## 3 Results and Discussion
### Core-Flooding Effluent Analysis
#### 3.3.2 First Normal Stress Differences and Oscillatory Measurement  
Viscoelastic behavior of diluted polymer solutions was evaluated by using first normal stress differences (N\({}_{1}\)) measurements and small-amplitude oscillatory shear (SAOS) response. Force normal to shear flow produces normal stress differences (N\({}_{1}\)) and measures the elastic behavior of the polymer solutions. Tension in the flow streamlines measures the N\({}_{1}\) effects.  
Similarly, the viscous and elastic properties of the polymer solutions were characterized through oscillatory measurements. These measurements focused on the viscous modulus (\(G^{\prime\prime}\)) and elastic modulus (\(G^{\prime}\)) measured as the function of angular frequency. The inverse of angular frequency (rad/second) at the crossover point of viscous and elastic moduli (\(G^{\prime}=G^{\prime\prime}\)) defines the relaxation time. High relaxation time of a material depicts dominant viscoelastic properties; however, viscous materials have less or no relaxation time property. Further details on experimental evaluation procedures can be found in [PERSON] et al. [15] and [PERSON] [7].  
The results of linear viscoelastic effects of solutions, crossover point angular frequency (right), and first normal stress difference (left) are presented in Figure 11. As expected, the solution with deionized water exhibited strong elastic behavior based on first normal stress differences, while other diluted solutions prepared in both brines, at 22 and 55 \({}^{\circ}\)C, showed no elastic response. Only at higher shear rates, the Flopaam 6035 S polymer solution prepared in synthetic seawater at 22 \({}^{\circ}\)C displayed an elastic response. Figure 11 (right) summarizes the non-elastic responses based on relaxation time measurements for the solutions prepared in both brines, at 22 and 55 \({}^{\circ}\)C. This non-elastic response from oscillatory measurements was confirmed due to semi-hard conditions (divalent cations and temperature).  
By comparing data presented in Figure 11 (left and right), we concluded that both measurements of viscoelastic behavior (first normal stress differences and oscillatory measurements) could not completely predict the fluid viscoelastic response in porous media. The results are in line with the investigation of [PERSON] et al. [84; 85]. The results from [PERSON] and [PERSON] [84] highlight the advantages of extensional rheology over oscillatory rheology. Furthermore, the authors also claim the validation of the capillary theory, using a modified capillary number.  
As reported by [PERSON] [7; 11], SAOS (small-amplitude oscillatory shear) can only provide an insight on whether a polymer might depict viscoelastic properties, but it fails to fully predict the behavior under flow. Similarly, [PERSON] et al. [85] suggested that the Deborah number and shear  
Figure 11: (**Right**) Oscillatory measurements as a function of angular frequency and (**left**) first normal stress differences as a function of shear rate for polymer solutions before core flood (B) and after core flood (A), at 22 and 55 \({}^{\circ}\)C, prepared with reservoir brine and synthetic seawater.  
rheology cannot predict the porous media flow. Therefore, extensional measurements using a capillary breakup extensional rheometer help us to understand flow behavior in porous media.