**4. Process Modeling**

In this section, the industrial two-stage acetylene hydrogenation processes are modeled on the mass and energy balance equation at pseudo-steady state conditions. The adopted assumptions in the considered model are:


The gas is at non-ideal condition and Redlich-Kwong equation of state is considered to predict gas phase property due to high pressure and low temperature conditions. The mass, energy and moment balance equations in the bed could be explained as follows:

$$\frac{dn\_A}{dz} = a \sum\_{i}^{N} \nu\_i r\_i \rho\_B A \tag{23}$$

$$\frac{dT}{dz} = \frac{A\rho\_B}{n\_i \mathbb{C}\_p} \sum\_{i}^{M} r\_j \times \left(-\Delta H\_j\right) \tag{24}$$

$$\frac{dP}{dz} = \frac{150\mu V(1-\varepsilon)^2}{\varrho^2 D\_p^2 \varepsilon^3} + \frac{1.75\rho V^2(1-\varepsilon)}{\varrho D\_p \varepsilon^3} \tag{25}$$

Combining balance equations, kinetic model, auxiliary equations to predict physical and chemical properties, and activity models result in a set of algebraic and partial differential equations. In the developed model, the mass and energy balance equations are written at a steady state condition, while the activity equation is a dynamic model.
