# Determination of Optimum Frequency for Electromagnetic-Assisted Nanofluid Core Flooding
## 3 Results and Discussion
### EM Wave Propagation
#### 3.4.1 Antenna Impedance and Return Loss
The antenna approaches the limit of an electrically large antenna at the high-frequency peak (shorter wavelength of the propagated EM wave), and an electrically small antenna at the lower frequency peak corresponding to the longer propagating wavelength [46; 47]. Figure 7: Input impedance of the antenna in sandstone medium at different saturations; (**a**) real impedance, (**b**) the imaginary part and (**c**) real and imaginary impedance in sandstone containing oil, brine and nanofluid. It can be inferred from the return loss graph that an increasing value of the permittivity of the medium due to an increase in the injected polar molecules causes the reflection loss peaks (equivalent to antenna resonant frequencies) to shift to lower frequencies. This trend is most prominent after including magnetite in the saturating fluid, with one of its reflection losses peaks (\(-\)18.91 dB) occurring at 800 MHz. This is a particularly important finding in the application of EM waves for the activation of injected nanoparticles, as it indicates that approximately 95% of the EM power supplied to the antenna is propagated within the medium. As earlier mentioned, the resonant frequency of the Berea sandstone sample saturated with oil, brine and magnetite nanofluid was observed to be 600 MHz, implying that there was a maximum response to the irradiated EM wave [48]. This connotes that the maximum response to externally applied EM waves will be obtained by tuning the EM frequency close to this value (600 MHz). Hence, a reasonable compromise could be made between applying EM waves at the resonant frequency of the transmitting antenna (800 MHz) or that of the reservoir medium (600 MHz). Albeit, it could be preferable to apply EM waves of frequency 600 MHz due to two compelling reasons. Firstly, the ability of the antenna to absorb and radiate roughly 94% of the input power (as indicated by the reflection loss of \(-\)13.75 dB) [48]. Secondly, maximum energy could be transferred to reservoir materials at this frequency due to resonance. Subsequently, sufficient EM energy is available for polarizing the magnetite nanoparticles and also overcoming the isotropic Van der Waal's attractive forces between the nanoparticles. This is brought about through reduction of Van der Waal interaction free energy relating to the Hamaker constant and anisotropic dipolar forces between the magnetite nanoparticles [49; 50]. Thus, improved activation of the nanoparticles is achieved. Table 3 presents a summary of the antenna characteristics at different fluid saturations. The return loss, input impedance, bandwidth and by implication the antenna radiation efficiency is significantly affected by the fluid content of the medium. Figure 8: Antenna return loss (dB) at different operating frequencies in different formation fluid saturations. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Dry Sandstone** & **Oil Saturated** & **Oil and Brine Saturated** & **Oil, Brine and Nanofluid Saturated** \\ \hline Resonant Frequency (GHz) & 1.30 & 1.20 & 1.00 and 1.40 & 0.80 and 1.30 \\ Return Loss (dB) & \(-\)20.70 & \(-\)21.47 & \(-\)21.12 and \(-\)21.36 & \(-\)18.911 and \(-\)20.00 \\ Real Impedance (I) & 52.04 & 50.62 & 44.39 and 53.31 & 40.51 and 46.35 \\ Imaginary Impedance (\(\Omega\)) & 9.22 & 8.50 & 6.13 and 8.21 & 3.82 and 8.96 \\ Bandwidth (GHz) & 0.91 & 1.01 & 1.10 & 1.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Antenna characteristics at different saturations.