## 3 Results and Discussion
### Single-Phase Polymer Flooding Results
#### 3.2.2 Pressure-Drop Differentiation Due to Shear and Elongation  
A typical pressure-response plot for single-phase core flood, as a function of increasing injection interstitial velocity for different conditions, is presented in Figure 8. \(\Delta P_{T}\) in the plot corresponds to the total pressure obtained during core flooding measurement of polymer solution. (\(\Delta P_{S}\)) describes the pressures associated with shear and was determined by using Darcy's law, using rheometer viscosity data, while \(\Delta P_{E}\) is pressure drop associated to extensional and was measured by using e-VROC. These pressure-drop results help to determine any additional pressure drop caused by the turbulence of flow streams in porous media. Mingling of flow lines at intermediate-to-high injection rates produces this excessive pressure drop, which resists the laminar flow and causes flow resistance in porous media. Figure 8 describes that the total pressure drop only matched the shear associated pressure drop at low interstitial velocity. The calculation for total pressure drop in core flood is performed with the following equation:  
\[\Delta P_{T}=(\Delta P_{S}+\Delta P_{E})+\Delta P_{t} \tag{3}\]  
where \(\Delta P_{T}\) = total pressure drop obtained during polymer flooding in core plug; (\(\Delta P_{S}+\Delta P_{E}\)) = pressure drop due to viscoelasticity of polymers (shear + extensional); \(\Delta P_{S}\) = pressure drop determined by using [PERSON]'s equation and Carreau-Yasuda flow curve fitted to rheometer data; \(\Delta P_{E}\) = pressure drop associated to polymer extensional response and measured with e-VROC; and \(\Delta P_{t}\) = excessive pressure drop linked to turbulence happening in porous media (\(\Delta P_{T}-\Delta P_{E}-\Delta P_{S}\)).  
Figure 7: Core flood measured pressure drop as a function of increasing interstitial velocity for HPAM Flopaam 6035 S/Hengfloc 63026 diluted polymer solutions. The data are plotted at two different temperatures prepared in reservoir brine and synthetic seawater.  
By comparing the experimental pressure data with the rheometer data, it can be seen in Figure 8 that shear forces dominate at low interstitial velocities. Furthermore, at low interstitial velocities, the pressure drop associated to elongational response is lower and can be neglected. The viscoelastic nature of the polymer solutions become dominant with an increase in interstitial velocity, and hence resulting in higher total pressure drop deviating from shear associated pressure drop. This viscoelastic behavior causes the increase in total pressure drop to deviate from the rheomter data after a critical interstitial velocity, associated to in situ critical shear rate. An increase in extensional pressure drop at higher interstitial velocities also confirms the viscoelastic response of the polymer. Figure 8 further presents that the extensional pressure drop almost matches the total pressure drop at high injection rates, thus concluding the extensional dominated flow at higher flux values. Crossover of pressure drop lines at medium flux (the triangular area) corresponds to the excessive pressure drop occurring in porous media, which was not measured by using rheometer or e-VROC. Red triangular points in Figure 8 represent the flow velocity of 5 ft./day, which falls within the shear-thinning response of polymer solutions.  
When we combine the observations from pressure across the cores (Figure 7) and the differentiation of that pressure by shear and elongation (Figure 8), both figures provide that, deep inside the reservoir, flow dynamics of polymer solutions could be predicted by using the approach here presented (linear viscoelastic part). However, around the injection and production wells, elongational/extensional measurements should be incorporated to completely understand the flow regimes in porous media.