Extensional Viscosity of Strain Hardening Fluid with e-VROC®

Extensional viscosity is the resistance of a fluid to extensional flow. Any flow field involving a change in cross-sectional area will be affected by this material property. Therefore, extensional viscosity is a fundamental parameter in many industrial processes. One particularly important application is in the use of large molecular weight water-soluble polymers for enhanced hydraulic fracturing (or fracking) during oil extraction and recovery (OER) and shale gas recovery. These polymer solutions improve extraction efficiency and demonstrate complex extensional behavior, as the viscosity dependence on the rate of deformation is not trivial. In this application note, we present extensional viscosity measurements on hydrolyzed polyacrylamide polymers (HPAM) solutions in salted water. Additionally, the characteristic Reynolds numbers for these experiments are calculated to ensure that measurements were done outside the elastic instability regime [1]. 

Figure 1. Extensional viscosity as a function of strain rate for different HPAM solutions. The inset shows estimated Reynolds numbers for the same measurements.

Materials and Setup

Two different hydrolyzed polyacrylamide polymers or HPAM (Aspiro™ P4201 and 29695 from BASF) dissolved in 1%NaCl water solution were tested for extensional viscosity over a wide range of strain rates (𝜀̇~100 – 500 1/s) using an EA20 e-VROC® cell. P2401 sample was also tested with an EC20 eVROC® cell with higher pressure limit over an extended range (~900 – 2,000 1/s). Tests were performed using 10 mL syringes and at a temperature of 25ºC. Note that both cells
used in this study have a characteristic Hencky strain 𝜀𝐻~2.1.

Results and Summary

Figure 1 shows the extensional viscosity measurements for both samples. The results indicate that P2401 and 29695 have significantly different behavior at low strain rates. For the P2401 sample, strain hardening is linear with strain rate over the range tested with the EA20 cell (i.e. extensional viscosity increases linearly with strain rate). At higher strain rates (EC20 cell results), the increase in viscosity starts to slow down. Note that these measurements have been corrected by using a correction factor CF=20 that ensures that ratio between extensional and shear viscosities (or Trouton ratio) for a Newtonian standard is Tr~4. This correction accounts for the presence of a shear component to flow [1,2], and also from flow deviations form ideal behavior around the flow cell constriction. All measurements in this study were performed below the Reynolds number limit of 10 in order to ensure that flow was stable before and after the constriction (see Figure 2 for a sketch of the flow cell shape) [1]. This can be checked by calculating an estimate of the Reynolds number as [1]:

where dh is the characteristic length of the constriction and lc is the throat length. At low and moderate strain rates the Reynolds number remains almost constant, indicating a constant ratio between strain rate and extensional viscosity. At high strain rates (>500 1/s), the increase in extensional viscosity slows down, resulting in a ratio higher than one and an increase in the Reynolds number. Our results show how e-VROC® technology is ideal for characterizing the extensional properties of complex fluids at controlled strain rates.

References

[1] T. J. Ober, "Microfluidic extensional rheometry using a hyperbolic contraction geometry," Rheologica Acta, 2013
[2] How to apply shear correction to e-VROC extensional viscosity measurements: http://www.rheosense.com/extensional-viscosityapplication-note-2