## 3 Results and Discussion
### Intensification of Single-Phase Filtration
#### 3.2.1 Medium-Permeability Sandstone
Despite the decrease in the permeability of the sample deposited in the pore space of paraffins and asphaltenes, before the third (as well as before the 1 st and 2 nd) activations, the permeability in the presence of nonlinear loading is restored from the current value \(k_{b}\) (permeability before) to the value \(k_{a}\) (permeability after), which is almost the original value of 60 mD. This effect can be explained by what happens in the pore space. At the beginning, when filtration proceeds without the nonlinear load applied, part of the paraffins and asphaltenes are deposited in the constrictions between the grains that make up the rock. After a nonlinear load is activated, these accumulated paraffins and asphaltenes, as a result of the relative displacements of the matrix and the liquid, are separated and carried away by the flow of the filtering liquid, which leads to the restoration of the permeability \(\Delta k\) to its initial value. A similar mechanism is also described in [11]. At the same time, due to the underrecovery of permeability, there is still a trend towards its decrease. This is primarily due to the duration of the previous filtration without nonlinear loading \(t_{b}\). Table 4 shows that with an increase in the duration of the previous filtration without treatment, the achievable value of the restored permeability decreases, despite the fact that the permeability returns from a deeper drop (permeability gain increases). At the same time, the duration of activation does not affect the oil permeability k = const. Permeability fluctuations in the second half of the shelf of the 3 rd activation are related to the search for the most effective frequency (20 kHz, 2 kHz) to try to increase the permeability (which did not happen). With a further increase in the filtration time without 4 linear loads applied, a certain threshold value of permeability is reached, after which non-linear loading is no longer able to restore and maintain the permeability. It can be seen that after the injection of a significant amount of pore volume in the interval of 67 to 85 min, the nonlinear load is not able to unblock the pore space of the rock. The effect of permeability reduction during filtration in the presence of nonlinear loading is the second observed effect, which corresponds to the 4 th and 5 th activations of the actuator. Apparently, by this moment, the pore space was blocked quite strongly, and, during liquid filtration, paraffins and asphaltenes continued to accumulate in intergranular channels, but part of the paraffins and asphaltenes, due to the resulting oscillations of the matrix, still came off and was carried away in the liquid flow, as a result of which an increase in permeability of 12 mD was observed (Table 5). \begin{table}
\begin{tabular}{c c c c} \hline \(t_{b}\), min & \(k_{b}\ldots k_{a}\), mD & \(\Delta k\), mD & \(\omega\), kHz \\ \hline
9 & from 52 to 62 & 10 & 20 \\ \hline
12 & from 48 to 61 & 13 & 20 \\ \hline
15 & from 40 to 58 & 18 & 20 \\ \hline \end{tabular}
\end{table} 
Table 4: Results on increased permeability of the first effect. The subsequent 5 th activation led to an increase in permeability of only 10 mD, although the previous filtration without a nonlinear load applied was only four minutes. If we extend the curve of permeability reduction during artificial nonlinear loading, we will see that soon the permeability will reach a very low value (as it happened in the 130 th minute) and then might stop completely due to blockage. The third effect is characterized by minimal restoration of permeability under nonlinear loading by an actuator from 20 to 40 kHz. It seems to be due to the fact that paraffins and asphaltenes accumulated in constrictions create a sufficiently strong structure in the pore space, and the combined effect of the energy of the fluid flow and the energy of vibration of the pore wall under nonlinear loading is not enough to overcome the strength of paraffins and asphaltenes and push it through.