COMSOL 6.4 - HI Batch Reactor

The batch reactor is a widely used system for production of chemicals in various chemical industries. This reactor type together with the continuous stirred tank reactor (CSTR) and plug-flow reactor can be treated as ideal. In the case of the batch reactor, ideal conditions equal perfectly mixed conditions, meaning that temperature and compositions are the same throughout the reactor, and thus that the problem can be modeled in 0D.

In this example the isothermal and nonisothermal behaviors of the gaseous hydrogen iodine (HI) reaction are modeled in a perfectly mixed Batch reactor. The model utilizes the Batch reactor feature with constant volume within the Reaction Engineering interface of the Chemical Reaction Engineering Module.

Model Description

A classical example on reaction kinetics, namely the hydrogen iodine reaction (Ref. 1), is modeled. The reversible bimolecular reaction is here assumed to properly describe the kinetics:

The model simulates experiments where an initially equimolar mixture of gas reacts. The reaction runs in a perfectly mixed batch reactor of constant volume. The balance equation for each species, i, that is solved in the Reaction Engineering interface is expressed as:

where ci is the concentration (SI unit: mol/m3) and Ri the sum of the reaction rate contributions from each participating reaction (SI unit: mol/(m3s)), which will give the production rate of species i. In this case we only have one reaction. Both isothermal and nonisothermal conditions are modeled. An energy balance for the Batch reactor is by default defined in the latter case, according to:

where Vr denotes the reactor volume (SI unit: m3), ci is the species concentration (SI unit: mol/m3), Cp,i is the species molar heat capacity (SI unit: J/(mol·K)), T is the temperature (SI unit: K), and p the pressure (SI unit: Pa). On the right-hand side, Q is the heat due to chemical reaction (SI unit: W), and Qext denotes heat added to the system (SI unit: W). The heat of reaction is calculated from the reactor volume, the molar enthalpy, Hi (J/mol), and the reaction rate, as given in the following equation:

The results are used to compare the conditions and to determine the reaction’s equilibrium constant at 700 K.

Results and Discussion

The concentration of the reactants and products for both reaction conditions are displayed in Figure 1. The plot shows that the reactor is close to steady state after roughly 36,000 s (10 hours) for the isothermal case. In the nonisothermal case, steady state is reached much faster, after approximately 2000 s.

Figure 1: Reactant and product concentrations as functions of time for the isothermal and nonisothermal conditions.

The equilibrium quotient, Qequil, is monitored with the following relationship:

which at steady state should yield the equilibrium constant. Figure 2 shows that the equilibrium expression asymptotically reaches the value of roughly 54.9 at isothermal conditions, which is also the relationship between kf and kr in the model.

Figure 2: Equilibrium expression at isothermal conditions.

In Figure 3, the temperature is shown to increase 110 K to 810 K as steady state is reached.

Figure 3: Reactor temperature as a function of time.

Figure 4 shows the heat of reaction for isothermal and adiabatic reactor. Note the logarithmic scale on the x-axis, and hence, how much faster the adiabatic reaction is compared to the isothermal case.