Experimental study of high-temperature foam for acid diversion

Journal of Petroleum Science and Engineering 58 (2007) 138 – 160 www.elsevier.com/locate/petrol

Experimental study of high-temperature foam for acid diversion S.I. Kam a,⁎, W.W. Frenier b , S.N. Davies b , W.R. Rossen a,1 a

Department of Petroleum and Geosystems Engineering, 1 University Station, C0300, The University of Texas at Austin, Austin, TX 78712-1061, USA b OCP, Well Services, 110 Schlumberger Drive, Sugar Land, TX 77478, USA Received 11 April 2006; received in revised form 6 December 2006; accepted 7 December 2006

Abstract Foam treatments are used worldwide for acid diversion in matrix acid well stimulation. Many field treatments require foam effectiveness at elevated temperature in the presence of both acid and corrosion inhibitor. This study examines four surfactant formulations at room temperature, 104 °C (220 °F) and 204 °C (400 °F), with and without acid and corrosion inhibitor. The surfactants included amphoteric as well as nonionic foaming agents. The acid formulation was a mixture of chelating agent and HCl, with pH about 4. Formulations were tested at all three temperatures for foaming with N2 gas (80% quality) at back-pressure of 600 psi (4.1 MPa) in sandpacks and for bulk-foam stability in a pressure cell. Foam was created in most cases at 24 °C (75 °F) without acid or corrosion inhibitor. Creating foam with acid and corrosion inhibitor at 204 °C was more difficult, requiring higher injection rates and lower foam quality. Once formed, strong foam had higher mobility at elevated temperatures than at room temperature. Addition of corrosion inhibitor was more adverse to foaming than acid itself. At 204 °C foam propagation was slower, and steady-state pressure gradient was lower, than at 24 °C. The two steady-state strong-foam regimes reported elsewhere were present at 104 °C and in the presence of acid. Pressure gradient at 104 °C was lower in both high-quality and low-quality foam regimes. The bulk-foam stability results agree qualitatively with the sandpack results, but quantitative relationships between the two tests are hard to draw. These results also suggest that these surfactants may degrade over a period of time, for example, a couple of hours at 204 °C. Residence time in the heated sandpack therefore should be properly accounted for in design of experiments. These results are consistent with decreasing foam stability at higher temperature; adverse interactions between foaming surfactant and inhibitor; easier foam generation and propagation at higher velocity and lower foam quality; and greater difficulty in creating foam under conditions that reduce steady-state foam strength. These results can aid design of high-temperature foam-acid diversion treatments. © 2007 Elsevier B.V. All rights reserved. Keywords: Foam; Diversion; Acidization; Well stimulation; Production enhancement

⁎ Corresponding author. Now at the Craft and Hawkins Department of Petroleum Engineering, Louisiana State University, 3523 CEBA Building, Baton Rouge, LA 70803, U.S.A. Tel.: +1 225 578 5216; fax: +1 225 578 6039. E-mail address: [email protected] (S.I. Kam). 1 Now at the Faculty of Civil Engineering and Geosciences, Delft University of Technology, P. O. box 5038, 2600 GA Delft, The Netherlands. 0920-4105/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2006.12.005

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

1. Introduction 1.1. Foam in the petroleum industry Foam has been widely used in petroleum industry (Schramm, 1994). Foam can increase sweep efficiency in gas-injection improved oil recovery by reducing gas mobility and redirecting gas flow (Schramm, 1994; Rossen, 1996). Foam can reduce gas influx into production wells by forming a barrier to gas flow from a gas cap or from gas-swept layers. Foam can aid acid well stimulation by diverting acid into damaged or lowpermeability layers near the wellbore (Ettinger and Radke, 1992; Gdanski, 1993; Thompson and Gdanski, 1993; Zerhboub et al., 1994; Zhou and Rossen, 1994; Parlar et al., 1995; Thomas et al., 1998; Robert and Rossen, 2000; Alvarez et al., 2000; Hirasaki et al., 2002; Cheng et al., 2002). Recently foam technology has been extended from the petroleum industry to subsurface environmental remediation (Hirasaki et al., 2002). Foam is also used in drilling, cementing, wellbore clean-up, and fracturing, because of its unique rheology, low density, ability to transport solid particles, and cost effectiveness (Schramm, 1994). 1.2. Foam in bulk and in porous media Foam used in drilling, fracturing, cementing and wellbore cleanup is called bulk foam, because in each case the foam bubbles are much smaller than the geometry of the flow channel in which foam acts. In the other applications listed above foam enters and acts in the pores of the geological interval. There are several important differences between bulk foams and foams in porous media. First, because the bubbles in bulk foam are small compared to the flow channel, bulk foam can be treated as a locally homogeneous, if rheologically complex, fluid. In porous media, one must account for the separate mobilities of gas and liquid and, in particular, for the huge effect of foam on the mobility of gas. Second, the stability of bulk foam is governed by diffusion and the rate at which liquid drains through the foam over relatively large distances (much greater than the bubble size) under gravity. In such a case, for instance, viscosifying the liquid can slow down the rate of liquid drainage and stabilize the foam. In porous media, bubbles are thought to be as large as, or larger than, individual pores (Ettinger and Radke, 1992). Diffusion is relatively unimportant to foam in porous media once bubbles are as large as pores (Rossen, 1996). Liquid drains from the liquid films, or lamellae, between bubbles in response to capillary pressure to nearby

139

pores, over a distance of order of pore size. Thus the lamellae in foam rapidly come to equilibrium with the capillary pressure of the surrounding medium. Therefore foam in porous media is more directly sensitive to the ability of the surfactant to stabilize lamellae between bubbles (Khatib et al., 1988) than in bulk foam, which can be stabilized simply by viscosifying the liquid. Third, creation of bulk foam often involves turbulent flow or bubbling gas through narrow tubes into the liquid. In porous media, processes of both creation and destruction of foam are dominated by capillary forces. 1.3. Foam in porous media 1.3.1. Strong and weak foams In porous media, the lamellae between bubbles in foam greatly restrict the mobility of gas. Therefore the number of these lamellae, or, in other words, the bubble size, governs the mobility reduction with foam (Falls et al., 1988a,b). Thus foam mobility depends on various processes that create or destroy lamellae, as well as other processes that mobilize or trap bubbles. It is sometimes useful to distinguish between “strong” foam and “weak” foam, although the distinction between strong and weak foam is not always quantified in the literature and in any case varies among studies. “Strong” foams reduce gas mobility greatly, by factors of 10,000 to 1,000,000 at the same water saturation (by smaller factors if comparisons are made at the same foam quality). “Weak” foams reduce gas mobility by smaller factors. 1.3.2. Foam generation “Foam generation” is a transformation, often abrupt, from a state of high gas mobility (weak foam or no foam) to one of low mobility (strong foam) (Friedmann and Jensen, 1986; Rossen and Gauglitz, 1990; Friedmann et al., 1991; Gauglitz et al., 2002; Tanzil et al., 2002; Kam and Rossen, 2003; Dholkawala et al., in press). Foam generation is a process where the rate of lamella creation greatly exceeds the rate of lamella destruction. Thus what one observes as “foam generation” in the laboratory is a result of both lamella creation and the stability of lamellae that are created. Separating these two factors can be difficult. Rossen and Gauglitz (1990) argue that in steady flow in homogeneous porous media foam generation results from mobilization of a small population of lamellae present initially. Foam mobilization and generation depends on exceeding a minimum pressure gradient that depends on injected gas volume fraction, surfactant formulation, the properties of the porous medium, and other factors. Once strong

140

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

foam is created, it can exist and advance through the porous medium at a lower injection rate (though not necessarily at lower pressure gradient) than that required to create the foam (Friedmann and Jensen, 1986; Friedmann et al., 1991; Shi, 1996; Gauglitz et al., 2002; Kam and Rossen, 2003; Dholkawala et al., in press). An example is shown in Fig. 1. Here foam generation (creating low-mobility strong foam out of weak or coarse foam) requires exceeding a minimum total interstitial velocity of about 2000 ft/day (7.06 × 10− 3 m/s). If gas and liquid are injected at fixed rates, there is an abrupt increase in pressure gradient at this threshold by a factor of about 100. Once strong foam is created, however, the injection rate can be reduced substantially and still maintain strong foam. This indicates that observing foam strong at a given injection rate can be affected by hysteresis. Careful studies at fixed pressure gradient rather than fixed injection rates find an unstable transient regime between the strong and coarse foams. Various studies support these findings (Friedmann and Jensen, 1986; Rossen and Gauglitz, 1990; Friedmann et al., 1991; Gauglitz et al., 2002; Tanzil et al., 2002; Kam and Rossen, 2003). Foam generation is favored by high pressure gradients (or high injection rates), low injected gas volume fractions (foam qualities), injecting alternating slugs of gas and liquid, and other factors that stabilize foam lamellae, such as relatively low temperature and high surfactant concentration (Friedmann and Jensen, 1986; Rossen and Gauglitz, 1990; Friedmann et al., 1991; Gauglitz et al., 2002; Tanzil et al., 2002; Kam and Rossen, 2003). The first three factors are thought to favor the creation of lamellae, and the other factors to favor survival of the lamellae once created.

Fig. 1. Foam-generation experiment of Gauglitz et al. (2002) for 90% quality foam in 7.1-darcy (7.1 × 10− 12 m2) Boise sandstone, and model fit to data by Kam and Rossen (2003). In an experiment with fixed injection rates, pressure gradient would increase abruptly as injection rate exceeded the threshold rate, and strong foam would remain if injection rates were then reduced.

Fig. 2. Steady-state pressure drop (psi) across 2-ft (0.6 m) sandpack at 302 °F as a function of gas (Ug) and water (Uw) volumetric fluxes, from Osterloh and Jante (1992), illustrating the two steady-state strong-foam regimes. Line at foam quality fg = fg⁎ = 0.94 (94%) is approximate division between high- and low-quality regimes for this surfactant formulation under these conditions. Each dark dot in the figure represents a steady-state datum (1 psi = 6.89 kPa).

1.3.3. Foam propagation Success in the field depends on both foam generation and foam advance, or propagation (Friedmann et al., 1994). It is not clear to what extent foam advances by the movement of bubbles and by creation of new bubbles ahead of the foam front — in other words, to what extent foam propagation is a separate issue from foam generation (Friedmann and Jensen, 1986). Foam can propagate at injection rates too low for foam generation, just as strong foam can be maintained at injection rates too low for foam generation (Fig. 1). On the other hand, the conditions that favor foam generation also favor foam propagation (Friedmann and Jensen, 1986). 1.3.4. Two strong-foam regimes Once strong foam is created, a number of studies find that foam exists in two regimes depending on injected gas volume fraction, i.e., foam quality fg (Osterloh and Jante, 1992; Rossen and Wang, 1999; Vassenden and Holt, 2000; Alvarez et al., 2001; Rong, 2002). Fig. 2 illustrates one such case. In the high-quality strong-foam regime (upper-left portion of figure), the pressure gradient is nearly independent of gas injection rate. In this regime foam properties are controlled by bubble coalescence and capillary pressure (Khatib et al., 1988), and bubble sizes change drastically as a function of gasinjection rate (Ettinger and Radke, 1992). Foam mobility can be shear-thinning, Newtonian or shear-

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

thickening at fixed foam quality in this regime (Alvarez et al., 2001; Rong, 2002). In the low-quality regime (lower-right portion of figure), the pressure gradient is nearly independent of liquid injection rate. In this regime, it is thought, bubble size is fixed and foam properties are controlled by bubble trapping and mobilization (Rossen and Wang, 1999; Alvarez et al., 2001). Rheology in the low-quality strong-foam regime is shear-thinning, often strongly so. Theory suggests that the high-quality regime should be more sensitive to factors that affect foam stability than the low-quality regime (Rossen and Wang, 1999; Alvarez et al., 2001), and experiments bear this out in part (Rong, 2002). The foam quality fg⁎ that separates the high-quality and lowquality regimes depends on surfactant formulation, porous medium, and any other factor that affects the stability of lamellae in the porous medium. This pattern of two strong-foam regimes is observed with a variety of surfactant formulations and gases, in porous media varying from consolidated cores to sandpacks and beadpacks, and over a wide range of injection rates (Osterloh and Jante, 1992; Rossen and Wang, 1999; Vassenden and Holt, 2000; Alvarez et al., 2001; Rong, 2002). The difference between these two regimes is important, because their rheology and ability to divert flow between layers differing in permeability is very different. There is only one study of these regimes at elevated temperature: that of Osterloh and Jante (1992), at 150 °C (302 °F), and no studies of the two flow regimes for foam with acid. 1.4. Objectives of study Field applications of foam for acid diversion must accommodate elevated temperatures as well as any adverse effects of acid and corrosion inhibitors on foam stability. Even if foam and acid are injected in alternating slugs in the field, process success depends on the compatibility of foam with acid (and corrosion inhibitor) (Zhou and Rossen, 1994). The effect of temperature and acid on the two steady-state strongfoam regimes also affects the design of the foam-acid process. There are studies of foam at elevated temperature in connection with steam (Maini and Ma, 1984; Duerksen, 1986; Strycker et al., 1987; Isaacs et al., 1988; Hamida et al., 1990; Friedmann et al., 1991; Stoll et al., 1993) and acid diversion (Thompson and Gdanski, 1993; Zerhboub et al., 1994; Parlar et al., 1995; Behenna, 1995). But none of them are at elevated temperature with acid, and only one study (Osterloh and Jante, 1992) addresses the two steady-state strong-foam regimes at elevated temperature but without acid.

141

In this study, four surfactant formulations are examined to compare foam generation and propagation at temperatures from room temperature (∼ 24 °C (75 °F)) to 204 °C (400 °F). The effects of acid and of corrosion inhibitor are also investigated. In additional experiments, gas and liquid injection rates were varied to confirm the existence of the two steady-state strong-foam regimes at elevated temperature and in the presence of acid. The effects of oil on foam and direct interactions between formation damage and foam are excluded from this study. 2. Experimental method Experiments conducted in this study comprise two parts: bulk-foam stability tests in a high-pressure visual cell, and flow experiments in sandpacks. In both cases, temperature ranges from room temperature (24 °C) to 204 °C. 2.1. Fluids The brine solution was 3 wt.% KCl in deionized water. Four commercial surfactants were used. Table 1 lists the chemical type of each surfactant. Surfactant solutions were prepared by adding 0.5 vol.% of the given surfactant as delivered to the brine solution, which is a typical concentration for field application. “Acid” was a 20 wt.% solution of chelating agent trisodium hydroxyethylethylenediamine triacetate with HCl added to lower the pH to 4. We refer to this solution as “acid” in the rest of this report. There was no KCl in the acid solution. For the experiments with acid and surfactant, 0.5 vol.% of surfactant was added to the acid solution. For experiments with surfactant, acid and corrosion inhibitor, 0.5 vol.% of surfactant and 0.4 vol.% of solution of a common commercial corrosion inhibitor, formulated to protect steel from attack by organic acids and chelating agents, were added into the acid solution. Bulk-foam stability tests were conducted with surfactant solution in the absence of acid and corrosion Table 1 Description of surfactants Surfactant

Type

A B C

Amphoteric alkyl amine Blend of ethoxylated alcohols Blend of ammonium alcohol, ethoxysulfate and ethoxylated alcohols Formulated amphoteric alkyl amine

D

142

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

inhibitor, while sandpack tests were performed with surfactant solution, surfactant solution with acid, and surfactant solution with acid and corrosion inhibitor. The gas phase was nitrogen throughout the experiments. The nominal injected volume fraction of gas fg, i.e. foam quality, was 80% unless otherwise indicated below. Nominal foam quality is foam quality computed at the apparatus back-pressure. 2.2. Bulk-foam stability test The vapor pressure of water is significant at high temperature (Perry and Chilton, 1973). Therefore the bulk-foam stability test was conducted using a highpressure visual cell (Jerguson cell, Temco Inc., Tulsa, OK), 12-inch (0.3 m) tall and 1 in. (0.025 m) in diameter. Fig. 3 shows a schematic of the bulk-foam test apparatus. Gas and liquid can be introduced through a 1/16-inch (0.00159 m) ID tube into the cell from the bottom, and there is also a valve at the top of the cell. The cell was wrapped with heating tape and temperature was controlled and monitored using a separate thermocouple between the cell and the heating tape. Layers of fiberglass surrounded the cell and the heating tape to insulate the apparatus. The heating tape and insulation were wrapped so as to allow one to view the glass wall of the cell. Tests of bulk-foam stability were conducted as follows. Initially, 20% of the volume in the cell was filled with surfactant solution, introduced into the bottom of the cell with the valve at the top open to atmosphere. The valve at the top of the cell was closed, and the cell was then heated if the test was to be

Fig. 3. Schematic of bulk-foam stability test apparatus.

conducted above room temperature. It took about 3 h to heat the cell to 204 °C (400 °F), but less time to heat to less-elevated temperatures. Then nitrogen gas was injected into the cell at a fixed inlet pressure 150 psi (1.0 MPa) above the vapor pressure of water at the temperature of the test. Gas continued to enter the apparatus until the pressure in the cell attained the injection pressure. Thus the air originally in the cell was compressed as the gas was introduced. We tried injection at fixed mass flow rate and at fixed inlet pressure, and the latter gave a more-uniform foam with smaller bubbles. Gas was not preheated before it entered the cell. Once the foam was formed, its height was monitored visually through the glass wall of the cell and recorded as a function of time. The process of foam formation in this procedure is complex. Dry gas takes up water as it bubbles through the surfactant solution. In the foam above the liquid, gas bubbles shrink from compression as more gas enters and the pressure continues to rise, and much of the water vapor in the bubbles condenses and flows down through the foam. At each temperature, gas was introduced at a pressure 150 psi (1.0 MPa) greater than the initial pressure in the cell and the cell eventually came to that higher pressure. At room temperature, the initial pressure was 14.7 psia (0.10 MPa) and the final pressure 165 psia (1.14 MPa). At 104 °C (220 °F), the initial pressure was 60 psia (0.41 MPa) and the final pressure 210 psia (1.73 MPa). At 204 °C, the initial pressure was 250 psia (1.73 MPa) and the final pressure 400 psia (2.76 MPa). Therefore, the volumes of gas introduced and of foam formed would be somewhat different at different temperatures even without differences in foam stability. Foam can be viewed only through the window of the steel high-pressure cell. Therefore one observes the level of foam against this wall of the cell, not throughout the cell. For all these reasons, this test is intended as only a qualitative measure of bulk-foam stability. Much less foam stability in general is experienced in porous media because of higher capillary pressure. (cf. Maini and Ma, 1984; Duerksen, 1986; Strycker et al., 1987; Isaacs et al., 1988; Hamida et al., 1990; Stoll et al., 1993). At the end of each experiment, when foam had collapsed and the cell cooled, gas was released through the valve and tubing at the top of the cell. In most cases liquid was replaced with fresh solution after each test at each temperature; in specific cases identified below, a solution used for a test at 204 °C was left in the cell for a repeat of the room-temperature test. In this case, the cell was allowed to cool down starting immediately after the first test.

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

2.3. Sandpack experiments Fig. 4 shows a schematic of the sandpack apparatus. The stainless-steel packholder was 12-inch (0.3 m) long and had inner diameter 0.84 in. (0.0213 m), with three pressure taps along its side to allow measurement of pressure differences across four sections of the pack. The sections were 2.37-, 3.63-, 3.63-, and 2.37-inch (0.06, 0.092, 0.092 and 0.06 m) long, respectively. The packholder was mounted vertically, with injection from the top. Because of the large pressure drops expected (and observed), the differential-pressure transducers (Validyne Engineering, Northridge, CA) had ranges of 0 to 250, 500, 500, and 500 psi (1.7, 3.4, 3.4, 3.4 MPa) for Sections 1, 2, 3 and 4, respectively. This means that measured pressure gradients in the range of about 15 psi/ft (0.34 MPa/m) and 25 psi/ft (0.56 MPa/m), respectively, are near the resolution of the transducers in Sections 1 and the other sections. All pressure transducers were isolated from injected fluids using isolation diaphragms. The packholder was filled with silica sand (F-95 silica sand, US Silica, Ottawa, IL); sieve analysis found that most grains fall between 70 and 170 mesh in this sand (Rong, 2002). In making a pack, sand was added to the pack continuously for about 50 min as the pack was vibrated. A fresh pack was prepared each time the chemical formulation of the liquid was altered (changing surfactant, or adding acid or corrosion inhibitor). In all

143

experiments, the permeability of the pack was between 7.5 and 9 darcies (7.5 and 9 × 10− 12 m2), and porosity between 28 and 31%, with pore volume between 30 and 33 cm3. If a sandpack was to be reused for a second experiment with the same liquid composition, more than 60 PV of brine solution was injected to flush out surfactant, followed by injection of gas to confirm (by lack of a rise in pressure gradient) that no foam was formed and therefore that relatively little surfactant remained in the pack. Whether a fresh or reused sandpack was used, it was vacuum-saturated with brine at the start of each new experiment. The packholder was wrapped with heating tape, and then covered with fiberglass insulation. Temperature was controlled in the same way as in the high-pressure bulk-foam cell, i.e., with a thermocouple between the heating tape and the packholder, connected to an electronic unit controlling the heating tape. Gas injection was regulated by a mass flow meter (Brooks Instrument Div., Emerson Process Management, St. Louis, MO). Liquids to be injected were stored in accumulators and displaced into the sandpack by injection of deionized water from a syringe pump (model LC-5000, ISCO Inc., Lincoln, NE) into the accumulator. A Beckman reciprocating dual-piston pump (Beckman Instruments Inc., Fullerton, CA) was used to inject brine solution into the sandpack for measuring permeability and to flush the sandpack after experiments.

Fig. 4. Schematic of laboratory sandpack apparatus and data-acquisition system.

144

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

A foam generator, i.e., a filter with 2-μm openings, was installed upstream of the packholder, and a visual cell downstream of the foam generator was used to confirm the generation of fine-textured foam at room temperature. In this visual cell, unlike the high-pressure cell in the bulk-foam tests, foam flows through a narrow gap between parallel glass plates (Friedmann and Jensen, 1986). The foam generator is intended to represent foam generation in flow down tubing in a field application. A length of tubing was wrapped in a coil, and then attached to the pack inlet (downstream of the foam generator and visual cell). Then both coil and pack inlet were wrapped with heating tape and surrounded with fiberglass insulation, in order to preheat injection fluids to the pack temperature. A length of tubing at least 1-ft (0.3 m) long was used for experiments at elevated temperatures below 149 °C (300 °F), and a length of 2 ft (0.6 m) for experiments at 149 °C (300 °F) or above. In experiments above room temperature this change in temperature could well have caused degradation or collapse of foam created in the generator before fluids reached the sandpack. Even at room temperature, flow through the tubing could cause foam to degrade before it reached the pack. Tubing throughout the apparatus had 1/ 8-inch (0.00032 m) OD and 1/16-inch (0.000159 m) ID. If the foam survives heating and transport to the pack, then the sandpack experiments constitute tests of foam propagation. Then one would expect foam to appear immediately in the first section of the pack and advance downstream. If foam created in the generator collapses completely before it reaches the pack, then the sandpack experiments are tests of foam generation in the pack. Foam could appear first in any section of the pack, or everywhere simultaneously. As shown below, the results fit neither picture perfectly. In a typical experiment, there was a delay in the first appearance of strong foam in the pack, but it consistently appeared first in Section 1 and then moved downstream. In experiments at elevated temperature, another coil of tubing at the exit of the packholder, immersed in a beaker of ice water, allowed high-temperature fluids to cool before reaching the backpressure regulator. A backpressure regulator (Temco Inc., Tulsa, OK) maintained the pressure at the outlet of the apparatus at 600 psi (4.1 MPa) in all experiments. Data from the pressure transducers were collected automatically using a personal computer and LabView™ (National Instruments Corp, Austin, TX) software. A nominal total volumetric flux Ut of 26.7 ft/day (9.42 × 10− 5 m/s; denoted by Utb below) at a nominal foam quality of 80% ( fg = 0.8) was selected as the base case for all experiments.

2.3.1. Distinguishing strong and weak foam In the sandpack data below, there is a fairly clear-cut division between cases with a pressure gradient ∇p of hundreds of psi/ft and of less than about 50 psi/ft (1.1 MPa/m). Moreover, measurement of ∇p less than about 25 psi/ft (0.56 MPa/m) is near the resolution of the pressure transducers. Therefore we refer to foam with ∇p greater than 100 psi/ft (2.3 MPa/m) as “strong foam” here. To put this in perspective, consider the “effective viscosity” μg,app of gas in foam, computed from Darcy's law, where we assume for illustration that all resistance to gas flow is in the viscosity: o lg;app ¼ ðk krg jpÞ=ðUt fg Þ

ð1Þ

o where k is permeability, krg gas relative permeability at the same water saturation in the absence of foam, Ut total volumetric flux, and fg foam quality, expressed as a fraction between 0 and 1. In Eq. (1) all variables are assumed to be in consistent units. At low water saturations expected with foam in a sandpack (Osterloh o and Jante, 1992), one expects krg ≅ 1 (Collins, 1961). Using a representative permeability of 8 darcies (8 × 10 − 12 m 2 ), and the base-case injection rates (Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s) and fg = 0.8), one finds

lg;app ¼ 2:4jp

ðfor Ut ¼ 26:7 ft=day and fg ¼ 0:8Þ ð2Þ

lg;app ¼ 2:4 ð26:7=Ut Þ ð0:8=fg Þjp

ðotherwiseÞ

ð3Þ

where μg,app is in cp, ∇p in psi/ft, Ut in ft/day and fg a fraction between 0 and 1. For ∇p = 500 psi/ft (11.3 MPa/m) with Ut =Utb = 26.7 ft/day (9.42 × 10− 5 m/s) and fg = 0.8, a typical value below, μg,app = 1200 cp. For ∇p = 25 psi/ft (0.56 MPa/m), near the resolution of the pressure transducers, μg,app = 60 cp. The viscosity of N2 gas at 1 atm and room temperature is less than 0.02 cp (Perry and Chilton, 1973), and that of saturated steam is well below 0.02 cp even at 204 °C (Boberg, 1988). Thus a foam with ∇p = 500 psi/ft (11.3 MPa/m) at the base-case injection rate has an effective viscosity 60,000 times that of free gas. Even a pressure gradient at the resolution of the transducers could reflect an effective gas viscosity 3000 times that of free gas. Our apparatus could not distinguish with confidence between this reduction in gas mobility and no reduction at all.

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 5. Results of bulk-foam stability test using surfactant A without acid or corrosion inhibitor at 24°, 104° and 204 °C (75°, 220° and 400 °F); temperature in the legend in °F.

Thus a “strong” foam as we define it reduces gas mobility by a factor of 10,000 to 100,000. Our apparatus could not well resolve the behavior of weak foams. 3. Results 3.1. Bulk-foam stability tests Bulk-foam stability tests were conducted using surfactants A, B, C and D without acid or corrosion inhibitor at room temperature (∼ 24 °C), 104 °C and 204 °C. Bulk-foam tests provide only qualitative

Fig. 6. Results of bulk-foam stability test using surfactant B without acid or corrosion inhibitor at 24°, 104° and 204 °C (75°, 220° and 400 °F); temperature in the legend in °F.

145

Fig. 7. Results of bulk-foam stability test using surfactant C without acid or corrosion inhibitor at 24°, 66°, 104° and 204 °C (75°, 150°, 220° and 400 °F); temperature in the legend in °F. “T = 76 after” represents the experiment at room temperature reusing surfactant solution that has been used in the experiment at 204 °C.

information about foam behavior in porous media. Figs. 5–8 show the results of these tests. The heavy, horizontal line there represents the initial level of surfactant solution in the cell. In comparisons between temperatures, the original height of foam differs in part because the relative volume of gas introduced varies with temperature and pressure, as noted in the Experimental method section. It is fair to compare different surfactants at the same temperature, and the relative rate of decay of foam height with time at different temperatures.

Fig. 8. Results of bulk-foam stability test using surfactant D without acid or corrosion inhibitor at 24°, 104° and 204 °C (75°, 220° and 400 °F); temperature in the legend in °F. “T = 76 after” represents the experiment at room temperature reusing surfactant solution that has been used in the experiment at 204 °C.

146

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 5 shows the results for surfactant A. At 24 °C, the froth was quite stable for more than 20 min. Even an hour later, one could see foam above the liquid surface. Foam collapsed more quickly as temperature increased, but foam did not collapse immediately even at 204 °C. With surfactant B (Fig. 6) less foam was created, and at all temperatures the created foam was less stable than with surfactant A. Foam collapsed almost immediately at 204 °C. Additional tests were conducted with surfactant C (Fig. 7), including a test at 66 °C (150 °F) and a second test at room temperature reusing the solution tested at 204 °C. Bulk foam with surfactant C has stability intermediate between surfactants A and B. Most notably, foam stability was markedly lower in the retest at 24 °C after the same solution was exposed to higher temperature. This suggests that the surfactant is chemically altered by exposure to high temperature in this test. Fig. 8 shows results for surfactant D. Foam collapses almost immediately at 104 °C and 204 °C. As in Fig. 7, a retest at room temperature, using the solution tested at 204 °C, shows greatly reduced surfactant performance. In all cases, bulk-foam stability decreased significantly with increasing temperature, as in previous studies (Maini and Ma, 1984; Duerksen, 1986; Strycker et al., 1987; Isaacs et al., 1988; Hamida et al., 1990; Stoll et al., 1993). In two separate tests, it appears surfactant degraded chemically when tested at 204 °C, also in agreement with previous studies. It takes about 3 h to heat the cell to 204 °C, up to an hour to run a test, and then many hours to cool the cell down for a repeat test at room temperature the next day. Therefore the liquid spends several hours at temperatures in the

vicinity of 204 °C, and many hours at elevated temperature, in these repeat tests. In separate tests (not shown), foam stability was similar at room temperature with fresh liquid and with liquid previously tested at 104 °C. Evidently the adverse effect of temperature occurs at temperatures greater than 104 °C, though it should be noted that the time to heat and cool the cell was also less in those cases. No bulk-foam tests were conducted with acid or corrosion inhibitor, due to safety concerns about the long-term effects of exposure of the high-pressure cell to acid. 3.2. Sandpack study of foam generation and propagation The four surfactant formulations were tested for foam generation and propagation in sandpacks at different temperatures. Effects of acid and/or corrosion inhibitor were also tested. Except where noted, nominal foam quality (i.e., the ratio of gas volumetric injection rate to total injection rate, computed at apparatus backpressure) was 80% (fg = 0.8). If a large pressure drop builds across the sandpack, actual foam quality in the sandpack, especially near the inlet, is lower. In all experiments but one, foam was successfully generated in the foam generator (at room temperature) and visually confirmed in the visual cell. The only exception was with Surfactant B with acid and corrosion inhibitor. 3.2.1. Surfactant A Fig. 9 shows results of a sandpack experiment using nominal 80% quality foam with surfactant A at the total volumetric flux Ut at the base-case value Utb = 26.7 ft/

Fig. 9. Sandpack experiment using surfactant A at base case (nominal foam quality fg = 0.8, total volumetric flux Utb = 26.7 ft/day (9.42 × 10− 5 m/s)). Temperature is initially 24 °C (75 °F), then increases to 104 °C (220 °F) starting about 9.5 PV injection (point “a”). Gas injection rate Qg (in units of standard cm3/min) is reduced at “a” to take account of the change of gas molar volume at the higher temperature.

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

day (9.42 × 10− 5 m/s), at room temperature. After a delay of 2 to 3 pore volumes (PV) injection, the pressure gradient (called dpdl in these figures) starts to rise significantly in the first section. As soon as pressure levels off in the first section, pressure gradient begins to increase in the second section, and so on through the sandpack. It is not clear why there is a delay in the appearance of foam (inferred from pressure gradient) in the data, or why once formed foam requires 3 PV to propagate to the end of the sandpack. Slow foam propagation has been reported in cases when a core or pack is initially saturated with brine or pre-flooded with brine and gas (Friedmann and Jensen, 1986; Friedmann et al., 1991; Kibodeaux et al., 1994; Zeilinger et al., 1995; Rossen and Wang, 1999). The decline in the pressure gradient in Section 2 after about 5 PV may reflect compression of gas as pressure gradient rises in downstream sections. It is not clear why the pressure gradient falls so drastically in Section 1 starting about the same time. As the temperature approaches 104 °C, pressure in the second, third, and fourth section falls simultaneously and appears to level off. It is not clear why the pressure gradient in the first section increases, though the volumetric gas flow rate has increased due to reduced gas compression resulting from the lower pressure gradients downstream. As shown in Fig. 9, the increase in temperature causes a reduction in foam strength, but the pressure gradient at 104 °C is still quite high, implying that reduction in gas mobility is still significant at 104 °C.

147

Fig. 10(a) shows a separate test, with the same volumetric fluxes as in Fig. 9 but with the sandpack initially at 104 °C. The steady-state pressure gradients are roughly the same as in Fig. 9, except in Section 1, where the pressure gradient is lower. After about 6 PV, gas injection is stopped, and liquid injection maintained at its original rate. Fig. 10(b) shows a continuation of the experiment in Fig. 10(a). Between Fig. 10(a) and (b) the pack was cooled to room temperature, flushed with 60 PV brine, and then heated to 204 °C. This is not quite the initial condition of a new experiment, because there was gas in the pack at the start of foam injection. This can have some effect on foam generation. At the start of Fig. 10 (b) (“0 PV”), the temperature is 204 °C, and injection of gas and surfactant solution has just resumed. The pressure drop is higher than with gas and water alone, but not indicative of strong foam as defined here. As temperature is reduced from 204 °C toward 24 °C, a strong foam advances from the inlet to the outlet, starting when the thermocouple outside the pack is at a temperature of about 54 °C (130 °F). Figs. 9 and 10 suggest that foam generation and propagation is more difficult to achieve with this surfactant as temperature increases. Fig. 11 shows results of a sandpack experiment with surfactant A and acid. The experiment begins with injection at nominal foam quality 80% and Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s) into a brine-saturated sandpack. After some delay, foam slowly propagates through the pack. Steady-state pressure gradients are

Fig. 10. Sandpack experiment in a sandpack using surfactant A at base case ( fg = 0.8, Utb = 26.7 ft/day (9.42 × 10− 5 m/s)) at elevated temperatures of (a) 104 °C (220 °F) and (b) 204 °C (400 °F). Gas flow is shut off at point “a” for post-foam liquid injection following foam; temperature is lowered to 24 °C (75 °F) at point “b”.

148

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 11. Sandpack experiment using surfactant A and acid at Utb. Post-foam liquid injection between “a” and “b” and between “c” and “d”; temperature increases to 104 °C (220 °F) and 204 °C (400 °F) at “b” and “d,” respectively; temperature decreases to 149 °C (300 °F) and 104 °C (220 °F) at “e” and “f,” respectively.

comparable to those without acid (Fig. 9). After 9 PV injection (point “a”), gas injection ceases, to allow postfoam surfactant injection. At point “b” the set-point temperature was raised to 104 °C and foam injection resumes. Steady-state pressure gradient at 104 °C is lower than that at 24 °C, but the reduction in gas mobility is still significant. Foam injection is again followed by surfactant-only injection at point “c.” Starting at point “d” the pack is heated to 204 °C and foam injection resumes. As the temperature approaches 204 °C the pressure gradient in all sections falls close to zero.

The pack cools to 149 °C (300 °F) starting at point “e,” but there is no remarkable change in pressure gradients. A second decrease in temperature to 104 °C, starting at point “f” eventually results in propagation of strong foam. As in Figs. 9 and 10 without acid, temperatures higher than 104 °C inhibited foam generation and propagation. Fig. 12 shows a similar experiment, but with surfactant A, acid, and corrosion inhibitor. The experiment starts with injection of gas and liquid as in the base case (fg = 0.8, Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s)) but foam does not propagate during 10 PV of injection.

Fig. 12. Sandpack experiment using surfactant A, acid, and corrosion inhibitor at fg = 0.8. Utb doubles from = 26.7 ft/day (9.42 × 10− 5 m/s) to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) at “a”; post-foam liquid injection at “b”; gas injection resumes and temperature increases to 104 °C (220 °F) at “c”; temperature decreases to 149 °C (300 °F) at “d”; temperature increases to 204 °C (400 °F) at “e”.

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Increasing the injection rate is one way to promote foam generation and propagation (Friedmann and Jensen, 1986; Rossen and Gauglitz, 1990; Friedmann et al., 1991; Shi, 1996; Gauglitz et al., 2002; Tanzil et al., 2002; Kam and Rossen, 2003). The foam injection rate doubles (Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s), fg = 0.8) at point “a;” there is an increase of pressure gradient in Section 4, followed, after a time, by the other sections. As the pressure gradient rises in the other sections it falls for a time in Section 4, but then rebounds. Gas injection ceases at point “b” to show the response to injection of liquid without gas (i.e., surfactant A, acid, and inhibitor). Foam injection at Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) resumes at point “c” as the temperature increases to 104 °C. There is an initial surge of the pressure gradients as foam injection resumes, but as the temperature approaches 104 °C, the pressure gradients fall throughout the sandpack. Even injection at 2Utb does not produce strong foam at 104 °C. The temperature is allowed to fall to 66 °C (150 °F) starting at point “d.” Stronger foam again starts to propagate through the sandpack. Foam collapses abruptly when temperature is raised to 204 °C starting at point “e.” 3.2.2. Surfactant B Surfactant B was tested in the sandpack with and without acid and corrosion inhibitor. In all cases, including injection rates up to twice the base case, there was no evidence of foam at 24 °, 104 °, or 204 °C. Fig. 13 shows the sandpack results for surfactant B and acid, without corrosion inhibitor. There is no significant increase in pressure gradient at any temperature even at

149

Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s). Similar results (not shown) were observed without acid at Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s). 3.2.3. Surfactant C Fig. 14(a) shows the results with surfactant C with Ut = Utb and fg = 0.8. After some delay, foam successfully propagates through the pack at 24 °C. At point “a” gas injection ceases while the pack temperature is raised to 104 °C. Foam injection is resumed, as shown in Fig. 14 (b). As in Fig. 10(b) the sandpack was first cooled and flushed with 60 PV brine, but not vacuum-saturated with brine, before the experiment resumed. The pressure gradient remains low, though higher than that expected in gas–liquid flow without foam. There was little change in pressure gradient when the pack temperature was raised to 204 °C starting at point “b.” Fig. 15 shows a second experiment with the same surfactant at 104 °C and 204 °C. Because foam did not propagate with Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s) at 104 °C without acid, the experiment begins with Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s). There is no appreciable pressure gradient at this injection rate. Ut is raised to 3Utb = 80.1 ft/day (2.83 × 10− 4 m/s) at point “a” and then foam does propagate through the pack. When the pack temperature is increased to 204 °C starting at point “b,” however, pressure gradients decrease to 30 psi/ft (0.68 MPa/m) or less; near the resolution of the transducers, but still much greater than expected with gas and water without foam. Slowly reducing the pack temperature, starting at point “c,” again results in foam propagation.

Fig. 13. Sandpack experiment with surfactant B and acid. Ut increases from Utb = 26.7 ft/day (9.42 × 10− 5 m/s) to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) at “a;” temperature increases to 104 °C (220 °F) and 204 °C (400 °F) starting at “b” and “c,” respectively. Pressure gradient never exceeds a few psi/ft in any section of the pack (1 psi/ft = 22.6 kPa/m).

150

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 14. Sandpack experiment in a sandpack using surfactant C with Utb = 26.7 ft/day (9.42 × 10− 5 m/s) at temperatures of (a) 24 °C (75 °F) and (b) 104 °C (220 °F) and 204 °C (400 °F). Post-foam liquid injection at “a;” temperature increases from 104 °C (220 °F) to 204 °C (400 °F) starting at “b.”

Fig. 16 shows the results of the experiments using surfactant C and acid. Foam propagates at 24 °C (75 °F) and 104 °C (220 °F), but not at 149 °C (300 °F) and 204 °C (400 °F). A volumetric flux Ut = 2Utb = 53.4 ft/ day (1.88 × 10 − 4 m/s) is not sufficient for foam propagation at the higher temperatures. Fig. 17 shows a similar experiment with corrosion inhibitor and acid. Unlike Fig. 16, injection at Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s) is insufficient for foam propagation even at room temperature. Increasing Ut to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) causes foam propagation after a long delay. Because both gas injection rate and set-point temperature were adjusted at the same

time in previous experiments (cf. Figs. 15 and 16), injection rates were adjusted here first and temperature was raised later, after strong foam was fully developed at the new injection rate. At about 42 PV, as the temperature is raised, foam begins to weaken and continues to weaken as the sandpack is heated to 204 °C. 3.2.4. Surfactant D Similar experiments were conducted using surfactant D as shown in Fig. 18. Foam is initially injected into the brine-filled sandpack at Ut = 53.4 ft/day (1.88 × 10− 4 m/s) at 24 °C (“a”). Once foam reaches steady state, the temperature is raised to 104 °C (“b”). This results in a

Fig. 15. Sandpack experiment using surfactant C starting with 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s). Ut increases to 3Utb = 80.1 ft/day (2.83 × 10− 4 m/s) at “a;” temperature increases from 104 °C (220 °F) to 204 °C (400 °F) starting at “b;” temperature decreases starting at “c.”

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

151

Fig. 16. Sandpack experiment using surfactant C and acid, initially at Utb = 26.7 ft/day (9.42 × 10− 5 m/s). Post-foam liquid injection at “a;” resume foam injection and increase temperature from 24 °C (75 °F) to 104 °C (220 °F) starting at “b;” post-foam liquid injection at “c” and then shortly afterwards resume foam injection and increase temperature from 104 °C (220 °F) to 149 °C (300 °F); double Ut from to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) at “d;” increase temperature from 149 °C (300 °F) to 204 °C (400 °F) starting at “e.”

rapid reduction in pressure gradients in the third and fourth sections, but less rapidly in the second section. The pressure gradient in the first section does not change significantly. Upon the subsequent increase in temperature to 204 °C (“c”), foam weakens rapidly throughout the pack. Larger injection rates and lower foam qualities favor both foam generation and propagation (Friedmann and Jensen, 1986; Rossen and Gauglitz, 1990; Friedmann et al., 1991; Shi, 1996; Gauglitz et al., 2002; Tanzil et al., 2002; Kam and Rossen, 2003). Shortly after point “c,” Ut

is raised to 2Utb = 53.4 and then to 6Utb = 160.2 ft/day (1.88 × 10− 4 to 5.65 × 10− 4 m/s; point “d”), keeping the nominal foam quality fixed at 80%. This represents the maximum gas-injection rate of the mass flow meter. Shortly after, there is a rise in pressure gradient in the fourth section followed by an abrupt decline, simultaneous with an abrupt rise in pressure gradient in the first section. The pressure gradient in the first section continues a slow increase, with no visible rise in the other sections. Finally the liquid injection rate is increased to its

Fig. 17. Sandpack experiment using surfactant C, acid, and corrosion inhibitor; Ut = Utb = 26.7 ft/day (9.42 × 10− 5 m/s) initially. Double Ut to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) at “a;” post-foam liquid injection at “b;” adjust injection rates to correspond to 104 °C (220 °F) at ”c” (but without raising temperature); increase temperature from 24 °C (75 °F) to 104 °C (220 °F) starting at “d” and to 204 °C (400 °F) starting at “e.”

152

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 18. Sandpack experiment with surfactant D and a variety of injection rates and foam qualities. Experiment begins (“a”) with 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) and fg = 0.8; temperature increases to 104 °C (220 °F) starting at “b;” temperature increases to 204 °C (400 °F) starting at “c,” followed by increase in Ut to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s); Ut increases to 6Utb = 160.2 ft/day (5.65 × 10− 4 m/s), with nominal fg still 0.8, at “d;” maximum attainable gas and liquid injection rates at “e:” Ut = 217.6 ft/day (7.68 × 10− 4 m/s) and fg = 0.59.

maximum attainable: Ut = 217.6 ft/day (7.68 × 10− 4 m/s) and fg = 59%. Foam now propagates to the downstream sections, though there is a long delay in reaching the fourth section. Fig. 19 shows another experiment with surfactant D without acid or corrosion inhibitor. Foam propagates at room temperature with U t = U tb = 26.7 ft/day (9.42 × 10− 5 m/s). A sudden drop in gas injection rate around 7 PV (“b”) was due to the depletion of nitrogen tank upstream. Pressure gradients come back to comparable values as gas injection resumes. At about

9.5 PV of foam injection (“c”), the temperature is increased to 104 °C. Foam weakens at 104 °C, though time is not sufficient here to see how completely foam would collapse. Foam strength rebounds as temperature drops from 104 °C to 24 °C (“d”). Foam weakens again as temperature rises to 104 °C (“e”), though again time is not sufficient to see how complete the collapse will be. As the temperature rises to 149 °C (300 °F) (“f”) the collapse of foam seems virtually complete except in Section 1, despite an increase in Ut from Utb = 26.7 to 2Utb = 53.4 ft/day (9.42 × 10− 5 to 1.88 × 10− 4 m/s).

Fig. 19. Sandpack experiment using surfactant D. Experiment begins with Utb = 26.7 ft/day (9.42 × 10− 5 m/s) at “a;” gas injection ceases for a time due to depletion of N2 cylinder around “b;” at “c,” adjust gas injection rate for temperature increase, followed by temperature increase, at about 11 PV, to 104 °C (220 °F); temperature drops from 104 °C (220 °F) to 24 °C (75 °F) starting at “d;” temperature increases to 104 °C (220 °F) starting at “e;” temperature increases to 149 °C (300 °F) starting at “f,” followed by increase in Ut to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s); Ut increases at “g” to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s), still at 149 °C (300 °F) and fg = 0.8.

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

153

Fig. 20. Sandpack experiment using surfactant D and acid. Experiment begins with 2Ut = 53.4 ft/day (1.88 × 10− 4 m/s) at “a;” Ut decreases to Utb = 26.7 ft/day (9.42 × 10− 5 m/s) at “b;” temperature increases to 104 °C (220 °F) starting at “c,” followed by increase in Ut to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s); temperature increases to 149 °C (300 °F) starting at “d,” followed by increase in Ut to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s); temperature increases to 204 °C (400 °F) at “e,” followed by increase in Ut to 6Utb = 160.2 ft/day (5.65 × 10− 4 m/s), with fg still 0.8; maximum gas and liquid injection rates at “f:” Ut = 217.6 ft/day (7.68 × 10− 4 m/s) and fg = 0.59.

When Ut increases to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s) at 149 °C, foam slowly propagates from Section 1 to Section 2. Figs. 18 and 19 make clear that foam generation and propagation are harder to achieve at higher temperature with this surfactant, but that higher injection rates and lower quality (within the range studied) both aid foam generation and propagation. Fig. 20 shows a sandpack experiment with surfactant D and acid. Initially U t is 2 U tb = 53.4 ft/day (1.88 × 10− 4 m/s) and foam propagates through the pack. When Ut drops to Utb = 26.7 ft/day (9.42 × 10− 5 m/ s; “b”), foam weakens, but it is not clear whether it was

going to collapse completely. As the temperature increases to 104 °C (“c”), foam weakens at an increasing rate, except in the first section. An increase in Ut to 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) helps foam again propagate successfully. As temperature increases to 149 °C at “d,” foam remains strong in Sections 1 and 2 but collapses in Sections 3 and 4. An increase in Ut from 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) to 106.8 ft/day (3.77 × 10− 4 m/s) shortly thereafter, at about 27.5 PV, eventually revives foam in Sections 3 and 4. An increase in temperature to 204 °C (“e”) has mixed results. The pressure gradient drops sharply in Sections 2 and 3, is

Fig. 21. Sandpack experiment using surfactant D, acid, and corrosion inhibitor. Experiment begins with 2Ut = 53.4 ft/day (1.88 × 10− 4 m/s) at “a;” temperature increases to 104 °C (220 °F) at “b,” followed by increase in Ut to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s) at “c;” temperature increases to 204 °C (400 °F) at “d,” followed by increase in Ut to 6Utb = 160.2 ft/day (5.65 × 10− 4 m/s) at “e.”

154

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 22. Second sandpack experiment using surfactant A. Injection starts (“a”) at 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) with fg = 0.8 at 104 °C (220 °F); temperature increases to 149 °C (300 °F) at “b,” with 2Ut = 53.4 ft/day (1.88 × 10− 4 m/s); Ut increases to 4Utb = 106.8 and 5.5Utb = 146.5 ft/day (3.77 × 10− 4 and 5.17 × 10− 4 m/s) at about 9 and 14 PV, still with fg = 0.8; temperature increases to 176 °C (350 °F) at “c,” followed by an increase in Ut from 146.5 to 5.75Utb = 153.5 ft/day (5.17 × 10− 4 to 5.42 × 10− 4 m/s; “d”) at fg = 0.8; increases in liquid injection rate raise Ut to 162.9 ft/day (5.75 × 10− 4 m/s) at fg = 0.75 at “e,” and to 176.2 ft/day (6.22 × 10− 4 m/s) at fg = 0.7 at “f;” temperature increases to 204 °C (400 °F) with 6Utb = 160.2 ft/day (5.65 × 10− 4 m/s) at fg = 0.8 at “g,” followed by maximum gas and liquid injection rates at “h:” Ut = 217.6 ft/day (7.68 × 10− 4 m/s) and fg = 0.59.

maintained in Section 1, and increases in Section 4. An increase in Ut to 6Utb = 160.2 ft/day (5.65 × 10− 4 m/s) at about 45 PV helps the pressure gradient rebound some in Sections 2 and 4, but not in Section 3. Starting at “f” both liquid and gas are injected at their maximum attainable rates (Ut = 217.6 ft/day (7.68 × 10− 4 m/s) and fg = 59%). The pressure gradient rises in Sections 2 and 3 and holds roughly steady in Sections 1 and 4.

Fig. 21 shows experimental results with surfactant D, acid and corrosion inhibitor. Foam propagates through the pack at Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) at 24 °C (“a”). As the temperature rises to 104 °C starting at “b,” pressure gradient collapses in Section 4, and for a time in Section 3, but not in Sections 1 or 2. An increase in Ut to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s) at “c” causes pressure gradient to fluctuate in Section 3 but

Fig. 23. Second sandpack experiment using surfactant D. Injection starts at 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) with fg = 0.8 at 104 °C (75 °F) (“a”); temperature increases to 149 °C (300 °F) at “b,” followed shortly thereafter by an increase in Ut to 5.3Utb = 141.5 ft/day (4.99 × 10− 4 m/s), still at fg = 0.8; temperature increases to 176 °C (350 °F) at “c;” increases in liquid injection rate raise Ut to 162.9 ft/day (5.75 × 10− 4 m/s) at fg = 0.75 (“d”), and finally to 176.2 ft/day (6.22 × 10− 4 m/s) at fg = 0.7 (“e”); temperature increases to 204 °C (400 °F) with Ut = 160.2 ft/day (5.65 × 10− 4 m/s) at fg = 0.8 (“f”), followed by maximum gas and liquid injection rate (Ut = 217.6 ft/day (7.68 × 10− 4 m/s), fg = 0.59) at “g;” liquid injection stopped for a time at “h” while the syringe pump was refilled, and then the experiment continued.

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

155

Table 2 Summary of sandpack foam-generation and propagation results 24 °C

104 °C

204 °C

Yes at Utb. a Yes at Utb. Yes at 2Utb. (66 °C: Yes at 2Utb.)

Yes at Utb. Yes at Utb. No, up to 2Utb.

No at Utb. Yes at EC b No at Utb. (149 °C: No at Utb.) No, up to 2Utb

b) Surfactant B Surfactant (not shown) Surfactant and acid (Fig. 13) Surfactant, acid, and inhibitor (not shown)

No at Utb. No up to 2Utb. No up to 2Utb.

No at Utb. No up to 2Utb. No up to 2Utb.

No at Utb. No up to 2Utb. No up to 2Utb

c) Surfactant C Surfactant (Figs. 14 and 15) Surfactant and acid (Fig. 16) Surfactant, acid, and inhibitor (Fig. 17)

Yes at Utb. Yes at Utb. Yes at 2Utb.

Yes at 3Utb. Yes at Utb. No up to 2Utb.

No at Utb. Yes at EC No up to 2Utb. No up to 2Utb.

d) Surfactant D Surfactant ((Figs. 18, 19 and 23)) Surfactant and acid (Fig. 20) Surfactant, acid, and inhibitor (Fig. 21)

Yes at Utb. Yes at Utb. Yes at 2Utb.

104 °C: c149 °C: yes at EC Yes (?) at 2Utb and yes at 4Utb. Yes (?) at 4Utb.

No at Utb. Yes at EC No at Utb. Yes at EC No up to 6Utb

a) Surfactant A Surfactant (Figs. 9, 10 and 22) Surfactant and acid (Fig. 11) Surfactant, acid, and inhibitor (Fig. 12)

Utb represents total volumetric flux Ut of 26.7 ft/day (9.42×10− 5 m/s) at 80% foam quality. EC represents extreme injection condition at the largest attainable value of total volumetric flux (Ut = 217.6 ft/day (7.68 × 10− 4 m/s)) and, occasionally, reduction in foam quality below 80% (down to 59%). c Foam is weakening, but time is insufficient to tell if it will collapse completely. a

b

does not revive foam in Section 4. Upon raising the temperature to 204 °C, foam weakens in all sections, even at Ut = 6Utb = 160.2 ft/day (5.65 × 10− 4 m/s) at nominal foam quality of 80%. 3.2.5. Repeat experiments with surfactants A and D Two more experiments were conducted at high temperature using surfactants A and D, primarily focusing on high temperatures between 104 ° and 204 °C and lower foam qualities. Fig. 22 shows the results of a second sandpack experiment with surfactant A. At the start (“a”), Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) at 104 °C; strong foam propagates through pack. As the temperature increases to 149 °C, foam collapses, despite an increases in Ut to 4Utb = 106.8 ft/day (3.77 × 10− 4 m/s). A further increase to Ut = 146.5 ft/day (5.17 × 10− 4 m/s) ≅ 5.5Utb causes slow foam propagation downstream at least as far as Section 3. As the temperature increases to 176 °C (350 °F) with Ut = 146.5 ft/day (5.17 × 10− 4 m/s) at “c,” foam collapses in Sections 3 and 4. A slight increase in Ut to 153.5 ft/day (3.77 × 10 − 4 m/s) ≅ 5.42Utb (at maximum attainable gas injection rate) with nominal foam quality still 80% (“d”) does not revive foam in Sections 3 and 4. Increases in liquid injection rate raise Ut to 162.9 ft/day (5.75 × 10− 4 m/s), at a nominal foam quality of 75% (“e”), and then to Ut = 176.2 ft/day

(6.22 × 10− 4 m/s) at a nominal foam quality of 70% (“f”). Foam eventually revives in Section 3. At 204 °C (“g”) foam weakens again in Section 3, but remains strong in Sections 1 and 2. At the maximum attainable injection rates (Ut = 217.6 ft/day (7.68 × 10− 4 m/s) at a nominal foam quality of 59%), foam revives in Section 3. A similar experiment, shown in Fig. 23, was conducted using surfactant D. Initially, Ut = 2Utb = 53.4 ft/day (1.88 × 10− 4 m/s) and nominal foam quality is 80% at 104 °C; foam propagates through the pack. As the temperature rises to 149 °C (“b”) foam collapses, but it revives in Sections 1 and 2 as Ut rises to 5.3Utb = Table 3 Criteria for success in Table 2 Criterion Yes

Yes (?) No

Strong foam advances through pack, or Strong foam maintained throughout pack, or Strong foam advances to downstream sections, but not through entire pack during experiment. Strong foam already present in upstream sections is maintained but does not advance. Large ∇p present at lower T falls below 30 psi/ ft (0.68 MPa/m) throughout pack (or appears to be in process of doing so), or ∇p never rises above 30 psi/ft (0.68 MPa/m) anywhere in pack.

156

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Fig. 24. Schematic of factors affecting foam generation and propagation in porous media. Part (a) is reproduced after Rossen and Gauglitz (1990).

141.5 ft/day (4.99 ×10− 4 m/s); possibly it is starting to propagate to Section 3 at about 30 PV. As the temperature rises to 176 °C (350 °F) at “c,” foam weakens in Section 2 and collapses in Section 3, but at Ut = 176.2 ft/day (6.22 × 10 − 4 m/s) and nominal foam quality 70% (“e”) foam revives in Sections 2 and, eventually, 3. At 204 °C, with Ut = 217.6 ft/day (7.68 × 10− 4 m/s) and nominal foam quality 59% (“g”) foam propagates into Section 3. Foam does not

reach Section 4, however, after more than 40 PV injection at these rates. 3.2.6. Summary of results The sandpack experiments can be summarized as shown in Tables 2 and 3 for the four surfactants. In all cases tested, increasing injection rates and decreasing foam quality help foam propagate through the sandpack as shown schematically in Fig. 24. Fig. 24(a) is

Fig. 25. Pressure gradient (psi/ft) as a function of volumetric fluxes of gas (Ug) and water (Uw) in steady-state strong-foam flow through a sandpack: surfactant A at room temperature; no acid or corrosion inhibitor. Horizontal numbers are contour values, and vertical numbers represent the individual data (1 psi/ft = 22.6 kPa/m; 1 ft/day = 3.35 × 10− 6 m/s).

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

157

Fig. 26. Pressure gradient (psi/ft) as a function of volumetric fluxes of gas (Ug) and water (Uw) in steady-state strong-foam flow through a sandpack: surfactant A with acid (no corrosion inhibitor) at 104 °C (220 °F). Horizontal numbers are contour values, and vertical numbers represent the individual data (1 psi/ft = 22.6 kPa/m; 1 ft/day = 3.35 × 10− 6 m/s).

consistent with the studies of Rossen and Gauglitz (1990) and Gauglitz et al. (2002). Fig. 24(b) shows a similar trend for temperature, i.e., a threshold temperature below which foam generation and propagation occurs. 3.3. Two strong-foam regimes Alvarez et al. (2001) and Rong (2002) show that, for a wide variety of surfactant formulations, gases, and porous media, strong foam exists in two steady-state regimes (cf. Fig. 2). Data for foam at high temperature are lacking, however, except for the study of Osterloh and Jante (1992) (Fig. 2). We know of no studies of the two strong-foam regimes with acid present. Two cases were examined here: surfactant A at room temperature, and surfactant A with acid at 104 °C. Fig. 25 shows the results in the absence of acid at room temperature. The volumetric fluxes of gas and water Ug and Uw here are much higher than those in the foamgeneration experiments at room temperature. Two flow regimes are observed as in other studies (cf. Fig. 2). At fixed foam quality, the data suggest a power-law exponent of approx. 0.5 in the high-quality regime and 0.3 in the low-quality regime: i.e., shear-thinning behavior in both regimes. The transition between high- and low-quality foams occurs at a foam quality fg⁎ of about 85% in this range of volumetric fluxes. One should be careful about extrapolating this value of fg⁎ beyond the range of the

data, however, because with non-Newtonian rheology in the two regimes the transition foam quality is itself a function of total volumetric flux (Alvarez et al., 2001). Fig. 26 shows the results at 104 °C with surfactant A and acid. Though the pressure gradient is lower, the figure clearly shows the two flow regimes. At fixed foam quality, the data suggest a power-law exponent of approx. 0.5 in the high-quality regime and 0.35 in the low-quality regime: i.e., shear-thinning behavior in both regimes. The transition foam quality fg⁎ is about 90%. Both results are consistent with earlier studies (Osterloh and Jante, 1992; Rossen and Wang, 1999; Vassenden and Holt, 2000; Alvarez et al., 2001; Rong, 2002). The two flow regimes appear to extend to elevated temperatures and to foam in the presence of acid, once (and if) strong foam is created. 4. Discussion Results of the bulk-foam stability test were consistent with sandpack experiments in that foam stability is reduced significantly as temperature increases. Bulk foams made with surfactant B were less stable than the others at room temperature and surfactant B was the worst performer in the sandpacks. More quantitative comparisons are difficult, especially given the differences between mechanisms of foam formation and stability for bulk foams and foam in porous media. Bulk foams made with surfactants C and

158

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

D all collapsed quickly at 104 °C, but those same surfactants were capable of creating strong foam at high injection rates in sandpacks. Surfactant A stabilized bulk foams the best of those tested at all temperatures, but was not always markedly better in foaming in sandpacks. Various studies (Friedmann and Jensen, 1986; Rossen and Gauglitz, 1990; Friedmann et al., 1991; Shi, 1996; Gauglitz et al., 2002; Tanzil et al., 2002; Kam and Rossen, 2003) plot the conditions for foam generation schematically shown in Fig. 24. For the surfactants studied here, an extension to higher temperatures is shown schematically in Fig. 27. Foam propagation is more difficult at higher temperature and easier at higher injection rates and lower foam quality. At higher temperatures and low pressures, where steam is a major or the dominant component in the dispersed gas phase in foam, evaporation and condensation of H2O on the liquid films can destabilize foam (Falls et al., 1988a,b; Hatziavrimidis, 1992). It is dangerous to extrapolate the effect of temperature to all surfactants, however, especially if surfactant solubility changes with temperature. Temperature changes many colloidal properties that could affect foam stability, possibly in different ways for different surfactant formulations. 4.1. Degradation of surfactant at elevated temperature The repeat bulk-foam stability tests at 24 °C, using surfactant tested at 204 °C, show that exposure to high temperature for several hours can chemically degrade the surfactant (cf. Maini and Ma, 1984; Duerksen, 1986; Strycker et al., 1987; Isaacs et al., 1988; Hamida et al., 1990; Friedmann et al., 1991; Stoll et al., 1993). Hydrolysis is a likely cause of this degradation. The residence time of surfactant in the sandpack was much shorter, however. The water saturation expected with

Fig. 27. A schematic of three-dimensional surface for foam generation inferred from experiments.

strong foam in a sandpack is of order 0.06 (Osterloh and Jante, 1992). In an 80%-quality foam at a total volumetric flux Ut of 26.7 ft/day (9.42 × 10− 5 m/s), i.e., Uw = 5.34 ft/day (1.88 × 10− 5 m/s), water spends only about 15 to 20 min in a 1-ft sandpack at that water saturation. Therefore these sandpack results may not adequately represent foam stability over longer periods in field application. Residence times in the sandpack are shorter at higher injection rates; if degradation rates are very rapid, it could be argued that this might explain part of the benefit of increased injection rate in these experiments. However, the surfactant solution degraded only partially over several hours at 204 °C in the bulk-foam tests (Figs. 7 and 8); therefore we don't believe there was any significant degradation in the sandpack tests. 5. Conclusions Four surfactant formulations were tested at the concentration of 0.5 vol.% for static foam stability and foaming in sandpacks at room temperature, 104 °C (220 °F) and 204 °C (400 °F), alone, with acid, and with acid and corrosion inhibitor (pH about 4). In addition, one formulation was examined in detail alone at room temperature and with acid at 104 °C (220 °F) to delineate the two steady-state strong-foam regimes at high and low foam qualities. The results might be affected by surfactant concentration and pH of the acids, which is beyond the scope of this study. 1. Foam was created in most cases at 24 °C (75 °F) without acid or corrosion inhibitor. Creating foam with acid and corrosion inhibitor at 204 °C (400 °F) was possible using higher injection rates and lower foam quality. Addition of corrosion inhibitor was more adverse to foaming than acid itself. At 204 °C (400 °F) foam propagation was slower, and steadystate mobility was higher, than at 24 °C (75 °F). 2. Like the sandpack results, the bulk-foam stability tests showed decreasing foam stability at higher temperature. Quantitative comparisons between the surfactants based on the bulk-foam tests were difficult, however, and did not necessarily correspond to sandpack results. 3. The foam stability tests suggest that these surfactants may degrade over several hours at 204 °C (400 °F). Residence time in the sandpack (15–20 min or less) may have been too short to fully represent field application at 204 °C (400 °F). 4. These results are consistent with decreasing foam stability at higher temperature; adverse interactions

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

between foaming surfactant and corrosion inhibitor; and easier form generation at higher velocity and lower foam quality. 5. The high- and low-quality steady-state strong-foam regimes were observed both at room temperature and with acid at 104 °C (220 °F) with one of the surfactants. In both regimes, foam showed shearthinning rheology. Acknowledgments This work was conducted with a grant from Schlumberger, Inc., and also with the support of the National Petroleum Technology Office of the U.S. Department of Energy, through contracts #DE-AC2699BC15208 and DE-FC26-01BC15318. We thank Glen Baum and Tony Bermudez for their indispensable help with the experiments. References Alvarez, J.M., Rivas, H., Navarro, G., 2000. An optimal foam quality for diversion in matrix acidizing projects. SPE 58711 presented at the 2000 SPE International Symposium on Formation Damage Control, Lafayette, LA, 23–24 Feb. Alvarez, J.M., Rivas, H., Rossen, W.R., 2001. A unified model for steady-state foam behavior at high and low foam qualities. SPE J., 325–333 (Sept.). Behenna, F.R., 1995. Acid diversion from an undamaged to a damaged core using multiple foam slugs. SPE 30121 presented at the 1995 SPE European Formation Damage Conference, The Hague, Netherlands, 15–16 May. Boberg, T.C., 1988. Thermal Methods of Oil Recovery. John Wiley & Sons, New York. Cheng, L., Kam, S.I., Delshad, M., Rossen, W.R., 2002. Simulation of dynamic foam-acid diversion processes. SPE J., 316–324 (Sept.). Collins, R.E., 1961. Flow of Fluids Through Porous Materials. Research & Engineering Consultants, Inc., Englewood, CO. Dholkawala, Z.F., Sarma, H.K., Kam, S.I., in press. Application of fractional flow theory to foams in porous media. J. Pet. Sci. Eng. Duerksen, J.H., 1986. Laboratory study of foaming surfactants as steam-diverting additives. SPERE, 44–52 (Jan.). Ettinger, R.A., Radke, C.J., 1992. The Influence of texture on steady foam flow in Berea sandstone. SPERE, 83–90 (Feb.). Falls, A.H., Lawson, J.B., Hirasaki, G.J., 1988a. The role of noncondensible gas in steam foams. J. Pet. Technol., 95–104 (Jan.). Falls, A.H., Hirasaki, G.J., Patzek, T.W., Gauglitz, P.A., Miller, D.D., Ratulowski, J., 1988b. Development of a mechanistic foam simulator: the population balance and generation by snap-off. SPERE, 884–892 (Aug.). Friedmann, F., Jensen, J.A., 1986. Some parameters influencing the formation and propagation of foams in porous media. SPE 15087 presented at the 1986 SPE California Regional Meeting, Oakland, CA, April 2–4. Friedmann, F., Chen, W.H., Gauglitz, P.A., 1991. Experimental and simulation study of high-temperature foam displacement in porous media. SPERE, 37–45 (Feb.).

159

Friedmann, F., Smith, M.E., Guice, W.R., Gump, J.M., Nelson, D.G., 1994. Steam-foam mechanistic field trial in the midway-sunset field. SPERE, 297–303 (Nov.). Gauglitz, P.A., Friedmann, F., Kam, S.I., Rossen, W.R., 2002. Foam generation in porous media. Chem. Eng. Sci. 57, 4037–4052. Gdanski, R.D., 1993. Experience and research show best designs for foam-diverted acidizing. Oil Gas J. 6, 85. Hamida, F.M., Demiral, B.M.R., Shallcross, D.C., Castanier, L.M., Brigham, W.E., 1990. Further characterization of surfactants as steamflood additives. SPE 20065 presented at the 1990 SPE California Regional Meeting, Ventura, CA, April 4–6. Hatziavrimidis, D., 1992. Stability of thin evaporating/condensing films in the presence of surfactants. Int. J. Multiph. Flow 18, 517–530. Hirasaki, G.J., Jackson, R.E., Jin, M., Lawson, J.B., Londergan, J., Meinardus, H., Miller, C.A., Pope, G.A., Szafranski, R., Tanzil, D., 2002. Field demonstration of the surfactant/foam process for remediation of a heterogeneous aquifer contaminated with DNAPL. In: Fiorenza, S., Miller, C.A., Oubre, C.L., Ward, C.H. (Eds.), NAPL Removal: Surfactants, Foams, and Microemulsions. Lewis Publishers, Boca Raton. Isaacs, E.E., McCarthy, F.C., Maunder, J.D., 1988. Investigation of foam stability in porous media at elevated temperatures. SPERE, 565–572 (May). Kam, S.I., Rossen, W.R., 2003. A model for foam generation in homogeneous porous media. SPE J., 417–425 (Dec.). Khatib, Z.I., Hirasaki, G.J., Falls, A.H., 1988. Effects of capillary pressure on coalescence and phase mobilities in foams flowing through porous media. SPERE, 919–926 (Aug.). Kibodeaux, K.R., Zeilinger, S.C., Rossen, W.R., 1994. Sensitivity study of foam diversion processes for matrix acidization. SPE 28550 presented at the 1994 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 26–28. Maini, B.B., Ma, V., 1984. Relationship between foam stability measured in static tests and flow behavior of foams in porous media. SPE 13073 presented at the 1984 SPE Annual Technical Conference and Exhibition, Dallas, TX, Sept. 16–19. Osterloh, W.T., Jante Jr., M.J., 1992. Effects of gas and liquid velocity on steady-state foam flow at high temperature. SPE 24179 presented at the 1992 SPE/DOE Symposium on EOR, Tulsa, OK. Parlar, M., Parris, M.D., Jasinski, R.J., Robert, J.A., 1995. An experimental study of foam flow through berea sandstone with applications to foam diversion in matrix acidizing. SPE 29678 presented at the 1995 Western Regional Meeting, Bakersfield, CA, Mar. 8–10. Perry, R.H., Chilton, C.H., 1973. Chemical Engineer's Handbook, 5th ed. McGraw-Hill, NY, pp. 3-206–3-210. Robert, J.A., Rossen, W.R., 2000. Fluid placement, diversion and pumping strategy, In: Economides, M.J., Nolte, N.G. (Eds.), Reservoir Stimulation, 3rd ed. Prentice Hall, Englewood Cliffs, NJ. Rong, J.G.. 2002. Experimental Evaluation of Foam in Environmental Remediation. Ph.D. dissertation. The University of Texas at Austin. Rossen, W.R., 1996. Foams in enhanced oil recovery. In: Prud'homme, R.K., Khan, S. (Eds.), Foams: Theory, Measurements and Applications. Marcel Dekker, New York. Rossen, W.R., Gauglitz, P.A., 1990. Percolation theory of creation and mobilization of foam in porous media. AIChE J. 36, 1176–1188. Rossen, W.R., Wang, M.-W., 1999. Modeling foams for matrix acid diversion. SPE J., 92–100 (June). Schramm, L.L., 1994. Foams: Fundamentals and Applications in the Petroleum Industry. ACS advances in chemistry series, vol. 242. Am. Chem. Soc., Washington, DC.

160

S.I. Kam et al. / Journal of Petroleum Science and Engineering 58 (2007) 138–160

Shi, J.-X., 1996. Simulation and Experimental Studies of Foam for Enhanced Oil Recovery. Ph.D. dissertation, The University of Texas at Austin, 1996. Stoll, R.D., Gudenau, H.W., Lupik, M.W., 1993. Mobility control for steamflooding with high-temperature-resistant additives. SPERE, 281–284 (Nov.). Strycker, A.R., Madden, M.P., Sarathi, P., 1987. Effectiveness of screening tests as predictive models for steamflood additives. SPEREE, 543–548 (Nov.). Tanzil, D., Hirasaki, G.J., Miller, C.A., 2002. Conditions for foam generation in homogeneous porous media. SPE 75176 presented at the 2002 SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 13–17 April. Thomas, R.L., Ali, S.A., Robert, J.A., Acock, A.M., 1998. Field validation of a foam diversion model: a matrix stimulation case study. SPE 39422 presented at the 1998 SPE International

Symposium on Formation Damage Control, Lafayette, LA, Feb. 18–19. Thompson, K., Gdanski, R.D., 1993. Laboratory study provides guidelines for diverting acid with foam. SPEPF, 285 (Nov.). Vassenden, F., Holt, T., 2000. Experimental foundation for relative permeability modeling of foam. SPEREE, 179 (April.). Zeilinger, S.C., Wang, M., Kibodeaux, K.R., Rossen, W.R., 1995. Improved prediction of foam diversion in matrix acidization. SPE 29529 presented at the 1995 SPE Production Operations Symposium, Oklahoma City, OK, April 2–4. Zerhboub, M., Touboul, E., Ben Naceur, K., 1994. Matrix acidizing: a novel approach to foam diversion. SPEPF 121–126 (May). Zhou, Z.H., Rossen, W.R., 1994. Applying fractional flow theory to foams for diversion in matrix acidization. SPEPF, 29–35 (Feb.).