6.3.1. Model Validation

In this research, two different methods are utilized to investigate the accuracy of the developed kinetic model [31]. Thermodynamically, the comparison adsorption constants of compartments and the thermo-dynamic value, present a quality base criterion to investigate validity of kinetic equation. In this regard, combining the entropy concept with gas universal constant provide a procedure for finding the thermodynamic compatibility. In detail, if the overall entropy of the gaseous state of components is higher than the entropy of adsorbed components, the thermo-dynamic compatibility is reached. In more detail, according to this concept, if the kinematic constants match the following equations, it is possible to claim the thermodynamic compatibility:

$$
\Delta\_{ads} S^0\_{i,j} = S^0\_{ads.i.j} - S^0\_{\mathbb{S}^{.i}} < 0 \tag{30}
$$

$$\exp\frac{\Delta\_{\text{ads}}S^0\_{i,j}}{R} = \mathcal{K}\_{j,i\infty} \tag{31}$$

$$\left|\Delta\_{ads}S\_{i,j}^{0}\right| < \mathcal{S}\_{g,i}^{0} \tag{32}$$

$$\left| \Delta\_{ads} \mathcal{S}\_{i,j}^{0} \right| > -\text{R.ln} \frac{\theta\_i}{\theta\_{cr,i}} \approx 41.8 \text{ J/(mol.K)} \tag{33}$$

$$
\Delta\_{ads}S\_{i,j}^0 < -51 \frac{J}{mol.K} + \frac{0.00141}{K} \times \Delta\_{ads}H\_{i,j} \tag{34}
$$

$$
\text{In validity of the developed model, the simulation results are compared.}
$$

In addition, to prove the validity of the developed model, the simulation results are compared with the real plant data at the dynamic condition. Figure 11a,b shows the comparison between outlet acetylene concentration from guard bed and calculated concentration by the model. The mean absolute error of the model and plant data is below 3.0%. Thus, the proposed model is a practical tool in predicting the performance of a hydrogenation process. In addition, to prove the validity of the developed model, the simulation results are compared with the real plant data at the dynamic condition. Figure 11a,b shows the comparison between outlet acetylene concentration from guard bed and calculated concentration by the model. The mean

**Figure 11.** Comparison between outlet acetylene concentrations calculated by the model and plant data in (a) lead and, (b) guard beds. **Figure 11.** Comparison between outlet acetylene concentrations calculated by the model and plant data in (**a**) lead and, (**b**) guard beds.

#### 6.3.2. Reactor Simulation 6.3.2. Reactor Simulation

In this section, the concentration and temperature profiles, along the reactors, are presented during the process run-time. Based on the simulation results, after 400 days of continuous operation, the activity of catalyst in the Lead bed decreased to 0.2, while the activity of the catalyst in the Guard bed is 0.5. Figure 12 shows the acetylene molar flow rate along the Lead and guard beds during the process run-time. It appears that the acetylene concentration decreases along the reactor length. Due to catalyst deactivation, the acetylene concentration in the outlet stream from lead bed increases during the process run-time and approaches from 7.43 mol s-1 to 10.09 mol s-1. Typically, the acetylene conversion decreases during the process run-time in the Lead bed and approaches from 67.2% at the start of the run to 55.5% at the end of run. Decreasing acetylene conversion in the Lead bed proves the philosophy of the Guard bed in the acetylene hydrogenation process. The unconverted acetylene is converted to ethane and ethylene in the Guard bed. It appears that acetylene molar flow rate in the outlet stream from the Guard bed increases during the process run-time and approaches from 0.19 to 0.21 mol s-1. In this section, the concentration and temperature profiles, along the reactors, are presented during the process run-time. Based on the simulation results, after 400 days of continuous operation, the activity of catalyst in the Lead bed decreased to 0.2, while the activity of the catalyst in the Guard bed is 0.5. Figure 12 shows the acetylene molar flow rate along the Lead and guard beds during the process run-time. It appears that the acetylene concentration decreases along the reactor length. Due to catalyst deactivation, the acetylene concentration in the outlet stream from lead bed increases during the process run-time and approaches from 7.43 mol s−<sup>1</sup> to 10.09 mol s−<sup>1</sup> . Typically, the acetylene conversion decreases during the process run-time in the Lead bed and approaches from 67.2% at the start of the run to 55.5% at the end of run. Decreasing acetylene conversion in the Lead bed proves the philosophy of the Guard bed in the acetylene hydrogenation process. The unconverted acetylene is converted to ethane and ethylene in the Guard bed. It appears that acetylene molar flow rate in the outlet stream from the Guard bed increases during the process run-time and approaches from 0.19 to 0.21 mol s−<sup>1</sup> .

**Figure 12.** Acetylene flow rate along the Lead and guard beds during the process runtime. **Figure 12.** Acetylene flow rate along the Lead and guard beds during the process runtime. **Figure 12.** Acetylene flow rate along the Lead and guard beds during the process runtime.

Figure 13 shows the temperature profile along the Lead and Guard beds during the process runtime. Since the acetylene hydrogenation reaction is exothermic, temperature increases along the reactors. Typically, catalyst decay decreases the rate of acetylene hydrogenation in the Lead and guard beds, and the temperature of outlet stream from the Lead and guard beds decreases gradually. Lower acetylene hydrogenation in the Lead and guard beds increases acetylene concentration in the feed of Guard bed reactor during the process run time. Thus, increasing acetylene concentration in the Guard bed increases heat generation through a hydrogenation reaction and temperature increases at the outlet of Guard bed. Generally, lower acetylene conversion in the Guard bed results in the lower temperate rise in the reactor. Figure 13 shows the temperature profile along the Lead and Guard beds during the process runtime. Since the acetylene hydrogenation reaction is exothermic, temperature increases along the reactors. Typically, catalyst decay decreases the rate of acetylene hydrogenation in the Lead and guard beds, and the temperature of outlet stream from the Lead and guard beds decreases gradually. Lower acetylene hydrogenation in the Lead and guard beds increases acetylene concentration in the feed of Guard bed reactor during the process run time. Thus, increasing acetylene concentration in the Guard bed increases heat generation through a hydrogenation reaction and temperature increases at the outlet of Guard bed. Generally, lower acetylene conversion in the Guard bed results in the lower temperate rise in the reactor. Figure 13 shows the temperature profile along the Lead and Guard beds during the process runtime. Since the acetylene hydrogenation reaction is exothermic, temperature increases along the reactors. Typically, catalyst decay decreases the rate of acetylene hydrogenation in the Lead and guard beds, and the temperature of outlet stream from the Lead and guard beds decreases gradually. Lower acetylene hydrogenation in the Lead and guard beds increases acetylene concentration in the feed of Guard bed reactor during the process run time. Thus, increasing acetylene concentration in the Guard bed increases heat generation through a hydrogenation reaction and temperature increases at the outlet of Guard bed. Generally, lower acetylene conversion in the Guard bed results in the lower temperate rise in the reactor.

**Figure 13.** Temperature profile along the Lead and Guard beds during the process runtime. **Figure 13.** Temperature profile along the Lead and Guard beds during the process runtime. **Figure 13.** Temperature profile along the Lead and Guard beds during the process runtime.
