# A Computational Study of Polymer Solutions Flow Regimes during Oil Recovery from a Fractured Model
## Materials and Methods
### Investigation of the Properties of the Tested Fluids
With increasing shear rate, the viscosity of the 0.1% concentration solutions decreased for all polymer samples tested (see Figure 3). This dependence is most pronounced for the 2540 polymer, while the viscosity of the 2515 polymer changes insignificantly while varying the shear rate. Thus, all the solutions exhibit non-Newtonian behavior. A study of the rheological characteristics of 0.1% solutions of different polymers has shown that the viscosity was higher for 2540 polymer, while the flow-behavior index for this polymer grade was the lowest. Polymer 2515 had the lowest viscosity at a concentration of 0.1%, while its flow-behavior index was higher than that of the other solutions. A comparison of the rheological parameters is shown in Table 3. \begin{table}
\begin{tabular}{c c c} \hline
**wt.\%** & **\(n\)** & **K, mPa\(\times\)s** \\ \hline
0 & 1.00 & 0.89 \\ \hline
0.01 & 0.8103 & 5.60 \\ \hline
0.05 & 0.4556 & 258.6 \\ \hline
0.1 & 0.5016 & 440.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Rheological parameters of aqueous solutions on weight concentration of A2020 polymer. Figure 3: Dependence of the dynamic viscosity of polymer solutions on the shear rate. It was found that when increasing the charging density and molecular weight of the polymer, the effect of the additive on the viscosity and rheology of the solution increased. Moreover, at close molecular weights, the effect of polymer addition was stronger the higher the charging density. The interfacial tension \(\sigma\) of the boundary of an aqueous solution of the polymer oil and the wetting angle \(\theta\) were investigated using the technique, which was employed earlier [22]. A CoreLab TEMCO IFT-820-P hanging drop surface-tension measurement system was used to measure interfacial tension. The IFT cell operates at pressures of up to 68.95 MPa and temperatures of up to 176 \({}^{\circ}\)C. Within this range, most reservoir conditions can be accurately and safely simulated. This allows experiments to be carried out in an oxygen-free atmosphere. The contact angle and interfacial tension were both measured using the DropImage Advanced ver. 2.5.02 software (Rame-Hart Instrument Co., Succasunna, NJ, USA). All surface tension and contact-angle measurements were performed at atmospheric pressure and 25 \({}^{\circ}\)C.  
Figure 4 shows photos of experiments to determine the effect of A2020 polyacrylamide concentration on the wetting angle. The interfacial tension was determined based on the geometric dimensions of the drop. Figure 5 shows photographs of an oil drop in water and in A2020 polymer solutions of 0.05 and 0.1% concentrations. Figure 4: Photos of an oil drop on the rock in water (**a**), 0.05% A2020 polymer solution (**b**), and 0.1% polymer solution (**c**). Figure 5: Photographs of an oil drop in water (**a**), 0.05% A2020 polymer solution (**b**), and 0.1% polymer solution (**c**). The results of determining the wetting angle of the system consisting of displacing fluid, oil, and rock, as well as the interfacial tension of the system consisting of displacing fluid and oil, are presented in Table 4.  
The interfacial tension at the interface of polymer solutions with oil increased slightly compared to that for water. Adding polymer had a more significant effect on the wetting angle. The wetting angle increased (due to increased hydrophilicity) from 105 to 161\({}^{\circ}\) with the increasing polymer concentration. Wettability was most affected by the addition of a 2540 polymer with a charging density.