## 3 Results and Discussion
However, higher heater temperature ensures more energy consumption, and an enhanced GHSV is more important than a heater temperature increase, thus requiring optimization of other operational variables such as GHSV and length ratio before finalizing the reactor wall temperature for more efficient operation of the COS hydrolysis reactor. Figure 8: Predicted results of the COS hydrolysis reactor according to temperature; (**a**) COS conversion rate, (**b**) COS concentration and temperature profiles. In view of the previously performed numerical modeling analysis results, regression analysis was made incorporating GHSV, length ratio, temperature, and conversion rate: Equations (15)-(18). \[CR_{\text{cos}}=41.1-22.3A+3.1B+7.0C+3.1A^{2}-0.8B^{2}-0.4 AB \tag{15}\]  
Here,  
\[A=1.44\ln(GHSV)-15.83 \tag{16}\]  
\[B=0.96\ln\Bigl{(}R_{length}\Bigr{)}-0.88 \tag{17}\]  
Figure 4:0  
Figure 9 schematically compares Equation (15) and the numerically modeled COS conversion rate, showing an accuracy of \(\pm 10\%\). Based on this result, the Monte Carlo simulation was performed for sensitivity confirmation of individual parameters considering probability distribution characteristics of GHSV, length ratio, and temperature for estimation of the COS conversion rate. Monte Carlo simulation is usually performed by adopting a stochastic model for probabilistic distribution of a specific parameter with uncertainty involved. In general, an analytical solution is obtained for a definitely defined model, but a stochastic model usually does not guarantee such a solution. Numerical modeling is thus needed for an analytic solution, and the probability distribution of a specific parameter should be obtained by a trial and error method. Figure 4:1 Comparison of the COS conversion rate between the proposed regression equation and the numerical data. For that purpose, performance parameters of a COS hydrolysis reactor were chosen to be GHSV, length ratio, and temperature to estimate performance efficiency via probability analysis within the variation range of individual parameters. For this, variation ranges of GHSV, length ratio, and temperature were selected to be 10,000-15,000 h\({}^{-1}\), 0.884-7.062, and 543-603 K, respectively. Variation ranges were taken as a 3\(\sigma\) level considering reasonably efficient reactor performance and normal distribution with relevant average and standard deviation values, as listed in Figure 4:2 Table 6 lists the distribution of individual performance parameters obtained by using normalization of individual performance parameters as specified in Figure 4:3  
In the application of the Monte Carlo simulation, more than 1,000,000 random numbers were created for increased probabilistic credibility. Variation of individual performance parameters was defined within a 3\(\sigma\) level considering a credible level of operational control. Figure 8 illustrates the COS conversion rate for sensitivity of performance parameters and their distribution. Figure 10a was obtained by limiting the variation range of the GHSV and temperature within a 3\(\sigma\) level and more than a 95% of conversion rate efficiency with reliability level of 98.9%. On the other hand, sensitivity of the COS performance efficiency was evaluated in Figure 10b, and temperature, GHSV, and length ratio were rated as important at 57.3% (temperature) and \(-\)38.6% (GHSV). Therefore, GHSV and temperature should be controlled within a tolerable margin for efficient performance improvement of the COS reactor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Mean Value** & **Standard Deviation** & **Distribution** \\ \hline GHSV [h\({}^{-1}\)] & 12,500 & 833 \\  & & \\ Length Ratio [-] & 3.97 & 1.03 \\  & & \\ Temperature [K] & 573 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Normal distribution of operating and geometrical parameters.