# A Computational Study of Polymer Solutions Flow Regimes during Oil Recovery from a Fractured Model
## 3 Results and Discussion  
### Influence of Polymer Concentration on Oil-Displacement Process  
The influence of concentration on the oil-displacement efficiency and pressure drop has been studied for aqueous polyacrylamide solutions. Calculations were carried out for a capillary number equal to 4 \(\times\) 10\({}^{-5}\), which corresponded to the displacement-agent velocity of 1.25 \(\times\) 10\({}^{-3}\) m/s, set at the inlet. Calculations were conducted for oil with a density of 900 kg/m\({}^{3}\) and a viscosity of 0.1 Pa\(\times\)s. The density and viscosity of the oil were measured at 25 \({}^{\circ}\)C.  
The study of the effect of the polymer concentration was carried out for a polyacrylamide polymer with a molecular weight equal to ~18 min c.u. at weight concentrations of 0.05 and 0.1%. During the numerical study of the displacement process, distribution patterns of the displacing agents and oil phases in the computational domain were obtained. The displacing agents used were water and polyacrylamide solutions with polymer weight concentrations of 0.05 and 0.1%. Figure 8 shows the distribution patterns of these displacing  
Figure 7: Geometry (**a**) and fragment of the computational mesh (**b**). As can be seen from the phase distribution patterns presented in Figure 8, when displaced with water, oil is displaced in a rather narrow region of the model. During the displacement process, a \"channel\" is formed through which water continues to filter, leaving large areas filled with oil. The use of polymer solutions leads to an expansion of the displacement front compared to water, and, thus, additional areas of the fractured medium are involved in the process of oil displacement. With an increase in the concentration of the polymer solution from 0.05% to 0.1%, this effect intensifies. The main mechanism of influence of the molecular weight and surface charge density of an acrylic polymer is a change in the rheological characteristics of its aqueous solutions. As shown in Table 1, all other things being equal, with an increasing mass concentration of the polymer in an aqueous solution, the viscosity of solutions changes significantly (the higher the polymer content, the higher the viscosity). As the polymer concentration increases, the flow-behavior index of the power-law model decreases. It was found that with increasing charge density and molecular weight of the polymer, the influence of the additive on the viscosity and rheology of the solution increased. The higher the molecular weight and charge density of the polymer, the lower the flow-behavior index and the more pronounced the non-Newtonian properties of solutions are. The non-Newtonian properties of solutions significantly affect the characteristics of their flow and the efficiency of oil displacement. With a decrease in the flow-behavior index \(n\) of the rheological model, a significant change in the velocity field in the channels of the porous medium occurs. An analysis of the distribution of viscosity of aqueous solutions in channels of a porous medium is presented in Figure 8.  
Figure 8: Phase distribution of the displacing agent and oil in a fractured medium during the displacement process. Effect of polymer concentration. medium at different polymer concentrations shows that the viscosity of solutions decreases greatly from the centers of the channels to the walls. Moreover, with a decrease in the flow-behavior index, this effect intensifies. This is due to the fact that, when approaching the walls, the shear rate increases significantly, and, consequently, the viscosity decreases. This influence of the non-Newtonian properties of polymer solutions with an increase in their concentration leads to a flattening of the velocity in the channels and the appearance in its center of the so-called quasi-solid flow region. Due to the fact that the velocity values in the central part of the channel decrease, and the fluid flow rate is fixed, the velocity increases in the wall part of the channel.