期刊首页 优先出版 当期阅读 过刊浏览 作者中心 关于期刊 English

《工程(英文)》 >> 2022年 第18卷 第11期 doi: 10.1016/j.eng.2022.06.011

基于样地调查的地质碳储量的贝叶斯优化

a Center for Subsurface Modeling, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
b IBM Research United Kingdom, Warrington WA4 4AD, UK

收稿日期: 2021-12-15 修回日期: 2022-06-06 录用日期: 2022-06-20 发布日期: 2022-07-25

下一篇 上一篇

摘要

We present a framework that couples a high-fidelity compositional reservoir simulator with Bayesian optimization (BO) for injection well scheduling optimization in geological carbon sequestration. This work represents one of the first at tempts to apply BO and high-fidelity physics models to geological carbon storage. The implicit parallel accurate reservoir simulator (IPARS) is utilized to accurately capture the underlying physical processes during CO2 sequestration. IPARS provides a framework for several flow and mechanics models and thus supports both stand-alone and coupled simulations. In this work, we use the compositional flow module to simulate the geological carbon storage process. The compositional flow model, which includes a hysteretic three-phase relative permeability model, accounts for three major CO2 trapping mechanisms: structural trapping, residual gas trapping, and solubility trapping. Furthermore, IPARS is coupled to the International Business Machines (IBM) Corporation Bayesian Optimization Accelerator (BOA) for parallel optimizations of CO2 injection  strategies during field-scale CO2 sequestration. BO builds a probabilistic surrogate for the objective function using a Bayesian machine learning algorithm—the Gaussian process regression, and then uses an acquisition function that leverages the uncertainty in the surrogate to decide where to sample. The IBM BOA addresses the three weaknesses of standard BO that limits its scalability in that IBM BOA supports parallel (batch) executions, scales better for high-dimensional problems, and is more robust to initializations. We demonstrate these merits by applying the algorithm in the optimization of the CO2 injection schedule in the Cranfield site in Mississippi, USA, using field data. The optimized injection schedule achieves 16% more gas storage volume and 56% less water/surfactant usage compared with the baseline. The performance of BO is compared with that of a genetic algorithm (GA) and a covariance matrix adaptation (CMA)-evolution strategy (ES). The results demonstrate the superior performance of BO, in that it achieves a competitive objective function value with over 60% fewer forward model evaluations. 

图片

图1

图2

图3

图4

图5

图6

图7

图8

参考文献

[ 1 ] Ausfelder F, Baltac S. Special report on carbon capture utilization and storage—CCUS in clean energy transitions Report. Paris: IEA; 2020.

[ 2 ] Navarre-Sitchler AK, Maxwell RM, Siirila ER, Hammond GE, Lichtner PC. Elucidating geochemical response of shallow heterogeneous aquifers to CO2 leakage using high-performance computing: implications for monitoring of CO2 sequestration. Adv Water Resour 2013;53:45‒55. 链接1

[ 3 ] Zhao X, Liao X, Wang W, Chen C, Rui Z, Wang H. The CO2 storage capacity evaluation: methodology and determination of key factors. J Energy Inst 2014;87(4):297‒305. 链接1

[ 4 ] Zhao X, Rui Z, Liao X. Case studies on the CO2 storage and EOR in heterogeneous, highly water-saturated, and extra-low permeability Chinese reservoirs. J Nat Gas Sci Eng 2016;29:275‒83. 链接1

[ 5 ] Lu X, Lotfollahi M, Ganis B, Min B, Wheeler MF. An integrated flowgeomechanical analysis of flue gas injection in Cranfield. In: Proceedings of SPE Improved Oil Recovery Conference; 2018 Apr 14‒18; Tulsa, OK, USA. OnePetro; 2018. p. SPE-190300-MS. 链接1

[ 6 ] Zoback MD, Gorelick SM. Earthquake triggering and large-scale geologic storage of carbon dioxide. Proc Natl Acad Sci USA 2012;109(26):10164‒8. 链接1

[ 7 ] Cappa F, Rutqvist J. Impact of CO2 geological sequestration on the nucleation of earthquakes. Geophys Res Lett 2011;38(17):L17313. 链接1

[ 8 ] Liu Y, Rui Z. A storage-driven CO2 EOR for a net-zero emission target. Engineering. . . 10.1016/j.eng.2022.02.010

[ 9 ] Li H, Leung WT, Wheeler MF. Sequential local mesh refinement solver with separate temporal and spatial adaptivity for non-linear two-phase flow problems. J Comput Phys 2020;403:109074. 链接1

[10] Singh G, Wheeler MF. Compositional flow modeling using a multi-point flux mixed finite element method. Computat Geosci 2016;20(3):421‒35. 链接1

[11] Ganis B, Singh G, Wheeler MF. A parallel framework for a multipoint flux mixed finite element equation of state compositional flow simulator. Computat Geosci 2017;21(5‒6):1189‒202.

[12] Mikelic´ A, Wang B, Wheeler MF. Numerical convergence study of iterative coupling for coupled flow and geomechanics. Computat Geosci 2014;18(3‒4):325‒41.

[13] Lu X, Wheeler MF. Three-way coupling of multiphase flow and poromechanics in porous media. J Comput Phys 2020;401:109053. 链接1

[14] Class H, Ebigbo A, Helmig R, Dahle HK, Nordbotten JM, Celia MA, et al. A benchmark study on problems related to CO2 storage in geologic formations. Computat Geosci 2009;13(4):409‒34. 链接1

[15] Delshad M, Kong X, Tavakoli R, Hosseini SA, Wheeler MF. Modeling and simulation of carbon sequestration at Cranfield incorporating new physical models. Int J Greenh Gas Control 2013;18:463‒73. 链接1

[16] Wheeler MF, Delshad M, Kong X, Thomas S, Wildey T, Xue G. Role of computational science in protecting the environment: geological storage of CO2. In: Proceedings of the International Congress of Mathematicians 2010 (ICM 2010); 2010 Aug 19‍‒‍27; Hyderabad, India. Hyderabad, India: World Scientific; 2011. p. 2864‒85. 链接1

[17] Peng DY, Robinson DB. A new two-constant equation of state. Ind Eng Chem Fundamen 1976;15(1):59‒64. 链接1

[18] Delshad M, Kong X, Wheeler MF. On interplay of capillary, gravity, and viscous forces on brine/CO2 relative permeability in a compositional and parallel simulation framework. In: Proceedings of SPE Reservoir Simulation Symposium; 2011 Feb 21‍‒‍23; The Woodlands, TX, USA. OnePetro; 2011. p.SPE-142146-MS. 链接1

[19] Kumar A, Noh M, Pope GA, Sepehrnoori K, Bryant S, Lake LW. Reservoir simulation of CO2 storage in deep saline aquifers. In: Proceedings of SPE/DOE Symposium on Improved Oil Recovery; 2004 Apr 17‍‒‍21; Tulsa, OK, USA. OnePetro; 2004. p. SPE-89343-MS. 链接1

[20] Beygi MR, Delshad M, Pudugramam VS, Pope GA, Wheeler MF. Novel threephase compositional relative permeability and three-phase hysteresis models. SPE J 2015;20(1):21‒34. 链接1

[21] Lotfollahi M, Kim I, Beygi MR, Worthen AJ, Huh C, Johnston KP, et al. Foam generation hysteresis in porous media: experiments and new insights. Transp Porous Media 2017;116(2):687‒703. 链接1

[22] White D, Ganis B, Liu R, Wheeler MF. A near-wellbore study with a Drucker‒Prager plasticity model coupled with a parallel compositional reservoir simulator. In: Proceedings of SPE Reservoir Simulation Conference; 2017 Feb 20‒22; Montgomery, TX, USA. OnePetro; 2017. p. SPE-182627-MS. 链接1

[23] Onwunalu JE, Durlofsky LJ. Application of a particle swarm optimization algorithm for determining optimum well location and type. Computat Geosci 2010;14(1):183‒98. 链接1

[24] Min B, Sun AY, Wheeler MF, Jeong H. Utilization of multiobjective optimization for pulse testing dataset from a CO2-EOR/sequestration field. J Petrol Sci Eng 2018;170:244‒66. 链接1

[25] Lu X, Ganis B, Wheeler MF. Optimal design of CO2 sequestration with three-way coupling of flow-geomechanics simulations and evolution strategy. In: Proceedings of SPE Reservoir Simulation Conference; 2019 Apr 10‍‒‍11; Galveston, TX, USA. OnePetro; 2019. p. SPE-193849-MS. 链接1

[26] Bangerth W, Klie H, Wheeler MF, Stoffa PL, Sen MK. On optimization algorithms for the reservoir oil well placement problem. Computat Geosci 2006;10(3):303‒19. 链接1

[27] Fonseca RRM, Chen B, Jansen JD, Reynolds A. A stochastic simplex approximate gradient (StoSAG) for optimization under uncertainty. Int J Numer Methods Eng 2017;109(13):1756‒76. 链接1

[28] Zandvliet MJ, Handels M, van Essen GM, Brouwer DR, Jansen JD. Adjoint-based well-placement optimization under production constraints. SPE J 2008;13(4):392‒9. 链接1

[29] Zhang K, Li G, Reynolds AC, Yao J, Zhang L. Optimal well placement using an adjoint gradient. J Petrol Sci Eng 2010;73(3‒4):220‒6.

[30] Nwachukwu A, Jeong H, Sun A, Pyrcz M, Lake LW. Machine learning-based optimization of well locations and WAG parameters under geologic uncertainty. In: Proceedings of SPE improved oil recovery conference; 2018 Apr 14‍‒‍18; Tulsa, OK, USA. OnePetro; 2018. p. SPE-190239-MS. 链接1

[31] Zhu Y, Zabaras N. Bayesian deep convolutional encoder‒decoder networks for surrogate modeling and uncertainty quantification. J Comput Phys 2018;366:415‒47. 链接1

[32] Tang M, Liu Y, Durlofsky LJ. A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems. J Comput Phys 2020;413:109456. 链接1

[33] Snoek J, Larochelle H, Adams RP. Practical Bayesian optimization of machine learning algorithms. In: Proceedings of the 26th Conference on Neural Information Processing Systems (NIPS 2012); 2012 Dec 3‒8; Lake Tahoe, NV, USA. NIPS; 2012. p. 2951‒9.

[34] Burger B, Maffettone PM, Gusev VV, Aitchison CM, Bai Y, Wang X, et al. A mobile robotic chemist. Nature 2020;583(7815):237‒41. 链接1

[35] Calandra R, Seyfarth A, Peters J, Deisenroth MP. Bayesian optimization for learning gaits under uncertainty. Ann Math Artif Intell 2016;76(1‒2):5‒23.

[36] Marchant R, Ramos F. Bayesian optimisation for intelligent environmental monitoring. In: Proceedings of 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems; 2012 Oct 7‒12; Vilamoura-Algarve, Portugal. IEEE; 2012. p. 2242‒9. 链接1

[37] Frazier PI. A tutorial on Bayesian optimization. 2018. arXiv:1807.02811.

[38] Abdollahzadeh A, Reynolds A, Christie M, Corne D, Davies B, Williams G. Bayesian optimization algorithm applied to uncertainty quantification. SPE J 2012;17(3):865‒73. 链接1

[39] Chen Z, Huan G, Ma Y. Computational methods for multiphase flows in porous media. Philadelphia: SIAM; 2006. 链接1

[40] Thomas SG. On some problems in the simulation of flow and transport through porous media [dissertation]. Austin: University of Texas at Austin; 2009.

[41] Kulkarni MM, Rao DN. Experimental investigation of miscible and immiscible water-alternating-gas (WAG) process performance. J Petrol Sci Eng 2005; 48(1‒2):1‒20.

[42] Ma K, Ren G, Mateen K, Morel D, Cordelier P. Modeling techniques for foam flow in porous media. SPE J 2015;20(3):453‒70. 链接1

[43] Matérn B. Spatial variation. 2nd ed. New York: Springer; 1986. 链接1

[44] Stein ML. Interpolation of spatial data: some theory for kriging. New York: Springer; 1999. 链接1

[45] Mockus J, Tiesis V, Zilinskas A. The application of Bayesian methods for seeking the extremum. Towar glob optim 1978;2:117‒29. 链接1

[46] Lizotte DJ. Practical Bayesian optimization [dissertation]. Edmonton:University of Alberta; 2008.

[47] Jasrasaria D, Pyzer-Knapp EO. Dynamic control of explore/exploit trade-off in Bayesian optimization. In: Proceedings of Science and Information Conference; 2018 Apr 27‒29. Jeju, Korea: Springer; 2018. p. 1‒15. 链接1

[48] Brochu E, Cora VM, de Freitas N. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. 2010. arXiv:1012.2599.

[49] Hernández-Lobato JM, Requeima J, Pyzer-Knapp EO, Aspuru-Guzik A. Parallel and distributed Thompson sampling for large-scale accelerated exploration of chemical space. In: Proceedings of the 34th International Conference on Machine Learning; 2017 Aug 6‍‒‍11; Sydney. NSW, Australia: PMLR; 2017. p.1470‒9.

[50] Shahriari B, Swersky K, Wang Z, Adams RP, de Freitas N. Taking the human out of the loop: a review of Bayesian optimization. Proc IEEE 2016;104(1):148‒75. 链接1

[51] Kumar A. A simulation study of carbon sequestration in deep saline aquifers [dissertation]. Austin: University of Texas at Austin; 2004. 链接1

[52] Fortin FA, de Rainville FM, Gardner MA, Parizeau M, Gagné C. DEAP:evolutionary algorithms made easy. J Mach Learn Res 2012;13:2171‒5. 链接1

相关研究