*3.3. Kinetic Model*

In this section, based on the considered mechanism, a reaction network comprising six reactions is selected. The considered reactions are as follows:

$$\rm C\_2H\_2 + H\_2 \to C\_2H\_4 \tag{15}$$

$$\rm{C\_2H\_4} + \rm{H\_2} \rightarrow \rm{C\_2H\_6} \tag{16}$$

$$\text{2C}\_2\text{H}\_2 + \text{H}\_2 \rightarrow \text{C}\_4\text{H}\_6\tag{17}$$

$$\text{2 C}\_2\text{H}\_2 + 2\text{H}\_2 \rightarrow \text{C}\text{is} - \text{C}\_4\text{H}\_8 \tag{18}$$

$$\text{2 C}\_2\text{H}\_2 + 2\text{H}\_2 \rightarrow \text{Trans}-\text{C}\_4\text{H}\_8 \tag{19}$$

$$2\,\mathrm{C}\_{2}\mathrm{H}\_{2} + 2\mathrm{H}\_{2} \to 2-\mathrm{C}\_{4}\mathrm{H}\_{8} \tag{20}$$

To simplify the acetylene hydrogenation to 1-butene, cis-2-butene and trans-2-butene reactions are lumped to acetylene hydrogenation to butene group. Based on the considered reaction network and Langmuir-Hinshelwood-Hougen-Watson mechanism, a detail kinetic model is proposed to predict the rate of reactions and the coefficients of the considered model are calculated based on experimental data [26]. The considered rate of reactions is as follows:

$$r\_i = \frac{k\_i \prod P\_j^{n}}{\left(1 + \sum K\_j P\_j\right)^m} \tag{21}$$
