### “Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem”

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

**Affiliation:**Telemark University College and Statoil

**Reference:**2012, Vol 33, No 1, pp. 13-25.

**Keywords:**Optimization, non-linear programming, cascade control structure, gas lifted oil well, hill climbing, self-optimization

**Abstract:**Proper allocation and distribution of lift gas is necessary for maximizing total oil production from a field with gas lifted oil wells. When the supply of the lift gas is limited, the total available gas should be optimally distributed among the oil wells of the field such that the total production of oil from the field is maximized. This paper describes a non-linear optimization problem with constraints associated with the optimal distribution of the lift gas. A non-linear objective function is developed using a simple dynamic model of the oil field where the decision variables represent the lift gas flow rate set points of each oil well of the field. The lift gas optimization problem is solved using the

*fmincon*solver found in MATLAB. As an alternative and for verification, hill climbing method is utilized for solving the optimization problem. Using both of these methods, it has been shown that after optimization, the total oil production is increased by about 4%. For multiple oil wells sharing lift gas from a common source, a cascade control strategy along with a nonlinear steady state optimizer behaves as a self-optimizing control structure when the total supply of lift gas is assumed to be the only input disturbance present in the process. Simulation results show that repeated optimization performed after the first time optimization under the presence of the input disturbance has no effect in the total oil production.

PDF (476 Kb) DOI: 10.4173/mic.2012.1.2

**DOI forward links to this article:**

[1] Chukwuka G. Monyei, Aderemi O. Adewumi and Michael O. Obolo (2014), doi:10.1155/2014/289239 |

[2] Bartlomiej Bielecki and Andrzej Krajka (2015), doi:10.1155/2015/183982 |

[3] C.H.P. Ribeiro, S.C. Miyoshi, A.R. Secchi and A. Bhaya (2015), doi:10.1016/j.petrol.2015.11.004 |

**References:**

[1] American Petroleum Institute (1994). API gas lift manual, Book 6 of the Vocational Training series, Exploration and Production Department, Washington DC 2005-4070, USA, third edition edition.

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

[3] Brown, K.E. Beggs, H.D. (1977). 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.

[4] Camponogara, E. Nakashima, P. (2006). Solving a gas-lift optimization problem by dynamic programming, European Journal of Operational Research, 174:1220--1246 doi:10.1016/j.ejor.2005.03.004

[5] Edgar, T.E., Himmelblau, D.M., Lasdon, L.S. (2001). Optimization of chemical processes, McGraw-Hill Chemical Engineering Series, second edition edition.

[6] Juels, A. Wattenberg, M. (1994). Stochastic hill climbing as a baseline method for evaluating genetic algorithms, Dept. of Computer Science and Dept. of Mathematics, University of California at Berkeley.

[7] Kosmidis, V.D., Perkins, J., Pistikopoulos, E.N. (2005). A mixed integer optimization formulation for the well scheduling problem on petroleum fields, Journal of Computers and Chemical Engineering, 29:1523--1541 doi:10.1016/j.compchemeng.2004.12.003

[8] MathWorks Inc (2011). R2011a documentation - optimization toolbox [online], Available at: http://www.mathworks.com/help/toolbox/opti, /ug/fmincon.html.Accessed: 20 May 2011.

[9] PVTsim (2008). PVT simulation program developed for reservoir engineers, flow assurance specialists, PVT lab engineers and process engineers [online], Available at: http://www.pvtsim.com.Accessed, 20 January 2011.

[10] Rashid, K. (2010). Optimal allocation procedure for gas-lifted optimization, Industrial and Engineering Chemistry Research, 49:2286--2294 doi:10.1021/ie900867r

[11] Ray, T. Sarker, R. (2007). Genetic algorithm for solving a gas lift optimization problem, Journal of Petroleum Science and Engineering, 59:84--96 doi:10.1016/j.petrol.2007.03.004

[12] Saepudin, D., Soewono, E., Sidarto, K., Gunawan, A., Siregar, S., Sukarno, P. (2007). An investigation on gas lift performance curve in an oil producing well, International Journal of Mathematics and Mathematical Science, 2007:1--15 doi:10.1155/2007/81519

[13] Sharma, R., Fjalestad, K., Glemmestad, B. (2011). Modeling and control of gas lifted oil field with five oil well, In 52nd International Conference of Scandinavian Simulation Society, SIMS 2011, Sep 29-30. Västerås, Sweden, pp. 47--59.

[14] Souza, J. N.M., Medeiros, J.L., Costa, A. L.H., Nunes, G.C. (2010). Modeling, simulation and optmization of continuous gas lift systems for deepwater offshore petroleum production, Journal of Petroleum Science and Engineering, 72:277--289 doi:10.1016/j.petrol.2010.03.028

[15] Sukarno, P., Saepudin, S., Soewono, E., Sidarto, K., Gunawan, A. (2009). Optimization of gas injection allocation in a dual gas lift well system, Journal of Energy Resources Technology, 13.3 doi:10.1115/1.3185345

[16] Zhong, H., Li, Y., Liu, Y. (2004). An approach for optimization of gas-lift allocation to a group of wells and oil field, In 3rd International Symposium of National Key Laboratory for Oil and Gas Reservoir Exploitation. Chengu, China, pp. 1--11.

**BibTeX:**

@article{MIC-2012-1-2,

title={{Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem}},

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

journal={Modeling, Identification and Control},

volume={33},

number={1},

pages={13--25},

year={2012},

doi={10.4173/mic.2012.1.2},

publisher={Norwegian Society of Automatic Control}

};