A method for constructing a diesel steam cracking reaction network
The construction of a diesel steam cracking reaction network through the automatic reaction network generation tool RMG solves the problem of time-consuming and labor-intensive traditional methods and difficulty in describing free radical interactions, and achieves the effect of fast construction and detailed description of the reaction process at low cost.
Patent Information
- Application Number
- CN202210097198.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-01-27
- Publication Date
- 2025-04-11
- Estimated Expiration
- 2042-01-27
AI Technical Summary
Traditional methods are time-consuming, laborious, costly, and difficult to accurately describe the interactions at the free radical level, especially the regulation mechanism of heteroatomic components on olefin products.
The automatic reaction network generation tool Reaction Mechanism Generator (RMG) is used to analyze the components of diesel, select representative molecules, and generate a single molecule reaction network, and finally merge to form a total reaction network. This method couples hydrocarbon molecules with a reaction network containing sulfur and nitrogen-containing compounds.
It realizes the fast construction of a diesel steam cracking reaction network at low cost, can describe the free radical reaction process in detail, and predict product distribution, reducing manual finishing and calculation time.
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Figure CN114496106B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of petrochemical industry, and in particular to a low-cost rapid construction method of a diesel steam cracking reaction network. Background Art
[0002] In recent years, diesel production capacity has been significantly oversupplied, and many refineries have used diesel as one of the important raw materials for steam cracking units to produce high value-added low-carbon olefins. Patent specifications with publication numbers CN101139529A and CN105622310A respectively use coking diesel and Fischer-Tropsch diesel for steam cracking reactions to expand the source of raw materials for steam cracking to produce olefins.
[0003] As is known to all, the thermal cracking of hydrocarbons follows a free radical mechanism, and its reaction process is highly random and complex. Diesel is a complex hydrocarbon mixture, and the cracking reaction path is extremely complex. For the kinetic modeling of complex reaction processes, the traditional reaction kinetic model construction method generally aggregates multiple components, and relies on manual arrangement of reaction paths and estimation of kinetic parameters according to the known reaction rules or templates of each family composition. The patent specification with publication number CN108108572A adopts six lumped kinetic models for the wax oil hydrocracking process to reduce the complexity of the reaction network. The patent specification with publication number CN109698014A establishes multiple reaction rules for catalytic reforming raw materials, and follows the formulated reaction rules to determine the reaction path between the raw materials and the products. For the steam cracking process of complex mixtures such as diesel, the traditional reaction kinetic model construction method is time-consuming and labor-intensive, and the cost is extremely high, and the lumped kinetic model or the kinetic model at the molecular reaction level is difficult to accurately describe the interaction at the free radical level, especially the regulation mechanism of heteroatom components on olefin products.
[0004] With the rapid development of computer technology, reaction network automatic generation tools have emerged. With the help of automatic reaction network generators, detailed reaction networks at the free radical level can be obtained in a short time with minimal human and material consumption. In existing literature reports, reaction network automatic generation technology is mostly used for reaction network generation of pure substances and relatively pure naphtha fractions.
[0005] Compared with traditional naphtha cracking raw materials, diesel has a more complex composition, a higher content of heavy components, and contains a certain proportion of heteroatom compounds represented by sulfur-containing compounds and nitrogen-containing compounds. The number of carbon atoms in the diesel fraction can reach 22, and the isomers increase exponentially with the increase in carbon number, making the scale of its steam cracking reaction network extremely large. In addition, the thermal cracking of sulfur-containing compounds and nitrogen-containing compounds is more complex and variable than that of hydrocarbons, and the intermediates will also have a modulating effect on the coking process of steam cracking to produce olefins.
[0006] Therefore, the use of automatic reaction network generation technology can not only quickly construct the diesel steam cracking reaction network at low cost, but also explain the interaction between hydrocarbon substances and sulfur-containing compounds and nitrogen-containing compounds in diesel from the free radical level, and predict the distribution of diesel steam cracking products. Summary of the invention
[0007] The present invention provides a method for constructing a diesel steam cracking reaction network, which has low construction cost and high speed. The constructed total reaction network of diesel steam cracking includes a heteroatom composition reaction network represented by sulfur-containing compound molecules and nitrogen-containing compound molecules, and couples the hydrocarbon molecule reaction network with the sulfur-containing compound and nitrogen-containing compound reaction networks.
[0008] A method for constructing a diesel steam cracking reaction network comprises the steps of:
[0009] (1) Analyze the composition of diesel fuel, select representative hydrocarbon molecules as the hydrocarbon composition of diesel fuel, and select representative sulfur-containing compound molecules and nitrogen-containing compound molecules as the heteroatom composition of diesel fuel;
[0010] (2) Using the reaction network generation tool Reaction Mechanism Generator (RMG) to automatically generate single-molecule reaction networks for each molecule in the hydrocarbon composition and heteroatom composition;
[0011] (3) The reaction networks of all generated hydrocarbon component molecules and heteroatom component molecules are combined to construct the overall reaction network of diesel steam cracking.
[0012] In step (1), the composition of diesel can be analyzed using chromatography technology.
[0013] In step (1), the hydrocarbon molecules include straight-chain alkanes, isoalkanes, olefins, cycloalkanes and aromatics. Although straight-chain alkanes and isoalkanes belong to the same alkanes, their cracking paths and cracking product distributions are quite different, so the present invention divides them into two subclasses for molecular statistics. Alkynes can be ignored due to their extremely low content in diesel.
[0014] The lower the mass fraction threshold is set, the more representative diesel components are screened, and the more realistic the diesel composition can be described. However, the number of single-molecule reaction networks that need to be constructed is also greater, and the overall calculation time is longer. Moreover, molecules with too low a content have little effect on the diesel steam cracking reaction process. Therefore, in order to be able to describe the diesel composition nearly realistically and take into account efficiency, in step (1):
[0015] The representative hydrocarbon molecules are hydrocarbon molecules that account for no less than 0.3% (preferably no less than 0.5%) by mass in diesel;
[0016] The representative sulfur-containing compound molecules and nitrogen-containing compound molecules are sulfur-containing compound molecules and nitrogen-containing compound molecules that account for no less than 0.05% (preferably no less than 0.1%) by mass in diesel.
[0017] In step (2), the automatic generation process of the single-molecule reaction network is to specify the temperature, pressure, reactant molecule types and ratios, termination conditions and user-defined tolerance factors of the corresponding single-molecule reaction system, and start the reaction network generation tool Reaction Mechanism Generator to perform automatic reaction network generation of the reaction system.
[0018] During the automatic generation of a single-molecule reaction network, the temperature of the reaction system can be set to 780-900°C, which is a temperature range that belongs to the conventional steam cracking furnace temperature operating range. For automatic reaction network generation, a high-temperature reaction system is compatible with a low-temperature reaction system. The higher the temperature setting, the more detailed the reaction network, but the longer the calculation time of a single reaction network. Based on this, the temperature of the reaction system is preferably set to 800-850°C, and more preferably set to 820-850°C.
[0019] During the automatic generation of the single-molecule reaction network, the pressure of the reaction system can be set to 0.1-0.3 MPa, which is within the pressure operating range of a conventional steam cracking furnace.
[0020] In the process of automatic generation of the single-molecule reaction network, the feed composition is preferably the corresponding hydrocarbon component molecules or heteroatom component molecules and water molecules, wherein the water molecules are only used as feed component molecules and are not reactive. The mass ratio of the corresponding hydrocarbon component molecules or heteroatom component molecules and water molecules can be 1 to 2:1, and this dilution ratio range belongs to the conventional steam cracking furnace dilution ratio operation range.
[0021] The higher the molar conversion rate of the termination condition, the more detailed the reaction network is, but the longer the calculation time is. In the process of automatic generation of the reaction network of a single molecule, the termination condition is preferably that the molar conversion rate of the corresponding hydrocarbon component molecule or heteroatom component molecule is greater than 85%, and more preferably that the molar conversion rate of the corresponding hydrocarbon component molecule or heteroatom component molecule is 90% to 95%.
[0022] The user-defined tolerance factor is a criterion for distinguishing the core reactions included in the reaction network from the marginal reactions that are excluded. This value has a great impact on the scale of the reaction network and the calculation time. The smaller the tolerance factor, the more detailed the reaction network, but the longer the calculation time of a single reaction network. In the process of automatic generation of single-molecule reaction networks, the user-defined tolerance factor is preferably set to 0.5-0.01. It is further preferably set to 0.1-0.01, and further preferably set to 0.05-0.03.
[0023] Taking into account that the network merged first has priority in the merging process, that is, the same reaction path will be based on the network merged first, in step (3), the merging rule of the overall reaction network is that the sulfur-containing compound reaction network and the nitrogen-containing compound reaction network are first merged into network 1, the purpose is to completely retain the reaction networks of sulfur-containing compounds and nitrogen-containing compounds, and the aromatic reaction network is merged on the basis of network 1 to obtain network 2, the purpose is to retain the aromatic reaction network as much as possible, and the cycloalkane reaction network is merged on the basis of network 2 to obtain network 3, the purpose is to retain the cycloalkane reaction network as much as possible, and the linear alkane reaction network is merged on the basis of network 3 to obtain network 4. The linear alkane reaction network will contain a part of aromatics. The reaction paths of aromatic hydrocarbons and cycloalkanes are placed in network 3 and then merged. The isoalkane reaction network is merged on the basis of network 4 to obtain network 5. The isoalkane reaction network will contain some reaction paths of aromatic hydrocarbons, cycloalkanes and linear alkanes, so it is placed in network 4 and then merged. Finally, the olefin reaction network is merged on the basis of network 5 to obtain the overall reaction network of diesel steam cracking. Olefins are both cracking raw materials and important cracking products of hydrocarbon substances. The reaction networks of aromatic hydrocarbons, cycloalkanes, linear alkanes and isoalkanes already contain some important olefin cracking paths, so the olefin reaction network is placed at the end and merged, so that the olefin cracking paths of other types of hydrocarbon molecules remain intact.
[0024] Compared with the prior art, the present invention has the following main advantages:
[0025] (1) The reaction network and corresponding kinetic parameters at the free radical mechanism level of diesel steam cracking can be obtained at low cost and in a short time. The time required is only the running time of the RMG program, and no additional manual combing work is required;
[0026] (2) Using the chromatographic analysis results as the basis for selecting representative molecules of diesel, setting minimum mass content thresholds for hydrocarbon composition and heteroatom composition as the standard for selecting molecules, and nearly realistically describing the composition of diesel participating in the steam cracking reaction;
[0027] (3) The reaction network of heteroatom compound molecules is used as the first step in RMG network merging to avoid the elementary reactions related to sulfur-containing compounds and nitrogen-containing compounds being covered during the network merging process. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] Figure 1 The present invention provides a flow chart for constructing a diesel steam cracking reaction network. DETAILED DESCRIPTION
[0029] The present invention will be further described below in conjunction with the accompanying drawings and specific examples. It should be understood that these examples are only intended to illustrate the present invention and are not intended to limit the scope of the present invention. The operating methods in the following examples without specifying specific conditions are usually carried out under conventional conditions or under conditions recommended by the manufacturer.
[0030] like Figure 1 As shown, the diesel sample is sent to the chromatograph for component analysis, and representative hydrocarbon molecules are screened as the hydrocarbon composition of diesel according to the chromatographic results, and representative sulfur-containing compound molecules and nitrogen-containing compound molecules are screened as the heteroatom composition of diesel; the reaction network generation tool RMG is used to automatically generate single-molecule reaction networks for the hydrocarbon composition and heteroatom composition of each type of diesel; the reaction networks of all generated diesel hydrocarbon component molecules and heteroatom component molecules are merged according to specific merging rules to obtain the total reaction network of diesel steam cracking. The hydrocarbon component molecules include straight-chain alkanes, isoalkanes, olefins, cycloalkanes and aromatics. The merging rule is that the sulfur-containing compound reaction network and the nitrogen-containing compound reaction network are first merged into network 1, and the aromatic reaction network is merged on the basis of network 1 to obtain network 2, and the cycloalkanes reaction network is merged on the basis of network 2 to obtain network 3, and the straight-chain alkane reaction network is merged on the basis of network 3 to obtain network 4, and the isoalkanes reaction network is merged on the basis of network 4 to obtain network 5, and finally the olefins reaction network is merged on the basis of network 5 to obtain the total reaction network of diesel steam cracking.
[0031] Example 1
[0032] The diesel sample was sent to a chromatograph for component analysis. The chromatograph has the function of analyzing hydrocarbon molecules, sulfur-containing compound molecules and nitrogen compound molecules. Based on the obtained chromatographic analysis results, the mass fractions of all detected diesel components were normalized, and hydrocarbon molecules with a mass fraction of not less than 0.3% were taken as the hydrocarbon composition of diesel, and sulfur-containing compound molecules and nitrogen-containing compound molecules with a mass fraction of not less than 0.05% were taken as the heteroatom composition of diesel, which were used together as representative molecules to describe the composition of diesel. A total of 121 hydrocarbon molecules were screened out, with the number of carbon atoms ranging from 10 to 22; 9 sulfur-containing compound molecules, namely mercaptans, sulfides, thiophenes, benzothiobenzenes, etc.; 4 nitrogen-containing compound molecules, namely pyridines, pyrroles, tetrahydropyrroles, etc.
[0033] The reaction network generation tool Reaction Mechanism Generator was used to automatically generate single-molecule reaction networks for the above 134 representative diesel molecules. The temperature of all single-molecule reaction systems was uniformly set to 900°C, the pressure was set to 0.2MPa, the feed composition was the corresponding diesel hydrocarbon component molecules or heteroatom component molecules and water molecules, the mass ratio of the two was set to 1:1, the user-defined tolerance factor was set to 0.01, and the termination condition was set to the molar conversion rate of the corresponding diesel hydrocarbon component molecules or heteroatom component molecules reaching 99%. Start the reaction network generation tool Reaction Mechanism Generator to perform automatic reaction network generation for each single-molecule reaction system. The average time required to generate 134 single-molecule reaction networks was 12.1 hours, and the average scale of the reaction network was 316 species and 6894 reactions.
[0034] The 134 single-molecule reaction networks obtained above were merged according to the following merging rules: the reaction networks of 9 sulfur-containing compound molecules and 4 nitrogen-containing compound molecules were first merged into network 1, with a scale of 3898 species and 60156 reactions; on the basis of network 1, the reaction networks of 8 aromatic hydrocarbon molecules in hydrocarbon molecules were merged to obtain network 2, with a scale of 6011 species and 98995 reactions; on the basis of network 2, the reaction networks of 14 cycloalkane molecules in hydrocarbon molecules were merged to obtain network 3, with a scale of 10231 species and 113 754 reactions; on the basis of network 3, 13 straight-chain alkane molecular reaction networks in hydrocarbon molecules were merged to obtain network 4, with a scale of 13131 species and 147565 reactions; on the basis of network 4, 79 isomeric alkane molecular reaction networks in hydrocarbon molecules were merged to obtain network 4, with a scale of 16523 species and 171322 reactions; on the basis of network 5, 7 olefin molecular reaction networks in hydrocarbon molecules were merged to finally obtain the overall reaction network of diesel steam cracking, with a total reaction network scale of 17344 species and 174325 reactions.
[0035] The diesel steam cracking overall reaction network obtained above uses a lower mass fraction threshold to screen representative molecules, as well as a higher reaction temperature, a lower user-defined tolerance factor, and a higher target conversion rate. Therefore, the reaction network is large in scale, with the number of species in the reaction network reaching about 17,000 and the number of reactions reaching about 170,000, which can describe the diesel steam cracking free radical reaction process in great detail.
[0036] Example 2
[0037] The same diesel sample as in Example 1 was sent to the chromatograph for analysis of the content of hydrocarbon molecules, sulfur-containing compound molecules and nitrogen compound molecules. Based on the obtained chromatographic analysis results, the mass fractions of all detected diesel components were normalized, and hydrocarbon molecules with a mass fraction of not less than 0.5% were taken as the hydrocarbon composition of diesel, and sulfur-containing compound molecules and nitrogen-containing compound molecules with a mass fraction of not less than 0.1% were taken as the heteroatom composition of diesel, and were used together as representative molecules to describe the composition of diesel. A total of 92 hydrocarbon molecules, with a carbon atom number ranging from 10 to 22; 5 sulfur-containing compound molecules, namely mercaptans, sulfides, thiophenes, benzothiobenzenes, etc.; 2 nitrogen-containing compound molecules, namely pyridines, pyrroles, etc.
[0038] The reaction network generation tool Reaction Mechanism Generator was used to automatically generate single-molecule reaction networks for the above 99 representative diesel molecules. The temperature of all single-molecule reaction systems was uniformly set to 850°C, the pressure was set to 0.2MPa, the feed composition was the corresponding diesel hydrocarbon component molecules or heteroatom component molecules and water molecules, the mass ratio of the two was set to 1:1, the user-defined tolerance factor was set to 0.01, and the termination condition was set to the molar conversion rate of the corresponding diesel hydrocarbon component molecules or heteroatom component molecules reaching 99%. Start the reaction network generation tool Reaction Mechanism Generator to perform automatic reaction network generation for each single-molecule reaction system. The average time required to generate 99 single-molecule reaction networks was 11.9 hours, and the average scale of the reaction network was 325 species and 6822 reactions.
[0039] The 99 single-molecule reaction networks obtained above were merged according to the following merging rules: the reaction networks of the five sulfur-containing compound molecules and the two nitrogen-containing compound molecules were first merged into network 1, with a scale of 2101 species and 32076 reactions; on the basis of network 1, the reaction networks of the five aromatic hydrocarbon molecules in the hydrocarbon molecules were merged to obtain network 2, with a scale of 3799 species and 60655 reactions; on the basis of network 2, the reaction networks of the ten cycloalkane molecules in the hydrocarbon molecules were merged to obtain network 3, with a scale of 6569 species and 992 31 reactions; on the basis of network 3, 13 straight-chain alkane molecular reaction networks in hydrocarbon molecules were merged to obtain network 4, with a scale of 9469 species and 133042 reactions; on the basis of network 4, 64 isomeric alkane molecular reaction networks in hydrocarbon molecules were merged to obtain network 4, with a scale of 12754 species and 149952 reactions; on the basis of network 5, 7 olefin molecular reaction networks in hydrocarbon molecules were merged to finally obtain the overall reaction network of diesel steam cracking, with a total reaction network scale of 13365 species and 152134 reactions.
[0040] Compared with Example 1, the diesel steam cracking total reaction network obtained in this example uses a relatively high mass fraction threshold to screen representative molecules, so that the number of representative molecules is reduced from 134 to 99, and the number of species in the final total reaction network is reduced to about 13,000, and the number of reactions is reduced to about 150,000, which is consistent with the experimental results. The network can also describe the diesel steam cracking free radical reaction process in detail.
[0041] Example 3
[0042] The same diesel sample and the same mass fraction threshold as in Example 2 were used to screen representative molecules, i.e., hydrocarbon molecules with a mass fraction of not less than 0.5% were used as the hydrocarbon composition of diesel, and sulfur-containing compound molecules and nitrogen-containing compound molecules with a mass fraction of not less than 0.1% were used as the heteroatom composition of diesel. A total of 92 hydrocarbon molecules were selected, with the number of carbon atoms ranging from 10 to 22; 5 sulfur-containing compound molecules were mercaptans, sulfides, thiophenes, benzothiobenzenes, etc.; and 2 nitrogen-containing compound molecules were pyridines, pyrroles, etc.
[0043] The reaction network generation tool Reaction Mechanism Generator was used to automatically generate single-molecule reaction networks for the above 99 representative diesel molecules. The temperature of all single-molecule reaction systems was uniformly set to 850°C, the pressure was set to 0.2MPa, the feed composition was the corresponding diesel hydrocarbon component molecules or heteroatom component molecules and water molecules, the mass ratio of the two was set to 1:1, the user-defined tolerance factor was set to 0.05, and the termination condition was set to the molar conversion rate of the corresponding diesel hydrocarbon component molecules or heteroatom component molecules reaching 90%. Start the reaction network generation tool Reaction Mechanism Generator to perform automatic reaction network generation for each single-molecule reaction system. The average time required to generate 99 single-molecule reaction networks was 9.3 hours, and the average scale of the reaction network was 239 species and 4821 reactions.
[0044] The 99 single-molecule reaction networks obtained above were merged according to the following merging rules: the reaction networks of the five sulfur-containing compound molecules and the two nitrogen-containing compound molecules were first merged into network 1, with a scale of 1203 species and 22345 reactions; on the basis of network 1, the reaction networks of the five aromatic hydrocarbon molecules in the hydrocarbon molecules were merged to obtain network 2, with a scale of 2210 species and 41523 reactions; on the basis of network 2, the reaction networks of the ten cycloalkane molecules in the hydrocarbon molecules were merged to obtain network 3, with a scale of 4021 species and 69 231 reactions; on the basis of network 3, 13 straight-chain alkane molecular reaction networks in hydrocarbon molecules were merged to obtain network 4, with a scale of 6112 species and 93326 reactions; on the basis of network 4, 64 isomeric alkane molecular reaction networks in hydrocarbon molecules were merged to obtain network 4, with a scale of 8044 species and 104252 reactions; on the basis of network 5, 7 olefin molecular reaction networks in hydrocarbon molecules were merged to finally obtain the overall reaction network of diesel steam cracking, with a total reaction network scale of 8116 species and 105713 reactions.
[0045] Compared with Example 2, the diesel steam cracking overall reaction network obtained in this example adopts a medium reaction temperature, a medium user-defined tolerance factor, and a lower target conversion rate. On the basis of the unchanged number of representative molecules, the number of species in the final overall reaction network is further reduced to about 8,000, and the number of reactions is further reduced to about 100,000, which is consistent with the experimental results. The network can still describe the diesel steam cracking free radical reaction process in detail.
[0046] In addition, it should be understood that after reading the above description of the present invention, those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the claims attached to this application.
Claims
1. A method for constructing a diesel steam cracking reaction network, characterized in that: Includes steps: (1) Analyzing the composition of diesel, screening representative hydrocarbon molecules as the hydrocarbon composition of diesel, and representative sulfur-containing compound molecules and nitrogen-containing compound molecules as the heteroatom composition of diesel; the hydrocarbon molecules include straight-chain alkanes, isoalkanes, olefins, cycloalkanes and aromatics; (2) Using the reaction network generation tool Reaction Mechanism Generator to automatically generate a single-molecule reaction network for each molecule in the hydrocarbon composition and the heteroatom composition; during the automatic generation of the single-molecule reaction network, the temperature of the reaction system is set to 780-900°C, and the pressure of the reaction system is set to 0.1-0.3MPa; during the automatic generation of the single-molecule reaction network, the feed composition is the corresponding hydrocarbon composition molecules or heteroatom composition molecules and water molecules, and the mass ratio of the two is 1-2:1; (3) The reaction networks of all generated hydrocarbon component molecules and heteroatom component molecules are merged to construct the overall reaction network at the free radical mechanism level of diesel steam cracking; the merging rule of the overall reaction network is as follows: the reaction network of sulfur-containing compounds and the reaction network of nitrogen-containing compounds are first merged into network 1, the aromatic reaction network is merged on the basis of network 1 to obtain network 2, the cycloalkane reaction network is merged on the basis of network 2 to obtain network 3, the straight-chain alkane reaction network is merged on the basis of network 3 to obtain network 4, the isoalkane reaction network is merged on the basis of network 4 to obtain network 5, and finally the olefin reaction network is merged on the basis of network 5 to obtain the overall reaction network at the free radical mechanism level of diesel steam cracking.
2. The construction method according to claim 1, characterized in that: In step (1): The representative hydrocarbon molecules are hydrocarbon molecules that account for no less than 0.3% by mass in diesel; The representative sulfur-containing compound molecules and nitrogen-containing compound molecules are sulfur-containing compound molecules and nitrogen-containing compound molecules that account for no less than 0.05% by mass in diesel.
3. The construction method according to claim 1, characterized in that: In step (2), the automatic generation process of the single-molecule reaction network is to specify the temperature, pressure, reactant molecule types and ratios, termination conditions and user-defined tolerance factors of the corresponding single-molecule reaction system, and start the reaction network generation tool Reaction Mechanism Generator to perform automatic reaction network generation of the reaction system.
4. The construction method according to claim 3, characterized in that: During the automatic generation of the single-molecule reaction network, the termination condition is that the molar conversion rate of the corresponding hydrocarbon component molecules or heteroatom component molecules is greater than 85%.
5. The construction method according to claim 3, characterized in that: During the automatic generation of single-molecule reaction networks, the user-defined tolerance factor was set to 0.5–0.01.
Citation Information
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