6.2.5. Developed Kinetic and Decay Models

In this section, the proposed kinetic model, which predict the rate of reactions, is presented. In this regard, an optimization problem is formulated and the coefficient of proposed rate equations are determined by considering the absolute difference between experimental data and estimated rate as the objective function. Table 5 shows the reactions and proposed kinetic equations to calculate the reaction rate.


**Table 5.** Kinetics of reactions and proposed kinetic model.

Where

$$K\_{\mathbb{C}\_2H\_2} = 2.128 \times e^{\frac{2983.8}{RT}} \tag{27}$$

$$K\_{\mathbb{C}\_2H\_4} = 0.7295 \times e^{\frac{3621}{RT}} \tag{28}$$

The coefficient of the proposed deactivation model is calculated based on the integration of process model and developed the kinetic model. The proposed activity model is inserted in the developed dynamic model of the acetylene hydrogenation process. Then, an optimization problem is formulated to calculate the parameters of the proposed activity model, Kd, Ed, and n, considering the sum of absolute difference between plant data and simulation results, during a process run-time as the objective function. The industrial data points have been presented in the Supplementary Data Set 2. In addition, the composition of green oil as a deactivation agent is presented in the Supplementary Data Set 3. The obtained deactivation model could be explained as:

$$\frac{da}{dt} = -0.21 \, e^{-\left(\frac{8904.4}{RT}\right)} \times a^{2.4} \times \text{C}^{0.13} \tag{29}$$
