# Investigating the Adsorption Behavior of Zwitterionic Surfactants on Middle Bakken Minerals
## 3 Results and Discussion
### Adsorption Isotherms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Surfactant** & **Adsorbent** & \multicolumn{2}{c}{**Langmuir**} & \multicolumn{2}{c}{**Freundlich**} & \multicolumn{2}{c}{**Temkin**} \\ \hline \multirow{4}{*}{CG3} & Bakken & K\({}_{\text{L}}\) (Lmg\({}^{-1}\)) & 0.2064 & K\({}_{\text{F}}\) (mg/g(L/mg)\({}^{1/n}\)) & 8.3311 & BT (J\(\cdot\)mol\({}^{-1}\)) & 5.3508 \\ \cline{2-6}  & Crush & q\({}_{\text{m}}\) (mg.g\({}^{-1}\)) & 9.9206 & n & 0.5126 & A (L\(\cdot\)g\({}^{-1}\)) & 1.0034 \\ \cline{2-6}  & sample & R\({}^{2}\) & 0.975 & R\({}^{2}\) & 0.9381 & R\({}^{2}\) & 0.9463 \\ \hline \multirow{4}{*}{CD2} & Bakken & K\({}_{\text{L}}\) (Lmg\({}^{-1}\)) & 0.1148 & K\({}_{\text{F}}\) (mg/g(L/mg)\({}^{1/n}\)) & 1.17355 & BT (J\(\cdot\)mol\({}^{-1}\)) & 1.2775 \\ \cline{2-6}  & Crush & q\({}_{\text{m}}\) (mg.g\({}^{-1}\)) & 10.60454 & n & 1.409 & A (L\(\cdot\)g\({}^{-1}\)) & 3.148 \\ \cline{2-6}  & sample & R\({}^{2}\) & 0.9973 & R\({}^{2}\) & 0.976 & R\({}^{2}\) & 0.9016 \\ \hline \multirow{4}{*}{ME1} & Bakken & K\({}_{\text{L}}\) (Lmg\({}^{-1}\)) & 0.0044094 & K\({}_{\text{F}}\) (mg/g(L/mg)\({}^{1/n}\)) & 1.8141 & BT (J\(\cdot\)mol\({}^{-1}\)) & 8.4687 \\ \cline{2-6}  & Crush & q\({}_{\text{m}}\) (mg.g\({}^{-1}\)) & 38.167939 & n & 1.0695 & A (L\(\cdot\)g\({}^{-1}\)) & 0.6053 \\ \cline{1-1} \cline{2-6}  & sample & R\({}^{2}\) & 0.9984 & R\({}^{2}\) & 0.9919 & R\({}^{2}\) & 0.9078 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Adsorption isotherm parameters. Figure 9: Plot of linearized Langmuir adsorption isotherm fitting for (**a**) CG3, (**b**) CD2, and (**c**) ME1 onto Bakken sample. The circles in the figure represent the experimental data points, and the dotted line represents the fitted model. Figure 10: Plot of linearized Freundlich adsorption isotherm fitting for (**a**) CG3, (**b**) CD2, and (**c**) ME1 onto Bakken sample. The circles in the figure represent the experimental data points, and the dotted line represents the fitted model. The Freundlich adsorption isotherm model has the lowest R\({}^{2}\) for CG3, while the Temkin model gave the lowest R\({}^{2}\) for CD2 and ME1. Conversely, the Langmuir model showed the highest R\({}^{2}\) for all zwitterionic surfactants on adsorbents. This significant observation supports monolayer adsorption on homogeneous active sites on the adsorbent surface, as the Langmuir isotherm assumes surface homogeneity. Figure 11: Plot of linearized Temkin adsorption isotherm fitting for (**a**) CG3, (**b**) CD2, and (**c**) ME1 onto Bakken sample. The circles in the figure represent the experimental data points, and the dotted line represents the fitted model. It was determined that the Langmuir adsorption isotherm model had a slightly better fit after analyzing the mean square error and regression coefficient (R2) values. This model may be able to provide a more precise description of the adsorption isotherm for zwitterionic surfactants on Bakken formation. While it is commonly observed that high salinity promotes the formation of vesicles, this study did not observe a similar trend due to the relatively low concentration of surfactant used at the beginning.