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NEW INSIGHTS INTO POLYMER RETENTION
IN POROUS MEDIA
By
GUOYIN ZHANG
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF PETROLEUM ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY
DECEMBER, 2013
DEDICATION
Dedicated to my Mom, Huatang Xu, and my Dad, Xingshan Zhang.
ABSTRACT
When water-soluble, high molecular weight polymers are used to reduce water mobility
and improve volumetric sweep efficiency in enhanced oil recovery technology, polymer
retention occurs when propagating through the reservoir. It is widely accepted that
polymer retention comprises the adsorption on the rock surface, mechanical entrapment
in small pores, and flow-induced hydrodynamic retention. Retention leads to polymer
loss in reservoir and delay oil bank during a polymer flooding. Therefore, proper
characterization of polymer retention in porous media is critical for a polymer flooding
project.
In this study, we first investigated the effect of concentration on HPAM retention
because the literature showed controversial results on this issue. To accomplish this, both
static adsorption on disaggregated sands and dynamic retention in sandpacks and
sandstone cores were measured. Different retention behaviors were observed in dilute,
semidilute and concentrated regions. In both dilute and concentrated regions, polymer
retention is basically concentration-independent. In contrast, in the semidilute region,
polymer retention shows concentration-dependent behavior. Little re-adsorption occurs at
high concentration after the adsorbent’s pre-contact with low concentration polymer. The
results also show macromolecule polymers have high adsorption tendency on rock
surface and the adsorption can be considered almost instantaneous and irreversible.
Based on experimental results, a concentration-related retention mechanism is
proposed which correlates the orientation of adsorbed polymer molecules on rock surface
with the interaction between molecular coils in solution.
Next, hydrodynamic retention caused by the increase of hydrodynamic force acting
upon polymer molecules was evaluated. As flow rate rises from 3.26 ft/day (base
reference) to 6.52 ft/day and 52.13 ft/day, retention of 500 ppm HPAM in 1.9 Darcy
sandstone core increases by 13.2% and 39.16%, respectively. Hydrodynamic retention
shows strong flow dependence. In low flow region, the retention increases abruptly with
increased flow rate. By comparison, in high flow region, the increase becomes much
more gradual. Our results also demonstrate that this flow-induced retention is totally
reversible (no incremental irreversible retention) and residual resistance factor is not
affected by this reversible retention.
To prove polymer rheology in porous is an intrinsic property, not caused by retention
related permeability reduction, xanthan polymer was also tested. The results indicate with
increase of flow rate, both HPAM and xanthan retention goes up in a 71 md sandstone
core. However, the resistance factor measurements show HPAM and xanthan show
distinct rheology in porous media. At low flow rate, even with retention increase, HPAM
shows Newtonian fluid behavior and no resistance factor increase is observed. In contrast,
xanthan polymer exhibits shear thinning behavior. Therefore, the hydrodynamic retention
has limited effect on polymer rheology in porous media.
Negative polymer inaccessible pore volume (IAPV) is observed with increase of flow
rate and decrease of permeability. This presence of negative IAPV is caused by reversible
polymer retention. Adsorptive retention on rock surface proves to be almost irreversible,
therefore, the mechanical entrapment and hydrodynamic retention should account for this
phenomenon.
Keywords: Adsorption, mechanical entrapment, hydrodynamic retention, reversibility,
inaccessible pore volume, core flooding
ii
ACKNOWLEDGEMENTS
There are many people who helped me during my study at New Mexico Institute of
Mining and Technology. This work would have never been done without them.
First, I would like to thank my advisor, Dr. Randall Seright for his persistent guidance,
encouragement, patience and tolerance. His extraordinary knowledge, wisdom in science
and engineering and attitude toward pursuit of truth always impress and inspire me.
Next, I would like to thank my committee members, Dr. Thomas Engler, Dr. Mike Kelly
and Dr. Reid Grigg for reading my dissertation and providing valuable comments and
suggestions.
I want to thank Kathryn Wavrik for her tremendous help in the lab. She taught me how to
use rheometer, TOC analyzer, prepared cores and setup equipment for me. I learned a lot
by working with her.
I would also thank Dr. Jianjia Yu and James Mclemore. They offered me generous help
whenever I got into trouble with my experiment. Thanks also go to Dr. Robert Lee, Dr.
Ning Liu, Elizabeth Bustamante, Xu Han, and other PRRC staff.
Finally, special thanks go to my wife, Ms. Dongling Xu and our daughter Yifan Zhang,
who have been creating a loving and supportive family environment for me.
iii
TABLE OF CONTENTS
DEDICATION
ABSTRACT
ACKNOWLEDGEMENTS ............................................................................................... ii
TABLE OF CONTENTS ................................................................................................. iii
LIST OF FIGURES ......................................................................................................... v
LIST OF TABLES ......................................................................................................... viii
CHAPTER 1. INTRODUCTION ....................................................................................... 1
1.1 Significance of Polymer Retention during Polymer Flooding ................................... 1
1.2 Statement of Problem ............................................................................................... 4
1.3 Approach ................................................................................................................... 7
1.3.1 Batch Adsorption or Static Retention Measurement. ......................................... 8
1.3.2 Flow Experiment or Dynamic Retention Measurement. .................................... 8
1.4 Outlines of Dissertation ........................................................................................... 10
CHAPTER 2. LITERATURE REVIEW .............................................................................. 11
2.1 Brief Introduction to Polymer Flooding .................................................................. 11
2.2 Overview of Polymer Retention Mechanisms in Porous Media ............................. 13
2.2.1Mechanisms of Polymer Retention in Porous Media ........................................ 14
2.2.2 Polymer Inaccessible Pore Volume (IAPV) ...................................................... 16
2.2.3 Factors Influencing Polymer Retention in Porous Media ................................ 19
2.3 Langmuir Adsorption Isotherm ............................................................................... 29
2.4 Concluding Remarks ................................................................................................ 31
CHAPTER 3. METHODS AND PROCEDURES ................................................................ 33
3.1 Introduction ............................................................................................................. 33
3.2 Equipment and Material ......................................................................................... 33
iv
3.3 Experimental Procedures ........................................................................................ 39
3.4 Polymer Injection at Different Concentrations. ...................................................... 45
3.5 Polymer Injection at Different Flow Rates. ............................................................. 46
CHAPTER 4. RESULTS AND DISCUSSIONS ................................................................... 47
4.1 Introduction ............................................................................................................. 47
4.2 Dependence of Retention on HPAM Concentration ............................................... 48
4.2.1 Static Measurements ......................................................................................... 48
4.2.2 Dynamic Measurements ................................................................................... 53
4.2.3 Proposed Adsorption Model ............................................................................. 62
4.2.4 Overlap Concentration (C* and C**) Measurement ........................................ 66
4.3 Effect of Flow Rate on Polymer Retention .............................................................. 69
4.3.1 Method Established to Detect Hydrodynamic Retention ................................. 70
4.3.2 Hydrodynamic Retention in 1.9 Darcy Dundee Sandstone Core ..................... 73
4.3.3 Is HPAM Shear Thickening Behavior Caused by Hydrodynamic Retention? . 80
4.3.4 Hydrodynamic Retention in 71 mD Berea Sandstone Core ............................. 83
4.4 Polymer Inaccessible Pore Volume (IAPV) .............................................................. 88
4.5 Effect of Polymer Retention on Permeability Reduction ........................................ 93
4.6 Steady-State Flow in Porous Media ........................................................................ 95
CHAPTER 5. CONCLUSIONS ....................................................................................... 98
5.1 Conclusions .............................................................................................................. 98
5.2 Discussions and Future Work ................................................................................ 100
NOMENCLATURE .................................................................................................... 103
REFERENCES ........................................................................................................... 106
v
LIST OF FIGURES
Fig. 1. 1-Polymer bank delay factors associated with polymer retention. ......................... 3
Fig. 1. 2-Delay in oil recovery caused by retention............................................................. 4
Fig. 2. 1-Polymer retention mechanisms in porous media (Szabo and Corp, 1975). ....... 16
Fig. 2. 2-Effect of polymer retention and IAPV on polymer propagation. ........................ 18
Fig. 2. 3-Typical Langmuir adsorption isotherm. .............................................................. 30
Fig. 3. 1-Rheology of HPAM polymer in a viscometer. ..................................................... 35
Fig. 3. 2-Viscosity vs. concentration at shear rate of 7.3 s-1. ............................................ 35
Fig. 3. 3-Sand shaker (IKA KS 4000). .................................................................................. 36
Fig. 3. 4-Schematic diagram of polymer retention determination system. ..................... 39
Fig. 3. 5-Roller for static measurement. ........................................................................... 40
Fig. 3. 6-Total Organic Carbon (TOC) analyzer for concentration determination. ........... 41
Fig. 3. 7-Correlation between TOC and polymer concentration. ..................................... 42
Fig. 3. 8-Polymer retention and inaccessible pore volume (IAPV) determination. .......... 43
Fig. 3. 9- p vs. Cp when HPAM flowing through a 10 m filter. ...................................... 45
Fig. 4. 1-Kinetics of polymer adsorption on sand. ............................................................ 49
Fig. 4. 2-Desorption tests for 100-, 500-, and 1,000-ppm HPAM. .................................... 50
Fig. 4. 3-Adsorption isotherm of HPAM using static method. .......................................... 51
Fig. 4. 4-Comparsion of retention on fresh sands and used sands. ................................. 52
vi
Fig. 4. 5-Adsorption isotherm using dynamic method (fresh sandpacks used for each
case). ................................................................................................................................. 54
Fig. 4. 6-Retention determination for 50 ppm HPAM. ..................................................... 55
Fig. 4. 7-Retention determination for 500 ppm HPAM. ................................................... 55
Fig. 4. 8-Retention of 1,000 ppm in pre-treated sandpack with 500 ppm. ...................... 56
Fig. 4. 9-Effect of concentration on polymer retention, 347 mD core. ............................ 58
Fig. 4. 10-Retention determination for 80 ppm HPAM, 347 mD core. ............................. 58
Fig. 4. 11-Retention isotherm of HPAM in 71 mD core. ................................................... 59
Fig. 4. 12-Retention determination for 20 ppm HPAM. ................................................... 60
Fig. 4. 13-Retention determination for 40 ppm HPAM. ................................................... 60
Fig. 4. 14-Polymer molecule interaction at different concentrations. ............................. 64
Fig. 4. 15-Proposed polymer adsorption mechanism on the rock surface. ...................... 64
Fig. 4. 16-Overlap concentration (C*) determination by linearity deviation. .................. 68
Fig. 4. 17-Overlap concentration (C*) determination by intrinsic viscosity. .................... 68
Fig. 4. 18-Polymer retention in the near wellbore region, radial flow. ............................ 70
Fig. 4. 19-Mehod to determine hydrodynamic retention. ............................................... 72
Fig. 4. 20-Effect of flow rate on KI (tracer) retention. ...................................................... 73
Fig. 4. 21-Polymer retention at flow rates from 3.26 ft/day to 52.16 ft/day. .................. 74
Fig. 4. 22-Incremental retention of HPAM vs. flux. .......................................................... 75
Fig. 4. 23-Determination of irreversible retention at 13.04 ft/day. ................................. 77
Fig. 4. 24-Determination of irreversible retention at 52.16 ft/day. ................................. 77
Fig. 4. 25-Resistance factor of HPAM at different flow rates. .......................................... 79
Fig. 4. 26-Rheology of HPAM and xanthan polymers in a viscometer. ............................ 81
vii
Fig. 4. 27-Hydrodynamic retention of 150 ppm xanthan in 1.9 Darcy core. .................... 82
Fig. 4. 28-Resistance factor of xanthan at different flow rates. ....................................... 83
Fig. 4. 29-Hydrodynamic retention and resistance factor for HPAM. .............................. 86
Fig. 4. 30-Hydrodynamic retention and resistance factor for xanthan. ........................... 87
Fig. 4. 31-IAPV determination for 100 ppm HPAM, 60 ml/hr, 347 mD core. ................... 88
Fig. 4. 32-IAPV determination for 20 ppm at flow rate of 1,000 ml/hr. ........................... 90
Fig. 4. 33-IAPV determination for 20 ppm HPAM at flow rate of 60 ml/hr. ..................... 91
Fig. 4. 34-2nd injection of 160 ppm HPAM and tracer at 60 ml/hr, 71 mD core. ............ 92
Fig. 4. 35-2nd injection of 1,000 ppm HPAM and tracer at 240 ml/hr, 71 mD core. ....... 92
Fig. 4. 36-Effect of polymer concentration on residual resistance factor, 347 mD core. 94
Fig. 4. 37-Effect of polymer concentration on residual resistance factor, 71 mD core. .. 94
Fig. 4. 38-Pressure drop during polymer injection in 347 mD core. ................................. 96
Fig. 4. 39-Pressure drop during polymer injection in 71 mD core. ................................... 96
viii
LIST OF TABLES
Table 2.1-Summary of Polymer Retention Using Dynamic Measurement....................... 22
Table 3.1-Core Properties. ................................................................................................ 37
Table 4.1-Dynamic Retention in Sandpacks ..................................................................... 54
Table 4.2-Retention on Sandstone Cores ......................................................................... 61
Table 4.3-Summary of Adsorption vs. Polymer Concentration ........................................ 65
Table 4.4-Properties of the Dundee Sandstone Core. ...................................................... 74
Table 4.5-Retention Summary. ......................................................................................... 74
1
CHAPTER 1. INTRODUCTION
1.1 Significance of Polymer Retention during Polymer Flooding
When water-soluble, high molecular weight polymers are used for enhanced oil recovery
(EOR), polymer retention delays polymer propagation into the formation. The presence
of the polymer is needed to provide high viscosity and low mobility levels—which in
turn are needed to improve oil displacement and sweep efficiency. Consequently, high
polymer retention can substantially delay oil displacement and recovery. To illustrate this
point, consider the range of polymer retention levels reported in the literature—9 to 700
g/g (Green and Willhite 1998)—and the range of polymer concentrations used in
polymer floods—500 to 3,000 ppm. Given the rock density ( rock, 2.65 g/cm3 for quartz),
porosity ( e.g., 0.3), polymer retention in g/g (Rpret), and polymer concentration in
ppm (Cpoly), Eq. 1.1 can be used to calculate the delay (PVret, pore volume delay per pore
volume injected).
(1 ) / /ret rock pret polyPV R C …………………………………………………...(1.1)
Using this equation and the parameters mentioned above, Fig. 1.1 shows delay factors.
With a very low retention level of 10 g/g and a polymer concentration of 2,000 ppm, the
2
delay factor is only about 3% of one pore volume (PV). In contrast, for a high retention
of 500 g/g and a polymer concentration of 500 ppm, the delay factor is over 6 PV. For
more typical values of 150 g/g for retention and a polymer concentration of 1,500 ppm,
the delay factor is about 0.6. For this latter combination, a 20% difference in retention
would mean an extra 12% PV polymer bank needed (if the retention is higher) or not
needed (if the retention is lower) to accomplish a given objective. In one 40-acre 5-spot
pattern with a height of 20 ft and a porosity of 0.3, 0.12 PV of 1,500-ppm HPAM
(costing $1.5/lb) would represent a polymer cost of about $176,000.
From another viewpoint, the mass of rock in the above 40-acre pattern is
40*43560*(12*2.54)3*2.65*(1-0.3)/0.3=6.10 x10
12 grams. Given the retention levels of
10, 50, 120, 150, 180, and 500 g/g, and an HPAM cost of $1.5/lb, the polymer costs
required to satisfy the retention requirements of the rock would be $201,777, $1,008,883,
$2,421,320, $3,026,650, $3,631,980, and $10,088,835, respectively.
Of course, the delay in polymer propagation also delays oil recovery. Fig. 1.2
illustrates this point using fractional flow calculations (from
http://baervan.nmt.edu/randy/). For these calculations, we assumed oil viscosity of 1,000
cp, water viscosity of 1 cp, and the reservoir was initially at connate water saturation
(Swr=0.3). The reservoir was then flooded with one PV of water (before continuous
polymer flooding with 100-cp polymer), one homogeneous layer was present, flow was
linear, and the following relative permeability curves (Eq. 1.2 and 1.3) were used.
20.1 [( 0.3) / (1 0.3 0.3)]rw wk S ………………………………………….………(1.2)
3
21 [(1 0.3 ) / (1 0.3 0.3)]ro wk S ………………………………………….……...(1.3)
In Fig. 1.2, the term, IAPV, refers to inaccessible pore volume, which is defined as the
fraction of the pore space being inaccessible to the large polymer molecules but
accessible to the small solvent and salt molecules and ions. IAPV accelerates polymer
propagation, whereas polymer retention (PVret) retards it. Three different levels were
considered in Fig. 1.2—where retention plus IAPV (1) were perfectly balanced to cause
no delay in polymer propagation (i.e., PVret + IAPV=0), (2) caused a one PV delay (i.e.,
PVret + IAPV=-1), and (3) caused a 2.5 PV delay (i.e., PVret + IAPV=-2.5). Figure. 1.2
illustrates that the delay in the arrival of the oil bank is directly proportional to the delay
in polymer propagation. Consequently, high polymer retention is economically
detrimental because of increased cost for polymer and delayed oil recovery.
Fig. 1. 1-Polymer bank delay factors associated with polymer retention.
0.01
0.1
1
10
1 10 100 1000
Po
re v
olu
me
de
lay
fact
or
Polymer retention, µg/g
500 ppm
1000 ppm
1500 ppm
2000 ppm
Porosity=0.3
rock=2.65 g/cm3
IAPV=0
4
Fig. 1. 2-Delay in oil recovery caused by retention.
In this research, experimental studies are performed to yield some new insights into
polymer retention in porous media. The effects of concentration, injection rate, and core
permeability on polymer retention are investigated. The permeability reduction caused by
polymer retention as well as retention reversibility is also analyzed based on experimental
results.
1.2 Statement of Problem
When enhanced oil recovery (EOR) polymers propagate through reservoir matrix, they
tend to adsorb on the rock surface due to the affinity of polymer molecules for many
reservoir rocks. In addition to the adsorption, polymer molecules tend to be trapped and
accumulate in the small pores. The latter retention is commonly known as mechanical
entrapment. Another retention, which is called hydrodynamic retention, may occur when
flow rate suddenly increases. Retentions caused by different mechanisms show different
40
50
60
70
80
90
100
1 1.5 2 2.5 3 3.5 4 4.5 5
% o
f m
ob
ile
oil
rec
ove
red
PV injected
PVret + IAPV = 0 PVret + IAPV
= -1
PVret + IAPV = -2.5
krw = 0.1 [(Sw-0.3)/(1-0.3-0.3)]2
kro = 1 [(1-0.3-Sw)/(1-0.3-0.3)]2
1,000 cp oil, 1 cp water, 100 cp polymer
5
reversibility and permeability reduction behaviors. Many factors prove to influence
polymer retention in porous media. Briefly, they can be divided into three categories.
(1) Formation properties. These include rock permeability, mineralogy, clay content,
salinity and pH of formation brine, and rock wettability, as well as reservoir
temperature. Generally, polymer retention increases dramatically with decreasing
permeability for less permeable rock (below several hundred mD). If more clay is
present, retention tends to increase because of increased surface area. Compared
with permeability and clay content, other parameters may also affect polymer
retention, but generally, they show minor impact (Smith 1970; Hirasaki and Pope
1974; Vela et al 1976; Espinasse and Siffert; 1979; Shah et al. 1985; Huang and
Sobie 1993; Broseta et al. 1995).
(2) Polymer and solvent types. Due to their molecule orientation in the solution or the
distinct functional groups in the molecules, different types of polymers such as
xanthan polymers, polyacrylamides (PAM), and partially hydrolyzed
polyacrylamides (HPAM) show different retention behaviors under the same
conditions (Chiappa et al 1999; Sydansk and Romero-Zeron 2011). Adsorption of
polyacrylamide on silica sand decreases with increasing hydrolysis (Martin and
Sherwood 1975). A study conducted by Meiste et al (1980) confirms that the
increase of hydrolysis of polyacrylamide reduces retention on the negatively
charged surface. Research from He et al (1990) indicates that smaller polymer
molecules, instead of larger molecules tend to be preferentially adsorbed if a
polymer mixture was injected simultaneously, resulting in a higher weight-
averaged Mw for the early effluent than for the injected polymer. Studies from
6
both Koral et al (1957) and Stromberg et al (1959) show solvents also play an
important role in polymer adsorption. About two to four times as much polymer
was absorbed from poor solvent (high solubilization ability) as from the good
solvent (low solubilization ability).
(3) Besides these factors mentioned above, polymer flow rate should also be taken
into account when investigating polymer retention in porous media. The increase
of flow rate is accompanied with additional polymer retention in porous media.
Extensive work has been done to describe the retention behaviors of the EOR
polymers. Nevertheless, there are still some areas needed to be clarified. Among them,
the effect of polymer concentration on retention is an outstanding one. Dawson and Lantz
(1972) proposed that polymer retention in porous media follows the Langmuir isotherm
without justification. Most of these researchers who claimed that polymer retention in
porous media either fits the Langmuir isotherm or is strongly concentration-dependent
arrived at their conclusions based on static adsorption measurements (Mungan 1969;
Szabo and Corp 1975; Deng et al 2006). Zheng et al (1998) suggest their experimental
data obtained from dynamic method using the same core fits the Langmuir isotherm.
However, a careful examination of their data shows the highest retention at 1,500 ppm is
less than 1.5 times higher than the lowest value at 250 ppm and no retention data was
provided from concentrations below 250 ppm. Few researchers except Vela et al (1976),
Shah et al (1978), and Szabo and Corp (1975) have tried to measure retention through
dynamic measurement. Again, the data is very limited. Currently, the Langmuir
adsorption model which is well-known for describing reversible adsorption is used in
most chemical flooding simulators to describe polymer retention in porous media which
7
shows little reversibility (Satter et al. 1980, Vossoughi et al. 1984, Camilleri et al. 1987,
Yuan et al. 2010, Dang et al. 2011).
Next, we will focus on how the flow rate influences polymer retention in porous rock.
Previous studies (Maerker 1973; Dominguez and Willhite 1976; Aubert and Tirrell 1980;
Zaitoun and Kohler 1987; Huh et al 1990) reported that more polymer molecules would
be retained with injection rate increase. However, no specific amount of retention is
measured at increased flow rates. Chauveteau et al (1974) suggested that shear
thickening behavior that was widely reported for HPAM solutions in porous media was
caused by “bridging adsorption”. In our study, we will address this question: whether
polymer rheology in porous media is an intrinsic property, or strongly affected by this
flow-induced retention.
We will also investigate the reversibility of polymer retention under various
conditions and how polymer retention in porous media alters the rock permeability.
Basically, the following issues will be addressed in this study:
1) Does polymer retention in porous media depend on polymer concentration? Or,
does it follow the Langmuir isotherm?
2) How can quantify hydrodynamic retention be quantified for different rates?
3) Under what circumstances does polymer retention becomes more reversible?
4) Does hydrodynamic retention dominate polymer rheology in porous media?
5) How does polymer retention affect rock permeability?
1.3 Approach
Two approaches were devised to measure polymer retention in porous rocks. One is
called batch adsorption or static retention measurement and the other is called flow
8
experiment or dynamic retention measurement. They are chosen based on different
scenarios.
1.3.1 Batch Adsorption or Static Retention Measurement.
Batch adsorption is used to estimate polymer retention on disaggregated sand grains or in
unconsolidated rocks with relatively high permeability where the adsorptive retention
dominates. To determine the adsorption, sand grains with a particular size distribution are
prepared by grinding sandstone cores. Next, a polymer solution with known
concentration is contacted sufficiently with known mass of dry and fine sand grains. The
system containing both sand grains and polymer solution will be thoroughly mixed. After
the retention reaches equilibrium, the upper liquid phase is separated from the solids and
sands are removed by centrifuging. Polymer concentration is determined by total organic
carbon (TOC) analyzer. The amount of polymer adsorbed on the sand surface is
calculated by mass balance.
1.3.2 Flow Experiment or Dynamic Retention Measurement.
If consolidated porous media is used to determine polymer retention, the batch adsorption
method is no longer applicable. This is because extra surface area will be generated
during the fine grain preparation and the application of batch adsorption may introduce
significant error. As a result, dynamic retention measurement that involves the injection
of polymer solution through a porous media is used. Both polymer adsorption retention
and mechanic entrapment retention can be measured this way. To date, it is still a
challenging task to distinguish between these two types of retentions in porous media.
9
Several methods have been proposed to measure dynamic polymer retention in
porous media (API RP63 1990, Dawson and Lantz 1972, Szabo 1975, 1979, Dominguez
and Willhite 1977, Gupta and Trushenski 1978, Castagno et al. 1987, Huh et al. 1990,
Mezzomo et al. 2002). Several of them advocate injection of a slug of polymer solution,
followed by brine, and performance of a mass balance on the polymer (i.e., retention =
polymer injected minus polymer produced). Key problems with this type of method are:
(1) recovery of the polymer may require an extended period of brine injection because of
the unfavorable displacement and (2) cumulative errors associated with measurements of
low polymer concentrations in the produced fluid can introduce considerable uncertainty
to the mass balance.
We prefer the method used by Lotsch et al. (1985), Hughes et al. (1990), and
Osterloh and Law (1998). In this method, two banks of polymer solution are injected
which are separated by a brine slug. Polymer retention can be determined by the plot of
the two effluent polymer concentration profiles versus pore volume injected.
Hydrodynamic retention can also be measured this way by varying polymer injection rate.
Another important parameter affecting polymer propagation in porous media is
polymer inaccessible pore volume (IAPV). It is defined as the faction of pore space not
contacted by polymer molecules due to a smaller inlet diameter compared to the size of
polymer molecules. To estimate the inaccessible pore volume, KI tracer with
concentration of 40 ppm is injected together with polymer solution and its concentration
in the effluent is measured by an absorbance detector. The area between the second
polymer and tracer breakout curves is used to estimate polymer inaccessible pore volume.
10
During dynamic retention measurement, pressure drops across the core will be
recorded which are used to calculated resistance factor and residual resistance factor.
Again, polymer rheology in porous and its dependence on hydrodynamic retention will
also be addressed in our study.
1.4 Outlines of Dissertation
Chapter 2 is the literature review. It will briefly introduce the concept of polymer
flooding, polymer retention and the retention mechanisms in the porous media proposed
by the researchers. Most importantly, in Chapter 2, the effect of polymer concentration,
and flow rate on retention will be reviewed in detail.
Chapter 3 describes the experimental equipment setup and testing procedures. As
introduced earlier, polymer retention will be estimated using both static and dynamic
methods. The measurement of polymer and tracer concentration in the effluent is a key
part of this test. In Chapter 3, a new and convenient method to determine effluent
polymer concentration is established.
Chapter 4 deals with the experiment results and discussions. The effect of
concentration, flow rate on HPAM retention, polymer reversibility and permeability
reduction caused by retention will be included in this chapter. Besides these observations,
a concentration-related retention mechanism is proposed that considers the orientation of
the adsorbed polymer molecules and the interaction between molecular coils in solution.
Chapter 5 summarizes this work and recommends areas needs further study.
11
CHAPTER 2. LITERATURE REVIEW
In this chapter, a brief introduction to polymer flooding and the main role of polymer in
improving sweep efficiency is provided, followed by the concept and mechanisms of
polymer retention in porous media. Most importantly, the previous findings associated
with the effect of concentration and flow rate on polymer retention will be reviewed.
2.1 Brief Introduction to Polymer Flooding
Waterflooding is usually performed after the primary recovery during the development of
a typical oil reservoir. However, due to the low viscosity of water or brine, viscous
fingers form during water injection, resulting in an early breakthrough and poor sweep
efficiency. To mitigate this unfavorable situation, a water-soluble, high molecular weight
polymer is usually added to the water phase to increase its viscosity and thus reduce its
mobility. Both biopolymers (e.g., xanthan) and synthetic polymers such as partially
hydrolyzed polyacrylamide polymer (HPAM) have been tried. Currently, HPAM
polymers are most widely used in polymer flooding due to their low cost, vast
commercial availability, excellent viscosity-enhancing performance and resistance to
microbial degradation.
12
Mobility ratio, M, the ratio of the displacing phase to displaced phase mobility, is the
most important parameter for polymer flooding operation.
( ) / ( )rw roD
d w o
k kM ……………………………………………………………… (2.1)
where, D is mobility of the displacing phase (water) and d is mobility of the displaced
phase (crude oil). krw and kro are the relative permeability to water and oil, respectively.
w and o refer to the water viscosity and oil viscosity.
Based on the value of mobility ratio (M) relative to unity, the displacing process is
considered to be either favorable, where M ≤ 1, or unfavorable, where M > 1. To attain a
favorable mobility ratio (M) and to improve the sweep efficiency, increasing viscosity of
the water phase is the most common way used.
The most important mechanism of polymer flooding is its capability of improving
volumetric sweep efficiency and conformance control, which can be attributed to
viscosity-enhancing property of polymers. Polymer flooding is not expected to reduce
residual oil saturation lower than waterflooding because the addition of polymer into the
aqueous solution does not significantly change the interfacial tension between aqueous
phase and oil phase. However, some researchers (Mohammad et al. 1992, Wang et al.
2001, Mojdeh, et al. 2008, Zhang et al. 2010, Urbissinova et al. 2010, Wang 2010)
proposed that the viscoelasticity of polymer solution could improve the microscopic
sweep efficiency after extensive pore volumes of water injection. So far, this is still a
controversial subject.
13
Polymer flooding has been applied in the field on a substantial scale. For instance, in
Daqing oilfield, China, it presently contributes to about one quarter of the annual oil
production. There are 37 polymer flooding operations and about 9,000 wells involved as
of 2005 and over 10 percent original oil in place (OOIP) has been recovered by
conducting this technique (Liu et al. 2009). Early screening criteria indicated that
polymer flooding should be applied in reservoirs with oil viscosity between 10 and 150
cp (Taber et al. 1977a, 1977b). However, with extensive use of horizontal wells and
fracturing technology, polymer flooding also shows great potential for heavy oil recovery
(Seright 2010, Delamaide et al. 2013).
2.2 Overview of Polymer Retention Mechanisms in Porous Media
Among the factors influencing the performance of a polymer flooding, polymer retention
is recognized as very important. Suppose severe retention occurs in the reservoir but it is
not properly considered during the project design, it may cause polymer flooding to fail
technologically and economically.
In this section, three mechanisms on how polymer molecules tend to be retained in
the porous media are first reviewed. When dealing with polymer retention, another
parameter called inaccessible pore volume (IAPV) should not be avoided. IAPV describes
the fraction of pore space that cannot be contacted by the injected polymers due to the
small pore diameter relative to the polymer molecule size. The combination effect of
IAPV and retention on polymer propagation in reservoir will be demonstrated. Finally,
the review of effects of polymer concentration, flow rate, rock mineralogy on retention,
14
retention reversibility as well as the role of retained polymer molecules in altering
permeability will be conducted.
2.2.1Mechanisms of Polymer Retention in Porous Media
Polymer retention primarily comprises three mechanisms. The first mechanism is caused
by physical adsorption onto the pore surface. It is the result of the high affinity of
polymers for many reservoir rocks, for example, due to van der Waal’s and hydrogen
bonding forces (Stutzmann and Sffert 1977, Pefferkorn et al. 1985, Shah et al. 1985,
Sorbie 1991). This retention is believed to be basically irreversible and the amount of
polymer adsorption is proportional to the surface area accessible to polymer molecules.
The second retention is called mechanical entrapment, which happens when polymer
molecules enter pores with smaller outlet diameter relative to the size of polymer
molecule. Small molecules such as water and salt can travel through, but large polymer
molecules will be trapped and accumulate in these small pores (Gogarty 1967; Szabo and
Corp, 1975).
The third retention is called hydrodynamic retention, which is associated with the
local velocity of the polymer. After the retention reaches equilibrium, sudden increase of
flow rate will cause extra polymer loss in the porous media. This flow-related
hydrodynamic retention is believed to be reversible, i.e., when the flow rate is reduced or
flow is completely stopped, the newly-retained polymer molecules will be released and
migrate to the main flow channels (Maerker 1973, Dominguez and Willhite 1977, Huh et
al. 1990). Maerker (1973) suggested that a significant pressure gradient causes polymer
molecules to deform and become trapped within the core, particularly in relatively small
15
pores. Zitha et al (1998) and Chauveteau et al (2002) proposed a mechanism called
“bridging adsorption” to explain hydrodynamic retention. In concept, polymer molecules
may be stretched sufficiently in the elongational flow field during flow through a porous
medium so that the molecules can span the distance over a pore constriction. If the ends
of the molecules attach to the rock, a plugging or increased resistance to flow might
develop. Chauveteau et al. (1974, 2002) suggested that the shear-thickening behavior that
was widely reported for HPAM solutions in porous media was caused by “bridging
adsorption”.
Figure. 2.1 shows the polymer retention model proposed by Szabo and Corp (1975).
In medium-permeability (several hundred millidarcies), high surface-area Berea cores,
physical adsorption is more dominant than mechanical entrapment. By comparison, in
low permeability rocks (several tens of millidarcies), mechanical entrapment is expected
to increase. As shown by Fig. 2.1, adsorption dominates the retention in the main flow
channel, while, mechanical entrapment occurs in the small pores with a pore throat inlet
large enough for polymer molecules to enter but an outlet small enough to trap polymer
molecules. In these pores, though restricted, a slow flow of brine is allowed. It also
demonstrates the concept of polymer inaccessible pore volume (IAPV), i.e., pores with a
small inlet that prevents the polymer penetration will be unreachable for polymer
molecules. Mungan (1969) suggests that if only connate water-not oil-occupies these
small and narrow channels, oil recovery by polymer flooding could be significantly
improved.
16
Fig. 2. 1-Polymer retention mechanisms in porous media (Szabo and Corp, 1975).
2.2.2 Polymer Inaccessible Pore Volume (IAPV)
As mentioned earlier, inaccessible pore volume (IAPV) plays a significant role in
influencing polymer propagation in porous media. Results show that IAPV exists for
EOR polymers (Shah et al. 1978, Vela et at. 1976, Liauh et al. 1978, Lotsch et al. 1985).
The presence of IAPV theoretically accelerates the polymer propagation to be more than
expected from the pore volume injected. On the other hand, polymer retention will retard
polymer transportation in porous media.
The combined effect of IAPV and retention of polymer propagation in the reservoir is
illustrated in Fig. 2.2 (Dawson and Lantz 1972), assuming piston-like displacement.
Case A: no retention and no IAPV. Polymer breaks through at precisely 1 PV;
Case B: no retention, 0.25 PV IAPV. The polymer slug breaks through at 0.75 PV;
Case C: 0.25 PV retention and no IAPV present, polymer bank breaks through at 1.25
PV;
17
Case D: 0.2 PV retention, 0.25 PV IAPV. For this case, the polymer bank emerges at
0.95 PV.
Undoubtedly, if both the retention and IAPV are 0.25 PV, the breakthrough of
polymer solution still happens at 1 PV.
A. No retention, no inaccessible pore volume.
B. No retention, inaccessible pore volume=0.25.
PV
0.25 0.5 0.75 1 1.25 1.5
0.5
0
1
Cp/C0
1.75 2 2.25
PV
0.25 0.5 0.75 1 1.25 1.5
0.5
0
1
Cp/C0
1.75 2 2.25
18
C. 0.25 PV retention, no inaccessible pore volume.
D. 0.2 PV retention, PV inaccessible pore volume=0.25.
Fig. 2. 2-Effect of polymer retention and IAPV on polymer propagation. (Modified from Dawson and Lantz, 1972).
One might expect IAPV to increase with decreasing permeability. However,
confusing results were reported in the literature. For instance, using Pusher 700 HPAM,
Dawson and Lantz (1972) observed almost the same IAPV in 470 mD Berea core (22%)
as in 2090 mD Bartlesville sandstone core (24%). Using Pusher 500 HPAM, Dabbous
(1977) noted an IAPV value of 19% in 761 mD Berea with no residual oil. In contrast, for
the same polymer in Berea with a 28—35% residual oil, the permeability to water ranged
from 49 to 61 mD, and IAPV ranged from 17% to 37%. Osterloh and Law (1998)
reported IAPV values up to 48% in sand packs with permeabilities up to 11 darcies.
However, they acknowledged the experimental difficulties of accurately determining
IAPV values.
PV
0.25 0.5 0.75 1 1.25 1.5
0.5
0
1
Cp/C0
1.75 2 2.25
PV
0.25 0.5 0.75 1 1.25 1.5
0.5
0
1
Cp/C0
1.75 2 2.25
19
2.2.3 Factors Influencing Polymer Retention in Porous Media
Polymer retention in porous media has proven to be a very complicated process and many
factors need to be taken into consideration when dealing with this problem. A broad
range of research has been completed by earlier researchers to unveil polymer retention
mechanisms. In this chapter, special efforts will be made to review the effects of polymer
concentration, polymer injection rate, rock permeability on retention and retention
reversibility because these are also the areas the author attempts to investigate.
2.2.3.1 Effect of Polymer Concentration on Retention.
Numerous studies have been done to investigate the effect of polymer concentration on
retention by researchers. However, most of them were completed using the static method.
No systematic studies on this issue have been carried out using dynamic method.
Mungan (1969) measured the co-polymer (containing approximately 25%
polyacrylate and 75% polyacrylamide) retention on unconsolidated rocks using static
approach. His results revealed that adsorption is higher on rocks with high specific
surface area and it increases with polymer concentration. For instance, retention on
Ottawa sand with BET equal to 0.50 m2/g is 340 g/g sand at polymer concentration of
1,000 ppm (in distilled water). For the same polymer solution, the retention increases to
680 g/g sand when Silica power with BET of 1.65 m2/g is used. In contrast to the
retention at 1,000 ppm, retention decreases to 310 g/g sand at polymer concentration of
250 ppm for the same Silica sand. Dynamic measurement was performed for the
consolidated Berea sand-packed core; the results indicate that the retention is only about
20
55 g/g rock at 500 ppm polymer concentration, which is much lower than the value
obtained from the static method (610 g/g).
Szabo and Corp (1975) studied retention of hydrolyzed polyacrylamide polymers on
sand grains using the static method. They found that polymer retention showed almost
linear dependency on polymer concentration, i.e., the polymer retention increases with
increased concentration. But if sufficient brine or water (over 40 PV dilution) is used for
sand soaking to remove the reversible adsorption, residual polymer retention depends
only slightly on the initial polymer concentration. They ascribed this phenomenon to the
partially reversible adsorption on the surface. Deng et al (2006) measured retention of
three polyacrylamides (PAMs), cationic, nonionic and anionic polymers on clay
minerals—smectite, kaolinite and illite. Their results show that the adsorption isotherms
of anionic PAM and nonionic PAM are L-type and could be fitted with Langmuir
equations. Again, the amount of retention is obtained through static adsorption
measurement.
Retention isotherms from Chiappa et al (1998) show that polymer concentration plays
different roles in polymer retention on pure quartzite. For cationic polyacrylamide (CAT),
retention at high concentration could be several fold higher than that at low concentration.
In contrast to CAT, the retention of 1% hydrolysis polyacrylamide (PAM) shows only
slight concentration-dependence.
Only a few papers mentioned the polymer retention results in porous media via
dynamic measurement; see Table 2.1. Shah et al (1978) measured HPAM polymer
retention in Berea core. The result indicates that retention increases from about 25 g/g
21
sand at concentration of 51 ppm, to 27 g/g sand at 500 ppm and 31.5 g/g sand at 1069
ppm. Therefore, polymer retention only increases a little bit with increased concentration.
Vela et al (1976) measured the retention of 300 ppm and 600 ppm HPAM (5.5 million
Mw, 20% hydrolysis) in porous media and the amounts of retention are almost
independent of the concentration. As mentioned earlier, Zheng et al (1998) claimed
Langmuir isotherm applied to their results; however, they only measured retention for
250, 750 and 1,500 ppm polymer solutions. In addition, the highest retention at 1,500
ppm is less than 1.5 times that from the lowest concentration (250 ppm). Szabo and Corp
(1975) determined retention by injecting polymer solution into 1,200 mD unconsolidated
sand. Polymer retention increased from 3.50 g/g rock at 300 ppm to 6 g/g rock at 600
ppm. This concentration-dependent retention could be ascribed to the similar scenario of
static measurement, since unconsolidated sand was used. Mungan (1969) only measured
retention for 500 ppm copolymer flowing through porous media. Huang and Sobie (1993)
found that retention of Scleroglucan in Bollotini packed columns increased from 8.21
g/g to 11.71 g/g, increasing by 43% as concentration rose from 50 ppm to 200 ppm.
Dawson and Lantz (1972) provided a curve to propose that Langmuir isotherm could be
used to describe polymer retention in porous media, but no actual data measurement was
performed.
22
Table 2.1-Summary of Polymer Retention Using Dynamic Measurement.
References Porous Media Polymer Type Polymer
conc, ppm
Polymer Retention,
g/g rock
Remarks
Shah et al 1978
Berea core HPAM with 5 million Daltons Mw
51 25.0 Same core used
500 27.0
1069 31.5
Zheng et al 1998
623.8 mD Berea core
HPAM with 22 million Daltons Mw
250 4.0 Same core used
750 5.4
1500 5.9
Vela et al 1976
120 mD HPAM with 5.5 million Daltons Mw and 20% hydrolysis
300 12.2 Assuming
=20%,
g=2.65 g/cm3 600 13.9
Szabo and Corp 1975
1,200 mD sand (unconsolidated)
HPAM with 18-20% hydrolysis
300 7.34 Sor=0
600 12.93
Mungan 1969
Berea core
25% polyacrylate+ 75% polyacrylamide, 3-10 million Mw
500 55
Huang and Sobie 1993
Bollotini packed columns
Scleroglucan
50 8.21
100 8.73
200 11.71
Dawson
and Lantz
1972
Propose Langmuir isotherm
Results reported in different literature studies are comparable only if measurements
were conducted under similar conditions. This is especially true when comparing results
from static measurements with those from dynamic measurements. In this study, a series
of tests were designed to clarify literature discrepancies concerning how polymer
concentration affects retention in porous media. Several types of experiments were
performed, including static measurements of polymer retention on fresh sand for each
concentration case, and dynamic measurements of polymer retention in new sandpacks
with similar permeability and porosity for different HPAM concentrations. We also
examined polymer retention measurements where a single sand, sandpack, or sandstone
core was exposed to successive solutions with increasing polymer concentration. HPAM
23
polymer solutions with a broad concentration range (from 10 to several thousand parts
per million) were utilized.
2.2.3.2 Effect of Flow Rate
As mentioned previously, the increase of flow rate will cause additional polymer loss
in porous media by mechanical entrapment. These phenomena have been observed by
many researchers (Maerker 1973, Dominguez and Willhite 1976, Aubert and Tirrell 1980,
Zaitoun and Kohler 1987, Huh et al 1990). By monitoring polymer concentration profile
in the effluent, they found when the retention equilibrium was reached at a low flow rate,
subsequent increase in flow rate would render the effluent concentration lower than the
concentration injected. Conversely, a decrease of flow rate will cause the effluent
concentration to be higher than the injected concentration, which demonstrates that this
flow-induced retention is reversible to some extent.
An example is shown here. Using an 86 md core prepared by compressing Teflon
powder, Dominguez and Willhite (1976) observed that the increase of interstitial velocity
from 3.22 ft/day to 6.32 ft/day caused the effluent concentration to decrease from 391
ppm to 367 ppm. Because polymer adsorption on the Teflon powder was almost
negligible, they believed the extra polymer loss in porous media due to flow rate
variation should be attributed to mechanical entrapment. The results also revealed that a
quantity of this flow-induced retention was reversible (reduction of the flow rate from
10.2 ft/day to 0.38 ft/day caused the normalized concentration to increase from 0.92 to
1.07).
24
By monitoring the mobility reduction (pressure drop during polymer injection divided
by that during brine injection) or residual resistance factor instead of direct measurement
of polymer retention, Zitha et al (2001) proposed a concept of pore-bridging adsorption.
It could cause severe polymer loss at high flow rate if other conditions such as high
polymer adsorption and low permeability are satisfied simultaneously, which leads to an
unsteady-state flow (continuous build-up of injection pressure). Chauveteau et al (2002),
Ogunberu and Asghari (2004) arrive at conclusions that if the shear rate (injection rate) is
greater than the critical value ( > c), the increased hydrodynamic force will push
additional macromolecules into the already adsorbed polymer layer and increase both the
density and thickness of the adsorbed layer.
There is no doubt polymer retention is affected by flow rate, but very limited
retention data is published to quantify this hydrodynamic retention for different flow rates.
A correct description of the flow rate-retention relationship may be of great significance
to the understanding of polymer propagation through reservoir because the polymer flow
rate in reservoirs varies considerably with distance to the wellbore. Other questions
related to this hydrodynamic retention are whether all or part of this retention is
reversible and how does it affect polymer rheology and rock permeability? Our
experiments conducted a thorough investigation on these issues.
2.2.3.3 Degree of Retention Reversibility
Polymer reversibility is a controversial subject. For example, Szabo and Corp (1975)
measured the residual polymer adsorption on the surface of sand grains and found it
decreased with desorption time before it eventually reached a constant level. Therefore,
25
they concluded that retention adsorption on the rock surface is partially reversible. At the
same time, they proposed that little or no desorption occurred in the area of mechanical
entrapment in small pores. Ogunberu and Asghari (2004) found that the residual
resistance factor determined after the polymer retention depended on the brine injection
rate. After the injection of polymer solution at shear rate greater than 110 s-1
, the residual
resistance factor would decrease if the subsequent injection rate of brine was greater than
5.0 ml/min. However, at low flow rates, such as 0.8-2.0 ml/min were applied, an
increased residual resistance factor was encountered. Therefore, they arrived at
conclusion that the polymer adsorbed on the rock surface could be weakened by brine
injection.
On the contrary, experimental results from Maerker (1973), Dominguez and Willhite
(1976) suggested that the polymer retained in the form of mechanical entrapment proved
to be reversible. Zaitoun and Kohler (1987) also showed that at higher clay content or
lower permeability core, reversible polymer retention (mechanical entrapment in finest
pore throats) occurred. Deng et al (2006) observed that after four consecutive washings
with water, an accumulative of less than 3% of the adsorbed polymer (regardless of the
charge type they have) was removed; therefore, the degree of reversibility of polymer
adsorption on the rock surface was negligible.
In our study, we investigated the reversibility of polymer adsorption on rock surface
by determining residual adsorption after washing sands with adsorbed polymer molecules.
For the dynamic case, if present, a negative IAPV could be a good indicator of retention
reversibility. The variation of retention reversibility with the flow rate and rock
26
permeability was also studied in order to provide some ideas on the issues of which kind
of retention, physical adsorption or mechanical entrapment, is more likely to be reversible.
2.2.3.4 Effect of Polymer Retention on Rock Permeability
When the retained polymer molecules form an adsorption layer on the rock surface, the
effective pore size is reduced, resulting in a decrease of rock permeability or increase of
residual resistance factor. This phenomenon becomes more severe when the rock
permeability decreases (Smith 1970, Vela et al. 1976, Seright 1992, Seright and Martin
1993).
Hirasake and Pope (1974) proposed a model that correlated polymer adsorption on
the pore surface with polymer molecular weight, water salinity, rock permeability,
porosity, and flow rate. In their model, the adsorption of polymer is assumed to form a
monolayer of polymer molecular coils with thickness approximately equal to the
diameter of the molecular coil in that particular solvent based on previous findings
(Rowland 1963, Rowland and Eirich 1966). This layer may be laterally compressed,
resulting in an increase in segment density. The increase of segment density results in
increased polymer loss due to adsorption, but will not affect the adsorbed layer thickness.
Therefore, the permeability will not be further reduced.
When polymer molecules adsorb on pore surface and form a thin layer, the effective
pore size will be reduced, resulting in a reduced permeability. However, in the literature,
few people have reported measuring how the resistance factor and the residual resistance
factor vary with hydrodynamic retention. In our study, by measuring residual resistance
factors after different concentration injection with same injection rate and also the same
27
polymer solution with different injection rates, we addressed the question whether the
rock permeability varies dramatically when remarkable hydrodynamic retention occurs.
2.2.3.5 Other Factors Influencing Polymer Retention
Other factors influencing polymer retention in porous media have also been studied.
Smith (1970) found that the adsorption of HPAM varies from one type of mineral to
another. For instance, the retention on calcium carbonate is five times higher than that on
silica, which shows calcium carbonate appears to have a much greater affinity for
polymer than silica. This increased retention is ascribed to the high content of calcium
ions on the surface, which may provide calcium bridges to enhance polymer retention.
They also found polymer adsorption increases with salt concentration. The amount of
polymer retained increases from about 11 g/m2 at 1% NaCl to 60 g/m
2 at 10% NaCl.
Broseta et al. 1995 found that in oil-wet porous media, polymer retention (PAM) in
the presence of residual oil saturation (Sor=0.1-0.19) will decrease considerably by factors
ranging from 2 to 5 compared to the retention when the core is 100% water-saturated. But
in water-wet porous media, the influence of residual oil saturation is less noticeable. For
example, the retention with Sor=0.2 is 7.5 g/g sand compared with the retention of 10
g/g sand at Sor=0. They suggest the variation in polymer retention is due to the change
of interfaces accessible to the polymer under these conditions.
Chiappa et al (1998) investigated the role of electrostatic interactions in polymer
adsorption. They tested polymers with different charges (cationic, anionic and weakly
28
anionic) on quartzite, which is negatively charged. Effects of clay content with a high
specific surface area, ion strength and composition were also studied. Their results
showed that polymer adsorption is dominated by electrostatic interactions between the
charged groups that present at the polymer/brine and rock/brine interfaces. A correct
match between the polymer and the surface charges can greatly increase adsorption. For
example, adsorption on negatively-charged quartzite increased from 270 to 340 and 610
g/g sand when polymer of HPAM (anionic), PAM (weakly anionic) and CAT (cationic)
were used, respectively. Because of the high surface area and predominately negative
charge of the clay mineral, a small amount of clay can cause a significant increase in
polymer retention. The retention of cationic polymer increased from 610 to 1.45*104,
1.8*105 g/g sand when the porous media was switched from pure quartzite to 8% clay
quartzite with 8% clay and 100% clay. Again, the presence of divalent cation (as Ca2+
)
can greatly enhance the adsorption of negatively changed polymers (HPAM and PAM)
onto quartzite. For instance, HPAM retention of approximately 80, 340 and 800 g/g
sand was determined on the pure quartzite in the system containing 0, 2% and 8% CaCl2.
Chiappa et al also suggest that the present of divalent calcium ions can enhance the
adsorption of negatively charged polymers by forming an ion bridge.
Efforts were also made to distinguish the adsorptive retention from the mechanical
entrapment retention by Cohen and Christ (1986). In their study, they used HPAM with
an estimated molecular weight of 5.5 million and degree of hydrolysis of 25%. Two kinds
of packed silica sand beds were applied as the porous media. One was an adsorbing
material and the other was a non-adsorbing material generated by the chemical
modification of a siliceous surface. Their results showed that adsorption accounted for
29
about 35.2% of the total polymer retention and the remaining 64.8% was attributed to
mechanical entrapment.
2.3 Langmuir Adsorption Isotherm
Some researchers proposed that retention of EOR polymers on reservoir rocks depends
on polymer concentration, or the Langmuir adsorption model applies. Therefore, it is
necessary to make a brief introduction to this adsorption model. Equation 2.1 describes
the Langmuir adsorption isotherm which shows the solute adsorption on the substrate
surface is a function of solute concentration.
1 1
11
a b C
b C……………………………………………………………………………..2.1
where, is solute adsorption. C is solute concentration in solution and a1, b1 are
constants.
30
Fig. 2. 3-Typical Langmuir adsorption isotherm.
For adsorption fits to the Langmuir isotherm model, constants of a1 and b1 can be
determined graphically. Plotting 1/ versus 1/C on a linear scale ends up with a straight
line. The slope of this line is 1/a1b1 and it intercepts with y-axis at 1/a1.
Fig. 2.3 shows a typical Langmuir adsorption isotherm where a1 and b1 are assumed
to be 25 and 0.02, respectively. For the Langmuir adsorption model, the adsorption
depends strongly on the concentration. Especially in the low concentration range, the
adsorption increases linearly with the concentration. When concentration approaches zero,
the adsorption is also decreasing to zero.
0
5
10
15
20
25
0 500 1000 1500
Ad
sorp
tio
n,
g/g
rock
Concentration, ppm
a1=25 b1=0.02
31
2.4 Concluding Remarks
The literature review shows that retention is a very complex process. Though several
mechanisms are proposed to elucidate this phenomenon, many disagreements still exist.
For instance, what role does polymer concentration plays in polymer retention? Besides
the claim made by Dawson and Lantz (1972) without actual retention measurement, some
researchers (Mungan 1969, Szabo and Corp 1975, Deng et al 2006) found that polymer
retention is a function of polymer concentration; or, the retention follows the Langmuir
isotherm based on the static measurement. However, a careful analysis of limited
experimental results from dynamic measurement (Szabo and Corp 1975, Vela et al 1976,
Shah et al 1978, Zheng et al 1998) shows that retention is almost independent of polymer
concentration. A systemic study on the effect of concentration on retention using
dynamic method is highly recommended.
Researchers (Maerker 1973, Dominguez and Willhite 1976, Aubert and Tirrell 1980,
Zaitoun and Kohler 1987, Huh et al 1990) observed flow-induced, or hydrodynamic,
retention by monitoring polymer concentration in the effluent. Nevertheless, few studies
found in the literature quantified retention for different rates. This may be of great
importance if retention is highly velocity-dependent because the flow velocity in the
reservoir varies considerably as the invasion radius changes.
Regarding to the degree of retention reversibility, results from Szabo and Corp (1975)
and Ogunberu and Asghari (2004) suggest polymer adsorption on the rock surface shows
partially reversible behavior. On the contrary, Deng et al (2006) conclude that the
reversibility of adsorption is almost negligible. Results from Dominguez and Willhite
(1976) Zaitoun and Kohler (1987) indicate polymer molecules retained in the form of
32
mechanical entrapment proves to be reversible. In our study, we will investigate the
reversibility of polymer retention on rock surface and in porous media. This may provide
some ideas on the issue of which kind of retention, physical adsorption or mechanical
entrapment, is more likely to be reversible.
Polymer retention on the rock surface forms an adsorption layer that reduces effective
pore size and causes permeability reduction. Some researchers propose that the increase
of flow rate may either induce pore-bridge adsorption ,which results in an unsteady-state
flow (continuous injection build-up) (Zitha et al 1998 and 2001) or increases both the
density and thickness of the adsorbed layer (Chauveteau et al 2002, Ogunberu and
Asghari 2004). If it is true for either case mentioned above, the polymer resistance
factor/residual resistance will be dramatically increased. In our research, we probed if
severe pore-bridge adsorption occurred in our tests by recording the polymer injection
pressure under various conditions. We also focused on the relationship of hydrodynamic
retention and permeability reduction.
In summary, to better understand the retention behaviors of HPAM polymers in
porous media, as mentioned previously, the following issues were addressed in our study:
1) Does polymer retention in porous media depend on polymer concentration? Or,
does it follow the Langmuir isotherm?
2) How should quantify hydrodynamic retention be quantified for different rates?
3) Under what circumstances, does polymer retention becomes reversible?
4) Does hydrodynamic retention dominate polymer rheology in porous media?
5) How does polymer retention affect rock permeability?
33
CHAPTER 3. METHODS AND PROCEDURES
3.1 Introduction
In this section, the materials, experimental equipment, and procedures will be introduced.
Again, both static and dynamic measurements will be used to determine polymer
retention in porous media.
3.2 Equipment and Material
Polymer and Brine. A partially hydrolyzed polyacrylamide (HPAM) (SNF Flopaam
3230S) and a xanthan polymer (Kelco Oil Field Group) were used in our tests. Both were
provided by the manufacturer as white granular powders. HPAM is estimated to have a
molecular weight of 6—8 million daltons and degree of hydrolysis of approximately 30%.
HPAM solution was prepared using the magnetic stirrer vortex method. Xanthan solution
was prepared using a blender. After the polymer solutions were preparation, they were
filtered through a 10 m filter to remove any possible microgels and other debris present
in the solution. The purpose of this filtration is to minimize the face plugging effect
caused by these impurities. Studies show that during polymer injection, presence of this
34
debris and microgel may plug the core face by forming external filter cake (Seright et al.
2009).
Two kinds of brine were used. One was 2% NaCl for the static measurements,
dynamic retention in sandpacks, and polymer hydrodynamic retention measurements in
consolidated cores. The other brine containing 2.52% TDS (2.3% NaCl and 0.22%
NaHCO3) was used when dynamic retentions were measured in consolidated sandstone
cores. Both brines were filtered through 0.45- m filters before application.
The rheology of HPAM polymer was determined in an Anton Paar rheometer
(Xanthan rheology will be shown in Chapter 4). As shown in Fig. 3.1, at concentration
below 320 ppm, it behaves like a Newtonian fluid within the broad range of shear rates
between 1 to 1,000 s-1
, i.e., polymer viscosity is almost independent of shear rate.
Polymer solutions with concentration of 640 and 1,000 ppm, at shear rate less than 10 s-1
,
they show Newtonian behavior. For shear rate greater than 10 s-1
, they show slightly
shear thinning. No shear thickening behavior is observed in a viscometer. The correlation
of viscosity at shear rate of 7.3 s-1
with polymer concentration is shown by Fig. 3.2. The
viscosity of 20 ppm is about 1 cp, increasing to 3.8 cp at concentration of 1,000 ppm.
Tracer. 40 ppm Potassium iodide (KI) was added into the polymer solution as a tracer.
Its concentration in the effluent was monitored by a Tunable Absorbance Detector
(Waters 486) as an indicator of brine propagation through porous rock.
35
Fig. 3. 1-Rheology of HPAM polymer in a viscometer.
Fig. 3. 2-Viscosity vs. concentration at shear rate of 7.3 s-1.
0
2
4
6
1 10 100 1000 10000
Vis
cosi
ty, c
p
Shear rate, 1/s
20 ppm
80 ppm
320 ppm
640 ppm
1,000 ppm
HPAM 6-8 million MW 30% hydrolysis 2.52% TDS 25 °C
0
1
2
3
4
0 200 400 600 800 1000 1200
Vis
cosi
ty, c
p
Polymer concentration, ppm
HPAM 6-8 million MW 30% hydrolysis 2.52% TDS 25 °C
36
Sand Preparation. Sand grains with particle sizes between 106–180 m were prepared
as the adsorbent by crushing and sieving Berea sandstone core cuttings. To reduce the
presence of very fine particles and carbons released by the sands, special processes were
undertaken for the treatment of these disaggregated sands. First, sands were put into a
bottle with brine and rotated at 300 rpm for 8 hours on an IKA KS 4000 shaker, (Fig. 3.3).
The purpose of mixing sands with brine is to minimize the release of carbon with the
sands themselves. Then, the upper mud-like phase was separated from the sand. Next, the
sand was washed with distilled water to remove newly-generated fine particles and
residual salt until the upper water phase was totally clear. Finally, the sand was dried at
110 °C.
Fig. 3. 3-Sand shaker (IKA KS 4000).
Porous Media. Disaggregated sands prepared as described above were used for static
adsorption measurements. To determine dynamic and hydrodynamic polymer retention in
37
porous media, both consolidated sandstone cores and high permeability sandpacks were
used. Four consolidated sandstone cores were used in our tests, among them, three
rectangular Dundee cores and one cylindrical Berea sandstone core. Dundee sandstone
cores cast in epoxy resin (Core #1, #2 and #3) have permeability of 347 mD, 449 mD,
and 1.9 darcies respectively. The fourth core (Core #3) is a Berea sandstone core with a
permeability of 71 mD. It is a cylindrical core with a section area of 11.4 cm2. This core
was cast in the metal before being assembled in the Hassler-type core holder. All cores
were 15 cm long except core #4, which is 12.8 cm long. Two internal pressure taps
divided the Dundee cores into three sections with lengths of 2.5 cm, 10 cm, and 2.5 cm.
For the Berea core, these three sections were 1.5 cm, 10 cm, and 1.5 cm in length.
Sandpacks with high permeability and porosity were prepared from the same sands used
for static measurements. Sandpacks were 6.35 cm long and 14.5 cm2 in cross section.
Table 3.1-Core Properties.
Core No. L, cm A, cm2 PV, ml , % k, mD Note
1 15 14.5 49 22.5 347
Dundee 2 15 14.5 51 23.4 449
3 15 14.5 52.4 24.1 1,900
4 13 11.4 27 18.2 71 Berea
Experimental Setup. Figure. 3.4 shows the schematic diagram of the experimental unit
for determining polymer retention in porous media. It can be divided into three major
sections based on their functionalities: polymer injection, tracer concentration
determination and effluent polymer concentration determination. All these three parts
were assembled in series.
38
1) The first part deals with polymer injection into the core. The polymer flow rate can be
accurately controlled by an ISCO syringe pump (Model 500HP). The pressure drop
across the core is indicated by a Honeywell pressure transducer, which is connected
to the two internal pressure taps on the core.
2) The second part is setup to determine tracer concentration in the effluent. In this part,
the fluid exiting the core outlet flows through the absorbance detector (Waters 486)
and the concentration of KI can be measured versus pore volume injected at light
wavelength of 232 nm. Note that a 7 m Swagelok metal filter is attached in the flow
line between the core and the absorbance detector to prevent any large particulates
from flowing downstream.
3) The third part is used for the determination of polymer concentration in the effluent.
As shown in Fig. 3.4, the effluent leaving the absorbance detector is first collected in
a container and then fills the small accumulator beneath the container via the second
ISCO pump every 10 or 20 minutes. Then, the fluid is forced to flow through a 10 m
Millipore filter combination at a constant flow rate (controlled by another ISCO pump)
and the pressure drop across the filter is recorded. For HPAM polymer concentration
higher than 150 ppm, the filter combination can be connected directly to the core.
39
Fig. 3. 4-Schematic diagram of polymer retention determination system.
Note: 1. ISCO syringe pump #1 (Model 500HP); 2. Core; 3. Pressure transducer #1; 4. 7
m Swagelok filter; 5. Absorbance detector (Waters 486); 6. Beaker; 7. 10 m Millipore
filter combination; 8. Pressure transducer #2; 9. Fluid container; 10. Accumulator; 11.
ISCO syringe pump #2 (Model 500D).
3.3 Experimental Procedures
Static Measurement. After mixing known concentration solution and known mass sands,
bottles containing both sand and polymer solution were tied on a roller which rotate at a
speed of 6 RPM for 1 hr to complete the adsorption process. One hour contact was
considered to be sufficient because polymer adsorption on the rock surface is believed to
be instantaneous (the adsorption kinetic will be discussed in Chapter 4). To reduce the
effect of carbon released by sands themselves, a blank sample only containing sands and
brine was prepared.
1) Polymer solutions with known concentration were prepared in 2% NaCl brine;
2) Known amounts of sand grains were added into the polymer solutions;
40
3) The bottle containing both polymer solution and sand grains was mounted on a roller
(Fig. 3.5). The system was rotated at 6 rpm for 1 hr;
4) After the rotation, the upper polymer solution was transferred to a plastic tube to be
centrifuged at speed of 3,000 rpm for about 1 hr to separate the residual polymer
solution from sand particles;
5) Equilibrium polymer concentration was determined by Total Organic Carbon (TOC)
Analyzer. Dilution was needed for high concentration cases;
6) Polymer adsorption for each concentration case is calculated:
0( ) /eq p sgC C V W
where, is polymer adsorption, g/g sand, C0 and Ceq are initial and equilibrium
polymer concentrations, ppm. Vp is polymer volume, ml. Wsg is the weight of sand
grains, g. Both polymer and brine density were assumed to be 1 g/ml.
Fig. 3. 5-Roller for static measurement.
41
Determination of Polymer Concentration. A TOC analyzer (Shimaduz Model TOC—
VCSH, Fig. 3.6) was used to determine polymer concentration before and after
adsorption. This is based on the excellent linearity between total organic carbon content
and polymer concentration. As seen from Fig. 3.7, a very good correlation exists between
these two parameters. To reduce systematic error, samples with concentration higher than
200 ppm were diluted with the same brine for polymer preparation before examination.
The reason for diluting high polymer concentration solutions is because a range of 0 to
200 ppm TOC calibration curve was used.
Fig. 3. 6-Total Organic Carbon (TOC) analyzer for concentration determination.
42
Fig. 3. 7-Correlation between TOC and polymer concentration.
Dynamic Measurement. The detailed procedures of this method are described below
and the determinations of polymer retention and IAPV are shown graphically by Fig. 3.8:
1) Core was initially saturated with degassed brine after evacuation and then the
permeability to water was determined. Based on the amount of brine saturated and the
core dimension, total pore volume (PV) and porosity were obtained.
2) Polymer solution was injected with KI tracer until polymer concentration Cp in the
effluent achieved the injected concentration C0. Polymer concentration and tracer
concentration (relative to the injected concentrations, Cp/C0) were plotted versus pore
volumes injected.
y = 1.8611x + 0.706 R² = 0.994
0
20
40
60
80
100
120
0 10 20 30 40 50 60
Po
lym
er c
on
cen
trat
ion
, pp
m
TOC, ppm
43
3) Core was flushed with brine until polymer was not detectable in the effluent. In our
tests, 60 to100 PV of brine were injected with intervening periods of no flow.
4) A second polymer and tracer bank were injected with the same concentration until Cp
achieved the injected concentration C0. Again polymer and tracer concentrations
(Cp/C0) were plotted versus pore volumes injected.
5) Retention is given by the area between the two plots of polymer concentration
breakout curves.
6) IAPV is given by the area between the second polymer and tracer concentration
breakout curves.
Fig. 3. 8-Polymer retention and inaccessible pore volume (IAPV) determination.
44
Note: all the tests are conducted at room temperature around 25 °C. Unless otherwise
specified, polymer solution is injected at a flow rate of 60 ml/hr which is about 1
meter/day or 3.3 ft/day.
Attention should be paid when this method is utilized to determine polymer retention
and IAPV. Firstly, any reversibly retained polymer should be flushed from the core
during the extensive brine injection. The reoccurrence of this retention during the second
polymer injection will make the effluent concentration profile shift closer to the first one.
As a consequence, reversible retention is excluded or only irreversible retention is
measured via this dynamic method. Secondly, IAPV measurement will be affected if
substantial reversible retention occurs. Both of these two situations were encountered in
our tests and will be discussed in the later sections.
Determination of Polymer Concentration in the Effluent. How to accurately monitor
polymer concentration in the effluent is very important for this test. After some
experimentation, we established a rheological method based on shear-thickening
behaviors of HPAM polymer flowing through porous media. HPAM polymers show
Newtonian behavior at low flow rate in the porous rock, while, at moderate to high flux,
they become definitely shear thickening, i.e., the resistance factor increases with
increased flux. Results from Seright et al. (2011) show that shear thickening behavior of
HPAM solution with a concentration even as low as 25 ppm is evident in porous media.
45
Fig. 3. 9- p vs. Cp when HPAM flowing through a 10 m filter.
Based on this finding, we established a filter combination that uses a Millipore
AP10TM
filter pad upstream of a 10 m Sterlitech membrane filter to mimic porous media.
When polymer solutions flow through this filter combination at constant flow rate,
pressure drops given by the Honeywell pressure transducer correlate well with polymer
concentrations. Fig. 3.9 is one standard curve that shows the sound linear relationship
between polymer concentration and pressure drop.
3.4 Polymer Injection at Different Concentrations
To investigate the effect of polymer concentration on retention, a series of polymer
solutions with concentration from 20 ppm to 1,000 ppm were injected into the Dundee
sandstone core. As described previously, for one specific concentration, two identical
polymer solution banks with tracer were injected which were separated by a brine slug
y = 0.0082x + 0.207 R² = 0.99
0
2
4
6
8
10
0 200 400 600 800 1000 1200
Pre
ssu
re d
rop
, psi
Polymer concentration, ppm
HPAM 6-8 million Daltons Mw 30% hydrolysis 2.52% TDS 40 ppm KI 300 ml/hr 10 micron filter 25 C
46
injection. The tracer and polymer concentrations in the effluent were determined by
Absorbance Detector and Millipore filter combination. By plotting Cp/C0 versus pore
volumes injected for the first and second polymer slugs and second tracer slug, both
polymer retention and inaccessible pore volume can be determined. Again, polymer
retention is given by the area between the two polymer concentration curves and IAPV is
given by the area between the second tracer and second polymer concentration curves.
This process was repeated for the next concentration case. The tests were run in the
sequence of low concentration to high concentration. All the tests were performed under
room temperature, which is approximately 25°C.
3.5 Polymer Injection at Different Flow Rates.
Hydrodynamic retention was measured by injecting polymer solutions in core #3 and #4
at various flow rates. Again, two polymer banks were injected separated by large pore
volumes of brine injection, and effluent polymer concentrations were recorded. To
determine whether this flow-related retention significantly affects polymer rheology in
porous media, both HPAM and xanthan polymers were tested. Polymer pressure drops
across the core during polymer injection and subsequent brine injection for these cases
were recorded. These pressure drops were used to calculate polymer resistance factors
and residual resistance factors.
47
CHAPTER 4. RESULTS AND DISCUSSIONS
4.1 Introduction
This chapter deals with the experimental results and discussions. Mainly, two sections are
included here. First, is an account of the investigation of the dependence of retention on
polymer concentration. Porous media, such as disaggregated sands, high permeability
sandpacks and low permeability sandstone cores were used. Based on the observed
retention behaviors, a concentration-related retention model is proposed. The second part
of this chapter focuses on hydrodynamic retention of both HPAM and xanthan polymers.
A method is established to show, as flow rate increases, the amount of total incremental
retention and how to distinguish irreversible and reversible retention. To clarify whether
this flow-induced retention has strong impact on polymer rheology in porous media, the
rheology and retention of both HPAM and xanthan polymer in porous media were
examined.
The evaluation of reversibility of retention under different flow rates and rock
permeabilities and the effect of reversibility of polymer retention on IAPV is also
discussed. In this section, we will also address the question of how permeability
48
reduction (residual resistance factor) is affected by polymer retention and under what
circumstances, the increase of polymer retention will reduce rock permeability.
4.2 Dependence of Retention on HPAM Concentration
Both static and dynamic measurements were used to estimate the impact of concentration
on retention. Porous media employed include disaggregated sand grains, high
permeability sandpacks and low permeability consolidated sandstone cores. Furthermore,
retention in pre-contacted porous media was also studied before the proposition of a
concentration-related adsorption model. Here, the term “pre-contacted porous media”
refers to the porous media whose retention is previously satisfied at low concentration.
4.2.1 Static Measurements
Adsorption Kinetics. The kinetics of polymer adsorption were first explored by mixing
100-ppm polymer solution with disaggregated sands. The bottle containing both polymer
solution and sands was mounted to a roller and rotated at 6 RPM for 20 hrs. Liquid
samples were taken periodically from the upper phase for polymer concentration
determination using TOC analyzer. The adsorption calculated based on mass balance was
plotted as a function of time. As shown by Fig. 4.1, adsorption reached the maximum
plateau (about 40 g/g sand) within about three minutes and then leveled off. This
indicates that the long chain HPAM molecule shows a very high adsorption tendency on
rock surface and that the adsorption can be completed instantaneously. In our tests, the
contact of polymer solution and sands lasted 1 hr to ensure adsorption equilibrium.
49
Fig. 4. 1-Kinetics of polymer adsorption on sand.
Desorption Test. After the completion of adsorption, desorption tests were carried out to
estimate the amount of polymer that can be removed from the surface. In this test, excess
polymer solution was decanted from the top of the sand after sufficient contact. Then
fresh brine was added and again the bottle containing both sand and brine was rotated at 6
RPM for 1 hr. After the sands settled, the upper phase was sampled for polymer
concentration determination. The residual polymer adsorption was calculated using mass
balance. This procedure was repeated until no more desorbed polymer was detected.
Figure. 4.2 shows the results for 100-, 500-, and 1,000-ppm HPAM. Calculations show
that the percentage of the reversible adsorption for these three cases was 6.6%, 2.4%, and
2.9%, respectively. This result was similar to that from Chauvetear and Kohler (1974),
Deng et al. (2006). Because EOR polymers have high molecular weights and extended
chains, many polar groups along the polymer chain will attach to many different polar
points on the rock surface. It is statistically very unlikely that a polymer molecule would
1
10
100
1 10 100 1000 10000
Ad
sorp
tio
n,
g/g
san
d
Time, min
HPAM 6-8 million Daltons Mw 106-180 µm sands 100 ppm Rotated at 6 rpm 2% NaCl 25°C
50
release all points of attachment at the same time. Therefore, polymer adsorption on the
sand surface can be treated as almost irreversible.
Fig. 4. 2-Desorption tests for 100-, 500-, and 1,000-ppm HPAM.
Effect of Polymer Concentration. To investigate the effect of polymer concentration,
retention from polymer solutions with concentrations from 10 ppm through 6,000 ppm
was examined. The results are illustrated in Fig. 4.3, which suggests three distinct
concentration-related retention behaviors. First, in the very low concentration region
(from 10 ppm to about 100 ppm), polymer retention stabilized approximately at a value
of 20 g/g. In the intermediate-concentration region (from 100 ppm to about 4,000 ppm),
polymer retention increased from 35 to 420 g/g, increasing almost linearly with polymer
concentration. In the very high concentration region (above 4,000 ppm), nearly constant
retention (~ 420 g/g) was achieved.
0
50
100
150
200
250
300
0 1 2 3 4
Res
idu
al a
dso
rpti
on
, g/
g sa
nd
Brine/sand ratio, (weight/weight)
100 ppm 500 ppm 1000 ppm
51
These results (especially the concentration-dependent observation) agree with the
previous findings where most of the measurements were made in the intermediate
concentration region (Mungan 1969; Espinasse and Siffert 1979). Our findings indicate
that polymer retention does not fit the Langmuir isotherm, which is commonly used to
describe the reversible adsorption of small molecules such as surfactants and gas. For
EOR polymers with high molecular weights and extended chains, their adsorption on
rock shows little reversibility (see Fig. 4.2). It is postulated that at very low concentration,
polymer molecules continue to be adsorbed until the maximum coverage is reached.
During this process, few adsorbed polymer molecules are likely to detach from the
surface. Therefore, unlike the adsorption described by the Langmuir isotherm, polymer
adsorption at very low concentration approaches a constant non-zero value.
Fig. 4. 3-Adsorption isotherm of HPAM using static method.
Re-Adsorption Test. Fresh sands were used for each case to generate the adsorption
isotherm shown in Fig. 4.3, which illustrates the concentration-related adsorption
1
10
100
1000
1 10 100 1000 10000
Ad
sorp
tio
n,
g/g
san
d
Polymer concentration, ppm
106-180 m sand grains Rotated at 6 rpm for 1 hr 2% NaCl 25 °C
52
behaviors. After the desorption tests described in Fig. 4.2, 1,000-ppm polymer solution
was added to the sands previously contacted with 100-ppm and 500-ppm polymer
solution to check if polymer re-adsorption occurred. The results (Fig. 4.4) show little
additional polymer was adsorbed onto the used sands. For instance, for the 100-ppm
concentration case, the retention increased from 32.4 to 35.8 g/g, increasing by 10.3%.
For the 500-ppm case, retention rose from 132.9 to 141.1 g/g—merely a 6.1% increase.
Compared to the adsorption of 243 g/g at 1,000 ppm, a substantial retention difference
existed between the fresh sands and pre-contacted sands whose retention was previously
satisfied by low-concentration polymer. Apparently, even though adsorption was
relatively small at low concentration, the surface was already fully covered by adsorbed
polymer molecules, and no vacant sites were available for further attachment.
Fig. 4. 4-Comparsion of retention on fresh sands and used sands.
32.4 35.8
132.9 141.1
243.0
0
50
100
150
200
250
300
1 2 3 4 5 6 7
Ad
sorp
tio
n,
g/g
san
d
106-180 µm sand grains Rotated at 6 rpm for 1 hr 2% NaCl 25 °C
Adsorption at 100 ppm
Re-adsorption at 1,000 ppm
Adsorption at 500 ppm
Re-adsorption at 1,000 ppm
Adsorption at 1,000 ppm
53
4.2.2 Dynamic Measurements
Retention in Sandpacks. Dynamic measurements were performed in sandpacks made
from the same sand source that was used for static measurements. Sandpacks were
constructed by tapping sands into a cylindrical Teflon-made container with both ends
sealed by O-rings. A pair of stainless steel meshes with pore size of 15 microns was
placed on both ends of the container to prevent any downstream clogging and 0.125-in
OD tubing was welded onto end caps. Procedures were followed as described in Chapter
3 for dynamic measurement. For each concentration case, a new sandpack was used.
As shown in Table 4.1, these sandpacks had very similar properties. Permeability
ranged from 4.69 to 5.51 darcies, and porosity ranged from 0.43 to 0.44. Due to the high
sandpack permeability, it was suggested that adsorptive retention dominated the retention
for these cases (Szabo and Corp 1975, Huh et al. 1990). Polymer solutions with
concentrations of 20, 50, 100, 500, 1,000 and 2,000 ppm were investigated at an injection
rate of 120 cm3/hr (6.6 ft/day flux). The results were shown in Table 4.1 and Fig. 4.5.
Retention was around 5 g/g at low concentrations from 20 ppm to 100 ppm. With the
increase of concentration from 100 ppm to 2,000 ppm, retention increased from 5.71 to
27.8 g/g—increasing by a factor of nearly 5.
After completion of measurements for 100- and 500- ppm cases (Sandpacks #4 and
#3 in Table 4.1), a 1,000-ppm solution was injected. Retention increases of 5.6% and
7.3% , respectively, were detected in two used sandpacks. This agrees with the results
from the static measurements on used sands, which also confirms that the adsorbed
54
molecules occupied almost all the vacant sites on the sand surface and prevented further
attachment.
Table 4.1-Dynamic Retention in Sandpacks
SP No. L, cm
A, cm
2
Wsd, g PV, cm
3 k, D Cp, ppm Rpret, g/g
sand
1
6.25 14.19
140.4 39.1 0.441 5.51 2,000 27.8
2 139.7 39.0 0.440 5.04 1,000 14.3
3 140.2 38.7 0.436 4.88 500 10.2
4 141.4 38.3 0.432 4.69 100 5.71
5 141.0 38.7 0.436 5.03 50 4.85
6 140.6 39.1 0.441 5.37 20 4.63
Fig. 4. 5-Adsorption isotherm using dynamic method (fresh sandpacks used for each case).
Among this series of tests, two examples are given here. Figure. 4.6 shows the first
and second effluent polymer concentration profiles for 50 ppm HPAM injection. The area
between these two breakout curves is an output of polymer retention in porous media.
The same test was carried out for 500-ppm polymer solution, and with the result shown in
Fig. 4.7. Retentions calculated for 50 ppm and 500 ppm are 4.85 g/g sand and 10.2 g/g
1
10
100
10 100 1000 10000
Ad
sorp
tio
n,
g/g
san
d
Polymer concentration, ppm
HPAM 6-8 million Daltons Mw 30% hydrolysis 2% NaCl, 120 ml/hr 25 °C
55
sand, respectively. We can see that when polymer concentration rises from 50 ppm to 500
ppm, retention increases by about 110%.
Fig. 4. 6-Retention determination for 50 ppm HPAM.
Fig. 4. 7-Retention determination for 500 ppm HPAM.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, pv
1st polymer injection
2nd polymer injection
5.03 Darcies sandpack 50 ppm HPAM
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, pv
1st polymer injection
2nd polymer injection
4.88 Darcies sandpack 500 ppm HPAM
56
Static measurements show that no significant re-adsorption occurred in used sands
(Fig. 4.4). To check whether this is also true for dynamic measurement, 1,000 ppm
polymer solution was injected through the sandpack whose retention was originally
satisfied at 500 ppm (SP No. 4 in Table 4.1). Approximately 0.75 g/g sand (Fig 4.8) or
7.3% additional retention was determined in this sandpack. Again, the re-occurrence of
retention is negligible for pre-contacted porous media, even though the injected solution
had much higher concentration than the previous one.
Fig. 4. 8-Retention of 1,000 ppm in pre-treated sandpack with 500 ppm.
Retention in Sandstone Cores. To date, polymer retention in high permeability
sandpacks has been evaluated where adsorptive retention is believed to dominate.
However, besides adsorption on rock surface, mechanical entrapment occurs
simultaneously in pore throat constrictions and dead-end spaces when consolidated cores
are used (Huh et al. 1990, Ranjbar et al. 1991). To investigate the dependence of polymer
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, pv
1st polymer injection
2nd polymer injection
4.88 Darcies Sandpack Pre-treated with 500 ppm HPAM 1,000 ppm HPAM
57
retention on concentration in less permeable porous media, retention of HPAM with
different concentrations was measured in several consolidated sandstone cores. The first
measurement was performed using 347 mD Dundee sandstone core (see the description
of this core in Chapter 3). In this experiment, a series of polymer solutions were injected
sequentially through this core at a rate of 60 ml/hr. Concentrations of 20, 40, 80, 100, 200,
400, 700 and 1,000 ppm were considered. A higher flow rate was used when dealing with
the hydrodynamic effect on retention; this will be discussed in the next section.
For this series of tests, the same sandstone core was repeatedly used and retention
measurement followed the concentration sequence from low to high. For instance, the
retention at 40 ppm was measured only after the retention at 20 ppm (the lowest
concentration) was completed. Accordingly, the retention for the highest concentration
case (1,000 ppm for this series of tests) was carried out in the final run. The results are
shown in Fig. 4.9. From 20 ppm through 1,000 ppm, all the retention values fall into the
range of approximately 15—16 g/g sand with a relative error of 1.1%. When polymer
concentration was greater than 100 ppm, the retention reached a plateau, with the
maximum retention of approximately 16 g/g rock. Therefore, if one core was repeatedly
used, polymer concentration showed almost no influence on polymer retention. The result
was consistent with other studies where the same core was used repeatedly (Shah et al.
1978, Zheng et al. 1998).
Fig. 4.10 shows two effluent concentration profiles from the following 80 ppm
polymer solution injection. The small area between these two curves represents the
increased retention, which is only 0.7 g/g sand.
58
Fig. 4. 9-Effect of concentration on polymer retention, 347 mD core.
Fig. 4. 10-Retention determination for 80 ppm HPAM, 347 mD core.
0
4
8
12
16
20
10 100 1000
Po
lym
er r
eten
tio
n,
g/g
san
d
Polymer concentration, ppm
Dundee sandstone core 347 mD Porosity: 23%
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
1st polymer injection
2nd polymer injection
Dundee sandstone core Porosity: 23% 347 mD
59
The above results were obtained from relatively high permeability core (Dundee
sandstone core with permeability of 347 mD). For the retention in low permeability
porous rock, a 71 mD Berea sandstone core was used. The same strategy was followed to
determine the polymer retention at different polymer concentrations. As shown in Fig.
4.11, the retention increases a little bit with the increase of polymer concentration, but
compared with the concentration increase from 20 ppm to 1,000 ppm which increases by
50 times, the increase of polymer retention is very small, only about 1.6 times. Figure.
4.12 demonstrates the effluent concentration profile for the first and second polymer slug
injections. For the 20 ppm case, around 16 PV of polymer were injected to satisfy the
polymer retention. Nevertheless, for the following 40 ppm case, shown by Fig. 4.13,
fewer than 4 PV of polymer are needed to reach the maximum retention.
Fig. 4. 11-Retention isotherm of HPAM in 71 mD core.
0
5
10
15
20
10 100 1000
Po
lym
er r
eten
tio
n,
g/g
san
d
Polymer concentration, ppm
Berea sandstone core 71 mD Porosity: 18.5%
60
Fig. 4. 12-Retention determination for 20 ppm HPAM.
Fig. 4. 13-Retention determination for 40 ppm HPAM.
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14 16 18 20
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
1st polymer injection
2nd polymer injection
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
1st polymer injection
2nd polymer injection
61
The two tests conducted on both high and low permeability sandstone cores indicate
that polymer concentration shows very little effect on retention in porous media if the
same core is repeatedly used. These results are consistent with our static measurements
and also agree with findings by other researchers (Shah et al. 1978, Zheng et al. 1998).
To make a comparison, a similar Dundee sandstone core with 23.4% porosity and 449
mD permeability was used. Polymer solution with concentration of 1,000 ppm was
injected and 56.5 g/g rock retention was measured. Again, for higher concentration,
more retention occurs if fresh core used. In addition, polymer retention shows strongly
concentration-dependent behavior.
Table 4.2-Retention on Sandstone Cores
Core No.
L, cm A, cm2 PV, ml
, % k, mD Polymer Conc, ppm
Retention,
g/g
1 15 14.5 49 22.5 347 20-1,000 16.1
2 15 14.5 51 23.4 449 1,000 56.5
3 12.8 11.4 27 18.5 71 20-1,000 9.77
When static and dynamic retentions were compared, we found that at the same
polymer concentration, static measurement showed much higher retention. For instance,
at concentration of 2,000 ppm, static retention of 335 g/g was detected on disaggregated
sand grains (Fig. 4.3). Nevertheless, dynamic retention was only about 27.8 g/g in 5.51
Darcy sandpack (Table 4.1). The usually high retention from static measurement is
attributed to the large surface area exhibited by disaggregated sand grains, which provide
more vacant sites for polymer molecule attachment. The other dynamic retention by 449
md fresh sandstone core is about 56.5 g/g at concentration of 1,000 ppm (the second
core in Table 4.2). The difference between these two dynamic retentions can be explained
62
by the effect of rock permeability. Research shows that polymer retention strongly
depends on the permeability of porous media. Polymer retention usually increases with
decrease of rock permeability (Vela et al. 1976).
4.2.3 Proposed Adsorption Model
Based on the experimental results, a polymer concentration-related retention model is
proposed, which accounts for the observed retention behaviors. It is well known that
polymer molecules may interact with each other in solution and the degree of interaction
depends greatly on polymer concentration. Three concentration regimes were proposed
(de Gennes 1979; Ying and Chu 1987) as dilute (C < C*), semidilute (C* < C < C**), and
concentrated (C** < C), where C* is the overlap concentration crossover from dilute to
semidilute regimes and C** is the overlap concentration crossover from semidilute to
concentrated regimes. More specifically, as shown in Fig. 4.14, in the dilute regime,
polymer molecules exist in solution as free coils where little interaction occurs. In the
semidilute regime where polymer concentration is greater than the overlap concentration,
C*, macromolecules start to contact each other and intermolecular interactions occur.
With further increase in concentration (especially when the concentration is above C**),
the intermolecular entanglements dominate the interaction, resulting in the formation of a
network structure (Ferry 1948). For our HPAM, brine, and temperature, we measured C*
to be 300 ppm and C** to be 3000 ppm (see the following section). When dealing with
polymer retention on sand surfaces, this concentration-based interaction among polymer
molecules in solution may be used to explain the adsorption mechanism.
63
In the dilute regime, polymer molecules exist in solution as free coils but tend to take
a flat orientation when they adsorb onto the rock surface. In this configuration, most, if
not all of the molecular segments are in contact with the surface. It was called two-
dimensional adsorption (Peterson and Kwei 1961). In this regime, two-dimensional
adsorption dominates retention, and polymer molecules continue to be adsorbed until the
maximum coverage is reached. As shown by Region A in Fig. 4.15, adsorption is
independent of polymer concentration. For practical purposes, the retention in the dilute
regime indicates the minimum amount of polymer needed to occupy the available vacant
sites. In field applications of polymer and chemical floods, reduced polymer retention
may be achieved by first injecting a low-concentration polymer bank.
In the semidilute regime, the intermolecular interaction in solution will result in a
mixed adsorption, i.e., some molecules will be adsorbed with all the segments in contact
with the surface, while others will be adsorbed with only partial segments in contact with
the surface. The latter orientation will be labeled as three-dimensional adsorption.
Increasing the polymer concentration will increase the three-dimensional adsorption as
well as the total adsorption, as shown by Region B in Fig. 4.15. Polymer retention is
concentration-dependent in the semidilute regime.
In the concentrated regime, the molecular entanglement in solution causes the three-
dimensional adsorption to dominate, i.e., most polymer molecules are adsorbed with
segments partially attached to rock surface. Put another way, only one end of the polymer
molecule is attached to the surface, while the majority of the molecule dangles free in the
solution. In this case, almost no additional polymer molecules can be adsorbed with
increasing concentration because all sites have already been occupied. As shown by
64
Region C in Fig. 4.15, the adsorption is concentration-independent. This concentration-
related adsorption model is also summarized in Table. 4.3.
Fig. 4. 14-Polymer molecule interaction at different concentrations.
Fig. 4. 15-Proposed polymer adsorption mechanism on the rock surface.
65
Table 4.3-Summary of Adsorption vs. Polymer Concentration
Polymer
concentration
Molecule interaction
in solution
Dominant adsorption
type on rock surface
Adsorption vs.
concentration
Dilute (Cp<C*) Little Two-dimensional Concentration
independent
Semidilute
(C*<Cp<C**) Intermediate Mixed adsorption Concentration
dependent
Concentrated
(C**<Cp) Entanglement Three dimensional Concentration
independent
This model also explains why no significant adsorption occurred during subsequent
exposure to a high-concentration solution after sand was first contacted with dilute
polymer solution. After the surface maximum coverage is achieved, no more vacant sites
are available.
The above explanation accounts for the dependence of adsorption on polymer
concentration. Nevertheless, besides adsorption on rock surface, mechanical entrapment
occurs simultaneously in pore throat constrictions and dead-end spaces when
consolidated cores are used (Huh et al. 1990, Ranjbar et al. 1991). Hence, the impact of
polymer concentration on mechanical entrapment should also be addressed. Based on the
experimental results depicted in Figs. 4.9 and 4.11, polymer retention that encompasses
both adsorption and entrapment shows concentration-independent behavior. Since
additional adsorption proves to be insignificant when used sands are employed (Fig. 4.4),
the mechanical entrapment, at least the irreversible accumulation of polymer molecules in
small pores and dead-end spaces shows little variation with increase of polymer
concentration. In other words, suppose two identical fresh cores are used. If a high
polymer concentration is injected, this will result in a higher adsorption relative to low
66
concentration injection, but the trapped polymer will remain about the same for the high-
and low-concentration cases.
4.2.4 Overlap Concentration (C* and C**) Measurement
As mentioned, two overlap concentrations exist in polymer solution. One is the overlap
concentration (C*) crossover from the dilute to the semidilute region, and the other is the
overlap concentration (C**) crossover from semidilute to concentrated region. These two
concentrations act as an indicator of molecular interaction in solution. Many approaches
have been proposed to measure C* (Ke et al. 2009). Here, one convenient method,
viscometry, is employed to estimate the overlap concentration for the HPAM polymer we
used.
Method 1: Linearity Deviation. In both low concentration and high concentration
regions, a linear relationship exists between viscosity and concentration. The point
derivates from the linearity should be polymer overlap concentration, C* (Grossman and
Soane 1991). Therefore, by measuring viscosity for polymer solutions from 10 ppm
through 2,000 ppm, Fig. 4.16 was generated which plots viscosity as a function of
concentration. As shown by Fig. 4.16, two line cross point gives the overlap
concentration C*, which is approximately equal to 310 ppm.
Method 2: Intrinsic Viscosity [ ]. Intrinsic viscosity is widely accepted to be correlated
with overlap concentrations:
10**C ……………………………………………………………………………………………………………..(4.1)
67
where n is a constant, and [ ] is the intrinsic viscosity of a polymer in dl/g. Slightly
different values of n have been proposed. For instance, Graessley (1974) came up with n
equal to 1, while, Viovy and Duke (1993) suggested n equaled 0.6. To obtain intrinsic
viscosity, similarly, viscosities of brine as well as polymer solutions with concentration
from 10 ppm to 2,000 were measured. Specific viscosity sp is defined as:
solution solvent
sp
solvent……………………………………………………………………………….(4.2)
where, solution and solvent are viscosities of polymers solution and solvent, respectively.
In Fig. 4.17, sp
C vs. C is plotted, where C is polymer concentration in g/dl. Intrinsic
viscosity equals sp/c when C approaches zero:
0
/lim
sp
c
C
C………………………………………………………………………………………………..…(4.3)
Therefore, intrinsic viscosity can be acquired graphically, i.e., the ratio of sp
Cwhen
C equals to zero or the intercept of the line on the vertical axis gives [ ]=19 dl/g. Hence,
C* = 526 ppm if n=1, or C*=316 ppm if n=0.6. The latter value is very close to that
obtained from the linearity deviation method.
Grassley also suggested C** should be close to 10
**C ; therefore, for the
polymer we used, C** can be approximated to be 3,160 ppm.
68
Fig. 4. 16-Overlap concentration (C*) determination by linearity deviation.
Fig. 4. 17-Overlap concentration (C*) determination by intrinsic viscosity.
0.1
1
10
100
1 10 100 1000 10000
Vis
cosi
ty, c
p
Polymer concentration, ppm
HPAM 6-8 million Daltons Mw 30% hydrolysis 2% NaCl 25 °C
1
10
100
0.001 0.01 0.1
sp/C
(d
l/g)
Polymer concentration, g/dl
HPAM 6-8 million Daltons Mw 30% hydrolysis 2% NaCl 25 °C
69
4.3 Effect of Flow Rate on Polymer Retention
Polymer retention in porous media not only depends on concentration; previous
research also shows that it may be affected by flow rate (Maerker 1973, Dominguez and
Willhite 1976, Aubert and Tirrell 1980, Zaitoun and Kohler 1987, Huh et al 1990). For a
practical application, when polymer solution is injected through an unfractured well (e.g.,
radial flow), the flow rate varies significantly as the polymer penetrates into the reservoir.
In a 20-acre well pattern with formation height of 20 ft, porosity of 20 % and polymer
injected via an openhole injector at a rate of 2,000 bbls/day, Fig. 4.18 demonstrates that
the velocity at which polymer travels through the matrix decreases inversely with the
increase of distance or the invading radius (as shown by Eq. 4.4). For instance, the
velocity (v) is about 67 ft/day at the distance of 1 ft but it decreases sharply to 0.67 ft/day
at the distance of 100 ft. Though the majority of the flow rate in a deep reservoir may be
relatively low, the flow pattern in the near-wellbore area may have tremendous impact on
polymer retention. Therefore, it is of great importance to address this issue.
67.019v
r……………………………...…………………………………...………4.4
where, r is the invading radius of polymer front, ft.
70
Fig. 4. 18-Polymer retention in the near wellbore region, radial flow.
4.3.1 Method Established to Detect Hydrodynamic Retention
Actually, the similar strategy can be applied to the laboratory measurement of
hydrodynamic retention. As shown by Fig. 4.19, if the measurement starts with a fresh
core, then polymer retention at low injection rate is first determined by the same
approach introduced previously, e.g., retention is given by the area between the two
effluent breakout curves. After the completion of retention at a low injection rate, two
high flow rate polymer bank injections are conducted, which are also intercepted with
large volumes of brine injection to flush out the mobile polymers in the porous media.
These two polymer breakout curves are plotted together with the second polymer
breakout curve at a low flow rate as a function of pore volumes injected, (see Fig. 4.19).
There are three curves in Fig. 4.19. To make the explanation simpler, the second breakout
curve at low flow rate is called Curve A, the first and second breakout curves at high flow
y = 67.019x-1 R² = 1
0.1
1
10
100
1 10 100 1000
Vel
oci
ty, f
t/d
ay
Invading radius, ft
20-ac 5-spot spacing rw=4.5 in
h=20 ft, =0.2 QInj=2,000 bbls/day Radial flow
71
rate are called Curve B, and Curve C, respectively. The total retention is given by the
area between the second breakout curve at low flow rate and the first breakout curve at
high flow rate, i.e., area between Curve A and Curve B. In addition to the total retention,
this method is also able to distinguish the irreversible retention from the reversible
retention. The principle behind this approach can be summarized as following:
a) If the area between Curve A and Curve B is zero, it means no incremental
retention is induced by flow rate variation. Theoretically, for a purely
homogeneous core, if no retention occurs with increase of flow rate, these three
breakout curves are supposed to overlap one another. Fig. 4.20 demonstrates the
retention of 40 ppm KI (used as a tracer) in 1.9 Dundee sandstone core. As flow
rate increases from 3.26 ft/day through 104.26 ft/day, almost no retention
difference is noticeable. For this case, the retention of KI in porous media shows
little dependence on flow rate.
b) If the area between Curve A and Curve B is not zero, but Curve B and Curve C
overlap each other or the area between these two curves is zero, this means there
is no incremental irreversible retention. In other words, all the retention can be
considered reversible.
c) If the area between Curve A and Curve B is not zero, but Curve B and Curve A
overlap each other or the area between Curve B and Curve A is zero, this means
there is no incremental reversible retention. In other words, all the retention can
be considered irreversible.
d) If the area between Curve A and Curve B is not zero and Curve C falls in the
middle of the other two curves (Curves A and B), then the area between Curves A
72
and C gives the incremental reversible retention and the area between Curves C
and B gives the incremental irreversible retention. Of course, the total incremental
retention is the addition of these above two.
Note: this method is valid to estimate flow rate induced retention based on the
assumption that polymer IAPV is independent of flow rate. If at high injection rate or
pressure gradient, polymer solution may penetrate into the unswept region which is
already occupied by brine (not polymer), then polymer IAPV will decreases with increase
of flow rate. If this is true, the phenomenon of IAPV decrease will also delay polymer
propagation somewhat and a scenario similar to that shown in Fig. 4.19 will be observed.
This question will be addressed in a later section.
Fig. 4. 19-Mehod to determine hydrodynamic retention.
73
Fig. 4. 20-Effect of flow rate on KI (tracer) retention.
4.3.2 Hydrodynamic Retention in 1.9 Darcy Dundee Sandstone Core
500 ppm HPAM Polymer. A Dundee sandstone core with relatively high permeability
of 1.9 darcies and porosity of 24.1% was used to estimate how flow rate affected polymer
retention (Table 4.4). As mentioned earlier, retention at low flow rate of 3.26 ft/day was
first measured, which was about 20.35 g/g rock. After that, the same 500 ppm HPAM
polymer solution was injected into thehigh permeability core at elevated injection rates
ranging from 6.52 ft/day to 52.14 ft/day. Again, 100 PV of brine were injected after each
polymer injection. The results are shown in Fig. 4.21 and Table 4.5. Because the area
between the second breakout curve at 3.26 ft/day and the increased flow rates is not zero,
the total retentions as a result of flow rate increase were estimated to be 2.69, 5.68, 7.97,
8.67, and 9.10 g/g rock as flow rates increases from 3.26 ft/day to 6.52, 13.03, 26.07,
52.13, and 104.26 ft/day, respectively.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
Tracer at 3.26 ft/day
Trace at 6.52 ft/day
Tracer at 13.03 ft/day
Tracer at 26.07 ft/day
Tracer at 104.26 ft/day
1.9 D sandstone core 40 ppm KI tracer 2% NaCl 25 °C
74
Table 4.4-Properties of the Dundee Sandstone Core.
L, cm A, cm2 PV, cm3 ,% k, D Retention @ 500 ppm, 3.26
ft/day
15 14.5 52.4 24.1 1.9 20.35
Table 4.5-Retention Summary.
Q, ft/day Total, g/g rock Incremental Irrev,
g/g
Incremental Rev, g/g rock
RRF
3.26 20.35 0 1.89
6.52 23.03 0 2.69 1.87
13.03 25.72 -0.31 5.68 1.92
26.07 28.52 0.20 7.97 1.86
52.13 28.45 -0.57 8.67 1.89
104.26 29.50 0.061 9.10 1.90
Notes: Total, Irrev, and Rev, refer to total, irreversible and reversible retention, respectively.
Fig. 4. 21-Polymer retention at flow rates from 3.26 ft/day to 52.16 ft/day.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
3.26 ft/day
6.52 ft/day
13.04 ft/day
52.16 ft/day
75
Retention vs. Flow Rate. We plotted incremental retention (percentage) as a function of
flux in Fig 4.22. Careful examination of Fig. 4.22 reveals that different trends are
observed in different flow regions. For instance, the curve slope of low region from 6.52
ft/day to 26.07 ft/day is approximately 19 times greater than that from 26.07 ft/day to
104.26 ft/day. This implies the retention increases drastically in the low region and when
the flow rate reaches a certain value, the retention rises much more gradually with the
increase of flow rate.
Fig. 4. 22-Incremental retention of HPAM vs. flux.
Reversibility of Hydrodynamic Retention. For each case, a second polymer bank was
injected after 100 PV of brine injection with intervening periods of no flow to check the
reversibility of this flow rate-related retention. Fig. 4.23 and Fig. 4.24 give the results for
13.03 ft/day and 52.16 ft/day injection, respectively. The area between the first and
10
100
1 10 100 1000
Incr
emen
tal r
eten
tio
n, %
Flux, ft/day
76
second breakout curves at same flow rate for both cases is close to zero. Based on the
principle explained earlier, it can be inferred that no incremental irreversible retention is
detected. In other words, all the incremental retention turns out to be reversible. These
results confirm that 100 PV brine injection in our study is sufficient to displace these
mobile polymers in the core. Otherwise, a non-zero area between these two breakout
curves should be recognized. They also prove that the same core can be repeatedly used
to measure retentions at other flow rates as long as sufficient brine injection is guaranteed.
Impact of Hydrodynamic Retention on Residual Resistance Factor. How does
hydrodynamic retention affect permeability? It can be predicted that, if all the flow-
induced retention is reversible as indicated by Figs. 4.23 and Fig. 4.24, there should be no
permeability reduction caused by this hydrodynamic retention. This postulation is
confirmed by residual resistance factor measurement after core exposure to 100 PV brine
injection for each case. As shown in Table 4.5, the residual resistance factors prove to be
quite stable for all these cases with values close to 1.9. Little dependence of residual
resistance factor on polymer injection rate also verifies that almost all the incremental
retention associated with flow rate increases can be flushed out of the core during the
brine postflush. These results agree with findings by Maerker (1973), Dominguez and
Willhite (1976). However, our results display a much better picture of retention
reversibility.
77
Fig. 4. 23-Determination of irreversible retention at 13.04 ft/day.
Fig. 4. 24-Determination of irreversible retention at 52.16 ft/day.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
1st polymer injection
2nd polymer injection
HPAM 6-8 million Daltons Mw 30% hydrolysis 500 ppm 2% NaCl
1.9 D Dundee sandstone core
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
1st polymer injection
2nd polymer injection
HPAM 6-8 million Daltons Mw 30% hydrolysis 500 ppm 2% NaCl
1.9 D Dundee sandstone core
78
HPAM Polymer Rheology in Porous Media. Polymer resistance factor is defined as
water mobility (before exposure to polymer) divided by polymer solution mobility. The
resistance factor is a measure of the effective viscosity of a polymer solution in a porous
media, relative to water. Pressure drops across the core during both polymer and brine
injection were recorded and used to calculate resistance factor for each case. As shown
by Fig. 4.25, except for the extremely high flow rate, HPAM polymer shows either
Newtonian or shear thickening behaviors. For instance, at low to moderate injection rates
from 3 ft/day to 10 ft/day, HPAM shows Newtonian behavior, i.e., apparent viscosity is
independent of flow rate or shear rate. While, with further increase of flow rates from 10
ft/day to 50 ft/day, it becomes shear thickening, i.e., apparent viscosity increases with
flow rate or shear rate. If flow rate keeps increasing, a decreased resistance factor may be
observed. This is attributed to the viscosity reduction caused by mechanical degradation
at high flux (Maerker 1975, Seright 1983). For a practical perspective, this unusually high
flow rate or shear rate is only anticipated to exist in the near-wellbore region from where
polymer solution leaves the wellbore and first enters the formation.
The rheology of HPAM in porous, especially shear thickening behavior, was
attributed to the viscoelastic character of HPAM and elongational flow field in porous
media (Durst et al. 1982; Macosko 1993). The rheology of HPAM in porous media can
be summarized as the following: In a typical brine solvent, polymer molecules usually
take a coiled configuration and significant energy needed to untangle this coil (i.e.,
expand and elongate this molecule). At low flow rate, polymer molecules have sufficient
time to react to the hydrodynamic force acting upon them and become somewhat
stretched. The main principle here is that a stretched molecule always shows less
79
resistance to flow than a coiled one. Therefore, the resistance factor exhibited in porous
media at low flow rate or shear rate is consistent with the viscosity measured in a
viscometer. However, at high flow rate or shear rate, polymer molecules do not have
sufficient time to become stretched before they flow through a constricted pore structure.
Hence, more energy (or pressure gradient) needed to force them through these small pore
throats, which results in a high resistance factor at increased flow rate or shear rate. This
is the reason why shear thinning behavior of HPAM exhibited in a viscometer will not be
observed in a porous media. In contrast, double-helix, rod-like xanthan polymer
molecules are already expanded even at low flow rate or shear rate. When they flow
through constricted pore throat, regardless of flow rate, no significant coil-to-stretched
transition occurs. Therefore, unlike HPAM polymer, xanthan always show shear thinning
behavior in both the viscometer and porous media.
Fig. 4. 25-Resistance factor of HPAM at different flow rates.
0
2
4
6
8
10
1 10 100 1000
Res
ista
nce
fac
tor
(RF)
Flux, ft/day
HPAM 6-8 million Daltons Mw 30% hydrolysis 500 ppm 2% NaCl 25 °C
1.9 D Dundee sandstone core
80
4.3.3 Is HPAM Shear Thickening Behavior Caused by Hydrodynamic Retention?
As polymer retention in porous media increases with increase of flow rate or shear rate,
simultaneously, the resistance factor of HPAM solution in porous media also increases.
The question can be raised: is this shear thickening behavior a result of retention-related
permeability reduction instead of elongational flow? To address this question, another
water-soluble EOR polymer, xanthan was tested by following the same procedures.
Before the retention measurement, both HPAM and xanthan rheology was measured in a
viscosity (Anton Paar rheometer). Figure 4.26 reveals that HPAM and xanthan show
similar rheology in the viscometer except for the low concentration HAPM (150 ppm),
which behaves more like a Newtonian fluid, i.e., viscosity depends little on shear rate.
150 ppm and 500 ppm xanthan solutions show obvious shear thinning behavior, while
500 ppm HPAM displays a mild shear thinning property. Figure 4.26 also demonstrates
that no shear thickening behavior of HPAM, which is displayed in porous media can be
observed in a viscometer.
81
Fig. 4. 26-Rheology of HPAM and xanthan polymers in a viscometer.
Hydrodynamic Retention of Xanthan in 1.9 Darcy Core. The same method was tried
to estimate how xanthan retention differs with flow rate. Unfortunately, no consistent
results could be attained. Analysis shows that pressure drops across the 10 micron filter
combinations were much less sensitive to effluent concentration, compared to HPAM
solution. To minimize experimental error, we switched to another approach for effluent
concentration determination. Effluent samples were collected periodically for total
organic carbon (TOC) content determination, as we did for static adsorption measurement.
Figure 4.27 plots two normalized concentration ratios as a function of pore volumes
injected. One is the breakout curve at low flow rate of 3.26 ft/day, and the other is from
polymer injection at a high flow rate of 26.07 ft/day. The area between these two curves
gives the incremental retention of only 0.81 g/g rock, which is much lower than that
from HPAM (7.97 g/g rock). This difference in retention reveals that different
1
10
100
1 10 100 1000 10000
Vis
cosi
ty, c
p
Shear rate, 1/s
500 ppm Xanthan
500 ppm HPAM
150 ppm HPAM
150 ppm xanthan
82
functional groups or molecular size among these two polymers may significantly affect
their retention behaviors in the same porous media. Since no appreciable amount of
xanthan is retained in this quite permeable core, a lower permeability core probably is
needed to study xanthan retention.
Fig. 4. 27-Hydrodynamic retention of 150 ppm xanthan in 1.9 Darcy core.
Rheology of Xanthan in Porous Media. Resistance factors of xanthan polymer were
also measured. As shown by Fig. 4.28 and 4.26, xanthan consistently shows shear
thinning behavior in both porous media and in a viscometer. For instance, resistance
factor is 8.5 at flux of 3.26 ft/day. It declines to 5.5 when flow rate rises to 52.13 ft/day.
These results agree with other findings (Seright et al. 2009, 2010).
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
Cp/Co at 3.26 ft/day
Cp/Co at 26.07 ft/day
Xanthan
500 ppm 2% NaCl, 60 ml/hr 25 °C
1.9 D Dundee sandstone core
83
Fig. 4. 28-Resistance factor of xanthan at different flow rates.
4.3.4 Hydrodynamic Retention in 71 mD Berea Sandstone Core
As discussed above, a relatively high permeability core may not be a good candidate to
capture the retention variation with flow rate for a xanthan polymer. A 71 md Berea
sandstone core was selected whose retention has been satisfied with large pore volumes
of HPAM polymer injection. Experiments were carefully designed to attack two kinds of
problems. 1) Is rheology an intrinsic property of a polymer solution itself, or it is closely
related to polymer retention in porous media? 2) Does polymer IAPV decrease with
increase of flow rate or pressure gradient? This second question has been mentioned
previously.
Experiment Procedures. To answer these two questions, the following procedures were
designed:
1
10
1 10 100
Res
ista
nce
fac
tor
(RF)
Flux, ft/day
Xanthan 500 ppm 2% NaCl 25 °C
1.9 D Dundee sandstone core
84
a) Inject 100 PV of brine with intervening periods of no flow to flush out all the
mobile polymer molecules in the porous media;
b) Inject polymer solution at a low flow rate (Qa) till the effluent concentration is the
same as injected. Note: from this point, during polymer injection in each step,
record pressure drop across the core and collect effluent samples periodically for
concentration determination via TOC analyzer;
c) Without any pause, raise flow rate abruptly to a level several times higher than the
previous one and continually inject polymer solution at this flow rate (Qb) until
several pore volumes have been injected;
d) Either pause for a while or without pause, reduce flow rate back to the lower level
(Qa) and continue polymer injection until several pore volumes have been injected;
e) Raise flow rate again from Qa to Qb and complete several pore volumes of
solution injection;
f) Plot normalized polymer concentration and polymer resistance factor vs. pore
volumes injected.
Retention and Rheology of 150 ppm HPAM in 71 mD Core. Injection of 150 ppm
HPAM was analyzed first. Figure 4.29 indicates that when a sudden increase of flow rate
from 4.14 ft/day to 16.57 ft/day was made after around 4 PV injection, an immediate
effluent polymer concentration decrease was detected. It indicates that more polymers are
stripped from the solution due to hydrodynamic force increase. This phenomenon agrees
with the finding mentioned previously in a 1.9 darcy core. After around 4 PV of injection,
effluent polymer concentration approached the initial polymer concentration. Next, the
abrupt flow rate decrease from 16.57 ft/day back to 4.14 was accompanied with a rise of
85
effluent concentration. Again, this demonstrates that the incremental retention caused by
applying more hydrodynamic force on polymer molecules will be released back to the
solution when flow rate is lowered. Finally, when flow rate once again increases to 16.57
ft/day, an approximately similar amount of polymer is retained by the porous media.
These results confirm our former finding that almost all hydrodynamic retention is
reversible. Comparing the three areas marked A, B and C in Fig. 4.29, within
experimental error, they are nearly the same, which means that almost all the retention is
reversible. Another significance of this test suggests that polymer IAPV varies little with
increase of flow rate. Otherwise, we would not expect to see these effluent concentration
variations with flow rate change.
Rheology of 150 HPAM in this 71 md core was continuously monitored during the
whole injection period. As shown by Fig. 4.29, the resistance factor is almost the same at
both injection rates of 4.14 ft/day and 16.57 ft/day with a value around 12.5 except at the
time when flow rate adjustment was just made. This Newtonian-like rheology is also
displayed in a viscometer shown in Fig. 4.26 (the solid triangle). Actually, a similar
phenomenon was observed from the previous tests for HPAM in 1.9 darcy core. When
flow rate increased from 3.26 ft/day to 6.52 ft/day and 13.03 ft/day, 2.56 g/g rock and
5.68 g/g rock incremental retention was detected (Table 4.5), respectively, but all the
resistance factors stabilized at 3.8 (Fig. 4.25) and no resistance factor increase was
observed with retention increase. Therefore, the rheology of polymer in porous media
should be its intrinsic property. Otherwise, the increase in hydrodynamic retention will
have a significant impact on permeability reduction, and as a consequence, the resistance
factor at elevated flow rate would be much higher than that from low injection rate.
86
Fig. 4. 29-Hydrodynamic retention and resistance factor for HPAM.
Retention and Rheology of 150 ppm Xanthan in 71 mD Core. Similar tests were
performed to 150 ppm xanthan polymer. The results are displayed in Fig. 4.30. Again, as
flow rate rises from 4.14 ft/day to 33.16 ft/day, more retention in porous media is
observed, i.e., the concentration ratio (Cp/C0) is less than 1. After several pore volumes of
polymer injection, the system was shut down for 2 hr to eliminate any hydrodynamic
force acting on the molecules. This allowed the deformed molecules to have sufficient
time to relax and take random-coil configurations. When flow was resumed, an effluent
concentration higher than the initial concentration was detected (Cp/C0>1). The highest
concentration ratio (Cp/C0) after the flow resumed was as high as 1.9.
1
10
100
1000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15
Res
ista
nce
fac
tor
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volume injected
4.14 ft/day 16.58 ft/day 4.14 ft/day 16.58 ft/day
A
B C
87
Again, when we checked the polymer rheology in porous media, we found xanthan
exhibits shear thinning behavior. For example, the resistance factor at low flow rate of
4.14 ft/day is 8.04. In contrast, the resistance factor decreases to 5.9 at high flow rate of
33.16 ft/day (see the solid triangle in Fig. 4.30). This rheology is consistent with that
from a viscometer (Fig. 4.26).
Fig. 4. 30-Hydrodynamic retention and resistance factor for xanthan.
If the incremental retention does not significantly impact polymer rheology in porous
media by reducing rock permeability, then, one may ask, where do these newly-retained
polymers go? Based on the experimental results, we postulate that they are either trapped
in the part of the porous media that contribute little to rock permeability before polymer
1
10
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12
Res
ista
nce
fac
tor
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
4.14 ft/day 33.16 ft/day 4.14 ft/day
88
injection (such as dead end pores or crevices), or in a structure whose permeability is not
altered much with the increased accumulation of polymer molecules.
4.4 Polymer Inaccessible Pore Volume (IAPV)
Several mechanisms can be envisioned to IAPV for polymers (Liauh et al. 1979, van
Domselaar and Fortmuller 1992). First, pores or parts of pore spaces may be large enough
to accommodate small molecules (such as solvent, salts or tracers) but too small to allow
entry of polymer molecules (Dawson and Lantz 1972). The presence of clay may also
contribute IAPV, if small molecules can freely penetrate the clay but large polymer
molecules cannot.
Fig. 4. 31-IAPV determination for 100 ppm HPAM, 60 ml/hr, 347 mD core.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
2nd polymer injection
2nd tracer injection
Dundee sandstone core Porosity: 23% 347 mD
89
In our method, Fig. 4.31 is a typical curve for calculating IAPV. It shows both
effluent concentration breakout curves of the second HPAM slug and the tracer slug. The
first polymer injection is supposed to satisfy polymer retention in the porous rock so no
irreversible polymer retention occurs during the second polymer slug injection. Therefore,
if the reversible retention is negligible, due to the presence of IAPV, the second polymer
front should travel faster than tracer front. This is the principal of IAPVestimation in our
tests.
Of course, if there is any reversible retention, these movable polymer molecules will
be flushed out during the following large pore volumes of brine injection, and then this
part of retention during the second polymer bank injection will reoccur. If this reversible
retention is significant, the two concentration breakout curves may be very close to each
other or their positions may even be switched, resulting in a very small or even a negative
IAPV. This is especially true with the increase of polymer injection rate and decrease of
core permeability, where reversible retention becomes severe. As shown by Fig. 4.32,
where 1,000 ppm polymer is injected into 347 mD Dundee core at a flow rate of 1,000
ml/hr, the second polymer concentration curve is below that of the tracer, which gives a
negative inaccessible pore volume. The same phenomenon was found by Vela et at
(1976). Nevertheless, if there is any reversible retention occurring, these curves could be
used as a very good indicator of the reversibility of polymer retention. This will be
discussed in the following section.
90
Fig. 4. 32-IAPV determination for 20 ppm at flow rate of 1,000 ml/hr.
Inaccessible pore volume calculated from Fig. 4.33 is about 0.22 PV. For this case, 20
ppm HPAM polymer was injected into 347 mD Dundee sandstone core at the flow rate of
60 ml/hr (around 3 ft/day). When 100 ppm HPAM solution was injected into the same
core at the same flow rate, IAPV determined as shown in Fig. 4.33 decreased to 0.15 PV.
Shah et al (1978) attributed this phenomenon to the decrease of hydrodynamic
dimensions of polymer macromolecules with increase of polymer concentration. They
postulated that the decrease of polymer dimensions makes it possible for some polymer
molecules to penetrate into some small pores that might not be contacted at low
concentrations. As a result, a smaller IAPV could be formed. However, further
examination is needed to determine how much this theory can be relied on. Instead, using
reversible retention theory seems more plausible, because at the same flow rate, the
increase of polymer concentration will lead to an increase in hydrodynamic force, as a
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
2nd polymer injection
2nd tracer injection
Dundee sandstone core Porosity: 23% 347 mD
91
consequence, the reversible hydrodynamic retention increases. As explained earlier, this
will lead to a decreased inaccessible pore volume.
Fig. 4. 33-IAPV determination for 20 ppm HPAM at flow rate of 60 ml/hr.
Although IAPV was estimated in our tests, we should be aware of the experimental
errors and limitations responsible for unrealistic IAPV values. Sorbie (1991) pointed that
the diameter of an EOR HPAM in a 3% NaCl brine is typically 0.5—0.8 m. Also, an
XMT analysis of 470-mD Berea sandstone revealed pores that were highly connected and
that 98% of the pores had an effective diameter greater than 26 m and a pore throat
diameter over 6.7 m (Seright et al. 2006). Thus, a typical EOR HPAM molecule in
solution is small compared to the pore sizes and throat sizes, so it should have access to
most spaces in the porous media. It seems likely that experimental errors and limitations
are responsible for the observed IAPV variations. Therefore, more research needs to be
done to clarify this discrepancy before reaching any decisive conclusions about polymer
IAPV.
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
2nd polymer injection
2nd tracer injection
Dundee sandstone core Porosity: 23% 347 mD
92
Fig. 4. 34-2nd injection of 160 ppm HPAM and tracer at 60 ml/hr, 71 mD core.
Fig. 4. 35-2nd injection of 1,000 ppm HPAM and tracer at 240 ml/hr, 71 mD core.
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected, PV
2nd polymer injection
2nd tracer injection
Barea sandston core Porosity: 18.5% 71 mD
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
Co
nce
ntr
atio
n r
atio
(C
p/C
0)
Pore volumes injected
2nd polymer injection
2nd tracer injection
Barea sandston core Porosity: 18.5% 71 mD
93
4.5 Effect of Polymer Retention on Permeability Reduction
Literature shows that polymer retention reduces the permeability or increases the residual
resistance factor of porous rock. This phenomenon becomes more severe when rock
permeability decreases (Vela et al 1976; Seright 1992; Seright and Martin 1993).
Residual resistance factors (RRF) are determined by conducting brine injection before
and after polymer retention until the pressure drop across the core stabilizes. Equation 4.4
is used to calculate the residual resistance factor.
( )
( )
A
B
PRRF
P………………………………………………………………………..….4.4
where, ( P)A ( P)B are pressure drops for brine injection after and before polymer
retention, respectively. Of course, the same brine injection rate should be maintained.
Figure 4.36 plots the relationship of the residual resistance factor vs. polymer
concentration for a high permeability core (347 mD Dundee core). As illustrated, the
residual resistance factor is only about 1.4 and it varies little with increase of polymer
concentration. Based on previous findings (Rowland 1963; Rowland and Eirich 1966),
the retention of polymer will form a monolayer on the solid surface, reducing the
effective pore size. As a consequence, rock permeability decreases. The constant residual
resistance factor with concentrations from 20 ppm to 1,000 ppm correlates well with the
amount of polymer retention, as indicated by Fig. 4.9, which is also independent of
polymer concentration.
94
Fig. 4. 36-Effect of polymer concentration on residual resistance factor, 347 mD core.
Fig. 4. 37-Effect of polymer concentration on residual resistance factor, 71 mD core.
0
1
2
3
4
10 100 1000
Res
idu
al R
esis
tan
ce F
acto
r (R
RF)
Polymer concentration, ppm
Dundee sandstone core 347 mD Porosity: 23%
0
2
4
6
8
10
10 100 1000
Res
idu
al R
esis
tan
ce F
acto
r (R
RF)
Polymer concentration, ppm
HPAM 6-8 million Daltons MW 30% hydrolysis 2.52% TDS 60 ml/hr 25 C
Barea sandston core 71 mD Porosity: 18.5%
95
For low permeability core (71 mD Berea core), the residual resistance factor is much
higher compared with that from high permeability core. As shown by Fig. 4.37, the value
of the residual resistance factor is in the range of 4.5—7.2, which is also consistent with
the result of polymer retention shown in Fig. 4.11.
4.6 Steady-State Flow in Porous Media
Literature (Zitha et al 2001) shows that an unsteady-state (continuous build-up of
polymer injection pressure) may be reached when polymer is flowing through porous
media if these conditions are satisfied: (a) the velocity gradient is large enough to induce
a coil-stretch transition, (b) the polymer adsorbs on the pore surfaces and (c) the length of
stretched macromolecules is larger than the effective pore throat diameter. During our
tests, we recorded the pressure drop for both high permeability (347 mD) and low
permeability core (71 mD). As shown in Figs. 4.38 and 4.39, regardless of the flow rate
and permeability, all the pressure drops across the core stabilized at around 1 PV polymer
injection. For these cases, no brine injection was conducted after polymer injection. This
means a steady-state flow was reached and no continual pressure build-up was observed.
In other words, no significant pore bridging phenomenon took place in our tests
regardless of rock permeability.
96
Fig. 4. 38-Pressure drop during polymer injection in 347 mD core.
Fig. 4. 39-Pressure drop during polymer injection in 71 mD core.
1
10
100
0 2 4 6
Pre
ssu
re d
rop
, psi
Pore volumes injected, PV
60 ml/hr
180 ml/hr
1000 ml/hr
1
10
100
1000
0 2 4
Pre
ssu
re d
rop
, psi
Pore volumes injected, PV
60 ml/hr
120 ml/hr
600 ml/hr
97
The increase of pressure drop with increased flow rate shown by these two figures
can be attributed to HPAM shear thickening rheology in porous media; i.e., the HPAM
resistance factor (effective polymer viscosity relative to brine viscosity) increases with
the flow rate (Jennings et al. 1971, Southwick and Manke 1988, Seright et al. 2010). For
instance, the pressure drop at injection rate of 60 ml/hr for 347 mD core was about 2 psi;
by comparison, the value rose to around 10 psi at 180 ml/hr. This trend was also true for
the 71 mD core where pressure drop was about 60 psi and 200 psi at flow rate of 60 ml/hr
and 120 ml/hr, respectively.
98
CHAPTER 5. CONCLUSIONS
5.1 Conclusions
This study focuses on EOR polymer retention in porous media. Factors such as polymer
concentration and flow rate were specially investigated. Retention reversibility and the
impact of retention on rock permeability reduction and flow rheology were also estimated.
The following conclusions were drawn from our experiments:
1. The adsorption of HPAM polymers on rock surface can be considered
instantaneous and irreversible. These results indicate that these long chain
molecules have high adsorption tendency. It is impossible for the adsorbed
molecules to lose all of their segment contact with rock surface at the same time.
2. Different polymer retention behaviors are observed in dilute, semi-dilute and
concentrated regions in the absence of oil saturation. In both dilute and
concentrated regions, polymer retention is basically concentration-independent. In
contrast, in the semi-dilute region, polymer retention is concentration-dependent.
3. If a porous medium is first contacted with dilute HPAM solution to satisfy the
retention, no significant additional retention occurs when exposed to higher
concentrations. In field applications of polymer and chemical floods, reduced
99
polymer retention may be achieved by first injecting a low-concentration polymer
bank.
4. Based on the experimental results, a concentration-related retention mechanism is
proposed that considers the orientation of the adsorbed polymer molecules and the
interaction between molecular coils in solution. More specifically, in dilute
regions, where there is little or no interaction between polymer molecules, the
polymer molecules will be adsorbed individually and take a flat orientation on the
rock surface with full segment attachment. For this case, two-dimensional
adsorption dominates and retention shows concentration-independence. In the
concentrated region, strong interaction between molecules exists in the solution
and the dominant adsorption will be three-dimensional which means almost no
molecules are in full segment contact. The retention in this concentrated region
also shows concentration-independent. In contrast, in the semi-dilute region, the
intermediate degree of molecular interaction leads to mixed retention, and three-
dimensional retention increases with the increase of polymer concentration,
therefore, polymer retention shows concentration dependent and increases with
concentration.
5. Polymer retention proves to be affected by flow rate. Retention of 500 ppm
HPAM in 1.9 sandstone core increases by 13.2% and 39.2% as flow rate rises
from 3.26 ft/day to 6.52 ft/day and 52.13 ft/day, respectively. Hydrodynamic
retention shows strong flow dependence. In low flow regions, the retention
increases abruptly. By comparison, in high flow regions, the increase becomes
much more gradual. Almost all the hydrodynamic retention proves to be
100
reversible. In other words, incremental irreversible retention associated with flow
rate increase is negligible.
6. In porous media, HPAM polymers exhibit Newtonian behavior at low to moderate
flow rate and shear thickening behavior and high flow rate, while, xanthan
polymers show shear thinning behavior. Results show rheology of EOR polymers
exhibited in porous media should be an intrinsic property. The hydrodynamic
retention has limited effect on flow behaviors.
7. Negative polymer inaccessible pore volume (IAPV) is observed with increase of
flow rate and decrease of permeability. This presence of negative IAPV is caused
by reversible polymer retention. Adsorption on rock surface was proved to be
almost irreversible, therefore, the mechanical entrapment and hydrodynamic
retention account for this phenomenon.
8. The residual resistance factors (RRF) determined after the polymer injection
increases with decrease of rock permeability as a result of polymer retention.
Residual resistance factors of 1.4 and over 4 were detected for high permeability
core (347 mD) and low permeability core (71 mD), respectively. Nevertheless, the
reversible hydrodynamic retention does not lead to permeability reduction.
5.2 Discussions and Future Work
This research focused on the effect of polymer concentration on retention and
measurements were carried out in monophasic conditions (in the absence of oil phase).
Previous work shows polymer retention is usually lower with residual oil saturation than
that without oil present—suggesting that the presence of residual oil may reduce HPAM
somewhat (Szabo 1975, Hughes et al. 1990, Broseta et al. 1995). Polymer retention
101
causes rock permeability reduction by forming a thin layer on rock surface (residual
resistance factor). The RRF increases with decrease of permeability (Jennings et al. 1971,
Hirasaki and Pope 1974, Seright 1993). In the future, the dependence of permeability
reduction and oil saturation on polymer concentration should be investigated further,
especially with regard to the concentration-dependence of polymer retention that was
reported in this paper.
As mentioned earlier, field applications may be interested in our finding that polymer
retention is low if the rock is first contacted with a low polymer concentration. Polymer
losses due to retention may be reduced considerably if a dilute polymer bank precedes the
main mobility-control bank. Whether or not this approach is practical will depend on
economics, timing, and the specific polymer retention levels that occur in the particular
field application.
Should our model and results replace the existing Langmuir isotherm formulations for
polymer retention in simulators? The Langmuir isotherm was always incorrect
mechanistically for polymer retention (because most polymer retention is irreversible), so
one could argue that it should never have been used. However, to be more supportive of
previous simulators, using the Langmuir isotherm may not result in grossly incorrect
predictions if the Langmuir plateau is set to be reached at a very low polymer
concentration, if the polymer front is sufficiently sharp, and if the injected polymer
concentration is relatively high. If these conditions are not met, there should be value in
incorporating our model into the polymer flooding simulator.
102
Accurate estimation of polymer IAPV should be addressed in the future. Controversial
results on IAPV are shown in petroleum literature. To better understand polymer
propagation through reservoirs, in addition to polymer retention, the magnitude of the
IAPV for a specific kind of reservoir should also be investigated.
103
NOMENCLATURE
A = core section area, cm2
a1 = constant in Langmuir isotherm adsorption equation
b1 = constant in Langmuir isotherm adsorption equation
C = solute concentration in Langmuir isotherm adsorption equation
C* = polymer overlap concentration crossover from dilute to semidilute regime
C** = polymer overlap concentration crossover from semidilute to concentrated
regimes
C0 = initial polymer concentration, ppm
Ceq = equilibrium polymer concentration, ppm
Cp = polymer concentration in effluent, ppm
Cpoly = polymer concentration, ppm
eH = effective hydrodynamic thickness of the adsorbed layer, m
h = formation height, ft
k = permeability, mD or D
kro = relative permeability to oil
krw = relative permeability to water
L = core lenth, cm
M = mobility ratio
Pinj = mass of polymer injected, lbm
104
Pre = mass of polymer retained in the reservoir, lbm
PVret = pore volume delay per pore volume injected
Qa, Qb = polymer injection rates
QInj = polymer injection rate, bbls/day
Rpret = polymer retention, g/g sand
r = invading radius, ft
rw = wellbore radius, in
Sor = residual oil saturation
Sw = water saturation
Swr = residual water saturation
v = velocity, ft/day.
Vp = volume of polymer solution, cm3
Wsg = weight of sand, g
( P)A = pressure drops for brine injection after polymer retention, psi
( P)B = pressure drops for brine injection before polymer retention, psi
[ ] = intrinsic viscosity, dl/g
p = pressure drop, psi
= solute adsorption in Langmuir isotherm
= porosity
= shear rate, s-1
c = critical shear rate, s-1
solution = solution viscosity, cp
solvent = solvent viscosity, cp
sp = specific viscosity
105
d = mobility of the displaced phase, mD/mPa·s
D = mobility of the displacing phase, mD/mPa·s
o = viscosity of crude oil, cp
p = viscosity of polymer solution, cp
w = viscosity of water, cp
g = density of sand grains, g/cm3
rock = rock density, g/cm3
Acronyms
BET = Brunauer, Emmett, and Teller
CAT = cationic polyacrylamide
EHT = effective hydrodynamic thickness
EOR = enhanced oil recovery
HPAM = partially hydrolyzed polyacrylamide
IAPV = inaccessible pore volume
Mw = molecular weight
OOIP = original oil in place
PAM = polyacrylamide
PV = pore volume
RPM = revolution per minute
RRF = residual resistance factor
SP = sandpack
TDS = total dissolved solids
TOC = total organic carbon
106
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SI Metric Conversion Factors
ft × 3.048* E−01 = m
in. × 2.54* E+00 = cm
lb × 4.535 9237 E−01 = kg
md × 9.869 233 E−01 = m2
*Conversion factor is exact.