Rheological Transition during Foam Flow in Porous Media - Industrial

Jun 15, 2012 - The flow of nitrogen foam in Bentheimer sandstone cores previously saturated with a surfactant solution has been investigated experimen...
0 downloads 11 Views 3MB Size
Article pubs.acs.org/IECR

Rheological Transition during Foam Flow in Porous Media M. Simjoo,*,† Q. P. Nguyen,‡ and P. L. J. Zitha† †

Department of Geoscience & Engineering, Delft University of Technology, Stevinweg 1, 2628CN Delft, The Netherlands Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, 1 University Station, C0300 Austin, Texas 78712-0300, United States



ABSTRACT: The flow of nitrogen foam in Bentheimer sandstone cores previously saturated with a surfactant solution has been investigated experimentally. The displacement process was visualized with the aid of a computed tomography (CT) scanner. CT data were analyzed to obtain water saturation profiles at different times. Pressure drops measured over core segments were recorded to determine foam mobility. It was found that foam undergoes a sharp transition from a weak to a strong state at a critical gas saturation of Sgc = 0.75 ± 0.02. This effect was interpreted successfully by the rise of foam yield stress as gas saturation exceeds the Sgc. It is suggested that confined jamming is the most likely mechanism responsible for the mobility transition.

1. INTRODUCTION When gas and surfactant solution are injected in a porous medium, gas is dispersed into the liquid phase leading to foaming. This has numerous applications in oil and gas recovery operations, including acid diversion during matrix stimulation,1−3 water and gas shutoff,4,5 and mobility control for enhanced oil recovery (EOR).6,7 Foam improves areal and vertical sweep efficiency as well as microscopic displacement by the drive fluid (i.e., gas and steam), leading to a significant increase of oil recovery.8−10 The performance of foam relies critically on its ability to lower gas mobility. Foam mobility, i.e., the ratio of the foam's relative permeability to its apparent viscosity, depends essentially on bubble density as well as on trapped and flowing gas fractions.3,11 The viscosity of foamed gas is higher than that of water due to the flow resistance resulting from movement of foam films in pores with a complex geometry.12 The trapped gas fraction, on the other hand, greatly reduces gas relative permeability by blocking a large fraction of the pore spaces.13,14 The flowing foam fraction not only affects apparent foam viscosity,13,15 but also leads to irregular foam patterns, which contribute to the complexity of foam rheology.16 In several recent studies17−20 an anomalous transition of foam mobility was observed, but no clear interpretation was provided. The mobility transition is crucial since it determines the mobility reduction factors used as input in modeling and numerical simulations of foam applications. This work is a dedicated attempt to demonstrate that the mobility transition is a real physical effect and to provide a plausible explanation. The premise of this study is that foam in porous media is a nonNewtonian fluid,13,21,22 which is characterized by a yield stress: when external forces are smaller than yield stress, foam does not shear, but when external forces are larger than yield stress, then foam shears with a power-law behavior. Since during foam flow we expect yield stress to increase, this rheological model could account for gas trapping and for the observed mobility transition. To check this hypothesis, we revisit the computed tomography (CT) scan foam experiments reported earlier by Nguyen et al.18 and by Simjoo et al.,20 where N2 and a surfactant solution were co-injected in a Bentheimer sandstone core. The paper proceeds © 2012 American Chemical Society

with the experimental details, which are recalled in section 2 in some detail for the sake of completeness. Next, the results of foam flow experiments are presented and discussed in section 3 in the light of the above new ideas. Then, the main conclusions of this study are drawn in section 4.

2. EXPERIMENTAL SECTION 2.1. Materials and Methods. Brine containing 0.5 M sodium chloride (NaCl, Merck) in deionized water (pH 6.8 ± 0.1) was used to prepare surfactant solutions. Two surfactants were used to perform foam experiments: (1) sodium dodecyl sulfate (SDS, IFraChem) with a molecular weight of 288 g/mol, and (2) C14−16 α-olefin sulfonate (AOS, Stepan) with a molecular weight of 315 g/mol. Fixed surfactant concentrations were used in the experiments: cSDS = 8.0 × 10−3 M and cAOS = 3.0 × 10−2 M. Both surfactant concentrations were above their critical micelle concentrations (cmcSDS = 5.0 × 10−4 M and cmcAOS = 1.3 × 10−4 M) for the indicated salinity. Nitrogen gas with a purity of 99.98% was used to conduct the experiments. The core samples used were quasi-homogeneous and isotropic Bentheimer sandstone. The physical properties of the core samples are presented in Table 1. The average porosity was estimated from the CT scans of the dry and fully brine-saturated core. The absolute permeability was determined from the measured pressure drops of the single-phase water flow at different flow rates. The core samples were encapsulated in a thin (4 ± 1 mm) layer of low X-ray attenuation Araldite (CW 2215) Table 1. Physical Properties of Bentheimer Sandstone Cores Used in the Experiments experiment

permeability (darcy)

porosity (%)

diameter (cm)

length (cm)

SDS foam AOS foam

1.1 ± 0.1 2.4 ± 0.1

22.0 ± 0.1 21.0 ± 0.1

4.4 ± 0.1 3.8 ± 0.1

18.0 ± 0.1 17.0 ± 0.1

Received: Revised: Accepted: Published: 10225

September 28, 2011 June 4, 2012 June 15, 2012 June 15, 2012 dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of the experimental setup used to perform foam experiments. A precision piston displacement pump was used to supply brine and surfactant solution. Gas is supplied by a mass flow controller. Local pressures were monitored using pressure transducers. Effluent was collected using a graded tube and a gas counter. Experimental data were stored in a personal computer equipped with a data acquisition system.

measured in Hounsfield units (HU) defined by the following equation:

glue with a hardener (CIBA HY 5160). The glue was necessary to avoid possible bypassing along the side of the core. After hardening, the glued core was machined to ensure that it fit precisely into the core holder. Two O-rings were used at the top and bottom of the core to make sure there was no flow along the gap between the core holder and the glue layer. The core holder was made of polyether ether ketone (PEEK), a material that combines both good mechanical properties and low X-ray attenuation. 2.2. Experimental Setup. The setup used to conduct the core flooding experiments is shown schematically in Figure 1. It consists of a core holder in line with a reciprocating positive displacement pump (Pharmacia Biotech P-500) in parallel with a mass flow controller (Sierra) and, on the other end, a backpressure regulator and a collector for the produced fluids. The mass flow controller was used to ensure the supply of nitrogen at a constant rate. The pump was also used to inject brine and surfactant solution at a constant rate. A data acquisition system was used to record pressure, liquid production, and gas and liquid injection rates. For the SDS foam experiment, the core holder was placed horizontally on the couch of the CT scanner. The experiment was conducted at a fixed back-pressure of 1.0 bar and ambient temperature (20 ± 1 °C). Four pressure transducers (EnressHauser) were used to monitor local pressures along the core length. The pressure ports divided the core into three sections of 6.0, 4.0, and 8.0 cm denoted sections 1, 2, and 3, respectively. For the AOS foam experiment, the core holder was fixed vertically to the edge of the CT scanner couch using a poly(methyl methacrylate) (PMMA) stand, equally transparent to X-rays. The experiment was conducted at a fixed back-pressure of 20.0 bar and ambient temperature (20 ± 1 °C). Local pressure drops were monitored over four sections along the core with equal lengths of 4.25 cm. 2.3. CT Imaging Principles. CT images were obtained using a third-generation SAMATOM scanner manufactured by Siemens. For this apparatus the X-ray source−detector arrays rotate continuously around the object, and the scanner measures the X-ray attenuations along thousands of X-rays traversing the object at all angles.23 CT images are reconstructed from a large number of measurements of X-ray transmission through the scanned object. The resulting images are tomographic maps of the X-ray linear attenuation coefficient. The CT attenuations are

⎛μ ⎞ HU = 1000⎜⎜ − 1⎟⎟ ⎝ μw ⎠

(1)

where μ and μw are the X-ray attenuation coefficients of the sample and pure water, respectively. During foam flow the attenuation coefficient μfoam is a combination of the attenuation coefficients of surfactant solution and gas phase. It can be described as follows:

μ = μg + Sw(μw − μg )

(2)

where Sw is water saturation (including both brine and surfactantrich brine solution), Sg is gas saturation, μwet is the attenuation coefficient of the surfactant-saturated core, and μdry is the attenuation coefficient of the dry core. Because of high contrast between the CT numbers of the gas and aqueous phases, no doping agent was used. The contribution of surfactant molecules at the concentration investigated was negligible for the attenuation coefficient of the aqueous phase. By combining eqs 1 and 2 and replacing Sg = 1 − Sw, we obtain the following equation for the local water saturation: Sw =

HUfoam − HUdry HUwet − HUdry

(3)

Since noise for the CT images typically ranges from 3 to 20 HU, the error in the obtained water saturation is about ±2%. In this study sequential scan mode was used for the acquisition of the CT images. This scanning mode is slower than the helical mode, but has a lower noise-to-signal ratio.24 The thickness of each CT slice was 3 mm, and one series of scan included five slices. A typical slice image consists of 512 × 512 pixels with a pixel size of 0.3 mm × 0.3 mm. More details about the CT imaging setting can be found elsewhere.19,20 2.4. Experimental Procedure. After extracting native contaminants by the Soxhlet method, the core sample was dried in an oven at 90 °C. Then it was saturated by injecting 200 pore volumes (PV) of brine (0.5 M NaCl) under vacuum to satisfy ion exchange and stabilize clay particles. Core saturation was followed by the injection of surfactant solution (200 PV for SDS and 2.0 PV for AOS) with the same concentration used for 10226

dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231

Industrial & Engineering Chemistry Research

Article

foam flooding to satisfy the adsorption capacity of the rock sample. Next, nitrogen and surfactant solution were co-injected to generate in situ foam at a fixed foam quality of 91%. Table 2 gives an overview of the foam flow experiments investigated in this study.

Red color corresponds to the core fully saturated with surfactant solution, and shifting from red to blue corresponds to a decrease in liquid saturation. The dimensionless time is expressed as a number of injected pore volumes or PV, i.e., as the ratio of the cumulative volume of injected fluids to the pore volume. Two foam displacement stages can be distinguished from the CT images. The first stage corresponds to the injection period before foam breakthrough at the core outlet, at about 0.91 ± 0.05 PV. During this stage, foam propagates throughout the core and displaces the surfactant solution in a characteristic frontlike manner. This foam propagation in the flow direction is called “forward foam”. For a well-developed foam front, three regions can be distinguished along the flow direction. In the upstream region (light yellowish blue), liquid saturation is generally low, except near the core inlet where liquid saturation remains relatively high. In the downstream region (red part), the liquid fraction is unity, and finally in the transition region a fine fingering pattern is present. The transition region is broad due to capillary diffusion. The second stage starts after foam breakthrough and ends when foam reaches a steady state at about 22 PV. This stage is characterized by a secondary liquid desaturation, i.e., by a diminishing saturation front propagating from the outlet to the inlet of the core. This is shown by the progressive darkening and spreading of the blue region in Figure 2. 3.2. Water Saturation Profiles. For a more detailed discussion of the foam propagation, we examine water saturation profiles shown in Figure 3. Each saturation point in Figure 3 was obtained by averaging water saturation over the core cross section (perpendicular to the flow direction) with a thickness of 0.4 mm. The three zones observed before foam breakthrough can be characterized further as follows: in the upstream region swept by foam, average water saturation is about 0.45 ± 0.02, while as we have already mentioned water saturation is unity in the downstream region. The transition zone is relatively short with water saturation increasing fairly steeply from 0.45 to 1.0. However, as already mentioned, the transition zone is not sharp due to capillary diffusion. When foam breaks through at the core outlet, water saturation near the core outlet remains high due to the capillary end effect; i.e., zero capillary pressure at the outlet boundary imposes high water saturation in the core near the outlet. This effect extends over a distance of 4.0 cm from the core outlet, where water saturation falls from 0.78 to 0.45. Beyond 1.4 PV the capillary end effect is eliminated and the entrance effect is partly compensated by the secondary liquid desaturation. Let us

Table 2. Overview of Foam Flow Experimentsa experiment

concn (M)

back-press. (bar)

liq velocity (m/ day)

gas velocity (m/ day)

SDS foam AOS foam

8.0 × 10−3 3.0 × 10−2

1.0 20.0

0.64 0.13

6.35 1.27

a

Foam quality was 91% in both experiments.

At each stage of the experiment, longitudinal CT images were obtained to reveal the propagation of the foam front and determine the distribution of fluid saturations in the porous medium. The central CT image was on the plane of the core axis (axis plane), and the other ones were taken from the vicinity of the axis plane. The central image was used to visualize foam flow in the core.

3. RESULTS AND DISCUSSION Foam flow experiments were analyzed in terms of CT scan images, water saturation profiles obtained from the CT images, and the foam mobility reduction factor (MRF). The latter was defined as the ratio of pressure drop during foam flow to the pressure drop for the water-saturated core, at the same superficial velocity: ΔPfoam MRF = ΔPwater (4) Other studies25−29 used mobility of gas/brine injection as a reference. However, brine displacement by gas is often an unstable process and the corresponding mobilities are generally not well-defined. Here, for greater accuracy, we prefer to use welldefined water mobility as a reference. Since the qualitative behavior of foam propagation in the sandstone porous medium is similar for the both surfactants investigated, we shall first focus on one prototypical experiment (SDS foam). Then the behavior of MRF versus gas saturation will be discussed separately for each experiment to examine foam mobility transition. 3.1. CT Scan Images. Figure 2 shows CT images for the displacement of SDS solution by foam from Bentheimer core.

Figure 2. CT images obtained during SDS foam flow in Bentheimer sandstone core. The time of each image is given in pore volumes of the injected fluids. Blue and red colors stand for gas and liquid phases. First, a forward foam front propagates throughout the core and breaks through around 0.91 ± 0.05 PV. After foam breakthrough a secondary desaturation front appears in the outlet region which propagates toward the inlet of the core like a backward wave. 10227

dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231

Industrial & Engineering Chemistry Research

Article

the core inlet region. This velocity difference indicates a rather different mechanism for the primary forward foam propagation and for the secondary backward desaturation front. There is a sudden drop of the locus of the wave at about 1.5 PV which is caused by the capillary end effect as discussed above. 3.3. Mobility Reduction Factors. Figure 5 shows the mobility reduction factors (MRFs) obtained during SDS foam

Figure 3. Water saturation profiles obtained from the CT images of SDS foam flow. The light-green profiles stand for forward foam front, and the blue ones indicate secondary backward foam front. Both fronts are diffusive due to the effect of capillary pressure.

consider the water saturation profile at 7.48 PV, for instance. As the secondary desaturation front crosses the downstream core section (section 3, located between the lengths of 10.0 and 18.0 cm), the average water saturation drops from 0.45 to 0.19. Thereafter, it remains practically constant for the rest of the injection. This part is followed by a long transition zone extending from 10.0 to 6.0 cm toward the core inlet. Throughout this distance water saturation increases from 0.19 to 0.45. After 22 PV, foam displacement reaches a steady state characterized by little change in the saturation profiles and nearly uniform water saturation of 0.19 ± 0.02 through the core length, except near the core inlet. Figure 4 shows the position of the forward and backward desaturation foam fronts versus number of pore volumes injected. The forward front velocity (slope of the curve) is almost constant and is nearly equal to 20 cm/PV. The velocity of the backward desaturation front is much lower and decreases over time. Initially the backward front velocity is nearly equal to 0.29 cm/PV, but it decreases to almost zero as the front reaches

Figure 5. Foam mobility reduction factor (MRF) obtained during SDS foam flow. MRF was defined as the ratio of pressure drop for foam and single-phase water flows. As the secondary desaturation front reaches a given section, the corresponding sectional MRF increases significantly. When MRF approaches a plateau value, it starts to grow in the next section. The evolution of MRF is in good agreement with the CT images and water saturation profiles.

flow for three successive core sections. For the upstream core section (section 1, 6.0 cm), MRF first increases rather steeply to a low value of 5 and then it remains constant until 15 PV. Thereafter, it increases gradually from 5 to 12. For the second section, MRF first increases slowly to about 3, and then remains practically unchanged until 9 PV. During the next 7 PV MRF grows from 3 to 18, and thereafter it increases at a slower rate and finally levels off to a plateau value of 23. The evolution of MRF for section 3 is very fast compared to the previous two sections. At early times, as the foam front advances through this section, MRF increases, but only up to 2.7 until foam breakthrough at the core outlet. Slightly after foam breakthrough, MRF rises sharply and reaches a value of 56 after 10 PV. Thereafter, it continues to grow at a much slower rate and finally levels off to a plateau of about 60. There is a remarkable correlation between MRF and water saturation profiles. Shortly after foam breakthrough, MRF builds up mainly in the downstream core section (section 3 with a length of 8.0 cm). This coincides with the development of the secondary foam front and the progressive decrease of water saturation in this section. For instance, at 7.48 PV the secondary foam front crosses the third section of the core where MRF rises from 5 to 47 and the average water saturation drops from 0.45 to 0.19. As the desaturation front moves through the middle section (section 2 with a length of 4.0 cm), water saturation decreases while MRF increases. At 15.87 PV, for instance, the average water saturation decreased to 0.22 and MRF increased to 19. Finally, MRF in the upstream section (section 1 with a length of 6.0 cm) increases gradually as the desaturation front moves through this section. Water saturation over this section does not drop considerably and MRF response is quite slow.

Figure 4. Displacement of the locus of the forward and backward desaturation foam fronts versus number of pore volumes injected for SDS foam flow. The forward front travels with a velocity of 20 cm/PV. The velocity of the backward desaturation front is much lower and decreases to almost zero as the front approaches the inlet region. 10228

dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231

Industrial & Engineering Chemistry Research

Article

nitrogen foam stabilized by AOS surfactant. In this experiment foam was generated at a total superficial velocity of 1.40 m/day at a back-pressure of 20.0 bar (see Table 2 for the experimental conditions). Figure 7 shows the dependence of the AOS foam

It is worthwhile to compare the magnitudes of foam mobility reduction after 22 PV, the time at which the backward desaturation front becomes practically stationary (see Figure 4). Since the core sections have different lengths, for a better comparison we examine the mobility reduction gradient (MRG), i.e., the ratio of the sectional MRF to the corresponding core section length. MRG is 2.1, 5.9, and 7.5 cm−1 for the successive core sections; i.e., foam strength increases along the core length. The corresponding average water saturations are 0.36, 0.20, and 0.19, respectively. It can therefore be concluded that the increase in MRG is accompanied by a decrease in water saturation. 3.4. Foam Mobility Transition. In order to inspect the relation between fluid saturation and foam mobility in porous media, we examine now the behavior of MRF as a function of gas saturation as shown in Figure 6 for SDS foam. Gas saturations

Figure 7. Mobility reduction factor (MRF) versus gas saturation for four successive core sections during AOS foam flow. Mobility transition occurs for AOS foam at Sgc = 0.75 ± 0.02 in a similar way to that for SDS foam. The MRF is much larger for AOS foam than for SDS foam.

mobility on gas saturation at four successive core sections with equal lengths of 4.25 cm. The overall behavior of the AOS foam mobility is similar to that of the SDS foam: a weak foam state with a very low MRF followed by a strong foam state with a high MRF through a transition stage at which gas saturation exceeds a critical value of 0.75 ± 0.02. At the same gas saturation above the critical value AOS foam exhibits a much larger MRF than SDS foam, which indicates that AOS foam is more stable than SDS foam. To develop a mechanistic description of foam mobility transition, we recall first that foam mobility reduction in porous media arises from two concurrent effects, namely the increase in foam viscosity and lowering of foam relative permeability. In the context of the stochastic bubble population (SBP) model,21,22 foam was described as a yield stress fluid obeying a Herschel− Bulkley rheological model. The yield stress and plastic viscosity depend essentially on bubble density. Foam trapping and associated residual gas saturation, the main factors leading to reduction of gas relative permeability, are a consequence of the buildup of yield stress. The interpretation of the transition from weak to strong foam can now be developed as follows. Before foam breakthrough, yield stress is very small throughout the flow domain. Therefore, foam viscosity remains low and, since there is practically no foam trapping, foam relative permeability remains high and possibly nearly equal to that of free gas. This leads to a relatively low mobility reduction factor being obtained in the experiments. After foam breakthrough, however, yield stress increases considerably due to the secondary desaturation front, leading to high foam viscosity and to foam trapping. The latter effect leads to a drastic reduction in the relative permeability of both water and foam. This explains the large MRF obtained in the strong foam regime. From the above discussion, it can be inferred that mobility transition is due essentially to buildup of yield stress. It follows then that yield stress must be negligible for low gas saturations,

Figure 6. Mobility reduction factor (MRF) versus gas saturation for three successive core sections during SDS foam flow. As gas saturation exceeds a critical value, MRF rises sharply indicating a transition from a weak to a strong foam state. This foam mobility transition occurs at a critical gas saturation of 0.75 ± 0.02.

were obtained by averaging the CT data over the core sections. For the first section, MRF remains at a low value, only slightly higher than 10, through the duration of the experiment. The average gas saturation over this section does not exceed 0.65. For the second section, MRF is initially very low, but when gas saturation exceeds a critical value, MRF increases steeply, reaching a final value of 23 at the gas saturation nearly equal to 0.80. The behavior in the third section is even more striking. MRF remains very low as long as gas saturation is below 0.60. However, above this value MRF increases steeply and reaches 60 at the gas saturation of 0.82. The critical gas saturation for the transition from a low (weak foam) to a high MRF region (strong foam) is given by the crossover of two lines and was estimated to be Sgc = 0.75 ± 0.02. MRF values do not show any tendency to become stable for the middle section. For section 3, MRF reaches a stable value and then decreases slowly at almost constant gas saturation. The maximum of MRF is probably very close to the critical capillary pressure for foam collapse (Pc*). The corresponding critical water saturation is approximately Sw* = 0.17 ± 0.02. This value is slightly lower than values reported in the literature for other sandstone samples. However, the observed strong foam behavior is in good agreement with the Pc* theory.30,31 For further validation of the concept of foam mobility transition, we provided another set of MRF vs Sg profiles for 10229

dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231

Industrial & Engineering Chemistry Research



but it rises sharply above the critical gas saturation. This dependence of yield stress on gas saturation is a commonly observed feature of bulk foams and concentrated emulsions.32−34 Following Princen and Kiss,33 the yield stress of bulk foams rises sharply when the gas fraction is higher than a critical value corresponding to the close-packed sphere configuration. This critical value is nearly equal to 0.74 for monodisperse spheres. At the critical gas fraction, gas bubbles are in contact with each other and each bubble is slightly deformed against the neighboring ones. With further increase in gas fraction, the bubbles interact strongly with each other and are strongly limited in their motion.35,36 This leads to the yield stress type of behavior. The analogies between foam yield stress in bulk and in porous media suggest that the sharp rise of yield stress in porous media at a critical gas saturation could also be due to jamming. In porous media the bubbles will be at least as large as the pores; therefore, the “confined jamming” will involve the interaction of the bubbles with the pore walls. Data are scarce in the literature to confirm these ideas, but we hope that more attention will be paid to jamming in future works on foam flow in porous media. Another question that remains to be resolved is what triggers the secondary desaturation. We suspect that the capillary effects are involved, but it is not completely clear yet how they induce the backward desaturation. This should also be addressed in future studies. Finally, we may ask, what is the relevance of the strong foam regime for the applications, since in most of them the injected foam hardly exceeds 1 PV? We believe that the mobility reduction factor obtained in the weak flow regime might be sufficient to achieve mobility control or blocking required in the oil production operations. Even a relatively modest mobility reduction factor implies that the apparent viscosity of foam is larger than that of water. This might be sufficient to ensure the desired mobility control in many cases.

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS We gratefully acknowledge Prof. P. K. Currie for a careful reading of the manuscript. The experiments were done as a part of research funded by Shell and Halliburton. M.S. acknowledges the financial support of the Iran Ministry of Science, Research, and Technology for his Ph.D. study.



REFERENCES

(1) Kibodeaux, K. R.; Zeilinger, S. C.; Rossen, W. R. Sensitivity Study of Foam Diversion Processes for Matrix Acidization. Annual Technical Conference and Exhibition, New Orleans, LA, Sept 25−28, 1994; SPE 28550. (2) Behenna, F. R. Acid Diversion from an Undamaged to a Damaged Core using Multiple Foam Slugs. SPE European Formation Damage Conference, The Hague, Netherlands, May 15−16, 1995; SPE 30121. (3) Rossen, W. R. Foams in Enhanced Oil Recovery. In Foams: Theory, Measurements and Applications; Prud’homme, R. K., Khan, S., Eds.; Marcel Dekker: New York, 1996. (4) Hanssen, J. E.; Dalland, M. Gas Blocking Foams. In Foams: Fundamentals and Applications in the Petroleum Industry; Schramm, L. L., Ed.; American Chemical Society: Washington, DC, 1994. (5) Zhdanov, S. A.; Amiyan, A. V.; Surguchev, L. M.; Castanier, L. M.; Hanssen, J. E. Application of Foam for Gas and Water Shut-off: Review of Field Experience. European Petroleum Conference, Milan, Italy, Oct 22−24, 1996; SPE 36914. (6) Patzek, T. W. Field Applications of Foam for Mobility Improvement and Profile Control. SPE Reservoir Eng. 1996, 11 (2), 79−86. (7) Turta, A. T.; Singhal, A. K. Field Foam Applications in Enhanced Oil Recovery Projects: Screening and Design Aspects. International Oil and Gas Conference and Exhibition in China, Beijing, China, Nov 2−6, 1998; SPE 48895. (8) Ali, J.; Burley, R. W.; Nutt, C. W. Foam Enhanced Oil Recovery from Sand Packs. Chem. Eng. Res. Des. 1985, 63, 101−111. (9) Andrianov, A.; Farajzadeh, R.; Mahmoodi Nick, M.; Talanana, M.; Zitha, P. L. J. Immiscible Foam for Enhancing Oil Recovery: Bulk and Porous Media Experiments. Ind. Eng. Chem. Res. 2012, 51, 2214−226. (10) Simjoo, M.; Dong, Y.; Andrianov, A.; Talanana, M.; Zitha, P. L. J. A CT Scan Study of Immiscible Foam Flow in Porous Media for EOR. SPE EOR Conference at Oil and Gas West Asia, Muscat, Oman, April 16−18, 2012; SPE 155633. (11) Kovscek, A. R.; Radke, C. J. Fundamentals of foam transport in porous media. In Foams: Fundamentals and Applications in the Petroleum Industry; Schramm, L. L., Ed.; American Chemical Society: Washington, DC, 1994. (12) Hirasaki, G. J.; Lawson, J. Mechanisms of Foam Flow in Porous Media: Apparent Viscosity in Smooth Capillaries. SPE J. 1985, 25 (2), 176−190. (13) Falls, A. H.; Hirasaki, G. J.; Patzek, T. W.; Gauglitz, P. A.; Miller, D. D.; Ratulowski, T. Development of a Mechanistic Foam Simulator: The Population Balance and Generation by Snap-off. SPE Reservoir Eng. 1988, 3 (3), 884−892. (14) Friedmann, F.; Chen, W. H.; Gauglitz, P. A. Experimental and Simulation Study of High Temperature Foam Displacement in Porous Media. SPE Reservoir Eng. 1991, 6 (1), 37−45. (15) Bretherton, F. P. The Motion of Long Bubbles in Tubes. J. Fluid Mech. 1962, 10 (2), 166−188. (16) Briceno, M. I.; Joseph, D. D. Self-lubricated Transport of Aqueous Foams in Horizontal Conduits. Int. J. Multiphase Flow 2003, 29 (12), 1817−1831.

4. CONCLUSIONS • Foam propagation in Bentheimer sandstone cores due to the co-injection of nitrogen and a surfactant solution (SDS and AOS) in 0.5 M NaCl brine was studied with the aid of an X-ray CT scanner to map fluid saturations at different times. • Foam propagation exhibited two foam fronts: (1) a primary forward foam front characterized by a low mobility reduction factor and a modest reduction in water saturation, and (2) a secondary backward desaturation foam front that appears after foam breakthrough and leads to a large foam mobility reduction and further liquid desaturation from the previously foam-filled porous medium. • A transition from a weak to a strong foam state occurs at the critical gas saturation of 0.75 ± 0.2. Consistent with the stochastic bubble population model, it was inferred that the mobility transition is due to the sharp rise of yield stress when gas saturation exceeds the critical value. • The critical gas saturation for surge of yield stress is nearly equal to the critical fraction of packing spheres at which bulk foams are subject to the jamming phenomenon. It is suggested that increase of yield stress and thus foam mobility transition is most probably due to a confined jamming. This needs confirmation by dedicated studies to be done in the future. 10230

dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231

Industrial & Engineering Chemistry Research

Article

(17) Apaydin, O. G.; Kovscek, A. R. Transient Foam Flow in Homogeneous Porous Media: Surfactant Concentration and Capillary End Effects. Transp. Porous Media 2001, 43 (3), 511−536. (18) Nguyen, Q. P.; Currie, P. K.; Zitha, P. L. J. Determination of Foam Induced Fluid Partitioning in Porous Media using X-ray Computed Tomography. SPE International Symposium on Oilfield Chemistry, Houston, TX, Feb 5−8, 2003; SPE 80245. (19) Zitha, P. L. J.; Nguyen, Q. P.; Currie, P. K.; Buijs, M. A. Coupling of Foam Drainage and Viscous Fingering in Porous Media Revealed by X-ray Computed Tomography. Transp. Porous Media 2006, 64 (3), 301−313. (20) Simjoo, M.; Dong, Y.; Andrianov, A.; Talanana, M.; Zitha, P. L. J. Novel Insight into Foam Mobility Control. International Petroleum Technology Conference, Bangkok, Thailand, Feb 7−9, 2012; SPE 15338. (21) Zitha, P. L. J. A New Stochastic Bubble Population Model for Foam in Porous Media. SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, April 22−26, 2006; SPE 98976. (22) Zitha, P. L. J.; Du, D. X. A New Stochastic Bubble Population Model for Foam Flow in Porous Media. Transp. Porous Media 2010, 83, 603−621. (23) Otani, J.; Obara, Y. X-ray CT for Geomaterials: Soils, Concrete, Rocks. International Workshop on X-ray CT for Geomaterials; A. A. Balkema Publishers: Kumamoto, Japan, 2003. (24) Mees, F.; Swennen, R.; Van Geet, M.; Jacobs, P. Application of Xray Computed Tomography in the Geosciences; Geological Society Special Publication 215; The Geological Society: London, 2003. (25) Maini, B. B.; Ma, V. Relationship between Foam Stability Measured in Static Tests and Flow Behavior of Foams in Porous Media. SPE Annual Technical Conference and Exhibition, Houston, TX, Sept 16−19, 1984; SPE 13073. (26) Mannhardt, K.; Novosad, J. J.; Schramm, L. L. Foam-Oil Interactions at Reservoir Conditions. SPE/DOE Improved Oil Recovery Symposium, Tulsa, OK, April 19−22, 1998; SPE 39681. (27) Siddiqui, S.; Talabani, S.; Saleh, S. T.; Islam, M. R. Foam Flow in Low-Permeability Berea Sandstone Cores: A Laboratory Investigation. J. Pet. Sci. Eng. 2002, 36 (3−4), 133−148. (28) Farajzadeh, R.; Andrianov, A.; Zitha, P. L. J. Investigation of Immiscible and Miscible Foam for Enhancing Oil Recovery. Ind. Eng. Chem. Res. 2010, 49, 1910−1919. (29) Aarra, M. G.; Ormehaug, P. A.; Skauge, A.; Masalmeh, S. K. Experimental Study of CO2- and Methane-Foam Using Carbonate Core Material at Reservoir Conditions. SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, Sept 25−28, 2011; SPE 141614. (30) Khatib, Z. I.; Hirasaki, G. J.; Falls, A. H. Effects of Capillary Pressure on Coalescence and Phase Mobilities in Foams Flowing through Porous Media. SPE Reservoir Eng. 1988, 3 (3), 919−926. (31) Rossen, W. R.; Zhou, Z. H. Modeling Foam Mobility at the Limiting Capillary Pressure. SPE Adv. Technol. Ser. 1995, 3 (1), 146− 153. (32) Khan, S. A.; Schnepper, C. A.; Armstrong, R. C. Foam Rheology: III. Measurement of Shear Flow Properties. J. Rheol. 1988, 32 (1), 69− 92. (33) Princen, H. M.; Kiss, A. D. Rheology of Foams and Highly Concentrated Emulsions: IV. An Experimental Study of the Shear Viscosity and Yield Stress of Concentrated Emulsions. J. Colloid Interface Sci. 1989, 128 (1), 176−187. (34) Weaire, D.; Hutzler, S. The Physics of Foams; Oxford University Press: Oxford U.K., 1999. (35) Denkov, N. D.; Tcholakova, S; Golemanov, K.; Lips, A. Jamming in Sheared Foams and Emulsions, Explained by Critical Instability of the Films Between Neighboring Bubbles and Drops. Phys. Rev. Lett. 2009, 103 (11), 11830-4. (36) Siemens, A. O. N.; van Hecke, M. Jamming: A Simple Introduction. Physica A: Stat. Mech. Its Appl. 2010, 389 (20), 4255− 4264.

10231

dx.doi.org/10.1021/ie202218z | Ind. Eng. Chem. Res. 2012, 51, 10225−10231