Search Advanced

Electronic Research Archive

2024, Volume 32, Issue 2: 915-927. doi: 10.3934/era.2024044
Previous Article Next Article
Research article Special Issues

Nonlinear modeling and interior point algorithm for the material flow optimization in petroleum refinery

  • 1.
    Petrochina Planning and Engineering Institute, Beijing 100086, China
  • 2.
    CNPC Laboratory of Oil & Gas Business Chain Optimization, Beijing 100086, China
  • 3.
    Cardinal Operations, Beijing 100102, China
  • 4.
    Shanghai University of Finance and Economics, Shanghai 200082, China
  • Received: 09 November 2023 Revised: 11 December 2023 Accepted: 14 December 2023 Published: 16 January 2024

  • This paper established a mathematical model with nonconvex bilinear terms. It formulated the complex material flow in the petroleum refinery scenario based on the concept of the "P model". The mathematical model described the nonlinear constraints such as linear and nonlinear mass and volume intersection flow blending of crude and middle material physical properties. Additionally, it described the complex inflow and outflow in secondary devices as nonlinear constraints such as delta-base structure and physical property transfer. It is highly difficult to determine the direction and quantity of each material in the network of refineries. An improved interior point algorithm with an initial point strategy was proposed to find a high-quality feasible solution in a short time. The real instances from the petroleum refinery were employed to compare and analyze the solutions from the improved algorithm and commercial solver. The experimental results show that the proposed algorithm framework can balance the solution quality and computational efficiency and perform well in different scenarios of refinery material flow networks.

    Citation: Fenglian Dong, Dongdong Ge, Lei Yang, Zhiwei Wei, Sichen Guo, Hekai Xu. Nonlinear modeling and interior point algorithm for the material flow optimization in petroleum refinery[J]. Electronic Research Archive, 2024, 32(2): 915-927. doi: 10.3934/era.2024044

    Related Papers:

  • This paper established a mathematical model with nonconvex bilinear terms. It formulated the complex material flow in the petroleum refinery scenario based on the concept of the "P model". The mathematical model described the nonlinear constraints such as linear and nonlinear mass and volume intersection flow blending of crude and middle material physical properties. Additionally, it described the complex inflow and outflow in secondary devices as nonlinear constraints such as delta-base structure and physical property transfer. It is highly difficult to determine the direction and quantity of each material in the network of refineries. An improved interior point algorithm with an initial point strategy was proposed to find a high-quality feasible solution in a short time. The real instances from the petroleum refinery were employed to compare and analyze the solutions from the improved algorithm and commercial solver. The experimental results show that the proposed algorithm framework can balance the solution quality and computational efficiency and perform well in different scenarios of refinery material flow networks.


    加载中


    [1] M. Ali, Pooling problem: Modeling, global optimization and computational studies survey, J. Comput. Appl. Math., (2021), 478.
    [2] C. A. Haverly, Studies of the behavior of recursion for the pooling problem, Acm Sigmap Bull., 25 (1978), 19–28. https://doi.org/10.1145/1111237.1111238 doi: 10.1145/1111237.1111238
    [3] A. Ben-tal, G. Eiger, V. Gershovitz, Global minimization by reducing the duality gap, Math. Program., 63 (1994), 193–212. https://doi.org/10.1007/BF01582066 doi: 10.1007/BF01582066
    [4] I. Quesada, I. E. Grossmann, Global optimization of bilinear process networks with multicomponent flows, Comput. Chem. Eng., 19 (1995), 1219–1242. https://doi.org/10.1016/0098-1354(94)00123-5 doi: 10.1016/0098-1354(94)00123-5
    [5] M. Tawarmalani, N. V. Sahindis, Convexification and global optimization in continuous and mixed-integer nonlinear programming, 2022, Boston, MA: Springer US. https://doi.org/10.1007/978-1-4757-3532-1
    [6] T. Kuno, T. Utsunomiya, A Lagrangian based branch-and-bound algorithm for production-transportation problems, J. Global Optim., 18 (2000), 59–73. https://doi.org/10.1023/A:1008373329033 doi: 10.1023/A:1008373329033
    [7] J. M. Zamora, I. E. Grossmann, A branch and contract algorithm for problems with concave univariate, bilinear and linear fractional terms, J. Global Optim., 14 (1999), 217–249. https://doi.org/10.1023/A:1008312714792 doi: 10.1023/A:1008312714792
    [8] J. P. Ruiz, I. E. Grossmann, Strengthening of lower bounds in the global optimization of Bilinear and Concave Generalized Disjunctive Programs, Comput. Chem. Eng., 34 (2010), 914–930. https://doi.org/10.1016/j.compchemeng.2009.10.016 doi: 10.1016/j.compchemeng.2009.10.016
    [9] C. A. Meyer, C. A. Floudas, Global optimization of a combinatorially complex generalized pooling problem, AIChE J., 52 (2006), 1027–1037. https://doi.org/10.1002/aic.10717 doi: 10.1002/aic.10717
    [10] M. L. Bergamini, P. Aguirre, I. Grossmann, Logic-based outer approximation for globally optimal synthesis of process networks, Comput. Chem. Eng., 29 (2005), 1914–1933. https://doi.org/10.1016/j.compchemeng.2005.04.003 doi: 10.1016/j.compchemeng.2005.04.003
    [11] R. E. Griffith, R. A. Stewart, A nonlinear programming technique for the optimization of continuous processing systems, Manage. Sci., 7 (1961), 379–392. https://doi.org/10.1287/mnsc.7.4.379 doi: 10.1287/mnsc.7.4.379
    [12] F. Palacios-Gomez, L. Lasdon, M. Engquist, Nonlinear optimization by successive linear programming, Manage. Sci., 28 (1982), 1106–1120. https://doi.org/10.1287/mnsc.28.10.1106 doi: 10.1287/mnsc.28.10.1106
    [13] T. E. Baker, L. S. Lasdon, Successive linear programming at Exxon, Manage. Sci., 31 (1985), 264–274. https://doi.org/10.1287/mnsc.31.3.264 doi: 10.1287/mnsc.31.3.264
    [14] L. S. Lasdon, A. D. Waren, S. Sarkar, Solving the pooling problem using generalized reduced gradient and successive linear programming algorithms, ACM Sigmap Bull., 27 (1979), 9–15. https://doi.org/10.1145/1111246.1111247 doi: 10.1145/1111246.1111247
    [15] Y. H. Dai, R. Diao, K. Fu, Complexity analysis and algorithm design of pooling problem, J. Oper. Res. Soc. China, 6 (2018), 249–266. https://doi.org/10.1007/s40305-018-0193-7 doi: 10.1007/s40305-018-0193-7
    [16] V. Pham, C. Laird, M. El-Halwagi, Convex hull discretization approach to the global optimization of pooling problems, Ind. Eng. Chem. Res., 48 (2009), 1973. https://doi.org/10.1021/ie8003573 doi: 10.1021/ie8003573
    [17] A. Gupte, S. Ahmed, S. S. Dey, Relaxations and discretizations for the pooling problem, J. Global Optim., 67 (2017), 631–669. https://doi.org/10.1007/s10898-016-0434-4 doi: 10.1007/s10898-016-0434-4
    [18] M. Alfaki, D. Haugland, Comparison of discrete and continuous models for the pooling problem. in 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, 2011. https://doi.org/10.4230/OASIcs.ATMOS.2011.112
    [19] C. A. Floudas, A. Aggarwal, A decomposition strategy for global optimum search in the pooling problem, ORSA J. Comput., 2 (1990), 225–235. https://doi.org/10.1287/ijoc.2.3.225 doi: 10.1287/ijoc.2.3.225
    [20] How Distributed Recursion Solves the Pooling Problem, 2022. Available from: https://www.haverly.com/kathy-blog/578-blog-4-howdrsolvespooling.
    [21] Y. R. He, H. Zhang, Solution of pooling problem in planning model with distributed recursive method, Pet. Process. Petrochem., 27 (1996), 4.
    [22] Y. R. He, J. Z. Xie, Application cases of refinery's production and operation plan optimization, Beijing: China Petrochemical Press, 2018.
    [23] A. Wachter, L. T. Biegler, Failure of global convergence for a class of interior point methods for nonlinear programming, Math. Program., 88 (2000), 565–574. https://doi.org/10.1007/PL00011386 doi: 10.1007/PL00011386
    [24] A. Wachter, L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), 25–57. https://doi.org/10.1007/s10107-004-0559-y doi: 10.1007/s10107-004-0559-y
    [25] J. B. Guo, M. S. Yang, Chemical industry's production planning and scheduling optimization, Beijing: Chemical Industry Press, 2006.
    [26] J. B. Guo, Linear programming technique in petroleum sector: a review, Comput. Appl. Chem., 21 (2004), 1–5.
    [27] R. H. Byrd, M. E. Hribar, J. Nocedal, An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 9 (1999), 877–900. https://doi.org/10.1137/S1052623497325107 doi: 10.1137/S1052623497325107
    [28] O, Güler, Barrier functions in interior point methods, Math. Oper. Res., 21 (1996), 860–885. https://doi.org/10.1287/moor.21.4.860 doi: 10.1287/moor.21.4.860
    [29] G. D. Pillo, L. Grippo, Exact penalty functions in constrained optimization, SIAM J. Control Optim., 27 (1989), 1333–1360. https://doi.org/10.1137/0327068 doi: 10.1137/0327068
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Electronic Research Archive
1 1.3

Metrics

Article views(826) PDF downloads(61) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(3)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog