Progress of research and application of P-graph theory in process network synthesis

doi:10.11949/j.issn.0438-1157.20160154

Abstract

Abstract:

With upsizing, complexifying and unifying in modern petro-chemical systems, the combined complexity among streams of mass, energy and information as well as among unit operations keeps increasing exponentially. P-graph theory has found widespread applications by generation of rigorous superstructures as a result of axiom constraints which may reduce creation of redundant structures. This review on P-graph theory began with the mathematical definition, fundamental axioms, solution algorithms and workflow, and a case study to show the modeling framework and graphic representation. A literature study of past 20 years' publications systemically summarized application of P-graph theory in traditional process system engineering of separation network synthesis, reaction path synthesis and heat exchange synthesis, and recent expansion in new areas of process technology selection, supply chain and process optimization. The advantages and disadvantages of P-graph theory and mathematical programming were compared, and improving ideas were proposed to solve nonlinear problems with P-graph theory. The prospective research and application of P-graph theory were forecasted, including multi-objective optimization in consideration of economic and environmental factors,effective solution of large complex nonlinear programming problems by the combination of both P-graph and mathematical programming, and other potential applications.

Key words: P-graph, process network synthesis, system engineering, model, optimization

摘要：

随着石化生产装置日趋大型化、复杂化和一体化，过程系统中的操作单元之间以及物料流、能量流和信息流之间的组合关联复杂度不断增加，P-图理论通过公理约束生成严格超结构，可减少冗余结构的产生，得到了越来越广泛的应用。首先概述了P-图理论的数学定义、基本公理和求解算法及工作流程等，通过案例介绍了P-图理论的建模框架和图形表示。然后系统总结了自1992年P-图理论提出以来，其在分离网络综合、反应路径识别、换热网络综合等传统过程网络综合的应用，以及近年来在工艺路w线选择、供应链与调度优化等新兴研究领域的扩展。最后，比较分析了P-图理论与数学规划法的各自优势，提出了利用P-图求解非线性问题的改进思路，展望了P-图理论未来的研究方向，包括考虑经济、环境等因素的多目标优化，以及P-图与数学规划相结合，高效处理复杂大规模非线性规划问题等。

关键词: P-图, 过程网络综合, 系统工程, 模型, 优化

CLC Number:

TQ021.8

XIAO Wu, ZHANG Yi, LÜ Junfeng, LI Zhonghua, HE Gaohong. Progress of research and application of P-graph theory in process network synthesis[J]. CIESC Journal, 2016, 67(10): 4029-4039.

肖武, 张毅, 吕俊锋, 李中华, 贺高红. P-图理论在过程网络综合中的应用研究进展[J]. 化工学报, 2016, 67(10): 4029-4039.

References 57

[1]	SARGENT R. Process systems engineering:a retrospective view with questions for the future[J]. Computers and Chemical Engineering, 2005, 29(6):1237-1241.
[2]	FRIEDLER F, FAN L T, IMREH B. Process network synthesis:problem definition[J]. Networks, 1998, 31(2):119-124.
[3]	姚平经, 杨友麒. 过程系统工程[M]. 上海:华东理工大学出版社, 2009. YAO P J,YANG Y L. Process Systems Engineering[M]. Shanghai:East China University of Science and Technology Press, 2009.
[4]	GROSSMANN I E, CABALLERO J A, YEOMANS H. Mathematical programming approaches to the synthesis of chemical process systems[J]. Korean Journal of Chemical Engineering, 1999, 16(4):407-426.
[5]	李萍, 华贲. 过程系统综合集成优化法的研究进展[J]. 广东化工, 2005, 32(1):80-83. LI P, HUA B. Development on optimizing approaches for process system integration and synthesis[J]. Guangdong Chemical Industry, 2005, 32(1):80-83.
[6]	GROSSMANN I E. Mixed-integer programming approach for the synthesis of integrated process flowsheets[J]. Computers and Chemical Engineering, 1985, 9(5):463-482.
[7]	BAGAJEWICZ M J, PHAM R, MANOUSIOUTHAKIS V. On the state space approach to mass/heat exchanger network design[J]. Chemical Engineering Science, 1998, 53(14):2595-2621.
[8]	GROSSMANN I E, TRESPALACIOS F. Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming[J]. AIChE Journal, 2013, 59(9):3276-3295.
[9]	VARGA V, HECKL I, FRIEDLER F, et al. PNS solutions:a P-graph based programming framework for process network synthesis[J]. Chemical Engineering Transactions, 2010, 21:1387-1392.
[10]	TICK J. P-graph-based workflow modelling[J]. Acta Polytechnica Hungarica, 2007, 4(1):75-88.
[11]	FRIEDLER F, TARJAN K, HUANG Y W, et al. Graph-theoretic approach to process synthesis:polynomial algorithm for maximal structure generation[J]. Computers and Chemical Engineering, 1993, 17:929-942.
[12]	FRIEDLER F, VARGA J B, FAN L T. Decision-mapping:a tool for consistent and complete decisions in process synthesis[J]. Chemical Engineering Science, 1995, 50(11):1755-1768.
[13]	许晓慧, 孙娜, 赵立新. 基于P-图理论的组合算法合成分离过程严格超结构[J]. 计算机与应用化学, 2014, 31(12):1496-1502. XU X H, SUN N, ZHAO L X. Rigorous superstructure generation of separation systems by the P-graph-based combinatorial algorithm[J]. Computer and Applied Chemistry, 2014, 31(12):1496-1502.
[14]	VARGA V, HECKL I, FRIEDLER F, et al. PNS solutions:a P-graph based programming framework for process network synthesis[J]. Chemical Engineering Transactions, 2010, 21:1387-1392.
[15]	许晓慧, 宋海华, 于兰平, 等. 加速分支定界算法在化工过程合成中的应用[J]. 计算机与应用化学, 2011, 28(4):451-457. XU X H, SONG H H, YU L P, et al. Application of accelerated branch and bound in process synthesis of chemical engineering[J]. Computer and Applied Chemistry, 2011, 28(4):451-457.
[16]	VARGA V, HECKL I, FRIEDLER F, et al. PNS solutions:a P-graph based programming framework for process network synthesis[J]. Chemical Engineering Transactions, 2010, 21:1387-1392.
[17]	ALMASI D, IMREH C, KOVACS T, et al. Heuristic algorithms for the robust PNS problem[J]. Acta Polytechnica Hungarica, 2014, 11(4):169-181.
[18]	KOVACS Z, FRIEDLER F, FAN L T. Recycling in a separation process structure[J]. AIChE Journal, 1993, 39(6):1087-1089.
[19]	KOVACS Z, FRIEDLER F, FAN L T. Parametric study of separation network synthesis:extreme properties of optimal structures[J]. Computers and Chemical Engineering, 1995, 19:107-112.
[20]	KOVACS Z, ERCSEY Z, FRIEDLER F, et al. Exact super-structure for the synthesis of separation-networks with multiple feed-streams and sharp separators[J]. Computers and Chemical Engineering, 1999, 23:S1007-S1010.
[21]	HECKL I, FRIEDLER F, FAN L T. Solution of separation-network synthesis problems by the P-graph methodology[J]. Computers and Chemical Engineering, 2010, 34(5):700-706.
[22]	BERTOK B, BARANY M, FRIEDLER F. Generating and analyzing mathematical programming models of conceptual process design by P-graph software[J]. Industrial and Engineering Chemistry Research, 2012, 52(1):166-171.
[23]	FENG G, FAN L T, FRIEDLER F. Synthesizing alternative sequences via a P-graph-based approach in azeotropic distillation systems[J]. Waste Management, 2000, 20(8):639-643.
[24]	FENG G, FAN L T, SEIB P A, et al. A graph-theoretic method for the algorithmic synthesis of azeotropic-distillation systems[J]. Industrial and Engineering Chemistry Research, 2003, 42(15):3602-3611.
[25]	DOUGLAS J M. A hierarchical decision procedure for process synthesis[J]. AIChE Journal, 1985, 31(3):353-362.
[26]	SEO H, LEE D Y, PARK S, et al. Graph-theoretical identification of pathways for biochemical reactions[J]. Biotechnology Letters, 2001, 23(19):1551-1557.
[27]	FAN L T, BERTOK B, FRIEDLER F, et al. Mechanisms of ammonia-synthesis reaction revisited with the aid of a novel graph-theoretic method of determining candidate mechanisms in deriving the rate law of a catalytic reaction[J]. Hungarian Journal of Industrial Chemistry, 2001, 29(1):71-80.
[28]	FAN L T, BERTOK B, FRIEDLER F. A graph-theoretic method to identify candidate mechanisms for deriving the rate law of a catalytic reaction[J]. Computers and Chemistry, 2002, 26(3):265-292.
[29]	FAN L T, LIN Y C, SHAFIE S, et al. Graph-theoretic and energetic exploration of catalytic pathways of the water-gas shift reaction[J]. Journal of the Chinese Institute of Chemical Engineers, 2008, 39(5):467-473.
[30]	LIN Y C, FAN L T, SHAFIE S, et al. Generation of light hydrocarbons through Fischer-Tropsch synthesis:identification of potentially dominant catalytic pathways via the graph-theoretic method and energetic analysis[J]. Computers and Chemical Engineering, 2009, 33(6):1182-1186.
[31]	LIN Y C, FAN L T, SHAFIE S, et al. Graph-theoretic approach to the catalytic-pathway identification of methanol decomposition[J]. Computers and Chemical Engineering, 2010, 34(5):821-824.
[32]	FAN L T, LIN Y C, SHAFIE S, et al. Exhaustive identification of feasible pathways of the reaction catalyzed by a catalyst with multiactive sites via a highly effective graph-theoretic algorithm:application to ethylene hydrogenation[J]. Industrial and Engineering Chemistry Research, 2012, 51(6):2548-2552.
[33]	YUN C, KIM T Y, ZHANG T, et al. Determination of the thermodynamically dominant metabolic pathways[J]. Industrial and Engineering Chemistry Research, 2012, 52(1):222-229.
[34]	NAGY A B, ADONYI R, HALASZ L, et al. Integrated synthesis of process and heat exchanger networks:algorithmic approach[J]. Applied Thermal Engineering, 2001, 21(13):1407-1427.
[35]	HECKL I, FRIEDLER F, FAN L T. Integrated synthesis of optimal separation and heat exchanger networks involving separations based on various properties[J]. Heat Transfer Engineering, 2005, 26(5):25-41.
[36]	FRIEDLER F, VARBANOV P, KLEMEŠ J. Advanced HENs design for multi-period operation using P-graph[J]. Chemical Engineering Transactions, 2009, 18(1):457-462.
[37]	HALASZ L, POVODEN G, NARODOSLAWSKY M. Sustainable processes synthesis for renewable resources[J]. Resources Conservation and Recycling, 2005, 44(3):293-307.
[38]	LAM H L, KLEMES J J, VARBANOV P S, et al. P-graph synthesis of open-structure biomass networks[J]. Industrial and Engineering Chemistry Research, 2012, 52(1):172-180.
[39]	HALASZ L, EDERZ M, SANDORZ N, et al. Optimal integration of sustainable technologies in industrial parks[J]. Chemical Engineering Transactions, 2010, 19:43-48.
[40]	KETTL K H, NIEMETZ N, SANDOR N, et al. Regional optimizer sustainable energy technology network solutions for regions[J]. Computer Aided Chemical Engineering, 2011, 29:1959-1963.
[41]	VARBANOV P, FRIEDLER F. P-graph methodology for cost-effective reduction of carbon emissions involving fuel cell combined cycles[J]. Applied Thermal Engineering, 2008, 28(16):2020-2029.
[42]	TAN R R, CAYAMANDA C D, AVISO K B. P-graph approach to optimal operational adjustment in polygeneration plants under conditions of process inoperability[J]. Applied Energy, 2014, 135:402-406.
[43]	TAN R R, BENJAMIN M F D, CAYAMANDA C D, et al. P-graph approach to optimizing crisis operations in an industrial complex[J]. Industrial and Engineering Chemistry Research, 2016, 55(12):3467-3477.
[44]	LOSADA J P, HECKL I, BERTOK B, et al. Process network synthesis for benzaldehyde production:P-graph approach[J]. Chemical Engineering Transactions, 2015, 45:1369-1374.
[45]	SHEN H B, HOOI H B, LOONG L H, et al. Synthesis of multiple biomass corridor via decomposition approach:a P-graph application[J]. Journal of Cleaner Production, 2016, 130:45-57.
[46]	XU X, ZHU C, MA Y, et al. A robust combinatorial approach based on P-graph for superstructure generation in downstream bioprocesses[J]. Brazilian Journal of Chemical Engineering, 2015, 32(1):259-267.
[47]	HECKL I, HALASZ L, SZLAMA A, et al. Process synthesis involving multi-period operations by the P-graph framework[J]. Computers and Chemical Engineering, 2015, 83:157-164.
[48]	TAN R R, AVISO K B. An extended P-graph approach to process network synthesis for multi-period operations[J]. Computers and Chemical Engineering, 2016, 85:40-42.
[49]	FAN L T, KIM Y, YUN C, et al. Design of optimal and near-optimal enterprise-wide supply networks for multiple products in the process industry[J]. Industrial and Engineering Chemistry Research, 2009, 48(4):2003-2008.
[50]	KIM Y, FAN L T, YUN C, et al. Graph-theoretic approach to optimal synthesis of supply networks:distribution of gasoline from a refinery[J]. Computer Aided Chemical Engineering, 2008, 25:247-252.
[51]	BERTOK B, KALAUZ K, SULE Z, et al. Combinatorial algorithm for synthesizing redundant structures to increase reliability of supply chains:application to biodiesel supply[J]. Industrial and Engineering Chemistry Research, 2012, 52(1):181-186.
[52]	HECKL I, CABEZAS H, FRIEDLER F. Designing sustainable supply chains in the energy-water-food nexus by the P-graph methodology[J]. Chemical Engineering Transactions, 2015, 45:1351-1356.
[53]	NG R T L, TAN R R, HASSIM M H. P-graph methodology for bi-objective optimisation of bioenergy supply chains:economic and safety perspectives[J]. Chemical Engineering Transactions, 2015, 45:1357-1362.
[54]	TICK J, KOVACS Z. P-graph based workflow synthesis[C]//International Conference on Intelligent Engineering Systems. Miami, 2008:249-253.
[55]	BARANY M, BERTOK B, KOVACS Z, et al. Optimization software for solving vehicle assignment problems to minimize cost and environmental impact of transportation[J]. Chemical Engineering Transactions, 2010, 21:499-504.
[56]	BARANY M, BERTOK B, KOVACS Z, et al. Solving vehicle assignment problems by process-network synthesis to minimize cost and environmental impact of transportation[J]. Clean Technologies and Environmental Policy, 2011, 13(4):637-642.
[57]	ADONYI R, HECKL I, OLTI F. Scheduling of bus maintenance by the P-graph methodology[J]. Optimization and Engineering, 2013, 14(4):565-574.