## 3 Results and Discussion
### Residual Oil Mobilization  
A medium-permeability sample was used to study the effect of nonlinear loading on water seepage in the presence of residual oil. When actuators are activated, the permeability of the rock increases linearly (Figure 7). The most intensive permeability increase \(\Delta k\) from the initial value \(k_{0}\) is observed when treating the sample with an ultrasonic frequency \(\omega\) of 28 kHz (slope or tan \(\beta\) = 2.22). In comparison with other frequencies at 28 kHz, the permeability reaches its maximum value, and the increase in permeability reaches 14% (see Table 3).  
Figure 6: A photograph depicting a general view of the experimental rig.  
Figure 7 shows that a linear increase in permeability corresponds to a linear decrease in pressure drop (since the Darcy filtration law is linear). After turning off the actuator, the filtration regime is restored; however, the permeability and pressure drop no longer return to their previous values; the permeability now remains at a value higher than it was before the activation of the nonlinear load, and the pressure difference has a value lower than before the activation of the actuator. In the time interval after the second hour of the experiment, these parameters reach asymptotic values, which indicates the opening of new filtration channels in the sample.  
After nonlinear loading, an additional amount of oil was released from the sample (Figure 8), which indicates an increase in displacement efficiency and a decrease in residual oil saturation in the sample. Distilled water, which was clear before treatment, has taken on an oily hue. Also, drops of oil are observed in distilled water, which most likely formed (dispersed) as a result of cavitation in the cone. In order to study the highest permeability achievable, the experiment was continued the next day under the same conditions. During the treatment, the permeability of the sample increased from 26 mD to 32.5 mD (20%), and in total, the permeability increased by almost 10 mD compared to the initial value of permeability (see Figure 7a) obtained after a long displacement of crude oil by distilled water without nonlinear effect (Figure 9). At the same time, the peak permeability reaches 34 mD at a pore pressure of 98.6 psi (or 0.68 Mpa).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\omega\), kHz & \(\tan\beta\) & **angle \(\beta\)** & \(k_{0}\), mD & \(\Delta k\), mD & \% \\ \hline
40 & 0.87 & 41 & 24 & 2.2 & 8.4 \\ \hline
20 & 0.13 & 7.4 & 24 & 1 & 4 \\ \hline
28 & 2.22 & 65.8 & 24 & 4 & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of experimental data processing.  
Figure 7: Graphs of changes in filtration parameters during the use of distilled water in the presence of residual oil: (**a**) permeability; (**b**) pressure drop. Segments 1, 3, and 5 correspond to sample treatment at 20 kHz, 40 kHz, and 28 kHz; sections 2, 4, and 6 correspond to turning of treatment and restoring filtration.  
The results of the experiment demonstrate the effect of nonlinear loading on the involvement of previously undrained oil in filtration. It can be seen that the impact of an online load contributes to an increase in the mobilization of capillary-trapped oil and an increase in water permeability.