## 3 Research Status of Numerical Simulation
### Reaction Kinetics  
In the study of SCWO and SCHC, the chemical reaction network theory [11], the overall reaction kinetic model and the DCKM are generally used to describe the reaction laws. The first holds that the initial organic reactants can be generally converted in three ways: direct oxidation to final products, indirect oxidation from unstable intermediate products to final products, and indirect oxidation from stable intermediate products to final products. The determination of intermediate products is the key. For an overall reaction kinetic model, the rate constant is obtained by determining the reactant concentration variation along with reaction time at different temperatures. Then, the activation energy and pre-exponential factor of the reaction are fitted according to Arrhenius law. With the generally low concentration of organic matter and less heat release in this kind of experiment, the temperature is basically stable during the reaction. By comparing and analyzing the reaction rate constants obtained from different experimental data, [PERSON] et al. found that the reaction rate constants were highly dispersed [81]. They held that the kinetic parameters of the reaction acquired by fitting were affected by the initial concentration of the material, the oxidation coefficient and the non-ideal flow mixing. Moreover, from the angle of the mechanism of free radical chain reaction, they also pointed out the deviations of the overall reaction kinetic model in the induction stage and the chain termination stage. Despite the poor extrapolation of the overall reaction kinetic model obtained by experimental fitting, its related researches and rich experimental data provide the basis for the verification of higher-order mechanisms. Compared with the first two methods, the more accurate DCKM includes all the reaction-related free radicals and intermediates, among which the elementary reactions may occur and thus lead to an accurate description of the induction stage, chain branching stage and chain termination stage. The kinetic data of these elementary reactions are generally derived from quantum chemistry and transition state theoretical calculations, and verified by standardized experiments. In 1991, [PERSON] et al. established the DCKM of C-1 based on the kinetic data of NIST, which has been used to simulate the SCWO of methane, methanol and formaldehyde [82]. Although the effect of pressure on the reaction kinetics was considered, the simulation results still underestimated the experimental reaction rate by nearly 10 times. [PERSON] assumed that the limitation of the model was due to the unobvious role of water in the conventional gas-phase combustion elementary reaction and the failure of the modified model to reflect the water's effects in the supercritical environment. [PERSON] et al. adopted the kinetic data of Professor [PERSON] from Princeton University, considered the role of water as the third body of collision, and refined the sub-mechanism of H\({}_{2}\)/O\({}_{2}\)[83]. These efforts assured a better prediction of the conversion of H\({}_{2}\), but still underestimated the conversion rate of CO under lean-burn conditions. [PERSON] et al. [84] and [PERSON] et al. [85] modified the rate constants of sensitive reactions in the existing model, so that the model was empirically in good agreement with the experimental data. [PERSON] et al. [86] established the DCKM of C-1 for SCWO usingthe kinetic parameters recommended by [PERSON] et al. [87; 88], and supplemented the kinetic data of single-molecule reactions and pressure-dependent bimolecular reactions under the high-pressure limit. Without any adjustment of experiment-based parameters, the predicted accuracy of the model was encouraging. On the basis of the detailed gas-phase combustion mechanism of benzene, [PERSON] et al. realized the accurate prediction of the concentration distribution of benzene and phenol under the condition at 813 K and 24.6 MPa by supplementing the new reaction pathway of C6H5 OO [89]. [PERSON] et al.