Kinetic Model of Urea-Related Deposit Reactions

The thermal analysis kinetic method was employed to solve the activation energies of the thermal decomposition reactions of urea and cyanuric acid, with the purpose of understanding the formation of deposits in the diesel engine SCR system. The deposit reaction kinetic model was established by optimizing the reaction paths and reaction kinetic parameters based on the thermal analysis test data of the key components in the deposit. The result shows that the established deposit reaction kinetic model can accurately describe the decomposition process of the key components in the deposit. Compared to the Ebrahimian model, the simulation precision of the established deposit reaction kinetic model is significantly improved above 600 K. The activation energies of the urea and cyanuric acid decomposition reactions are 84 kJ/mol and 152 kJ/mol, respectively, after model parameters identification. The identified activation energies were closest to those of the Friedman one-interval method indicating that the Friedman one-interval method is reasonable to solve the activation energies of deposit reactions.


Introduction
The need to control harmful gas emissions and improve environmental quality is becoming increasingly strong, with global environmental pollution becoming increasingly prominent and people's awareness of environmental protection gradually strengthening. Nitrogen oxides (NO x ) are one of the main harmful emissions from diesel engines, which has caused great harm to human health, the ecological environment and the climate. Nowadays, selective catalytic reduction (SCR) systems [1] have been increasingly used in diesel as the mainstream device to deal with NO x emissions [2,3].
Urea-SCR technology is to spray urea aqueous solution into the exhaust pipe of a diesel engine at a suitable location; it produces the reducing agent NH 3 after evaporation, pyrolysis and hydrolysis, and NH 3 converts the harmful NO x into harmless N 2 and H 2 O under the action of a catalyst. Numerous studies [4][5][6][7][8] have revealed that the exhaust pipe wall of diesel engines with urea-SCR systems was prone to form deposits consisting of undecomposed urea, biuret, and cyanuric acid (CYA). The deposits easily lead to partial or even total blockage of the exhaust pipe, which increases the exhaust back pressure and seriously affects the performance of diesel engines [9].
The mechanism of the urea pyrolysis reaction is complex. Dong, et al. [10] have studied the pyrolysis process of urea using thermogravimetric combined with Fourier infrared spectroscopy analytical methods. The result indicated that the urea pyrolysis process went through three stages. Each stage occurred at 193 • C, 250 • C and 400 • C, corresponding to residual mass fractions of 46.2%, 39.5% and 9.2%, respectively. The polymerization of HNCO and the condensation reaction with urea and biuret are the main reasons for producing polymeric compounds. Schaber, et al. [11] have studied the thermal decomposition process of urea in detail. The results indicated that the urea pyrolysis process could be divided into four reaction stages, where the first and second stages were the main reaction processes. The mass loss was mainly related to the urea decomposition in the first reaction processes. The mass loss was mainly related to the urea decomposition in the first reaction stage (room temperature to 190 °C). The urea was decomposed into the biuret and began to slowly synthesize complex products, such as cyanuric acid and cyanuric acid monoamide. The urea continued to decompose and the biuret began to decompose at the second reaction stage (190~250 °C). The production rate of cyanuric acid and cyanuric acid monoamide increased, while little cyanuric acid amide and melamine began to be generated. The third reaction stage (250~360 °C) and the fourth reaction stage (>360 °C) were mainly the decomposition and sublimation of residues. Zhao [12] from Tsinghua University studied the influence of the urea pyrolysis process at different temperatures and different heating rates by thermogravimetric tests. Thagard [13] has analyzed the urea pyrolysis process at 150-200 °C using the DBD method. The results indicated there was no difference in the urea pyrolysis by-products whether in wet or dry air, the main gaseous products were NH3 and HNCO, and the residual solid product was CYA. In addition, Stradella [14], Carp [15] and Lundström [16] have conducted studies related to urea pyrolysis as well.
The detailed kinetic model of the deposit reaction is required to quantitatively describe the production of the deposit. Ebrahimian [17] has established the reaction kinetic model of the urea pyrolysis process. It considered four kinds of components of deposit, including urea, biuret, CYA and ammelide, which provided a guide for the quantitative study of deposit formation. Brack, et al. [18] have revised the reaction path based on the Ebrahimian mechanism model. They re-identified the reaction kinetic parameters, according to the results of thermogravimetric tests with different urea initial masses, temperature heating rates and reactor configurations. However, Figure 1 shows that the simulation values of urea pyrolysis, respectively, from the above reaction kinetic models established by Ebrahimian and Brack, are different from the experimental values.
(a) In this study, thermal analysis technology was applied to the investigation of chemical reaction kinetics, and various classical thermal analysis kinetic methods were used to solve the activation energy of the decomposition reactions of urea and CYA. According to the Ebrahimian mechanism model, we re-identified the reaction kinetic parameters and established a deposit reaction kinetic model to describe the decomposition process of the key components in the deposit, attempting to provide a reference for the quantitative study of the deposit formation.    In this study, thermal analysis technology was applied to the investigation of chemical reaction kinetics, and various classical thermal analysis kinetic methods were used to solve the activation energy of the decomposition reactions of urea and CYA. According to the Ebrahimian mechanism model, we re-identified the reaction kinetic parameters and established a deposit reaction kinetic model to describe the decomposition process of the key components in the deposit, attempting to provide a reference for the quantitative study of the deposit formation.    According to the TG curves of urea pyrolysis, the temperature data corresponding to each conversion rate are obtained at different heating rates. Table 1 shows the result of the activation energy of urea decomposition by substituting these data into Equation (24). E 12 is the result from two sets of data with heating rates of 5 and 10 • C/min, E 23 , E 34 and E 45 to follow. As the results show in Table 1, E 34 has a large error in the process of calculating the activation energy of urea decomposition. The reason is that the two thermogravimetric curves of heating rates β 3 and β 4 almost coincide. The difference of temperature T corresponding to them is very small for the same conversion rate α, which brings a large error. Therefore, the set of data was discarded when calculating the total activation energy E. Finally, the activation energy of urea decomposition is 79 kJ/mol (95% confidence interval, CI: 74-83, as shown in Figure A1) calculated from the Ozawa method.

The Friedman-Reich-Levi Method
According to the TG curves of urea pyrolysis, dα/dT corresponding to each conversion rate is obtained at different heating rates. These data are substituted into Equation (28) to obtain the results of the activation energy of urea decomposition from the two-interval method (as shown in Table 2) and the one-interval method (as shown in Table 3).
As the results show in Tables 2 and 3, E 34 has a large error in the process of calculating the activation energy of urea decomposition. The reason is that the two thermogravimetric curves of heating rates β 3 and β 4 almost coincide. The difference between temperature T and dα/dT corresponding to them is very small for the same conversion rate α, which brings a large error. Therefore, the set of data was discarded when calculating the total activation energy E. Finally, the activation energy of urea decomposition is 80 kJ/mol (95% confidence interval, CI: 68-93, as shown in Figure A2) calculated from the Friedman two-interval method and 84 kJ/mol (95% confidence interval, CI: 66-103, as shown in Figure A3) calculating from the Friedman one-interval method. Table 2. The activation energy E F,2 of urea decomposition from two-interval method (Unit: kJ/mol).  As the results show in Tables 2 and 3, E34 has a large error in the process of calc the activation energy of urea decomposition. The reason is that the two thermograv curves of heating rates β3 and β4 almost coincide. The difference between temper and dα/dT corresponding to them is very small for the same conversion rate α, brings a large error. Therefore, the set of data was discarded when calculating th activation energy E. Finally, the activation energy of urea decomposition is 80 kJ/m confidence interval, CI: 68-93, as shown in Figure A2) calculated from the Friedma interval method and 84 kJ/mol (95% confidence interval, CI: 66-103, as shown in A3) calculating from the Friedman one-interval method. Figure 3 shows the DSC curves of urea pyrolysis at different heating rates. According to the DSC curves of urea pyrolysis, the peak temperature date T tained at different heating rates. Table 4 shows the result of the activation energy decomposition by substituting these data into Equation (32). According to the DSC curves of urea pyrolysis, the peak temperature date T p is obtained at different heating rates. Table 4 shows the result of the activation energy of urea decomposition by substituting these data into Equation (32). As the results show in Table 1, E 34 has a large error in the process of calculating the activation energy of urea decomposition. The reason is that the difference between the peak temperatures T p on the two DSC curves of heating rates β 3 and β 4 is very small, which brings a large error. Therefore, the set of data was discarded when calculating the total activation energy E. Finally, the activation energy of urea decomposition is 82 kJ/mol (95% confidence interval, CI: 55-110, as shown in Figure A4) calculated from the Kissinger method.

E24
102 As the results show in Table 4, E34 has a large error in the process of calculating the activation energy of urea decomposition. The reason is that the difference between the peak temperatures Tp on the two DSC curves of heating rates β3 and β4 is very small, which brings a large error. Therefore, the set of data was discarded when calculating the total activation energy E. Finally, the activation energy of urea decomposition is 82 kJ/mol (95% confidence interval, CI: 55-110, as shown in Figure A4) calculated from the Kissinger method. Figure 4 shows the TG curves of CYA pyrolysis at different heating rates. According to the TG curves of CYA pyrolysis, the temperature data corresponding to each conversion rate are obtained at different heating rates. Table 5 shows the result of the activation energy of CYA decomposition by substituting these data into Equation (24). Finally, the activation energy of CYA decomposition is 145 kJ/mol (95% confidence interval, CI: 138-153, as shown in Figure A5) calculated from the Ozawa method. According to the TG curves of CYA pyrolysis, the temperature data corresponding to each conversion rate are obtained at different heating rates. Table 5 shows the result of the activation energy of CYA decomposition by substituting these data into Equation (24). Finally, the activation energy of CYA decomposition is 145 kJ/mol (95% confidence interval, CI: 138-153, as shown in Figure A5) calculated from the Ozawa method.

The Friedman-Reich-Levi Method
According to the TG curves of CYA pyrolysis, dα/dT corresponding to each conversion rate is obtained at different heating rates. These data are substituted into Equation (28) to obtain the results of the activation energy of CYA decomposition from the two-interval method (as shown in Table 6) and the one-interval method (as shown in Table 7). Finally, the activation energy of CYA decomposition is 138 kJ/mol (95% confidence interval, CI: 128-148, as shown in Figure A6) calculated from the Friedman two-interval method and 153 kJ/mol (95% confidence interval, CI: 124-182, as shown in Figure A7) calculated from the Friedman one-interval method.  Figure 5 shows the DSC curves of CYA pyrolysis at different heating rates. According to the DSC curves of CYA pyrolysis, the peak temperature data Tp tained at different heating rates. Table 8 shows the result of the activation energy of decomposition by substituting these data into Equation (32). Finally, the activation e of CYA decomposition is 150 kJ/mol (95% confidence interval, CI: 109-190, as sho Figure A8) calculated from the Kissinger method. According to the DSC curves of CYA pyrolysis, the peak temperature data T p is obtained at different heating rates. Table 8 shows the result of the activation energy of CYA decomposition by substituting these data into Equation (32). Finally, the activation energy of CYA decomposition is 150 kJ/mol (95% confidence interval, CI: 109-190, as shown in Figure A8) calculated from the Kissinger method.
R12 Urea (aq) + NCO − + H + → Biuret However, the above mechanism model does not distinguish the different shapes of urea from the perspective of deposit formation in the diesel SCR system. Therefore, the additional reaction paths as shown in Equations (13) and (14) are proposed for the transformation of different urea forms based on the Ebrahimian mechanism model. Moreover, the mechanism model of deposit reaction is established according to Equations (1)- (14).

Reaction Rate Equation
The generation rate of the component k can be expressed as follows [19] for the reaction R1-R12.
where: ν ki is the stoichiometric coefficient of the component k in the i-step reaction; A i is the reaction pre-exponential factor; E a,i is the reaction activation energy; Cs j is the surface concentration of the component j. A i can be calculated by the following equation: where: Γ is the active site density; ni is the number of activity levels. The active surface can be calculated by the following equation, assuming the effective area of the model does not change during the whole calculation process.
where: σ k is the active site occupied by component k; W k is the molecular mass of the component k. Cs j can be calculated by the following equation: The generation rate of component k can be expressed as follows for the reaction R13.
)Cs urea_aq (19) where: K dying and A dying are coefficients; f H2O is the component concentration of water in the aqueous urea solution; f max H 2 O takes the value of 0.876.
The generation rate of component k can be expressed as follows for the reaction R14. (20) where: K cry and A cry are coefficients; C cry takes the value of 233.4 K.

The Model Parameters Identification and Validation
The kinetic parameters of the deposit reaction model were identified, according to the results of thermal analysis experiments for urea, biuret, and CYA. The initial values of the kinetic parameters for the reactions R1-R12 are referred to in the Ebrahimian mechanism model. The value range of activation energy is set to 78-85 kJ/mol for the urea decomposition reaction R1 and 137-153 kJ/mol for the CYA decomposition reaction R7, referring to the results in Sections 3.1 and 3.2. Table 9 shows the identification results of reaction kinetic parameters. It can be observed that the activation energy of the urea decomposition reaction is 84 kJ/mol and CYA is 152 kJ/mol after identification. Both of the identified activation energies are closest to the results of the Friedman one-interval method.  Figure 6a shows the simulation results of the deposit reaction kinetic model in this paper and the thermogravimetric experimental results. The model in this paper can describe the key components of deposit decomposition accurately. Ebrahimian also obtained the comparison of thermogravimetric test and simulation results for each component of the deposits, as shown in Figure 6b. In the Ebrahimian model, the simulation results have an appreciable error above 600 K, which is the initiation temperature of CYA decomposition. We have solved the chemical reaction activation energy of CYA decomposition through the thermogravimetric test. It is employed to constrain the value of parameter identification and enhance the simulation accuracy of the deposit reaction kinetic model over 600 K.
the comparison of thermogravimetric test and simulation results for each component of the deposits, as shown in Figure 6b. In the Ebrahimian model, the simulation results have an appreciable error above 600 K, which is the initiation temperature of CYA decomposition. We have solved the chemical reaction activation energy of CYA decomposition through the thermogravimetric test. It is employed to constrain the value of parameter identification and enhance the simulation accuracy of the deposit reaction kinetic model over 600 K.

Test Equipment
The integrated thermal analyzer STA449F3 made by German NETZSCH company was employed to simultaneously measure the mass and energy difference curves of the sample with temperature or time, which is to say the TG and DSC curves.

Test Sample
The purity of urea used in the test was not less than 99%, which was provided by Tianjin Guangfu Technology Development Company Limited.

Test Conditions
Each test sample was pulverized into powder form in an agate mortar, and about 10 mg of the sample was placed in an alumina crucible (3 mm in diameter). The purge gas in the heating furnace was Ar with a flow rate of 40 mL/min. The samples were heated from room temperature to 1000 °C at the heating rate of 2, 5, 10, 15, 20, and 25 °C/min.

Test Equipment
The integrated thermal analyzer STA449F3 made by German NETZSCH company was employed to simultaneously measure the mass and energy difference curves of the sample with temperature or time, which is to say the TG and DSC curves.

Test Sample
The purity of urea used in the test was not less than 99%, which was provided by Tianjin Guangfu Technology Development Company Limited.

Test Conditions
Each test sample was pulverized into powder form in an agate mortar, and about 10 mg of the sample was placed in an alumina crucible (3 mm in diameter). The purge gas in the heating furnace was Ar with a flow rate of 40 mL/min. The samples were heated from room temperature to 1000 • C at the heating rate of 2, 5, 10, 15, 20, and 25 • C/min.

The Flynn-Wall-Ozawa Method
The Ozawa equation is as follows [20,21]: where: β is the heating rate (generally constant); α is the conversion rate; A is the preexponential factor; E is the activation energy; R is the molar gas constant; T is the thermodynamic temperature. The intersection points (α, T 1 , β 1 ) and (α, T 2 , β 2 ) with the same conversion rate α on the two TG curves of different heating rates β 1 and β 2 are substituted into Equation (21) to obtain: Subtracting Equation (23) from Equation (22) to obtain: The values of α are usually 0.95, 0.90, 0.85, . . . , 0.15, 0.10. An α can solve a value of E, and the reasonable activation energy E can be eventually determined by analyzing all the solved E values logically.

The Kissinger-Akahira-Sunose Method
The Kissinger equation is as follows [24]: The points (T p1 , β 1 ) and (T p2 , β 2 ) at the peak temperature T p on the two DSC curves of different heating rates β 1 and β 2 are substituted into Equation (29) to obtain: Subtracting Equation (31) from Equation (30) to obtain: According to Equation (32), any two DSC curves can solve a value of E. All the solved E values are analyzed logically, and the reasonable activation energy E can be finally determined.

Conclusions
According to the thermogravimetric test results, we employed various classical thermal analysis kinetic methods to solve the activation energies of the thermal decomposition reactions of urea and CYA. The activation energy of the urea decomposition reaction: the result is 78.44 kJ/mol by the Ozawa method, 80.12 kJ/mol by the Friedman two-interval method, 84.34 kJ/mol by the Friedman one-interval method and 82.64 kJ/mol by the Kissinger method. The activation energy of CYA decomposition reaction: the result is 145.38 kJ/mol by the Ozawa method, 137.83 kJ/mol by the Friedman two-interval method, 152.57 kJ/mol by the Friedman one-interval method and 149.34 kJ/mol by the Kissinger method. After identifying the reaction kinetic parameters in the model of this paper, the activation energies of the decomposition reactions of urea and CYA are 84 kJ/mol and 152 kJ/mol, respectively. The established deposit reaction kinetic model can accurately describe the decomposition process of each key component of deposits. What is more, the simulation accuracy is significantly improved above 600 K, which can provide a reference for the quantitative study of deposit formation. Appendix A Figure A1. 95% confidence interval for the activation energy EO of urea pyrolysis reaction.