## 3 Results and Discussion
### Model Interpretation  
When filtering oil, paraffins, which are long molecular chains of a linear or branched form [43] capable of combining, are in a collapsed state. When they get into the pore throats, comparable to the size of paraffins and asphaltenes (or several linked molecules), they do not pass further but accumulate in front of the impassable area. This leads to a decrease in the flow area of the channel, an increase in the pressure of the injected oil at the entrance to the sample, and, accordingly, a decrease in the permeability of the rock. In the absence of a nonlinear load on the sample, paraffins and asphaltenes completely block channels of small diameter at first (comparable to the particle size of paraffins and asphaltenes and less), and then they can block channels of large diameter, which eventually leads to a filtration stop (Figure 17a). In the case of the activation of variable loading, elastic vibrations propagate through the sample matrix and lead to its elastic deformation (high-frequency, low-amplitude compression and expansion). The resulting vibration leads to the relative motion of the rock walls and the paraffins and asphaltenes located in the constrictions. As a result of relative motion, paraffins and asphaltenes are compacted and pushed by the flow of filtered  
Figure 15: There are large associations between paraffins and asphaltenes in crude oil and their high concentrations. oil deep into the sample. On their further path, paraffins and asphaltenes enter new pore channels and can either block them (if the pore throat size is much smaller than the size of paraffins and asphaltenes) or be filtered without restrictions or influence on permeability (Figure 17b). The creation of a mathematical model that would describe the effect of a nonlinear load on the intensity of paraffin and asphaltene deposition during the filtration of crude oil through rocks is a task that would allow us to interpret the experimental results obtained in this work and transfer them to the scale of the near-wellbore formation zone (near the production well). To date, among the existing models, a work by [6] can be distinguished that proposes a mathematical model that describes the deterioration of permeability and porosity of rock near a production well due to the deposition of paraffins caused by a  
Figure 16: Experimental data in the filtration of crude oil with a high concentration of paraffins and asphaltenes: (**a**) permeability; (**b**) pressure drop. Figure 17: The nature of the removal of paraffins and asphaltenes in the pore channels (schematically): (**a**) accumulation of paraffins and asphaltenes stuck in pore throats during crude oil filtration with no nonlinear load applied; (**b**) pushing paraffins and asphaltenes through the pore throats with the oil ow with a nonlinear load applied. decrease in reservoir pressure, as well as the effect of deterioration in permeability on the well flow rate. At the same time, models that would describe the effect of changing the permeability due to the impact of nonlinear loads are not widespread. Comparing with the Near Wellbore Formation Damage Model proposed by [6], the results of the present study suggest that the intensity of the paraffin and asphaltene flocculation and precipitation in the pore space of near-wellbore rocks would be decreased if the nonlinear load were applied to the wellbore surface. The degree of damage (DOD) to permeability would be lower, resulting in the restoration of permeability in eqn. (20). The skin factor would be lower accordingly, and reservoir pressure (see pressure profile in Figure 7) would be decreasing at a lower rate towards a production well (and would not fall sharply very near the well) if elastic waves, activated from a well, propagated towards a reservoir.