# 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  
Anionic polymers, based on polyacrylamide (PAA) of different grades were used in the present work, namely Praestol (2515, 2540) and Polyflock (A2020) with different molecular weights and charging densities. The 2515 and 2540 acrylic polymers had molecular weights of \(\sim\)9 and 13 mln units, respectively. They also differed significantly in the surface charging density, equal to 10% for 2515 polymer and 30% for 2540 polymer. Polymer A2020 differed significantly from the others by a molecular weight equal to \(\sim\)18 mln units and had a surface charging density of 20% (see Table 1). Molecular weight and charge data were provided by the manufacturer. Solutions with weight concentrations of 0.01, 0.5, and 0.1% were prepared. All polymer solutions used in the experiments were prepared using deionized water. Figure 1: Flowchart of the study of oil displacement by aqueous solutions of polymers. The rheology of the aqueous polymer solutions was measured using a Brookfield DV2T rotary viscometer (ULA and LV-61 spindles). The reproducibility limit of the viscosity measurements does not exceed 0.5%, and the limits of allowable reduced error for ULA and LV-61 spindles are \(\pm\)1% and \(\pm\)2%, respectively. The measurement technique is described in detail in [21]. The measurements were carried out at 25 \({}^{\circ}\)C.  
The dependence of viscosity on polymer concentration was investigated for A2020 aqueous polymer solutions. With the increasing polymer concentration, the viscosity changed as follows: increasing the concentration of A2020 polymer to 0.1% resulted in an increase in the dynamic viscosity coefficient \(\mu\) (Figure 2). As can be seen, the aqueous polymer solutions exhibit a characteristic non-Newtonian behavior. As the polymer concentration in the solution increases, the change in the shear rate starts to have a greater impact on the viscosity. For a PAA concentration of 0.01%, the dependence of viscosity on shear rate is less pronounced compared to that for concentrations of 0.05 and 0.1%. Since the viscosity of the solutions under study depends on the shear rate, the rheological characteristics of the polymer solutions were investigated. It was shown that the viscosity is well described by a power rheology law \(\mu\big{(}\dot{\gamma}\big{)}=K\dot{\gamma}^{(n-1)}\). Increasing the polymer proportion in the solution significantly affects the rheological characteristics (consistency index \(K\) and flow-behavior index \(n\)), which are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Trademark** & \begin{tabular}{c} **Molecular Weight,** \\ **Million Units** \\ \end{tabular} & \begin{tabular}{c} **Charge** \\ **Density, \%** \\ \end{tabular} & \
\begin{tabular}{c} **Hydrolysis** \\ **Degree, \%** \\ \end{tabular} &
\begin{tabular}{c} **Bulk Density,** \\ **kg/m3** \\ \end{tabular} & **Manufacturer** \\ \hline Poliflok A2020 & 17–20 & 20 & 20 & 600–800 & NPO Polyflok \\ \hline Praestol 2515 & 8–10 & 10 & - & 550–750 & CJSC Moscow-Stockhausen \\ \hline Praestol 2540 & 12–14 & 30 & - & 600–750 & CJSC Moscow-Stockhausen \\ \hline \end{tabular}
\end{table} 
Table 1: Polymer characteristics. Figure 2: Dependence of dynamic viscosity of A2020 aqueous polymer solution on the shear rate at different concentrations. The viscosity of the solutions changes significantly with the increasing polymer weight concentration, namely, the higher the polymer fraction, the higher the viscosity. As the polymer concentration increases, the flow-behavior index in the power model decreases, while the consistency index, on the contrary, increases. Thus, the non-Newtonian pseudo-viscoplastic properties enhance with the increasing concentration of the A2020 polymer additive. The viscosity of aqueous polymer solutions of different molecular weights and charging densities with a weight concentration of 0.1% was measured as a function of shear rate.