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Viscoelastic behavior of crude oilЦpolymer emulsions.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
Published online 23 October 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI:10.1002/apj.523
Special Theme Research Article
Viscoelastic behavior of crude oil–polymer emulsions
Mamdouh T. Ghannam*
Department of Chemical and Petroleum Engineering, College of Engineering, United Arab Emirates University, P.O. 17555, Al-Ain, United Arab
Emirates
Received 31 October 2009; Revised 14 September 2010; Accepted 19 September 2010
ABSTRACT: This study focuses on the investigation of the viscoelastic behavior of crude oil–Alcoflood polymer
(AFP) emulsions in terms of storage modulus, loss modulus, and complex modulus. Three different types of AFP were
examined in this investigation. North Sea crude oil was used to prepare the oil–polymer emulsions. The polymer and oil
concentrations exhibit a strong influence on the behavior of complex modulus vs frequency. The effect of polymer and
oil concentrations is more pronounced at low frequency. This effect diminishes with frequency. For the three polymers
used, the apparent complex modulus increases significantly with the concentration of polymer and crude oil. The crude
oil phase gradually increases the complex modulus of the emulsions. The complex modulus values of AF1275 and
AF1285 emulsions are similar to each other and significantly higher than that of the emulsions of AF1235. The polymer
concentration strongly increases the emulsion complex modulus. For a low polymer concentration of 2000 ppm, the
aqueous solutions and oil emulsions exhibit viscoelastic behavior with a liquid-like response at low frequencies and a
solid-like response at high frequencies. The addition of crude oil lowers the crossover frequency. However, at a higher
polymer concentration of 10 000 ppm, both aqueous solutions and emulsions exhibit only elastic behavior.  2010
Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: crude oil; Alcoflood polymer; emulsion; viscoelasticity; complex modulus; storage modulus; loss
modulus
INTRODUCTION
A limited amount, approximately 30–50%, of the original crude oil can be obtained from a well through conventional production techniques. Enhanced oil recovery
(EOR) is utilized in the crude oil production industry after the traditional production methods have been
exhausted. Polymer injection plays an important role in
the crude oil production industry during the EOR stage.
Alcoflood polymer (AFP) is one of the most widely
utilized water-soluble polymers in the EOR stage. During the polymer flooding process, an aqueous solution
of AFP is injected into a well formation. The aqueous
solution of AFP improves the mobility ratio and sweep
efficiency; thus, it raises oil recovery and the production
rate.
The injection of AFP aqueous solution into the oil
reservoir leads to the formation of crude oil–aqueous
solution of AFP emulsions. The oil in aqueous phase
emulsion comprises immiscible oil droplets phase dispersed through the aqueous continuous phase. Several
*Correspondence to: Mamdouh T. Ghannam, Department of
Chemical and Petroleum Engineering, College of Engineering,
United Arab Emirates University, P.O. 17555, Al-Ain, United Arab
Emirates. E-mail: mamdouh.ghannam@uaeu.ac.ae
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Curtin University is a trademark of Curtin University of Technology
articles have investigated the emulsion characteristics
from different aspects. A literature review of the rheological behavior of oil emulsions showed that several
studies have been carried out on oil emulsions in which
the continuous phase is Newtonian. Some examples of
these articles are Sherman,[1] Princen,[2,3] Princen and
Kiss,[4] and Pal and Rhodes.[5] The rheological behaviors of dispersed solid particles within liquid emulsions
have been covered in several articles, including Tanaka
and White,[6] Chan and Powell,[7] Metzner,[8] Gupta and
Seshadri,[9] and Poslinski et al .[10]
Limited work was found on the rheological behaviors
of oil emulsion in which the continuous phase is a nonNewtonian polymeric solution. Some examples of these
studies are Han and King,[11] Pal,[12] and Ghannam.[13]
In a previous study of flow properties of crude oil–AFP
emulsions,[13] it was found that the emulsion showed a
non-Newtonian profile of shear thinning behavior. The
emulsion viscosity increased with AFP concentration
and decreased with shear rate. The type of AFP dictated
the viscosity behavior at shear rates <10 s−1 . Owing
to the intrinsic viscosity of the employed polymer,
the AF1285 emulsion showed higher viscosity than
AF1275, AF1235, and water emulsions in this order.
For shear rates >10 s−1 , no differences were reported
Asia-Pacific Journal of Chemical Engineering
VISCOELASTIC BEHAVIOR OF CRUDE OIL–POLYMER EMULSIONS
for the three Alcoflood emulsions of AF1235, AF1275,
and AF1285. A previous study by Ghannam[13] also
concluded that the well-known Casson model[14] fits the
flow behavior of crude oil–AFP emulsions well:
τ = [τo0.5 + (γ̇ ηc )0.5 ]2
(1)
The work published by Langenfield et al .[15] described the viscoelastic behavior of highly concentrated
water-in-oil emulsions. They found that such emulsions
behaved as elastic solids. When highly concentrated
emulsions are exposed to small shear deformation, these
emulsions display strong elastic behavior and yield
stress.[16]
Polymer flooding of oil reservoirs has been applied
for several years as a practical way for improving
oil production. The viscosity of the injection fluid
is enhanced, which increases the sweep efficiency. A
semidilute polymer phase forms gel status if a connected network of polymer molecules can be established
through intermolecular interactions.[17] The most common way to establish these intermolecular interactions
is by a chemical cross-link.[18] However, if the polymer
solution is dilute, a cross-link cannot form a connected
network. In this case, nonlink aggregates of finite size
are formed, which are referred to as microgels.[19]
The dynamic test is a very useful technique to study
the viscoelastic behavior of the crude oil–polymer
emulsions. Through this test, an emulsion sample is
examined for its deformation response to the effect of
oscillating stresses or strains. Using the CS-mode of the
RS100, the stress may be applied as a sinusoidal time
function:
(2)
τ = τa sin(wt)
Materials that display viscoelastic response have long
chain molecules. These molecules loop with each other
to form a complicated structure at a minimum energy
state. During the deformation stage, these molecules
stretch and increase the angles of the bond vector and
their energy state will be higher. If the applied stress is
released, molecules try to regain their original structure
and energy state. Viscoelastic behavior can be examined
by applying the dynamic test and/or by utilizing the
creep-recovery test. The approaches of the two tests
are different. The two tests complement each other, as
some features of viscoelasticity are better described in
a creep-recovery test and others in a dynamic test.
The complex modulus of G ∗ , in Pa, indicates the total
resistance of the substance against the applied strain and
can be obtained from
G ∗ = τa /γo
(3)
Furthermore, the complex modulus G ∗ of the viscoelastic behavior can be divided into a recovery elastic
part and a permanently maintained viscous part as
G ∗ = G + iG (4)
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
The first term of Eqn (4), G , called the storage or
elastic modulus, provides the contribution of the stress
energy that is temporarily stored during the test and
can be recovered, whereas the second term of Eqn (4),
called viscous or loss modulus, G , presents the energy
that has been utilized to initiate the flow and can be
considered to be irreversibly dissipated into shear heat.
If the tested sample is purely viscous, then:
G = 0 and G = G ∗
(5)
However, if the tested sample is purely elastic, the
magnitude of deformation is proportional to the applied
shear stress. The deformation response is maintained as
long as the stress is applied. When the stress is released,
the deformation response will disappear simultaneously.
Then, Eqn (4) will be
G = G ∗ and G = 0
(6)
The investigation of the viscoelastic behavior of
crude oil–AFP emulsions is important for petroleum
industries. The objective of this work is to study the
viscoelastic behavior in terms of storage modulus and
loss modulus for crude oil–AFP emulsions using a
RheoStress RS100 rheometer. A wide range of crude
oil concentrations, AFP polymer concentrations, and
polymer types were studied.
EXPERIMENTAL WORK
Before preparing the crude oil–AFP emulsions samples, the polymer was completely dissolved first in the
aqueous phase over time without external agitation to
prevent any negative impact of mixing on the polymer network. Then, the crude oil–AFP emulsion was
prepared by a gradual mixing of crude oil into the polymer aqueous solution, which contained 1% by volume
of Triton X-100 as an emulsifying agent for crude oil.
North Sea crude oil was used in all experimental tests.
The density and viscosity of crude oil are 880.6 kg m−3
and 7.16 mPa s at 40 ◦ C respectively, whereas an acid
value of 1.2(10)−3 kg HOH kg−1 is reported.
Triton X-100 from Sigma–Aldrick Canada Ltd was
utilized as a surfactant with a specific gravity of 1.07
and flash point of 113 ◦ C. Surfactant materials are
usually added into aqueous solutions as an emulsifying agent for crude oil. The emulsifying agents play
an important role in lowering the interfacial tension
between the crude oil and the aqueous solution, and in
stabilizing the presence of oil droplets dispersed phase
within the aqueous continuous phase.[20]
To investigate the viscoelastic behavior of crude
oil–polymer emulsions, three AFPs were used. These
AFPs, AF1235, AF1275, and AF1285, were obtained
from Ciba Specialty Chemicals (Bradford, West Yorks,
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
DOI: 10.1002/apj
173
174
M. T. GHANNAM
England). AFPs are high molecular weight polyacrylamide copolymers supplied in a granular powder with
a bulk density of 800 kg m−3 . The intrinsic viscosities
of the three AFPs, AF1235, AF1275, and AF1285, are
12, 20, and 24 respectively. The three AFPs are manufactured for the EOR programs for polymer-augmented
water floods or alkali/surfactant/polymer water floods.
AF1235 has good handling characteristics with excellent solubility to promote better injection into low-tomedium permeability reservoirs (50–500 mD), whereas
AF1275 and AF1285 are utilized for high-permeability
reservoirs and they offer good handling characteristics
with excellent viscosity alteration power in water.
The viscoelastic tests in terms of storage modulus
and loss modulus of crude oil–AFP emulsions were
carried out completely at a room temperature of 22 ◦ C
using RheoStress RS100 from Haake. A water bath
was connected to the RS100 to control the applied
temperature in the rheometer system. The drive shaft
of the RS100 was centered by an air bearing to apply
the specified stress on the tested sample without any
friction. The RS100 analyzes the resulting deformation
of the examined material with a digital encoder, which
can process a million impulses per revolution. This
high resolution allows for the measurement of small
strain values. The RS100 offers operating modes of
controlled rate (CR) mode, controlled stress (CS) mode,
and oscillation (OSC) mode. One of the important
specifications of RS100 is its capability to apply shear
stress with extremely low inertia. The operating mode
of RS100 can be easily switched between CR and CS
modes, and it can also apply oscillating stress and
frequency sweep. The measurement data was collected
using a cone–plate sensor. The sensor system consisted
of a stainless steel cone and plate with 35 mm diameter
and 4◦ cone angle.
Asia-Pacific Journal of Chemical Engineering
Effect of oscillatory shear on complex modulus
The complex modulus G ∗ (in Pa) of the three AFP aqueous solutions with a concentration range of 500–104
ppm and their emulsions with crude oil over the concentration range of 0–75% by volume oil were investigated
using an oscillatory shear effect in the frequency range
of 0.05–10 s−1 . Figures 1 and 2 depict the complex
modulus behavior against frequency for the aqueous
solutions of AF1235 and AF1285 respectively. The
measured G ∗ increases gradually with frequency for all
tested aqueous solutions. For a diluted polymer concentration of 500 ppm, the relationship between G ∗ and
w is almost linear. However, for higher polymer concentrations, the behavior deviates significantly from the
low concentration profile. At low frequency, Figs 1 and
2 show that the polymer concentration has a strong
influence on G ∗ . This influence gradually diminishes
with frequency to the extent that all curves form almost
one master curve at a frequency of 10 s−1 . Furthermore, the presence of crude oil within the different
emulsions significantly enhances the measured values
of the complex modulus, as can be noticed in Figs 1 and
2. The aqueous solutions of the tested polymers form
a three-dimensional network structure under no-strain
conditions; when the oscillatory shear is applied, the
three-dimensional network structure deforms accordingly. The status of the three-dimensional network
structure enhances gradually with polymer concentration and crude oil concentration, as can be concluded
from Figs 1 and 2.
Equation (7) is utilized to model the complex modulus vs frequency for all tested aqueous solutions and
emulsions. The three-parameter model of Eqn (7) adequately fits the relationship between the complex modulus and frequency with the regression coefficient in
excess of 0.99. Figures 3 and 4 show typical examples of the complex modulus behavior for different
emulsions of AF1275 and AF1285, respectively. The
RESULTS AND DISCUSSION
A stress sweep test is utilized first to determine the
linear viscoelastic range. This is the range where the
complex modulus G ∗ is constant with the stress, which
indicates that the internal bonds of the sample structure
are still intact. Otherwise, at a higher stress range,
shear thinning will take place and a major part of the
introduced energy will be irreversibly lost as heat. After
determining the linear viscoelastic range, further tests
can be employed to determine extra features of the
viscoelastic behavior.
Thus, many tests of stress sweep at 1 Hz were carried
out for a wide range of polymer concentrations of the
three AFPs. The linear viscoelastic range for the AFP
solutions was found to be 2 Pa. All further tests were
carried out at a stress value of 1 Pa to avoid nonlinear
viscoelastic range conditions.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Figure 1. Complex modulus behavior for AF1235 solutions
and emulsions.
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
VISCOELASTIC BEHAVIOR OF CRUDE OIL–POLYMER EMULSIONS
range. The results of the modeling analysis according to
Eqn (7) are listed in Table 1 for all the tested solutions
and emulsions.
G ∗ = G ∗ o + a(w )b
Figure 2. Complex modulus behavior for AF1285
solutions and emulsions.
Figure 3. Complex modulus behavior for the emulsions
of AF1275.
Figure 4. Complex modulus behavior for the emulsions
of AF1285.
solid lines in Figs 3 and 4 are the plots of the threeparameter model of Eqn (7), which presents a reasonable agreement between the experimental measurements
and Eqn (7) predictions except at a very low frequency
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
(7)
The parameter G ∗ o in Eqn (7) provides the value
of the apparent complex modulus when the frequency
approaches zero. Table 1 shows that the parameters
G ∗ o and a increase significantly with the concentration
of both polymer and crude oil for the three polymer
types. However, on the other hand, the power index b
decreases significantly with the concentration of polymer and crude oil. The reduction in the power index b
can be attributed to the effect of the oscillatory shear on
the emulsion structure. When the oscillatory shear was
applied, the emulsion structure significantly deformed
and molecules stretched, which led to a lower value of
‘b’.
Figure 5 shows the complex modulus behavior for
different emulsions of AF1275. It shows the effect of
crude oil concentration on complex modulus for low
(i.e. 1000 ppm) and high (i.e. 10 000 ppm) polymer
concentrations. As can be concluded from Fig. 5, the
presence of the crude oil dispersed phase gradually and
significantly enhances the complex modulus. The contribution of the crude oil can be attributed to the interaction between the oil droplets dispersed phase and the
polymer continuous phase. The more the crude oil that
is added, the more is the response of the crude oil interaction, and consequently higher G ∗ is reported. Much
higher complex modulus measurements are reported
for the higher concentration of the used polymer, as
can be seen in Fig. 5. The solid lines in Fig. 5 are
the plots of values from Eqn (7), which show good
agreement with the experimental measurements. Similar behaviors are reported for the AF1235 and AF1285
emulsions. Figure 6 shows the comparison between the
dynamic test response behavior of the three polymer
emulsions of AF1235, AF1275, and AF1285 in terms
of complex modulus G ∗ vs frequency for the 25% crude
oil concentration. Two polymer concentrations of 2000
and 10 000 ppm were examined. This test revealed that
the complex modulus values for AF1275 and AF1285
emulsions are almost similar to each other and significantly higher than the complex modulus behavior of
the AF1235 emulsions. Higher polymer concentration
of 10 000 ppm provides higher complex modulus values
than the response of 2000 ppm. Again, the solid lines in
Fig. 6 present the modeling analysis of Eqn (7). Similar
behaviors were found for the 75% crude oil emulsions.
Emulsion viscoelastic behavior
The viscoelastic behavior of the crude oil–AFP emulsions can be investigated in terms of storage and loss
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
DOI: 10.1002/apj
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M. T. GHANNAM
Asia-Pacific Journal of Chemical Engineering
Table 1. Parameters of Eqn (7).
Aqueous solutions
25% Oil emulsions
75% Oil emulsions
(a) AF1235 solutions and emulsions
Concentration
(ppm)
G ∗o
a
2000
5000
104
11.1
216.5
344.2
60.9
184.1
244.8
1000
2000
5000
104
2.2
15.6
253.1
1017
56.3
61.1
111.1
394.2
1000
2000
5000
104
1.1
22.7
306.4
956.8
58.3
61
101.5
263.5
b
G ∗o
a
1.98
17.7
65.8
1.52
160.2
132
1.42
484.1
346.6
(b) AF1275 solutions and emulsions
2.02
3.3
58
1.97
95.5
80
1.73
578.8
252.3
1.23
1249
457.9
(c) AF1285 solutions and emulsions
1.99
6.4
58.4
1.97
100.3
72.3
1.76
492.5
127.8
1.36
1367
342.5
b
G ∗o
a
b
1.94
1.66
1.29
190.3
580.4
842.5
145.8
437.6
1047
1.61
1.16
0.87
2
1.86
1.39
1.16
8.7
212.8
785.8
1732
62.1
120.5
278.9
789.7
1.97
1.69
1.35
0.95
1.99
1.90
1.67
1.27
16.4
132.4
819.5
1982
62.2
78.2
204.1
454.8
1.96
1.87
1.48
1.17
Figure 5.
Complex modulus behavior for different
emulsions of AF1275.
Figure 6. Complex modulus behavior for different polymer
emulsions.
moduli. These moduli are determined from the analysis
of the complex modulus using the software package
associated with the RS100 rheometer. Figure 7a and
b depicts the viscoelastic behavior of various crude
oil–AF1275 emulsions vs frequency. Figure 7a displays the emulsion viscoelastic behavior for the low
polymer concentration of 2000 ppm, while Fig. 7b is
for the high polymer concentration of 10 000 ppm. The
solid symbols are for the storage modulus, whereas
the open symbols are for the loss modulus. The tested
sample exhibits liquid-like behavior if the G value is
smaller than the G value or it displays solid-like behavior if the G value is larger than the G value.
Figure 7 shows several remarks concluded from the
frequency dependence profiles of G and G moduli
for the 2000 and 10 000 ppm of AF1275 emulsions. At
the low concentration of 2000 ppm AF1275 aqueous
solution (i.e. no oil was added), the polymer aqueous
solution shows a pronounced viscoelastic behavior with
liquid-like response at low frequencies and a solidlike response at high frequencies (i.e. typical for gel
and solid-like behavior). This crossover occurred at wc .
The AF1275 aqueous solution of 2000 ppm displays an
elastic behavior if the frequency exceeds 0.3 s−1 since
G falls well above G . In the presence of crude oil (i.e.
in the case of emulsions), crude oil emulsions display
elastic behavior at a frequency smaller than 0.3 s−1
as the crossover occurred at 0.09 s−1 . Therefore, the
addition of crude oil to the polymer aqueous solutions
lowers the crossover frequency. At the higher polymer
concentration of 10 000 ppm, as in Fig. 7b, it shows a
predominantly elastic behavior as the storage modulus
values are well above the loss modulus for the whole
range of the examined frequency.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
VISCOELASTIC BEHAVIOR OF CRUDE OIL–POLYMER EMULSIONS
Figure 7. Viscoelastic behavior of different emulsions of
AF1275.
Figure 8. Effect of concentration on the behavior of G and
G .
Figure 8a and b shows the effect of polymer and
crude oil concentrations on the behavior of storage
modulus and loss modulus for the different emulsions
of AF1275, respectively. Three decades of frequency
(0.05–10 s−1 ) were covered to examine the emulsions
behavior in terms of storage and loss moduli on logarithmic scales to display the wide range of results of G and G vs w . Figure 8a shows that the storage modulus
increases significantly with frequency and oil concentration. The influence of crude oil is more pronounced at
low frequency; however, it diminishes with frequency
forming one curve at a frequency of 10 s−1 . Polymer
concentration displays a strong influence on the storage
modulus response at low frequency. Again, this influence decreases with frequency. Figure 8b shows that the
loss modulus increases slightly with frequency and oil
concentration for the low polymer concentration. This
behavior diminishes at high polymer concentration. For
this case, the values of both G and G are significantly higher at 10 000 ppm than their counterparts at
2000 ppm. Increasing polymer concentration leads to
the extension of the polymer chains, which may facilitate the formation of entanglements and thereby form a
stronger gel network.
The effect of frequency on the profiles of G and
G moduli for the three AFPs of 2000 and 10 000 ppm
polymer concentrations are depicted in Figs 9 and 10,
respectively. Two concentrations of 25% and 75% crude
oil were examined in each case. For the low polymer
concentration of 2000 ppm and 25% crude oil, Fig. 9a
shows that the AF1235 emulsion exhibits elastic behavior if the frequency exceeds 0.5 s−1 . The other two
polymer emulsions AF1275 and AF1285 display almost
similar behavior and show elastic behaviors since G falls above G if the frequency exceeds 0.09 s−1 . Both
polymer emulsions of AF1275 and AF1285 result in
higher values of G and G than the AF1235 emulsion
up to a frequency value of 2 s−1 . In the presence of
75% crude oil, Fig. 9b shows a similar behavior for the
25% oil polymer emulsions without a significant difference between the three polymers. Figure 9b shows
that the elastic behavior for the AF1235 emulsion starts
at 0.15 s−1 , whereas the elastic behavior for the other
two polymer emulsions starts at the same frequency of
0.09 s−1 . In the case of higher polymer concentration
of 10 000 ppm, as shown in Fig. 10, similar behavior as
that reported for 2000 ppm is seen, with a few changes.
Regarding AF1235, the crossover of G and G occurs
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
DOI: 10.1002/apj
177
178
M. T. GHANNAM
Figure 9. G and G for different emulsions of the three
polymers at 2000 ppm.
at 0.3 and 0.09 s−1 for the 25% and 75% emulsion
respectively. The other two polymer emulsions, AF1275
and AF1285, show similar behavior with predominantly
elastic behavior as the storage modulus values are well
above the loss modulus for the whole range of the examined frequency. The polymer emulsions of AF1275 and
AF1285 provide higher values of storage modulus than
the storage modulus values of the AF1235 emulsion.
Figure 11 shows the effect of crude oil concentration
on the behavior of storage and loss moduli for different emulsions of AF1235 as a typical example for the
other two polymers. All emulsions displayed in Fig. 11
provide higher storage modulus values than their counterparts of loss modulus for each polymer concentration.
For a lower polymer concentration of 2000 ppm, both
G and G increase slightly with crude oil concentration. However, for polymer concentrations higher than
2000 ppm, both of G and G increase significantly with
the crude oil concentration. The viscoelastic behavior of
the crude oil–polymer emulsions can be attributed to
the presence of the polymer continuous phase (which
itself is viscoelastic) and the elasticity characteristics
that result from the crude oil droplet’s interactions with
the polymer network. The solid-like behavior of the
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering
Figure 10. G and G for different emulsions of the three
polymers at 10 000 ppm.
Figure 11. Effect of crude oil concentration on the behavior
of G and G .
crude oil–polymer emulsions is attributed to the formation of network structure. Modeling analysis has been
carried out for the investigated emulsions to study the
effect of crude oil concentration on the behavior of storage and loss moduli according to Eqn (8), where x ,
a, and b represent the crude oil concentration and the
Asia-Pac. J. Chem. Eng. 2011; 6: 172–180
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
VISCOELASTIC BEHAVIOR OF CRUDE OIL–POLYMER EMULSIONS
CONCLUSIONS
Table 2. Parameters of Eqn (8).
G
G (a) AF1235
Concentration
(ppm)
2000
5000
104
1000
2000
5000
104
1000
2000
5000
104
b1
a1
r
59.278 0.028 0.95
435.901 0.013 0.98
788.545 0.014 0.99
(b) AF1275
107.649 0.002 0.99
163.958 0.015 0.98
699.467 0.009 0.90
1700.015 0.007 1.0
(c) AF1285
108.276 0.003 1.0
171.879 0.008 0.95
574.371 0.011 0.99
1508.711 0.009 0.98
a2
b2
r
24.404 0.029 0.99
160.774 0.021 0.98
473.637 0.010 0.99
8.293
41.736
220.523
578.754
0.018
0.019
0.009
0.005
0.99
0.98
0.95
0.99
8.491
38.506
149.231
405.963
0.019
0.012
0.008
0.005
0.99
0.95
0.99
0.99
fitting parameters, respectively. The results of the modeling analysis are listed in Table 2 for all the examined
emulsions where r is the regression coefficient. Equation (8) very adequately fits the relationship between
both of the dynamic moduli and crude oil concentration.
G = a1 exp(b1 × x )
G = a2 exp(b2 × x )
(8a)
(8b)
Through the investigation of the dynamic shear, the
crude oil–AFP emulsions exhibit viscoelastic behavior over the examined polymer concentration, crude oil
concentration, and frequency. The polymer and crude
oil concentrations significantly enhance the complex
modulus, which is the total resistance of the emulsion
against the applied strain. The changes in the dynamic
elastic modulus G and the viscous modulus G as a
function of frequency reveal important aspects to understand the rheological characteristics for the emulsions
of the three AFPs. Knowing how polymer emulsions
behave by investigating the viscoelastic behavior under
different conditions is of great value and provides an
excellent knowledge of the polymer molecular structure and enables the modification of this structure to
meet special application requirements. When the frequency increases beyond 0.5 s−1 for AF1235 emulsions
and 0.3 s−1 for AF1275 and AF1285 emulsions, the
general profile that emerges for the whole range of
polymer and crude oil concentrations is that G is significantly higher than G . This observation suggests
that the elastic response dominates, which is typical
for gels and solid-like behaviors. This indicates that
cross-linked networks have already been formed in the
polymer emulsions.[21]
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
The current investigation was carried out to study the
viscoelastic behavior of the crude oil–AFP emulsions.
The linear viscoelastic range is 2 Pa for all the investigated emulsions. Both polymer and oil concentrations
display significant effect on the behavior of G ∗ − w .
This effect is more pronounced at low frequency and
it diminishes with frequency. The complex modulus
shows a linear relationship with frequency for a dilute
polymer concentration of less than 2000 ppm, whereas
a nonlinear relationship is reported for the higher polymer concentrations. The apparent complex modulus,
G ∗ o , increases significantly with the concentration of
both polymer and crude oil for the three tested polymers. The presence of the crude oil phase gradually
and significantly enhances the complex modulus of the
emulsions. The complex modulus values of AF1275 and
AF1285 emulsions are similar and significantly higher
than the complex modulus of the AF1235 emulsions.
Polymer concentration strongly increases the emulsion
complex modulus. The polymer aqueous solution of
2000 ppm shows viscoelastic behavior with liquid-like
response at low frequencies and a solid-like response
at high frequencies. The addition of crude oil lowers
the crossover frequency. For the higher polymer concentration of 10 000 ppm, both aqueous solutions and
emulsions exhibit only elastic behavior. Both polymer
and crude oil concentrations display a strong influence
on the storage and loss moduli behavior for frequency
<10 s−1 . The storage modulus for both polymer emulsions of AF1275 and AF1285 exhibit similar behavior
and are significantly higher than the storage modulus for the AF1235 emulsions. Crude oil concentration
increases both storage and loss moduli for all tested
polymers and their concentrations.
NOMENCLATURE
G∗
G
G τ
τo
τa
w
γo
γ̇
ηc
Complex modulus, Pa
Elastic or storage modulus, Pa
Viscous or loss modulus, Pa
Applied shear stress, Pa
Apparent yield stress parameter, Pa
Stress amplitude, Pa
Frequency, s−1
Strain amplitude
Shear rate, s−1
Casson apparent viscosity, Pa s
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