Foam as a gas-blocking agent in petroleum reservoirs II: Mechanisms of gas blockage by foam

Journal of Petroleum Science and Engineering, 10 ( 1993) 135-156

135

Elsevier Science Publishers B.V., Amsterdam

Foam as a gas-blocking agent in petroleum reservoirs II: Mechanisms of gas blockage by foam Jan Erik Hanssen Rogaland Research (RF), Box 2503 Ullandhaug, N-4004 Stavanger, Norway (Received November 6, 1992; revised version accepted August 20, 1993)

ABSTRACT An experimental study is reported on gas-blocking foam in porous media. The methods used were visual observations of pore-level events and macroscopic displacement-front movement, an analysis of pressure-driven foam generation experiments in beadpacks, and the measurement of in situ saturation and pressure profiles. A qualitative characterization of the gas-blocking state consistent with previous observations is developed, including a simple analytical model for the generation of gas-blocking foam and a description of gas transport through a network of stagnant foam films.

Introduction

The use of foam to selectively control the mobility of injected gases or to reduce gas influx into producing wells has been much studied. Since the earliest investigations (Holbrook and Bond, 1958; Fried, 1961; Holm and Bernard, 1964), the behavior of foam confined in a porous medium has been studied by two different experimental approaches, defined here as rate-driven and pressure-driven. In rate-driven experiments, fluids are fed into the porous medium at controlled flow rates. The most common procedure is to coinjeer gas and foaming-agent solution into a porous medium (at some initial saturation state ), until a macroscopically steady state is observed. In pressure-driven experiments, the inlet and outlet pressures are controlled, flow rates and fractional flows are the resultant variables; most commonly gas is injected into porous media saturated with surfactant solution and residual oil. A recent status summary pointed out that foam properties may depend on the experimental procedure used, with the pres-

sure-driven mode being less well characterized (Hanssen, 1992), A companion paper (Hanssen, 1993, this issue) describes a series of pressure-driven experiments with foam in long porous media at flow rates and pressure gradients typical of reservoir flow. Foam generation produced low liquid saturations, at which liquid ceased flowing as a separate phase. Gas, then, is the only phase entering and leaving the porous medium; the flow rate and differential pressure corresponding to an apparent permeability of gas through foam is orders of magnitude lower than that of a foam-free case. These properties define the gas-blocking state of a confined foam; essentially transient but often persisting for months (Holm and Bernard, 1964; Persoff et al., 1990). This attracted some interest in the 1960s (Holm and Bernard, 1964; Grktekin, 1968; Holm, 1968; Holm and Bernard, 1970; Marsden and Albrecht, 1970; Raza, 1970), but has been less studied in recent years than the flowing steady state (De Vries and Wit, 1990; Heller and Lee, 1990; Persoffet al., 1991; Radke and Ettinger, 1992 ). Despite early reports indicating that the gas-blocking state

0920-4105/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.

136

occurred mainly in oil-free systems (Holm and Bernard, 1964; Holm, 1968 ), foams have been found that produce strong gas blockage in the presence of crude oil at high temperatures (Hanssen and Dalland, 1990), at full reservoir conditions (Hanssen and Dalland, 1991 ), and even by foaming a non-aqueous, nonwetting liquid (Hanssen and Haugum, 1991 ). The sensitivity of gas blockage to experimental parameters is characterized in the companion paper (Hanssen, 1993, this issue ). Of particular importance is the oil/foam interaction (Hanssen and Meling, 1990; Dalland et al., 1992), and the length of the porous medium (Hanssen and Haugum, 1991; Hanssen, 1993 ). Maintaining foam at the gas-blocking state is critical for controlling high gas/oil ratios in production wells (Heuer and Jacocks, 1968; Hanssen et al., 1989; Ekrann and Hanssen, 1990), but other applications may also depend on the blocking and diverting action of foam. Based on field experience, the practicality of "driving foam through a reservoir" was in fact questioned at an early date (Holm, 1970). The growth of a foam bank for at most a few meters, until flow stops, was argued as well as its main reservoir effects. Note that this does not preclude deep penetration, because foam treatment is not synonymous with foam injection: foam can be generated from injected gas and surfactant solution where local conditions are favorable. Most approaches to foam modeling do not represent the gas-blocking state (Falls et al., 1988; Islam and Farouq Ali, 1990; Patzek and Koinis, 1990; Friedmann et al., 1991; Radke and Ettinger, 1992). Gas trapping may be include, but no physical description of the trapped fraction as a function of measurable parameters has been derived. The study described in this paper investigated the possibility for a description of foam in porous media that fits the observations of the gas-blocking state better. For this, the mechanisms governing each of the three stages in the life of a gas-blocking foam must be described, i.e.:

J.E. HANSSEN

The gas/surfactant displacement generating foam and gas blockage; -Fluid transport through foam at the gasblocking state; and Loss of gas blockage at extended times or increased differential pressures. The aim of this paper is to develop a phenomenological understanding of these processes consistent with experimental evidence. This is attempted through the following three steps: (1) Pore-level observation in etched-glass micromodels; (2) Analysis of selected aspects of beadpack experiments; and (3) Measurement of Sw and pressure profiles in a foam-filled long porous medium. Pore-level o b s e r v a t i o n s Etched-glass micromodels are useful tools in multiphase flow studies, allowing direct observation of pore-level events, although the observations are limited to qualitative information because of their size and twodimensionality. Foam is one area in which micromodel studies have been instrumental (Mast, 1972; Owete and Brigham, 1987; Prieditis, 1988; Huh et al., 1989; Armitage and Dawe, 1990; Radke and Chambers, 1991 ). The present work was intended to shed light on phenomena controlling pressure-driven foam generation and the gas-blocking state.

Micromodel apparatus Two different micromodels were used, both strongly water-wet: the first etched with a regular pore pattern and the second etched from an enlarged (5x) image of a thin section of Kuparuk sandstone. Micromodel preparation has been described in Buckley (1991). The micromodels used a microscope, an image-recording system, and facilities for feeding fluids at fixed pressures or rates (Fig. 1 ). The microscope used with the regular model allowed

FOAM AS A GAS-BLOCKINGAGENT IN PETROLEUM RESERVOIRSII

~h - o-3m liq-

137

~ ~

video camer^ ~ptical microscope

inl '0-0.8bar Fig. 1. A p p a r a t u s for m i c r o m o d e l studies for foam at pressure-driven conditions. TABLE 1

Observations in regular micromodel

Properties of micromodels used Property

Regular pattern

Sandstone pattern

Pore area length × width ( m m ) Effective pore depth (#m) Pore throat diameter (/tm) Pore body diameter (#m) Measured internal volume (#1) Measured permeability (darcy) Porosity

98 × 29 150 50 150 165+10 38 _+5 ~ 0.4

70 × 44 75-125 25-125 150-300 180+30 2.2 + 0.5 0.42

magnifications to 600 ×; a single pore filled the entire field of view. Precise location of sites was possible using a frame and an x/y stage. The regular model was not fused to facilitate cleaning, but held together by the frame and a removable adhesive. The micromodel studies were done at atmospheric outlet pressure, ambient temperature, using doubly-distilled filtered water, and nitrogen gas, in the absence ofoil. Key properties are listed in Table 1. Pore diameters for the regular model were read from video images; values for the sandstone model are those of a previous study (Chambers, 1990). Internal volumes were measured gravimetrically.

In the regular-pattern model, the pore depth was measured with a mechanical depth gauge and porosity was estimated from the number and area of etched flow channels. The measured permeability is as expected for these pore sizes. A gas/water displacement was done first and produced lenses, pockets of water and instantly coalescing lamellae. Next, the model was saturated with 0.50% Hostapur SAS and gas introduced in the same manner. In two repeat experiments, AP~ 0.2 bar (all pressures quoted are absolute) initiated liquid production. Generation of lenses, lamellae, and bulklike foam occurred within seconds. After the first minute, leave-behind events as described by Radke and Chambers (1991) were observed, though lamella generation by snap-off was rare. No lamellae were seen translating from pore to pore, and no flow out of the micromodel was measured. (The term near-zero flow is used, as flow through minute leaks rather than the outlet channel cannot be entirely eliminated.) A characteristic "breathing" was noted: Lamellae periodically oscillated in their pore throats, the frequency and amplitude of oscillation varied in time. The

138

J.E. HANSSEN

Fig. 2. Foam in a regular-pattern micromodel; 0.5% Hostapur SAS in distilled water; LIP~0.2 bar. Digitized still photographs.

breathing was transmitted over large areas. Breathing periods initially lasted for a few minutes, with stagnant periods in between. Over the next hour at the original ziP, breathing periods became shorter and stagnant periods longer. The gas pressure was next increased to ~ 0.4 bar, which caused breathing to intensify and some lamellae to rupture in their pore throats. Lamella generation events occurred, but were too infrequent for precise identification of the mechanism. It is believed that a variety of snap-off mechanisms (Radke and Chambers, 1991 ) must have been operating, because there was too little liquid left in the pores for generation by leave-behind and no moving lameUae that could divide. No sites were seen to produced multiple lamellae and most of the porelevel events occurred within the first 10 min after the pressure increase. About 15 min after the pressure increase, flowing gas appeared in the outlet tubing, followed by some foam. Because no moving lamellae were seen in the po-

res, this foam must have formed at the outlet, which was obscured from view. Foam production was short-lived, but gas flow rate kept increasing. A new pressure increase to ~ 0.6 bar caused gas to flow faster, but no further lamella generation events and few additional ruptures were observed; breathing no longer occurred. Left overnight, noticeably fewer lamellae remained and the gas flow rate continued to increase. Figure 2 shows a representative picture of foam during the period of near-zero gas flow. Areas outlined in black are gas-flied pore sections, those outlined in grey contain liquid. The matrix ("rock") is light grey. Observations in sandstone micromodel Foam was generated from 0.50% BioTerge AS 40, an a-olefin sulfonate, in distilled water. A somewhat higher gas pressure ( ~ 0 . 3 bar) than in the regular model was needed to initiate surfactant displacement. Lamella genera-

FOAMASAGAS-BLOCKINGAGENTIN PETROLEUMRESERVOIRSII

139

Fig. 3. Foam in a sandstone-pattern micromodel. Site of lamella generation by snap-off and site of lamella termination are indicated; 0.5% BioTerge AS 40 in distilled water at 26°C. Digitized video images (composite of two frames). Scale is indicated by the large pore in upper frame which is approx. 300/~m in diameter.

tion and coalescence was more frequent than in the regular model, ascribed to the greater number of sites of suitable geometry and aspect ratio in the heterogeneous model, because both surfactants produce strong foams. In contrast to the regular model, flow of foam and gas out of the model was seen from the start, progressively more dominated by gas as the

model became depleted of surfactant. Fewer generation sites were active, and for shorter periods of time. The end result was a continuous-gas foam of little flow resistance. During the period of active generation and coalescence, several sites for snap-off and termination were examined. Events in different sites were often coupled. A typical snap-off site

140 at a narrow pore constriction is indicated on Fig. 3. Lamellae generated there moved rapidly through a tortuous pore channel and into the large pore body which was a termination site for thousands of lamellae, broken by "stretching and squeezing", or capillary-pressure-induced coalescence (Radke and Jimenez, 1989; Radke and Chambers, 1991 ). Note the lamellae just in the process of breaking. These two sites were always active simultaneously, for several periods of 5-10 min. Site coupling was very strong: not a single lamella broke on its way from site to site, and very few survived the killer site to move further downstream. The liquid contained in the flowing lamellae was seen to splash over the pore wall of the killer site as they broke. Despite the transport of large volumes of gas at high rate, no flow or accumulation of liquid was observed in the downstream pores. Between periods of activity, the flow channel connecting the two sites was static; only a few lamellae were situated near the generation site, displaying no curvature. Thus, there cannot have been any pressure difference between the sites during inactive periods, when flow must have been occurring elsewhere in the model. Liquid from the dead lamellae may have flowed back to the generation site during these inactive periods. A new cycle of generation, bubble-train flow and termination would start when enough liquid had collected at the generation site and a higher local gas pressure was applied triggered by some random event. The significance of these observations to gas-blocking foam is that a net flow of gas, impeded by moving lamellae, is conceivable without an associated net, timeaveraged flow of liquid. Summary of micromodel observations

Persistent gas blockage was not achieved in the two micromodels, although gas flow was blocked for some time in the regular m o d e l . The lack of gas blockage in the sandstone

J.E.HANSSEN model is most likely due to the enlargement from the actual rock pores. Gas blockage is difficult to achieve in media with very large pores (Holm and Bernard, 1964; Hanssen and Haugum, 1991; Hanssen, 1993 ). The low persistence of gas blockage in the regular model is ascribed to the insufficient length of the flow path (Hanssen and Haugum, 1991; Hanssen, 1993 ). Howevr, several valuable observations in understanding gas blockage were made: At near-zero gas flow rates, foam was not entirely stagnant but subject to periodic oscillations of stationary lamellae. When AP was increased at near-zero gas rate, lamellae or bubble trains were not mobilized. Rather, lamellae were broken, opening more pore channels to gas flow. Generation of new lamellae was observed for a brief period after a AP increase. Lamellae may move on a pore scale, impeding gas, e.g., from a generation site to a termination site, without necessarily causing a macroscopic net flow of liquid.

Analysis of pressure-driven foam generation In systems favorable for the generation of gas-blocking foam, a distinct displacement front forms after some distance of travel (Raza, 1970; Hanssen, 1993 ) as illustrated on Fig. 4. The near piston-like nature of the remaining displacement facilitates a simple analysis that can provide information about the growing foam without advanced in situ measurement techniques. The analysis is based on only what is termed the external data: production, inlet and outlet pressures, and front L

gasin ~

Xf

!iquidout

Fig. 4. Typical front behavior in fixed-pressuregas/surfactant solutiondisplacementin systemsfavorablefor the creation of a gas-blockingfoam.

141

FOAM AS A G A S - B L O C K I N G A G E N T IN P E T R O L E U M RESERVOIRS II

positions observed visually in a transparent pack. Assuming the presence of gas near the column walls to be identical to the pressure front (verified later), the overall/IP can be split between the section behind the front where foam is assumed to be present everywhere, and the section ahead of the front where only surfactant solution is present. Darcy's law can then be applied separately to each section. Ignoring gas compressibility:

( 1)

AP= APf + AP,iq A e l i q ]cA Qliq,out- ( 1 -xf)Lflliq

Q(xfL) APfA

= Og,in =

Q

(2)

2 f - - - -

(3)

S~f = 1 x f - Vp,liq xf

(4)

Produced liquid Vp,~iqis in pore volumes (at mean pressures of Pi, and Po,t); gas saturation in foam Sgf (foam quality) and foam mobility ).f are averaged over the growing foam. Foam mobility ( 2 = k / # ) is used for convenience; at this stage of the displacement two phases are still flowing, so free-gas viscosity cannot be used. The relative mobility reduction can be compared with gas-blockage performance data by multiplying the values of 2f by ,uJk. The application of Eqs. 1-4 to a previous experiment (Hanssen, 1993) is shown in Fig. 5. The foam front stabilized at a position x/ L,~ 0.12 and from there propagated at a nearly constant velocity of ~ 6 m / d . Note that most of the pressure drop occurred across the foam from the first measurement. This agrees with the micromodel observations of immediate lamella generation. The foam zone grew at a constant gas saturation of 0.80-0.85, a mobility three orders of magnitude lower than the surfactant-free case. The last measured mobility during growth of the foam bank corresponds (using the viscosity of free gas) to 3.6 mD. After breakthrough,

1

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front

advance,

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Fig. 5. Properties of growing foam in a pressure-driven gas/surfactant displacement, calculated from data in Hanssen (1993) using eqs. 1-4. N 2 displacing 2% Sulfotex R I F in distilled water in a 200-cm pack of 8 darcy glass beads, 21 ° C, AP= 1.5 bar, Pout ~ 5 bar; no oil. 33

(a)

, x,(tO 1

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Sw

(b)

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Fig. 6. Constructed pressure (a) and water-saturation profiles (b) for a growing strong foam in a piston-like, pressure-driven displacement.

no foam was produced out of the pack but liquid continued to drain slowly as the system was approaching its first gas-blocking state, at which kgf was measured as 2.3 mD. Considering the accuracy of the data and analysis, this

142

compares well with the last measured mobility during foam growth and indicates that the generation of foam and the establishment of a gas-blocking state is a continuous process. From the above analysis and only using external data, the model in Fig. 6 is constructed. The pressure and saturation profiles are shown for various points in time. The measured overall saturations and observed uniformity support the dashed lines for Sw. The average Sw behind the front is known at any time from Eq. 4. The pressure profiles for the liquid-containing portion of the pack, shown by solid lines, are known by Eq. 2, and the value at x / L = 0 is known. Over long periods, indications are that the pressure profile is uniform. As the present experiments provide no support for any other shape, straight lines are drawn to the observed location of the foam front xf(ti). Below, this simplistic model is tested on experimental data with measured Sw and P profiles. The model can be extended to include residual oil saturation and gas compressibility.

Measurement of in situ Sw and AP profiles Quantitative saturation and pressure profiles during pressure-driven foam generation and at the gas-blocking state was desirable in order to validate the foam generation model, test the conclusions of previous work from external data, and give information on the loss of gas blockage. A bead pack with multiple pressure taps was built and used in a flow apparatus with measurement of in situ water saturations by microwave attenuation.

Microwave apparatus A microwave apparatus for displacement studies was described by previous investigators (Sharma, 1987; Ettinger, 1989; Gillis, 1990). Local water saturation is measured by the attenuation of a microwave beam. A metal frame with a wave source, guides and detec-

J.E. HANSSEN

tors moves in the x- and y-directions by means of two stepper motors, allowing scans of the porous medium mounted on a table (see Fig. 7). A rectangular flow cell of packed-volume dimensions 95× 10× 1 cm was made from two half-cells of transparent polymethyl methacrylate joined by a flat rubber gasket, with removable inlet and outlet pieces. The cell has nine pressure taps in capillary contact with the packing and features for re-tightening. It was packed with 45-70/tm glass beads giving a pore volume of 380 cm 3 and a permeability of 1.7 and 1.5 darcy, respectively, in two different packings. Designed for 7 bar, the cell was operated at 3.5 bar and 26 °C. A BASIC program incorporating routines by Sharma (1987) was written to control the apparatus from an IBM XT computer and to record saturation and pressure data as ASCII files. Via two serial ports and a parallel port, the computer controls the entire apparatus, allowing flexible setup and unattended operation. For this experiment, a scan time of 2 s per location was used, covering 47 measurement points at x = 16.5-86.4 cm in 2 min with an accuracy in Sw of _+0.001 PV. Use of longer scan times will improve resolution. Pressures were measured to effectively _+0.01 bar. The input of gas to the beadpack was at fixed pressure. Gas can also be fed at fixed mass rate via a mass flow controller. A displacement pump delivers liquid at a fixed volumetric rate. Fluids flow out of the pack controlled by a sensing-piston back pressure regulator and are separated in an atmospheric separator allowing readings of liquid volume and gas rate by a bubble flowmeter. The foaming agent used in the test reported here was 0.50% Fenopon CD 128, an ammonium alkyl ethoxysulfate, in distilled water. It was chosen for its known tendency to form rather weak gas-blocking foams at test conditions, allowing breakdown as well as generation of foam to be observed over practical observation times.

143

FOAM AS A G A S - B L O C K I N G A G E N T IN P E T R O L E U M RESERVOIRS II

microwave transmitter

P2 P3

~

~'

Gas in

Pu mp

P4

P5

P6

P7

P9

P8

Pl - P9 at x = 5, 15, 25... cm. Microwave receiver below pack.

Liquid volu me I

Gas rate

BPR = back pressure regulator.

I

Fig. 7. Schematic representation of scanning microwave saturation flow apparatus with rectangular beadpack used. For details of microwave equipment, see Sharma (1987) and Ettinger ( 1989 ).

External observations 1.0

Production and pressure histories in the microwave experiment are shown in Fig. 8. As expected, the foam was a rather poor gasblocking agent. The front moved rapidly through the pack, followed by a long period of foam flow. The gas rate did not stabilize after liquid production ceased. Still, gas mobility was reduced by a factor of 40 or more through the passage of 500 pore volumes of gas. The improved gas blockage over that by the same surfactant in 8-darcy beads, where a kgf/ k ~ 0 . 1 was measured (Hanssen, 1993), is probably due to a lower permeability in the present test. The performance of this particular foam at these mild conditions is in fact a good model for that of a rather oil-sensitive foam at reservoir conditions.

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Time, hours

Several saturation scans are shown in the upper diagram of Fig. 9. An unexpectedly long gas finger (for a foam) to x / L ~ 0 . 2 is seen, due to imperfect packing. Once stabilized at x~

Fig. 8. Performance history of 0.5% Fenopon CD128 foam in microwave apparatus. (a) Production and (b) gas permeability and pressures. See text for details.

144

J.E. HANSSEN

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~ I

• I' \,

..j

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(hours):

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of scan

(hours) .....

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0.587 0,727 0.984 20.2 195

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3.2 0.1

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F i g . 9. Measured saturation (top) and pressure ( b o t t o m ) profiles for foam # 2 0 7 .

L ~ 0 . 4 , the front was piston-like for the remaining displacement, and saturations in the bypassed area were homogenized a few hours after breakthrough. The long period of intermittent gas and foam production appears in the Sw scans as a continuous drying. When liquid flow ceased after four days, Sw had a uniform value of 0.03 _+0.005. The average saturation, calculated from produced volume, was found to agree within _ 0.003 pore volumes with the integral of Sw in the scanned section. Thus, saturations in the scanned and unscanned por-

tions must be the same and capillary end effects insignificant. The Sw data agree well with other results obtained on foam at pressure-driven conditions. For eight different Hostapur SAS foams in 8darcy packs, at ambient temperature without oil, overall aqueous-phase saturations of 0.04 to 0.06 ( _+0.01 ) pore volume were obtained by material balance (Meling, 1989). There was no additional liquid production observed during several days of blockage, when up to 100 pore volumes of gas (at mean column pres-

FOAM AS A GAS-BLOCKING AGENT IN PETROLEUM RESERVOIRS II

sure) flowed through at mobilities reduced by two to four orders of magnitude. Visual observation at the onset of gas blockage showed that the surfactant solution was distributed uniformly across the foam-filled pack. Similarly, Sw values of 0.03-0.05 during gas blockage were measured for Sulfotex RIF, BioTerge AS 40, and CD 128 foams in 1-m long beadpacks (Hanssen, 1993 ). It is more difficult to obtain accurate saturation data in the presence of oil at high temperatures, but three experiments on 0.5% Fluowet OTN in seawater, with crude oil at 70°C in 8 darcy beads, gave Sw values of 0.04-0.08 (Hanssen and Dalland, 1991). Comparable residual nonwetting-phase saturations for the same 8-darcy medium in the absence of foam gave values of Swrg= 0.13 and Swro= 0.11 +_0.02; the latter is an average of 24 floods (Hanssen and Dalland, 1990). With foam under comparable conditions, others have also reported water saturations below "irreducible" (Holm, 1968; Prieditis, 1988). Steady-state foam flow has consistently been associated with Sw values above connate (Holm and Bernard, 1964; De Vries and Wit, 1990; Chou, 1991; Persoff et al., 1991; Radke and Ettinger, 1992 ). The favorable mobility ratio of the growing foam displacing surfactant cannot explain the lower value of Sw, because at breakthrough, Sw> Swrr After breakthrough, a slow drainage of liquid continues until gas flow stabilizes. Efficient drainage is conceivable, because with foam, gas does not flow in continuous channels as in normal two-phase flow (Holm, 1968). Capillary pressure suction, driven by the curvature of the contact areas between lamellae and pore walls, will continue to drain liquid from a lamella, possibly until a local saturation has been attained corresponding to a balance between Pc and the disjoining pressure zr of the foam film. Stability criteria for static and flowing lamellae are different (Radke and Jimenez, 1989 ), i.e., stagnant foam is not necessarily broken at conditions when flowing

145

foam would collapse by the overall Pc exceeding the critical P* (Khatib et al., 1988). The extremely low values of Sw in the present experiments are probably caused by evaporation into flowing gas that is not equilibrated with the liquid phase in the foam (see later) and by the regularity of beadpacks, which lack the small pores that hold most of the aqueous phase in steady-state foam flow in sandstone (Radke and Gillis, 1990). Two experiments in 1.3-darcy Bentheimer sandstone cores (Hanssen and Dalland, 1991 ) gave Sw values of0.18 and 0.2 l, i.e., comparable with flow of foam through the same rock (De Vries and Wit, 1990), although gas blockage was as strong as in beads with the same permeability. Thus, establishment of an overall Sw< Swrgis not a requisite for reaching the gas-blocking state of foam. The comparable efficiency of gas blockage in cores and beadpacks suggests that the actual gas-blocking foam is of a similar dry nature in both media but the sandstone also contains free water in the smallest pores. The fact that as little as one percent of liquid in the form of foam lamellae can maintain a large mobility reduction over long periods is remarkable. It has two main ramifications. First, the lamellae must be exceedinglythin, as has also been suggested by recent studies correlating foam properties in porous media with the stability of thin surfactant films (Bergeron, 1993 ). A bimolecular soap film only 4 nm thick was preserved for a year in a sealed container (Dewar, 1917). In porous media, thin films would be supported by the pore walls, although they would be destabilized by the random perturbations caused by abrupt changes of the gas flow path (Huh et al., 1989), and by diffusion. Second, the capillary pressure in media of low Sw are high, so that a moving lamella would break rapidly by capillary-pressure-induced coalescence (Khatib et al., 1988 ). The persistent mobility reduction in such dry porous media is yet another indication of stagnant lamellae. The pressures, on the lower diagram of Fig.

146

J.E. HANSSEN 3.8

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predicted. 15 min measured, 12 rain. , I i i i I

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Predicted versus measured profiles The characteristics of pressure-driven foam generation were confirmed. Quantitative

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1

O.8

0.6 9, increased during the first 24 h, mostly in the first section of the pack as by-passed liquid was produced, and became later constant. In contrast to Sw, the pressure profile does not become uniform, but retains distinct slopes in the section of initial bypassing and the section of piston-like movement. This conservation of local AP/Ax is typical of gas-blocking foams and has some practical consequences, e.g., in requiring great care when emptying a used pack. More important for reservoir application is that a gas-blocking foam can be regenerated by reapplying a gas pressure (Hanssen et al., 1989; Chou, 1991 ) because the lamellae remain largely intact. Note also that the pressure slope across a foam-filled section of porous medium is at its steepest during the initial passage of the front. This is favorable to trapping of lameUae (Marsden and Albrecht, 1970). Combining the Sw and P data at corresponding times, Fig. 10, shows the positions of the pressure and saturation fronts to coincide. Foam generation, therefore, must occur at or close to the gas front, and front positions observed on transparent packs are valid.

'

"'.

i--~

~ 04

o4

__ -

--

predicted

me?u,ed:2

264rain

,

,

,

,

-'"

J

(b)

0

'--'0.2

0.4

0.6

0.8

0 1

y/I

Fig. 11. Measuredand predictedSwand Pprofilesfor foam #207 usingthe "APsplit method" describedabove,at (a) 15 min; and (b) 26 min. comparison of measured Sw and P profiles with predictions using Eqs. 3 and 4, using only external observations in the present experiment, are shown in Fig. 11. The agreement is quite good, considering the bypassing in the imperfect pack, the rapid front movement and the simplistic nature of the predictive equations.

Loss of gas blockage by evaporation Sw scans between 144 and 335 h are shown in Fig. 12. Liquid saturation first drops uniformly to ~0.015. Then, zero liquid is recorded at the frontmost location. The dry section, having developed from the inlet, continues to grow with the passage of more gas through the pack. In previous experiments using dye in the aqueous phase, slight color gradients have been seen. With hindsight, these observations are taken in support of the microwave data, and conclude that gas blockage

FOAM AS A GAS-BLOCKINGAGENT IN PETROLEUM RESERVOIRSII

0.04

I

147

I

]

t I

/,

0.03

Time o t s c a n , hours

cO

_--

\

--- -.....

143.62 -171.97 195.81 220.08 -240.64 ..... 270.53 . . . . 309.64 -335.56

f ~

0.02

0.01

/

0 0.1

0.2

/ 0.3

,."i 0.4

0.5

0.6

x/L Fig. 12. M e a s u r e d water s a t u r a t i o n s in the later period o f foam # 2 0 7 .

in these experiments is broken by the foam drying from the pack inlet. Evaporation is not surprising since, with the standard procedure used, gas is not pre-equilibrated with the foamed liquid. The rising gas rate as the foam is drying agrees with the length dependence of gas blockage (Chou, 1991; Hanssen and Haugum, 1991; Hanssen, 1993 ), because the growing dry section in effect makes the foam shorter. In stronger foams, gas blockage often is lost in a faster, more catastrophic manner. Foam decay by evaporation will occur when the flowing gas phase is not in equilibrium with the liquid constituting the foam films, as is demonstrated by the above results. In the microwave experiment, 207 pore volumes of gas (at mean pressure ) were transported through the foam-filled pack between 220 and 336 h. In the same period, the Sw data show that the porous medium has lost 2.3 cm 3 of water, which must has been produced as vapor. The volume corresponds to a H20 partial pressure of 0.011; the saturated vapor pressure is 0.037. Gas thus did not become saturated in water even after stripping all the water from the first half of the pack. This poor mass transfer indicates that most of the liquid is effectively

"shielded" from the flowing gas because it exists in trapped foam. This trend is found in all the effective gas-blocking foams studied. The gas volume transported through foam at blockage is in all cases greater than expected if gas became saturated in the foamed liquid. There is, however, no consistent correlation between gas volume and foam gas-blocking efficiency, or with the liquid saturation at the onset of blockage (Hanssen and Dalland, 1991; Hanssen and Haugum, 199 l; Hanssen, 1993). Evaporation from a gas-blocking foam is difficult to model as one cannot assume equilibrium. Rates of evaporation are influenced by the presence of surfactant, and will depend on the type and concentration of surfactant as well as on the thickness and structure of the liquid film. The role of evaporation in gas blockage by a strong foam is seen in Fig. 13. A more persistent foam resulted from bubbling gas through a fluid cell containing water at injection pressure and slightly below column temperature, partially presaturating it. Due to liquid dropout problems, a presaturator is not used in the present gas-blockage test procedure, which emphasizes repeatability and relative per-

148

J.E.I-IANSSEN 0.010

r

Gas transport through foam

f

Network model

0.008

0.006

0.004

0.002

• • 2 I 100

L

I 200

dry - - h

I 300

N 2 ÷ H20 vapor F 400

L 500

Pore volumes gas injected

Fig. 13. Gas blockageperformance of 1% Fluowet OTN foams in 200-cm packs of 8 darcy beads, gas dry or partially saturated in H20 as indicated. T= 70°C, Pout~6 bar, AP~ 2 bar/m, sea water, Sotof crude oil. (Replotted from data in Hanssen and Dalland, 1991).

formance evaluation. It follows that the measured persistence of a gas-blocking foam, whether expressed as blockage time or pore volumes of gas transported, is useful in ranking foams but does not scale to field conditions. For the use of foam as a gas-coning barrier, evaporation is not likely to limit foam stability, because foam is created by reservoir gas which will be in equilibrium with both oil and water. However, in foam applications where a non-equilibrated gas is injected, evaporation could be important. With static foam and equilibrated gas, only diffusion remains as a decay mechanism. Recent studies (D. Cohen, T.W. Patzek, C.J. Radke, unpublished work, 1993) indicate that diffusion in confined foams rapidly (order of minutes) causes the liquid films to adjust their position in the pores to have no AP across the films. Further diffusion is then limited to a small flux in a few blocked channels in which there is still some AP. This is unlikely to cause massive foam decay, cf., the lack of gas/liquid equilibration.

Gas-blocking foams typically show a nonlinear response of flow to applied pressure. The yield point frequently observed and the powerlaw dependence of gas flow on AP suggested a percolation approach. A square, two-dimensional network model was defined with nonlinear element characteristics (Fig. 14):

0

q= a(Ap-Apt)

for dpApt

(6)

Let us assume that the conductances a are constant for all elements, and that the microscopic pressure thresholds Apt is uniformly distributed within a range 0-1. The macroscopic response of this network was calculated numerically by Moe (1989) as: 0 for AP<~AP-r Q= al (AP-APT) '~ for APT ~APn

I

(7) The power exponent a ~ 2 for a wide pore size distribution, al and a2 are constant conductances, APT is the macroscopic threshold pressure into a regime of power-law dependence on reduced pressure, and APH is a next threshold for transition into a linear regime. The resemblance of this theory to the present

/ Apt

..._

Ap

Fig. 14. Flow rate/differential pressure relationship for one network element.

149

FOAM AS A GAS-BLOCKING AGENT IN PETROLEUM RESERVOIRS II

problem of stagnant foam subjected to an increasing gas pressure gradient is readily seen. The gas permeability of different foams should fall on a c o m m o n straight line when plotted as a function of (AP-dPx)a/AP.

Comparison with experiments

O_ C13:&Pt= 1.6 bar [] C15:APt= 0 A C17:APt = 0 : = .

8

0

2

4

,1~ /

/

/

6

/

//

8

O n A •

0,006

C13 C15 C17 Blend linearfit of all data

& ~

"

/

-

/ //FI.[].

A ~

0,004

0,002

A set of gas-blockage data from Hanssen and Meling (1990) was used to test the network model. Foams generated in pressure-driven displacements of surfactant solution by gas reached a gas-blocking state with gas only entering and exiting the pack. Pressure drop was increased step-wise, the stabilized Qs and AP were measured at each successive gas-blocking state. The data are presented in Fig. 15 as flow rates at mean pressure. Figure 16 shows the same data replotted to kgf/k versus normalized and reduced pressure drop, in accordance with the network model. Threshold pressures were found by second-order polynomial fits on the Q versus AP data and the best-fit exponent a = 2.5 was found by trial-and-error linear fits on the kgf v e r s u s [ (AP-AP-r)'VAP] data; the linear correlation coefficient r~ =0.93. Fits at c~< 2 or a > 3 could be distinguished visually and gave rl ~<0.90. The accuracy is good considering the spread in the original measure-

10

0,008

/

10

12

AP / L, bar/m

Fig. 15. Data for foams consisting of 0.5% Hostapur SAS; indicated carbon number fractions in 100-cm 8 darcy beadpacks at 21 ° C, Pout~ 7 bar, no oil. Lines are interpolated, threshold pressures indicated. (Replotted from Hanssen et al., 1990).

, ~ l 0,000 0

I~ll 10

,

i

,

20

2.5 (AP-APt) lAP

i

,

30

40

Fig. 16. Fit of data of Fig. 15 using the relationship derived from the network model.

0.02

~10 , 0

0,00

0 C13 SAS hexadecane(APt= 2 bar; [] C15 SAS,hexadecaneI',Pt = 0) A SAS blendoctaneiAPt = 0p , --

/

[] /

/

Linear ~ frtof afllata m O• ~[]

10 (AP - AP 2t2 )/AP

20

Fig. 17. Generalization of data for foams at residual oil using the derived relationship. (Replotted from experimental data of Meling, 1989).

ments. Two points for C17SAS may be outside the power-law regime and higher r~ values result if these are excluded. A data set for the same surfactants in the presence of oil (Sor~0.05) was also generalized by a [ (AP-dPr)'~/,dP] function, (see Fig. 17). The match is poorer, q = 0 . 9 0 , but still quite convincing, taking into account the less effective mobility reduction which impairs the quality of gas-blockage data. The best-fit value of a was 2.2, not significantly different from the oil-free data. The agreement between the two sets of data is taken as an indication that residual oil does not change the flow mechanism of gas through a gas-blocking foam. The success of this simple modeling ap-

150

J.E. HANSSEN

proach shows the power of network modelling. For future work, the model could be extended to include more percolation features. As a first test, it would be of interest to compare predictions with data for well-characterized heterogeneous media to examine the influence of pore size distribution. Next, measurable terms could be developed for the percolation threshold to predict the macroscopic APr. Because of the complexity of calculating on a large nonlinear network, however, the main potential of networks in modeling foam is not as simulation tools but as scale-up tools from pore level to macroscopic level. The network model can be used to derive physically based foam behavior equations that could be used to interpret data at conditions where in situ observation is not possible.

Hysteresis Hysteresis is sometimes observed in gasblockage experiments. If, after a step-wise increase cycle, differential pressure is reduced to a previous level, a different kgf/k may be obtained. Hysteresis for two foams is shown in

Foam #206

_

o.ol

0.00!

Foam #205

0

2

4

6

AWL, bar/m

Fig. 18. Measured values of kgf/k for foam at increasing and decreasing AP in 100 cm, 8-darcy beadpacks at 25 ° C, Foam #205 is 0.83% BioTerge 1416 (an c~-olefin sulfonate). Foam #206 is 0.50% Fenopon CD 128 (an ammonium alkyl ethoxy sulfate). Initial PoutS7 bar, AP/ L ~ l . 5 bar/m. Solvent: 0.83% NaC1 brine. No oil, Aqueous-phase saturation during foam tests ,~ 0.03.

Fig. 18. The foam of the lower diagram gave a lower kgf/k value in the first hysteresis cycle but a higher one in the second cycle. The first cycle shows that an efficient gas-blocking foam can regain or surpass its original gas-blocking ability if the pressure is eased. The second cycle shows that its regenerative capacity may be limited (in this case, due to evaporation) so that permeability remains at the highest previous level. Some foams are initially too weak gas-blocking agents and display only the irreversible shear thinning. Discussion In their pioneering work on modeling foam in porous media, Shell researchers (Falls et al., 1988) differentiated between continuous-gas foams and discontinuous-gas foams. For gas to flow in a discontinuous-gas foam, lamellae must be forced through the pore network. Continuous-gas foams were considered to reduce gas mobility only by a factor of 5-10. In the present results, the gas-blocking state of foam is consistently associated with no lamellae exiting the porous medium, but the large mobility reduction associated with gas flow and the nonlinear response of gas mobility to increased differential pressure are not in line with the above picture of continuous-gas foams. Prieditis (1988) generated foams by fixedrate coinjection in a 35-cm pack of 75-85/zm beads ( k = 2 . 9 darcy) or 81-900 /tm beads ( k = 10 darcy). After a period of steady-state flow, gas mobility was measured as a function of gas and liquid rates over wide ranges including zero. At zero liquid rate, the data of Prieditis consistently showed gas mobility to be independent of the gas rate. This Newtonian rheology was interpreted as no lamellae being in the path of the gas, i.e., gas flows in a constant number of continuous channels created during the establishment of steady-state foam flow. These observations contrast with the pres-

F O A M AS A G A S - B L O C K I N G A G E N T I N P E T R O L E U M R E S E R V O I R S II

ent findings of mobility increasing with applied ziP (or Qg) by orders of magnitude, and are more in line with those reported by Holm (Holm and Bernard, 1964; Holm, 1968) who demonstrated the absence of continuous channels by the use of a gas tracer. Figure 19 compares the present results to those of Prieditis. The difference between the two sets of experiments is in the mode of foam generation. The pressure-driven foam data sets were selected to show the generality of the observed behavior, including a model system, a fluorosurfactant foam at 70°C with crude oil, and a non-aqueous foam. The data sets of Prieditis were selected for constant Sw during the period of no liquid flow. The effects of the experiment mode can be explained by considering the local ziP/zix, the driving force for lamella generation. This is finite in a pressure-driven displacement of surfactant solution by gas, but essentially unlimited at rate-driven coinjection of gas and surfactant. The effect is demonstrated most clearly in porous media of sufficient length to allow the formation of a stabilized foam front (Chou, 1991; Hanssen and Haugum, 1991; Hanssen, 1993). At fixed pressures, gas fingers or tongues form initially, as in the rate-driven mode. La0.020 • • 0.015

(]} [)

A

Priedifis, Table 7 1 4 Prleditis, Table 7 1 7 Pneclitis, Table 71 16

/

05% Perlankrol FN 65 2% FC 742 (IPA foam) 05% FFuow~tOTN

/ ~ •

-

•

• QL

0.010

•

¢

• 0.005

0.000

,/C)

/J

/6 /

•

#i

, Z~F-- , T ~ i

*

Z

........

10

; /

y

[]

i 100

. . . . . . . 103

vg, m/d

Fig. 19. Relative gas mobility as a function of gas velocity, at zero liquid flow, of foams generated by rate-driven coinjection in 2.9 and 10 darcy beadpacks, (Prieditis, 1988); and in the pressure-driven mode in 8 darcy beadpacks (Hanssen and Dalland, 1990; Hanssen and Haugum, 1991; Hanssen, 1993).

151

mellae are generated at the gas front. The same lamella-generation processes should operate in either mode, to the extent that the same conditions of velocity, saturation and capillary pressure at the pore level apply. The difference between experiment modes is one of different boundary conditions influencing the relative importance of the various processes. Lamellae are created first in the larger pores with the lowest capillary entry pressure Poe and, flowing or stagnant, impede further gas flow. For displacement to proceed, the advancing gas must now pass through a section of growing foam, whether the foam is viewed as propagating or simply considered as more lamellae to be generated further downstream. The flow resistance of the foam section thus increases with its length, being proportional to "the number of lamellae and the strength of individual films" (Holm, 1968 ). Here lies the key difference between pressure-driven and rate-driven foam generation, or, precisely, between fixedrate coinjection and fixed-pressure gas injection. In coinjection, the growing foam produces a rising inlet pressure to accommodate the transport of the imposed volume. This has profound effects on further foam generation. The rising pressure exceeds the Poe of smaller pores, generating more lamellae, causing yet higher flow resistance and higher 3P/ZIx. The latter may mobilize previously trapped lamellae, resuming flow as bubble trains and contributing more pressure buildup (Persoff et al., 1991 ). The net result is a massive generation of new lamellae and destruction of those initially formed, until a state is reached where generation and coalescence are in equilibrium and the trapped fraction is constant but less than 1. This state is associated with an overall pressure gradient 3P/L in excess of those in most reservoirs, even at low rates. At a fixed differential pressure, however, the net effect of foam generation is to slow down the displacement front as the growing foam consumes more of the limited driving force.

152

Gas fingering is dampened, the front sharpens and may stabilize as piston-like (Hanssen, 1993). This promotes trapping of lamellae, because the local ziP/zix never exceeds that during their generation. The result is a conservation of the original lamellae. If initial foam generation at the front is very efficient, nearly all pore throats are blocked by a liquid film, and growth of the foam bank stops at a few centimetres length resulting in complete plugging of gas and liquid. In less perfect cases, many initial lamellae are destroyed shortly after generation (cf., the micromodel observations) and a few flow paths develop through the foam, allowing gas to flow at low mobility. The observation of no produced liquid phase during gas blockage precludes gas from being transported by moving lamellae over samplespanning distances. If lamellae were translating at pack length scales, even though each contains only a minute volume of liquid, the large gas volumes transported would necessitate at least an accumulation of liquid near the outlet. This is consistently not observed. Micromodel observations in this paper indicate that gas flow may occur at distances greater than a pore diameter, but shorter than the length of a long core or pack, without associated net flow of liquid, by the operation of periodic time-averaged bubble train flow alternating with liquid washback. The hysteresis data in this paper suggest that strong gasblocking foams may regain their gas blocking ability upon reduction of ZIPas the result oflamella regeneration. Foams less effective in blocking gas develop continuous gas channels when subjected to high ziP which do not close again if ZIPis reduced. This points out the need, in field application, for replenishing liquid either by injectant within the treated volume, or by repeated injection. Fixed-rate gas injection is intermediate between rate-driven coinjection and pressuredriven gas injection. Inlet pressure may rise, reflecting the higher resistance of forcing the number of lamellae needed to transport a given

J.E. HANSSEN

volume, starting the sequence of rising Pc and generating lamellae in smaller pores as in coinjection. But since liquid is not being replenished, the lamella generation rate will drop and paths of continuous gas will form. Interpreting such experiments, especially at low pressures, is complicated by the use of mass flow controllers, which supply a gradually smaller volumetric rate as the injection pressure increases. A method of injecting gas at fixed volumetric rate has been developed (Dalland and Hanssen, 1989, unpubl, data). The pressure-driven mode might be said to correspond more closely to field cases of limited injectivity, where gas compressors are normally set not to exceed fracturing pressure (Kuehne et al., 1990). An experiment at "nearly fixed" rate worth mentioning has been conducted (Kovscek, 1993 ), injecting gas by a massflow controller, but keeping ziP~Pout nearly constant below 0.5. The beadpack, surfactant, and microwave apparatus described above was used. The displacement failed to produce the pressure buildup typical of coinjection experiments, but produced a foam reducing gas flow to the same order of magnitude as in the pressure-driven experiment described in this paper. In contrast, however, water saturation was strongly non-uniform in the downstream third of the pack, Sw increasing from a uniform 0.05 between the inlet and x / L ~ 0.6 to more than 0.30 at x / L >10.85. This could be an end effect, perhaps due to the use of atmospheric back pressure and/or low ziP, which is expected to give large end effects in the form of a stronger foam near the outlet (Rossen et al., 1991). However, the outlet liquid accumulation could also be caused by transport of gas and associated liquid in the form of bubble trains, lamellae breaking at the outlet acting as an infinitely large pore body. Others measuring in situ saturations at steady state and higher pressures (Persoff et al., 1991 ) have not reported such end effects. This comparison of the fixed-pressure and the fixed-rate gas injection tests indicate that replenishing surfactant may be more

153

FOAM AS A GAS-BLOCKING AGENT IN PETROLEUM RESERVOIRS II

critical for producing high flow resistance than injecting at fixed rate. Foam response to increased AP at the gasblocking state suggests the existence of two or three different regimes (not necessarily distinct in all cases). At zero or near-zero gas flow, no or very few gas flow paths are open. This occurs below a pressure threshold and shows at most a weak dependence on AP. At higher pressure drops, mobility increases with AP, as could happen if more lamella break-and-reform sites were activated, or further continuous-gas channels opened. At very high loads, gas rate is often seen to increase abruptly, as if a highly conductive continuous gas channel is suddenly opened. In this case, most foams will leave the gas-blocking state as gas rates continue to increase. Interestingly, the three flow regimes mentioned were quantified by the simple network model. This approach (cf., Fig. 20) could be a useful complement to the mechanistic approach of foam modeling, which requires a lamella number density and a trapped fraction, neither of which is easily measurable. Certain aspects of foam in porous media have been studied by percolation methods (Rossen and Gauglitz, 1990), although calculations may become quite complex (Chambers, 1990). The percolation model of Chou (1990) matches a wide range of data by several investigators; but, as formulated it does not describe the gas-blocking state. The experiments generally agree with those by Chou

Jt

Fig. 20. A bond percolation model of gas flow m a pore network containing foam lamellae blocking pore throats. Line intersections represent pore bodies.

( 1991 ) for Berea cores under pressure-driven conditions. The similar behavior in beadpacks and cores (Hanssen and Dalland, 1991 ), supported by the same flow mechanisms dominating in beadpacks of narrow and wide poresize distribution (Prieditis, 1988), indicate flow mechanisms to be more or less the same in homogeneous beadpacks, heterogeneous beadpacks, and cores, provided they are of similar permeability and length. The hysteresis data in this paper suggest that strong gas-blocking foams may regain their gasblocking ability upon reduction of AP as the result of lamella regeneration. On the other hand, a foam of less gas-blocking efficiency, or one that has been subjected to evaporation or long-time decay by diffusion, when subjected to high AP, will tend to develop continuous-gas channels that do not close again at reduced AP. With regard to field application of gas-blocking foams, this points out the need for replenishing some liquid to maintain the efficiency of gas blockage, either by unfoamed injectant from within the treated volume, or by repeated injection. Conclusions Gas blockage as strong and persistent as in long cores or beadpacks was not achieved in micromodels. However, zero gas flow was observed in the absence of very large pores for limited periods at low AP. At zero gas flow, foam lamellae were stagnant except for periodic oscillations. The response of a foam to an increased AP at zero gas flow in the micromodel resulted in lamella breakage and some regeneration (not in bubble-train mobilization), with the net effect of opening more pore channels for flow. In foams with moving lamellae, generation and termination sites are strongly coupled. The generation of gas-blocking foam by pressure-driven displacement of surfactant solution by gas, in a one-dimensional porous medium sufficiently long to allow the formation

154

of a stabilized foam front, can be described analytically. The data required are overall differential pressure and saturation, and front positions observed on a transparent pack. Predictions compare well with saturations and pressure profiles measured in situ. Gas-blocking foams can maintain order-ofmagnitude gas mobility reductions with as little as 0.01 pore volume of the foamed liquid phase remaining. This corresponds to high capillary pressures that would rapidly destroy any moving lamellae and this agrees with the micromodel observations of mainly stagnant lamellae. The main decay mechanism in this work--for gas-blocking foam with gas that was not pre-equilibrated with the foamed liquidm was evaporation, presumably causing driedout, brittle films to break by random perturbations. With equilibrated gas, the only remaining known decay mechanism is interbubble diffusion. Accordingly, using partly equilibrated gas produced a more long-lived foam. A model of a simple nonlinear network predicts gas flow regimes at the gas-blocking state which are in fair agreement with curve fits for two sets of foams in the absence and presence of oil. The performance data for each set are generalized to one line, with fitting parameters close to the network model parameters. The gas-blocking state of foam in porous media does not match the conceptual models established from steady-state foam flow. Gasblocking foams persistently, and over a wide range of conditions, maintain large mobility reduction factors through the passage of hundreds of pore volumes of gas, at liquid saturations much lower than those associated with the critical capillary pressure for the existence of stable moving lamellae. They display a nonlinear response to an increased flow rate or ziP, yet they do not appear to contain lamellae translating over macroscopic distances even on a time-averaged basis. The alternate description proposed in this paper, consistent with all experimental data from this study, is one ofes-

J.E. HANSSEN Nomenclature A

Cg/liq D h k L N P 3P 3P/L 3P/dx

Q q S v

v, X r

2 # ff

cross-sectional area coefficient of solubility (for gas in liquid) diffusion coefficient film thickness absolute permeability porous-medium length number of moles pressure differential pressure overall pressure gradient local pressure gradient volumetric flow rate (macroscopic) volumetric flow rate (network model element) saturation (fraction pore volume) linear (Darcy) velocity volume produced (fraction pore volume) position or length (fraction length ) correlation coefficient (of order l, 2...: rt, rz... ) power exponent mobility viscosity disjoining pressure conductance

Subscripts and superscripts c e f g gf in liq out rg ro t T H w *

capillary entry foam gas of gas in foam at porous-medium inlet liquid at porous-medium outlet residual to gas flood residual to oil flood threshold (microscopic) threshold (macroscopic) higher threshold (macroscopic) water critical

sentially all the foam lamellae being trapped and most generated during the initial passage of the foam front. Gas percolates through this network in a number of gas flow channels increasing over time (at a rate depending on the system) and with an increased ziP, but remaining capable of decreasing again with a decrease in ziP, by regenerating lameUae in critical sites as long as the pores contain sufficient foamable liquid. Periodic lamella-train movement over distances of a few pores is consistent with

FOAM AS A GAS-BLOCKING AGENT IN PETROLEUM RESERVOIRS II

this scheme, if accompanied by liquid backflow in inactive periods as inferred from observations of coupled sites so that no net transport of liquid results.

Acknowledgments I am greatly indebted to Prof. C.J. Radke for his inspiration during my stay at the University of California, Berkeley, and to Dr. Kurt Rune Jakobsen, now of Norske Shell, for the network modeling approach. Financial support from Rogaland University Center, NAVF, Norske Shell and Statoil is gratefully acknowledged.

References Armitage, P. and Dawe, R.A., 1990. The development of a probabilistic physical model for foam generation by snap-off in regular square grid network systems. SPE/ DOE 7th Symp. EOR, Tulsa, Okla., SPE/DOE 20217. Bergeron, V., 1993. Forces and structure in thin liquid films. Ph.D. thesis, Univ. California, Berkeley, Calif., 311 pp. Buckley, J.S., 1991. Multiphase displacements in micromodels. In: N.R. Morrow (Editor), Interracial Phenomena in Petroleum Recovery. Marcel Dekker, New York, N.Y., pp. 157-191. Chambers, K.T., 1990. Pore-level basics for modeling foam flow in porous media with randomly connected pore throats and bodies. M.Sc. thesis, Univ. California, Berkeley, Calif., 384 pp. Chou, S.I., 1990. Percolation theory of foams in porous media. SPE/DOE 7th Symp. EOR, Tulsa, SPE/DOE 20239. Chou, S.I., 1991. Conditions for generating foam in porous media. 66th Annu. SPE Tech. Conf. Exhib., Dallas, Tex., SPE 22628. Dalland, M., Hanssen, J.E. and Strum Kristiansen, T., 1992. Oil interaction with foam at static and flowing conditions in porous media, lEA Collaborative Project on EOR, 13th Int. Workshop and Symp., Banff, Canada. Colloids Surfaces. De Vries, A.S. and Wit, K., 1990. Rheology of gas/water foam in the quality range relevant to steam foam. SPE Res. Eng., 5: 185-192. Dewar, J., 1917. Soap bubbles of long duration. Proc. R. Inst. G. B., 22: 179-212. Ekrann, S. and Hanssen, J.E., 1990. U.S. Patent 4 903 771. Ettinger, R.A., 1989. Foam flow resistence in Berea sandstone. M.Sc. thesis, Univ. California, Berkeley, Calif.

15 5

Falls, A.H., Hirasaki, G.J., Patzek, P.W., Gauglitz, D.A., Miller, D.D. and Ratulowski, T., 1988. Development of a mechanistic foam simulator: The population balance and generation by snap-off. SPE Res. Eng., 3: 884892. Fried, A.N., 1961. The foam-drive process for increasing the recovery of oil. U.S. Bur. Mines, Rep. 5866. Friedmann, F., Chen, W.H. and Gauglitz, P.A., 1991. Experimental and simulation study of high-temperature foam displacement in porous media. SPE Res. Eng., 6: 37-45. Friedmann, F. and Jensen, J.V., 1986. Some parameters influencing the formation and propagation of foams in porous media. 56th SPE Calif. Reg. Meet., Oakland, Calif., SPE 15087. Gauglitz, P.A., 1990. Coalescence during division: A mechanism of lamella rupture in porous media. AiChE Natl. Meet., Chicago, IlL Gillis, J.V., 1990. Tracer detection and structure of stationary lamellae during foam flow through Berea sandstone. Ph.D. thesis, Univ. California, Berkeley, Calif. G~Sktekin, A., 1968. Experimentelle Untersuchungen fiber die Herstellung von Schiiumen in porSsen Medien im Zusammenhang mit die Steigerung der Ent/51ungeiner Lagerst~itte. Erd61-Erdgas Z., 84: 208-226. Hanssen, J.E., 1992. Foams for gas flooding. In: S.M. Skj~eveland and J. Kleppe (Editors), Recent advances in Improved Oil Recovery Methods for North Sea Sandstone Reservoirs. SPOR Monograph, Norw. Pet. Directorate, Stavanger, pp. 277-283. Hanssen, J.E., 1993. Foam as a gas-blocking agent in petroleum reservoirs. I: Empirical observations and parametric study. J. Pet. Sci. Eng., 10:117-133. Hanssen, J.E. and Dalland, M., 1990. Foams for effective gas blockage in the presence of crude oil at reservoir temperature. 7th SPE/DOE Symp. EOR, Tulsa, Okla., SPE/DOE 20193. Hanssen, J.E. and Dalland, M., 1991. Foam barriers for thin oil rims: Gas blockage at reservoir conditions. Proc. 6th Eur. Symp. Improved Oil Recovery, Stavanger, pp. 95-104. Hanssen, J.E. and Haugum, P., 1991. Gas blockage with non-aqueous foams. SPE Int. Symp. Oil-Field Chemistry, Anaheim, Calif., SPE 21002. Hanssen, J.E. and Meling, T., 1990. Gas-blocking foams in porous media: Effects of oil and surfactant hydrophobe carbon number. Progr. Colloid Polymer Sci., 82: 140-154. Hanssen, J.E., Rolfsvhg, T.A., Dalland, M. and Corneliussen, R., 1989. Foam barriers against gas coning in thin oil zones. Proc. 5th Eur. Symp. Improved Oil Recovery, Budapest, pp. 737-746. Hanssen, J.E., Jakobsen, K.R. and Meling, T., 1990. Interaction of gas-blocking foam with oil in model porous media. Progr. Colloid Polymer Sci., 81:264-265.

156 Heller, J.P. and Lee, H.-O., 1990. Laboratory measurements of CO2-foam mobility. SPE Res. Eng., 5: 193197. Heuer, G.J., Jr. and Jacocks, C.L., 1968. U.S. Patent 3 368 624. Holbrook, O.C. and Bond, D.C., 1958. U.S. Patent 2 866 507. Holm, L.W., 1968. Mechanism of gas and liquid flow through porous media in the presence of foam. Soc. Pet. Eng. J., 8: 359-369. Holm, L.W., 1970. Foam injection test in the SigginsField, Illinois. J. Pet. Technol., 22:1499-1507. Holm, L.W. and Bernard, G.G., 1964. Effect of foam on permeability of porous media to gas. Soc. Pet. Eng. J., pp. 267-274. Holm, L.W. and Bernard, G.G., 1970. Model study of foam as a sealant for leaks in gas storage reservoirs. Soc. Pet. Eng. J., pp. 9-15. Huh, D.G., Cochrane, T.D. and Kovarik, F.S., 1989. The effect of microscopic heterogeneity on CO2-foam mobility: Part 1-mechanistic study. J. Pet. Technol., 4 l: 872-879. Islam, M.R. and Farouq Ali, S.M., 1990. Numerical simulation of foam flow in porous media. J. Can. Pet. Technol., 29:47-51. Khatib, Z.I., Hirasaki, G.J. and Falls, A.H., 1988. Effects of capillary pressure on coalescence and phase mobilities in foams flowing through porous media. SPE Res. Eng., 3: 919-926. Kovscek, A.R., 1993. Ph.D. thesis, Univ. California, Berkeley, Calif. Kuehne, D.L., Ehman, D.I., Emanuel, A.S. and Magnani, C.F., 1990. Design and evaluation of a nitrogen-foam field trial. J. Pet. Technol., 42:504-512. Marsden, S.S. and Albrecht, R.A., 1970. Foams as blocking agents in porous media. Soc. Pet. Eng, J., pp. 5155. Mast, R.F., 1972. Microscopic behaviour of foam in porous media. 47th SPE Annu. Meet., San Antonio, Tex., SPE 3997. Meling, T., 1989. Gas-blocking foams in the presence of oil: A laboratory model study. M.Sc. thesis, Rogaland Univ. Center, Stavanger, Norway. Moe, K., 1989. Development of network model for nonNewtonian fluids in porous media. M.Sc. thesis, Rogaland University Center, Stavanger, Norway. Owete, O.S. and Brigham, W.E., 1987. Flow behavior of

J.E. HANSSEN foam: A porous micromodel study. SPE Res. Eng., 2: 315-323. Patzek, T.W. and Koinis, M.T., 1990. Kern River steamfoam pilots. J. Pet. Technol., 42: 496-503. Persoff, P., Pruess, K., Benson, S.M., Wu, Y.S., Radke, C.J., Witherspoon, P.A. and Shikari, Y.A., 1990. Aqueous foams for control of gas migration and water coning in aquifer gas storage. Energy Sources, 12: 479497. Persoff, P.J., Radke, C.J., Pruess, K., Benson, S.M. and Witherspoon, P.A., 1991. A laboratory investigation of foam flow in sandstone at elevated pressure. SPE Res. Eng., 6: 365-372. Prieditis, J., 1988. A pore level investigation of foam flow behavior in porous media. Ph.D. thesis, Univ. Houston, Houston, Tex. Radke, C.J. and Chambers, K.T., 1991. Capillary phenomena in foam flow through porous media. In: N.R. Morrow (Editor), Interracial Phenomena in Petroleum Recovery. Marcel Dekker, New York, N.Y., pp. 191-255. Radke, C.J. and Ettinger, R.A., 1992. The influence of texture on steady foam flow in Berea sandstone. SPE Res. Eng., 7: 83-90. Radke, C.J. and Gillis, J.V., 1990. A dual gas tracer technique for determining trapped gas saturation during steady foam flow in porous media. 65th SPE Annu. Tech. Conf. Exhib., New Orleans, La., SPE 20519. Radke, C.J. and Jimenez, A.I., 1989. Dynamic stability of foam lamellae flowing through a periodically constricted pore. In: J.K. Borchardt and T.F. Yen (Editors), Oil-Field Chemistry: Enhanced Recovery and Production Stimulation. Am. Chem. Soc., Washington, D.C., pp. 461-479. Raza, S.H., 1970. Foam in porous media: Characteristics and potential applications. Soc. Pet. Eng. J., 10: 328336. Rossen, W.R., 1988. Theories of foam mobilization pressure gradient. 6th SPE/DOE Symp. Enhanced Oil Recovery, Tulsa, Okla., SPE/DOE 17358. Rossen, W.R. and Gauglitz, P.A., 1990. Percolation theory of creation and mobilization of foams in porous media. AIChE J., 36(8): 1176-1188. Rossen, W.R., Zhou, Z.H. and Mamun, C.K., 1991. Modeling foam mobility in porous media. 66th SPE Annu. Tech. Conf. Exhib., Dallas, Tex., SPE 22627. Sharma, D.K., 1987. Kinetics ofoil bank formation. Ph.D. thesis, Univ. of California, Berkeley, Calif.