Abstract
In the development of naturally fractured reservoirs (NFRs), the existence of natural fractures induces severe fingering and breakthrough. To manage the flooding process and improve the ultimate recovery, we propose a numerical workflow to generate optimal production schedules for smart wells, in which the inflow control valve (ICV) settings can be controlled individually. To properly consider the uncertainty introduced by randomly distributed natural fractures, the robust optimization would require a large ensemble size and it would be computationally demanding. In this work, a hierarchical clustering method is proposed to select representative models for the robust optimization in order to avoid redundant simulation runs and improve the efficiency of the robust optimization. By reducing the full ensemble of models into a small subset ensemble, the efficiency of the robust optimization algorithm is significantly improved. The robust optimization is performed using the StoSAG scheme to find the optimal well controls that maximize the net-present-value (NPV) of the NFR’s development. Due to the discrete property of a natural fracture field, traditional feature extraction methods such as model-parameter-based clustering may not be directly applicable. Therefore, two different kinds of clustering-based optimization methods, a state-based (e.g., s w profiles) clustering and a response-based (e.g., production rates) clustering, are proposed and compared. The computational results show that the robust clustering optimization could increase the computational efficiency significantly without sacrificing much expected NPV of the robust optimization. Moreover, the performance of different clustering algorithms varies widely in correspondence to different selections of clustering features. By properly extracting model features, the clustered subset could adequately represent the uncertainty of the full ensemble.
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Aggarwal, C.C., Wolf, J.L., Yu, P.S., Procopiuc, C., Park, J.S.: Fast algorithms for projected clustering. In: Proceedings of ACM SIGMoD Record, vol. 28, pp. 61–72. ACM (1999)
Arabie, P., Hubert, L.J.: An overview of combinatorial data. Cluster. Classif. 5 (1996)
Arabie, P., Hubert, L.J., De Soete, G.: Clustering and classification. World Scientific (1996)
Armstrong, M., Ndiaye, A., Razanatsimba, R., Galli, A.: Scenario reduction applied to geostatistical simulations. Math. Geosci. 45(2), 165–182 (2013)
Barros, E., Yap, F., Insuasty, E., van den Hof, P., Jansen, J.: Clustering techniques for value-of-information assessment in closed-loop reservoir management. In: Proceedings of ECMOR XV-15th European Conference on the Mathematics of Oil Recovery (2016)
Brouwer, D., Jansen, J., et al.: Dynamic optimization of water flooding with smart wells using optimal control theory (2004)
Chen, B., Reynolds, A.C.: Optimal control of ICV’s and well operating conditions for the water-alternating-gas injection process. J. Pet. Sci. Eng. 149, 623–640 (2017)
Chen, C.: Adjoint-gradient-based production optimization with the augmented Lagrangian method (2011)
Chen, Y., Oliver, D.S., Zhang, D., et al.: Efficient ensemble-based closed-loop production optimization. SPE J. 14(04), 634–645 (2009)
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.-I.: Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation. Wiley (2009)
Datta-Gupta, A., Alhuthali, A.H., Yuen, B., Fontanilla, J., et al.: Field applications of waterflood optimization via optimal rate control with smart wells. SPE Reserv. Eval. Eng. 13(03), 406–422 (2010)
Do, S.T., Reynolds, A.C.: Theoretical connections between optimization algorithms based on an approximate gradient. Comput. Geosci. 17(6), 959–973 (2013)
Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011)
Fonseca, R., Kahrobaei, S., Van Gastel, L., Leeuwenburgh, O., Jansen, J., et al.: Quantification of the impact of ensemble size on the quality of an ensemble gradient using principles of hypothesis testing. In: Proceedings of SPE Reservoir Simulation Symposium, Society of Petroleum Engineers (2015)
Fonseca, R., Leeuwenburgh, O., Della Rossa, E., Van den Hof, P., Jansen, J.-D., et al.: Ensemble-based multiobjective optimization of on/off control devices under geological uncertainty. SPE Reserv. Eval. Eng. (2015)
Fonseca, R.R.-M., Chen, B., Jansen, J.D., Reynolds, A.: A stochastic simplex approximate gradient (StoSAG) for optimization under uncertainty. Int. J. Numer Methods Eng. (2016)
Forouzanfar, F., Della Rossa, E., Russo, R., Reynolds, A.: Life-cycle production optimization of an oil field with an adjoint-based gradient approach. J. Pet. Sci. Eng. 112, 351–358 (2013)
Heitsch, H., Römisch, W.: Scenario reduction algorithms in stochastic programming. Comput. Optim. Appl. 24(2-3), 187–206 (2003)
Li, Z., Zhu, D., et al.: Optimization of production performance with ICVS by using temperature-data feedback in horizontal wells. SPE Prod. Oper. 26(03), 253–261 (2011)
Lorentzen, R.J., Berg, A., Nævdal, G., Vefring, E.H., et al.: A new approach for dynamic optimization of water flooding problems. In: Proceedings of Intelligent Energy Conference and Exhibition, Society of Petroleum Engineers (2006)
Moinfar, A., Varavei, A., Sepehrnoori, K., Johns, R.T., et al.: Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs. In: Proceedings of SPE Reservoir Simulation Symposium, Society of Petroleum Engineers (2013)
Naus, M., Dolle, N., Jansen, J.-D., et al.: Optimization of commingled production using infinitely variable inflow control valves. SPE Prod. Oper. 21(02), 293–301 (2006)
Nocedal, J., Wright, S.: Numerical Optimization. Springer Science & Business Media (2006)
Sahinidis, N.V.: Optimization under uncertainty: State-of-the-art and opportunities. Comput. Chem. Eng. 28(6), 971–983 (2004)
Sarma, P., Chen, W.H., Xie, J., et al.: Selecting representative models from a large set of models. In: Proceedings of SPE Reservoir Simulation Symposium, Society of Petroleum Engineers (2013)
Scheidt, C., Caers, J.: Uncertainty quantification using distances and kernel methods–application to a deepwater turbidite reservoir, Tech. rep., Technical report. Stanford University, Energy resources Engineering Dep (2008)
van Essen, G., Jansen, J.-D., Brouwer, R., Douma, S.G., Zandvliet, M., Rollett, K.I., Harris, D., et al.: Optimization of smart wells in the St. Joseph field. SPE Reserv. Eval. Eng. 13(04), 588–595 (2010)
Xu, Y., Filho, J.S.A.C., Yu, W., Sepehrnoori, K.: Discrete-fracture modeling of complex hydraulic-fracture geometries in reservoir simulators. SPE Reserv. Eval. Eng. 20(02), 403–422 (2017)
Zhe, L., Younis, R., Jiang, J.: A diagnostic framework for bashed wells in unconventional reservoirs: A numerical simulation and model selection theory approach. In: Proceedings of unconventional resources technology conference. San Antonio, pp. 1139–1155. SEG, AAPG, SPE (2016)
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Liu, Z., Forouzanfar, F. Ensemble clustering for efficient robust optimization of naturally fractured reservoirs. Comput Geosci 22, 283–296 (2018). https://doi.org/10.1007/s10596-017-9689-1
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DOI: https://doi.org/10.1007/s10596-017-9689-1