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An ingenious characterization of reaction network using sub-network reconstruction
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An Ingenious Characterization of Reaction Network Using Sub-network Reconstruction Kexin Bi , Chen Zhang , Tong Qiu PII: DOI: Reference:
S0098-1354(19)31050-6 https://doi.org/10.1016/j.compchemeng.2019.106695 CACE 106695
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
9 October 2019 30 November 2019 21 December 2019
Please cite this article as: Kexin Bi , Chen Zhang , Tong Qiu , An Ingenious Characterization of Reaction Network Using Sub-network Reconstruction, Computers and Chemical Engineering (2019), doi: https://doi.org/10.1016/j.compchemeng.2019.106695
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Highlights:
An ingenious reaction network characterization method is proposed. A novel sub-network reconstruction method is applied to elucidate co-cracking mechanisms. Graph visualization of sub-network helps understand reaction mechanisms. The whole process can be applied to other reaction networks with proper kinetics.
An Ingenious Characterization of Reaction Network Using Sub-network Reconstruction Kexin Bi, Chen Zhang, Tong Qiu* Department of Chemical Engineering, Tsinghua University, Beijing 100084, China Beijing Key Laboratory of Industrial Big Data Systems and Applications, Tsinghua University, Beijing 100084, China *
Corresponding author’s e-mail: [email protected]
Abstract Reaction network model is essential for reactor simulation and kinetic profiling of a complex process. Comprehensive and valid proofs of network mechanism are usually lacking among experimental and simulation studies of complicated reaction process, such as ethylene furnace co-cracking. In this paper, a self-developed Ethylene cracker Simulation and Optimization System (EcSOS) software is applied for co-cracking process numerical simulation and an ingenious characterization method of reaction network is proposed for visualization and deep profiling of the radical reaction network. An effective sub-network reconstruction process is implemented by connecting the substance nodes using actual mass flow and refining key interactions. The product yield evolving trend in simulation and its reason was successfully explained by the reaction network analysis results. The radical reaction mechanism changing obtained by reaction backtracking was systematically sorted out and summarized.
Keywords:
reaction
network
characterization,
sub-network reconstruction,
EcSOS,
mechanism visualization
1. Introduction Ethylene is one of the most important products within the petrochemical industry, and China currently has the world’s second highest ethylene production capacity with an annual production in 2018 of approximately 18.41 million tons (NBSPRC, 2019). As the number of ethylene enterprises has increased and the scale of ethylene plant has expanded in China, there has been an increasingly serious shortage of cracking feedstock (Zhang et al., 2017). Diversification of feedstock sources and efficiency of feedstock utilization have therefore gradually become key factors in improving the profit margins of ethylene enterprises (Zhao et al., 2017). Simulation tools and software packages such as SPYRO (Goethem et al., 2001), CRACKER (Joo et al., 2000) and VMGSim (Virtual Materials Group, Inc., 2011) have been developed to allow calculation of the yields obtainable from different feedstocks. This has assisted in improving the product quality and increasing profit margins by optimization of feedstock allocation. These simulation and optimization processes all involve reaction network models as a fundamental element, to connect the molecular composition of the feedstock to the product distribution (Fakhroleslam and Sadrameli, 2019). The ethylene cracking reaction (ECR) network has received particular attention from engineers and researchers in recent years. To effectively model the complex reaction process in a cracking furnace, effective
characterization and visualization of the ECR network is required. Joo et al. (2001) applied sensitivity analysis and eigenvalue-eigenvector decomposition to the evaluation of the importance of various mechanisms, with the aim of generating a reduced reaction mechanism set. Fang et al. (2016) first introduced PageRank algorithm (Page et al., 1999) into network flow analysis algorithm (NFAA) and proposed an integrated network ranking and visualization method for analysis of an ECR network. Hua et al. (2018) used a feature mining process based on motif detection and demonstrated the feasibility of this approach via a convolutional neural networks (CNN) performance evaluation. This same work also implemented the visualization of the substrate network graph topology extracted by the NFAA in naphtha pyrolysis free radical network using the Gephi software package (Bastian and Heymann, 2009). The application of the NFAA has had a significant impact on our understanding of the reaction process and in improving the reaction networks in ethylene cracking furnaces. This, in turn, assists in enhancing the interpretation and overall performance of simulation models. Nevertheless, there are different types of users for the industrial reactor kinetic model of ethylene thermal cracking (Billa et al., 2017), and further research is required to ensure a comprehensive, in-depth understanding of various aspects of such processes. The remaining challenges include (i) visualization of the reaction model; (ii) understanding variations in the reaction mechanism when using different types of feedstock; and (iii) developing easy-tounderstand mechanism outputs. for further improvement of ethylene cracking software, the network characterization model should not only provide a general cognition of the ECR
network, but it also needs to be able to trace the importance reactions and key interactions between reactant and resultant. In this work, the co-cracking process in ethylene thermal cracking, which is widely employed to compensate for the shortage of traditional feedstocks such as naphtha (Khatib, 2014), is selected as an industrial case because the mechanism of this process is not fully revealed. The superposition of the reaction schemes for single-component cracking (Sundaram and Froment, 1978) and the interaction between the products of the cracking feedstock (Froment et al., 1976) are considered as the theoretical basis of the co-cracking process. Studies based on experimental work and simulations have produced varying results and hypotheses. Plehiers and Froment (1987) previously performed experimental work based on the cocracking of ethane and naphtha in a pilot plant and concluded that ethane cracking is strongly inhibited by the unsaturated reaction products of the naphtha. Belohlav et al. (2003) proposed a molecular reaction model for a thermal cracking plant and demonstrated the reliability of the optimized model in trials involving the co-cracking of mixtures of primary naphtha with alkenes. Yuan et al. (2016) performed simulations of the co-cracking of ethane and propane as well as liquefied petroleum gas and naphtha mixtures using software packages based on free-radical reaction mechanisms with a one-dimensional reactor model. Their group reported the effects of the mixing ratio, coil outlet temperature and pressure on the yields of some key products. However, specific and validated researches on the reaction network mechanism of co-cracking process are scarce and very incomplete, which has hindered our understanding of the manner in which various interactions affect the overall cracking kinetics and the product distributions when changing feedstocks.
With the aim of developing software that could potentially be employed by different types of users, we proposed an ingenious characterization of reaction network using sub-network reconstruction to that first profiled the co-cracking reaction mechanism systematically. In the present study, a software package of our own design, termed the Ethylene cracker Simulation and Optimization System (EcSOS) (Fang et al., 2017), was used as a simulation tool to calculate the distribution of pyrolysis products during the cracking of different feedstock mixtures. The corresponding free-radical reaction network in the software was subsequently analyzed by a novel characterization method and visualized using the Gephi software package. A sub-network reconstruction method was introduced in NFAA post-processing step and then the key information in the extracted sub-network was compared to ascertain the co-cracking reaction mechanism by backtracking the evolution of radical reaction rate. Based on current industrial practices, we used the co-cracking of ethane and naphtha as a test case.
2. Methods 2.1 EcSOS Software introduction EcSOS is an ethylene cracking process simulation and optimization software jointly developed by Petrochina and the Department of Chemical Engineering, Tsinghua University. The main function of the software is to convert feedstock input data into user-required output data such as product yield. For the purposes of studying the co-cracking mechanism, three fundamental models in the software were selected, as shown in Fig. 1.
Fig. 1. An architecture and function diagram showing the co-cracking models in the EcSOS.
When evaluating the co-cracking of ethane and naphtha, the software adopts a novel naphtha molecular reconstruction process (Bi and Qiu, 2019) to calculate the composition of a specific naphtha feedstock. The effective probability density functions of different homologues are constructed inspired by Seasonal-Trend decomposition (Cleveland et al., 1990), combining the basic gamma distribution, self-adaptive regional features, and uncertainty. The cloud model (Li et al., 2009) is employed for uncertainty addition of the distribution and a hybrid genetic algorithm-particle swarm optimization algorithm is selected
for parameter optimization of probability density functions. For practical industrial applications, the features of naphtha sample are considered by predetermined regional database and feedstock source. Then naphtha composition is converted into mole fraction and normalized after the addition of ethane. An in-tube reaction model is implemented to calculate detailed product information and the reactor state. The tubular reactor is divided into several segments and Gear’s method (Gear and Petzold, 1984) is applied in each segment to solve the ordinary differential equations for mass balance, momentum balance and heat balance, which are set as:
dN m S dt vim ri in dL dL i qv
vim ri
, i 1, ..., N R , m 1, ..., N S
i
f qm dP , m 1, ..., N S dL 5.07 104 Din 2
(1)
dN m dT dL , m 1, ..., N S dL mC pm N m C pH 2O N H 2O q Do dt mH 0fm
where
is the concentration of species m in the reaction tube;
residence time of pyrolysis gas in this micro-segment; species m in reaction i; gas;
flow area of the in-tube reactor;
reaction rate of reaction i;
pressure in the reaction tube; the tube segment; reactor; firebox; species m;
total number of reactions;
Fanning friction factor;
volume flow rate of pyrolysis total number of species;
inner diameter of the in-tube
temperature in the reaction tube;
outer diameter of the in-tube reactor;
heat flux from the
standard enthalpy of formation of
heat capacity of species m at constant pressure;
constant pressure; and
stoichiometric coefficient of
equivalent conversion coefficient of
mass flow rate of pyrolysis gas;
density of pyrolysis gas;
length of the reaction tube;
heat capacity of water at
concentration of water in the reaction tube.
In this model, reaction information including reaction equations and corresponding kinetic parameters is predetermined as a reaction network file. The other parameters in equation (1) can be obtained by feedstock composition, reactor geometry and operation condition except the heat flux from the firebox q. For this reason, a firebox heat transfer model was developed to calculate the heat flux from the firebox to the tubular reactor as well as the temperature field in the firebox. An adjusted Monte Carlo integral (AMCI) method (Zhou and Qiu, 2015) using a three-dimensional (3D) zone model is adopted in this software to solve energy balance problems. The coefficients for the heat transfer process are predetermined and the temperature distribution in the tubular reactor is read from an in-tube reaction model. The firebox geometry and firing conditions are obtained from a user interface, after which the heat flux can be calculated and updated in the in-tube reaction model. After the convergence of the coupled iterative process involving the in-tube reaction and firebox heat transfer models, the software will automatically generate a report of calculation results.
2.2 Automatic generation of a co-cracking reaction network In the in-tube reaction model within the software, the predetermined reaction information is integrated into a reaction network. The entire reaction network of naphtha consists of two parts: a light hydrocarbon network generated by the RMG open source software package (Gao et al., 2016) and a heavy hydrocarbon network based on a free radical mechanism involving compounds with more than four carbon atoms. The light hydrocarbon network employs the same kinetic parameters as the RMG software, while the kinetic parameters
associated with the heavy hydrocarbon network are obtained from several previous literature publications (Dente et al., 2010, 2007; Ranzi et al., 2001). The specific reaction network composition and kinetic parameters are provided in Table 1. The reaction network of ethane is incorporated in the auto-generated naphtha network, so that the ethylene co-cracking reaction (ECCR) network should be equivalent to the naphtha network according to the superposition rule of the reaction schemes (Sundaram and Froment, 1978). Table 1. The specific reaction network composition and kinetic parameters. Subcategories
Example reaction
Quantity
A(1/s)
E(kcal/mol)
0
CH3•+C2H6→C2H5•+CH4
2189
/
/
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
NC6H14→2C3H7• NC6H14→C2H5•+NC4H9• NC6H14→CH3•+C2H4+NC3H7• IC5H12→IC3H7•+C2H5• C2H5CYC 6H11→CYC 6CH2•+CH3• H•+NC5H12→H2+C3H6+C2H5• H•+NC5H12→H2+C4H8+CH3• IC3H7•+NC5H12→C3H8+C3H6+C2H5• IC3H7•+NC5H12→C3H8+NC4H8+CH3• H•+IC5H12→H2+IC4H8+CH3• H•+IC5H12→H2+C2H4+IC3H7• IC5H12+IC3H7•→C3H8+IC4H8+CH3• IC3H7•+IC5H12→C3H8+C2H4+IC3H7• H•+NC5H10→H2+C4H6+CH3• CH3•+NC5H10→CH4+C4H6+CH3• CH2CHCH2•+NC5H10→C3H6+C4H6+CH3• C2H5•+NC5H10→C2H6+C4H6+CH3• IC3H7•+NC5H10→C3H8+C4H6+CH3• H•+C2H5CYC 6H11→H2+C2H4+CYC6H11• IC3H7•+C2H5CYC6H11→C3H8+C2H4+CYC6H11•
NC5H10→C3H6+C2H4 NC5H10→CH4+C4H6
5 36 22 41 28 574 378 328 216 154 154 88 88
5×10
16
81.0
1×10
17
81.0
1×10
17
83.5
5×10
16
80.0
5×10
16
81.0
4×10
8
12.2
2×10
8
12.2
4×10
8
12.2
2×10
8
12.2
1×10
8
9.0
2×10
8
12.2
1×10
8
10.0
2×10
8
12.2 6
10
4.47×10
10
1×10
11
9.5
2×10
11
11.0
2×10
11
11.2
2×10
11
12.2
3×10
8
13.5
3×10
8
10 110 80 98 56 11 8
5.2
14.5
9.12×10
12
15.0
9.12×10
13
13.0
As shown in Table 1, the ECCR network consists of 4694 reactions, 93 molecules and 49 radicals. Reactions corresponding to subcategory 0 are obtained from the RMG software, representing the pyrolysis of light hydrocarbons. The reactions in the heavy hydrocarbon network can be sorted into 5 categories and 22 subcategories. The subcategories 15, 613, 1418, 1920 and 2122 respectively correspond to the unimolecular decomposition of C-C bonds, H-abstraction reactions of alkyl radicals, H-abstraction reactions of olefins, Habstraction reactions of naphthenes, and retro-Diels-Alder reactions.
2.3 Reaction network characterization using sub-network reconstruction The ECCR network is quite complicated as a result of the interactions between the products generated by the cracking of various feedstocks (Froment et al., 1976). The NFAA method proposed by Fang et al. (2016) can be applied to rationalize and visualize the unstructured reaction network. Initially, the reaction network is transformed into a petri-net (Koch, 2010), such that both the reactions and species can be considered as nodes in the network. Inspired by the PageRank algorithm, rank value initialization is used to extract information from the feedstock, while the transfer matrix employed for rank value iteration is determined from the weighted averages of the actual reaction rates in the tubular reactor. Then the rank value can be obtained after convergence of the iteration. The importance of each node can be represented by the convergent rank value, which integrates specific information related to the reactions and feedstock compositions. For further profiling of co-cracking mechanism, a
reaction network characterization method using sub-network reconstruction is introduced and shown in Fig. 2.
Fig. 2. Process of NFAA method and sub-network reconstruction characterization The NFAA is able to perform the entire network analysis for the ECR, which is composed of 142 substances and 4694 reactions, but does not provide an understanding of the specific effects of adding a second feedstock (such as ethane) to the naphtha. The proposed reaction network characterization method introduces a multiple sub-network reconstruction (MSNR) process to amplify the key component interactions. The reconstruction process is implemented in three steps, as detailed below. Step 1 (Redistribution): The rate information of reactions in the transfer matrix is recorded, after which the sub-network graph is reconstructed by deleting the reaction nodes. The substance nodes are connected with the weight using the sum of related reaction rates. The
initial value is reassigned using the feedstock composition and the rank values in the subnetwork are updated until the re-iteration of the PageRank algorithm is convergent. Step 2 (Autofocusing): Interactions are picked up based on the contact of key components in the sub-network. The transfer matrix is reconstructed using the autofocused interactions as a vector and the mass flow direction is recorded based on the sign of the rank value. Step 3 (Refining): The key interactions to be studied are refined. These interactions in the ECCR networks for different feedstock mixtures are compared and the evolving trends exhibited by product yields in the in-tube reaction model are analyzed. The evolution of the sub-network in the MSNR process is shown graphically in Fig. 3, using C2H5• as an example. The changes in the cracking mechanism after adding another feedstock can be visualized by plotting the sub-network using Gephi and analyzing the reactions related to key interactions.
Fig. 3. The evolution of the ECCR network as determined using the MSNR method. 2.4 Backtracking reaction mechanism using transfer matrix reconstruction calculations Data regarding the evolution of key interactions, as shown in Fig. 3, are insufficient to allow all EcSOS software users to understand the reaction mechanism evolving in the ECCR network. For a process engineer user (Billa et al., 2017), it is more helpful to provide rate fluctuation trends for specific reactions or reaction subcategories, since such data are more intuitive and understandable. Thus, after extracting the key interactions, a backtracking process is proposed to ascertain the related reaction rates of the interactions. A clear numerical meaning can be obtained from calculations involving the transfer matrix during the sub-network reconstruction. In the redistribution step, the conversion of substances and the reaction mix matrix to the substance transfer matrix can be described as:
S (i, j )
4836
(min( M (i, k ) , M (k , j ) )) , i, j 1, ..., 142
(2)
k 143
where
S (i, j )
is an element in the substance connection matrix;
reaction mix transfer matrix. If neither convert substance i to substance
j
M (i, k )
nor
M (k , j )
M (i, k )
element in substance-
is equal to 0, reaction k will
in the reaction network. The total rate of this kind of
conversion can be calculated by adding the related reactions. The mass flow between two substance nodes may be bidirectional because both of them can serve as reactant and resultant in the network. Thus, an actual mass flow rate transfer matrix is introduced:
A(i, j ) max( S (i, j ) S ( j, i ),0) , i, j 1, ..., 142
(3)
As mentioned in equation 2,
S (i, j )
is the total reaction rate from substance i to substance
The actual mass flow rate matrix A only records the positive value S (i, j ) S ( j, i )
is positive), and the negative
S (i, j ) S ( j, i )
A(i, j )
is filled in
j.
(when the value of
A( j, i )
after taking the
absolute value. Thus, it can be used as transfer matrix of sub-network reconstructed in redistribution step. Autofocusing of the key component in the sub-network can be implemented by searching the transfer matrix row and column vectors as: T
i, ki ( j ) AT ( j, i) A( j, i) , j 1, ..., 142 T
ki ( j )
(4)
is a row vector representing the mass flow rates and directions of a specific substance
i . AT ( j, i ) exhibits all interactions with substance i as mass flow source and A( j, i ) exhibits
all interactions with substance i as mass flow target. Thus, the mass flow direction can be T
recorded by sign of ki ( j ) . T
All non-zero components j in ki ( j ) are gathered into a set that collects all substances having a mass flow interaction with substance i . A refining process selects the important nodes in the substance set, after which the node numbers to be studied are entered and the backtracking process identifies all reactions between two selected species in the reaction network. This is accomplished using the original transfer matrix, which records the topology and rate weights of the reaction network. As an example, the backtracking process of the example reactions involving the conversion of C2H6 to C2H5• are shown in Fig. 4.
Fig. 4. The backtracking process for the conversion of C2H6 to C2H5• using the transfer matrix.
As a whole, the proposed ingenious characterization of reaction networks using sub-network reconstruction is able to generate a sub-network with the interactions between substances in a clear and understandable manner. The sub-network reconstruction process is inspired by the meaning of PageRank algorithm. Using the mass flow rate as the transfer matrix to iterate the rank value (the importance of the node) is interpretable. If more information (mass) flow into a node, the rank value of the node is higher and the yields of corresponding nodes are also increased. The sub-network displays the intensity of substance interactions by direct connection between substance nodes instead of indirect linking through reactions in the NFAA, such that key interactions are easier to discover and the sub-network is more concise. Thus, the sub-network reconstruction algorithm is better suited to analysis of the evolution of the ECCR mechanism as compared with the NFAA method. It is also more extendable and can be applied to other reaction network characterization tasks.
3. Results and discussion 3.1 Industrial case data input An ethylene plant in the northeast of China was selected as the industrial test case for this study. In this plant, the feedstock was cracked in a Stone & Webster Ultra-Selective Cracking (USC) furnace. The properties of the feedstock, the operational conditions in the tubular reactor, and the firing conditions in firebox are provided in Table A1. After the naphtha feedstock molecular composition was determined, the mole fractions of mixtures were normalized after adding different ratios of ethane. Subsequently, the product yield information was obtained via a coupled simulation using the in-tube reaction and firebox heat transfer models. Simultaneously, the corresponding reaction network and reaction rates were analyzed based on sub-network reconstruction characterization. 3.2 Software simulation result of product yield The ethane molar ratio in the feedstock was set at 10%, 20%, 30%, 40% or 50% and variations in the product yields from co-cracking were assessed. The separate cracking and different circumstances of co-cracking feedstock were simulated under equivalent conditions and the resulting product yields based on weight percentage are presented in Fig. 5. The values obtained for the product yield deviation (PYD), defined as the co-cracking yield minus the separate cracking yield obtained from an equal quantity of feedstock, are provided in Table 2.
Fig. 5. Detailed product yields of weight percentage when co-cracking and separate cracking Table 2. The evolutions of co-cracking PYD values with variations in the ethane molar ratio.
C2H4
Separate cracking yield/% Naphtha Ethane 30.4081 54.2732
10% 1.2822
Co-cracking PYD /% 20% 30% 40% 1.3672 1.5073 1.5893
50% 1.6388
CH4
16.6525
4.8973
0.9615
1.0983
1.2734
1.5505
1.4501
C3H6
15.3803
1.2429
-1.5020
-1.5261
-1.5571
-1.6509
-1.7509
C6H6
3.4504
0.0000
0.0596
0.0517
0.0680
0.0600
0.0629
H2
1.5823
4.4694
-0.6029
-0.6525
-0.7044
-0.6788
-0.6745
C7H8
2.8434
0.0000
-0.0036
0.0031
0.0355
0.0503
0.0909
C4H6
4.7481
4.2504
-0.3322
-0.5100
-0.6950
-0.8261
-1.0148
C2H6
1.4318
27.2122
0.4730
0.5097
0.6409
0.6840
0.7049
Product
The data in Fig. 5 and Table 2 demonstrate that the yields of some key products from cocracking deviate from the yields obtained from separate cracking using the same quantity of feedstock. With increases in the molar ratio of ethane, the ethylene PYD increases from 1.2822 to 1.6388, while the PYD values for propylene and butadiene decrease from -1.5020 to -1.7509 and from -0.3322 to -1.0148 respectively. With regard to the other high valueadded products, the yields of methane and ethane increase markedly, while the yield of hydrogen declines in conjunction with co-cracking. Finally, there are no obvious trends in the changes of the PYD values for benzene and toluene.
3.3 Simulation results explication using sub-network reconstruction characterization The sub-network reconstruction characterization method, as shown in Fig. 2, was applied when the EcSOS simulation finished, and reaction rates in each tube segment were generated. The MSNR analysis generated re-iterated PageRank values (RPRVs) in the redistribution step, and comparisons of the evolutions of the co-cracking PYD values and the RPRVs with changes in the ethane molar ratio are plotted in Fig. 6.
Fig. 6. Evolutions of co-cracking PYD values and RPRVs with changing ethane molar ratios for various products. As shown in Fig. 6, the RPRVs calculated by sub-network reconstruction characterization were in good agreement with the PYD values obtained from the EcSOS simulation. This consistency could be explained by the signification of RPRV in the concept of the PageRank algorithm. The PageRank values were determined from the information flowing into the node and, in the case of the ECCR, such values can be considered to indicate the mass quantity accumulated in a specific substance node of the substance network. The PYD values indicate the tendency to generate a specific product during the co-cracking process as compared with separate cracking, which can also be considered as the mass flow tendency of the corresponding node in the ECCR. The similar variational trends of the co-cracking PYD
values and RPRVs not only provide a mutual verification of the correctness of the simulation and network flow analysis results, but also help to characterize the co-cracking product distribution.
3.4 Interaction refining using sub-network reconstruction characterization The following reconstruction steps, autofocusing and refining, continued for deeper profiling of the ECCR. Three key radicals in the ethane reaction process, H•, CH3• and C2H5•, together with ethane itself, were selected as model species when studying the evolution of the radical mechanism during co-cracking. The variations in the key interactions after the refining step are shown in Fig. 7, in which the importance of each node is indicated by its size and color, and the intensity of each interaction is reflected in the thickness of the node connection. Values were assigned to the connections by summing the percentages of the rank values and the arrows beside each value show the evolution of the interaction intensity upon the addition of ethane. Specifically, these arrows represent the rate fluctuation trends of specific reactions, where the reactant is the initial node of the arrow and the product is the end node. These fluctuations can be regarded as equivalent to the slope of the product formation rate, which in turn can be estimated from the slope of the PYD. To allow a better understanding of the information conveyed by the arrows in Fig. 7, the related reactions in the entire network of connected nodes were backtracked, and key interactions and reaction rate fluctuation trends for example reactions were analyzed. The results are summarized in Table 3.
Fig. 7. The evolutions of key interactions during co-cracking.
Table 3. Reaction rate fluctuation trends for key interactions. Trend Strongly hindered
Hindered
Accelerated
Strongly accelerated
Subcategories 0 0 0 0 0 0 0 0 12 13 21 7 0 0 0 6 10 17 19
Example reaction H•+H•→H2 C3H5•+H•→C3H6 C4H5•+H•→C4H6 C3H5•+C2H6→C3H6+C2H5• C4H5•+C2H6→C4H6+C2H5• C2H6→CH3•CH3• C2H5•→C2H4+H• CH3•+C2H6→CH4+C2H5• C2H5•+IC9H20→C2H6+IC4H8+C2H4+NC3H7• C2H5•+IC9H20→C2H6+NC6H12+0.5*NC 3H7•+0.5*IC3H7• C2H5•+NC10H20→C2H6+C4H6+C2H4+NC4H9• C2H5•+C4H9CYC6H11→C2H6+2*C2H4+CYC6H11• H•+CH3•→CH4 C6H5•+C2H6→C6H6+C2H5• C2H3•+C2H6→C2H4+C2H5• C2H5•+NC10H22→C2H6+NC7H14+NC3H7• H•+IC5H12→H2+IC4H8+CH3• C2H5•+NC5H10→C2H6+C4H6+CH3• H•+C2H5CYC6H11→H2+C2H4+CYC6H11•
These interactions were all selected from the important connections (as indicated by thick purple lines) in Fig. 7 and are essentially in agreement with the interaction fluctuation trends shown by the arrows in this same figure. To allow a systematic analysis of the reactions involved with the co-cracking process, the mechanism evolution diagram is summarized in Fig. 8.
Fig. 8. The evolution of key reaction rates during co-cracking.
As shown in Fig. 8, C2H6 was more likely to react with hydrocarbon radicals than to undergo self-decomposition. The rates of the H-abstraction reactions between C2H6 and hydrocarbon radicals (R•) were increased significantly, such that a large quantity of C2H5• was generated. The C2H5• radicals also preferentially reacted with hydrocarbons (R), especially long-chain
alkanes, as opposed to undergoing self-decomposition. The H-abstraction reaction process with the participation of C2H6 and C2H5• produced more C2H4 during co-cracking, although the conversion of C2H6 was reduced because more C2H6 was generated. As a result of the high proportion of alkanes in naphtha, H• radicals tended to promote the pyrolysis of R species to generate CH3• and C2H4. As more CH3• was produced during co-cracking, the yield of CH4 was increased. However, as H• was consumed by other reaction routes, the production of H2 was reduced. Some major routes for the generation of C3H6 and C4H6 were inhibited as a result of competitive reactions consuming H• and C2H6. In this case, C3H5• and C4H5• were more likely to convert to other products. The proposed network characterization process using sub-network reconstruction has the potential to be applied to the analysis of other reaction networks. The matrix operation can be readily transplanted and the use of PageRank to assess inflow information or mass is applicable to most networks. The sub-network reconstruction method should assist engineering users in understanding reaction mechanisms by elucidating a specific subnetwork in a step-wise manner and backtracking the rate fluctuation trends of related reactions or reaction subcategories.
4. Conclusions The evolutions of the mechanisms involved in the co-cracking reaction network were elucidated using the proposed sub-network reconstruction characterization method. The newly-added MSNR module effectively searched for key components and interactions in the co-cracking process and the results from the mechanism analysis were verified by comparison to experimental data in the literature.
Variations in the yields of the primary co-cracking products could be obtained from the EcSOS software. The accuracy of co-cracking furnace simulation process and the subnetwork reconstruction characterization process were demonstrated by each other. This entire method could potentially be applied to the analysis of other cracking processes and, with proper reactor models and kinetic parameters, this characterization system may also be applicable to other reaction networks. Reaction network analysis involving quantification and visualization is expected to assist petrochemical enterprises in obtaining more comprehensive understandings of their processes. The ability to accurately profile various processes should result in reliable control and optimization, thus increasing profit margins.
CRediT author statement Kexin Bi: Conceptualization, Methodology, Software, Validation, Writing - Original Draft, Writing Review & Editing. Chen Zhang: Visualization, Investigation, Validation, Writing - Review & Editing. Tong Qiu: Conceptualization, Formal analysis, Visualization, Investigation, Supervision, Validation, Writing - Review & Editing.
Declarations of interest None.
Acknowledgements The authors gratefully acknowledge the National Natural Science Foundation of China for its financial support (Grant No. U1462206).
Declarations of interest None.
Nomenclature The following is the nomenclature used in the manuscript: Reaction network analysis methods network flow analysis algorithm convolutional neural networks multiple sub-network reconstruction Key variables element in substance-reaction mix transfer matrix element in substance connection matrix element in actual mass flow rate matrix ⃗⃗⃗
element in autofocused row vector product yield deviation re-iterated PageRank value
Key substances hydrogen free radical methyl free radical ethyl free radical free radicals responsible for propylene formation free radicals responsible for butadiene formation hydrocarbon radicals Hydrocarbons Hydrogen Methane Ethane Propylene
Butadiene Ethylene Benzene Toluene Others Ethylene cracker Simulation and Optimization System three-dimensional adjusted Monte Carlo integral method Stone & Webster Ultra-Selective Cracking
Appendix Table A1. Industrial case data input for EcSOS simulations.
Feedstock reconstruction
In-tube reaction (single furnace)
Firebox model
EcSOS user input Average molecular weight (amu) Hydrogen-carbon molar ratio (mol/mol) Specific density ASTM D86 boiling points (K) IBP 10% 30% 50% 70% 90% FBP PIONA (wt%) P I O N A Number of reactor tubes Inlet tube diameter (m) Outlet tube diameter (m) Hydrocarbon flow rate (t/h) Steam dilution (kg/kg) Coil inlet temperature (K) Coil outlet pressure (kPa) Length (m) Width (m) Height (m) Number of burners Emissivity of side wall Emissivity of tube skin Fuel gas flow rate (kg/s) Flame height (m)
106.29 2.09 0.7314 317.0 359.7 373.1 389.6 410.3 444.8 469.7 43.08 20.28 0.09 34.23 5.32 22 0.045 0.055 54.7 0.5 893.2 144 3.0 24.9 11.6 4 0.7 0.6 3.6 5.0
Heat transfer coefficient between furnace and tube wall (W/(m2·K))
10
Convective coefficient on tube wall (W/(m2·K))
180
Air and fuel gas inlet temperature (K) Fuel composition (wt%) CH4
298.2
H2
2.5
97.5
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An Ingenious Characterization of Reaction Network Using Sub-network Reconstruction Kexin Bi , Chen Zhang , Tong Qiu PII: DOI: Reference:
S0098-1354(19)31050-6 https://doi.org/10.1016/j.compchemeng.2019.106695 CACE 106695
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
9 October 2019 30 November 2019 21 December 2019
Please cite this article as: Kexin Bi , Chen Zhang , Tong Qiu , An Ingenious Characterization of Reaction Network Using Sub-network Reconstruction, Computers and Chemical Engineering (2019), doi: https://doi.org/10.1016/j.compchemeng.2019.106695
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Highlights:
An ingenious reaction network characterization method is proposed. A novel sub-network reconstruction method is applied to elucidate co-cracking mechanisms. Graph visualization of sub-network helps understand reaction mechanisms. The whole process can be applied to other reaction networks with proper kinetics.
An Ingenious Characterization of Reaction Network Using Sub-network Reconstruction Kexin Bi, Chen Zhang, Tong Qiu* Department of Chemical Engineering, Tsinghua University, Beijing 100084, China Beijing Key Laboratory of Industrial Big Data Systems and Applications, Tsinghua University, Beijing 100084, China *
Corresponding author’s e-mail: [email protected]
Abstract Reaction network model is essential for reactor simulation and kinetic profiling of a complex process. Comprehensive and valid proofs of network mechanism are usually lacking among experimental and simulation studies of complicated reaction process, such as ethylene furnace co-cracking. In this paper, a self-developed Ethylene cracker Simulation and Optimization System (EcSOS) software is applied for co-cracking process numerical simulation and an ingenious characterization method of reaction network is proposed for visualization and deep profiling of the radical reaction network. An effective sub-network reconstruction process is implemented by connecting the substance nodes using actual mass flow and refining key interactions. The product yield evolving trend in simulation and its reason was successfully explained by the reaction network analysis results. The radical reaction mechanism changing obtained by reaction backtracking was systematically sorted out and summarized.
Keywords:
reaction
network
characterization,
sub-network reconstruction,
EcSOS,
mechanism visualization
1. Introduction Ethylene is one of the most important products within the petrochemical industry, and China currently has the world’s second highest ethylene production capacity with an annual production in 2018 of approximately 18.41 million tons (NBSPRC, 2019). As the number of ethylene enterprises has increased and the scale of ethylene plant has expanded in China, there has been an increasingly serious shortage of cracking feedstock (Zhang et al., 2017). Diversification of feedstock sources and efficiency of feedstock utilization have therefore gradually become key factors in improving the profit margins of ethylene enterprises (Zhao et al., 2017). Simulation tools and software packages such as SPYRO (Goethem et al., 2001), CRACKER (Joo et al., 2000) and VMGSim (Virtual Materials Group, Inc., 2011) have been developed to allow calculation of the yields obtainable from different feedstocks. This has assisted in improving the product quality and increasing profit margins by optimization of feedstock allocation. These simulation and optimization processes all involve reaction network models as a fundamental element, to connect the molecular composition of the feedstock to the product distribution (Fakhroleslam and Sadrameli, 2019). The ethylene cracking reaction (ECR) network has received particular attention from engineers and researchers in recent years. To effectively model the complex reaction process in a cracking furnace, effective
characterization and visualization of the ECR network is required. Joo et al. (2001) applied sensitivity analysis and eigenvalue-eigenvector decomposition to the evaluation of the importance of various mechanisms, with the aim of generating a reduced reaction mechanism set. Fang et al. (2016) first introduced PageRank algorithm (Page et al., 1999) into network flow analysis algorithm (NFAA) and proposed an integrated network ranking and visualization method for analysis of an ECR network. Hua et al. (2018) used a feature mining process based on motif detection and demonstrated the feasibility of this approach via a convolutional neural networks (CNN) performance evaluation. This same work also implemented the visualization of the substrate network graph topology extracted by the NFAA in naphtha pyrolysis free radical network using the Gephi software package (Bastian and Heymann, 2009). The application of the NFAA has had a significant impact on our understanding of the reaction process and in improving the reaction networks in ethylene cracking furnaces. This, in turn, assists in enhancing the interpretation and overall performance of simulation models. Nevertheless, there are different types of users for the industrial reactor kinetic model of ethylene thermal cracking (Billa et al., 2017), and further research is required to ensure a comprehensive, in-depth understanding of various aspects of such processes. The remaining challenges include (i) visualization of the reaction model; (ii) understanding variations in the reaction mechanism when using different types of feedstock; and (iii) developing easy-tounderstand mechanism outputs. for further improvement of ethylene cracking software, the network characterization model should not only provide a general cognition of the ECR
network, but it also needs to be able to trace the importance reactions and key interactions between reactant and resultant. In this work, the co-cracking process in ethylene thermal cracking, which is widely employed to compensate for the shortage of traditional feedstocks such as naphtha (Khatib, 2014), is selected as an industrial case because the mechanism of this process is not fully revealed. The superposition of the reaction schemes for single-component cracking (Sundaram and Froment, 1978) and the interaction between the products of the cracking feedstock (Froment et al., 1976) are considered as the theoretical basis of the co-cracking process. Studies based on experimental work and simulations have produced varying results and hypotheses. Plehiers and Froment (1987) previously performed experimental work based on the cocracking of ethane and naphtha in a pilot plant and concluded that ethane cracking is strongly inhibited by the unsaturated reaction products of the naphtha. Belohlav et al. (2003) proposed a molecular reaction model for a thermal cracking plant and demonstrated the reliability of the optimized model in trials involving the co-cracking of mixtures of primary naphtha with alkenes. Yuan et al. (2016) performed simulations of the co-cracking of ethane and propane as well as liquefied petroleum gas and naphtha mixtures using software packages based on free-radical reaction mechanisms with a one-dimensional reactor model. Their group reported the effects of the mixing ratio, coil outlet temperature and pressure on the yields of some key products. However, specific and validated researches on the reaction network mechanism of co-cracking process are scarce and very incomplete, which has hindered our understanding of the manner in which various interactions affect the overall cracking kinetics and the product distributions when changing feedstocks.
With the aim of developing software that could potentially be employed by different types of users, we proposed an ingenious characterization of reaction network using sub-network reconstruction to that first profiled the co-cracking reaction mechanism systematically. In the present study, a software package of our own design, termed the Ethylene cracker Simulation and Optimization System (EcSOS) (Fang et al., 2017), was used as a simulation tool to calculate the distribution of pyrolysis products during the cracking of different feedstock mixtures. The corresponding free-radical reaction network in the software was subsequently analyzed by a novel characterization method and visualized using the Gephi software package. A sub-network reconstruction method was introduced in NFAA post-processing step and then the key information in the extracted sub-network was compared to ascertain the co-cracking reaction mechanism by backtracking the evolution of radical reaction rate. Based on current industrial practices, we used the co-cracking of ethane and naphtha as a test case.
2. Methods 2.1 EcSOS Software introduction EcSOS is an ethylene cracking process simulation and optimization software jointly developed by Petrochina and the Department of Chemical Engineering, Tsinghua University. The main function of the software is to convert feedstock input data into user-required output data such as product yield. For the purposes of studying the co-cracking mechanism, three fundamental models in the software were selected, as shown in Fig. 1.
Fig. 1. An architecture and function diagram showing the co-cracking models in the EcSOS.
When evaluating the co-cracking of ethane and naphtha, the software adopts a novel naphtha molecular reconstruction process (Bi and Qiu, 2019) to calculate the composition of a specific naphtha feedstock. The effective probability density functions of different homologues are constructed inspired by Seasonal-Trend decomposition (Cleveland et al., 1990), combining the basic gamma distribution, self-adaptive regional features, and uncertainty. The cloud model (Li et al., 2009) is employed for uncertainty addition of the distribution and a hybrid genetic algorithm-particle swarm optimization algorithm is selected
for parameter optimization of probability density functions. For practical industrial applications, the features of naphtha sample are considered by predetermined regional database and feedstock source. Then naphtha composition is converted into mole fraction and normalized after the addition of ethane. An in-tube reaction model is implemented to calculate detailed product information and the reactor state. The tubular reactor is divided into several segments and Gear’s method (Gear and Petzold, 1984) is applied in each segment to solve the ordinary differential equations for mass balance, momentum balance and heat balance, which are set as:
dN m S dt vim ri in dL dL i qv
vim ri
, i 1, ..., N R , m 1, ..., N S
i
f qm dP , m 1, ..., N S dL 5.07 104 Din 2
(1)
dN m dT dL , m 1, ..., N S dL mC pm N m C pH 2O N H 2O q Do dt mH 0fm
where
is the concentration of species m in the reaction tube;
residence time of pyrolysis gas in this micro-segment; species m in reaction i; gas;
flow area of the in-tube reactor;
reaction rate of reaction i;
pressure in the reaction tube; the tube segment; reactor; firebox; species m;
total number of reactions;
Fanning friction factor;
volume flow rate of pyrolysis total number of species;
inner diameter of the in-tube
temperature in the reaction tube;
outer diameter of the in-tube reactor;
heat flux from the
standard enthalpy of formation of
heat capacity of species m at constant pressure;
constant pressure; and
stoichiometric coefficient of
equivalent conversion coefficient of
mass flow rate of pyrolysis gas;
density of pyrolysis gas;
length of the reaction tube;
heat capacity of water at
concentration of water in the reaction tube.
In this model, reaction information including reaction equations and corresponding kinetic parameters is predetermined as a reaction network file. The other parameters in equation (1) can be obtained by feedstock composition, reactor geometry and operation condition except the heat flux from the firebox q. For this reason, a firebox heat transfer model was developed to calculate the heat flux from the firebox to the tubular reactor as well as the temperature field in the firebox. An adjusted Monte Carlo integral (AMCI) method (Zhou and Qiu, 2015) using a three-dimensional (3D) zone model is adopted in this software to solve energy balance problems. The coefficients for the heat transfer process are predetermined and the temperature distribution in the tubular reactor is read from an in-tube reaction model. The firebox geometry and firing conditions are obtained from a user interface, after which the heat flux can be calculated and updated in the in-tube reaction model. After the convergence of the coupled iterative process involving the in-tube reaction and firebox heat transfer models, the software will automatically generate a report of calculation results.
2.2 Automatic generation of a co-cracking reaction network In the in-tube reaction model within the software, the predetermined reaction information is integrated into a reaction network. The entire reaction network of naphtha consists of two parts: a light hydrocarbon network generated by the RMG open source software package (Gao et al., 2016) and a heavy hydrocarbon network based on a free radical mechanism involving compounds with more than four carbon atoms. The light hydrocarbon network employs the same kinetic parameters as the RMG software, while the kinetic parameters
associated with the heavy hydrocarbon network are obtained from several previous literature publications (Dente et al., 2010, 2007; Ranzi et al., 2001). The specific reaction network composition and kinetic parameters are provided in Table 1. The reaction network of ethane is incorporated in the auto-generated naphtha network, so that the ethylene co-cracking reaction (ECCR) network should be equivalent to the naphtha network according to the superposition rule of the reaction schemes (Sundaram and Froment, 1978). Table 1. The specific reaction network composition and kinetic parameters. Subcategories
Example reaction
Quantity
A(1/s)
E(kcal/mol)
0
CH3•+C2H6→C2H5•+CH4
2189
/
/
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
NC6H14→2C3H7• NC6H14→C2H5•+NC4H9• NC6H14→CH3•+C2H4+NC3H7• IC5H12→IC3H7•+C2H5• C2H5CYC 6H11→CYC 6CH2•+CH3• H•+NC5H12→H2+C3H6+C2H5• H•+NC5H12→H2+C4H8+CH3• IC3H7•+NC5H12→C3H8+C3H6+C2H5• IC3H7•+NC5H12→C3H8+NC4H8+CH3• H•+IC5H12→H2+IC4H8+CH3• H•+IC5H12→H2+C2H4+IC3H7• IC5H12+IC3H7•→C3H8+IC4H8+CH3• IC3H7•+IC5H12→C3H8+C2H4+IC3H7• H•+NC5H10→H2+C4H6+CH3• CH3•+NC5H10→CH4+C4H6+CH3• CH2CHCH2•+NC5H10→C3H6+C4H6+CH3• C2H5•+NC5H10→C2H6+C4H6+CH3• IC3H7•+NC5H10→C3H8+C4H6+CH3• H•+C2H5CYC 6H11→H2+C2H4+CYC6H11• IC3H7•+C2H5CYC6H11→C3H8+C2H4+CYC6H11•
NC5H10→C3H6+C2H4 NC5H10→CH4+C4H6
5 36 22 41 28 574 378 328 216 154 154 88 88
5×10
16
81.0
1×10
17
81.0
1×10
17
83.5
5×10
16
80.0
5×10
16
81.0
4×10
8
12.2
2×10
8
12.2
4×10
8
12.2
2×10
8
12.2
1×10
8
9.0
2×10
8
12.2
1×10
8
10.0
2×10
8
12.2 6
10
4.47×10
10
1×10
11
9.5
2×10
11
11.0
2×10
11
11.2
2×10
11
12.2
3×10
8
13.5
3×10
8
10 110 80 98 56 11 8
5.2
14.5
9.12×10
12
15.0
9.12×10
13
13.0
As shown in Table 1, the ECCR network consists of 4694 reactions, 93 molecules and 49 radicals. Reactions corresponding to subcategory 0 are obtained from the RMG software, representing the pyrolysis of light hydrocarbons. The reactions in the heavy hydrocarbon network can be sorted into 5 categories and 22 subcategories. The subcategories 15, 613, 1418, 1920 and 2122 respectively correspond to the unimolecular decomposition of C-C bonds, H-abstraction reactions of alkyl radicals, H-abstraction reactions of olefins, Habstraction reactions of naphthenes, and retro-Diels-Alder reactions.
2.3 Reaction network characterization using sub-network reconstruction The ECCR network is quite complicated as a result of the interactions between the products generated by the cracking of various feedstocks (Froment et al., 1976). The NFAA method proposed by Fang et al. (2016) can be applied to rationalize and visualize the unstructured reaction network. Initially, the reaction network is transformed into a petri-net (Koch, 2010), such that both the reactions and species can be considered as nodes in the network. Inspired by the PageRank algorithm, rank value initialization is used to extract information from the feedstock, while the transfer matrix employed for rank value iteration is determined from the weighted averages of the actual reaction rates in the tubular reactor. Then the rank value can be obtained after convergence of the iteration. The importance of each node can be represented by the convergent rank value, which integrates specific information related to the reactions and feedstock compositions. For further profiling of co-cracking mechanism, a
reaction network characterization method using sub-network reconstruction is introduced and shown in Fig. 2.
Fig. 2. Process of NFAA method and sub-network reconstruction characterization The NFAA is able to perform the entire network analysis for the ECR, which is composed of 142 substances and 4694 reactions, but does not provide an understanding of the specific effects of adding a second feedstock (such as ethane) to the naphtha. The proposed reaction network characterization method introduces a multiple sub-network reconstruction (MSNR) process to amplify the key component interactions. The reconstruction process is implemented in three steps, as detailed below. Step 1 (Redistribution): The rate information of reactions in the transfer matrix is recorded, after which the sub-network graph is reconstructed by deleting the reaction nodes. The substance nodes are connected with the weight using the sum of related reaction rates. The
initial value is reassigned using the feedstock composition and the rank values in the subnetwork are updated until the re-iteration of the PageRank algorithm is convergent. Step 2 (Autofocusing): Interactions are picked up based on the contact of key components in the sub-network. The transfer matrix is reconstructed using the autofocused interactions as a vector and the mass flow direction is recorded based on the sign of the rank value. Step 3 (Refining): The key interactions to be studied are refined. These interactions in the ECCR networks for different feedstock mixtures are compared and the evolving trends exhibited by product yields in the in-tube reaction model are analyzed. The evolution of the sub-network in the MSNR process is shown graphically in Fig. 3, using C2H5• as an example. The changes in the cracking mechanism after adding another feedstock can be visualized by plotting the sub-network using Gephi and analyzing the reactions related to key interactions.
Fig. 3. The evolution of the ECCR network as determined using the MSNR method. 2.4 Backtracking reaction mechanism using transfer matrix reconstruction calculations Data regarding the evolution of key interactions, as shown in Fig. 3, are insufficient to allow all EcSOS software users to understand the reaction mechanism evolving in the ECCR network. For a process engineer user (Billa et al., 2017), it is more helpful to provide rate fluctuation trends for specific reactions or reaction subcategories, since such data are more intuitive and understandable. Thus, after extracting the key interactions, a backtracking process is proposed to ascertain the related reaction rates of the interactions. A clear numerical meaning can be obtained from calculations involving the transfer matrix during the sub-network reconstruction. In the redistribution step, the conversion of substances and the reaction mix matrix to the substance transfer matrix can be described as:
S (i, j )
4836
(min( M (i, k ) , M (k , j ) )) , i, j 1, ..., 142
(2)
k 143
where
S (i, j )
is an element in the substance connection matrix;
reaction mix transfer matrix. If neither convert substance i to substance
j
M (i, k )
nor
M (k , j )
M (i, k )
element in substance-
is equal to 0, reaction k will
in the reaction network. The total rate of this kind of
conversion can be calculated by adding the related reactions. The mass flow between two substance nodes may be bidirectional because both of them can serve as reactant and resultant in the network. Thus, an actual mass flow rate transfer matrix is introduced:
A(i, j ) max( S (i, j ) S ( j, i ),0) , i, j 1, ..., 142
(3)
As mentioned in equation 2,
S (i, j )
is the total reaction rate from substance i to substance
The actual mass flow rate matrix A only records the positive value S (i, j ) S ( j, i )
is positive), and the negative
S (i, j ) S ( j, i )
A(i, j )
is filled in
j.
(when the value of
A( j, i )
after taking the
absolute value. Thus, it can be used as transfer matrix of sub-network reconstructed in redistribution step. Autofocusing of the key component in the sub-network can be implemented by searching the transfer matrix row and column vectors as: T
i, ki ( j ) AT ( j, i) A( j, i) , j 1, ..., 142 T
ki ( j )
(4)
is a row vector representing the mass flow rates and directions of a specific substance
i . AT ( j, i ) exhibits all interactions with substance i as mass flow source and A( j, i ) exhibits
all interactions with substance i as mass flow target. Thus, the mass flow direction can be T
recorded by sign of ki ( j ) . T
All non-zero components j in ki ( j ) are gathered into a set that collects all substances having a mass flow interaction with substance i . A refining process selects the important nodes in the substance set, after which the node numbers to be studied are entered and the backtracking process identifies all reactions between two selected species in the reaction network. This is accomplished using the original transfer matrix, which records the topology and rate weights of the reaction network. As an example, the backtracking process of the example reactions involving the conversion of C2H6 to C2H5• are shown in Fig. 4.
Fig. 4. The backtracking process for the conversion of C2H6 to C2H5• using the transfer matrix.
As a whole, the proposed ingenious characterization of reaction networks using sub-network reconstruction is able to generate a sub-network with the interactions between substances in a clear and understandable manner. The sub-network reconstruction process is inspired by the meaning of PageRank algorithm. Using the mass flow rate as the transfer matrix to iterate the rank value (the importance of the node) is interpretable. If more information (mass) flow into a node, the rank value of the node is higher and the yields of corresponding nodes are also increased. The sub-network displays the intensity of substance interactions by direct connection between substance nodes instead of indirect linking through reactions in the NFAA, such that key interactions are easier to discover and the sub-network is more concise. Thus, the sub-network reconstruction algorithm is better suited to analysis of the evolution of the ECCR mechanism as compared with the NFAA method. It is also more extendable and can be applied to other reaction network characterization tasks.
3. Results and discussion 3.1 Industrial case data input An ethylene plant in the northeast of China was selected as the industrial test case for this study. In this plant, the feedstock was cracked in a Stone & Webster Ultra-Selective Cracking (USC) furnace. The properties of the feedstock, the operational conditions in the tubular reactor, and the firing conditions in firebox are provided in Table A1. After the naphtha feedstock molecular composition was determined, the mole fractions of mixtures were normalized after adding different ratios of ethane. Subsequently, the product yield information was obtained via a coupled simulation using the in-tube reaction and firebox heat transfer models. Simultaneously, the corresponding reaction network and reaction rates were analyzed based on sub-network reconstruction characterization. 3.2 Software simulation result of product yield The ethane molar ratio in the feedstock was set at 10%, 20%, 30%, 40% or 50% and variations in the product yields from co-cracking were assessed. The separate cracking and different circumstances of co-cracking feedstock were simulated under equivalent conditions and the resulting product yields based on weight percentage are presented in Fig. 5. The values obtained for the product yield deviation (PYD), defined as the co-cracking yield minus the separate cracking yield obtained from an equal quantity of feedstock, are provided in Table 2.
Fig. 5. Detailed product yields of weight percentage when co-cracking and separate cracking Table 2. The evolutions of co-cracking PYD values with variations in the ethane molar ratio.
C2H4
Separate cracking yield/% Naphtha Ethane 30.4081 54.2732
10% 1.2822
Co-cracking PYD /% 20% 30% 40% 1.3672 1.5073 1.5893
50% 1.6388
CH4
16.6525
4.8973
0.9615
1.0983
1.2734
1.5505
1.4501
C3H6
15.3803
1.2429
-1.5020
-1.5261
-1.5571
-1.6509
-1.7509
C6H6
3.4504
0.0000
0.0596
0.0517
0.0680
0.0600
0.0629
H2
1.5823
4.4694
-0.6029
-0.6525
-0.7044
-0.6788
-0.6745
C7H8
2.8434
0.0000
-0.0036
0.0031
0.0355
0.0503
0.0909
C4H6
4.7481
4.2504
-0.3322
-0.5100
-0.6950
-0.8261
-1.0148
C2H6
1.4318
27.2122
0.4730
0.5097
0.6409
0.6840
0.7049
Product
The data in Fig. 5 and Table 2 demonstrate that the yields of some key products from cocracking deviate from the yields obtained from separate cracking using the same quantity of feedstock. With increases in the molar ratio of ethane, the ethylene PYD increases from 1.2822 to 1.6388, while the PYD values for propylene and butadiene decrease from -1.5020 to -1.7509 and from -0.3322 to -1.0148 respectively. With regard to the other high valueadded products, the yields of methane and ethane increase markedly, while the yield of hydrogen declines in conjunction with co-cracking. Finally, there are no obvious trends in the changes of the PYD values for benzene and toluene.
3.3 Simulation results explication using sub-network reconstruction characterization The sub-network reconstruction characterization method, as shown in Fig. 2, was applied when the EcSOS simulation finished, and reaction rates in each tube segment were generated. The MSNR analysis generated re-iterated PageRank values (RPRVs) in the redistribution step, and comparisons of the evolutions of the co-cracking PYD values and the RPRVs with changes in the ethane molar ratio are plotted in Fig. 6.
Fig. 6. Evolutions of co-cracking PYD values and RPRVs with changing ethane molar ratios for various products. As shown in Fig. 6, the RPRVs calculated by sub-network reconstruction characterization were in good agreement with the PYD values obtained from the EcSOS simulation. This consistency could be explained by the signification of RPRV in the concept of the PageRank algorithm. The PageRank values were determined from the information flowing into the node and, in the case of the ECCR, such values can be considered to indicate the mass quantity accumulated in a specific substance node of the substance network. The PYD values indicate the tendency to generate a specific product during the co-cracking process as compared with separate cracking, which can also be considered as the mass flow tendency of the corresponding node in the ECCR. The similar variational trends of the co-cracking PYD
values and RPRVs not only provide a mutual verification of the correctness of the simulation and network flow analysis results, but also help to characterize the co-cracking product distribution.
3.4 Interaction refining using sub-network reconstruction characterization The following reconstruction steps, autofocusing and refining, continued for deeper profiling of the ECCR. Three key radicals in the ethane reaction process, H•, CH3• and C2H5•, together with ethane itself, were selected as model species when studying the evolution of the radical mechanism during co-cracking. The variations in the key interactions after the refining step are shown in Fig. 7, in which the importance of each node is indicated by its size and color, and the intensity of each interaction is reflected in the thickness of the node connection. Values were assigned to the connections by summing the percentages of the rank values and the arrows beside each value show the evolution of the interaction intensity upon the addition of ethane. Specifically, these arrows represent the rate fluctuation trends of specific reactions, where the reactant is the initial node of the arrow and the product is the end node. These fluctuations can be regarded as equivalent to the slope of the product formation rate, which in turn can be estimated from the slope of the PYD. To allow a better understanding of the information conveyed by the arrows in Fig. 7, the related reactions in the entire network of connected nodes were backtracked, and key interactions and reaction rate fluctuation trends for example reactions were analyzed. The results are summarized in Table 3.
Fig. 7. The evolutions of key interactions during co-cracking.
Table 3. Reaction rate fluctuation trends for key interactions. Trend Strongly hindered
Hindered
Accelerated
Strongly accelerated
Subcategories 0 0 0 0 0 0 0 0 12 13 21 7 0 0 0 6 10 17 19
Example reaction H•+H•→H2 C3H5•+H•→C3H6 C4H5•+H•→C4H6 C3H5•+C2H6→C3H6+C2H5• C4H5•+C2H6→C4H6+C2H5• C2H6→CH3•CH3• C2H5•→C2H4+H• CH3•+C2H6→CH4+C2H5• C2H5•+IC9H20→C2H6+IC4H8+C2H4+NC3H7• C2H5•+IC9H20→C2H6+NC6H12+0.5*NC 3H7•+0.5*IC3H7• C2H5•+NC10H20→C2H6+C4H6+C2H4+NC4H9• C2H5•+C4H9CYC6H11→C2H6+2*C2H4+CYC6H11• H•+CH3•→CH4 C6H5•+C2H6→C6H6+C2H5• C2H3•+C2H6→C2H4+C2H5• C2H5•+NC10H22→C2H6+NC7H14+NC3H7• H•+IC5H12→H2+IC4H8+CH3• C2H5•+NC5H10→C2H6+C4H6+CH3• H•+C2H5CYC6H11→H2+C2H4+CYC6H11•
These interactions were all selected from the important connections (as indicated by thick purple lines) in Fig. 7 and are essentially in agreement with the interaction fluctuation trends shown by the arrows in this same figure. To allow a systematic analysis of the reactions involved with the co-cracking process, the mechanism evolution diagram is summarized in Fig. 8.
Fig. 8. The evolution of key reaction rates during co-cracking.
As shown in Fig. 8, C2H6 was more likely to react with hydrocarbon radicals than to undergo self-decomposition. The rates of the H-abstraction reactions between C2H6 and hydrocarbon radicals (R•) were increased significantly, such that a large quantity of C2H5• was generated. The C2H5• radicals also preferentially reacted with hydrocarbons (R), especially long-chain
alkanes, as opposed to undergoing self-decomposition. The H-abstraction reaction process with the participation of C2H6 and C2H5• produced more C2H4 during co-cracking, although the conversion of C2H6 was reduced because more C2H6 was generated. As a result of the high proportion of alkanes in naphtha, H• radicals tended to promote the pyrolysis of R species to generate CH3• and C2H4. As more CH3• was produced during co-cracking, the yield of CH4 was increased. However, as H• was consumed by other reaction routes, the production of H2 was reduced. Some major routes for the generation of C3H6 and C4H6 were inhibited as a result of competitive reactions consuming H• and C2H6. In this case, C3H5• and C4H5• were more likely to convert to other products. The proposed network characterization process using sub-network reconstruction has the potential to be applied to the analysis of other reaction networks. The matrix operation can be readily transplanted and the use of PageRank to assess inflow information or mass is applicable to most networks. The sub-network reconstruction method should assist engineering users in understanding reaction mechanisms by elucidating a specific subnetwork in a step-wise manner and backtracking the rate fluctuation trends of related reactions or reaction subcategories.
4. Conclusions The evolutions of the mechanisms involved in the co-cracking reaction network were elucidated using the proposed sub-network reconstruction characterization method. The newly-added MSNR module effectively searched for key components and interactions in the co-cracking process and the results from the mechanism analysis were verified by comparison to experimental data in the literature.
Variations in the yields of the primary co-cracking products could be obtained from the EcSOS software. The accuracy of co-cracking furnace simulation process and the subnetwork reconstruction characterization process were demonstrated by each other. This entire method could potentially be applied to the analysis of other cracking processes and, with proper reactor models and kinetic parameters, this characterization system may also be applicable to other reaction networks. Reaction network analysis involving quantification and visualization is expected to assist petrochemical enterprises in obtaining more comprehensive understandings of their processes. The ability to accurately profile various processes should result in reliable control and optimization, thus increasing profit margins.
CRediT author statement Kexin Bi: Conceptualization, Methodology, Software, Validation, Writing - Original Draft, Writing Review & Editing. Chen Zhang: Visualization, Investigation, Validation, Writing - Review & Editing. Tong Qiu: Conceptualization, Formal analysis, Visualization, Investigation, Supervision, Validation, Writing - Review & Editing.
Declarations of interest None.
Acknowledgements The authors gratefully acknowledge the National Natural Science Foundation of China for its financial support (Grant No. U1462206).
Declarations of interest None.
Nomenclature The following is the nomenclature used in the manuscript: Reaction network analysis methods network flow analysis algorithm convolutional neural networks multiple sub-network reconstruction Key variables element in substance-reaction mix transfer matrix element in substance connection matrix element in actual mass flow rate matrix ⃗⃗⃗
element in autofocused row vector product yield deviation re-iterated PageRank value
Key substances hydrogen free radical methyl free radical ethyl free radical free radicals responsible for propylene formation free radicals responsible for butadiene formation hydrocarbon radicals Hydrocarbons Hydrogen Methane Ethane Propylene
Butadiene Ethylene Benzene Toluene Others Ethylene cracker Simulation and Optimization System three-dimensional adjusted Monte Carlo integral method Stone & Webster Ultra-Selective Cracking
Appendix Table A1. Industrial case data input for EcSOS simulations.
Feedstock reconstruction
In-tube reaction (single furnace)
Firebox model
EcSOS user input Average molecular weight (amu) Hydrogen-carbon molar ratio (mol/mol) Specific density ASTM D86 boiling points (K) IBP 10% 30% 50% 70% 90% FBP PIONA (wt%) P I O N A Number of reactor tubes Inlet tube diameter (m) Outlet tube diameter (m) Hydrocarbon flow rate (t/h) Steam dilution (kg/kg) Coil inlet temperature (K) Coil outlet pressure (kPa) Length (m) Width (m) Height (m) Number of burners Emissivity of side wall Emissivity of tube skin Fuel gas flow rate (kg/s) Flame height (m)
106.29 2.09 0.7314 317.0 359.7 373.1 389.6 410.3 444.8 469.7 43.08 20.28 0.09 34.23 5.32 22 0.045 0.055 54.7 0.5 893.2 144 3.0 24.9 11.6 4 0.7 0.6 3.6 5.0
Heat transfer coefficient between furnace and tube wall (W/(m2·K))
10
Convective coefficient on tube wall (W/(m2·K))
180
Air and fuel gas inlet temperature (K) Fuel composition (wt%) CH4
298.2
H2
2.5
97.5
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