复杂反应系统分子尺度反应动力学研究
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摘要
分子尺度反应动力学模型是复杂反应系统动力学研究中继集总模型后的又一重大突破,已成为复杂反应系统动力学发展的必然趋势。其中,单事件方法因能解析复杂反应系统的整个反应网络,又可将所需估计的参数减少到可处理的范围内而得到了广泛关注。本文通过对催化重整单事件反应动力学模型建立全过程的研究,建立并优化了单事件方法。
本文首先对正己烷、正庚烷和2,2,4-三甲基戊烷三种模型化合物在Pt-Sn/Al2O3-Cl催化剂作用下的重整反应进行了研究,由结果可知异构化反应是各模型化合物发生的主要反应,环化反应和裂化反应速率比异构化反应要慢得多。由于2,2,4-三甲基戊烷的特殊结构,裂化反应很容易进行。在文献调查和实验研究的基础上,选定经典的双功能反应机理作为催化重整单事件反应动力学模型研究的基础。
通过布尔邻接矩阵实现各类分子的数字化,采用随机模式对分子中各碳原子进行编号。依据碳原子杂化状态并充分利用布尔邻接矩阵的主对角元素使分子中双键和荷电特征都在布尔邻接矩阵中得到清晰反映,从而避免了常规须使用的辅助向量。以分子布尔邻接矩阵为基础：(1)结合Golender图势能思想,创造性地计算了带双键和荷电分子的Golender's势能向量。并依此对分子的唯一性进行判别,避免了分子及反应在反应网络数据库中重复存储。(2)通过对矩阵各行或列的非主对角元素进行统计加和计算判断了各碳原子的级数。(3)通过遍历分子布尔邻接矩阵判断了分子类型。(4)提取了分子中各碳原子之间的纯连接关系矩阵,通过对其进行矩阵运算确定了分子中各碳原子之间的相对位置,并归纳了计算公式,为反应数字化提供了基础。
然后,结合催化重整反应机理,通过对分子布尔邻接矩阵的演算,实现了催化剂中金属活性中心和酸活性中心上的各类基本反应的数字化。
为了能快捷地实现反应网络生成过程和速率方程构建过程中分子及反应的查找、比较和存储,本研究对反应网络数据库进行了以下几点优化设计：(1)采用分子中碳原子数和分子类型的组合方式来命名各类分子存储文件名；(2)通过反应类型、反应物碳原子数、第一生成物碳原子数及第二生成物碳原子数的组合方式来命名各类反应存储文件名；(3)对分子布尔邻接矩阵的关键特征及计算耗时特征进行预存储,如分子的碳原子数、环碳原子编号、分子的Golender's势能向量等。
以经典的催化重整双功能反应机理为依据,构建了催化重整反应网络生成流程图,并编制了反应网络生成程序。通过程序生成了解析催化重整单事件反应动力学所需的详细反应网络。由于催化重整不考虑碳原子数增加的反应,根据相同碳原子数的分子之间转化的可逆性,生成的整个反应网络与初始反应分子种类无关,而只与初始反应分子的碳原子数有关。反应网络生成结果显示以相同的碳原子数的不同初始分子生成的反应网络是一致的。
以过渡态理论为基础,引入单事件概念：基本反应步骤的速率常数可以表示为单事件数和单事件速率常数之积。通过热力学约束进一步减少所需估计的单事件动力学参数。以气固催化反应理论和重整双功能反应机理为基础推导得到了各反应物的单事件反应动力学速率方程。
根据单事件数的定义,通过计算反应物和反应过渡态的全局对称数,便可得到基本反应步骤的单事件数。本文依据分子对称数的定义,实现了前人尚未做到的全局对称数的自动计算,并列举了以此算法为依据的全局对称数计算示例。该方法方便快捷地实现了大量基本反应步骤的单事件数计算,对单事件反应动力学的研究具有重要学术价值。
最后,采用局部极小优化算法-BFGS变尺度法和全局优化算法-模拟退火法(SA)联用的混合算法,以正己烷催化重整反应实验数据为基础,估计了C6催化重整反应的单事件速率常数。其结果表明,所得的动力学参数符合双功能重整机理,如：具有叔正碳离子参与的基本反应步骤的活化能比没有叔正碳离子参与的基本反应步骤的活化能低。支链数发生变化的PCP异构化反应的活化能比支链数不发生变化的甲基转移反应活化能高等。同时,也表明BFGS-SA混合算法具有较好的稳定性和收敛性。
以上研究实现了单事件方法在催化重整分子尺度反应动力学研究过程中的应用,对复杂反应系统单事件反应动力学模型的研究和发展具有重要理论意义和借鉴作用。
The molecular level kinetic model is an important breakthrough in the study of kinetic model for complex reaction systems after lumped kinetic model, and already becomes an inevitable development trend of kinetic model for complex reaction system. Among those molecular level kinetic models, the single-event method not only can retain the full detail of reaction network, but also can reduce the number of model parameters to a tractable level, so it attracts wide attentions. The single-event method was built and optimized by the study of single-event kinetic model for catalytic reforming.
The catalytic reforming of n-hexane, n-heptane and 2,2,4-trimethylpentane over Pt-Sn/Al22O3-Cl catalyst were studied in this paper. The results showed that isomerization is the main reaction occurred in reforming of three kinds of model compounds, cyclization and cracking reactions are much slower than isomerization. Cracking reaction of 2,2,4-trimethylpentane occurs easily due to its special molecular structure. The classical bifunctional reforming mechanism was chosen as the foundation of single-event kinetic model for catalytic reforming based on the literature survey and experimental research.
The digital representation of all kinds of molecules was carried out using Boolean relation matrix. The carbon atoms in molecule were labelled stochastically. According to hybrid state of carbon atoms, the C=C double bond and charge of carbon atom were clearly represented in Boolean relation matrix by utilization of main diagonal elements, which can avoid to use additional vectors. The Golender's potential vector of molecule with C=C double bond or charge was calculated creatively based on the Boolean relation matrix and Golender's graph potential, and it can be used to confirm the unique molecule to avoid redundance of molecule storage in reaction network database. The number of non-zero elements in a row without counting main diagonal elements in matrix determines whether the corresponding carbon atom is primary secondary, tertiary or quaternary. The type of molecule can be determined by inspecting the whole matrix. The pure connection between carbon atoms drawn out form Boolean relation matrix was used to determine the relative position between carbon atoms, and the calculation formula was put forward, it is necessary for digital representations of reactions
And then, the digital representations of reactions occurred at metallic and acidic sites by performance of Boolean relation matrix based on reaction mechanism of catalytic reforming were carried out.
In order to perform search, comparison, and storage of molecules and reactions during the reaction network generation and rate equation construction quickly, several optimization designs were executed for reaction network database:(1) the file name of molecule storage was the combination of carbon number and molecule type; (2) the file name of reaction storage was the combination of reaction type, carbon number of reactant, carbon number of first product, and second product; (3) the key and time-consuming characters of Boolean relation matrix were prestored in the database, for example, carbon number of molecule, Ring carbon atom number, Golender's potential vector, and so on.
The program for reaction network generation was completed according to the constructed program flow chart based on the bifunctional reaction mechanism. The detailed reaction network necessary for single-event kinetics resolution of catalytic reforming was generated via this program. Because chain growth reactions were not considered in catalytic reforming, the reaction network is only dependent of the carbon number of starting molecule, but independent of its type, due to the reversibility between molecules with the same carbon number. The results of network generation showed that the networks generated from different molecules with the same carbon number were consistent with each other.
The single-event concept was introduced based on transition state theory. The elementary-step rate coefficient is the product of single-event number and single-event rate coefficient. The number of parameters can be further reduced by thermodynamic restriction. The rate equations of single-event kinetic model were deduced based on gas-solid catalysis and bifunctional reforming mechanism.
According to the definition of single-event number, the single-event number of elementary step can be obtained from global symmetry number of reactant and transition state. The automatic calculation of global symmetry number was realized by the definition of symmetry number, and some examples were given. A large number of single-event numbers of elementary steps were calculated based on the program originated from automatic calculation algorithm. It is important for study of single-event kinetic model due to its academic value.
Finally, the single-event rate coefficients of C6 reforming were estimated based on the data of n-hexane reforming using the hybrid algorithm which is the combination of BFGS and simulated anneal algorithm. The results showed that obtained kinetic parameters were consistent with the bifunctional reforming mechanism; the activation energy of reactions with tertiary carbeniums is lower than that of reactions without tertiary carbeniums; the activation energy of reactions with branch degree change is higher than that of reactions without branch degree change. At the same time, the BFGS-SA hybrid algorithm appears good stability and astringency during parameter estimation.
The application of single-event method in the study of molecular level kinetics for catalytic reforming was realized by above research, and this study has important theoretical significance and reference values for the research and development of single-event kinetic model for complex reaction systems.
本文首先对正己烷、正庚烷和2,2,4-三甲基戊烷三种模型化合物在Pt-Sn/Al2O3-Cl催化剂作用下的重整反应进行了研究,由结果可知异构化反应是各模型化合物发生的主要反应,环化反应和裂化反应速率比异构化反应要慢得多。由于2,2,4-三甲基戊烷的特殊结构,裂化反应很容易进行。在文献调查和实验研究的基础上,选定经典的双功能反应机理作为催化重整单事件反应动力学模型研究的基础。
通过布尔邻接矩阵实现各类分子的数字化,采用随机模式对分子中各碳原子进行编号。依据碳原子杂化状态并充分利用布尔邻接矩阵的主对角元素使分子中双键和荷电特征都在布尔邻接矩阵中得到清晰反映,从而避免了常规须使用的辅助向量。以分子布尔邻接矩阵为基础：(1)结合Golender图势能思想,创造性地计算了带双键和荷电分子的Golender's势能向量。并依此对分子的唯一性进行判别,避免了分子及反应在反应网络数据库中重复存储。(2)通过对矩阵各行或列的非主对角元素进行统计加和计算判断了各碳原子的级数。(3)通过遍历分子布尔邻接矩阵判断了分子类型。(4)提取了分子中各碳原子之间的纯连接关系矩阵,通过对其进行矩阵运算确定了分子中各碳原子之间的相对位置,并归纳了计算公式,为反应数字化提供了基础。
然后,结合催化重整反应机理,通过对分子布尔邻接矩阵的演算,实现了催化剂中金属活性中心和酸活性中心上的各类基本反应的数字化。
为了能快捷地实现反应网络生成过程和速率方程构建过程中分子及反应的查找、比较和存储,本研究对反应网络数据库进行了以下几点优化设计：(1)采用分子中碳原子数和分子类型的组合方式来命名各类分子存储文件名；(2)通过反应类型、反应物碳原子数、第一生成物碳原子数及第二生成物碳原子数的组合方式来命名各类反应存储文件名；(3)对分子布尔邻接矩阵的关键特征及计算耗时特征进行预存储,如分子的碳原子数、环碳原子编号、分子的Golender's势能向量等。
以经典的催化重整双功能反应机理为依据,构建了催化重整反应网络生成流程图,并编制了反应网络生成程序。通过程序生成了解析催化重整单事件反应动力学所需的详细反应网络。由于催化重整不考虑碳原子数增加的反应,根据相同碳原子数的分子之间转化的可逆性,生成的整个反应网络与初始反应分子种类无关,而只与初始反应分子的碳原子数有关。反应网络生成结果显示以相同的碳原子数的不同初始分子生成的反应网络是一致的。
以过渡态理论为基础,引入单事件概念：基本反应步骤的速率常数可以表示为单事件数和单事件速率常数之积。通过热力学约束进一步减少所需估计的单事件动力学参数。以气固催化反应理论和重整双功能反应机理为基础推导得到了各反应物的单事件反应动力学速率方程。
根据单事件数的定义,通过计算反应物和反应过渡态的全局对称数,便可得到基本反应步骤的单事件数。本文依据分子对称数的定义,实现了前人尚未做到的全局对称数的自动计算,并列举了以此算法为依据的全局对称数计算示例。该方法方便快捷地实现了大量基本反应步骤的单事件数计算,对单事件反应动力学的研究具有重要学术价值。
最后,采用局部极小优化算法-BFGS变尺度法和全局优化算法-模拟退火法(SA)联用的混合算法,以正己烷催化重整反应实验数据为基础,估计了C6催化重整反应的单事件速率常数。其结果表明,所得的动力学参数符合双功能重整机理,如：具有叔正碳离子参与的基本反应步骤的活化能比没有叔正碳离子参与的基本反应步骤的活化能低。支链数发生变化的PCP异构化反应的活化能比支链数不发生变化的甲基转移反应活化能高等。同时,也表明BFGS-SA混合算法具有较好的稳定性和收敛性。
以上研究实现了单事件方法在催化重整分子尺度反应动力学研究过程中的应用,对复杂反应系统单事件反应动力学模型的研究和发展具有重要理论意义和借鉴作用。
The molecular level kinetic model is an important breakthrough in the study of kinetic model for complex reaction systems after lumped kinetic model, and already becomes an inevitable development trend of kinetic model for complex reaction system. Among those molecular level kinetic models, the single-event method not only can retain the full detail of reaction network, but also can reduce the number of model parameters to a tractable level, so it attracts wide attentions. The single-event method was built and optimized by the study of single-event kinetic model for catalytic reforming.
The catalytic reforming of n-hexane, n-heptane and 2,2,4-trimethylpentane over Pt-Sn/Al22O3-Cl catalyst were studied in this paper. The results showed that isomerization is the main reaction occurred in reforming of three kinds of model compounds, cyclization and cracking reactions are much slower than isomerization. Cracking reaction of 2,2,4-trimethylpentane occurs easily due to its special molecular structure. The classical bifunctional reforming mechanism was chosen as the foundation of single-event kinetic model for catalytic reforming based on the literature survey and experimental research.
The digital representation of all kinds of molecules was carried out using Boolean relation matrix. The carbon atoms in molecule were labelled stochastically. According to hybrid state of carbon atoms, the C=C double bond and charge of carbon atom were clearly represented in Boolean relation matrix by utilization of main diagonal elements, which can avoid to use additional vectors. The Golender's potential vector of molecule with C=C double bond or charge was calculated creatively based on the Boolean relation matrix and Golender's graph potential, and it can be used to confirm the unique molecule to avoid redundance of molecule storage in reaction network database. The number of non-zero elements in a row without counting main diagonal elements in matrix determines whether the corresponding carbon atom is primary secondary, tertiary or quaternary. The type of molecule can be determined by inspecting the whole matrix. The pure connection between carbon atoms drawn out form Boolean relation matrix was used to determine the relative position between carbon atoms, and the calculation formula was put forward, it is necessary for digital representations of reactions
And then, the digital representations of reactions occurred at metallic and acidic sites by performance of Boolean relation matrix based on reaction mechanism of catalytic reforming were carried out.
In order to perform search, comparison, and storage of molecules and reactions during the reaction network generation and rate equation construction quickly, several optimization designs were executed for reaction network database:(1) the file name of molecule storage was the combination of carbon number and molecule type; (2) the file name of reaction storage was the combination of reaction type, carbon number of reactant, carbon number of first product, and second product; (3) the key and time-consuming characters of Boolean relation matrix were prestored in the database, for example, carbon number of molecule, Ring carbon atom number, Golender's potential vector, and so on.
The program for reaction network generation was completed according to the constructed program flow chart based on the bifunctional reaction mechanism. The detailed reaction network necessary for single-event kinetics resolution of catalytic reforming was generated via this program. Because chain growth reactions were not considered in catalytic reforming, the reaction network is only dependent of the carbon number of starting molecule, but independent of its type, due to the reversibility between molecules with the same carbon number. The results of network generation showed that the networks generated from different molecules with the same carbon number were consistent with each other.
The single-event concept was introduced based on transition state theory. The elementary-step rate coefficient is the product of single-event number and single-event rate coefficient. The number of parameters can be further reduced by thermodynamic restriction. The rate equations of single-event kinetic model were deduced based on gas-solid catalysis and bifunctional reforming mechanism.
According to the definition of single-event number, the single-event number of elementary step can be obtained from global symmetry number of reactant and transition state. The automatic calculation of global symmetry number was realized by the definition of symmetry number, and some examples were given. A large number of single-event numbers of elementary steps were calculated based on the program originated from automatic calculation algorithm. It is important for study of single-event kinetic model due to its academic value.
Finally, the single-event rate coefficients of C6 reforming were estimated based on the data of n-hexane reforming using the hybrid algorithm which is the combination of BFGS and simulated anneal algorithm. The results showed that obtained kinetic parameters were consistent with the bifunctional reforming mechanism; the activation energy of reactions with tertiary carbeniums is lower than that of reactions without tertiary carbeniums; the activation energy of reactions with branch degree change is higher than that of reactions without branch degree change. At the same time, the BFGS-SA hybrid algorithm appears good stability and astringency during parameter estimation.
The application of single-event method in the study of molecular level kinetics for catalytic reforming was realized by above research, and this study has important theoretical significance and reference values for the research and development of single-event kinetic model for complex reaction systems.
引文
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