# Investigating the Adsorption Behavior of Zwitterionic Surfactants on Middle Bakken Minerals
## 3 Results and Discussion  
### Characterization of Adsorbent Samples  
#### 3.1.1 XRD Analysis of Adsorbent Samples  
Analyzing rock samples using X-ray diffraction (XRD) provides valuable insights into their mineralogy. XRD analysis was employed to determine the mineralogy of the samples, and the Whole Powder Pattern Fitting (WPPF) method was used to determine the quantitative mineralogy of the samples based on the XRD results of the Bakken samples. The XRD patterns of the Middle Bakken (MB) rock samples are depicted in Figure 3, with the corresponding mineralogical contents presented in Table 3. Figure 2 shows that the most common minerals in Middle Bakken samples were quartz, dolomite, calcite, and feldspar. The Bakken rock is a complex mixture of light gray limestone with approximately  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Model** & **Remarks** & **Nomenclature** \\ \hline \multirow{7}{*}{Langmuir} & & The Langmuir isotherm model & \(q_{e}\) represents the equilibrium \\  & & assumes that adsorption takes & adsorption, \(q_{m}\) denotes the \\  & Nonlinear form: & place in a monolayer fashion & maximum capacity for \\  & \(q_{e}=q_{m}\frac{K_{L}C}{1+K_{L}C}\) & on a homogenous surface & surfactant adsorption, and \(C\) \\  & Linear form: & featuring a specific number of & stands for the equilibrium \\  & \(\frac{1}{q_{e}}=\frac{1}{q_{m}}+\frac{1}{C}\cdot\frac{1}{q_{n}K_{L}}\) & distinct sites, with no & concentration of surfactant. \(K_{L}\) \\  & & interactions among the & signifies the Langmuir \\  & & adsorbed surfactant & equilibrium constant linked \\  & & molecules. & with the adsorption energy. \\ \hline \multirow{7}{*}{Freundlich} & Nonlinear form: & The assumption underlying & In this equation, \(K_{F}\) represents \\  & \(q_{e}=K_{F}C^{1/n}\) & this model is the diverse & the Freundlich constant, \\  & Linear form: & adsorption sites on the & which reflects the adsorption \\  & \(\log q_{e}=\log K_{F}+1/n\log C\) & heterogeneous surface, & capacity, while \(n\) is a \\  & & allowing for the description of & parameter indicating surface \\  & & multilayer adsorption. & heterogeneity. \\ \hline \multirow{7}{*}{Temkim} & & The Temkin isotherm model & \(K_{T}\) represents the Temkin \\  & & factors in the indirect & constant, while \(B\) is a constant \\  & & interactions among adsorbate & associated with the heat of \\  & Nonlinear form: & molecules. By restricting & adsorption. \\  & \(q_{e}=B\ln K_{T}C\) & extremely low and high solute & \\  & Linear form: & concentrations, this model & \\  & \(q_{e}=B\ln K_{T}+B\ln C\) & yields a linear reduction in the & \\  & & heat of adsorption for all & \\  & & molecules within the adsorbed & \\  & & layer as the surface coverage & \\  & & with surfactant increase. & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Adsorption isotherms models [7; 43].  
6.9 wt.% clay (illite), 31.2 wt.% dolomite, 11.1 wt.% feldspar (albite), 43.8 wt.% quartz, and 6.4 wt.% calcite.  
The Middle Bakken Formation is primarily composed of siltstone and sandstone with little to no organic matter. Its organic content is typically negligible, averaging less than 1%. In contrast, the Upper and Lower Bakken Members are composed of black shale and are characterized by significantly higher organic content ranging from 6% to 20%, with an average of 10% to 15%. This distinction is critical as the focus of this study lies on the Middle Bakken Formation, whose mineralogical composition (dominated by quartz and calcite) directly impacts surfactant adsorption behavior. The negligible organic matter in the Middle Bakken Formation minimizes its influence on adsorption processes, making it a suitable model for evaluating the role of inorganic mineralogy in surfactant-rock interactions. These observations align with established studies highlighting the mineralogical and compositional contrasts within the Bakken Formation [44; 45; 46].