“HMC Techniques for Reducing the Uncertainty of Gas-Lifted Oil Field Model”

Authors: Kushila Jayamanne and Bernt Lie,
Affiliation: University of South-Eastern Norway
Reference: 2023, Vol 44, No 1, pp. 17-29.

Keywords: Parameter estimation, Markov Chain Monte Carlo, Model uncertainty, Hamiltonian Monte Carlo, No-U-Turn Sampler

Abstract: Parametric model uncertainties could have a high impact on the predictive capabilities of a model. When process measurements become available, these uncertainties may be reduced using parameter estimation techniques. Estimation techniques founded on the Bayesian framework in particular are powerful: they produce a probability density function (PDF) of the estimated parameter rather than a single point estimate. In this paper, we consider a gas lifted oil field model whose predictions are highly sensitive to uncertainty in its parameters. We apply Markov Chain Monte Carlo (MCMC) methods, which follow the Bayesian paradigm, to estimate these parameters, and thereby reduce the uncertainty in the model predictions; two different algorithms, Hamiltonian Monte Carlo (HMC) and No-U-Turn Sampler (NUTS), are used. The probabilistic programming language (PPL), Turing in Julia is used for implementation. Monte Carlo simulations and/or data retrodiction is performed prior to and post parameter estimation, to evaluate the uncertainty in model predictions; the outcomes are compared to determine the efficacy of parameter estimation. Results show that the computed posterior distributions yield model predictions that are in close agreement with the observations, and that model uncertainty is effectively reduced.

PDF PDF (4788 Kb)        DOI: 10.4173/mic.2023.1.2

References:
[1] Ban, Z., Ghaderi, A., Janatian, N., and Pfeiffer, C.F. (2022). Parameter Estimation for a Gas Lifting Oil Well Model Using Bayes' Rule and the Metropolis–Hastings Algorithm, Modeling, Identification and Control. 43(2):39--53. doi:10.4173/mic.2022.2.1
[2] Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo, arXiv preprint arXiv:1701.02434. doi:10.48550/arXiv.1701.02434
[3] Bezanson, J., Edelman, A., Karpinski, S., and Shah, V.B. (2017). Julia: A Fresh Approach to Numerical Computing, SIAM Review. 59(1):65--98. doi:10.1137/141000671
[4] Brooks, S., Gelman, A., Jones, G., and Meng, X. (2011). Handbook of Markov Chain Monte Carlo, Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press.
[5] Carpenter, B., Gelman, A., Hoffman, M.D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., and Riddell, A. (2017). Stan: A Probabilistic Programming Language, Journal of Statistical Software. 76(1):1–32. doi:10.18637/jss.v076.i01
[6] Dhingra, N.K., Jovanović, M.R., and Luo, Z.-Q. (2014). An ADMM algorithm for optimal sensor and actuator selection, In 53rd IEEE Conference on Decision and Control. pages 4039--4044. doi:10.1109/CDC.2014.7040017
[7] Dixit, V.K. and Rackauckas, C. (2022). GlobalSensitivity, jl: Performant and Parallel Global Sensitivity Analysis with Julia. Journal of Open Source Software. 7(76):4561. doi:10.21105/joss.04561
[8] Duane, S., Kennedy, A., Pendleton, B.J., and Roweth, D. (1987). Hybrid Monte Carlo, Physics Letters B. 195(2):216--222. doi:10.1016/0370-2693(87)91197-X
[9] Ge, H., Xu, K., and Ghahramani, Z. (2018). Turing: a language for flexible probabilistic inference, In International Conference on Artificial Intelligence and Statistics, AISTATS 2018, 9-11 April 2018, Playa Blanca, Lanzarote, Canary Islands, Spain. pages 1682--1690. http://proceedings.mlr.press/v84/ge18b.html.
[10] Geman, S. and Geman, D. (1984). Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence. PAMI-6(6):721--741. doi:10.1109/TPAMI.1984.4767596
[11] Goodwin, G.C., Graebe, S.F., and Salgado, M.E. (2001). Control system design, Prentice Hall Upper Saddle River.
[12] Hoffman, M.D. and Gelman, A. (2014). The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research. 15(47):1593--1623. http://jmlr.org/papers/v15/hoffman14a.html.
[13] Jayamanne, K.R. (2021). Optimal Operation of Processes Under Uncertainty Using Robust Model Predictive Control, Master's thesis, University of South-Eastern Norway. https://hdl.handle.net/11250/2765105.
[14] Lodoen, O.P. and Tjelmeland, H. (2007). Bayesian calibration of reservoir models using a coarse-scale reservoir simulator in the prior specification, In EAGE Conference on Petroleum Geostatistics. 2007. doi:10.3997/2214-4609.201403057
[15] Manohar, K., Kutz, J.N., and Brunton, S.L. (2021). Optimal Sensor and Actuator Selection Using Balanced Model Reduction, IEEE Transactions on Automatic Control. 67(4):2108--2115. doi:10.1109/TAC.2021.3082502
[16] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equation of state calculations by fast computing machines, The journal of chemical physics. 21(6):1087--1092. doi:10.1063/1.1699114
[17] Moen, O.R., Mo, S., and Varagnolo, D. (2022). A Bayesian Approach for Improved Estimation of Inflow Profiles in Oil Wells, In SPE Norway Subsurface Conference. OnePetro. doi:10.2118/209573-MS
[18] Muske, K.R. and Georgakis, C. (2003). Optimal measurement system design for chemical processes, AIChE Journal. 49(6):1488--1494. doi:10.1002/aic.690490612
[19] Pan, Y., Li, G., Qin, J., Zhang, J., Deng, L., and Bi, R. (2021). A Novel Probabilistic Approach for GOR Forecast in Unconventional Oil Reservoirs, In Unconventional Resources Technology Conference, 26--28 July 2021. Unconventional Resources Technology Conference (URTeC), pages 1811--1830. doi:10.15530/urtec-2021-5068
[20] Papp, T. (2021). DynamicHMC, jl. https://www.tamaspapp.eu/DynamicHMC.jl/dev/. (Accessed: 27 October 2022).
[21] Rackauckas, C. and Nie, Q. (2017). DifferentialEquations, jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia. The Journal of Open Research Software. 5(1):15. doi:10.5334/jors.151
[22] Revels, J., Lubin, M., and Papamarkou, T. (2016). Forward-Mode Automatic Differentiation in Julia, arXiv:1607.07892 [cs.
[23] RuizMaraggi, L.M., Lake, L.W., and Walsh, M.P. (2022). A Bayesian Framework for Addressing the Uncertainty in Production Forecasts of Tight-Oil Reservoirs Using a Physics-Based Two-Phase Flow Model, SPE Reservoir Evaluation & Engineering. 25(03):486--508. doi:10.2118/209203-PA
[24] Sakha, M.S. and Shaker, H.R. (2017). Optimal sensors and actuators placement for large-scale unstable systems via restricted genetic algorithm, Engineering Computations. doi:10.1108/EC-04-2016-0138
[25] Salvatier, J., Wiecki, T.V., and Fonnesbeck, C. (2016). Probabilistic programming in Python using PyMC3, PeerJ Computer Science. 2:e55. doi:10.7717/peerj-cs.55
[26] Sandl, E., Cahill, A., Welch, L., and Beckie, R. (2021). Characterizing oil and gas wells with fugitive gas migration through Bayesian multilevel logistic regression, Science of The Total Environment. 769:144678. doi:10.1016/j.scitotenv.2020.144678
[27] Sharma, R., Fjalestad, K., and Glemmestad, B. (2011). Modeling and control of gas lifted oil field with five oil wells, In 52nd International Conference of Scandinavian Simulation Society, SIMS. pages 29--30.
[28] Taghavi, S. and Ghaderi, A. (2022). On Uncertainty Analysis of the Rate Controlled Production (RCP) Model, Scandinavian Simulation Society. pages 271--278. doi:10.3384/ecp21185271
[29] Xu, K., Ge, H., Tebbutt, W., Tarek, M., Trapp, M., and Ghahramani, Z. (2020). AdvancedHMC, jl: A robust, modular and efficient implementation of advanced HMC algorithms. In Symposium on Advances in Approximate Bayesian Inference. PMLR, pages 1--10. https://proceedings.mlr.press/v118/xu20a.html.
[30] Zare, A., Mohammadi, H., Dhingra, N.K., Georgiou, T.T., and Jovanović, M.R. (2020). Proximal Algorithms for Large-Scale Statistical Modeling and Sensor/Actuator Selection, IEEE Transactions on Automatic Control. 65(8):3441--3456. doi:10.1109/TAC.2019.2948268


BibTeX:
@article{MIC-2023-1-2,
  title={{HMC Techniques for Reducing the Uncertainty of Gas-Lifted Oil Field Model}},
  author={Jayamanne, Kushila and Lie, Bernt},
  journal={Modeling, Identification and Control},
  volume={44},
  number={1},
  pages={17--29},
  year={2023},
  doi={10.4173/mic.2023.1.2},
  publisher={Norwegian Society of Automatic Control}
};