Drag reduction behavior of hydrolyzed polyacrylamide/xanthan gum mixed polymer solutions
Drag reduction behavior of hydrolyzed polyacrylamide/xanthan gum mixed polymer solutions
Mehdi Habibpour 0
Peter E. Clark 0
0 School of Chemical Engineering, Oklahoma State University , Stillwater, OK 74078 , USA
Partially hydrolyzed polyacrylamide (HPAM) as the main component of slickwater fracturing fluid is a shear-sensitive polymer, which suffers from mechanical degradation at turbulent flow rates. Five different concentrations of HPAM as well as mixtures of polyacrylamide/ xanthan gum were prepared to investigate the possibility of improving shear stability of HPAM. Drag reduction (DR) measurements were performed in a closed flow loop. For HPAM solutions, the extent of DR increased from 30% to 67% with increasing HPAM concentration from 100 to 1000 wppm. All the HPAM solutions suffered from mechanical degradation and loss of DR efficiency over the shearing period. Results indicated that the resistance to shear degradation increased with increasing polymer concentration. DR efficiency of 600 wppm xanthan gum (XG) was 38%, indicating that XG was not as good a drag reducer as HPAM. But with only 6% DR decline, XG solution exhibited a better shear stability compared to HPAM solutions. Mixed HPAM/XG solutions initially exhibited greater DR (40% and 55%) compared to XG, but due to shear degradation, DR% dropped for HPAM/XG solutions. Compared to 200 wppm HPAM solution, addition of XG did not improve the drag reduction efficiency of HPAM/XG mixed solutions though XG slightly improved the resistance against mechanical degradation in HPAM/ XG mixed polymer solutions.
Slickwater; Polyacrylamide; Drag reduction; Shear stability; Xanthan gum
Due to the development of horizontal drilling and hydraulic
fracturing technology in recent years, oil and gas
production from unconventional resources such as shale
formations has played an important role in supplying energy in
the USA (Larch et al. 2012; Palisch et al. 2010). Reaching
economic rates of hydrocarbon production from shale
formations is only possible when micro-fractures are
created and connected through effective stimulation
treatments such as horizontal fracturing in multiple stages
(Loveless et al. 2014; Barati and Liang 2014; Wu et al.
Creation of openings in the reservoir rock involves
pumping fracturing fluids into the wellbore at elevated flow
rates and pressures. The viscosity of a fracturing fluid has a
remarkable effect on the fracture initiation and the final
size of the fracture (Kalgaonkar and Patil 2012). The main
component of low-viscosity fracturing fluids is water and
low concentrations of polymer ranging from 0.25 to 10 lb
per thousand gallons (Bunger et al. 2013; Palisch et al.
2010). In the last decade, an amazing shift from traditional
gel-based fracturing fluids toward using slickwater has
occurred. Because of the relatively low viscosity of
slickwater, cleanup problems and damage associated with using
viscous fluids are minimized, which makes slickwater
suitable for fracturing low-permeability reservoirs (Wu
et al. 2013; Palisch et al. 2010). As a result of lower
viscosity, slickwater cannot suspend and transport proppants
as effectively as gelled fluids. To overcome poor proppant
transport, higher pumping rates are applied, which in turn
leads to significant energy loss due to friction and
turbulence in the tubular pipeline (Palisch et al. 2010; Kaufman
et al. 2008). In order to lower the surface pumping
pressures and compensate for the energy losses during
pumping, a small amount of high molecular weight polymer is
dissolved in the fluid, which acts as a drag reducer. In
slickwater treatments, friction reducer is a significant
component of the fluid. Long, flexible chain
polyacrylamide-based polymers are known to be the most effective
drag reduction polymers (Kim et al. 1998).
When a polymer solution is subjected to turbulent flow,
the large molecules present in the solution undergo different
conformational changes such as flow orientation, stretching,
and relaxation. These conformational changes alter the flow
field and dynamics of turbulent structures in the vicinity of
pipe wall. In the macroscopic scale, those variations result
in large drag reduction. However, mechanical degradation
of polymer solutions complicates their use (Campolo et al.
2015; Moussa and Tiu 1994). Several theories have been
proposed to explain mechanical degradation of polymer
solutions, among which extreme stretching of polymer
chains and scission of the polymer chain have been most
accepted (Rodriguez and Winding 1959). Another study
reports that chain scission occurs near the midpoint of the
polymer which is caused by the extensional features of the
turbulent flow (Lim et al. 2003; Merrill and Horn 1984).
Due to the susceptibility of PAM molecules to shear
degradation under turbulent flow conditions, researchers
have considered other candidates such as rigid
polysaccharide molecules to improve the shear stability of drag
reducers. Kim et al. used a rotating disk apparatus to verify
the DR behavior of 100 wppm XG solutions with four
different molecular weights. They observed that XG is more
resistant to shear forces than most flexible polymers (Kim
et al. 1998). Other researchers compared solutions of
polyethylene oxide (PEO), PAM, XG, and guar gum (GG).
They observed that synthetic polymers initially induced
greater DR efficiency, but as result of mechanical
degradation, DR efficiency of synthetic polymers declined more
quickly than the polysaccharides. The available data in the
literature suggest that XG is shear resistant at turbulent flow
conditions, but DR induced by XG is small compared to
synthetic polymers such as PAM (Soares et al. 2015;
Kulmatova 2013; Wyatt et al. 2011; Kenis 1971). According to
the literature, binary solutions of polymers can give rise to
DR efficiency and shear stability. Dingilian and
Ruckenstein (1974) investigated the DR behavior of PAM, PEO,
and carboxymethylcellulose (CMC) single and binary
solutions. They observed negative deviation from additivity
for binary solutions of two flexible polymer molecules
(PEO/PAM) and positive deviation for PAM/CMC and
PEO/CMC binary solutions, where flexible and rigid
molecules coexist in the solution. Dschagarowa and
Bochossian (1978) also observed synergism in the DR
behavior of poly-isobutylene and l,4-cis-isoprene rubber
binary solutions. They also concluded that flow conditions
can affect the degree of deviation from additivity. Malhotra
et al. (1988) verified DR of PAM/GG, GG/XG, and PAM/
XG binary solutions and concluded that the degree of DR
and synergism depend on polymer concentration and flow
rate. They also concluded that positive deviation in
additivity occurs when both polymers are rigid. But, they
mentioned that their conclusions are limited to their
experimental conditions and synergism might be observed
in many other binary mixtures at higher concentrations.
Reddy and Singh (1985) verified the same binary solutions
at higher concentrations (C [ 200 wppm) and in a larger
experimental setup. Contrary to previous authors, they
observed negative deviation for PAM/polysaccharide
binary solutions. They also verified the shear stability of the
polymer solutions and concluded that the solutions showing
synergism in DR produce better shear stability (Reddy and
Singh 1985). Recently Sandoval and Soares (2016) verified
the DR behavior of PAM/XG and PEO/XG binary solutions
in a pressure-driven flow loop. The authors reported clear
synergism between polymers. They concluded that the
improvement observed in the mixed solutions was related to
the change in the polymeric conformation from coiled to
elongated (Sandoval and Soares 2016). Regarding the DR
behavior of binary polymer solutions, very limited work is
reported in the literature. On the other hand, the existing
published research is limited to certain conditions such as
small-scale experimental setups (capillary tube), low flow
rates and Reynolds numbers, and certain concentrations or
molecular weights. Also, some of the available data
contradict each other. As mentioned above, Reddy and Singh
(1985) had a different observation from Sandoval and
Soares (2016) regarding the DR behavior of PAM/XG
binary solution, which we believe arises from the
differences in the experimental setup and the molecular weights
of the polymers.
In this work, we focus on studying the DR behavior and
shear stability of anionic HPAM/XG binary polymer
solution. Anionic PAM is the partially hydrolyzed form of
polyacrylamide with more flexibility and relatively large
molar mass. Both polymers are widely used in industrial
applications such as slickwater treatments. There has been
little or no work regarding the DR behavior of anionic
HPAM and XG mixtures. We believe that it would be
interesting to verify the DR behavior of two negatively
charged molecules coexisting in a solution. Since various
HPAM and XG molecules with different molecular weights
are available in the market, we also study the behavior of
single polymer solutions, so that we can compare them
with binary solutions and assess the degree of improvement
in shear stability.
2 Materials and methods
2.1 Materials and preparation
Anionic polyacrylamide as a linear flexible polymer and
XG as a semirigid polymer were chosen for this
investigation. The molecular weights provided for PAM (Kemira
Co.) and XG (PFP Technology) by the vendors are (6–
8) 9 106 kg mol-1 and (4–5) 9 106 kg mol-1,
respectively. The accurate values for molar mass were measured
using light scattering (for HPAM) and viscometry (for XG)
methods. In the light scattering experiments, all solvents
were filtered through 0.02 lm cellulose acetate Millipore
filters. The HPAM solutions were prepared by dissolution
of a known amount of polymer in the 0.5 mol L-1 NaCl
solvent. The solutions were filtered through a 0.45 lm
cellulose acetate Millipore filters. A concentration range of
the polymer solutions (0.2–2.0 g L-1) were analyzed using
the batch mode (without size separation) of a multi-angle
light scattering (MALS) detector (DAWN-HELEOS II,
Wyatt Technology) with a laser wavelength of 658 nm.
The specific refractive index increments (dn/dc) value of
the HPAM in 0.5 mol L-1 NaCl solution, which was
determined by an OPTILAB T-reX differential
refractometer (Wyatt Technology) at 633 nm and 25 C, was
0.162 mL/g. Viscosity averaged molecular weight of XG
was measured using the method described in the literature
(Sohn et al. 2001). In this method, the intrinsic viscosity [g]
was measured with an Ubbelohde capillary viscometer
(diameter capillary 0.46 mm, Schott-Gerate), immersed in
a water bath maintained at 25.0 ± 0.1 C. First, the
specific viscosity gsp was calculated from the relative
viscosity, which is the ratio of the viscosity of xanthan gum
solution at a certain concentration to that of the solvent.
Each concentration was measured five times. The plot of
gsp/C versus C (C is the concentration of solutions) gave a
straight line, the intercept of which was [g]. Then, using the
Mark–Houwink equation the molar mass was calculated:
The measured values for the molecular weights of the
polymers, HPAM and XG, were 7.2 9 106 kg mol-1 and
3.9 9 106 kg mol-1, respectively.
To establish a baseline for further studies, deionized
water was used throughout. Using an analytical balance,
polymer powders were weighed with an accuracy of
±1 mg (Mettler Toledo XS603s). The preparation of the
polymer solutions took place in a separate tank. First, the
polymer powders were gradually sprinkled into the solvent
and slowly agitated at 30 rpm, in order to prevent particles
from clumping on the surface. Then the prepared solutions
were stored overnight for complete hydration. The studied
concentrations of HPAM solutions were 100, 150, 200,
500, and 1000 wppm. In order to investigate the effect of
XG, mixed polymer solutions of 100 wppm
HPAM ? 100 wppm XG (total C = 200 wppm), 150
wppm HPAM ? 100 wppm XG (total C = 250 wppm),
and for comparison, 600 wppm XG solutions were
2.2 Drag reduction and viscosity measurements
A closed-loop flow system was used for drag reduction and
turbulent flow measurements (Fig. 1). The system is
comprised of a 60-L supply tank connected to a progressive
cavity pump (SEEPEX BN 10-12) with a pumping capacity
of 30 GPM (113.56 L/min), and a seamless stainless steel
horizontal pipe test section of L = 8 ft. (2.44 m) and inner
diameter of 1 in. (2.54 cm). The flow rate of the system
was measured using a mass flow meter (OPTIMASS 1000,
KROHNE) with an accuracy of ±0.15% and a repeatability
of ±0.05% as stated by the manufacturer. The pressure
drop data along the measuring length of the pipe were
gathered using a membrane differential pressure transducer
(PX409, OMEGA). At each flow rate, the Fanning friction
factor is calculated by:
Here, f is the Fanning friction factor, q is the fluid density,
U is the average velocity, DP is pressure drop in the
measurement length of L, and D is the internal diameter of
In the flow experiments, the drag reduction efficiency of
the polymer solutions was defined as:
where subscripts ‘‘w’’ and ‘‘s’’ stand for water and polymer
solution, respectively, and ‘‘Re = const.’’ signifies the fact
that the comparison between the flows is made at the same
Reynolds numbers. Here Re = qUD/ga, and ga is fluid
viscosity. In drag reduction experiments, the flow rate was
increased stepwise (and kept constant for 1 min at each
flow rate), and then, the polymer solutions were sheared in
the flow loop at maximum flow of 30 GPM for 2 h and
sampling was performed eight times at shearing periods of
t = 0, 15, 30, 45, 60, 80, 100, and 120 min. After the
shearing process, the flow rate was decreased stepwise in
the same manner as it was increased.
Viscosity measurements were carried out in a DHR
controlled stress rheometer. The instrument is equipped
with a Peltier system to control sample temperature. In our
experiments, sample temperature was maintained at
25 ± 0.01 C. The geometry used in the apparent viscosity
Data acquisition and control
Fig. 1 Schematic illustration of the flow loop; instrumentation consists of a digital flow meter (F), differential pressure transducer (P), valves
(V), and temperature sensors (T)
measurements was cone and plate. The cone diameter and
angle were 60 mm and 2 , respectively. Approximately,
2 mL of the solution was placed between the cone (rotating
plate) and the fixed plate and the instrument was set to the
strain control mode. In this mode, shear rate (c_) was
logarithmically increased from 0.01 to 1000 s-1 and shear
stress was measured simultaneously, and then, apparent
viscosity was calculated using ga ¼ r=c_ correlation, where
r and ga are shear stress and apparent viscosity,
respectively. The power-law and Carreau–Yasuda viscosity
models were used for fitting the viscosity data.
In the power-law model, n (behavior index) is a measure
of deviation from Newtonian behavior and K (consistency
index) is a measure of average viscosity. K and n known as
power-law parameters were used in friction factor
In the Carreau–Yasuda equation, g is the shear viscosity,
and g0 and g? are viscosities at zero-shear and
infiniteshear plateaus, while k, n, and a represent the inverse shear
rate at the onset of shear thinning, power-law index, and
transition index, respectively.
3 Results and discussion
3.1 Polyacrylamide solutions
In order to assess the degree of drag reduction and polymer
degradation, several samples were taken at specified
intervals over the shearing process. Shear stress and
apparent viscosity of the samples were measured in the
rheometer, and the power-law and Carreau–Yasuda
parameters were calculated. For Newtonian fluids, the
value of n is 1 and for shear-thinning fluids, such as
polymer solutions, n is \1. As the value of n deviates from
1, the degree of non-Newtonian behavior increased. The
Carreau–Yasuda and power-law parameters calculated for
different concentrations of the anionic polyacrylamide are
shown in Table 1 and Fig. 2a, b, respectively. Comparison
of power-law parameters of fresh (zero shearing time)
HPAM solutions showed that by increasing concentration,
values of K increased and n values decreased, indicating
increased non-Newtonian behavior. It can also be found
that, as the shearing time increased, the values of
powerlaw parameters changed for all the polymer solutions.
Figure 2a shows that, over the shearing time, K values of
HPAM solutions decreased and n values increased and get
close to one (Newtonian behavior). The difference in the
n values of the solutions before and after the shearing was
Table 1 Parameters of
Carreau–Yasuda model for
HPAM, XG, and HPAM/XG
Fig. 2 Power-law model parameters variation over shearing time for HPAM solutions
large (35%–152% increase for various concentrations). The
overall change in n values (after the shearing period) was
35% for a 100 wppm solution, and by increasing
concentration, the maximum change in n values (152%) appeared
at 200 wppm. As the concentration increased above
200 wppm, n droped to 69% for the 1000 wppm solution.
As a result of shear degradation and consequently viscosity
reduction, K values declined. By increasing concentration
from 100 wppm to 1000 wppm, K values reached a
maximum decline of 64% at 200 wppm, but with further
concentration increase a 33% decline in K value was found for
1000 wppm HPAM solution.
Another indication of shear degradation is shown in
Fig. 3, where the apparent viscosity of the 200 wppm
HPAM solution, at shear rates under 10 s-1, undergoes
drastic reduction as the circulation time increases. The
reason that we only saw changes at lower shear rates might
be related to the scission of the molecules that belong to the
high tale of the molecular weight distribution of the
Concentration of solution
Fig. 3 Apparent viscosity of 200 wppm sheared HPAM samples
(samples 1–8: fresh, 15, 30, 45, 60, 80, 100, and 120 min shearing
polymer (Liberatore et al. 2004). Those molecules
contributed to the formation of the zero-shear viscosity
Prandtl–Karman coordinates are a semilog graph of f
versus Re.f , where f and Re are Fanning friction factor and
Reynolds number, respectively. Using Prandtl–Karman
coordinates, the degree of DR of polymer solutions can be
compared with respect to the boundaries of drag reduction;
the onset of drag reduction as the point of departure from
Prandtl–Karman law and maximum drag reduction (MDR)
or Virk’s asymptote (White and Mungal 2008; Virk 1975).
Prandtl–Karman plot for different concentrations of HPAM
is shown in Fig. 4. Three flow regimes can be detected:
Repffifffi\200; laminar flow. All polymer solutions
obey Poiseuille’s law.
200\Repffifffi\350; laminar to turbulent transition.
Repffifffi [ 350; turbulent flow.
It is observed that except for the laminar to turbulent
transition region, the turbulent friction factor data for the
solutions are bounded in the area between the two universal
asymptotes and the data points are linear for all
Results of linear fitting of the data points in the turbulent
region (Table 2) revealed that by increasing the
concentration of polymer, the slope of the lines tended to increase.
According to the literature, the slope increment with
respect to the Prandtl–Karman law (d) is proportional to the
square root of polymer concentration (d / pffiCffiffi) with a
proportionality constant that is the characteristic of the
polymer (Virk and Baher 1970). The slope increment
values are reported in Table 2. The proportionality constant
for the HPAM used in this work is calculated to be
0.27 ± 0.05. Figure 4 shows that by increasing HPAM
concentration, the extent of DR increases and the data
points approach Virk’s asymptote. Among different
concentrations, the extent of DR and slope of data points for
100 wppm HPAM solution were closest to the Prandtl–
Karman line (the onset of DR). On the other hand, the
greatest DR belongs to the 1000 wppm solution. For
solutions with polymer content greater than 200 wppm, in
200\Repffifffi\500 range, the data points were nearly
tangential to the MDR line, but by increasing the flow rates
(Reynolds number), the data points tended to deviate from
MDR. Results indicated that further increase in
concentration did not have a large effect on the degree of DR in
the experimental conditions of this work.
The effect of polymer concentration and mechanical
degradation on the Fanning friction factor of HPAM
solutions is shown in Fig. 5a, b, respectively. It can be seen
that even at low concentrations of polymer (100 wppm),
Fanning friction factor values were much lower than those
of water. Increasing polymer concentration resulted in
further reduction in friction factors (data points get close to
the maximum drag reduction asymptote), and
consequently, drag reduction efficiency increased. The smallest
values of friction factors at different Reynolds numbers
belong to 1000 wppm solution. It was also observed that
the difference between turbulent friction factors of 200,
500, and 1000 wppm solutions was very small, which is in
agreement with the results shown in Prandtl–Karman
coordinates, indicating that at the studied range of
Reynolds numbers, DR efficiency was close to its maximum
value (MDR); further increase in concentration did not
change friction factors. We can also observe that as the
Reynolds numbers increased, the data points tended to
deviate from MDR.
Shearing had a large impact on reducing the DR ability
of polyacrylamide solutions. Comparing the friction factors
of 200 wppm HPAM solution at different Reynolds
numbers (Fig. 5b) showed a 30%–50% decline after 2 h of
shearing. It can be observed that as a result of shearing,
friction factor values moved away from MDR line and
shifted toward water friction factors at different Reynolds
numbers. Although flow rate was constant for all the
experiments, a shift in the data points of the sheared
samples toward lower Reynolds numbers was observed.
Slope increment (d)
Fig. 4 Prandtl–Karman coordinates for HPAM solutions
Table 2 Linear fit results of
Linear fit equation
Fig. 5 Friction factor versus Re: a effect of HPAM concentration and b effect of shearing on 200 wppm HPAM
Fig. 6 %Drag reduction for different concentrations of HPAM at
30 GPM (113.56 L/min)
The shift was an indication of alteration in the flow regime,
which occurred due to the change in the rheological
properties of the solutions as a result of shear degradation.
Figure 6 shows the changes in the DR% over shearing time
for different concentrations of HPAM at constant flow rate.
It was observed that, for fresh samples (t = 0), the extent
of DR increased from 30% to 67% by increasing polymer
concentration from 100 to 1000 wppm. Results also
indicated that solutions above 200 wppm produced nearly
identical DR at the early stages of shearing (t \ 20 min),
which corresponds to the results shown in Prandtl–Karman
coordinates (Fig. 4). But beyond 20 min, the DR curves
tended to diverge, indicating that the degree of shear
degradation was different for each polymer concentration.
Ptasinski et al. (2003) reported that in flexible polymers
such as HPAM, as shear force reached a certain level, the
molecules stretch and consequently effective viscosity
increased, the turbulent buffer layer thickened, and due to
dissipation of the energy from turbulent fluctuations drag
was reduced. It is also known that drag is reduced when
turbulent flow interacts with polymer networks. When
polymer concentration is high enough (above critical
overlap concentration, C*), polymer chains are packed
closer and begin to interact with each other and form
entangled networks (Skelland and Meng 1996).
The decline in the degree of DR was observed at all the
concentrations of HPAM solution. Resistance to
mechanical degradation over the shearing period is shown in Fig. 7.
Results showed that, as the concentration increased, the
resistance to mechanical degradation also increased. This
made the 100 wppm solution the least resistant and
1000 wppm solution the most resistant to mechanical
degradation. These results agreed with those reported by as
Soares et al. (2015), indicating that increasing polymer
concentration (PAM or PEO) in the solution could increase
the resistance to mechanical degradation. It was also
observed that the shear stabilities of 100, 150, 200 wppm
solutions were very close and followed the same trends. In
other words, 200 ppm solution was only slightly more
resistant to degradation (DRt=120/DRmax = 0.5) than
Fig. 7 Resistance to mechanical degradation (DR/DRmax) for HPAM
solutions at 30 GPM (113.56 L/min)
100 wppm solution (DRt=120/DRmax = 0.39). But, above
200 wppm a sudden rise in the shear resistance of the
solutions was observed. Both 500 and 1000 wppm
solutions showed superior shear stability compared to other
solutions. We found that although 200 wppm HPAM
solution had similar initial DR% to 500 and 1000 wppm
solutions (Fig. 6), it had a larger decline in DR (Fig. 7).
The values of DRt=120/DRmax for 500 and 1000 wppm
solutions were 0.62 and 0.72 at the end of 2-h shearing
period, respectively. It is also interesting to note that the
DR/DRmax declined at a slower rate after t = 60 min. For
example, the reduction in DR/DRmax value for 1000 wppm
solution from t = 60 min to t = 120 min was only 0.06.
From viscosity measurements, the critical overlap
concentration (the concentration that marks the beginning of
polymer–polymer interaction) of the HPAM solution was
determined to be 200 wppm. At C \ 200 wppm, there was
no polymer network, so there was no decline due to
polymer network breakup, but at C [ 200 wppm, the
networks were more entangled and upon deformation can
recover quickly. Also, it seems that at higher
concentrations (C [ 200 wppm), the extensional force from the
turbulent flow was distributed among a larger number of
molecules, which resulted in a lower number of chain
scissions and higher DR stability. But at C \ 200 wppm
polymer networks just began to form and were weak.
Therefore, at the beginning of the shearing process DR
efficiency increased, but gradually as shear forces acted,
unstable polymer networks, as well as individual polymer
molecules broke up, which resulted in a large decline in the
DR efficiency of C \ 200 wppm HPAM solutions
compared to higher concentrations.
Another result was that the rate of DR decline was fast
in the first 60–80 min of the shearing process. This is
probably due to the presence of longer chains of polymer in
the fresh solutions, which are more susceptible to chain
scissions (require less energy to break). After 60 min, the
gap between DR lines (Fig. 6) remained nearly constant,
which indicated that polymer chains were broken up at a
similar rate at all the concentrations.
Several models for correlating the DR behavior of
polymer solutions can be found in the literature. Two of the
most common models are the exponential decay model
(Bello et al. 1996) and Brostow’s model (Brostow 1983).
Based on the exponential decay model proposed by Bello
et al. (1996), DR follows an exponential decline with time
for polyacrylamide and polysaccharide solutions:
DR%ðtÞ=DR%ð0Þ ¼ eð t=kÞ
where DR% (t) and DR% (0) (or DRmax) are percent drag
reduction at times t and t = 0, respectively, and k is an
adjustable parameter. Brostow’s equation is a more general
model, which has been applied to various shear degradation
applications (Lim et al. 2003) and has been developed to
quantitatively describe DR and its changes with time:
DR%ðtÞ=DR%ð0Þ ¼ ½1 þ Wð1
Here W is the average number of vulnerability points per
chain and h is called rate constant.
The two models were used in this work to correlate the
DR data of HPAM and HPAM/XG solutions. Calculated
model parameters and goodness of fit (R2) for both models
are reported in Table 3. The solid lines in Fig. 6 represent
the fitting results. It can be found that for the studied
concentrations of HPAM solution, both models describe
the degradation behavior well, though Brostow’s model
gives better fits and its predicted values are more accurate.
Table 3 Parameters of Brostow
and exponential decay models
for HPAM solutions
Exponential decay model
3.2 HPAM/XG mixed solutions
In order to verify the possibility of stabilizing HPAM with
XG, mixed solutions were prepared and sheared in the
same manner as the HPAM solutions. Based on the results
obtained from the previous section, the DR behavior of
binary polymer solutions was compared to that of
200 wppm HPAM solution. Several authors have
mentioned that the degree of DR in XG solutions depends on
the concentration and molar mass of XG (Soares et al.
2015; Pereira et al. 2013). So higher concentrations of XG
are required to reach the same level of DR as HPAM. Our
preliminary experiments showed that the DR efficiency of
600 wppm XG was close to the DR values of 200 wppm
The Carreau–Yasuda model fitting results of the mixed
solutions and a solution containing XG are included in
Table 1. Also, friction factors of the mixed polymer
solutions and solutions of 600 wppm XG and 200 wppm
HPAM are shown in Fig. 8a. It was found that, although
polymer concentration in the 600 wppm XG solution was
greater than that of 200 wppm HPAM solution, the
600 wppm XG solution possessed greater friction factors.
Higher flexibility of HPAM polymer chains with respect to
semirigid XG chains resulted in higher energy adsorption
(stretching) due to interaction with dynamic turbulent flow
and subsequently, superior drag reduction capability of
flexible polymers. Also, it was found that in the fresh
binary solutions, there is no outstanding synergetic effect
between HPAM and XG molecules. Even the 150 wppm
HPAM ? 100 wppm XG solution, which has a higher total
polymer concentration, showed larger friction factors than
200 wppm HPAM.
Figure 8b compares the friction factors of the solutions
after 120 min of shearing. Because of high shear stability,
XG solution maintained its initial friction reduction
100 wppm HPAM+100 wppm XG
150 wppm HPAM+100 wppm XG
100 wppm HPAM+100 wppm XG
150 wppm HPAM+100 wppm XG
Fig. 8 Fanning friction factor of mixed solutions in a fresh form and b after shearing for 120 min
efficiency, with a relatively small change in friction factor
values. But for the mixed HPAM/XG solutions, the friction
factor values largely increased as a result of shearing. It is
interesting to note that 200 wppm HPAM solution had a
larger increase in its friction factors than mixed solutions
(Fig. 8b). This suggested that addition of XG was
beneficial in controlling the shear degradation of HPAM. The
decline in the DR efficiency and shear resistance of the
samples over shearing time is shown in Figs. 9 and 10.
Also, as mentioned above, Brostow’s and exponential
Fig. 9 %Drag reduction for mixed HPAM/XG solutions at 30 GPM
Fig. 10 Effect of shearing on DR decline for mixed HPAM/XG
Table 4 Parameters of Brostow
and exponential decay models
for mixed HPAM/XG solutions
decay models were used to correlate DR with time (solid
lines in Fig. 9; Table 4).
The results indicated that the DR efficiencies of both
HPAM and XG binary solutions were smaller than that of
200 wppm HPAM solution, indicating that partially
replacing HPAM with XG in the binary solutions had
reduced the DR efficiency of the single HPAM solution.
Regarding the DR behavior of HPAM/XG binary mixtures,
different views can be found in the literature. Sandoval and
Soares (2016) recently reported that the DR efficiency of
HPAM/XG mixture is close to the DR values of the single
HPAM solution at the same total concentration. However,
they confirmed that the synergetic effect in PAM/XG
mixture is not as notable as PEO/XG. Reddy and Singh
(1985) also studied PAM/XG mixtures and reported that
the single PAM solution has a higher DR efficiency than a
binary mixture. Their data were limited to fresh solutions.
We believe that the differences in the reported data might
be attributed to the differences in the experimental
conditions. In our work, since we were dealing with two
negatively charged polymers in the solution, we would expect
to obtain different results. We also believed that due to the
higher flexibility (higher molecular weight) of the anionic
HPAM used in our experiments, HPAM molecules were
more susceptible to scission and the interaction between
HPAM and XG was reduced. Compared to 600 wppm XG
solution, the DR% of 100 wppm HPAM/150 wppm XG
solution was high only in the first 60 min of the shearing
process and after that, as a result of mechanical degradation
the DR values declined. Also, it was found that the
100 wppm HPAM/100 wppm XG solution was less
efficient in DR than the 600 wppm XG solution from the
beginning till end of the shearing period. Comparison of
the shear resistance (DR/DRmax) of the solutions revealed
that, as expected, 600 wppm XG solution had the best
shear stability among all the solutions and the least decline
in DR over the shearing period (0.15 decline in DR/DRmax
value). Contrary to XG, 200 wppm HPAM and the binary
HPAM/XG solutions suffered from poor shear resistance
and a large decline in their DR efficiencies. These results
are in agreement with the results reported by Sandoval and
Soares (2016). It is interesting to note that the shear
resistance of both binary solutions and 200 wppm HPAM
solution was nearly identical.
From the obtained friction factor results, it can be
inferred that addition of XG reduced the DR capability of
mixed solutions (DR% = 40% and 55%) with respect to
200 wppm HPAM solution. Also results suggested that
increasing HPAM concentration in the mixed solutions
does not change the DR efficiency decline significantly.
Since there was only a small amount of chain degradation
in semirigid polymers, the extent of DR depended only on
the interaction between polymer chains and entanglements,
which is directly related to polymer concentration. It
should be considered that the concentration of XG was
100 wppm for mixed solutions, which is below the critical
concentration of XG (C* & 300 ppm). Hence, as
suggested by other authors (Wyatt et al. 2011; Berman 1978),
mixing HPAM with higher concentrations of XG would be
more beneficial in maintaining high DR efficiency and
even better control of shear degradation of polyacrylamide
solutions, which is the subject of our future work. Same as
for the HPAM solutions, Brostow and exponential decay
models were used to correlate the drag reduction behavior
over time for the HPAM/XG mixed solutions. The result is
shown in Fig. 9 and Table 4. It can be found that both
models give good fitting, but similar to HPAM solutions,
the Brostow’s model correlated the DR reduction data
The results from this work show that among different
concentrations of HPAM, 1000 wppm solution has the
highest drag reduction efficiency and the lowest decline in
DR%. Increasing the concentration above 200 wppm does
not change the DR% of the fresh samples significantly,
though increasing concentration increases resistance to
mechanical degradation. Results also indicate that mixing
flexible HPAM with XG did not improve the degree of DR
significantly, but slightly improved the DR stability of
HPAM solutions. Since the drag reduction of rigid
polymers depends only on concentration, mixing HPAM with
higher concentrations of XG might be beneficial in
maintaining the DR efficiency of HPAM as well as improving
its shear stability. Brostow and exponential decay models
were used to correlate the drag reduction decline data.
Results indicate that both models can correlate the DR
behavior of HPAM, as well as mixed HPAM/XG solutions.
Brostow’s model gave slightly better fits.
Acknowledgements The authors would like to thank the Research
Partnership to Secure Energy for America (RPSEA) and Oklahoma
State University Chemical Engineering Department for partial support
of this project.
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