## 3 Results and Discussion  
### Influence of Fluid Salinity  
#### Influence of Pore Fluid Salinity  
The influence of fluid salinity on the formation is reflected on its influence on the conductivity of the porous medium and the electrokinetic coupling coefficient [5; 10]. Since the formation dynamic conductivity in the logging frequency band varies little with frequency, we use the low-frequency dynamic conductivity form given by [PERSON] [69]:  
\[\sigma\approx\sigma_{f}\frac{\phi}{\alpha_{\infty}} \tag{16}\]  
\[\sigma_{f}=e^{2}\hat{z}^{2}N_{f}(b_{+}+b_{-}) \tag{17}\]  
In Equations (16) and (17), \(\sigma\) is the conductivity of the formation, \(\alpha_{\infty}\) is the tortuosity of the pore. \(\sigma_{f}\) and \(\phi\) are the pore fluid conductivity and the porosity, respectively. \(e=1.602\times 10^{-19}C\) is the electronic charge and \(\hat{z}\) is the ion valence of the electrolyte solution. In this paper, the borehole fluid or the pore fluid is regarded as NaCl solution, so \(\hat{z}=1\). \(N_{f}=Na\times 10^{3}\times C_{f}\) is the pore fluid ion concentration, where \(Na=6.022\times 10^{23}Mol^{-1}\) is Avogadro constant and \(C_{f}\) is the pore fluid salinity. \(b_{+}\) and \(b_{-}\) are the absolute mobility of cations and anions, respectively. Both of these values are equal to \(3\times 10^{11}Ns/m\). According to Equations (16) and (17), the influence of \(C_{f}\) on \(\sigma\) is due to its influence on \(\sigma_{f}\). When \(C_{f}\) increases monotonically, the formation conductivity \(\sigma\) increases monotonically as well, and \(\sigma\) is proportional to \(C_{f}\). Next, we investigate the influence of \(C_{f}\) on the electrokinetic coupling coefficient \(L(\omega)\). According to [PERSON] et al. [9], \(L(\omega)\) is given by Equations (18) and (19). \[L(\omega)=L_{0}\left[1-i\frac{m}{4}\frac{\omega}{\omega_{c}}\left(1-2\frac{ \widetilde{d}}{\Lambda}\right)^{2}\left(1-i^{3/2}\frac{\widetilde{d}}{ \widetilde{d}}\right)^{2}\right]^{-1/2} \tag{18}\]\[L_{0}=-\frac{\phi}{\alpha_{\infty}}\frac{\varepsilon_{f}\zeta}{\eta}\Bigg{[}1-2 \alpha_{\infty}\frac{\widetilde{d}}{\Lambda}\Bigg{]} \tag{19}\]  
\(L_{0}\) is the static electrokinetic coupling, and \(\Lambda\) is the pore feature size. \(m=\frac{\phi\Lambda^{2}}{\alpha_{\infty}\kappa_{0}}\), where \(\kappa_{0}\) is the absolute permeability. Research by [PERSON] et al. [70] shows that the above equation can well describe the electrokinetic coupling coefficient of the cylindrical pores, but it overestimates the influence of the pore geometry. For any pore geometry, m could be taken as 8. \(\eta\) is the viscosity coefficient and \(\varepsilon_{f}\) is the fluid permittivity. \(\delta\) is the skin depth and \(\zeta\) is the zeta potential. \(\omega_{c}\) is the frequency turning point. \(\widetilde{d}\) is the electric double layer thickness, and its value is close to Debye length d. Therefore, Debye length d is usually used to replace \(\widetilde{d}\). According to Equations (18) and (19), the influence of \(C_{f}\) on \(L(\omega)\) is reflected on its influence on the Debye length d and the zeta potential \(\zeta\). The expression of Debye length is given by Equation (20) [10]. \[d=\sqrt{\frac{\varepsilon_{f}k_{B}T}{\varepsilon^{2}z^{2}N_{f}}} \tag{20}\]  
where \(k_{B}\) and T are [PERSON]'s constant and the absolute temperature, respectively. According to Equation (24), \(C_{f}\) influences the Debye length d by influencing the ion concentration \(N_{f}\). According to [PERSON] and [PERSON] [8], \(\zeta\) is given by Equation (21), and the value of \(C_{f}\) directly affects the zeta potential of the electric double layer. Figure 2 shows the dependence of \(L(\omega)\) on the frequency and pore fluid salinity. \[\zeta=0.008+0.026\log_{10}\Big{(}C_{f}\Big{)} \tag{21}\]  
As shown in Figure 2, as the frequency increases, the electrokinetic coupling coefficient decreases monotonically. It implies the electrokinetic coupling weakens with increasing frequency.