## 2 Numerical Model Development  
### COS Hydrolysis Reactor Model  
Performance analysis of the COS hydrolysis reactor was evaluated via numerical modeling with variation of operational and geometrical parameters. These modeling results were used to derive relevant parameters affecting reactor performance for proper guidance criteria on efficient reactor design. A schematic diagram of the COS hydrolysis reactor used in the present study is shown in Figure 2.  
A gaseous reactant mixture containing COS is introduced to upper tube. The reactant gas is transported to the lower part of the reactor and enters into the catalyst layer of Kaiser 201. Heat is supplied to the reactor via an external heater to activate the catalytic reaction. A portion of the reactant gas mixture is converted into products after passing through the catalyst layer, and the reacted gas mixture exits via the lower exhaust pipe. The COS hydrolysis reaction is generally affected by gas temperature, is sensitive to operational parameters such as gas hourly space velocity (GHSV), and it also depends on reactor geometry.  
Figure 2: Geometric diagram of carbonyl sulfide (COS) hydrolysis reactor.  
For quantitative analysis of transport properties within the COS hydrolysis reactor, internal heat and fluid transfer behavior of gas had to be numerically modeled as did the ensuing chemical reactions. For heat and fluid behavior modeling, commercially available ANSYS Fluent 18.0 software was used; the user-defined function mode enabled numerical modeling of specific chemical reactions. The relevant governing equations for heat and fluid behavior modeling and chemical reaction analysis are described by Equations (1)-(6).  
Mass conservation equation  
\[\frac{\partial\rho}{\partial t}+\
abla\cdot\left(\rho\overset{\rightarrow}{u} \right)=0 \tag{1}\]  
Momentum conservation equation  
\[\frac{\partial\left(\rho\overset{\rightarrow}{u}\right)}{\partial t}+\
abla \cdot\left(\rho\overset{\rightarrow}{u}\overset{\rightarrow}{u}\right)=- \
abla p+\
abla\cdot\left(\mu\
abla\overset{\rightarrow}{u}\right) \tag{2}\]  
Transport equation for \(\kappa\) (standard k-\(\varepsilon\) model)  
\[\frac{\partial(\rho k)}{\partial t}+\
abla\cdot\left(\rho\overset{\rightarrow} {u}\right)=\
abla\cdot\left[\left(\mu+\frac{\mu_{t}}{\sigma_{k}}\right)\
abla k \right]+G_{k}+G_{b}-\rho\varepsilon \tag{3}\]  
Transport equation for \(\varepsilon\) (standard k-\(\varepsilon\) model)  
\[\frac{\partial(\rho\varepsilon)}{\partial t}+\
abla\cdot\left(\rho\varepsilon \overset{\rightarrow}{u}\right)=\
abla\cdot\left[\left(\mu+\frac{\mu_{t}}{ \sigma_{\varepsilon}}\right)\
abla\varepsilon\right]+C_{1\varepsilon}\frac{ \varepsilon}{k}(G_{k}+G_{3\varepsilon}G_{b})+C_{2\varepsilon}\rho\frac{ \varepsilon^{2}}{k} \tag{4}\]  
Energy conservation equation  
\[\frac{\partial\left(\rho C_{p}T\right)}{\partial t}+\
abla\cdot\left(\rho C_{ p}T\right)=\
abla\cdot\left(k_{eff}\
abla T\right)+S_{\varepsilon} \tag{5}\]  
Species transport equation  
\[\frac{\partial(C_{k})}{\partial t}+\
abla\cdot\left(C_{k}\overset{\rightarrow} {u}\right)=\
abla\cdot\left(D_{k}\
abla C_{k}\right)+S_{k} \tag{6}\]  
An internal fluid flow analysis within the COS reactor was made using mass and momentum conservation equations while turbulent flow was numerically modeled by a standard k-\(\varepsilon\) model for turbulence analysis. On the other hand, the species transport equation was solved to analyze pertinent chemical reactions, numerically analyzing formation and depletion of reactant gas species and quantitatively giving their concentrations. Reaction kinetics under prevailing parameter conditions were modeled using empirically-derived kinetics and user-defined function enabled calculation and integration on a real-time basis. Lastly, the energy equation was used to incorporate heat transfer as affected by internal heater and heat energy variation as affected by chemical reactions.