A computational analysis of multidimensional piecewise-linear models with applications to oil production optimization

European Journal of Operational Research

Volumn 232, Issue 3, 2014, Pages 630-642

  Silva, Thiago Lima ^a   Camponogara, Eduardo ^a  

^a FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

Integer programming; Multidimensional functions; Oil production; OR in energy; Piecewise linearization; Pressure constraints

Indexed keywords

MULTIDIMENSIONAL FUNCTION; OIL PRODUCTION; OR IN ENERGY; PIECEWISE LINEARIZATION; PRESSURE CONSTRAINTS;

FUNCTIONS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; OIL FIELDS; OIL WELLS;

PIECEWISE LINEAR TECHNIQUES;

EID: 84884593886     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2013.07.040     Document Type: Article

References (30)

1. G.A. Alarcón, C.F. Torres, and L.E. Gómez Global optimization of gas allocation to a group of wells in artificial lift using nonlinear constrained programming Journal of Energy Resources Technology 124 4 2002 262 268
2. A. Balakrishnan, and S.C. Graves A composite algorithm for a concave-cost network flow problem Networks 19 2 1989 175 202
3. E.M.L. Beale Branch and bound methods for numerical optimization of non-convex functions Computational Statistics 80 1980 11 20
4. Beale, E. M. L., & Tomlin, J. A. (1970). Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In Proceedings of the fifth international conference on operations research (pp. 447-454).
5. D. Beggs, and J. Brill A study of two-phase flow in inclined pipes Journal of Petroleum Technology 25 5 1973 607 617
6. Buitrago, S., Rodríguez, E., & Espin, D. (1996). Global optimization techniques in gas allocation for continuous flow gas lift systems. In SPE gas technology symposium. Calgary, Canada.
7. E. Camponogara, and A. de Conto Lift-gas allocation under precedence constraints: MILP formulation and computational analysis IEEE Transactions on Automation Science and Engineering 6 3 2009 544 551
8. E. Camponogara, L.F. Nazari, and C.N. Meneses A revised model for compressor design and scheduling in gas-lifted oil fields IIE Transactions 44 5 2012 342 351
9. A. Codas, and E. Camponogara Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing European Journal of Operational Research 212 2012 222 231
10. K.L. Croxton, B. Gendron, and T.L. Magnanti A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems Management Science 49 2003 1268 1273
11. G. Dantzig On the significance of solving linear programming problems with some integer variables Econometrica 28 1 1960 30 44
12. V. Gunnerud, and B. Foss Oil production optimization - A piecewise linear model, solved with two decomposition strategies Computers & Chemical Engineering 34 11 2010 1803 1812
13. T. Ibaraki Integer programming formulation of combinatorial optimization problems Discrete Mathematics 16 1976 39 52
14. R. Jeroslow, and J. Lowe Experimental results on the new techniques for integer programming formulations Journal of the Operational Research Society 36 5 1985 393 403
15. R.G. Jeroslow, and J.K. Lowe Modelling with integer variables Mathematical Programming at Oberwolfach II Vol. 22 1984 Springer Berlin Heidelberg 167 184
16. A.B. Keha, I.R. de Farias Jr., and G.L. Nemhauser Models for representing piecewise linear cost functions Operations Research Letters 32 2004 44 48
17. V. Kosmidis, J. Perkins, and E. Pistikopoulos Optimization of well oil rate allocations in petroleum fields Industrial & Engineering Chemistry Research 43 14 2004 3513 3527
18. V.D. Kosmidis, J.D. Perkins, and E.N. Pistikopoulos A mixed integer optimization formulation for the well scheduling problem on petroleum fields Computers & Chemical Engineering 29 7 2005 1523 1541
19. J. Lee, and D. Wilson Polyhedral methods for piecewise-linear functions I: The lambda method Discrete Applied Mathematics 108 3 2001 269 285
20. Litvak, M., & Darlow, B. (1995). Surface network and well tubinghead pressure constraints in compositional simulation. In Proceedings of the SPE reservoir simulation symposium.
21. R.R. Meyer Mixed integer minimization models for piecewise-linear functions of a single variable Discrete Mathematics 16 2 1976 163 171
22. R. Misener, C.E. Gounaris, and C.A. Floudas Global optimization of gas lifting operations: A comparative study of piecewise linear formulations Industrial & Engineering Chemistry Research 48 13 2009 6098 6104
23. M. Padberg Approximating separable nonlinear functions via mixed zero-one programs Operations Research Letters 27 1 2000 1 5
24. H.D. Sherali On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions Operations Research Letters 28 4 2001 155 160
25. Silva, T. L., Codas, A., & Camponogara, E. (2011). Test instance of the lift-gas allocation problem with pressure constraints and well-separator routing in AMPL format. < http://www.das.ufsc.br/∼camponog/IFAC-2012/ >.
26. Silva, T. L., Codas, A., & Camponogara, E. (2012). A computational analysis of convex combination models for multidimensional piecewise-linear approximation in oil production optimization. In Proceedings of the IFAC workshop on automatic control in offshore oil and gas production.
27. M. Todd Union jack triangulations S. Karamardian, Fixed points: Algorithms and applications 1977 Academic Press 315 336
28. J. Vielma, and G. Nemhauser Modeling disjunctive constraints with a logarithmic number of binary variables and constraints Mathematical Programming 128 2011 49 72
29. J.P. Vielma, S. Ahmed, and G. Nemhauser Mixed-integer models for nonseparable piecewise-linear optimization: Unifying framework and extensions Operations Research 58 2 2010 303 315
30. J.P. Vielma, A.B. Keha, and G.L. Nemhauser Nonconvex, lower semicontinuous piecewise linear optimization Discrete Optimization 5 2 2008 467 488