Effect of Charge Distribution on the Viscosity and Viscoelastic

Jul 27, 2015 - Although products with the same molecular weight and average degree of hydrolysis can be made, the two processes give rise to products ...
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Effect of Charge Distribution on the Viscosity and Viscoelastic Properties of Partially Hydrolyzed Polyacrylamide Kristine Spildo* and Endre I. Ø. Sæ Department of Chemistry, University of Bergen, Allégaten 41, 5007 Bergen, Norway ABSTRACT: The majority of the polymers used in enhanced oil recovery (EOR) processes are water-soluble, acrylamide-based polymers, typically partially hydrolyzed polyacrylamide (HPAM). Industrial-scale production of HPAM polymers for EOR involves either posthydrolysis of polyacrylamide or copolymerization of acrylamide and sodium acrylate. Although products with the same molecular weight and average degree of hydrolysis can be made, the two processes give rise to products with different distributions of charge between individual polymer molecules. In this work, we show that charge distribution at constant molecular weight and average degree of hydrolysis has a significant effect on HPAM viscosity and viscoelasticity of calciumcontaining brines. In EOR processes, viscosity and viscoelastic properties are key performance parameters, and calcium ions are an inherent part of most formation and injection waters. Thus, knowledge of the average degree of hydrolysis is not sufficient for performance prediction. To our knowledge, this is the first comprehensive study of the effect of charge distribution on the rheological behavior of industrial HPAM obtained by copolymerization and posthydrolysis.

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INTRODUCTION The majority of the polymers used in EOR processes are watersoluble, acrylamide-based polymers. A typical example is partially hydrolyzed polyacrylamide (HPAM), which is an acrylamide−acrylate polymer. Key performance parameters are viscosity and viscoelastic properties, which in turn are linked to polymer molecular weight (Mw), concentration, average fraction of acrylate monomers per polymer chain, and ionic composition of the aqueous solution. The average fraction of acrylate monomers per polymer chain is referred to as the degree of anionicity/charge or the degree of hydrolysis. HPAM gets it name from one of the most common manufacturing processes of the product: hydrolysis of polyacrylamide (PAM). Another important synthesis route to HPAM is copolymerization of acrylamide and sodium acrylate. In either case, the resulting product is a acrylamide−acrylate copolymer with a given average fraction of acrylate monomers per polymer chain. The molar fraction of the acrylate monomer is commonly referred to as the degree of hydrolysis. The latter can be tuned by varying the reaction conditions. Although each of these methods can give products with the same average molecular weight and degree of hydrolysis, the microscopic distribution of charge along the polymer backbone is different.1,2 Truong et al.1,2 performed 13C NMR spectroscopy studies, which showed that copolymerization (CP) leads to the formation of longer acrylamide and acrylate sequences compared to posthydrolysis (PH). PH gave a structure with more isolated acrylamide and acrylate monomers along the molecular chain. The block distribution of acrylate monomers in CP polymers corresponds to the presence of highly charged parts along the chain. This could affect cation binding and thus the behavior of these polymers in aqueous solution. Francois et al.3 later demonstrated such a difference in aqueous phase behavior between CP and PH polymers. Commercial EOR polymers have a very high molecular weight (Mw ≈ 10−20 million Da), and a broad Mw distribution. With respect to industrial-scale manufacturing of HPAM by © XXXX American Chemical Society

posthydrolysis of PAM, the posthydrolysis step commonly occurs on grains of insoluble PAM.4 This is different from the laboratory procedure used by Truong et al.1 where alkaline hydrolysis was performed on aqueous PAM solutions. Consequently, the industrial process is affected by diffusion of the alkali into the PAM grains as well as the kinetics of the hydrolysis step. Because the hydrolysis step is the same in the industrial and laboratory procedure, the individual polymer chains are expected to have a similar microstructure with respect to distribution of acrylamide and acrylate sequences. However, the diffusion dependence of the industrial process likely generates differential hydrolysis,4 with some polymer chains having a very high degree of anionicity and others very low. The copolymerization on the other hand leads to a polymer with a more uniform distribution of anionicity between the individual chains. As mentioned, key performance parameters in the use of HPAM processes are viscosity and viscoelastic properties. Recently, enhanced displacement efficiency has been attributed to viscoelasticity.5−8 Both viscosity and viscoelastic properties are sensitive to polymer charge and aqueous phase composition, in addition to polymer molecular weight. Still, to our knowledge, no systematic studies on the influence of charge distribution in industrial HPAM products on viscosity and viscoelasticity has been published. The present paper thus presents such a study for two industrial HPAM polymers with the same Mw and average degree of hydrolysis, but with different distributions of charge between individual polymer molecules as a result of different synthesis routes.

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BACKGROUND Polymers in Solution. In dilute solutions, polyelectrolytes such as HPAM exist as individual chains. Polymer conformations

Received: May 12, 2015 Revised: July 1, 2015

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DOI: 10.1021/acs.energyfuels.5b01066 Energy Fuels XXXX, XXX, XXX−XXX

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achieved and the viscosity levels out. For pure NaCl brine, no further decrease in viscosity was observed when the NaCl concentration was increased above 3% (0.51 M) in solutions of high molecular weight and an average degree of hydrolysis of 30%.14 In petroleum applications, divalent ions such as Ca2+ are frequently present in formation and injection waters. Thus, HPAM rheology in mixed brines of NaCl and CaCl2 is of considerable interest and has been investigated by several researchers (see for example Francois et al.,3 Levitt and Pope,14 Mungan,16 and Ward and Martin17). Although Na+ ions typically act as point charges that screen the intra- and intermolecular electrostatic interactions, Ca2+ ions may bind onto one or two negative carboxylate sites.3,15,18−21 The COO−−Ca2+−COO− binding can take place either between carboxylate groups on the same polymer chain (intramolecular) or between carboxylate groups on adjacent chains (intermolecular). At a high degree of hydrolysis, in the presence of an excessive amount of Ca2+, HPAM will precipitate. According to Zatouin and Potie,22 HPAM will precipitate in the presence of excessive amounts of multivalent cations if the degree of hydrolysis exceeds approximately 33%. When HPAM is present in the reservoir at elevated temperatures, unhydrolyzed amide groups are hydrolyzed to form acrylate groups and release ammonium ions. This results in an increase in the polymer’s degree of hydrolysis, which may lead to polymer precipitation if the Ca2+ is sufficiently high. Consequently, the critical amount of Ca2+ needed to precipitate the polymer decreases with increasing temperature (increasing degree of hydrolysis). Peng and Wu21 studied changes in the hydrodynamic radius for HPAM polymers in dilute aqueous solutions (10 ppm) with degree of hydrolysis and Ca2+ concentration. Their results showed an increase hydrodynamic radius with increasing degree of hydrolysis and Ca2+ concentration, which was interpreted as an increase in intermolecular COO−−Ca2+−COO− interactions. These results contrasts those obtained previously by Flory and Osterheld15 and Huber18 for dilute and semidilute solutions of polyacrylates, i.e., a pronounced geometric shrinking with increasing Ca2+ concentration, beyond that observed for comparable concentrations of Na+. The affinity of Ca2+ for the COO− binding sites has been reported to depend on the total Ca2+ concentration23 as well as on the ratio of Na+ to Ca2+.18 Sinn et al.23 studied the binding of Ca2+ to various polyelectrolytes with COO− as the charged group in the absence of other added cations. They ascribed the decreasing ability to bind Ca2+ at higher calcium concentrations to conformational changes and progressing collapse of the Ca−polymer complex, burying the remaining binding sites for Ca2+ in the interior of the hydrophobic coils. Axelos et al.18 showed that at a given Ca2+ concentration a large excess of Na+ was able to remove Ca2+ from COO− binding sites on polyacrylates. Similarly, Zaitoun and Potie22 reported redissolution of HPAM precipitated by Ca2+ when the NaCl concentration exceeds the CaCl2 concentration. This indicates that the effect of adding Ca2+ should be less at high NaCl concentration. The effect of adding an increasing amount of Ca2+ at constant ionic strength in a mixed NaCl/CaCl2 brine on solution viscosity in semidilute solutions of high-molecular-weight HPAM with 24, 30, and 35% hydrolysis was studied by Ward and Martin.17 The results showed a decrease in viscosity with increasing calcium concentration. The decrease in viscosity with increasing calcium concentration was found to be more significant at high polymer concentrations and degree of

range from highly extended to tightly coiled, depending on the interactions between monomers in the chain (attractive or repulsive) and between monomers and the solvent. For HPAM, the degree of hydrolysis and salinity of the aqueous solution are important parameters governing the interactions between monomers in the chain and between monomers and the solvent. The structure and dynamics of polymer solutions vary depending on their concentration regime. Consequently, it is important to establish which concentration domain one is working within. In the dilute regime, in the absence of any interactions between the polymer chains, we only need to account for polymer−solvent interactions. The viscosity is governed by the hydrodynamic volume of the polymer coil, which depends on the solvent quality and type of polymer. As the polymer concentration (Cp) is increased, the conformations of the individual chains start to overlap at the critical overlap concentration (C*). C* depends on the hydrodynamic volume of the individual chains. For polyelectrolytes, C* thus depends on the polymer structure, Mw, and solution salinity. C* marks the transition between the dilute and semidilute regimes. In the semidilute regime, intermolecular polymer−polymer interactions have to be taken into account in addition to polymer−solvent interactions. As Cp increases above C* in the semidilute, unentangled regime, the number of interactions between neighboring chains increases. This gives a marked increase in viscosity and an increase in the concentration dependence on viscosity (see for example Wyatt and Liberatore9 and Donnelly et al.).10 At concentrations significantly larger than C*, chain entanglements occur at the entanglement concentration (Ce). At Ce, there is an abrupt change in power law exponent for the concentration dependence of viscosity by roughly a factor of three. For a polyelectrolyte, the semidilute, unentangled concentration regime is expected to cover several decades of concentration (Ce ≫ C*) and is thus very important (see Colby11 and references cited therein). For a polyelectrolyte in the presence of NaCl, C* and Ce increase by a factor of 2−3 because of a decrease in the coil size and thus an increase in the concentration needed to induce coil overlap. Experimental Observations of Polyelectrolytes in Saline Solutions. It has been shown that the viscosity of HPAM solutions in the 600−1500 ppm concentration range increases with increasing degree of hydrolysis up to around 40% (see for example Martin and Sherwood,12 Kulicke and Hörl,13 and Levitt and Pope).14 When the degree of hydrolysis is increased above approximately 70%, the viscosity drops below the values observed for 30% hydrolysis.13 Thus, the viscosity versus degree of hydrolysis curve is roughly bellshaped. This was attributed to increased repulsion between negatively charged monomers along the polymer backbone, which gives a more extended polymer conformation. Consequently, the molecule occupies a greater volume in the solvent, resulting in higher viscosity. Addition of an inert salt like NaCl counteracts this increase in chain dimension by electrostatic screening of the repulsion between the acrylate groups on the polymer backbone. Thus, an inert salt contributes to a decrease in viscosity. Furthermore, it is well-known that the extent of shrinking increases with increasing concentration of inert salt (see for example Martin and Sherwood,12 Levitt and Pope,14 and Flory and Osterheld15). The degree of coiling continues to increase with increasing salinity, closely followed by a decrease in viscosity, until complete screening is B

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Energy & Fuels hydrolysis. Furthermore, a more significant reduction was found at low ionic strengths. The latter is consistent with results obtained by Axelos et al.,19 showing a decrease in the affinity of Ca2+ for the COO− sites at increasing ionic strength. Francois et al.3 reported shear viscosities of dilute and semidilute HPAM solutions for polymer prepared by the copolymerization or posthydrolysis process, respectively. At the same molecular weight, average fraction of acrylate groups, and polymer concentration, their results showed that the shear viscosity for the CP polymer (CPP) was lower than for the PH polymer (PHP) in the presence of increasing amounts of Ca2+. The effect of increasing the Ca2+ concentration on solution viscosity increased with increasing polymer concentration, in accordance with the results obtained by Ward and Martin.17 The lower viscosity for CPP compared to that of PHP solutions was attributed to a high fraction of acrylate diads and triads in CPP, promoting the formation of intramolecular COO−− Ca2+−COO− dicomplexes. Such intramolecular complexes are expected to give a significant shrinking of the radius of the polymer coils and thus lower shear viscosity. According to the authors, such intramolecular complex formation would be less likely for PHP with mostly isolated carboxylate groups. Thus, PHP should maintain a higher shear viscosity in the presence of Ca2+ and be more stable against precipitation in the presence of calcium at high temperatures. Linear Viscoelasticity in Polymer Solutions. Dynamic rheology experiments in the linear viscoelastic area can be used to obtain information about temporary networks because of intermolecular interactions under small oscillatory deformations. In the linear viscoelastic area, the strain amplitude of the oscillation is sufficiently small as to not perturb the overall structure. The frequency dependence of the elastic (storage) modulus, G′, and viscous (loss) modulus, G′′, in combination with the crossover frequency and ratio of viscous to elastic modulus (tan δ), are used to gain information related to changes in polymer conformation and intermolecular interactions. The crossover frequency, ω*, is defined as the frequency where G′ = G′′. A purely elastic solid is characterized by frequencyindependent dynamic moduli with G′ > G′′, whereas for a purely viscous fluid, G′′ > G′ over the entire frequency range.24 Viscoelastic systems, however, behave like a viscous fluid at low frequencies (long time scales) and as an elastic solid at high frequencies (short time scales). With increasing frequency, and thus faster motion, the temporary network becomes more rigid and inflexible. Because of the restricted motion of polymer chains relative to each other, more deformation energy is now stored and less is lost by friction as the molecules move relative to each other. At low frequencies, however, the time scales are much longer. This means that there is more time for breaking of temporary network structures and thus more movement of the molecules relative to each other. As a consequence, more deformation energy is lost by friction and less is stored, giving increasingly viscous dominance (G′′ > G′). A shift in ω* toward the left, i.e., to lower frequencies, indicates that the system is becoming more elastically dominated.

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Table 1. Molecular Weight (Mw) and % Hydrolysis in the Investigated Polymers polymer

Mw (×106 Da)

% hydrolysis

CPP PHP

21 ± 1 23 ± 1

30 ± 1 31 ± 1

Table 2. Brine Solution Compositions I = 0.086 M Na+ (M)

X2 0 0.1 0.25

0.086 0.065 0.043 I = 0.344 M

Ca2+ (M) 0 0.007 0.014

X2

Na+ (M)

Ca2+ (M)

0 0.1 0.25

0.344 0.258 0.172

0 0.029 0.057

Figure 1. Shear viscosity at 10 s−1 as a function of polymer concentration for solutions of PHP and CPP containing 0.086 and 0.344 M NaCl. described by Thomas et al.4 The polymers are labeled CPP (copolymerization polymer) and PHP (posthydrolysis polymer) to distinguish them from each other and have near identical molecular weight and fraction of anionic charge (Table 1). The average molecular weight and degree of hydrolysis were both obtained from the supplier. However, the average degree of hydrolysis was also verified by colloid titration25 at pH 10.5. The experimental values thus obtained were found to be in agreement with those given by the supplier. The polymer solutions were prepared in high (0.344 M) and low (0.086 M) ionic strength NaCl brines. The effect of an increasing mole fraction of Ca2+ ions (X2) at constant ionic strength was investigated by replacing some of the NaCl by CaCl2. X2 is defined as

EXPERIMENTAL SECTION

X2 =

Preparation of Polymer Solutions. In this study, we used two partially hydrolyzed polyacrylamides, one prepared by copolymerization of acrylamide and sodium acrylate and one by posthydrolysis of polyacrylamide, both supplied by SNF SAS. The posthydrolysis process was performed on granules of insoluble polyacrylamide, as

[Ca 2 +] [Na ] + [Ca 2 +] +

where [Na+] and [Ca2+] are the concentration in moles per liter (M) ̀ of the sodium and calcium ions, respectively. For each of the ionic strengths, two levels of Ca2+ were studied: X2 = 0.1 and 0.25. The molar concentrations of Na+ and Ca2+ in the different solutions C

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Energy & Fuels Table 3. Shear Viscosity at 10 s−1 for Solutions of PHP and CPP as a Function of Ionic Strength in the Absence of Added Calcium I = 0.086 mol/L

stock solution was diluted to the desired solution concentration using the relevant brine. Shear Rheology Measurements. Rheological measurements were performed using a Malvern Kinexus pro rheometer, equipped with cone−plate geometry (angle = 4° and diameter = 40 mm). The temperature was maintained at 22 ± 0.1 °C. Following regular rotational shear measurements, linear viscoelastic properties were determined using oscillatory shear measurements. To determine the linear viscoelastic (LVE) range, amplitude sweeps were performed at a frequency of 5 Hz. Following this, frequency sweeps in the range 0.01−10 Hz were performed at an amplitude within the LVE range. The oscillatory measurements were performed on 5000 ppm polymer solutions because the elastic properties for solutions with lower polymer concentration were too low for accurate determination of storage and loss moduli.

I = 0.344 mol/L

Cp (ppm)

ηCPP (cP)

ηPHP (cP)

ηCPP (cP)

ηPHP (cP)

5000 2000 1000 600

455.0 81.7 26.9 13.7

476.8 94.1 28.6 14.5

218.5 39.9 12.7 6.5

278.0 47.8 15.8 7.4

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RESULTS AND DISCUSSION Rheological Behavior in NaCl Brines. Steady Shear Flow Measurements. Figure 1 and Table 3 shows the shear viscosity at 10 s−1 in the concentration range 600−1000 ppm for solutions of PHP and CPP at different total ionic strengths. Considering the shape of the curves, previous observations, and discussions relating to the dependence of polyelectrolyte viscosity on concentration (e.g., Wyatt and Liberatore,9 Donnelly et al.,10 and Colby11), the investigated concentration ranges appears to be within the semidilute, unentangled regime. As expected, there is a marked decrease in the viscosity with increasing ionic strength. The decrease in viscosity is due to reduced electrostatic repulsion between the charged acrylate groups, leading to increased coiling of the polymer and consequently lower hydrodynamic volume. Although the viscosity of PHP solutions was found to be consistently higher than those of CPP solutions, the effect of increasing ionic strength on shear viscosity was similar between solutions of CPP and PHP. It is well-known that viscosity in the presence of an inert salt such as NaCl increases with increasing degree of hydrolysis and that the change is slower at a higher degree of hydrolysis. With a broader distribution of charge between the different polymer molecules, the solutions of PHP contain a larger fraction of polymer chains with lower and higher degrees of hydrolysis, relative to the mean value, compared to solutions of CPP (Figure 2). In this case, assuming equal molecular weights,

Figure 2. Illustration of the difference in distribution of charge (% hydrolysis) between CPP and PHP (based on Thomas et al.)4 employed are given in Table 2. Because the polymer charge varies with pH, all brines were maintained at a pH of around 6.8 ± 0.7. Preparation of all polymer solutions started from a stock solution of 5000 ppm. The stock solution was prepared by adding polymer powder slowly into a vortex established in the relevant brine solution using a magnetic stirrer. The stirring rate was then reduced, and the polymer solution was left on stirring for about 12 h. Following this, the

Figure 3. G′ and G′′ as a function of oscillation frequency for 5000 ppm solutions of PHP and CPP at I = (a) 0.086 M and (b) 0.344 M in the absence of added Ca2+. D

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also found by Li et al.26 for solutions of high-molecular-weight HPAM in the presence of increasing concentrations of NaCl. This is likely due to a decrease in the number of mechanically active, intermolecular junctions because the cross-sectional area of the polymer decreases with increasing salinity. The effect of increasing concentrations of NaCl on viscoelasticity is similar for the two polymers. Comparing Steady Shear Viscosity and Oscillatory Complex Viscosity. The complex viscosity obtained during the oscillatory measurements was compared to the steady shear viscosity at equivalent shear rates and frequencies to check if the polymers follow the Cox−Merz rule.27 If the Cox−Merz rule is followed, then the complex viscosity equals the steady shear viscosity at equivalent shear rates and frequencies. For all cases, the curves were roughly superimposed, i.e., the Cox−Merz rule is followed (Figure 5). Rheological Behavior in Mixed NaCl/CaCl2 Brines. Steady Shear Flow Measurements. Table 4 shows the effect of adding an increasing fraction of Ca2+ ions on the viscosity of 5000 and 1000 ppm solutions of the two polymers at high and low ionic strengths. ηx is the viscosity for a solution with a given mole fraction (X2) of Ca2+, η is the corresponding viscosity value in the absence of Ca2+, and ηx/η is the fraction of viscosity retained in the presence of Ca2+. The results for Cp = 1000 ppm are shown graphically in Figure 6, with ηx/η on the y axis. Results at 5000 ppm are qualitatively similar; however, at this higher polymer concentration, the difference between the two polymers is less pronounced. As can be seen from Figure 6, adding Ca2+ at constant ionic strength gave a significant decrease in viscosity for solutions of both polymers. More viscosity is retained by CPP at both ionic strengths; however, the difference between the two polymers is significantly larger at X2 = 0.1 than at X2 = 0.25. For both polymers, there is a trend for less viscosity reduction at high ionic strength. Still, the differences are small, particularly at high calcium ratios. These results are in qualitative agreement with the studies published by Flory and Osterheld,15 Martin and Ward,17 Axelos et al.,19 and to some extent that of Sinn et al.23 However, contrary to the study published by Francois et al.,3 we find that PHP solutions have lower viscosity than CPP solutions in the presence of increasing amounts of Ca2+ under otherwise

Figure 4. Tan δ as a function of oscillation frequency for 5000 ppm solutions of PHP and CPP at high (0.344 M) and low (0.086 M) ionic strengths.

average degree of hydrolysis, and a symmetrical distribution of hydrolysis, simple calculations show that the average viscosity of a polymer solution with a wider charge distribution, such as that of PHP, will be roughly similar to that of a solution with a more narrow charge distribution, such as that of CPP, in the presence of NaCl only. In our case, however, a slightly higher viscosity is found for PHP. This is likely due to the slightly higher Mw for PHP compared to CPP (see Thomas et al. for examples).4 Viscoelastic Behavior. G′, G′′, and loss tangent, tan δ = G′′/G′, are plotted as a function of oscillation frequency for solutions of PHP and CPP at high (0.344 M) and low (0.086 M) total ionic strengths in Figures 3 and 4. At low ionic strength, solutions of both CPP and PHP are elastically dominated (tan δ < 1) over the investigated frequency range (Figure 4). When the ionic strength is increased, G′ and G′′ both decrease (Figure 3). The relative decrease in elasticity is, however, higher, as seen by the increase in tan δ (Figure 4). The adverse effect of increasing salinity on elasticity is also evident from the shift in ω* toward the right, i.e., higher frequencies. An upward shift in ω* was

Figure 5. Viscosity (η) as a function of shear rate (s−1) and complex viscosity (η*) as a function of angular frequency (rad/s) for (a) PHP and (b) CPP at high and low ionic strengths in the absence of added Ca2+. E

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Table 4. Shear Viscosity at 10 s−1 for Cp = 1000 and 5000 ppm Solutions of the Two Polymers at Different Total Ionic Strengths as a Function of Mole Fraction of Ca2+ (X2) I = 0.086 M Cp = 1000 ppm

Cp = 5000 ppm PHP

CPP

X2

η

ηx/η

η

0 0.1 0.25

476.8

1 0.54 0.50

455.0

PHP ηx/η 1 0.68 0.53 I = 0.344 M

CPP

η

ηx/η

η

ηx/η

28.6

1 0.44 0.40

26.9

1 0.66 0.45

Cp = 1000 ppm

Cp = 5000 ppm PHP

CPP

PHP

CPP

X2

η

ηx/η

η

ηx/η

η

ηx/η

η

ηx/η

0 0.1 0.25

278.0

1 0.59 0.47

218.5

1 0.79 0.57

15.8

1 0.52 0.39

12.7

1 0.76 0.50

lar COO−− Ca2+− COO− bonds likely give a decrease in the hydrodynamic volume of the polymer coils, with a corresponding decrease in viscosity. In accordance with this, Flory and Osterheld15 showed that Ca2+ caused a much stronger coil contraction of polyacrylates than the corresponding amount of Na+ beyond what one would expect from the electrostatic screening effect alone. This stronger contraction correlates with a greater decrease in viscosity, as observed by Martin and Ward17 for HPAM solutions in the semidilute regime when some of the Na+ ions in solution were replaced by Ca2+ ions. Intermolecular bonds, in contrast, are thought to contribute to the formation of network structures and thus contributing to increased viscosity and elasticity. Combining this with the results obtained here, it is thus reasonable to conclude that for the conditions studied adding Ca2+ to the polymer solutions mainly results in the formation of intramolecular COO−− Ca2+− COO− bonds. In accordance with the results obtained here, Axelos et al.19 reported a decrease in the affinity of Ca2+ for the COO− sites at increasing ionic strength. Furthermore, Sinn et al.23 reported a decreasing ability for polyelectrolytes to bind Ca2+ at higher calcium concentrations. If this is the case, then it is reasonable to expect that a nonlinear decrease in viscosity with respect to increasing Ca2+ content as observed for PHP. For CPP, however, the trend seems to be rather linear in the investigated range of calcium concentrations. The difference between CPP and PHP is complex. Although not confirmed by direct experiments in the present study, PHP and CPP studied here likely differ in both charge distribution between different polymer molecules4 and with regards to microscopic distribution of charge on the individual polymer molecules.3 According to Francois et al.,3 the higher fraction of acrylate diads and triads in CPP promotes the formation of intramolecular COO−−Ca2+−COO− dicomplexes relative to that of PHP, thus giving lower shear viscosity for CPP compared to that of PHP. This is in contrast to our observations and implies that the distribution in the degree of hydrolysis between individual polymer chains is dominating. As discussed previously, solutions of PHP contain a larger fraction of polymer chains with lower and higher degrees of hydrolysis compared to that of solutions of CPP (Figure 2). Martin and Ward17 reported that a decrease in the amount of viscosity retained in mixed NaCl/CaCl2 solutions decreases with increasing degree of hydrolysis. If we use this information

Figure 6. Effect of mole fraction of calcium added at constant ionic strength on fraction of viscosity retained at 10 s−1 ([ηx/η]10) for 1000 ppm solutions of PHP and CPP at high and low ionic strengths.

equal conditions. Before proceeding to a discussion on the similarities and differences between the present study and that of Francois et al.,3 it is useful to remember that there are some important differences between the industrial, PHP used in our study compared to the ones used by Francois et al. As mentioned in the introduction, the diffusion dependence of the industrial posthydrolysis process likely generates differential hydrolysis.4 Consequently, some polymer chains have a very high degree of anionicity, and others have a very low degree of anionicity. The polymers used by Francois et al., however, were synthesized in a laboratory process. This results in a product where the charge distribution between the individual polymer chains is more uniform. Thus, although the charge distribution on the individual polymer chains is expected to be the same for the two types of PHPs, the charge distribution between the individual polymer chains is different. Although Na+ and Ca2+ ions both screen electrostatic charge and thus induce polymer coiling and viscosity reduction, Ca2+ can also specifically bind to negative sites on the polymer.4,18,19,21 These bindings can be between COO− groups on the same polymer molecule (intramolecular) or between COO− groups on adjacent polymer molecules (intermolecular). IntramolecuF

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Figure 7. (a and c) G′ and G′′ and (b and d) tan δ as a function of angular frequency in the LVE area for solutions of CPP as a function of increasing mole fraction of Ca2+ (X2) at low (a and b) and high (c and d) ionic strength. The arrows indicate the crossover frequencies, ω*, listed in Table 5.

measurements, both with respect to the effect of Ca2+ and to the difference between the two polymers. As for the polymer solutions in the absence of Ca2+, the Cox−Merz rule was also followed in the presence of Ca2+. There is a marked decrease in viscoelasticity with increasing calcium content. The effect is particularly striking for low ionic strength solutions of PHP when X2 is increased from 0 to 0.1 (Figure 8), similar to what we found for the shear viscosity. Furthermore, at the same ω, ionic strength, and X2, CPP solutions are more elastically dominated (lower tan δ) compared to PHP. CPP also has a lower relative loss in elasticity when calcium is added to the solution compared to that of PHP. The difference between the polymers is largest at X2 = 0.1. The crossover frequencies listed in Table 5, which are consistently shifted to lower frequencies for CPP, also confirm the higher elasticity of CPP solutions.

and assume equal molecular weights, average degree of hydrolysis, and a symmetrical distribution of hydrolysis, then simple calculations show that the average viscosity of a polymer solution with a broader distribution of charge will have a significantly lower viscosity when dissolved in a mixed NaCl/ CaCl2 brine. This is in accordance with the results obtained and thus is supportive of the proposed importance of the polymer charge distribution on solution viscosity. However, it is not only the solution viscosity that is highly affected by the polymer charge distribution but also likely the thermal stability. In this context, lower thermal stability refers to polymers with a higher tendency for precipitation in the presence of Ca2+ at elevated temperatures because of increased hydrolysis. Thus, with a larger fraction of polymer chains having a high degree of hydrolysis, PHP is also expected to have thermal stability lower than that of CPP. Viscoelastic Behavior. Figures 7 and 8 show frequency sweeps of solutions of CPP and PHP at two levels of ionic strength and ratios of divalent ions to total amount of cations (X2). Corresponding crossover frequencies, ω*, are listed in Table 5. The figures confirm the trends from the shear viscosity

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SUMMARY AND CONCLUSIONS We have studied changes in shear viscosity and viscoelasticity as a function of brine composition for two high-molecular-weight G

DOI: 10.1021/acs.energyfuels.5b01066 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels

Figure 8. (a and c) G′ and G′′ and (b and d) tan δ as a function of angular frequency in the LVE area for solutions of PHP as a function of increasing mole fraction of Ca2+ (X2) at low (a and b) and high (c and d) ionic strength. The arrows indicate the crossover frequencies, ω*, listed in Table 5.

polymer, CPP) or posthydrolysis (posthydrolysis polymer, PHP). The two different procedures results in products with the same average Mw and degree of hydrolysis but different distributions of charge between individual polymer molecules. The CPP and PHP have near identical shear viscosity and viscoelastic properties in pure NaCl brines. Variations in response to changes in salinity are similar for the two polymers, and as expected for HPAM polymers. In mixed NaCl/CaCl2 brines, shear viscosity and viscoelastic properties for the two polymers differ significantly, particularly at moderate fractions of Ca2+ added. The polymer with broader charge distribution (PHP) loses more viscosity and viscoelasticity compared to the polymer with a more narrow charge distribution (CPP). This is opposite to results previously obtained, which showed improved calcium tolerance for PHP. We attribute this divergence to differences between the industrial and laboratory posthydrolysis process.

Table 5. Crossover Frequencies at Different Combinations of Ionic Strength and X2 for the Two Polymers I = 0.086 M ω* (rad/s) X2

PHP

CPP

0.1 0.25

0.4 0.4 I = 0.344 M

0.2 ω* (rad/s)

X2

PHP

CPP

0.1 0.25

2.0 2.5

0.5 1.2

HPAM polymers. The two polymers were synthesized in industrial processes by either copolymerization (copolymerization H

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Energy & Fuels

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Our study demonstrates that charge distribution should be considered in addition to average degree of hydrolysis and Mw when evaluating HPAM for an EOR application. However, in order to complete the comparison between the two polymers with regards to EOR applications, thermal stability, extensional viscosity, and/or porous media flow should also be evaluated.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge SNF for supplying polymer samples and Dr. Nicolas Gaillard for many fruitful discussions.

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ABBREVIATIONS EOR = enhanced oil recovery HPAM = partially hydrolyzed polyacrylamide Mw = molecular weight PAM = polyacrylamide CP = copolymerization PH = posthydrolysis CPP = copolymerization polymer PHP = posthydrolysis polymer Cp = polymer concentration C* = critical overlap concentration Ce = critical entanglement concentration η = shear viscosity G′ = elastic (storage) modulus G′′ = viscous (loss) modulus η* = complex viscosity ω = angular frequency ω* = crossover frequency LVE = linear viscoelastic X2 = ratio of calcium concentration to total concentration of positive ions

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REFERENCES

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DOI: 10.1021/acs.energyfuels.5b01066 Energy Fuels XXXX, XXX, XXX−XXX