Abstract
Intelligent wells (I-wells) provide layer-by-layer production and injection control. This flow control flexibility relies on the real-time operation of multiple, downhole interval control valves (ICVs) installed across the well completion intervals. Proactive control of I-wells, with its ambition of creating an optimal, operational strategy of ICVs over the full well lifetime, is a high-dimensional optimization problem with a computationally demanding and uncertain objective function based on one or more simulated reservoir model(s). This paper illustrates how a stochastic search algorithm based on the simultaneous perturbation stochastic approximation (SPSA) coupled with a utility function approach to define an objective function to account for the uncertainty in the reservoir’s description can efficiently solve the proactive, I-well control problem. The utility function accounts for both the expectation and variance of the net present value (NPV) by modifying the objective function to consider multiple reservoir model realizations. Simultaneous optimization of full ensemble of model realizations is prohibitively expensive. By contrast, choosing a small ensemble of model realizations is computationally less demanding, but the small ensemble has to be itself selected. We introduce the use of k-means clustering for selecting a representative ensemble of model realizations that performs in an equivalent manner to all available realizations. A distance measure, tailored to the proactive optimization application, is used to define the similarity/dissimilarity of the different realizations which is then employed to perform the clustering. Moreover, we show that this robust proactive optimization process can either focus on the specific objective of increasing the mean or of reducing the variance (this is achieved via adjustable weights in the utility function). The relative importance of these conflicting objectives has to be taken into account during the model realization selection process to ensure the near-global success of the obtained control scenario. The proposed robust optimization framework has been tested on a representative test case (PUNQ-S3). This is a small field developed with an intelligent producer in which the uncertainty in the model has been quantified by several geological realizations. Our results demonstrate the computational efficiency of employing an ensemble of systematically selected realizations rather than the traditional methods that rely on either a single model realization or a randomly selected ensemble of realizations. Our results show the success of the developed framework in identifying control scenarios that correspond to an acceptable improvement in the expected added value at a controlled risk level while substantially reducing the computation time compared to using full ensemble of model realizations.
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References
Robinson, M.: Intelligent well completions (2003)
Peters, L., Arts, R., Brouwer, G., Geel, C.: Results of the Brugge benchmark study for flooding optimisation and history Matching (2010)
Grebenkin, I.M., Davies, D.R.: A novel optimisation algorithm for inflow control valve management. In: SPE Europec/EAGE annual conference, SPE-154472-MS (2012)
Alghareeb, Z., Horne, R.N., Yuen, B.B.W., Shenawi, S.H.: Proactive optimization of oil recovery in multilateral wells using real time production data. In: SPE annual technical conference and exhibition, SPE-124999-MS (2009)
Almeida, L.F., Vellasco, M.M.B.R., Pacheco, M.A.C.: Optimization system for valve control in intelligent wells under uncertainties. J. Pet. Sci. Eng. 73(1–2), 129–140 (2010). doi:10.1016/j.petrol.2010.05.013
Haghighat Sefat, M., Muradov, K.M., Davies, D.R.: Field management by proactive optimisation of intelligent wells—a practical approach. In: SPE Middle East intelligent energy conference and exhibition, SPE-167453-MS (2013)
Guyaguler, B., Byer, T.J.: A new rate-allocation-optimization framework. SPE d. Oper. 23(04), 448–457 (2008). doi:10.2118/105200-PA
Wang, C., Li, G., Reynolds, A.C.: Production optimization in closed-loop reservoir management. SPE J. 14(3), 506–523 (2009). doi:10.2118/109805-pa
Jansen, J.-D., Brouwer, R., Douma, S.G.: Closed loop reservoir management. In: SPE reservoir simulation symposium, SPE-119098-MS (2009)
Brouwer, D.R., Jansen, J.-D.: Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE J. 9(4), 391–402 (2004). doi:10.2118/78278-pa
Sarma, P., Chen, W.H., Durlofsky, L.J., Aziz, K.: Production optimization with adjoint models under nonlinear control-state path inequality constraints. In: Intelligent energy conference and exhibition, SPE-99959-MS (2006)
Suwartadi, E., Krogstad, S., Foss, B.A.: On state constraints of adjoint optimization in oil reservoir waterflooding. In: SPE/EAGE reservoir characterization and simulation conference, SPE-125557-MS (2009)
Giles, M., Pierce, N.: An introduction to the adjoint approach to design. Flow, Turbulence and Combustion 65(3–4), 393–415 (2000). doi:10.1023/a:1011430410075
Essen, G.v., Hof, P.V.d., Jansen, J.-D.: Hierarchical long-term and short-term production optimization. SPE J. 16(1), 191–199 (2011). doi:10.2118/124332-pa
Asadollahi, M., Naevdal, G.: Waterflooding optimization using gradient based methods. In: SPE/EAGE reservoir characterization and simulation conference, SPE-125331-MS (2009)
ECLIPSE: ECLIPSE reference manuals. In: Technical description, Chapter 49, vol. Version 2012. 1. Schlumberger, Abingdon (2012)
Forouzanfar, F., Li, G., Reynolds, A.C.: A two-stage well placement optimization method based on adjoint gradient. In: SPE annual technical conference and exhibition, SPE-135304-MS (2010)
Mohaghegh, S.: Virtual-intelligence applications in petroleum engineering: part 2—evolutionary computing. J. Pet. Technol. 52(10), 40–46 (2000). doi:10.2118/61925-ms
Zingg, D.W., Nemec, M., Pulliam, T.H.: A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique 17(1–2), 103–126 (2008). doi:10.3166/remn.17.103-126
Pinto, M.A.S., Barreto, C.E., Schiozer, D.J.: Optimization of proactive control valves of producer and injector smart wells under economic uncertainty. In: SPE Europec/EAGE annual conference, SPE-154511-MS (2012)
Asadollahi, M., Nævdal, G., Dadashpour, M., Kleppe, J.: Production optimization using derivative free methods applied to Brugge field case. J. Petrol. Sci. Eng. 114(0), 22–37 (2014). doi:10.1016/j.petrol.2013.12.004
van Essen, G., Zandvliet, M., Van den Hof, P., Bosgra, O., Jansen, J.-D.: Robust waterflooding optimization of multiple geological scenarios. doi:10.2118/102913-PA (2009)
Chen, Y., Oliver, D.S., Zhang, D.: Efficient ensemble-based closed-loop production optimization. SPE J. 14(4), 634–645 (2009). doi:10.2118/112873-PA
Lorentzen, R.J., Berg, A., Naevdal, G., Vefring, E.H.: A new approach for dynamic optimization of water flooding problems (2006)
Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 37(3), 332–341 (1992). doi:10.1109/9.119632
Do, S., Reynolds, A.: Theoretical connections between optimization algorithms based on an approximate gradient. Comput. Geosci. 17(6), 959–973 (2013). doi:10.1007/s10596-013-9368-9
Haghighat Sefat, M., Muradov, K.M., Elsheikh, A.H., Davies, D.R.: Proactive optimization of intelligent well production using stochastic gradient-based algorithms. Submitted (2015)
Spall, J., Hill, S., Stark, D. Theoretical framework for comparing several stochastic optimization approaches. In: Calafiore, G., Dabbene, F. (eds.) : Probabilistic and randomized methods for design under uncertainty, pp. 99–117. Springer, London (2006)
Zhao, H., Chen, C., Do, S., Oliveira, D., Li, G., Reynolds, A.: Maximization of a dynamic quadratic interpolation model for production optimization. doi:10.2118/141317-PA (2013)
Zhao, H., Li, Y., Yao, J., Zhang, K.: Theoretical research on reservoir closed-loop production management. Sci. China Technol. Sci. 54(10), 2815–2824 (2011). doi:10.1007/s11431-011-4465-2
Chen, Y., Oliver, D.S.: Ensemble-based closed-loop optimization applied to Brugge field (2009)
Chen, C., Li, G., Reynolds, A.C.: Robust constrained optimization of short and long-term NPV for closed-loop reservoir management (2011)
Haghighat Sefat, M., Muradov, K.M., Elsheikh, A.H., Davies, D.R.: Reservoir uncertainty-tolerant, proactive control of intelligent wells. In: ECMOR XIV—14th European conference on the mathematics of oil recovery (2014)
Park, K.: Modeling uncertainty in metric space. PhD Thesis, Stanford University (2011)
Scheidt, C., Caers, J.: Uncertainty quantification in reservoir performance using distances and kernel methods—application to a West Africa deepwater turbidite reservoir. doi:10.2118/118740-PA (2009)
Wang, H., Echeverría-Ciaurri, D., Durlofsky, L., Cominelli, A.: Optimal well placement under uncertainty using a retrospective optimization framework. SPE J. 17(1), 112–121 (2012). doi:10.2118/141950-PA
Speyer, J.L., Jacobson, D.H.: Primer on optimal control theory. Soc. Ind. Appl. Math. (2010)
Mulvey, J.M., Vanderbei, R.J., Zenios, S.A.: Robust optimization of large-scale systems. Oper. Res. 43(2), 264–281 (1995)
Chen, W., Wiecek, M.M., Zhang, J.: Quality utility—a compromise programming approach to robust design. J. Mech. Des. 121(2), 179–187 (1999). doi:10.1115/1.2829440
Zang, C., Friswell, M.I., Mottershead, J.E.: A review of robust optimal design and its application in dynamics. Comput. Struct. 83(4–5), 315–326 (2005). doi:10.1016/j.compstruc.2004.10.007
Petvipusit, K., Elsheikh, A., Laforce, T., King, P., Blunt, M.: Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates. Comput. Geosci. 18(5), 763–778 (2014). doi:10.1007/s10596-014-9425-z
Sadegh, P., Spall, J.C.: Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 43(10), 1480–1484 (1998). doi:10.1109/9.720513
Kiefer, J., Wolfowitz, J.: Stochastic estimation of the maximum of a regression function. Ann. Math. Stat. 23(3), 462–466 (1952). doi:10.2307/2236690
Spall, J.C.: Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Trans. Aerosp. Navig. Electron. 34(3), 817–823 (1998). doi:10.1109/7.705889
Spall, J.C.: Introduction to stochastic search and optimization: estimation, simulation, and control. Wiley (2003)
Gao, G., Li, G., Reynolds, A.C.: A stochastic optimization algorithm for automatic history matching. SPE J. 12(2), 196–208 (2007). doi:10.2118/90065-pa
Tavakoli, R., Srinivasan, S., Wheeler, M.F.: Rapid updating of stochastic models by use of an ensemble-filter approach. SPE J. 19(3), 500–513 (2014). doi:10.2118/163673-PA
Demyanov, V., Gopa, K., Arnold, D., Elfeel, M.A.: Production optimisation under uncertainty in fractured reservoirs. In: ECMOR XIV—14th European conference on the mathematics of oil recovery (2014)
Borg, I., Groenen, P.J.: Modern multidimensional scaling: theory and applications. Springer (2005)
Seber, G.A.F.: Multivariate observations. Wiley (2004)
Floris, F.J.T., Bush, M.D., Cuypers, M., Roggero, F., Syversveen, A.-R.: Methods for quantifying the uncertainty of production forecasts: a comparative study. Pet. Geosci. 7(S), S87–S96 (2001). doi:10.1144/petgeo.7.S.S87
Grebenkin, I., Davies, D.R.: Analysis of the impact of an intelligent well completion on the oil production uncertainty. In: SPE Russian oil and gas conference and exhibition, SPE-136335-MS (2010)
Ben-Hur, A., Elisseeff, A., Guyon, I.: A stability based method for discovering structure in clustered data. In: Pacific symposium on biocomputing 2001, pp. 6–17
Thorndike, R.: Who belongs in the family? Psychometrika 18(4), 267–276 (1953). doi:10.1007/BF02289263
Bowman, A.W., Azzalini, A.: Applied smoothing techniques for data analysis : the kernel approach with S-Plus illustrations: The kernel approach with S-Plus illustrations. OUP Oxford (1997)
Olken, F.: Random sampling from databases. University of California at Berkeley (1993)
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Haghighat Sefat, M., Elsheikh, A.H., Muradov, K.M. et al. Reservoir uncertainty tolerant, proactive control of intelligent wells. Comput Geosci 20, 655–676 (2016). https://doi.org/10.1007/s10596-015-9513-8
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DOI: https://doi.org/10.1007/s10596-015-9513-8