*2.2. Catalyst Characterization*

**3. Kinetic Modeling**

*3.1. Experiment Design*

*3.2. Reaction Mechanism* 

adsorbed on the catalyst surface as:

ଶଶ

ௗ௦ௗ ௦ ር⎯⎯⎯⎯⎯⎯⎯⎯ሮ ⎩ ⎪ ⎨ ⎪

The supplied catalyst is characterized by BET, TGA, XRD, SEM, and TEM analysis. BET analysis is used to measure the specific surface area and the pore size distribution of catalyst. The SEM test is used to analysis the surface and morphology of catalyst by scanning the surface with a focused beam of electron. TGA is a thermal method used to investigate the stability of a catalyst during heating. In this regard, the mass of the catalyst is measured over time during the heating. The XRD technique is an analytical tool used to determine the phase and dimension of crystalline material. In the present research, the SEM and TEM analyses were performed by using Philips XL 30 (FEI Company, Hillsboro, OR, USA) and FEI Tecnai G<sup>2</sup> F20 (FEI Company, Hillsboro, OR, USA), respectively. The XRD pattern of the catalyst was recorded on a Rigaku D/Max-2500 (Rigaku, Austin, TX, USA) diffractometer at a scanning speed of 4 min−<sup>1</sup> over the 2θ range of 10–80◦ . The TGA and DTA (differential thermal analysis) analysis of the fresh and deactivated catalysts were performed by Mettler Toledo Model 2007. The nitrogen adsorption and desorption tests were measured by Quanta chrome Autosorb at 70 K. The specific surface area of the catalyst was calculated by the Brunauer–Emmett–Teller equation. In addition, the Horvath and Kawazoe equation were used to calculate the pore size and volume of catalyst particles.

The supplied feed stream contains acetylene, ethylene, and ethane contaminated with a trace of propylene and methane. After regulation of the temperature and flow rate, feed stream enters to the reactor and passes over the ceramic ball and catalyst layers. The ceramic ball layer is considered to uniform distribution of feed along the catalytic bed. To detect the product distribution, the effluent is attached to the gas chromatography and product composition is measured on-line. Figure 1 shows the designed reactor to investigate kinetic of acetylene hydrogenation. *Processes* **2019**, *7*, x FOR PEER REVIEW 5 of 22

**Figure 1.** The designed reactor to investigate kinetic of acetylene hydrogenation. **Figure 1.** The designed reactor to investigate kinetic of acetylene hydrogenation.

**Table 3.** The variation range and number of data points.

Pressure (Bar) 15 20 3 Temperature 35 60 4 GHSV 2600 6200 6

In this research, acetylene conversion to ethylene, ethane, butenes, and butadiene are considered as independent reactions in the considered network. Typically, the ethylene and acetylene could be

> <sup>⎧</sup>− = − − − ≡ − − − ଷ ℎℎ − = ଶ − − ଷ ℎ = = ଶ ⎭

⎪ ⎬ ⎪ ⎫

(1)

Hydrogen to acetylene ratio 0.5 1.5 3

 **Lower Upper Number of Levels** 

full factorial design method, 216 independent experiments are designed.

During the past decade, several designs of experimental approaches have been developed to reduce the numbers of experiments [23]. In the current research, the factorial design method, based on the cubic pattern, is used to determine the experiments. In statistics, the full factorial is an experimental design method, whose design consists of two or more factors, each with discrete possible levels. In the first step, the effective parameters, ranges, and levels are selected to cover a wide range of operating condition. The considered independent variables are temperature, pressure, hydrogen to acetylene ratio, and GHSV. The fraction of products in the outlet stream is selected as the objective function. Table 3 shows the variation range and the number of data points. Considering
