*3.1. Experiment Design*

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 full factorial design method, 216 independent experiments are designed.

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


### *3.2. Reaction Mechanism*

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 adsorbed on the catalyst surface as:

$$\begin{aligned} \text{C}\_{2}\text{H}\_{2} \overset{\text{AdS-orbit}}{\overset{\text{As}}{\leftrightarrow}} \Leftrightarrow \begin{cases} -\text{CH}=\text{CH}-\qquad\text{id}-\sigma-\text{Adsorbed} \\ \text{CH}\equiv\text{CH} \\ -\text{CH}-\text{CH}\_{3} \\ -\text{CH}=\text{CH}\_{2} \\ -\text{C}-\text{CH}\_{3} \\ -\text{C}=\text{CH}\_{2} \end{cases} \Leftrightarrow \begin{cases} \text{H}-\text{CH}=\text{CH}-\qquad\text{C}=\text{C}\_{\text{C}}\text{complex} \\ -\text{CH}=\text{CH}\_{2} \\ -\text{C}-\text{CH}\_{3} \\ -\text{C}=\text{CH}\_{2} \end{cases} \Leftrightarrow \begin{cases} \text{V} \\ \text{V} \\ \text{V} \\ \text{V} \\ \text{V} \\ -\text{C}\text{H}-\text{C}\text{H}\_{2} \\ -\text{C}\text{H}-\text{CH}\_{3} \\ -\text{C}\text{H}-\text{CH}\_{3} \\ -\text{C}\text{H}-\text{CH}\_{2} \\ -\text{C}-\text{CH}\_{3} \end{cases} \end{aligned} \tag{1}$$

Based on the density functional theory, selective acetylene hydrogenation to ethylene considering vinyl layer as the intermediate is the most dominant mechanism [24]. Based on the considered reaction mechanism, hydrogen is adsorbed on the catalyst surface as:

$$2H\_2 + 2\text{ S} \leftrightarrow 2H-\text{S} \tag{3}$$

In addition, acetylene is adsorbed on the surface and reacts with adsorbed hydrogen to produce ethylene:

$$\text{C}\_2\text{H}\_2(\text{g}) + \text{S} \xrightleftharpoons[]{} \text{CH}\_2\text{CH}\_2\text{CH}-\text{S} \xrightarrow{+H} \text{CH}\_2\text{CH}\_2(\text{g}) + \text{s} \tag{4}$$

In addition, ethylene in the gas phase is adsorbed on the surface and reacts with adsorbed hydrogen in two steps to produce ethane as:

$$\text{CH}\_2\text{CH}\_2\text{ (g)} + \text{S} \longleftrightarrow \longrightarrow \text{CH}\_2\text{CH}\_2-\text{S} + H-\text{S} \longleftrightarrow \longrightarrow \text{CH}\_3\text{CH}\_2-\text{S} + \text{S} \tag{5}$$

$$\text{CH}\_3\text{CH}\_2-\text{S} + H-\text{S} \longleftrightarrow \text{CH}\_3\text{CH}\_3(\text{g}) + 2\text{S} \tag{6}$$

In general, there are two possible pathways to produce butadiene. According to the first path:

$$\text{CHCH}(\text{g}) + \text{S} \longleftrightarrow \underset{\longleftrightarrow}{\longrightarrow} \text{CH}\_{2}\text{CH}-\text{S} \xrightarrow[\text{-H}]{+H} \text{CH}\_{3}\text{CH}-\text{S} \tag{7}$$

$$\text{HCH}(\text{g}) + \text{S} \longleftrightarrow \longrightarrow \text{CH}\_2\text{C}-\text{S} \tag{8}$$

$$\text{CH}\_3\text{CH}-\text{S} + \text{CH}\_2\text{C}-\text{S} \xrightarrow{\text{---}} \text{CH}\_2\text{CH}\text{CHCH}\_2\text{(g)}\tag{9}$$

According to the second path:

$$\text{C}\_2\text{H}\_2(\text{g}) + \text{S} \xrightleftharpoons[]{+H} \text{CH}\_2\text{CH}-\text{S} \tag{10}$$

$$\text{C}\_2\text{H}\_2(\text{g}) + \text{S} \xrightleftharpoons[-H]{^+H} \\ \text{C}\_2\text{C}\_2\text{H}-\text{S} \end{cases} \tag{11}$$

$$\text{CH}\_2\text{CH}-\text{S} + \overset{\text{\textasciicircum}}{\text{C}} \text{H}\_2\text{CH}-\text{S} \xrightarrow{\text{\textasciicircum}} \text{CH}\_2\text{CHCHCH}\_2\text{H}\_2\text{(g)} + 2\text{ S} \tag{12}$$

Typically, 1,3-butadiene could be found in two different states, including in the gas phase and on the solid surface. In the first state, butadiene is detected in the outlet stream from the reactor, while the second state is a complex state that causes oligomer production. The produced oligomer is precipitated on the catalyst surface and leads to deactivation of the catalyst by blocking active sites [17,25]. Thus, to investigate butadiene and oligomer formation, the outlet gas stream from the reactor is analyzed by

GC-mass and PIONA. The results of GC-mass has been presented in the Supplementary Materials (Data Set 3). The mechanism of 1-butene formation on the catalyst surface is:

$$\text{C}\_2\text{H}\_2(\text{g}) + \text{S} \xrightleftharpoons[\text{H}\_2\text{CH}\_2\text{CH}-\text{S} \xrightleftharpoons[\text{H}\_2\text{CH}\_3\text{CH}-\text{S} + \text{CH}\_2\text{CH}-\text{S} \xrightleftharpoons\text{CH}\_2\text{CHCH}\_2\text{CH}\_3(\text{g}) \tag{13}$$

In addition, the mechanism of cis-2-butane and trans-2-butane formation is as:

$$\text{C}\_{2}\text{H}\_{2}(\text{g}) + \text{S} \xrightleftharpoons[]{+H} \text{CH}\_{2}\text{CH}-\text{S} \xrightleftharpoons[]{+H} \text{H}\_{3}\text{CH}-\text{S} + \text{CH}\_{3}\text{CH}-\text{S} \xrightleftharpoons\text{CH}\_{3}\text{CHCH}\text{CH}\_{3}(\text{g}) \quad \text{(14)}$$
