## 3 Results and Discussion
### Optimization and Validation of Optimized Conditions  
Table 6 depicts the optimization criteria between the independent variables and the corresponding response employed in the study. From the experimental design, the lower and upper limits were obtained for the independent variables (see Table 3). While the upper limit was set at \(\leq\)10\({}^{-8}\) m/s for the response, in accordance with [48]. The individual desirability functions (_di_) for the response and the calculated geometric mean as the maximum overall desirability (D = 1) for solution number 1 is represented in the bar graph as shown in Figure 12. As seen from the figure, both the independent variables and the response all have a desirability function equal to 1. Hence, indicating how well-matched the response is at a selected level of independent variables.  
The use of the desirability function for each factor with the pre-selected goal gave an optimized specific response value (see Table 7) and presented in Figure 13 for solution number 1. The ideal hydraulic conductivity value of 2.0 \(\times\) 10\({}^{-11}\) m/s was attained at  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Name** & **Goal** & **Lower Limit** & **Upper Limit** & **Lower Weight** & **Upper Weight** & **Importance** \\ \hline A: Olivine content & in range & 10 & 30 & 1 & 1 & 3 \\ B: Carbonation time & in range & 6 & 23.5 & 1 & 1 & 3 \\ C: Carbonation press. & in range & 100 & 200 & 1 & 1 & 3 \\ Hydraulic conductivity & minimize & 6.34 \(\times\) 10\({}^{-11}\) & 1.0 \(\times\) 10\({}^{-8}\) & 1 & 1 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Optimization of the individual responses (di) in order to obtain the overall desirability response (D).  
Figure 12: Bar graph representing individual desirability of all responses (_di_) in correspondence with combined desirability (D).  
24.7% olivine content, 20.1 h carbonation time, and 161 kPa carbonation pressure, with a designated maximum desirability function (D = 1.0). Furthermore, 100 desirable solutions for attaining suitable hydraulic conductivity values are recommended. However, only the first 20 of the suggested solutions are reported in this manuscript for the sake of simplicity (see Table 7).  
Using the optimal conditions for solutions 1-10, extra duplicate experiments were carried out to compare the predicted results with their experimental equivalents. The  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Olivine Content (\%)** & **Carbonation Time (hm)** & **Carbonation Pressure (\&Pa)** & **Hydraulic Conductivity (m/s)** & **Desirability** \\ \hline
1 & 29.8 & 15.9 & 154 & \(3.79\times 10^{-11}\) & 1.000 \\
2 & 30 & 23.5 & 150 & \(5.16\times 10^{-11}\) & 1.000 \\
3 & 2  
mean values of the hydraulic conductivity and the percentage error compared to the model values are presented in Table 8. There is a strong agreement between the experimental values and predicted optimized values of the established model based on the findings. Hence, it can be concluded that the established model is relatively precise for predicting the hydraulic conductivity of the carbonated olivine-admixed clay.