Enhanced optimization of single and multi-component mass exchanger networks using parallelization and adaptive relaxation

Abstract

This paper proposes an innovative simultaneous optimization approach for single and multi-component mass exchanger network synthesis (MENS). A retrofitted stage-wise superstructure and a parallelized random walk algorithm with compulsive evolution (RWCE) are adopted. An iterative calculation method is designed to satisfy the requirements of multi-component mass transfer, with a relaxation for the outlet composition of the lean streams. The parametric analysis shows that the relaxation coefficient plays a major role in driving the convergence of the method. To improve the robustness of the established model, an adaptive relaxation coefficient strategy is implemented for multi-component MENS problems. In a divergence situation, the outlet concentration of the lean stream can be adjusted automatically by a random relaxation coefficient. Finally, three industrial MENS examples are considered in this work, whose total annual cost (TAC) are reduced by 7179, 2212, and 551 $·year^–1. The corresponding optimization times are obtained to be 336, 125, and 145 s. The results indicate improvements in the economy and time, demonstrating that the parallelized RWCE can yield an optimal TAC and optimization efficiency compared to previous results. Overall, the adaptive relaxation coefficient strategy enhances the convergence for multi-component MENS problems.

Graphical abstract

Keywords

mass exchanger network (MEN) / stage-wise superstructure / parallelization algorithm / incompatible multi-component / optimization efficiency / adaptive relaxation

References

[1] Xu K, Zhao P Y, Gao Y. The impact of green finance on industrial pollution emissions: empirical evidence from economic and environmental perspectives. Environmental Science and Pollution Research International, 2023, 30(43): 98417–98439

[2] Zhou R H, Yang X M, Han Y. Cleaner production and total factor productivity of polluting enterprises. Journal of Cleaner Production, 2023, 423: 138827

[3] Padley P J. Handbook of energy systems engineering production and utilization. International Journal for Numerical Methods in Engineering, 1986, 23(7): 1391

[4] Short M, Isafiade A J. Thirty years of mass exchanger network synthesis—a systematic review. Journal of Cleaner Production, 2021, 304: 127112

[5] El-Halwagi M M, Manousiouthakis V. Synthesis of mass exchange networks. AIChE Journal. American Institute of Chemical Engineers, 1989, 35(8): 1233–1244

[6] Hallale N, Fraser D M. Capital and total cost targets for mass exchange networks. Part 1: simple capital cost models. Computers & Chemical Engineering, 2000, 23(11–12): 1661–1679

[7] Hallale N, Fraser D M. Supertargeting for mass exchange networks. Part II: applications. Chemical Engineering Research & Design, 2000, 78(2): 208–216

[8] Farrag N M, Kamel D A, Ghallab A O, Gadalla M A, Fouad M K. A novel graphical approach for mass exchange networks using composition driving force. Chemical Engineering Transactions, 2018, 70: 259–264

[9] Oladosu W A, Wan Alwi S R, Manan Z A. A new algebraic tool for simultaneous targeting and design of a mass exchange network with stream splitting for sustainable environment. Journal of Cleaner Production, 2020, 249: 119361

[10] Gupta A, Manousiouthakis V. Waste reduction through multicomponent mass exchange network synthesis. Computers & Chemical Engineering, 1994, 18(Suppl): S585–S590

[11] Zhou R J, Li L J, Dong H G. Optimal design of batch mass exchange networks with multipurpose exchange units. Computers & Chemical Engineering, 2016, 84: 536–545

[12] Gadalla M A. A new graphical-based approach for mass integration and exchange network design. Chemical Engineering Science, 2015, 127: 239–252

[13] Zhang R, Xiao Y. A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique. International Journal for Numerical Methods in Engineering, 2023, 124(22): 5102–5119

[14] Papalexandri K P, Pistikopoulos E N, Floudas A. Mass exchange networks for waste minimization: a simultaneous approach. Chemical Engineering Research & Design, 1994, 72: 279–294

[15] Velázquez-Guevara M Á, Uribe-Ramírez A R, Gómez-Castro F I, Ponce-Ortega J M, Hernández S, Segovia-Hernández J G, Alfaro-Ayala J A, Ramírez-Minguela J J, Ramírez-Minguela J d J. Synthesis of mass exchange networks: a novel mathematical programming approach. Computers & Chemical Engineering, 2018, 115: 226–232

[16] Yi Z K, Cui G M, Xiao Y, Xu Y. A novel chessboard model for optimization of mass exchange network synthesis. Industrial & Engineering Chemistry Research, 2023, 62(41): 16794–16810

[17] Papalexandri K P, Pistikopoulos E N. Multiperiod MINLP model for the synthesis of flexible heat and mass exchange networks. Computers & Chemical Engineering, 1994, 18(11/12): 1125–1139

[18] Duan H H, Yang L, Xiao Y, Huang X H, Cui G M. A heuristic algorithm with a dynamic generation strategy for optimizing energy systems. Applied Thermal Engineering, 2024, 236: 121833

[19] Szitkai Z, Farkas T, Lelkes Z, Rev E, Fonyo Z, Kravanja Z. Fairly linear mixed integer nonlinear programming model for the synthesis of mass exchange networks. Industrial & Engineering Chemistry Research, 2006, 45(1): 236–244

[20] Isafiade A J, Fraser D M. Interval based MINLP superstructure synthesis of mass exchange networks. Chemical Engineering Research & Design, 2008, 86(8): 909–924

[21] Liu L L, Du J, El-Halwagi M M, Ponce-Ortega J M, Yao P J. Synthesis of multi-component mass-exchange networks. Chinese Journal of Chemical Engineering, 2013, 21(4): 376–381

[22] Tao S, Jiang M, Liu M, Ding L. A mixed discrete PSO algorithm for synthesis of mass exchange network with incompatible multicomponent. Chemical Engineering Transactions, 2017, 61: 709714

[23] Zhu M J, El-Halwagi M M. Synthesis of flexible mass-exchange networks. Chemical Engineering Communications, 2007, 138(1): 193–211

[24] Azeez O S, Isafiade A J, Fraser D M. Supply and target based superstructure synthesis of heat and mass exchanger networks. Chemical Engineering Research & Design, 2012, 90(2): 266–287

[25] Azeez O S, Isafiade A J, Fraser D M. Supply-based superstructure synthesis of heat and mass exchange networks. Computers & Chemical Engineering, 2013, 56: 184–201

[26] Yang Y H, Yan Q Z, Huang Y L. A unified model for the prediction of structural disturbance propagation in mass exchanger networks. Chemical Engineering Research & Design, 1999, 77(3): 253–266

[27] Yan Q Z, Huang Y L. A disturbance rejection model for designing a structurally controllable mass exchanger betwork with recycles. Chemical Engineering Research & Design, 2002, 80(5): 513–528

[28] Short M, Isafiade A J, Biegler L T, Kravanja Z. Synthesis of mass exchanger networks in a two-step hybrid optimization strategy. Chemical Engineering Science, 2018, 178: 118–135

[29] Isafiade A J, Short M. Synthesis of mass exchange networks for single and multiple periods of operations considering detailed cost functions and column performance. Process Safety and Environmental Protection, 2016, 103: 391–404

[30] Chen C L, Hung P S. Simultaneous synthesis of mass exchange networks for waste minimization. Computers & Chemical Engineering, 2005, 29(7): 1561–1576

[31] Xiao Y, Cui G M, Xu Y, Xiong S H. An efficient and random synthesis method for mass exchange networks with multi-component using a node-based vertical non-structural model. Journal of Cleaner Production, 2023, 416: 137951

[32] Liu L L, El-Halwagi M M, Du J, Ponce-Ortega J M, Yao P J. Systematic synthesis of mass exchange networks for multicomponent systems. Industrial & Engineering Chemistry Research, 2013, 52(39): 14219–14230

[33] Pavão L V, Costa C B B, Ravagnani M A D S S. Automated heat exchanger network synthesis by using hybrid natural algorithms and parallel processing. Computers & Chemical Engineering, 2016, 94: 370–386

[34] Pavão L V, Costa C B B, Ravagnani M A S S. Heat exchanger network synthesis without stream splits using parallelized and simplified simulated annealing and particle swarm optimization. Chemical Engineering Science, 2017, 158: 96–107

[35] Yee T F, Grossmann I E. Simultaneous optimization models for heat integration-II. Heat exchanger network synthesis. Computers & Chemical Engineering, 1990, 14(10): 1165–1184

[36] Treybal R E. Mass Transfer Operations. 3rd ed. Singapore: McGraw-Hill, 1981

[37] Xiao Y, Cui G M, Zhang G H, Ai L Z. Parallel optimization route promoted by accepting imperfect solutions for the global optimization of heat exchanger networks. Journal of Cleaner Production, 2022, 336: 130354

[38] Hermanns M. Parallel Programming in Fortran 95 Using OpenMP., 2002

[39] Hallale N, Fraser D M. Capital cost targets for mass exchange networks a special case: water minimisation. Chemical Engineering Science, 1998, 53(2): 293–313

[40] Emhamed A M, Lelkes Z, Rev E, Farkas T, Fonyo Z, Fraser D M. New hybrid method for mass exchange network optimization. Chemical Engineering Communications, 2007, 194(10): 194

[41] Isafiade A J, Fraser D M. Extended interval-based mixed integer nonlinear programming superstructure synthesis of heat and mass exchanger networks. Industrial & Engineering Chemistry Research, 2010, 49(1): 166–179

[42] Zhou Z Q, Cui G M, Xiao Y. A novel node-based non-structural model for mass exchanger network synthesis using a stochastic algorithm. Journal of Cleaner Production, 2022, 376: 134227

[43] El-Halwagi M M, Manousiouthakis V. Simultaneous synthesis of mass-exchange and regeneration networks. AIChE Journal, 1990, 36(8): 1209–1219

[44] ComeauxR. Synthesis of MENS with minimum total cost. University of Manchester Institute of Science and Technology, 2000

[45] Alva-Arga’ez A, Vallianatos A, Kokossis A. A multi-contaminant transhipment model for mass exchange networks and wastewater minimisation problems. Computers & Chemical Engineering, 1999, 23(10): 1439–1453

Acknowledgements

Financial support from the National Natural Science Foundation of China (Grant No. 21978171) and the China Postdoctoral Science Foundation (Grant No. 2020M671171) is greatly appreciated.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11705-025-2522-9 and is accessible for authorized users.

Competing interests

The authors declare that they have no competing interests.

RIGHTS & PERMISSIONS

2025 Higher Education Press