Effects of salts and temperature on rheological and viscoelastic behavior of low molecular weight HPAM solutions

The hydrolyzed polyacrylamide (HPAM) is the most often used polymer in Enhanced Oil Recovery (EOR) activities. The molecular weight of HPAM has a direct relationship with the molecular size and the permeability of the porous media through the polymer will be injected. The polymer flooding has been documented in EOR process for different types of geologic formations, salinity and temperature conditions. This work aims to investigate the effects of salts and temperature on the rheological and viscoelastic behavior of polymer solutions for low permeability formations. The knowledge of the rheological behavior is imperative to evaluate the mobility ratio improvement, while elastic properties are associated with an additional oil mobilization. For this reason, an experimental study was conducted using Flopaam 3230S over two temperatures and three different brine compositions. The flow curves show a significant reduction polymer viscosity when the concentration of ionic species increases, reducing the hydrodynamic size of the polymer. The Ostwald-de Waele law and Carreau-Yasuda model were used to describe the rheological properties of the solutions. The variation of viscosity with temperature was also studied and adjusted to Arrhenius equation. Regarding the viscoelastic properties, comparisons were made between the different polymeric solutions, and we observed the reduction of the linear viscoelastic region (LVR) according to the increase of temperature, divalent ions concentration, and more diluted solutions. The viscous modulus is predominant for all solutions. These results contribute to the design of low molecular weight polymeric solutions under conditions of salinity with a high concentration of divalent ions, which is useful for low permeability formations.


Introduction
Mobility control is one of the most important concepts in any enhanced oil recovery process (Sheng, 2011). It can be achieved through injection of chemicals to change displacing fluid viscosity, with the addition of foams to reduce specific fluid relative permeability or through injection of chemicals to modify the wettability (Abidin, Puspasari & Nugroho, 2012).
Those procedures are known as Chemical methods for Enhanced Oil Recovery (CEOR) (Lake, 1991). The polymer flooding is one of these methods and is used to change displacing fluid mobility by adding watersoluble polymers. A better mobility control improves the vertical and areal sweep efficiencies (Melo et al., 2002) and also lowers the total volume of water needed to achieve the residual oil saturation (Martin, García, Lizcano & Buendia, 2014). Additionally, polymer adsorption decreases the permeability to water, also reducing the mobility (Littmann, 1988) ( Díaz, 2014). HPAM polymers are much more widely used than XG because it has advantages in price and large-scale production (Sheng, 2013). Besides that, HPAM solutions are more viscoelastic than XG solutions. The term Partially Hydrolyzed is associated with the conversion of some amide groups (CONH 2 ) to carboxyl groups ( ) of the Polyacrylamide. This process is known as Hydrolysis and ranges from 15% to 35% in commercial products (Wang, Han, Shao, Hou & Seright, 2008). In other words, the HPAM is a flexible polyelectrolyte with negative charges on the carboxylate groups, which implies a strong interaction between the polymer chains and any cation present in the water (Lopes, Silverira & Moreno., 2014).
When a monovalent salt (i.e., NaCl, KCl) is added in a homogenous HPAM solution, the carboxylic group is surrounded by the cations, which shield the charge and reduce the carboxylic group repulsion, the hydrodynamic volume becomes smaller, therefore, the viscosity decreases (Sheng, 2011 Dissolved salts in a solution of a flexible polyelectrolyte cause mutual repulsion of the charges along the chain (Martin & Páez, 2017). This effect is represented by the ionic strength (I s ) of the solution (Sorbie, 2013).
where is the molar concentration of the ith ion and z i is its charge.
The temperature also influences the rheological behavior of the polymeric solution generating a detrimental effect on the viscosity, significant changes are reported for 333, 15 and 363,15 K (Muller, 1981). Several authors (Ghosh & Maiti, 1997;Maiti and Mahapatro, 1988;Zhou, Willett & Carriere, 2000) documented that the relationship between the apparent viscosity of polymeric solution and temperature satisfies the Arrhenius equation: where is the apparent viscosity of the polymeric solution (Pa*s), A is a constant characteristic of polymeric solution (Pa*s), T is the absolute temperature (K), is the viscous activation energy or the activation energy for flow (kJ/mol), and R is the universal gas constant (kJ*K -1 *mol -1 ).
A plot of vs 1/T gives a straight line with a slope of . The viscous activation energy is related to the dependence of the viscosity on temperature of the polymeric solution, and higher viscous activation energy indicates greater influence of the temperature on the viscosity (Samanta, Bera, Ojha & Mandal, 2010) alkali, and surfactants on the rheological properties of partially hydrolyzed polyacrylamide (PHPAM. The polymers are classified as pseudoplastic fluids under the majority of the conditions (Castro-García, et al, 2016). These types of fluids show a reduction of the viscosity as shear rate increases (Díaz, Navarro & Tavera, 2007). They are known as shear thinning fluids (Barnes, Hutton & Walters, 1989) and are represented by a curve with three notable regions. The first region is a plateau characterized by a constant viscosity at very low shear rates or stress (η 0 ). The second region describes the shear thinning behavior, known as a pseudoplastic region. The third region is also a plateau and indicates the final of the pseudoplastic region and the beginning of the constant behavior of viscosity for high rates (η ͚ ).
There are several models to describe the form of that curve (Sorbie, 2013), but the most commonly used is the power law model, also called as Ostwald-de Waele law (Cardenas, López y Pinto, 2011; Sheng, 2011), which describes the pseudoplastic region. Mathematically, the formula is: where τ is the shear stress (Pa), is the shear rate (s -1 ), is the flow behavior index (dimensionless), and K is the consistency index . For pseudaplastic fluids, n < 1. The equation describes with a good accuracy only the pseudoplastic regime, however it is inaccurate at high and low shear rates (Perttamo, 2013). A more satisfactory model for the complete shear rate range, capable of fitting data in the three regions of the characteristic curves of thinning fluids, is the Carreau-Yasuda model (Sheng, 2011;Yasuda, Armstrong & Cohen, 1981).
where (η ͚ ) is the limiting viscosity at the upper shear rate and is generally taken as water viscosity (Sheng, 2011), n is the same as power law index, λ is a time constant generally taken as 2 (Sheng, 2011), η 0 is the viscosity at very low shear rates or stress.
If the viscosity versus polymer concentration is plotted for a particular shear rate, the dilute and semidilute regimes are identified. In the first, the macromolecules are separated from each other and behave independently. In the semi-dilute regime, the macromolecules are entangled and thus impose frictions on each other, increasing the viscosity of the fluid. The overlapping concentration C* measures the transition between these regimes and is characterized by a change in the shape of the viscosity concentration plot (Al Hashmi et al., 2013;Sorbie, 2013). Concentration values below C* are associated with diluted regime and values above C* with the semidilute regime.
There is another important property that needs to be considered during the design for polymer flood operations. It is the viscoelasticity (Ordoñez & Fajardo, 2015). Laboratory results have reported an increase in oil recovery when are using viscoelastic polymeric solutions (Huifen, Fanshun, & Junzheng, 2004;Wang et al., 2001). This improvement has been attributed to the elastic properties of the polymeric solutions, and their effect on the displacement efficiency increase ( . This study is focused on analyzing the behavior of the storage modulus (G'), also named elastic modulus, which is related to the Hooke's law (Sorbie, 2013). It is associated with "memory" or elasticity of the polymeric solution, it means, the material returns to its original configuration when any deforming force is removed. Moreover, the changes caused on the loss modulus (G''), known as viscous modulus (Barnes et al., 1989), gives information about the viscous properties of the solution. If G' and G'' exist simultaneously and are parallel horizontally in an amplitude sweep test (AST), we can affirm that the material has a linear viscoelastic region (LVR) (Silveira, Lopes, & Moreno 2016; Sorbie, 2013).
During a polymer flooding, a previous rheological laboratory study allows designing the better polymeric solution under a target composition and conditions, aiming to minimize the rheological changes within the reservoir. For this reason, this study is focused on evaluating the rheological behavior and some viscoelastic properties on three different polymeric solutions. These solutions were prepared using Flopaam 3230S, and synthetic brines (SB) including monovalent and divalent salts and different ionic strengths. The tests were made at two temperatures. The rheological behavior of the polymeric solutions was adjusted using the power law and the Carreau-Yasuda model. Finally, the temperature effects on the viscosity were modeled using the Arrhenius equation.

Experimental section Materials
A Synthetic HPAM (Flopaam 3230S, SNF Floerger) was selected to run the tests. This polymer has a molecular weight (Mw) of 5 x 10 6 g/mol, 30% of hydrolysis degree, water content less than 1% and thermal stability up to 433,15 K (Melo & Lucas, 2008). Table 1 shows the synthetic brines used. Mainly, the table includes the type of salt and their respective concentration and ionic strength.

Preparation of HPAM Solutions
The procedure followed was API RP 63. A stock HPAM solution containing 5000 ppm of the polymer was prepared using the synthetic brines mentioned in Table 1. Every SB was deaerated using a vacuum bomb. These HPAM solutions were agitated using a magnetic stirrer during (5 -7) h to form a consistent solution, i.e., the solution exhibited a homogenous aspect, and it did not have insoluble particle (fisheye). All of the HPAM solutions were prepared carefully with the minimum degree of agitation (60-80 rpm) to avoid mechanical degradation of the long-chain molecules. The stock solutions were left still overnight to ensure full hydration.
Then, the stock solutions were diluted with SB up to 100 ppm. The new solutions were put into a beaker and homogenized by magnetic stirrer at low speed (80 rpm) for 10 minutes. All of the HPAM solutions were stored in closed recipients to minimize oxygen uptake.

Measurements
In the present study, the rheological and viscoelastic parameters were measured using a rheometer HAAKE MARS III, which is a high precision instrument. The sensor used was the concentric cylindrical (DG41) due to this is preferable for low viscous fluids. The temperature control used was the THERMO HAAKE C25P refrigerated bath with a Phoenix II Controller. A new sample was applied for each test, and every data analyzed were within the measuring range of the sensor and were compared with the rheological behavior of a fluid pattern (IPT-83).
The flow curves are recorded at shear rates between

Shear Stress and Shear Rate Curves
This section shows the results for shear stress-shear rate data of the prepared HPAM solutions with different polymer salt concentration obtained at two temperature levels. The solutions with high polymer concentration present the first plateau and the pseudoplastic behavior. In these cases, both regions can be fit using the Carreau-Yasuda model. Adjusted curves showed good accuracy (R 2 values showed in Appendix A is closer to 1).
Whereas for low polymer concentration, the Carreau-Yasuda model became similar to Ostwald-de Waele law, it happens when the value of η ͚ becomes approached to the value of η 0 . In this case, the calculation to obtain the Carreau-Yasuda constants carries a greater uncertainty, i.e., the R 2 get away from 1. These values are the SB viscosity at these temperatures.
Dashed lines represent the Carreau-Yasuda fits, and continuous lines represent the Ostwald de Waele fits.
The parameters for the best fits using the mentioned models for all HPAM solutions are presented in Appendix A. By eq 3, the values of K and n can be calculated from the intercept and slope of the best fitted straight line, respectively in the Figure 1a,b (see continuous lines).
All of samples showed good fits to the theoretical models (R 2 >0,98), and showed that when more diluted was the solution is closer to the Newtonian fluid behavior (n = 1), presenting negligible changes with shear rate.
As the polymer concentration increases, the consistent index decrease. That is to say, as the solution has a high polymer concentration it also has greater resistance to the fluid flows. Therefore, at a fixed shear rate the solution exhibits larger shear stress, as presented by other authors ( In Figures 2-4, the viscosities show a plateau at low shear rates, it is η 0 , which can be measured by extrapolating the viscosity curve to the viscosity at very low shear rate. Also, can be observed as the concentration decreases, the viscosity tends to lose the pseudoplastic region, and the plateau increases. This behavior turns the use of the Carreau-Yasuda model for low concentration unnecessary, since the Ostwald de Waele law gives a simpler and accurate method to calculate the viscosity behavior for these conditions. Comparing the series a and b from Figures 2-4, we also can see that temperature imposes a detrimental effect on the HPAM solutions viscosity.      Despite the difference in the ionic strength presented by the HPAM solutions prepared with SB II and SB III, the viscosity reduction as a function of temperature was not meaningful in both cases. The smallest viscosity reduction is exhibited by the HPAM solution prepared using SB III, which has the lowest ionic strength.

Temperature Effect on HPAM Solutions Viscosity
Notwithstanding, the viscosity reduction can slightly influence the displacement flooding efficiency at field operation, the largest contribution to the notable viscosity decreases is due to the presence of ions (monovalent and divalent ions) in the synthetic brine, which interacts with the polymer negative charges, neutralizing the effect of the macromolecular expansion.

Salt's Effect on HPAM Solutions Viscosity
As was mentioned above, the existence of ions influences the rheological behavior strongly. As the concentration of the monovalent ions of Na+ increases, the apparent HPAM solution viscosity diminishes, particularly at the low shear rates (see Figure 6). A critical shear rate represents the transition between the Newtonian behavior or initial plateau and the beginning of the shear-thinning behavior γ c (see Figure  6). The reduction in the polymer chain size due to charge shielding according to the increase in Na + concentration gives a higher critical shear rate. Accordingly, the Newtonian behavior will extend over a wider range of shear rate.
The reaction mechanism for monovalent cations (Na + , K + ) can be summarized as an electrolyte chargeshielding effect, which results in molecule chains shrinking, thus, raising the flexibility and diminishing the hydrodynamic radius. On the other hand, there is a molecular process more complex such as the reaction of divalent cations (Ca 2+ , Mg 2+ ). In this case, the polymer coils up at lower divalent ions concentration and reduces the hydrodynamic radius of the polymer chain, causing a reduction in the degree of polymer chain entanglement. Thus, they generated a more pronounced detrimental to the rheological behavior (Melo et al., 2002;Melo & Lucas, 2008).

Overlapping concentration (C*)
The effect on the C* was analyzed for the three HPAM solutions. Figure 7a shows the behavior of these regimes and the C* for shear rates of 7.8 and 143.8 s -1 at 298.15 K. Figure 7b shows the C* behavior at a shear rate of 7.8 s -1 and both temperatures. In the Figures 7a-b, dashed lines and continuous lines represent the dilute and semidilute regimes, respectively.
In the figure 7a, we can observe that the C* is an inverse function of the shear rate for the tested HPAM solutions, i.e., as the shear rate increases the C* diminishes. Accordingly, as the macromolecules are closer from each other, the diluted regime decreases while the semidiluted increases. Furthermore, as expected, the apparent viscosity decreases while the shear rate increases and ions concentration increases.   The C* behavior was mathematically adjusted by potential trend lines as it was made for others authors (Lopes et al., 2014;Silveira et al., 2016). Appendix C shows the fitting parameters.
Using the Figure 7b and the tables a-c of Appendix C to analyze the temperature effect, it is possible to see that the C* is a direct function of the temperature. As higher is the temperature, lower are the average intermolecular forces (Samanta et al., 2010)alkali, and surfactants on the rheological properties of partially hydrolyzed polyacrylamide (PHPAM, whereby, the macromolecules are more separated and present a more free performance, an extended dilute regime, and higher C* is obtained. Besides that, the apparent viscosity decreases while the temperature increases.

Viscoelastic Behavior of HPAM Solutions
The increase in the oil recovery using viscoelastic HPAM solutions is due to the phenomena of expansion and contraction of the fluid during the flow through porous media (Urbissinova et al., 2010). This effect modifies the forces (capillary and viscous) that maintain the oil trapped and induces the movement of a part of the residual oil (Wang et al., 2001). Initially, we carried out AST for all HPAM solutions. The Figure 8a shows a comparison of results of AST for HPAM solutions with SB I and SB II. The figure 8b shows the same results for HPAM with SB II and SB III. The linear viscoelastic region will be present between the ranges of shear rates where exists a plateau for a constant angular frequency for both G' and G''. The end of this plateau is named yield point, which represents the highest shear stress applied at a given condition before the network of associating polymers starts to deform and split up (Perttamo, 2013). The yield point is estimated at the end of the linear viscoelastic range on the dominating modulus. The Tables 2 and 3 show all yield points.   Analyzing the Figure 8a, we can see a smaller LVR and a reduction of yield point when the solution includes divalent ions, due to higher ionic strength seems to reduce the strength of the intermolecular interactions (Perttamo., 2013). Similar performance has been reported for other authors (Silveira et al., 2016). For the HPAM solution with SB I (the highest divalent ions content) the LVR was present up to 4000 ppm. The other HPAM solution has LVR up to 3000 ppm.
In the figures, 8b is possible to see small changes in the viscoelastic behavior of the HPAM solutions with SB II and SB III. It due to the low difference in the Na + content and the despite variation of the ionic strength. Comparing both, the HPAM solutions with SB III have better viscoelastic behavior than HPAM solutions with SB II. The LVR disappears for the HPAM solution with SB I at 323.15 K (Figure 9). In figures 10 a,b have identified the reduction of LVR when the temperature increase.
For the HPAM solutions with SB II and SB III, the LVR is present up to 4000 ppm at 323.15 K.
The FST results for HPAM solutions with SB I and SB II show that the G' is more affected when the solution includes divalent ions than the G'' modulus (see Figure  11a). Thus, the measured value of elasticity decreased earlier at lower shear stress value for HPAM solution with SB I as compared to HPAM solution with SB II. Similar performance has been reported (Urbissinova et al., 2010).

Conclusions
The polymeric solution with synthetic Brine III presented higher yield points values, a more extended Linear Viscoelastic Region, and higher viscosity values. Therefore, it shows the best rheological and viscoelastic performance.
The presence of divalent cations in the polymer solution reduced its viscosity more than the monovalent cations content. This observation agreed with the literature, and the effects are attributed to a more significant shielding effect of the former.
The overlap concentration is an inverse function of the shear rate for the tested polymeric solutions, i.e., the diluted regime range diminish while the semi-diluted raise when shear rate increases. On the other hand, the overlap concentration is a direct function of the temperature. As temperature increases, the dilute regime extends, and C* is higher.
The increase in the polymer concentration raises the viscosity solution, while the rise in shear rate does the opposite.
Carreau-Yasuda model satisfactory adjusted the experimental data obtained for highly concentrated polymer solutions. On the other hand, the use of Ostwald-de Waele Law was enough to fit the data for a solution with polymer concentration below 1000 ppm. Finally, the reduction of the linear viscoelastic region (LVR) was observed according to the decrease in polymer concentration into the solutions, increasing of temperature and the mono and divalent ions content. Under the tested conditions, the viscous modulus (G'') was predominant for all solutions, and the elastic modulus (G') was more affected by the tested conditions. Can be expected that polymeric solutions less concentrated than 4000 ppm will have only a viscous influence on the oil recovery process.