## 3 Results and Discussion
### Isomerization  
The three reactors in series in the isomerization process were initially simulated under adiabatic operation using Fortran code, following the procedure described in Section 2.2. However, in the first reactor, a temperature prediction error of 6.72% was observed compared to plant data, probably due to energy losses [17]. The model considers energy losses in the first reactor, which are mainly attributed to its thermal insulation. According to the data reported by [PERSON] et al. [15], none of the studied reactors have a cooling system; therefore, it is not necessary to include the influence of external heating or cooling effects in the model under industrial conditions [24]. Figure 1: Chemical equilibrium compositions for reaction Schemes 1 (**a**) and 8 (**b**) of the C\({}_{6}\) series. Considering heat transfer between the reactor and its surroundings, the lack of detailed information on the construction materials and insulation type prevents accounting for its effect through the heat transfer coefficient, U. Thus, a non-adiabatic model was adopted, assuming a heat loss of Q = \(-2.70\times 10^{6}\) Kj/h [17] in the energy balance, Equation (12), where \(Q_{n}=Q/n\). This consideration was applied to the first reactor for all eight reaction schemes. In the literature on petroleum refining processes, such as catalytic reforming (CCR) and isomerization, where kinetic parameters are estimated from experimental data at both industrial and laboratory scales, a frequent limitation has been noted: the experimental data available for industrial-scale processes are often scarce and, in most cases, fewer in number than the kinetic parameters required for their modeling [7; 11; 14; 16; 27; 28; 29; 30]. [PERSON] and [PERSON] [30] highlight that, under this condition, the set of estimated values for the kinetic parameters cannot be unique. The challenge of having fewer plant experimental data compared to the number of kinetic parameters required to model petroleum refining processes has been a historical issue. Despite this difficulty, the simulation of these processes remains a fundamental tool, particularly for the development of applications such as Operator Training Simulation (OTS). In a nonlinear parameter estimation problem, to avoid potential overfitting, it is necessary for the number of experimental data to be greater than the number of parameters to be determined in the modeling. To ensure that the model does not incur in overfitting, only 16 frequency factors were estimated against a total of 20 plant experimental data [15]. Initially, 16 kinetic parameters corresponding to the frequency factor (Aj) were determined through optimization for Scheme 1, as the activation energy (Bj) values taken from [PERSON] et al. [17] remained fixed. The Aj and Bj values for the reactions of the C4 and C5 series, as well as for benzene saturation and cracking reactions, were fixed, and subsequently, the predictive performance of the remaining schemes in the C6 series was evaluated. These parameters are presented in Table 3.  
For the reactions in the C6 series, the values of Aj and Ej were optimized individually for each reaction, independent of the scheme in which they were included. Therefore, the kinetic parameters of a specific reaction can be applied to any combination, provided that the reaction is part of the scheme. Table 4 lists all the reactions used in the eight schemes, along with their corresponding kinetic  
Figure 2: _Cont._  
Regarding temperature, the eight schemes exhibit an average prediction error of 1.44%. The temperature profile among the three reactors is shown in Figure 3. Since the prediction errors for both molar flows and temperatures are nearly identical, it can be concluded that any of the eight analyzed schemes allow for the accurate modeling of the phenomenon. As proposed by [PERSON] et al.