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Evaluation of oil foam as a displacing phase to improve oil recovery: A
laboratory study
Hazim H. Al-Attar
United Arab Emirates University, Chemical & Petroleum Engineering Department, Al-Ain P.O. Box 17555, UAE
a b s t r a c ta r t i c l e i n f o
Article history:
Received 20 December 2010
Accepted 15 August 2011Available online 23 August 2011
Keywords:
foam
plastic viscosity
miscible displacement
non-Newtonian fluids
EOR
oil displacement
The objective of this work is to investigate the possibility of considering oil foams for practical use in the re-
covery of oil. To achieve this objective a multifunction laboratory setup was designed to provide capillary
tube-foam viscosity measurements, selective core configuration, selective foam generation scheme, and
good control of gas injection-pressure and liquid injection-rate.
The porous medium was represented by a 2 ft2 in. cylindrical Berea sandstone core with absolute perme-
ability of 139.6 md and porosity of 23.1%. Kerosene (viscosity of 1.458 cp) and Nitrogen (specific gravity of
0.9672) were used as the liquid and gas components of the oil foam, respectively. A surfactant with code
name FC-432 was used as foaming agent at a concentration of 1% by volume. The effects of imposed pressure
differential, slug size of surfactant solution, and gravity on oil displacement by internally-generated foam
scheme were investigated. The displacement of oil by externally generated foam was tested for three foam
qualities of 70, 80, and 90% under imposed pressure differential of 15 psia. Gas drive and water flood tests
were conducted for comparison purposes. Injection pressure in all tests was near 830 psia.
The results of this work revealed that oil foams behave as non-Newtonian fluids with low yield stress and
that their plastic viscosities increase with increased foam quality. Oil recoveries by oil foam displacement
were significantly higher than those observed in gas drive and water drive tests. Vertical core configuration
was found to yield higher oil recoveries than horizontal core configuration. Also higher oil recoveries were
generally associated with lower imposed pressure drops, lower foam qualities, and larger slug size of surfac-
tant solution.The mechanism of foam flow in the core was deduced from gas breakthrough, relative permeability concepts,
and capillary tube model. A new iterative scheme of calculations is proposed to determine average foam satura-
tion inside the core.
2011 Elsevier B.V. All rights reserved.
1. Introduction
Foams may be defined as a relatively homogeneous dispersion of gas
in a foaming-surfactant solution and at some shear rates for certain
foam qualities they exhibit non-Newtonian fluid properties (Calvert and
Nezhati, 2003; Liu, Zhang, Guo, and Ghalambor, 2010), Marsden and
Khan, 1966; Mitchell, 1971; Weaire, 2007. Foams are composed of a
large numberof gas/liquidinterfacesor lamellae that separate gas bubbles
(Kam and Rossen, 2003). These interfaces form thermodynamically un-
stable systems whose surface energy tends to decrease as they degener-
ate into gas and liquid phases.
Foams can be classified according to their qualities (fraction of the
total foam volume which is gas) as dry foams for high quality or
strong foams and wet foams for low quality or weak foams (Alvarez
et al., 2001; Gauglitz, et al., 2002; Kam and Rossen, 2003). They can
also be classified according to their bubble size as coarse for large
bubble size and fine for small bubble size (Gauglitz et al., 2002).
The smaller the bubble the more gasliquid interfaces per unit
volume of equal foam qualities. Foams are compressible fluids
because of the presence of gas and can undergo compression and de-
compression cycles because of the elasticity of the liquid films. These
films are stabilized by the surfactant molecules concentrated at the
gas/surfactantsolution interface.
The viscosity of foam is the physical property of greatest interest
to rheologists and engineers. Dry foams have been found to display
high apparent viscosities (Calvert and Nezhati, 2003), Marsden and
Khan, 1966; Raza and Marsden, 1970; Weaire, 2007. Marsden and
Khan (1966) showed the non-Newtonian behavior of foams through
their apparent viscosity measurements using a modified Fann VG
meter. They found that water foam viscosity decreases as the shear
rate increases and that it increases as the foam quality is increased.
They considered foam flow in porous media to be dependent on foam
viscosity and concluded that the gas and liquid phases in the presence
of foaming agents can and usually flow simultaneously through the
Journal of Petroleum Science and Engineering 79 (2011) 101112
Corresponding author. Tel:. +971 50 5836642; fax: +971 3 7624262.
E-mail address: hazim.alattar@uaeu.ac.ae.
0920-4105/$ see front matter 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.petrol.2011.08.013
Contents lists available at SciVerse ScienceDirect
Journal of Petroleum Science and Engineering
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same pore channels in the form of bubbles or froth. Mitchell (1971)
measured water foamviscosity under high pressure using 8-ft long cap-
illary tubes of various sizes. Based upon the linearity and the 45 slope
of his shear stress-shear rate plots, he concluded that for foam quality
in the range of 054% the foam behaved as Newtonian. Also, for foam
quality between 54 and 96% foam displayed Newtonian characteristics
and laminar flow at shear rates higher than 20,000 s1. At shear rates
less than 20,000 s1 his foam displayed non-Newtonian characteristics.
Mitchell's data showed plugfl
ow behavior rather than laminarfl
ow be-havior at these lower shear rates. Based on cone and plate rheometer
flow and pipe flow, Calvert and Nezhati (2003) showed that flow of
foams may be represented by a modified Bingham plastic model, with
the addition of a liquid-rich slip layer caused by bubble migration
away from a solid-surface. They also observed that yield stress of
foams is dependent on bubble size distribution. Modeling of foams
with fixed bubble size as a Bingham plastic wasalso proposed by others
(Bird et al., 1960).
Practical uses of foams in oil and gas reservoirs have increased inter-
est in the mechanism of two-phase flow through porous media in the
presence of foam. Foams have been suggested as drilling fluids (Holm,
1970; Mitchell, 1971). Such light fluids are suitable for operating in
reservoirs with low fluid pressure where mud weight is a problem.
They have also been recommended to prevent gas leakage through cap
rocks in storage reservoirs (Bernard and Holm, 1970 and Minssieux,
1972) and are used as fracturing fluids (Blauer and Kholhass, 1974;
Wheeler, 2010). Foamshave also been proposed to improve liquid lifting
from low-pressure gas wells (Yang and Siddiqui, 1999) and as cheap,
economical and effective light-weight cement for application in forma-
tions with a low fracture gradient (Davies and Hartog, 1981). Foam can
improve sweep efficiency in gas-injection EOR (Schramm, 1994; Rossen,
1996) and surfactant EOR (Li et al., 2008), redirect acid flow in matrix
acid stimulation (Gdanski, 1993; Nguyen et al., 2003), and increase the
efficiency of remediation of aquifers (Hirasaki et al., 2000; Mamun et
al., 2002). Foaming injected gases has been found to increase the gas-
phase resistance dramatically, thereby providing mobility control to im-
prove the sweep efficiency and oil production (Chen et al., 2008).
The behavior of foam flow in porous media has been investigated
experimentally. Using tracer techniques and microscopic observa-tions, Holm (1968) concluded that in the presence of foam, gas and
liquid flow separately through porous media and that the liquid
moves through the film network and the gas moves progressively
through the system by breaking and reforming bubbles. He also
added that in the presence of foam, the effective permeability of the
porous medium to each phase is greatly reduced and that this perme-
ability behavior might suggest some flow channel blockage. Accord-
ing to other published gas tracer studies (Friedmann et al., 1991;
Radke and Gillis, 1990; Tang and Kovscek, 2006), the fraction of gas
trapped within a foam at steady state in sandstones ranges from 85
to 99%. The large gas blockage reduces the relative permeability of
the gas phase significantly and lowers gas mobility further. Minssieux
(1972) used sand packs and natural sandstone cores in his experi-
ments. He discussed the effects of using highly effective foamingagents where they can cause complete gas blockage. He concluded
that during foam generation inside the pores, it will be invariably
regenerated by breaking and reforming of the foam bubbles. He also
reported higher oil recoveries with low permeability sandstone
cores (130 md) and lower foam qualities (6070%). Bond and Bernard
(1966) investigated the rheology of foams in porous media and con-
cluded that liquid flow followed fixed channels whether or not
foam was present and that these fixed channels depends solely
upon the liquid saturation. They also stated that a negligible quantity
offluid could flow through the liquid membranes of the foam com-
pared with that flowing through the liquid channels. Fried (1961)
studied the use of water foam in oil recovery and described the flow
of foam as non-Newtonian plug type flow. He observed that as foam
was injected inside the porous medium an oil bank built up and
the oil recovery was then controlled by (1) flow in previously unaf-
fected pores, (2) the high viscosity of the displacing phase (foam)
and (3) the high pressure gradient at the flood front. Fried concluded
that higher oil recoveries by foam displacement were mainly attribut-
ed to the stability of foam and that foam can be regenerated within
the porous medium. Mast (1972) investigated the microscopic be-
havior of foams in porous media and concluded that some of the liq-
uid and gas may be transported as foam and that their proportions are
a function of foam stability. He also concluded that when foam is sta-ble both phase can flow as foam in the porous medium with some
breaking and regeneration. Raza (1970) conducted flow experiments
of foam in sand packs and naturally consolidated sands. He put pres-
sure taps at equal distances over the entire length of his porous medi-
um and measured the pressure drop across the various sections of the
core as a function of time. He observed a linear relationship between
the applied pressure differential and the size of the foam-filled por-
tion of the porous medium vs. time.
A variety of recent theoretical models have been developed to
model foam flow in porous media based on documented laboratory
observations. These models rely on the fact that foam texture deter-
mines the strength and mobility of foam and that foam texture itself
depends on many factors, such as pore structure, surfactant formula-
tion, permeability, capillary pressure, flow rates, and presence of oil
phase. Therefore, most of the models modify gas mobility according
to the presence of foam. These models range from population-
balance models (Chang et al., 1990; Chen et al., 2008, Fergui et al.,
1995; Friedmann et al., 1991; Kovscek et al., 1995; Patzek, 1988; ) to
empirical and semi-empirical models (Fisher et al., 1990;Mohammadi
et al., 1993; Patzek and Myhill, 1989), to fractional-flow theory (Zhou
and Rossen, 1995; Rossen, 1996), and to percolation models (Chou,
1990; Rossen and Gauglitz, 1990).
The majority of research on the rheology of foams, the mechanics
of foam flow in porous media and applications of foams has been in
the area of water-based foams. In the present study the capillary
tube-viscometer was used to investigate the rheological properties
of oil foams of various qualities. The effectiveness of oil foams in dis-
placing oil in a one foot long, naturally consolidated core sample was
then examined using a multipurpose experimental setup designed toproperly achieve the above objectives. Two major types offlow exper-
iments were conducted, the first type involves oil displacement by
continuous injection of externally-generated oil foam and the second
considers oil displacement by internally-generated oil foam. The
flow mechanism of oil foam in porous media was investigated by
two fundamental concepts; (1) representing the core sample by a
bundle of equal length capillary tubes of various diameters, (2) rela-
tive permeability and by monitoring gas breakthrough times. A new
iterative scheme of calculations is proposed to determine average
foam saturation inside the core.
2. Methodology
The experimental work performed in this study was designed toaddress three major issues. The first part dealt with measurements
of foam viscosity using capillary tube viscometer. The second part
catered for investigating the effectiveness of oil displacement in po-
rous media by continuous oil foam injection of various foam qualities
and by continuous oil foam injection of various foam qualities
followed by gas drive. The third part involved investigating the effec-
tiveness of oil displacement in porous media by internally-generated
oil foams of two surfactant solution slugs.
2.1. Oil foam viscosity
2.1.1. Equipment and apparatus
A schematic flow diagram of the equipment used is illustrated in
Fig. 1. The foam generating unit consists of a thick-wall steel pipe
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10 in. long and 0.5 in. inside diameter filled with a mixture of 200
mesh sand and very fine glass beads. To keep the sand and beads in
place, four layers of glass wool and wire mesh were squeezed at
both ends of the steel pipe. A two-cylinder positive displacement
pump with 48 different speeds was used to inject the liquid in all
experiments.
The liquid phase in all experiments is kerosene (sp. gr. of 0.81, vis-
cosity of 1.458 cp at 70 F and surface tension of 25.85 dynes/cm at
70 F). The foaming agent used in all experiments is a product under
the code name ofFLUORAD FC-432 and Table 1 presents the most
important properties of this surfactant. A minimum surface tension
of 20.3 dynes/cm was obtained when kerosene was mixed with the
above surfactant at a concentration of 1% by volume. The selection of
this foaming agent was based on the results of drainage tests con-
ducted on kerosene foams containing various types of surfactants at
a concentration of 1% by volume. These results are presented in
Table 2.
The gas phase used in all tests is nitrogen [sp. gr. of 0.9672 (air= 1)
and viscosityof 0.0178 cp at 70 F]which is supplied in special cylinders
at 2500 psi. A pressure regulator was used to regulate gas pressure and
a specially designed diaphragm control valve was used to control gas
flow rate including extremely low rates.
A stainless steel capillary tube (not shown in Fig. 1) 31 in. long and
0.032 in. inside diameter served as the viscometer which was cali-
brated for kerosene viscosity. A differential cell pressure transducer
equipped with a digital readout screen served in continuous display
of pressure drop across the capillary tube. The liquid rate leaving
the viscometer was continuously monitored in a graduated cylinder
and the rate of gas effluent was continuously measured by a wet-
test meter.
2.1.2. Foam generation and viscosity measurements
The gas (compressed nitrogen) and the surfactant solution (kero-
sene+ 1% by volume foaming agent) were injected simultaneously
into the foam generating unit. The gas was injected at a constant pres-
sure while the surfactant solution was pumped at a constant rate. The
generated foam was then passed through the capillary tube viscometer
and the pressure drop across the tube was recorded after steady-state
flow condition has been reached. The flow line pressure was about
530 psig and the outlet pressure was controlled by a dome-loaded
type back pressure regulator, which drew off the produced fluids
under atmospheric pressure. To calculate foam quality under flowing
Fig. 1. Schematic diagram of test apparatus (foam is the displacing phase).
Table 1
Properties of the surface-active agent FLUORAD FC-432.
Typical properties
Form 25% active in heptane
Color colorless to pale yellowViscosity 5.00 cp
Density 0.78 g/cm3 at 25 C
Refractive index 1.4
Solubility
Water b0.2
Methyl alcohol b0.2
Dimethylformamide b0.2
Isopropyl alcohol b0.2
Ethyl acetate 0.20.5
Cellosolve acetate 0.20.5
Methyl ethyl ketone 0.20.5
1, 1, 1-Trichloroethane N20
Perchloroethylene N20
Tolouene N20
Benzene N20
Heptane N20
Table 2
Drainage test for 1% by volume surfactant solutions of various foaming agents; Initial
foam volume is 100 cm3 and stirring time is 1 min.
Product code Ionic type Liquid drained after
one hour (cm3)
Notes
FC-432 NA 15 Stable foam; fine bubbles
FC-431 NA 33 Stable foam; medium-fine
bubbles
FC-134 Cationic 67 Unstable foam; coarse bubbles
FSA Anionic 90 Poor hydrocarbon foaming
agent
FSB Amphoteric 96 Poor hydrocarbon foaming
agent
FSN Nonionic 96 Poor hydrocarbon foaming
agent
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conditions, the gas volume is corrected to flowing pressure. Foam qual-
ity was varied by adjusting the liquid injection rate.
2.1.3. Results and discussion
The results of calculations of shear rates and shear stress for three
foam qualities (70, 80 and 90%) are plotted on log-log scale as illus-
trated in Fig. 2. These plots show some curvature and yield stress
which is indicative of non-Newtonian behavior of the kerosene foam.
For water foam, Mitchell (1971) demonstrated with 821 pieces of
data that his foam behaved as a non-Newtonian fluid and closely fits
the Bingham-plastic model. The oil foam data obtained in this study
seem to compare favorably with Mitchell's data as shown in Figs. 3,
4, and 5 for foam qualities of 90, 80, and 70%, respectively. In these
figures and at high shear rates (between 10 4 and 105 s1), the for-ward extrapolations of the straight line portion of the oil foam viscos-
ity data become asymptotic to the water foam data. This convergence
at high shear rates may indicate that the flow regime of the oil foam is
basically laminar and it continues in this regime to much lower shear
rates than the water foam measurements. The difference in the
behavior of the two foams at lower shear rates may be attributed to
different base liquids and foaming agents used in the two studies.
The Bingham model was applied to calculate the plastic viscosity of
oil foam and the results for the three foam qualities investigated in
this study are illustrated in Fig. 6. The yield stress was found for
each foam quality by finding the value of shear stress that would
yield the best linear relationship of the data presented in Fig. 2, and
the results are presented in Fig. 7. Similar to water foam, oil foam vis-
cosity was found to increase as the foam quality is increased. Oil
foams, however, were found to exhibit a little higher viscosity and a
much lower yield point than water foams of similar foam quality
range. The low yield points observed in oil foams may be attributed
to the non-polar nature of the kerosene and the lower surface tension
of kerosene-surfactant solution as compared with water-surfactant
solution. Modeling of foams as Bingham-plastic fluids have been
reported by other investigators (Bird et al., 1960; Calvert and Nezhati,
2003; Weaire, 2007).
2.2. Oil displacement by externally generated oil foam
2.2.1. Experimental setup, core sample and core holder assembly
The experimental setup shown in Fig. 1 was used in all tests and a
2 ft long2 in. inside diameter Berea sandstone core was used as the
Fig. 2. Oil foam viscosity for three foam quality ranges.
Fig. 3. Capillary tube-viscosity measurements: water foam (after Mitchell, 1971) and
oil foam (present study). Foam quality range: 89
92%.
Fig. 4. Capillary tube-viscosity measurements: water foam (after Mitchell, 1971) and
oil foam (present study). Foam quality range: 8082%.
Fig. 5. Capillary tube-viscosity measurements: water foam (after Mitchell, 1971) and
oil foam (present study). Foam quality range: 70
73%.
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porous medium. The core was coated with a thin layer of two pre-
mixed epoxy resins and then centered in a 27 in. long2.75 in. inside
diameter steel pipe threaded on both ends. Two heavy steel bull plugs
with in. hole in the center of each were screwed on both ends of thesteel pipe and the whole assembly was then vertically positioned
with the lower end plugged. A melted woods metal was then poured
through the in. hole of the upper bull plug to fill in the annulus
space between the inner walls of the steel pipe and the coated core
sample. The core holder assembly was left in that position overnight
so that the melted metal would have enough time to solidify. Finally,
a in. diameter hole was drilled in the center of each bull plug to
provide the necessary connection between the isolated core sample
and the rest of the flow system.
2.2.2. Measurements of absolute permeability, porosity, irreducible water
saturation and effective permeability to oil
The core assembly was weighted when the core sample was empty.The absolute permeability using nitrogen was measured at different
flow rates while monitoring the pressure gradient across the core for
each rate. The data were then plotted as recommended by Klinkenberg
(1957). The extrapolated permeability (liquid equivalent) was found
equal to 144 md.
To determine the porosity, vacuum was pulled at the downstream
end of the core with the upstream end connected to the liquid pump.
After 5 h of vacuuming, distilled water (sp. gr. of 1 and viscosity of
1.2 cp at 60 F) was injected under variable pressure (5 to 50 psi) at
different rates to insure complete saturation. A cumulative volume of
3000 cm3 of injected distilled water was needed to fully saturate the
core. The difference between the weight before and after core satura-
tion was divided by the density of the distilled water to determinethe
core pore volume (found equal to 287.75 cm3). The core porosity was
then calculated by dividing the pore volume by the bulk volume
(1235.33 cm3) and found equal to 23.108%.
The core absolute permeability to water was then measured withthe core 100% saturated with distilled water and found equal to
139.6 md.Thisvalueis very close to that obtained from theapplication
of Klinkenberg standard procedure. Kerosene was then injected to
displace the distilled water until no traces of water appeared in the
effluent. About two pore volumes of kerosene had to be injected in
the core sample to reach the irreducible water saturation (Swir) at
30%. Consequently, the initial kerosene saturation (hydrocarbon
pore volume) was 70% which is equivalent to 200 cm3. The core effec-
tive permeability to kerosene (ko) was then measured at Swir and
found equal to 98 md.
2.2.3. External foam generation
Foam was injected into the core sample in a horizontal position by
two methods:
1. Continuous foam injection Foam of a pre-determined quality was
generatedin thefoam generating unit (see Fig. 1) and continuously
injected into thecore samplefor thefull term of theexperiment.Oil
displacement and recovery by this foam injection scheme were ob-
served and monitored vs. time under a pressure differential of
15 psi across the core. Tests were performed for foam qualities of
70, 80, and 90% with injection pressure near 830 psi.
2. Slug injection of foam foam was generated in the foam generat-
ing unit and continuously injected into the core sample until free
gas production broke through at the outlet. From the time of gas
break through only gas was injected under the same pressure con-
ditions. Oil displacement and recovery by this foam slug followed
by gas injection scheme was monitored vs. time under a pressure
differential of 15 psi across the core. Tests were performed forfoam qualities of 70, 80, and 90% with injection pressure near
830 psi.
2.2.4. Core cleaning
After each test liquid propane was injected into the core sample at
150 psi for 8 to 10 h. Liquid propane has the ability of extracting the
foaming agent that has been adsorbed by the sand grains without af-
fecting the irreducible water saturation. Vacuum was then pulled at
one end of the core for 5 h while the other end connected to the kero-
sene pump. The purpose of vacuuming is to extract the residual liquid
propane in the core. Pure kerosene was then injected at a rate of
224 cm3/h to ensure complete core cleaning and re-saturation. The
surface tension of the effluent kerosene was continuously measured
and compared with that of the pure kerosene, and when the twovalues were equal, the porous medium was free of any residual foam-
ingagent. At that point theeffective core permeabilityto kerosene was
found to restore itsoriginalvalue of nearly98 md. Three pore volumes
of kerosene had to be circulated in the core to restore its original state
of permeability and saturation.
2.2.5. Reference tests
Two reference tests were conducted for comparison purposes and
these include oil displacement by gas drive and oil displacement by
water drive.
2.2.6. Results and discussion
This part of the study consists of two sets of experiments and each
set includes of three runs. Each run in the first set involves oil
Fig. 6. Plastic viscosity of oil foam.
Fig. 7. Yield stress of oil foam.
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displacement by continuous foam injection for a specifi
c foam quality.Each run in the second set involves oil displacement by injection of a
slug of foam of a certain quality until gas breakthrough followed by
dry gas injection. A summary of the results of the two sets of experi-
ments and their corresponding reference tests are presented in
Table 3.
When foam was continuously injected throughout the experiment,
foam quality was the only variable. Tests for foam qualities of 70, 80,
and 90% conducted under 15 psi pressure differentials have resulted
in oil recoveries of 56.5, 51, and 49% of the initial oil in place, and that
1.225, 1.127, and 1.1078 pore volumes of foam had to be injected to
achieve these oil recoveries, respectively. Therefore, ultimate oil
recoveries seem to be higher with lower foam qualities or foams with
lower viscosities. This observation is consistent with Minssieux (1972)
conclusions. The results of this set of experiments also show that for
the three foam qualities there has been an incremental increase in oil
recovery of 8.0, 5.25, and 4.25% over that of the corresponding gas
drive test, respectively (see Fig. 8).
When foam was injected as a slug, foam quality was once again
the only variable. Slug sizes were determined by observing gas break-
through and for foam qualities of 70, 80, and 90% the slug sizes were
141, 115, and 83 cm3, respectively. The corresponding oil recoveries
were 52, 49, and 47.5% of the initial oil in place. Higher foam qualities
have resulted in earlier gas breakthrough, smaller slug size, and lower
oil recovery, consistent with Minssieux (1972) observations with
foamed water. The results of this set of experiments also show that
for the three foam qualities there has been an incremental increase
in oil recovery of 5.75, 4.25, and 3.5% over that of the corresponding
gas drive test, respectively.
A comparison between the performances of one pair of tests, one
from each set of the above experiments, for foam quality equal to
90% is shown in Fig. 9.In an attempt to explain the existence and flow mechanism of oil
foam inside the porous medium, a conceptual model of capillary tubes
was implemented to predict the experimental results of foam tests.
This theoretical model is based upon the assumption that porous
media maybe represented by a bundleof variousradii, straight capillary
tubes connected only at the ends. The velocity and distance travelled by
the fluids in each one of these capillary tubes are calculated with
Poiseuille's law (1962) for laminar flow and the results in terms of
fluid volumes vs. time are then compared with the experimental data.
The radii of the theoretical capillary tubes were determined by the
miscible displacement test procedure proposed by Klinkenberg
(1957) and the results are illustrated in Fig. 10. Klinkenberg showed
that the pore size distribution of porous media is a function of the
technique used in running the test and that a wider distribution
would be obtained when the capillary pressure technique is applied.
However, the results of the miscible displacement test were imple-
mented in this study because of the size of the core sample. The
derivation of foam velocity equation in the process of oil displace-
ment by oil foam is presented in Appendix A. A similar approach
was applied in the development of the oil velocity equation in the im-
miscible displacement process of water by oil, and the gas velocity
equation in the immiscible displacement process of oil by gas.
In the process of oil displacement by water (reference test), a rea-
sonable match between the experimental data and the results of the
conceptual model is obtained as shown in Fig. 11. The breakthrough
time is matched by adjusting the value of cos in the capillary term,
which is positive in this case, and is found equal to 20. This small
value of contact angle is indicative of the strong wettability of the
coresample to water. Referringto Fig. 11, the capillarytubes model pre-dicted higher oil recoveries than the experimental results after water
breakthrough and would eventually produce all the oil in place. The
discrepancy mayhave been partially the resultof application of the mis-
cible displacementtechniquein deducing the pore size distribution. The
capillary tubeflow model, however, have shown fairly goodpredictions
Table 3
Summary of foam tests results.
Type of test and foam p (psi) Foam
quality (%)
Oil recovery %
of OOIP
A. Externally-generated foam
A.1) Horizontal configuration continuous
foam injection.
15 70 56.5 (40.5)a
15 80 51.0
15 90 49.0
A.2) Horizontal configuration slug foam
injection followed by gas injection.
15 70 52.0
15 80 49.015 90 47.5
B. Internally-generated foam
B.1) Horizontal configuration slug size
of 40 cm3.
15 61.5 (40.5)
5 66.5 (42.0)
2.5 70.0 (42.5)
B.2) Horizontal configuration slug size
of 20 cm3.
15 52.5 (40.5)
5 60.0 (42.0)
2.5 66.0 (42.5)
B.3) Vertical configuration slug size
of 40 cm3.
5 85.5
B.4) Vertical configuration slug size
of 20 cm3.
5 74.0
a Numbers within brackets represent gas-drive oil recoveries at the indicated pressure
differential.
Fig. 8. Performance of oil displacement by continuous injection of externally-generated
oil foam; (p =15 psi).
Fig. 9. Performance of oil displacement by continuous injection of externally-generated
oil foam and by continuous injection of externally-generated oil foam followed by gas
injection; p =15 psi and =90%.
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of oil recoveries in the continuous foam injection process. A sample ofthese results for foam quality of 70% is illustrated in Fig. 12. Failure to
match the initial gas breakthrough time may be partially attributed to
the fact that the capillary tubes model implicitly assumed that foam
did not degenerate while propagating inside the core sample. Thus, it
may be postulated that foam was breaking and regenerating inside
the core.
Nicklin and Koch (1968) suggested that in gasliquid systems, the
liquid leaves a film behind as it is being displaced by the gas and that
at low interfacial shear stress the film thickness can have a wide
range of values. However, their mathematical expression of film
thickness did not agree with his observed data. In their study and
assuming constant liquid film thickness, the oil recoveries by gas
drive predicted by the conceptual model did not match the experi-
mental results. However, when the liquid film thickness is set assome function of capillary tube radius a fairly good match is obtained.
In this study an empirical expression is developed that correlates liq-
uid film with capillary tube radius and as follows.
ft 1:904E 16e2:144E05 r
1
The reduction in film thickness in the presence of foams may ex-
plain the improvement in oil recovery. In fact, foam tests have
shown a longer recovery life after gas breakthrough which may be in-
dicative that foam did reducethe oilfilms left behind the gas front and
therefore increased oil recovery. Theflow of foam in the systemmight
have been a series of slugs, gasoil-foam, not known but postulated.
No attempt has been made to simulate this type offlow with the cap-
illary tubes model. An excellent treatment of liquid film creation and
mobilization can be found elsewhere (Rossen, 1996).
2.3. Oil displacement by internally generated oil foam
In this part of the study a series of six of tests were conducted withthe core sample in a horizontal position. These tests involved the injec-
tion of a certain volume of kerosene-surfactant solution (slug) in the
core sample followed by gas injection. Being porous and permeable,
the core sample thus acts as a foam-generating unit wherein foam is
generated inside the core. Two sets of experiments (three runs each)
representing two slug sizes of 20 cm3 and 40 cm3 were conducted
under pressure differentials of 15, 5, and 2.5 psi. For comparison pur-
poses, two additional runs were performed for the same slug sizes at a
pressure differential of 5 psi with the core in a vertical position.
2.3.1. Results and discussion
A summary of the results of this part is also illustrated in Table 3
and a brief discussion of these results follows.
1. Horizontal core configuration For the 20 cm3
slug size the observedoil recoveries were 52.5, 60, and 66% of the initial oil in place at
pressure differentials of 15, 5, and 2.5 psi, respectively. The corre-
sponding volumes of gas injection were 1.2858, 1.1903, and 1.1653
hydrocarbon pore volumes, respectively. For the 40 cm3 slug size
the observed oil recoveries were 61.5, 66.5, and 70% of initial oil in
place at the above pressure drops and their corresponding injected
gas volumes were 1.1804, 1.140, and 1.1111 hydrocarbon pore vol-
umes, respectively. In both sets of experiments, a significant increase
of oil recovery was observed over the gas drive test under similar
pressure drop conditions. For the above pressure differential levels,
the 20 cm3 slug internally-generated foam tests have shown incre-
mental increase of oil recovery of 6, 9, and 11.75%, respectively. The
40 cm3 slug internally-generated foam tests have shown incremental
increase of oil recovery of 10.5, 12.25, and 13.75%, respectively.
Fig. 10. Analysis of pore size distribution.
Fig. 11. Comparison between experimental and theoretical results of oil displacement
by continuous foam injection; p =15 psi, f=0.051 poise and =70%.
Fig. 12. Calculated average gas saturation curves; p =15 psi.
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2. Vertical core configuration The effect of slug size on foam effective-
ness in displacing oil was investigated under 5 psi pressure differential
with foam flowing downward. Observed oil recoveries were 74 and
85.5% of the initial hydrocarbon pore volume for the 20 cm3 slug and
40cm3 slug, respectively. These oil recoveriesrepresent14 and19% in-
crease over the horizontal tests under similar pressure differentials.
Also, with the vertical core configuration, gas breakthrough time is
50 min longer than that for the horizontal core configuration coupled
with a signifi
cant decrease in observed produced gas volumes.
2.3.2. Horizontal core configuration: internal vs. external foam
generation
At 15 psi pressure differentials, tests of externally-generated continu-
ous foam injection at 70% quality have shown similar performance to
tests of internally-generated foam with slug size of 40 cm3 (20% of the
hydrocarbon pore volume). The liquid content of this slug would be
enough to completely saturate the core pore volume with 80% quality
foam. Likewise, tests of externally-generated continuous foam injection
at 80% quality have shown similar performance to tests of internally-
generated foam with slug size of 20 cm3 (10% of the hydrocarbon pore
volume). The liquid content of this slug would be enough to completely
saturate the core pore volume with 90% quality foam. Dueto this similar-
ity in the results, no attempt was madeto model the internally-generated
foam tests. However, it must be resolved whether the foam was generat-
ed within the core or only at the producing face.
The existence of foam within the core during the displacement
test may be indicated by relative permeability calculations. In this
study the Welge's method (1952) of calculating relative permeability
ratio for gas displacing oil is modified for foam displacing oil. Accord-
ing to Welge (1952) and neglecting capillarity, the fractional flow of
gas at the producing face may be expressed as,
fg
p qg= qg qo
1= 1 kog=kgo
h i2
Solving for the ratio kg/ko,
kg=ko 1= 1=fg
1h i
o=g
h in o3
If all the gas is flowing as foam then the above relationships may be
written as,
ff
p 1= 1 kof=kfo
h i4
kf=ko 1= 1=ff
1
h io=f
n o5
where:
(fg)p is fractional flow of gas at the producing end, dimensionless,
(ff)p is fractional flow of foam at the producing end, dimensionless,kg, ko, kf are effective permeabilities to gas, oil, and foam, respectively,
Darcy,
g, o, f are viscosities of gas, oil, and foam, respectively, cp.
Ifsome ofthe gas isflowing as foam, then (fg)p maytake the following
expression,
fg
p qg qf
= qg qf
qo qf 1
h in o6
where is foamquality, fraction. Theapparent gas saturation at the pro-
ducing end may be expressed as,
Sg
p
Sg Sf 7
Therefore,
1
Sg
p
So Sf 1 8
where:
fg
p is apparent fractional flow of gas at the producing end,
dimensionless,
Sg
p is apparent gas saturation at the producing end,
fraction, qg, qo, qf are free gas flow rate, in-place oil flow rate, and
foamflow rateat the producing endcalculated at downstreampressure,respectively, cm3/s, Sg, So, Sfare free gas saturation, in-place oil satura-
tion and foam saturation at the producing end, respectively, fraction,
and oil and gas regardless of their source, however, were being
monitored with time at the separator. Hence, Eq. (2) is implicitly set
equal to Eq. (6) and the fractional flow of gas at the producing end
was thus calculated. Data including cumulative oil produced (Qo), cu-
mulative gas produced (Qg), and cumulative gas injected percent of
hydrocarbon pore volume (Gi)HPV are employed to calculate average
gas saturation at the producing end (Sg)AV, fractional flow of oil, kg/ko
and apparent gas saturation at the producing end
Sg
p
. The results
of these calculations for gas-drive test, 20 cm3-slug size internally-
generated foam test and 40 cm3-slug size internally-generated foam
test, all under 5 psi pressure differential, are plotted as (Sg) AVvs. (Gi)HPV
and kg/ko vs.
Sg
pas illustrated in Fig. 13 and Fig. 14, respectively. It
can be observed that for a given kg/ko average gas saturation at the pro-
ducing end (Sg)AVis greater for greater slug size. Also, for a given ( Sg)AVa higher kg/ko ratio corresponds to the smaller slugsize. This dependence
of internalflow characteristics on liquid slug volume indicates that foam
was generating within the core sample. Similar observations are found
for the above tests at pressure differentials of 2.5 psi and 15 psi.
Mathematically, it can be shown that most of the free gas was
actually flowing as foam by considering the following steps:
1. From gas-drive test, plot fgvs. Sg, both at the producing end. Deter-
mine (Sg)AVat different locations on the fgvs. Sgplot by extrapolat-
ing the slopes at these locations to fg=1.0. Report the values offgand their corresponding values of (Sg)AV.
2. Assume total production rate under flowing conditions (qt) to be
constant and calculate ko for each value of (Sg)AV determined in
step 1 by solving the following equation.
qt 1 fg
SGAV
A ko=o p=L h
9
Fig. 13. Gas/oil permeability ratio; p =5 psi.
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where:
qt is total production rate under flowing conditions, cm3/s,
(fg)SGAV is fractional flow of gas at (Sg)AV, dimensionless,
A is cross sectional area of the core sample, cm 2,
ko is effective permeability to oil, Darcy,
o is oil viscosity, cp,
p is pressure drop across the core sample, atm.,
L is core length, cm.
3. Plot ko vs. (Sg)AV on the same graph paper of the kg/ko- Sg
p plot
(such as Fig. 14) and for each value ofko draw a horizontal line and
observe its intersection with the ko curve. From the intersection
point proceed vertically upward or downward as may deem neces-
sary to intersect with the kg/ko
Sg
pcurve. The new intersection
point should yield the value of kg/ko and its corresponding value of
(Sg)AV, and hence, the effective permeability to gas at this (Sg)AVcanbe determined. Repeat this step forother valuesofko and arrange
the results in a table form that contains ko/kabs, kg/kabs and (Sg)AV,
where kabs is the absolute permeability of the core sample.
4. Plot ko/kabs and kg/kabs vs. (Sg)AV.
5. The measured gas production rate and oil production rate at the
outlet face of the core may be expressed in terms offluids perme-
abilities as follows.
qg kg=g
kf=f
h i10
qo ko=o kf 1 =f
h in o11
Therefore,
kg
Sg
= ko So g=o
qg kf=f
=qokf 1 =f
h in o12
where:
qg and
qo are slopes of production performance curves at any
Sg
p; cm3/s, and kf is effective permeability to foam, Darcy.
The foam saturation that makes both sides of Eq. (12) equal may
be determined by the following proposed trial and error procedure.
a) Select test conditions ofp and slug size.
b) For any
Sg
p, determine the corresponding qg and
qo .
Guess on Sg Calculate Sf using Eq. (7), knowing foam quality ()
Calculate So using Eq. (8)
Determine kgat Sgand ko at So from the plot constructed in step
3 above. Assuming that foam has the same flow characteristics
as oil, kf at Sf can be estimated from the ko vs. So curve. Substitute values ofkg, ko, kf,
qg,qo , , g, o and f in Eq. (12).
If both sides are equal then the correct value of Sfhas been de-
termined, otherwise a new guess on Sghas to be made and the
calculations are repeated.
It is found that lower values ofSgwould result in a match between
the values of both sides of Eq. (12) indicating that most of the injected
gas was flowing as foam inside the core sample. A complete numeri-
cal example on the application of the proposed iterative scheme
calculations is presented in Appendix B.
The observed performance of oil displacement by internally-
generated oil foam has shown decreased oil recoveries with increased
pressure differentials. It seems that the resident time of gas in porous
media is a crucial factor in generating foams.Assumingthat foam hasa normaldistribution of bubble sizes, then at
a low pressure differential foam moves first into the largest pore chan-
nels until a large bubble comes along and blocks the pore opening to
the point where foam is injected into the next smaller size pore channel.
Depending on the foam stability, the large bubble has a limited lifetime
and the blocking effect should end to allow gas and foam to flow once
again in the large pore channel until another large bubble comes along.
This sequence of entering large and small pore channels will continue
until the entire permeable section accepts foam. At higher pressure dif-
ferentials, however, chances are such that large bubbles may deform
and/or shear and flow of gas and foam in the large pore channels may
continue without entering the small pore channels, resulting in lower
oil recoveries. Earlier gas breakthrough were observed to associate
with higher pressure differentials which supports the aforementioned
hypothesis and indicates that gas and/or foam moved faster within the
large pore channels. Similar interpretations regarding the mechanism
of foam flow in porous media were reported by others (Alvarez et al.,
2001; Aronson et al., 1994; Katib et al., 1988; Mamun et al., 2002 ).
3. Conclusions
Based on the experimental results of this study it may be concluded
that:
1. Oil foams behave as non-Newtonianfluidsand their behavior closely
fit the Bingham-plastic model. These foams, however, have shown a
much lower yield point than water foams of similar foam quality
range.
2. The viscosity of oil foams is found to increase as the foam quality isincreased.
3. Tests of continuous injection of externally-generated foams have
shown 4.5, 2.0 and 1.5% higher oil recoveries than tests of slug
foam injection followed by gas drive for foam qualities of 70, 80
and 90% qualities, respectively. These differences might be partially
the result of continuous foam injection.
4. Based on the capillary tubes conceptual model, the externally-
generated oil foam appears to flow partially as foam inside the core
sample.
5. For multiphase flow systems involving wetting and non-wetting
phases, the capillary tubes model seems to be a realistic or at
least an adequate measure of duplicating laboratory observations.
6. The capillary tubes model also appears to be a reasonable approach
to determine rock wettability.
Fig. 14. Fractional flow of gas (gas drive test at p =5 psi).
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7. The reduction in liquidfilm thickness may explain the improvement
in oil recovery in the presence of foams.
8. Internally-generated oil foams with slug sizes of 20% and 10% of the
hydrocarbon pore volume have shown similar flow characteristics
and mechanism to externally-generated oil foams with foam quali-
ties of 80 and 90%, respectively.
9. Utilizing gravity in tests performed with vertical core configuration
is found to increase the effectiveness of oil foam in the displacement
of oil in porous media and to further improve the recovery of oil.Hence, a foam blanket between the oil zone and the gas zone could
provide a successful oil recovery technique.
Nomenclature
A cross sectional area of the core sample, cm2,
(fg)p fractional flow of gas at the producing end, fraction,
(ff)p fractional flow of foam at the producing end, fraction,
fg
p
apparent fractionalflow of gas at the producing end, fraction,
(fg)SGAV fractional flow of gas at (Sg)AV, fraction,
ft liquid film thickness, cm,
(Gi)HPV cumulative gas injected percent of hydrocarbonpore volume,
fraction,
kabs absolute permeability of core, Darcy,
kf, kg, ko effective permeabilities to foam, gas, and oil, respectively,Darcy,
L core length, cm,
Lf foam length, cm,
Lo oil length, cm,
pi inlet pressure, dunes/cm2,
pint pressure at the foamoil interface, dynes/cm2,
po outlet pressure, dynes/cm2,
qf, qg, qo flow rates of foam, free gas, and in-place oil at the producing
end calculated at downstream pressure, respectively, cm3/s,
qt total production rate under flowing conditions, cm3/s,
Qg cumulative gas produced, cm3,
Qo cumulative oil produced, cm3,
qg slope of gasproductionperformance curve at any Sg
p;cm3/s,
qo slope of oilproduction performance curve at any Sg
p;cm
3
/s,R capillary tube radius, cm,
Sf, Sg, So foam saturation, free gas saturation, and in-place oil satura-
tion at the producing end, respectively, fraction,
(Sg)AV average gas saturation at the producing end, fraction,
Sg
p; apparent gas saturation at the producing end, fraction,
Swir irreducible water saturation, fraction,
vf foam velocity, cm/s,
vo oil velocity, cm/s.
Greek letters
p pressure drop across the core sample, atm,
foam quality, fraction or percent,
f, g, o, viscosities of foam, gas, and oil, respectively, cp.
Appendix A. Derivation of foam velocity equation when displacing
oil by oil foam
According to Poiseuille's Law (1962) for laminar flow of a fluid in
capillary tubes, foam velocity can be expressed as
vf r2
pipint =8fLf A 1
where:
vf
foam velocity, cm/s,
r radius of capillary tube, cm,
pi inlet pressure, dunes/cm2,
pint pressure at the foamoil interface, dynes/cm2,
f effective foam viscosity, poise,
Lf length of foam, cm.
Similarly, oil velocity can be expressed as
vo r2
pintpo =8oLo A 2
where:
vo oil velocity, cm/s,
po outlet pressure, dynes/cm2,
o oil viscosity, poise,
Lo oil length, cm.
Rearranging Eq. (A-1) and solving for pint yields
pint pivf 8fLf=r2
Substituting in Eq. (A-2)
vo r2
pivf 8fLf=r2
h ipo
n g=8oLo
Simplifying and solving for vf, yields
vf r2
pipo 8oLovo =8fLf
But vf= vo and Lo=LcLf, where Lc is the length of capillary tube, cm,
and therefore
vf r2
pipo = 8fLf 8o LcLf
h iA 3
Appendix B. Estimating foam saturation (Sf) using the proposed
iterative scheme procedure of calculations
Given information:
Pressure differential across core sample=5 psi
Surfactantsolution slug size= 20 cm3
Foam quality= 80%
Foam viscosity= 6.1 cp
Oil viscosity= 1.458 cp
Gas viscosity=0.0178 cp
Apparent gas saturation at the producing end,
Sg
p; is deduced
from Fig. 12.
q g and q o values which correspond to
Sg
p; are deduced from
Fig. 13.
The fractional flow of gas drive curve is presented in illustrated in
Fig. 14 and the calculated ko at different average gas saturations are
listed in Table B1.
The relative permeability curves for gas and oil are plotted as illustrat-
ed in Fig. B2. Let
Sg
p=0.50, therefore,
qg =0.0114 cm3/s and
qo =
0.0015 cm3/s.
Assume Sg=0.21 and apply Eq. 7 to calculate foam saturation as fol-
lows. Sf=
Sg
p=Sg=0.500.21= 0.29; and thus Sf=0.29/0.8=0.36.
The oil saturation is then calculated by rearranging Eq. 8, So= 1
Sg
pSf (1) =10.30.50.36 (10.8)=0.428.
Next, Fig. B2 is used to find the effective permeability to oil, gas
and foam and the results are:
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ko at So=0.144E03 Darcy, kg at Sg=0.019E03 Darcy and kf at
Sf=0.043E03 Darcy.
Substituting these values into Eq. (12), it is found that the L.H.S. =
0.132 and the R.H.S.= 0.09966. Hence, another guess on Sg must be
made. Since the L.H.S. is greater than the R.H.S. then a lower value
ofSg should be assumed.
Setting Sg=0.17 results in Sf=0.413, So=0.418 and from Fig. B2
the values of ko, kg and kf are deduced to be 0.135E03 Darcy,
0.014E03 Darcy and 0.144E03 Darcy, respectively. Substituting
these results in Eq. (12) the LH.S.=0.1037 and the R.H.S.=0.09976
which are much closer than before and the correct value of Sgwould be a little less than 17%. Using straight line convergence ap-
proach the correct value of Sg is found equal to 0.167. Therefore, for
foam quality of 80% the foam saturation was found to be 0.413 and
80% of that was measured as free gas.
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Fig. B1. Permeability ratios vs. apparent gas saturation at producing end curves; gas
drive test; p =5 psi.
Fig. B2. Relative permeability curves; gas drive test at p =5 psi.
Table B-1
Results of determination ofko/kabs ratio.
(Sg)AV (fg)SGAV ko (md) ko/kabs
0.32 0.840 10.464 0.0727
0.39 0.940 3.924 0.0273
0.45 0.983 1.112 0.0072
The ko/kabs values are then plotted on the kg/kovs. Sg
pgraph as shown in Fig. B1. The
corresponding kg/ko values at (Sg)AV are illustrated in Table B-2.
Table B-2
Results of determination ofkg/kabs ratio.
(Sg)AV ko (md) kg/ko kg (md) (kg/kabs) 100 (ko/kabs)100
0.32 10.464 0.04 0.4186 0.300 7.267
0.39 3.924 0.70 2.7468 1.908 2.725
0.45 1.112 41.00 44.500 30.902 0.772
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