Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 9, No. 2, 2024 149 Cascading Propagation Path of Vinyl Chloride Process Risk Based on Complex Network Xixi Li1, * 1 Henan Polytechnic University, CO 454150, China * Corresponding author: Xixi Li (Email: 3212697193@qq.com) Abstract: In the production of vinyl chloride, small parameter fluctuations may lead to large-scale cascade fluctuations, causing serious economic losses and casualties, in order to ensure the safety and stability of production, it is necessary to study the cascade fluctuation propagation path of vinyl chloride production process. In this paper, a complex network model of vinyl chloride production process is constructed based on complex network theory, and the concept of comprehensive degree considering network direction is introduced to identify important nodes in the network: secondly, the fluctuation overload propagation probability and material hazard degree of the edge are used to define the fluctuation overload propagation intensity of the edge; finally, according to the fluctuation overload propagation intensity, the risk propagation path of cascading fluctuations under different overload modes is obtained by using ant colony algorithm, it provides a basis for the prevention of cascade overload and the selection and protection of key monitoring nodes. Keywords: Cascade fluctuation, Complex network, Fluctuation risk propagation path, Vinyl chloride production. 1. Introduction Vinyl chloride is an important raw material in the plastic industry. It can also be used as an extractant for dyes and spices. The production process of vinyl chloride is a typical process industrial production with continuity. At the same time, the production process system is huge, and various parts in the production process are interrelated. The fluctuation of one parameter may cause the fluctuation of other parameters in the follow-up, which may lead to the occurrence of cascade failure, and eventually lead to the interruption of production and even vinyl chloride leakage. At present, scholars' research on cascaded volatility mainly focuses on the establishment of cascaded volatility models [1], the study of resilience in the face of volatility [2], the study of risk propagation paths [3], the study of cascaded volatility mechanisms [4]. It has been widely studied in different disciplines, such as transportation network [5], power network [6], communication network [7], water supply network [8], biological network [9], chemical network [10], which shows that complex network is an effective method suitable for the study of risk cascade propagation path of process parameter fluctuation. Wang and others [10] constructed three cascaded volatility models based on complex network theory, which provided a reference for the model establishment in this paper. But it does not judge the importance of a node from the global view of the network. Based on this, some scholars [11] proposed a method to identify the key nodes of complex networks by considering the various topological characteristics of nodes and the characteristics of the networks they study, but it does not take into account the directionality of complex networks. In this paper, the ant colony algorithm [12] is used to comprehensively consider the topological characteristics of the network and the risk of materials on the basis of other scholars [13] to identify the cascading risk propagation path of parameter fluctuations in the vinyl chloride production process, which provides a certain basis for the prevention of cascading overload and the selection and protection of key monitoring nodes. 2. Methods 2.1. Establishment of Complex Network Model In the chemical production process, according to the complex network theory, the flow rate of materials in and out of the vinyl chloride production process and the various reaction parameters are abstracted as the nodes of the network, and the interaction relationship between them is abstracted as the edge of the network, defining the adjacency matrix A: A= ๐‘Ž โ‹ฏ ๐‘Ž โ‹ฎ โ‹ฑ โ‹ฎ ๐‘Ž โ‹ฏ ๐‘Ž (1) where aij represents whether there is an association between node i and node j. ๐‘Ž = 1๏ผŒnode i and node j are related๏ผ› 0๏ผŒnode i and node j are not related (2) The complex network model can be obtained by entering the established adjacency matrix into the software Ucinet6.0. 2.2. Establishment of Cascade Wave Model for Complex Networks The initial load, load capacity, load redistribution rules for the nodes in this article are as follows. (1) The initial load of the node: According to the degree of the node and the degree of the neighbor node, the initial load Ni of the node i is defined: ๐‘ =๐‘˜ (1+โˆ‘ ๐‘˜โˆˆ )-๐‘˜ (3) Where ki is the degree of node i and ๐œ is the set of neighbor nodes of the node. (2) Load capacity of the node: Assuming that the load 150 capacity of the node and the initial load are linearly related, the load capacity Ci of the node is defined: ๐ถ =๏ผˆ1+๐›ฝ๏ผ‰๐‘ (4) where B is the tolerance parameter, taking 0.06 (3) Node Load Redistribution Rule: Assuming that node i fails, the load of node i will be assigned to the node to which it points, and if node j is a pointing node of the node i, the load โˆ†๐‘ assigned to node j is defined: โˆ†๐‘ = โˆ‘ โˆˆ (5) where ๐œ€ is the set of neighbor nodes to which node i points. 2.3. Node importance judgment Based on the K-shell method, this paper introduces the concept of comprehensive degree. The degree of integration of a node is defined: C(i)=K(i)+๐œ‡ ๐ท ๐‘– (6) where K(i) is the degree of the node, D(i) is the number of secondary neighbors of the node, and ๐œ‡ is the influence coefficient. According to the degree K(i) of the node and the total number N(i) of nodes in the two-step neighborhood of the node, ๐œ‡ is defined: ๐œ‡ (7) The mean value of the node's in-degree synthesis ๐ถ ๐‘– and out-degree synthesis ๐ถ ๐‘– is taken as the final synthesis value: ๐ถ (i)= (8) 2.4. Complex network fluctuation cascade propagation intensity ๐‘ฐ๐’Š๐’‹ In a complex network, the stronger the fluctuation propagation ability of an edge, the easier it is for the fluctuation to propagate along this edge. At the same time, a large number of raw materials and products in the production process of vinyl chloride have certain risks, which will also have a certain impact on the cascade propagation of fluctuations. Therefore, the article defines the intensity of fluctuation propagation ๐ผ on the opposite side: ๐ผ = + (9) ๐ฟ is the fluctuation propagation probability of the edge on the network, which is determined by the fluctuation propagation probability ๐‘„ of the node and the fluctuation propagation capability ๐‘† of the edge. The fluctuation propagation probability ๐‘„ of the node is determined by the fluctuation probability ๐‘ƒ of the node and the propagation capability ๐‘† after the node fluctuates. The fluctuation propagation capability ๐‘† of the edge is determined by the fluctuation propagation capability ๐‘† of the nodes at both ends of the edge. ๐‘Š is the risk of materials on the network, including toxic, corrosive and flammable and explosive, taking into account subjective and objective factors, the combination of hierarchical analysis and rough set theory to quantify the risk of materials. Finally, the fluctuation propagation intensity ๐ผ of the edge is obtained. 3. Establishment of Cascade Fluctuation Model for Vinyl Chloride Production Process 3.1. Establishment of Complex Network of Vinyl Chloride Production Process The process for the production of vinyl chloride by the equilibrium oxychlorination method is shown in Figure 1 and consists of five main parts: chlorination of ethylene, oxychlorination, dichloroethane refining, dichloroethane cracking, vinyl chloride refining. Figure 1. Flow Chart of Production of Vinyl Chloride by Equilibrium Oxygen-chlorine Process According to the complex network theory, the material flow rate and each reaction parameter in the vinyl chloride production process are abstracted as the nodes of the network, as shown in Table 1. The adjacency matrix is entered into Ucine6.0 to generate a complex network model as shown in Figure 2. Figure 2. Complex network model of vinyl chloride production process 151 Table 1. Network Node Definition No. Name No. Name 1 Flow of chlorine into chlorination reactor 25 Bottom temperature of deweight tower 2 Flow of ethylene into chlorination reactor 26 Dehydration tower pressure 3 Flow of mixture out of chlorination reactor 27 Off-light tower pressure 4 Temperature of chlorination reactor 28 Heavy tower pressure 5 Pressure of chlorination reactor 29 Flow rate of cracking gas out of cracking furnace 6 Flow of crude dichloroethane out of condenser 1 30 Cracking temperature 7 Flow of ethylene tail gas in chlorination reaction 31 Cracking pressure 8 Flow of crude dichloroethane into separator 1 32 Flow rate of mixed condensate out of quench tower 2 9 Flow of crude dichloroethane out of separator 1 33 Flow rate of Hcl out of Hcl tower 10 Flow of ethylene into oxychlorination reactor 34 Top temperature of Hcl tower 11 O2 and Hcl flow into the chlorination reactor 35 Bottom temperature of Hcl removal tower 12 Flow of crude dichloroethane out of the oxychlorination reactor 36 Pressure of Hcl removal tower 13 Temperature of the oxychlorination reaction fluidized bed 37 Crude vinyl chloride flow out of Hcl removal tower 14 Pressure of the oxychlorination reaction fluidized bed 38 Crude dichloroethane flow out of VCM1 tower 15 Flow of crude dichloroethane out of the quench tower 1 39 Crude vinyl chloride flow out of VCM1 tower 16 Flow of crude dichloroethane into the dehydrating tower 40 Top temperature of VCM1 tower 17 Flow of crude dichloroethane out of the dehydrating tower 41 Bottom temperature of VCM1 tower 18 Flow of crude dichloroethane out of the off-light tower 42 Top temperature of VCM1 tower 19 Flow of crude dichloroethane out of the off-weight tower 43 Bottom temperature of VCM2 tower 20 Dehydration tower top temperature 44 Bottom temperature of VCM2 tower 21 Dehydration tower bottom temperature 45 Pressure of VCM2 tower 22 Top temperature of off-light tower 46 Crude vinyl chloride flow out of VCM2 tower 23 Bottom temperature of off-light tower 47 Vinyl chloride flow out of the dryer 24 Top temperature of deweight tower 3.2. Vinyl chloride production process Complex network Node importance First, the Ks value of each node of the complex network model of the vinyl chloride production process is calculated, and then the comprehensive degree of the node is obtained according to the formula (6)-(9), and the results are shown in Figure 3. Figure 3. Comprehensive degree of nodes 3.3. VCM production process complex network parameter fluctuation cascade propagation intensity ๐‘ฐ๐’Š๐’‹ First, according to the formula (3), (4) to find the initial load and load capacity of the complex network node of the vinyl chloride production process, on this basis to obtain the parameter fluctuation probability Pi of the node, the parameter fluctuation propagation capacity Si of the node and the fluctuation propagation probability Q_i of the node, as shown in Figure 4. The edge's parameter fluctuation propagation capability Sij is then multiplied by the node's parameter fluctuation propagation probability Qi to obtain the edge's parameter fluctuation propagation probability Lij, as shown in Table 2. Figure 4. Node and edge metrics 152 Table 2. Fluctuation Propagation Capability ๐‘† of an Edge and Fluctuation Propagation Probability ๐ฟ of an Edge Edge ๏ผˆiโ†’j๏ผ‰ ๐‘บ๐’Š๐’‹ ๐‘ณ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘บ๐’Š๐’‹ ๐‘ณ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘บ๐’Š๐’‹ ๐‘ณ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘บ๐’Š๐’‹ ๐‘ณ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘บ๐’Š๐’‹ ๐‘ณ๐’Š๐’‹ 1โ†’3 0.280 0 11โ†’12 0.400 0.144 24โ†’17 0.300 0. 003 31โ†’30 0.240 0.002 40โ†’39 0.340 0.007 1โ†’7 0.280 0 12โ†’15 0.355 0.156 24โ†’19 0.340 0.003 32โ†’33 0.460 0.193 40โ†’42 0.255 0.005 2โ†’3 0.280 0 13โ†’12 0.320 0.003 24โ†’28 0.255 0.003 32โ†’37 0.460 0.193 41โ†’39 0.340 0.007 2โ†’7 0.280 0 13โ†’14 0.200 0.002 25โ†’17 0.300 0. 003 33โ†’11 0.430 0.077 41โ†’42 0.255 0.005 3โ†’6 0.330 0.053 14โ†’12 0.320 0.003 25โ†’19 0.340 0.003 34โ†’33 0.415 0.012 42โ†’39 0.355 0.011 3โ†’8 0.315 0.050 14โ†’13 0.200 0.002 25โ†’28 0.255 0.003 34โ†’36 0.355 0.011 42โ†’40 0.255 0.008 4โ†’3 0.300 0.006 15โ†’16 0.315 0.085 26โ†’17 0.315 0.009 34โ†’37 0.415 0.012 42โ†’41 0.255 0.008 4โ†’5 0.240 0.048 17โ†’18 0.400 0.044 26โ†’20 0.315 0.009 35โ†’33 0.415 0.012 43โ†’45 0.220 0.007 4โ†’7 0.300 0.006 18โ†’19 0.440 0.194 26โ†’21 0.235 0.007 35โ†’36 0.355 0.011 43โ†’46 0.235 0.007 5โ†’3 0.300 0.006 19โ†’29 0.440 0.194 27โ†’22 0.315 0.009 35โ†’37 0.415 0.012 44โ†’45 0.220 0.007 5โ†’4 0.240 0.048 20โ†’17 0.360 0.007 27โ†’23 0.315 0.009 36โ†’33 0.440 0.022 44โ†’46 0.235 0.007 5โ†’7 0.300 0.006 20โ†’19 0.400 0.008 28โ†’19 0.355 0.014 36โ†’34 0.355 0.018 45โ†’43 0.220 0.011 6โ†’8 0.285 0.086 20โ†’26 0.315 0.006 28โ†’24 0.255 0.010 36โ†’35 0.355 0.018 45โ†’44 0.220 0.011 6โ†’16 0.330 0.099 21โ†’26 0.235 0.002 28โ†’25 0.255 0.010 36โ†’37 0.440 0.022 45โ†’46 0.255 0.013 7โ†’10 0.300 0.033 22โ†’18 0.320 0.006 29โ†’32 0.430 0.189 37โ†’38 0.430 0.077 46โ†’47 0.250 0.025 8โ†’3 0.300 0.081 22โ†’27 0.235 0.005 30โ†’29 0.340 0.003 37โ†’39 0.470 0.085 8โ†’9 0.235 0.063 23โ†’18 0.320 0.006 30โ†’31 0.240 0.002 38โ†’16 0.360 0.130 10โ†’12 0.355 0.096 23โ†’27 0.235 0.005 31โ†’29 0.340 0.003 39โ†’47 0.340 0.150 For the measurement of material hazard ๐‘Š , the subjective weight ๐œ” =(0.27,0.12,0.61) of toxicity, corrosiveness and easy explosion can be obtained, and the calculated weight is reasonable after inspection.The objective weight of explosiveness ๐‘ =(0.5,0.25,0.25). Finally, the comprehensive weight ๐œƒ =(0.385,0.185,0.43) is obtained. As shown in Table 3, the fluctuation propagation intensity ๐ผ is shown in Figure 5. Figure 5. Intensity of wave propagation ๐ผ Table 3. Hazard degree of materials ๐‘Š Edge ๏ผˆiโ†’j๏ผ‰ ๐‘พ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘พ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘พ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘พ๐’Š๐’‹ Edge ๏ผˆiโ†’j๏ผ‰ ๐‘พ๐’Š๐’‹ 1โ†’3 3.015 11โ†’12 3.800 24โ†’17 2.675 31โ†’30 7.405 40โ†’39 2.790 1โ†’7 3.015 12โ†’15 2.675 24โ†’19 2.675 32โ†’33 2.675 40โ†’42 2.790 2โ†’3 2.290 13โ†’12 6.090 24โ†’28 2.675 32โ†’37 2.675 41โ†’39 2.790 2โ†’7 2.290 13โ†’14 6.090 25โ†’17 2.675 33โ†’11 1.940 41โ†’42 2.790 3โ†’6 2.675 14โ†’12 6.090 25โ†’19 2.675 34โ†’33 7.405 42โ†’39 2.790 3โ†’8 2.675 14โ†’13 6.090 25โ†’28 2.675 34โ†’36 7.405 42โ†’40 2.790 4โ†’3 5.305 15โ†’16 2.675 26โ†’17 2.675 34โ†’37 7.405 42โ†’41 2.790 4โ†’5 5.305 17โ†’18 2.675 26โ†’20 2.675 35โ†’33 7.405 43โ†’45 2.790 4โ†’7 5.305 18โ†’19 2.675 26โ†’21 2.675 35โ†’36 7.405 43โ†’46 2.790 5โ†’3 5.305 19โ†’29 2.675 27โ†’22 2.675 35โ†’37 7.405 44โ†’45 2.790 5โ†’4 5.305 20โ†’17 2.675 27โ†’23 2.675 36โ†’33 7.405 44โ†’46 2.790 5โ†’7 5.305 20โ†’19 2.675 28โ†’19 2.675 36โ†’34 7.405 45โ†’43 2.790 6โ†’8 2.675 20โ†’26 2.675 28โ†’24 2.675 36โ†’35 7.405 45โ†’44 2.790 6โ†’16 2.675 21โ†’26 2.675 28โ†’25 2.675 36โ†’37 7.405 45โ†’46 2.790 7โ†’10 2.290 22โ†’18 2.675 29โ†’32 4.730 37โ†’38 2.790 46โ†’47 2.790 8โ†’3 2.675 22โ†’27 2.675 30โ†’29 7.405 37โ†’39 2.790 8โ†’9 2.675 23โ†’18 2.675 30โ†’31 7.405 38โ†’16 2.675 10โ†’12 2.290 23โ†’27 2.675 31โ†’29 7.405 39โ†’47 2.790 153 4. Identification and Analysis of Risk Propagation Path of Cascade Fluctuation in Vinyl Chloride Production Process Using the ant colony algorithm to solve the cascade fluctuation risk propagation path of the complex network of vinyl chloride production process when the three fluctuation modes of important node fluctuation, high load node fluctuation and random fluctuation are 10%, 20% and 30%, respectively, the fluctuation propagation path is shown in Figure 6. It can be seen from fig. 6 that when the load capacity is 100 and there are 10% important node fluctuations, the cascade fluctuation risk propagation path of vinyl chloride production process is 35 โ†’ 36 โ†’ 34 โ†’ 37 โ†’ 39 โ†’ 47, which indicates that in the initial production process, when a few nodes fluctuate, nodes 35, 36, 34, 37, 39 and 47 are more prone to cascade fluctuations, it can be seen that the reaction conditions in the Hcl removal tower are the most severe, and the flow rates of materials out of the Hcl removal tower, the VCM1 tower and the dryer also need to be controlled more accurately. With the increase of the number of important nodes of fluctuation, nodes 18, 19, 29, 32, 12, 15, 16, 6, 8 and 3 will also have cascade fluctuation, that is to say, with the increase of the number of important nodes of fluctuation, the flow rate of ethylene chlorination reaction, oxychlorination reaction and crude dichloroethane purification process is extremely easy to be abnormal, and the flow rate of materials in the reaction process needs to be strictly monitored. Figure 6. Cascading Volatility Risk Propagation Path 5. Conclusion Based on the complex network theory, combined with the actual production process, the network model of vinyl chloride production process is established, and on the basis of this model, the cascade fluctuation propagation model is further constructed based on the cascade fluctuation theory, and the cascade fluctuation propagation path of vinyl chloride production process network is studied by using this model. The main conclusions are as follows: (1) In the production process of vinyl chloride, the reaction pressure, temperature and flow rate of reactants are prone to cascade fluctuations when crude vinyl chloride is refined. The parameters on this path should be the main focus of monitoring to ensure that timely measures can be taken to prevent the spread of cascade fluctuations and ensure the safe and stable operation of the vinyl chloride production process. (2) In the establishment of complex network model, we not only consider the direction of the network, topological properties and the risk of materials, but also comprehensively compare and analyze the fluctuation risk propagation path under different fluctuation overload modes, which can better predict the cascade risk propagation path in the process of vinyl chloride production, and provide a reliable theoretical basis for the development of monitoring plan in the process of vinyl chloride production, and accurately and timely block the propagation of failure. Acknowledgment This work was supported in part by the Natural Science Foundation of Henan Province(Fund Number:232300420083) and Scientific and Technological Project in Henan Province(Fund Number:222102320412). 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