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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: [email protected].

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

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / p e t r o l
http://dx.doi.org/10.1016/j.petrol.2011.08.013http://dx.doi.org/10.1016/j.petrol.2011.08.013http://dx.doi.org/10.1016/j.petrol.2011.08.013mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.petrol.2011.08.013http://www.sciencedirect.com/science/journal/09204105http://www.sciencedirect.com/science/journal/09204105http://dx.doi.org/10.1016/j.petrol.2011.08.013mailto:[email protected]://dx.doi.org/10.1016/j.petrol.2011.08.013


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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

102 H.H. Al-Attar / Journal of Petroleum Science and Engineering 79 (2011) 101112


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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%.


oil foam (present study). Foam quality range: 8082%.


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.


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.


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:



11/12

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

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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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