zhang, D.: Efficient and accurate quantification of uncertainty for multiphase flow with the probabilistic collocation method. SPE J. 14, 665–679 (2009). doi:10.2118/114802-PA

    Google Scholar 

  35. Li, H., Zhang, D.: Probabilistic collocation method for flow in porous media: comparisons with other stochastic methods. Water Resour. Res. 43 (2007). doi:10.1029/2006WR005673

  36. Lin, G., Tartakovsky, A.: An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media. Adv. Water Resour. 32, 712–722 (2009)

    Article  Google Scholar 

  37. Loeven, G., Bijl, H.: Probabilistic collocation used in a two-step approach for efficient uncertainty quantification in computational fluid dynamics. Comput. Model. Eng. Sci. 36, 193–212 (2008)

    Google Scholar 

  38. Loeven, G., Witteveen, J., Bijl, H.: Probabilistic collocation: an efficient non-intrusive approach for arbitrarily distributed parametric uncertainties, paper AIAA 2007-317. In: 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NA, 8–11 January 2007

  39. Lohne, A., Fjelde, I.: Surfactant flooding in heterogeneous formations, paper SPE 154178. In: Eighteenth SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma 14–18 April (2012). doi:10.2118/154178-MS

  40. Longstaff, F., Schwartz, E.: Valuing American options by simulation: a simple least-squares approach. Rev. Finan. Stud. 14(1), 113–147 (2001). doi:10.1093/rfs/14.1.113

    Article  Google Scholar 

  41. Mathelin, L., Hussaini, M.: A stochastic collocation algorithm for uncertainty analysis. National Aeronautics and Space Agency http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030016674_2003020380.pdf (2003). Accessed 29 June 2012

  42. Matlab, version 7.14. The Mathworks, Inc, Natick (2012)

  43. Moreno, M., Navas, J.: On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Rev. Deriv. Res. 6(2), 107–128 (2003)

    Article  Google Scholar 

  44. Onorato, G., Loeven, G., Ghornaiasl, G., Bijl, H., Lacor, C.: Comparison of intrusive and non-intrusive polynomial chaos methods for CFD applications in aeronautics, paper 1809. In: European Conference on Computational Fluid Dynamics, ECCOMAS CFD, Lisbon, Portugal, 14–17 June (2010)

  45. PERM PUNQ-S3 Test Case. Petroleum Engineering and Rock Mechanics Group (PERM). http://www3.imperial.ac.uk/earthscienceandengineering/research/perm/punq-s3model/onlinedataset. Accessed 5 May 2012

  46. Pope, G., Wang, B., Tsaur, K.: A sensitivity study of micellar/polymer flooding. SPE J. 19, 357–368 (1979)

    Google Scholar 

  47. Powell, W.: Approximating value functions. In: Approximate Dynamic Programming: Solving the Curses of Dimensionality, Chap, p 8. Wiley, Princeton (2011)

    Book  Google Scholar 

  48. Puerto, M., Hirasaki, G., Miller, C., Barnes, J.: Surfactant systems for EOR in high-temperature, high-salinity environments. SPE J. 17, 11–19 (2012)

    Article  Google Scholar 

  49. PYTHON, version 2.7.3. Python Software Foundation. http://www.python.org/download/releases/2.7.3/ (2012). Accessed 1 February 2012

  50. Sarma, P., Xie, J.: Efficient and robust uncertainty quantification in reservoir simulation with polynomial chaos expansions and non-intrusive spectral projection, paper SPE 141963. In: SPE Reservoir Simulation Symposium, The Woodlands, TX, 21–23 February 2011

  51. Smith, W.: On the Simulation and Estimation of the Mean-Reverting Ornstein-Uhlenbeck Process. http://commoditymodels.files.wordpress.com/2010/02/estimating-the-parameters-of-a-mean-reverting-ornstein-uhlenbeck-process1.pdf (2010). Accessed 9 Jan 2012

  52. Solairaj, S., Britton, C., Kim, D., Weerasooriya, U., Pope, G.: Measurement and analysis of surfactant retention, paper SPE 154247. In: Eighteenth SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma 14–18 April 2012. doi:10.2118/154247-MS

  53. Tatang, M., Pan, W., Prinn, R., McRae, G.: An efficient method for parametric uncertainty analysis of numerical geophysical models. J. Geophys. Res. 102, 21925–21932 (1997)

    Article  Google Scholar 

  54. Thomas, S.: Chemical EOR: The past—does it have a future? paper SPE 108828. In: SPE Distinguished Lecture during the 2005–2006 season (2006)

  55. Uhlenbeck, G., Ornstein, L.: On the theory of the Brownian motion. Phys. Rev. 36(5), 823–841 (1930). doi:10.1103/Phys-Rev.36.823

    Article  Google Scholar 

  56. Weiss, W., Baldwin, R.: Planning and implementing a large-scale polymer flood. J. Pet. Technol. 37, 720–730 (1985). doi:10.2118/12637-PA

    Google Scholar 

  57. Wiener, N.: The homogeneous chaos. Am. J. Math. 60, 897–936 (1938)

    Article  Google Scholar 

  58. Willigers, B., Bratvold, R.: Valuing oil and gas options by least-squares Monte Carlo simulation. SPE Proj. Facil. Constr. 4(4), 146–155 (2009). doi:10.2118/116026-PA

    Google Scholar 

  59. Wyatt, K., Pitts, M., Surkalo, H.: Economics of field proven chemical flooding technologies, paper SPE 113126. In: SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma, 20–23 April 2008. doi:10.2118/113126-MS

  60. Xiu, D., Hesthaven, J.: High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 27, 1118–1139 (2005)

    Article  Google Scholar 

  61. Xiu, D., Karniadakis, G.: The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24, 619–644 (2002)

    Article  Google Scholar 

  62. Zhang, J., Delshad, M., Sepehnoori, K., Pope, G.: An efficient reservoir-simulation approach to design and optimize improved oil-recovery-processes with distributed Computing, paper SPE 94733. In: SPE Latin American and Caribbean Petroleum Engineering Conference, Rio de Janeiro 20–23 June (2005). doi:10.2118/94733-MS

  63. Zheng, C., Gall, B., Gao, H., Bryant, R.: Effects of polymer adsorption and flow behaviour on two-phase flow in porous media. SPE Reserv. Eval. Eng 3, 216–223 (2000). doi:10.2118/64270-PA

    Google Scholar 

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  1. Earth Science and Engineering, Imperial College London, London, UK

    Ali Alkhatib & Peter King

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  1. Ali Alkhatib
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Alkhatib, A., King, P. An approximate dynamic programming approachto decision making in the presence of uncertainty for surfactant-polymer flooding. Comput Geosci 18, 243–263 (2014). https://doi.org/10.1007/s10596-014-9406-2

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