### “Optimal control strategies with nonlinear optimization for an Electric Submersible Pump lifted oil field”

**Authors:**Roshan Sharma and Bjørn Glemmestad,

**Affiliation:**Telemark University College

**Reference:**2013, Vol 34, No 2, pp. 55-67.

**Keywords:**Electric Submersible Pump, nonlinear optimization, optimal control, oil production

**Abstract:**In an Electric Submersible Pump (ESP) lifted oil field, the ESP of each oil well should be operated inside its operating window. The total power consumed by the ESPs in the oil field should be minimized. The speed of the ESPs and the production choke valve opening should be optimally chosen for maximizing the total oil produced from the oil field. At the same time, the capacity of the separator should not be exceeded. In this paper, nonlinear steady state optimization based on Sequential Quadratic Programming (SQP) is developed. Two optimal control structures are proposed in this paper. In the first case, the optimal pump speed is controlled by a PI controller by varying the electrical excitation signal to the motors. The optimal fluid flow rate through each oil well is controlled by another PI controller by varying the production choke valve opening. The paper shows that the production choke valve for each oil well has to be always 100% open to maintain the optimal fluid flow rate. In the second case, the production choke valves are considered to be always 100% open as hard constraints. The optimal fluid flow rate through each oil well is controlled by a PI controller by varying the pump speed. It is shown that when the optimal fluid flow rate is tracked by the controller, the speed of each of the pumps is equal to the optimal pump speed calculated by the optimizer. This basically means that we can achieve the optimization objective with the same optimal results as in the first case by using only a single PI controller. The limitations of these two optimal control structures for very low values and for very high values of the separator capacity are discussed. For the feasible range of separator capacities, the optimal locus of the fluid flow rate and the pump speed are shown in this paper.

PDF (1437 Kb) DOI: 10.4173/mic.2013.2.2

**DOI forward links to this article:**

[1] Roshan Sharma and Bjørn Glemmestad (2014), doi:10.7763/IJMO.2014.V4.386 |

[2] Roshan Sharma and Sharma Glemmestad (2014), doi:10.7763/IJMO.2014.V4.419 |

[3] B. J. T. Binder, D. K. M. Kufoalor, A. Pavlov and T. A. Johansen (2014), doi:10.1109/CCA.2014.6981402 |

[4] Morteza Mohammadzaheri, Reza Tafreshi, Zurwa Khan, Matthew Franchek and Karolos Grigoriadis (2015), doi:10.1016/j.jocs.2015.10.009 |

[5] Dinesh Krishnamoorthy, Elvira M. Bergheim, Alexey Pavlov, Morten Fredriksen and Kjetil Fjalestad (2016), doi:10.1016/j.ifacol.2016.07.399 |

[6] Jorge Andres Prada Mejia, Luis Angel Silva and Julian Andres Pena Florez (2018), doi:10.1109/ICRIEECE44171.2018.9009145 |

[7] David Echeverria Ciaurri, Jhonatan Camacho Navarro and Jorge A. Mejia (2020), doi:10.2118/201257-MS |

[8] E.A. Costa, O.S.L. de Abreu, T.de O. Silva, M.P. Ribeiro and L. Schnitman (2021), doi:10.1016/j.petrol.2021.108880 |

[9] Tiago de Oliveira Silva, Marcio Fontana, Erbet Almeida Costa, Odilon Santana Luiz De Abreu, Marcio Andre Fernandes Martins, Leizer Schnitman and Marcos Pellegrini Ribeiro (2020), doi:10.48072/2525-7579.rog.2020.207 |

[10] Jorge Andres Prada Mejia, Luis Angel Silva and Julian Andres Pena Florez (2018), doi:10.1109/ANDESCON.2018.8564581 |

[11] Bruno A. Santana, Raony M. Fontes and Marcio A.F. Martins (2022), doi:10.1016/j.petrol.2022.110816 |

[12] Raony M. Fontes, Daniel D. Santana and Marcio A.F. Martins (2022), doi:10.1016/j.petrol.2022.110867 |

[13] Anna Sadowska, Leo Steenson, Michael Williams, Andrew Meredith, Jonathan Chong, Jeffery Anderson and Dwayne Kelly (2022), doi:10.2118/209758-MS |

**References:**

[1] ANSI/ISA (1989). S75:01: Flow Equations for Sizing Control Valves, Standards and Recommended Practices for Instrumentation and Control, Vol 2, 10th edition.

[2] Brown, K.E. Beggs, H.D. (197). The technology of artificial lift methods, Volume 1, Inflow Performance, Multiphase flow in pipes, The flowing well, PennWell Publishing Company, Tulsa, Oklahoma, ISBN: 0-87814-031-X.

[3] Pedersen, G. Yang, Z. (2008). Efficiency optimization of a multi-pump booster system, In Proc. of Genetic and Evolutionary Computation Conference. Atlanta, Georgia, USA, pp. 1611--1618.

[4] Pettersson, F. Westerlund, T. (1996). Global optimization of pump configurations using binary separable programming, Journal of Computers and Chemical Engineering, 21(21):521--529 doi:10.1016/S0098-1354(96)00285-2

[5] Serghide, T.K. (1984). Estimate friction factor accurately, Chemical Engineering, 9.5:63--64.

[6] Sharma, R., Fjalestad, K., Glemmestad, B. (2011). Modeling and control of gas lifted oil field with five oil wells, In 52nd International Conference of Scandinavian Simulation Society, SIMS. Västerås, Sweden, pp. 47--59, ISBN: 978-91-977493-7-4.

[7] Sharma, R. Glemmestad, B. (2013). Modeling and simulation of an electric submersible pump lifted oil field, Submitted to International Journal of Oil, Gas and Coal Technology.

[8] Takacs, G. (2009). Electric Submersible Pumps Manual: Design, Operations and Maintenance, Gulf Professional Publishing, Burlington, USA.

[9] Westerlund, T., Pettersson, F., Grossmann, I. (1994). Optimization of pump configurations as a minlp problem, Journal of Computers and Chemical Engineering, 18(9):845--858 doi:10.1016/0098-1354(94)E0006-9

[10] Yang, Z., Soleiman, K., Løhndorf, B. (2012). Energy efficient pump control for an offshore oil processing system, In Proc. of the IFAC Workshop on Automatic Control in Offshore Oil and Gas Production. Norwegian Univesity of Sciences and Technology, Trondheim, Norway, pp. 257--262.

**BibTeX:**

@article{MIC-2013-2-2,

title={{Optimal control strategies with nonlinear optimization for an Electric Submersible Pump lifted oil field}},

author={Sharma, Roshan and Glemmestad, Bjørn},

journal={Modeling, Identification and Control},

volume={34},

number={2},

pages={55--67},

year={2013},

doi={10.4173/mic.2013.2.2},

publisher={Norwegian Society of Automatic Control}

};