Properties of multi-phase foam and its flow behavior in porous media

Abstract

Aqueous foams were produced with partially hydrophobic SiO₂ nanoparticles and sodium dodecyl sulfate (SDS) dispersions. The injection behavior of SiO₂ stabilized foam (SiO₂/SDS foam) was analyzed and compared with SDS stabilized foam (SDS foam). The experimental results showed that the SiO₂ nanoparticles and SDS surfactants had a synergistic effect on foam stability at proper SDS concentration. And the effect was accompanied with a slight decrease in foam volume. The adsorption of nanoparticles on the bubble surface was confirmed by laser-induced confocal fluorescence microscopy. And the effect of absorbed nanoparticles on bubble surface viscoelasticity was also verified by the interfacial dilational rheological measurement. The dilational viscoelasticity increased with increasing SiO₂ concentration, corresponding to foam stability. The plugging flow experiment demonstrated that the maximum differential pressure in SiO₂/SDS foam flooding was 1.9 MPa, much higher than that in SDS foam flooding. The SiO₂/SDS foam had better diversion properties and resistance to water flushing than SDS foam. In the oil displacement experiments, SiO₂/SDS foam could reduce the residual oil saturation noticeably. The enhanced oil recovery and the final oil recovery could reach to 41.2% and 75.7%, respectively. It was deduced that the enhanced foam stability and dilational viscoelasticity were the main reasons for the effective performance in porous media.

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1. Introduction

Water flooding is a kind of general and economic secondary oil recovery technique. However water usually flows along high-permeability zones or fractures, and thus the oil in the low-permeability zones can not be displaced effectively.^1,2 Besides, the viscous fingering caused by the adverse viscosity ratio between oil and water is another reason for poor oil recovery.³ The viscous fingering is the formation of patterns in a morphologically unstable interface between two fluids in porous medium. It occurs when a less viscous fluid is used to displace a more viscous one. More than 60% of the oil originally in place (OOIP) remains in the reservoir as residual oil after exploiting with conventional oil recovery methods (including primary and secondary recovery techniques).

The oil recovery is enhanced by either increasing sweep volume or improving oil displacement efficiency.^4–8 Foam flooding has been proved to be an effective method to increase sweep volume. It has been used on site since the 1960s in China and has already developed into a series of oil displacement techniques after half a century.⁹ Since gas is wrapped into bubbles in aqueous foam, the gas flow is controllable and the volumetric sweep efficiency is also improved.^10–13 The apparent viscosity of foam is several orders of magnitude greater than that of either gas or liquid, so the foam fluids can inhibit viscous fingering and thus increase the oil recovery. Especially in heterogeneous formation, which contains layers of different permeabilities, foam can block the high-permeability layer first, and then divert subsequent fluid into the low-permeability layer.

Bubbles are thermodynamically unstable in nature, especially in porous media under formation conditions. Thus, increasing foam stability is a prerequisite for better application in the field of oil recovery. Foam stabilized by nanoparticles has recently attracted special attention in food-making processes,¹⁴ flotation,¹⁵ and water borne coatings.¹⁶ Like surfactant molecules, nanoparticles with proper surface amphiphilicity could adsorb at the air/liquid interface and enhance foam stability. The adsorption of nanoparticles is usually irreversible and its adsorption energy determines the foam stability.¹⁷ Furthermore, the adsorbed nanoparticles at the air/water interface resist the water flow on liquid film and separate the dispersed phase, thus slowing down the liquid film thinning and bubble shrinkage.^18–21 Previous studies indicated that the dilational viscoelasticity of the particle-coated bubble surface was another key parameter of foam stabilization.²² The dilational property is usually used to characterize the physical process in the dispersion surface layer and provides useful information about the adsorption of nanoparticles at the air/water interface. The enhanced viscoelasticity indicated resistance of the bubble film to dilational distortion, and thus the bubble became more stable against coarsening.

Many researchers have been studying the behavior of emulsions or foams stabilized by surface-active nanoparticles, and several valuable reviews have been published recently.²³ Lumsdon et al.²⁴ found that the stability of the emulsion produced by silica could be enhanced by adjusting the extent of particle flocculation with electrolytes (such as NaCl). Addition of surfactant to nanoparticle systems could also affect their efficiency as emulsifiers. Rodrigues et al.²⁵ proposed that the adsorption of proper surfactant molecules onto the particle surface enabled particle adsorption at the oil/water interface. The surfactant could influence the particle stabilized emulsion in three ways: (a) decrease of the interfacial tension, facilitating droplet formation; (b) adsorption of the particle surface, affecting its hydrophobicity; (c) allowing particle flocculation.²⁶ Garrett et al.²⁷ studied foams stabilized by latex nanoparticles in surfactant solutions, and proposed that the latex nanoparticles depleted the surfactant concentration by adsorption and stabilized the thin liquid films against drainage through stratification. Binks et al.²⁸ investigated the behavior of air-in-water foams stabilized by a mixture of silica nanoparticles and cationic surfactant in detail. It was shown that the synergism between the nanoparticles and the surfactant enhanced the foam stability. The application of nanoparticle-stabilized foams in oilfields is attracting the interest of more and more researchers. Yu et al.²⁹ investigated the particle hydrophobicity on CO₂ foam generation in porous media under reservoir conditions. The results indicated that more CO₂ foams were generated as the nanoparticle changed from hydrophilic to hydrophobic. Aminzadeh et al.³⁰ studied the effect of nanoparticles on sweep efficiency during CO₂ injection using CT scanning techniques. It was shown that the addition of nanoparticles increased the sweep volume and reduced the gravity override in CO₂ flooding. Lee et al.³¹ studied the transportation and retention of nanoparticles in three different porous media. It was proved that the nanoparticles could pass through the porous media with little retention in the sandpack model. Sun et al.³² and Nguyen et al.³³ evaluated the nanoparticle-stabilized foam stability and effectiveness in enhanced oil recovery at the pore scale and the micromodel scale. It was found that the foam showed a significant improvement in stability and EOR.

Despite meaningful research activities on surfactants with hydrophilic nanoparticles, the surface properties of a foam produced by partially hydrophobic nanoparticles in surfactant solution have not been well investigated. Besides, the performance of nanoparticle-stabilized foam on plugging properties and oil recovery still need further study. In this paper, partially hydrophobic SiO₂ nanoparticles and SDS surfactant were used to prepare aqueous foam. The properties of SiO₂/SDS foams were investigated, and the optimal ratio of SDS to SiO₂ was also determined on account of foam stability. The effect of SiO₂ concentration on foam plugging, diversion and oil displacement efficiency were studied by both single and dual sandpack displacement tests.

2. Experimental section

2.1. Materials

Deionized water was purified by ion exchange and its surface tension was about 72.2 mN m⁻¹ at 25 °C. Sodium dodecyl sulfate (SDS) was purchased from Sigma (U.S.A.), at a purity of more than 99%. The crude oil was from Shengli oilfield, Shandong Province, China. Its viscosity and density were 840 mPa s and 0.89 g cm⁻³ at 25 °C, respectively.

SiO₂ nanoparticles (HDK, H18) were supplied by Germany Wacker Chemical Co., Ltd. The particles appeared as a white powder and were nearly spherical, with a mean diameter of ∼14 nm. The surface of the particles was hydrophobically modified by the manufacturer. The silanol group density is 0.5 silanol per nm² and the specific surface area is 200 ± 30 m² g⁻¹. All glassware was cleaned with a surfactant free cleaning agent. Experiments were conducted at room temperature (25 °C) unless specified otherwise.

2.2. SiO₂/SDS dispersion preparation

The SiO₂/SDS dispersions were prepared by dispersing a certain mass of SiO₂ nanoparticles and SDS into deionized water. The pH of the dispersions was fixed at 7.0. Then the mixture was stirred for 12 h to attain adsorption equilibrium, followed by two hours of sonication. Finally, the prepared dispersion was sealed and laid aside in a constant temperature oven overnight before use. The relative SDS concentration in the dispersions was given bywhere RC was the relative SDS concentration, C_SDS was the SDS concentration (wt%) in the dispersions and C_SiO2 was the SiO₂ concentration (wt%) in the dispersions.

2.3. Foams stabilized by SiO₂/SDS dispersions

Foams were produced with SDS solutions or SiO₂/SDS dispersions using a Warning Blender (Qingdao Senxin Machinery Equipment Co., Ltd, China) operated at 8000 rpm for 3 min. The volume of the solution or dispersion used for making foam was 100 mL. When the blender was stopped, foams were immediately transferred into a glass cylinder. The foamability was defined as the initial foam volume after preparation. The foam stability was evaluated by the time required for 50 mL of the liquid to drain from the foams. During the experiments, Parafilm was used to seal the top of the cylinder in order to minimize the effect of environmental humidity on foam stability.

The determination of foam properties was also performed by Foamscan apparatus (Teclis, France). The schematic of Foamscan was shown in Fig. 1. The main parts of the instrument included a light source, a glass tube, two CCD cameras, electrodes, a conductance meter and mass flow controller.^34,35 The principle is to foam a known quantity of solution (dispersion) by sparging gas through a porous glass disc (pore diameter 0.2–0.4 μm), then the generated foam would rise along a glass column. The images for bubble coalescence and rupture were recorded by CCD cameras. A pair of electrodes, at the bottom of the tube, was used to measure the liquid content that drained from the foam, while the quantity of liquid in the foam was measured by conductimetry. During the experiments, 60 mL of solution was injected into the glass column. Then the nitrogen was sparged in at a constant flow rate of 200 mL min⁻¹ to generate foams. The foam volume was recorded by a CCD camera, and the gas injection would be stopped as long as the foam volume reached 220 mL. There was a second CCD camera around the foam height of about 10 cm, to collect the images and record the bubble size development. All of the data and images were transmitted to a computer and analyzed with software. Details about the Foamscan can be found elsewhere.³⁶

Fig. 1 Schematic of the Foamscan apparatus.

2.4. Interfacial dilational rheology

The interfacial dilational rheology was measured by an automatic interfacial rheometer (Tracker-H, TECLIS, France). During the experiments, a pendant aqueous drop was created by injecting liquid through a stainless steel needle attached to a gas-tight syringe. When the drop shape was deformed by dilation, a feedback of the drop volume would be given by the shape apparatus. So the dynamic surface tension was obtained by shape analysis via the Young–Laplace equation. Droplets of the dispersions were kept for at least 3000 s to reach the equilibrium surface tension before oscillations. Then the dosing system, controlled by the software, triggered periodical oscillations at a frequency of 0.1 Hz with a volume amplitude of 1 μm³. The surface dilational viscoelasticity in compression and expansion was defined aswhere γ was the interfacial tension, and A was the area of the interface. It gave the interfacial resistance to changes in area or volume. Details about the methods were given elsewhere.³⁷

2.5. Adsorption of nanoparticles at the bubble surface

The laser-scanning confocal microscope (Olympus Fluoview 500, Japan) was used to investigate the adsorption of SiO₂ particles at the bubble surface. The fluorescent probe was FITC (fluorescein isothiocyanate), which had a maximum excitation wavelength at 525 nm. The SiO₂ nanoparticles were first labeled with FITC, and then the SiO₂/SDS dispersion was washed with deionized water to remove the free FITC in the bulk. The fluorescent images of the SiO₂/SDS foam were observed by the laser-induced confocal microscope when the foams were produced.

2.6. Sandpack experiments

2.6.1. Apparatus. Silica sands with different diameters were used to obtain sandpacks with different permeabilities. The inner diameter of the sandpack was 2.5 cm and the length was 30.0 cm. Table 1 lists the key parameters of the sandpack models. A back pressure regulator (BPR) with an accuracy of <0.001 MPa was used during the experiments. For all of the sandpack experiments the back pressure was set at 2.0 MPa. For foam flooding, the foam was pre-generated by a foam generator, which was packed with 70–100 μm silica sand and was placed upstream of the sandpack model. The temperature of the experiments was controlled by putting the sandpacks in a fixed-temperature chamber. Details of the sandpack flooding apparatus can be found elsewhere.^32,38 For SiO₂/SDS dispersions, the SiO₂ concentrations were 0.5 wt%, 1.0 wt%, 1.5 wt%, 2.0 wt%, with the relative SDS concentration of RC = 0.4. And for the pure SDS solution, the SDS concentration was 0.5 wt%.

Table 1 Parameters of sandpack models

Model no.	Permeability (mD)	Porosity (%)	Permeability ratio^b	Initial oil saturation (%)
a #6–#10 are parallel sandpack models.b The permeability ratio is defined as the permeability of high-permeability sandpack divided by that of low-permeability sandpack.
#1	2083	40.8	—	—
#2	2106	40.2	—	—
#3	2013	39.6	—	—
#4	2201	42.1	—	—
#5	2133	43.1
#6^a	3841	41.3	5.83	—
	659	38.5
#7^a	3783	41.0	5.81	—
	651	38.4
#8^a	3954	41.3	5.92	—
	668	38.5
#9^a	3713	41.0	5.73	—
	648	38.4
#10^a	3741	42.4	5.76	—
	649	39.1
#11	1323	35.79	—	88.47
#12	1267	33.31	—	85.29
#13	1289	32.88	—	84.82
#14	1365	34.32	—	86.67
#15	1402	35.78	—	87.68

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2.6.2. Single sandpack experiment. In the single sandpack experiment, SDS foam and SiO₂/SDS foam were injected into five single sandpack models with nearly the same permeability (#1–#5), respectively. Each experiment began with water saturation, and the pore volumes were recorded. After that, firstly, water was injected for 0.6 PV (pore volume) at a rate of 1.0 mL min⁻¹. Secondly, 1.8 PV of foam was injected into the sandpack. The injecting rates of both foam agent solution and gas were 0.5 mL min⁻¹. At last, water was injected again at a rate of 1.0 mL min⁻¹. During the injection period, the pressure difference (ΔP, given in units of MPa) was measured over a certain time interval. The permeability of sandpack models in the waterflooding process was calculated using the following equations:where Q was the injection rate (mL s⁻¹), μ was the fluid viscosity (mPa s), A was the sectional area of the sandpack model (cm²), and L was the length of the sandpack (cm).

2.6.3. Dual sandpack experiment. Five heterogeneous dual sandpack models (#6–#10) were used in this study. Each sandpack model began with water saturation, and then pore volumes and permeabilities were tested. After that, firstly, the water was injected for 0.55 PV at an injecting rate of 2.0 mL min⁻¹. Secondly, 2.75 PV of foam was injected into the sandpack. The injecting rates of solution and gas were both 1.0 mL min⁻¹. Finally, the water was injected again at a rate of 2.0 mL min⁻¹ to investigate the resistance of foam to water flushing. The flow volumes for high and low permeability sandpack (Q_H and Q_L) were measured at fixed time intervals. The diversion ratio was defined as the ratio of flow volume (Q_H or Q_L) to total flow volume (Q_H + Q_L).

2.6.4. Oil displacement experiment. The sandpack flooding test was conducted horizontally. The experimental procedure was briefly described as follows. After the permeabilities and pore volumes of the sandpacks (#11–#15) were measured, the sandpacks were subsequently saturated with crude oil. The oil injection was continued until no water was produced (water cut less than 2.0%), and the initial oil saturation was calculated. Then 2.0 PV of water was injected into the sandpack until the oil production became negligible (oil cut less than 2.0%). After the initial waterflooding, 1.5 PV foam was followed by extended waterflooding. During the flooding test, the produced oil and pressure changes were recorded with time. Unless explicitly stated, the water injecting rate was 1.0 mL min⁻¹, and the rates of both foaming agent solution and gas were 0.5 mL min⁻¹.

3. Results and discussion

3.1. Properties of SiO₂/SDS foam

The foam volume and foam stability of SDS solutions are shown in Fig. 2. Both the foamability and the stability increased with SDS concentration and remained unchanged above its CMC (0.23 wt%). The maximum foam volume and half life time of SDS foam were about 685 mL and 430 s, respectively. The foam volume of SiO₂/SDS dispersions, shown in Fig. 3, was lower than that of SDS solution, and decreased with increasing SiO₂ concentration. It might be related to the increased viscosity of the dispersion (Fig. 4). The enhanced viscosity meant more energy cost to create gas–liquid surfaces. Moreover, some of the surfactant molecules might adsorb onto the SiO₂ surface and the concentration of free SDS in the dispersion decreased, which can also effect the foam volume.³⁹

Fig. 2 Foam stability and foam volume of different SDS solutions.

Fig. 3 Foam volume of SiO₂/SDS system as a function of SDS (wt%) at different SiO₂ concentrations.

Fig. 4 Viscosity of SiO₂/SDS dispersion vs. SiO₂ concentration at fixed SDS concentration of 0.5 wt%.

The stability of SiO₂/SDS foam was shown in Fig. 5. The concentrations of SiO₂ in the dispersions were 0.5 wt%, 1.0 wt%, 1.5 wt%, 2.0 wt%, and the relative SDS concentrations varied from RC = 0 to 1 at each nanoparticle concentration. The foam stability increased with increasing nanoparticle concentration. For each nanoparticle concentration, the most stable foams were formed at the same concentration ratio of SDS to SiO₂ (about RC = 0.4). At fixed SiO₂ concentration, four regions were defined according to the half life time of the foam. Little foam could be produced at relatively low (RC = 0 to 0.15) SDS concentration (region I). The half life time increased gradually on increasing the relative SDS concentration until the maximum value was reached at RC = 0.4 (region II), and then the foam stability decreased (region III). In region IV, the foam stability did not decrease further. In region I, the half life time of SiO₂/SDS foam was lower than that of SDS foam (above CMC). Hardly any stable foams were formed. In regions II and III, the foam stabilized by SiO₂/SDS was more stable than those stabilized by SDS alone. In region IV, the foam stability was only a little higher than that of SDS foam. It could be inferred that the SiO₂/SDS dispersion had a synergistic effect on foam stability at proper SDS concentration. And the synergy became more obvious with the increase of SiO₂ concentration. The reason may be that the adsorbed surfactant molecules could help to pull the particles together to the air/water interface when the hydrophobic nanoparticles adsorbed a modest amount of surfactant.⁴⁰ Besides, some researchers⁴¹ also found that the surfactant could lead to the production of open interconnected structures with strong steric integrity, which also increased the foam stability at moderate surfactant concentration.

Fig. 5 Half life of foams stabilized by the SiO₂/SDS system as a function of relative SDS concentration (RC) at different particle concentrations as indicated above (wt%).

The effect of SDS concentration on the foam stability in different regions could be explained by particle attachment amount on the bubble surface, which was quantified approximately. The drainage process was thought to be nearly finished when the drained liquid only varied a little. Then the liquid was sucked out by syringe. The remaining dried foam was washed with water and centrifuged four times to remove the free SDS molecules. The obtained particles were dried and weighed. Then the attachment amount of SiO₂ particle can be calculated as follows:

where A was the attachment amount (g mL⁻¹), m_particle was the total weight of the particles on the bubble surface (g), and V_foam was the initial foam volume after preparation (mL). Fig. 6 showed the attachment amount on bubble surfaces with different relative SDS concentrations (RC). And the SiO₂ concentration was fixed at 1.5 wt%. It showed that the amount of particles attached to the bubble surface increased as the relative SDS concentration increased first, and then decreased. In region I (RC < 0.15), the attachment amount was low, so no stable foam was formed. The attachment increased with increasing relative SDS concentration in region II, and reached a maximum at RC = 0.4. The attached particles were enough to enhance the foam stability against Ostwald ripening, and stable foam could be formed in region II. The attachment decreased as the relative SDS concentration continued to increase (region III, 0.4 < RC < 0.8). In region IV, the attachment reached a platform, and the half life c of the foam also remained unchanged. It seemed that the amount of particle attachment had a great effect on foam stability. The dense film formed by the nanoparticles adsorbed on the bubble surface was a primary mechanism improving the foam stability. A laser-scanning confocal microscopy experiment was performed to monitor the adsorption of nanoparticles at the interface in regions II and III. It seemed that some of the particles were located between the two bubbles in the surrounding continuous phase, as shown in Fig. 6 (insert picture). The particles could stabilize foams because they retarded drainage and provided a steric barrier to film rupture, a barrier called as “colloidal armour”.¹⁴ The nanoparticles adsorbed onto the bubble were parts of particle network in the bulk aqueous solution.²¹

Fig. 6 Attachment amount of particles on the bubble surface as a function of relative SDS concentration (RC) at a SiO₂ concentration of 1.5 wt% (inset: confocal fluorescence image).

Fig. 7 showed the evolution of SiO₂/SDS foam (produced by Foamscan) with different relative SDS concentrations (RC) throughout aging time at a particle concentration of 1.5 wt%. For SDS foam, the concentration of SDS was 0.5 wt%. It seemed that the average diameters of bubbles increased with time for both SDS foam and SiO₂/SDS foam (Fig. 7a). The bubble size grew with time due to the pressure differences caused by the Young–Laplace effect. The pressure difference acted as the driving force for gas diffusion from small to bigger bubbles. For SDS foam, there were no bubbles after 3000 s. The most stable bubble appeared at RC = 0.4 for SiO₂/SDS dispersion. And the average diameter was lower than 180 μm. The diameter became bigger at higher RC values, indicating decreased stability of the foam. The liquid content in SiO₂/SDS foams was also recorded by FoamScan (Fig. 8). Higher liquid content in foam meant that it could resist liquid drainage from the bubble film more effectively. For each relative SDS concentration (RC), the liquid content in SiO₂/SDS foam decreased with time. It decreased rapidly at first for both SDS foams and SiO₂/SDS foams, and then reached a plateau when the time was over 1500 s. The liquid content matched well with the stability of the foam at fixed SiO₂ concentration. At certain times, the liquid content increased gradually with increasing relative SDS concentration, reached a maximum at RC = 0.4 and then decreased. For SDS foam, the liquid content in the foam was 0.0% after 3000 s, i.e. there was no foam left. This implies that the SDS foam was rather unstable. For SiO₂/SDS foam, the final liquid content was about 9.5% at a relative SDS concentration of RC = 0.4. It was proved that the adsorbed nanoparticles at the bubble surface can resist water flow in liquid film and slow down liquid drainage. At higher concentrations of surfactant (RC = 1.0), the particle attachment was low (Fig. 6). Hence, there were not enough particles at bubble interfaces as steric barriers to restrain liquid drainage and bubble coalescence.

Fig. 7 (a) Average diameters of bubbles as a function of time; from (b) to (e), the optical micrographs showing the variation of bubbles at a time of 3000 s after generation, and the RC values of SDS are 0.1, 0.4, 0.6 and 1.0, respectively. The particle concentration is fixed at 1.5 wt%.

Fig. 8 Liquid content in the foam as a function of time at a SiO₂ concentration of 1.5 wt%.

3.2. Surface properties and foam behaviors of SiO₂/SDS dispersions

The dilational rheological properties of the composite SiO₂/SDS interfacial layers were investigated by measuring the dilational viscoelasticity (E). The concentrations of SiO₂ in the dispersions were 0.5 wt%, 1.0 wt%, 1.5 wt% and 2.0 wt%. For each SiO₂ concentration, the relative SDS concentration ranged from RC = 0.0 to 1.0. The dilational viscoelasticity of SDS solution without particles was measured first (not shown in Fig. 9). It showed that the air/water interface presented very small values of E for all the SDS concentrations. And its maximum value was less than 10 mN m⁻¹. But for the SiO₂/SDS interfacial layer, the dilational viscoelasticity was much higher, and it increased appreciably with increasing particle concentration, especially in region II and region III. The dilational viscoelasticity of dispersion, shown in Fig. 9, was in accordance with the stability of the SiO₂/SDS foams. The maximum E also appeared at relative SDS concentrations of RC = 0.4 for each particle concentration. Hunter et al.⁴¹ studied a similar system combining octyl grafted silica particles with Triton X-100 through surface rheology. Their results also proved that the presence of nanoparticles increased E at the proper surfactant concentration. The mechanical strength of air/water or the oil/water interface could be strongly increased by particle attachment, contributing to the stability of the foam or emulsion.⁴² A similar effect⁴³ was investigated concerning surfactant systems typically used for the stability of foam, where the surface condensed phase formation, or solid-like aggregates, conferred an elastic property on the interfacial layer. The interface with low viscoelasticity was less rigid and easily collapses, while the interface with high viscoelasticity could resist the external disturbances to avoid the bubble coalescence and rupture.⁴³

Fig. 9 Surface dilational properties of SiO₂/SDS dispersions as a function of relative SDS concentration (RC) at the frequency of 0.1 Hz.

The adsorption behaviors of SiO₂ on the air/water interface in different SDS concentration regions are illustrated in Fig. 10. In region I, the relative SDS concentration was low and unstable bubble surfaces were contained with a low percentage of particles and SDS molecules. At moderate SDS concentration (region II), more and more particles were adsorbed on the bubble surface. The SDS molecules adsorbed on the SiO₂ surface through hydrophobic interaction. And the surfactant molecules helped the particles to be more apt to attach to the air/water interface.⁴⁰ The participation of particles enhanced the intensity and dilational viscoelasticity of the interfacial layer, thus increasing the foam stability. As the relative SDS concentration increased continuously (region III), more and more SDS molecules adsorbed onto the particle and left the hydrophilic headgroup exposes to the liquid. The particles might become more hydrophilic and they could not dominate the foam stability any more. Besides, there were more free surfactant molecules in the dispersion and they adsorbed competitively with the particles on the interface. So the stability of the foam decreased gradually. In region IV, most of the hydrophilic particles tended to disperse in the liquid phase. Only a few particles might attach on the bubble surface, and the foam stability was only a little higher than that of the SDS foam.

Fig. 10 Schematic representation of foam stabilized by SiO₂ and different concentrations of SDS.

Optical microscope images of foams stabilized by SiO₂/SDS dispersions are shown in Fig. 11. The pictures were taken when the foams were prepared after 60 s. The bubble diameter initially decreased, then increased with increasing the relative SDS concentration (RC). The bubble diameter distribution was shown in Fig. 11e. The bubble size of the most stable foam was the smallest. The size distribution was wide at low or high relative SDS concentration but was the narrowest for the most stable foam (at RC = 0.4). The bubble diameter result was in strong agreement with the dilational viscoelasticity and foam stability results.

Fig. 11 Optical microscope images of foams stabilized by SDS solution (a, C_SDS = 0.5 wt%) and SiO₂/SDS dispersions (b–e). From (b) to (e), the relative SDS concentrations (RC) are 0.3, 0.4, 0.5 and 0.8, respectively. (f) Size distributions of these bubbles (the results are based on the statistic of 800 bubbles). The SiO₂ concentration was fixed at 1.5 wt%.

3.3. Sandpack experiment

3.3.1. Experimental study on the plugging properties of SiO₂/SDS foam. Five flooding tests were conducted in single sandpack models (#1–#5) to check the foam plugging properties in homogeneous formation. The differential pressures during the injection process are shown in Fig. 12.

Fig. 12 Pressure changes during foam flooding as a function of SiO₂ concentration. The relative SDS concentration is fixed at RC = 0.4 for SiO₂/SDS dispersions.

During the experiments, water was injected into the sandpack until the differential pressure was stable and then the foam was injected. It was observed that the differential pressure for the SDS foam system increased slowly at the beginning of foam injection. It gradually increased after 0.5 PV foam was injected. At the end of foam flooding, the differential pressure reached 0.55 MPa. In the subsequent waterflooding, the differential pressure decreased rapidly. After 1.5 PV water injection, the differential pressure was almost the same as waterflooding, indicating there was no foam left in the sandpack. For SiO₂/SDS foam flooding, the differential pressure increased with increasing SiO₂ concentration. When 1.8 PV foams were injected, the differential pressures for 0.5 wt%, 1.0 wt%, 1.5 wt% and 2.0 wt% SiO₂ were 0.8 MPa, 1.0 MPa, 1.4 MPa and 1.9 MPa, respectively. During the subsequent waterflooding, the SiO₂/SDS foam system had a greater resistance to water erosion than the SDS foam. The higher the SiO₂ concentration, the better the resistance to water erosion. Even after nearly 10.0 PV of water was subsequently injected after foam flooding, the differential pressure for 2.0 wt% SiO₂ still remained over 0.2 MPa. The SiO₂ concentration has a great influence on the foam plugging properties. One possible reason was that the foam stability is enhanced with increasing SiO₂ concentration. The adsorbed particles could form a stronger steric layer that strongly hindered both shrinkage and expansion of the bubbles. Wang et al.⁴⁴ also proved that the foam stability had a positive impact on foam plugging. For SDS foam, it was unstable in porous media, and the bubbles broke easily, causing cross flows of the gas phase and low efficiency of foam plugging. But for SiO₂/SDS foam, the foam stability was enhanced and more gas was trapped in it, thus the gas channel was avoided. In addition, the enhanced dilational viscoelasticity of the SiO₂/SDS foam might also enhance the plugging performance. Bubbles usually remain spherical without any perturbation, but are deformed when they migrate through the pore-throats. Because of the high viscoelasticity of the bubble film, the bubbles recovered their spherical shape, resulting in a micro-force on the pore-throats. Thus, the bubble could not migrate in the pore-throats smoothly. The schematic mechanism of SDS foam and SiO₂/SDS foam migrating through the pore-throat is shown in Fig. 13. Initially, the SDS foam was more apt to deform when it came into contact with the pore-throat (Fig. 13a). The deformation became larger as the bubble entered further into the pore-throat (Fig. 13b). Once through the narrowest part of the pore-throat, the bubble migrated easily and gradually returned to a spherical shape (Fig. 13c). Finally, when the bubble left the pore-throat completely, the bubble recovered their original shape and size (Fig. 13d). But for the SiO₂/SDS foam, its shape was difficult deform when it made initial contact with the pore-throat (Fig. 13e). Once the SiO₂/SDS foam was in the pore-throat, the bubble deformed elastically (Fig. 13f) and the micro-force began to act on the pore wall. The force increased when the bubble entered further (Fig. 13g), and the friction between the walls and the deformed bubble was taken into account to balance the driving force of the fluid. In the end, the bubble was stuck in the pore-throat and produced an additional flow resistance (Fig. 13h).

Fig. 13 The different migration behaviors of SDS foam (a–d) and SiO₂/SDS foam (e–h) in the pore-throat. The flow direction is indicated with the red arrow.

3.3.2. Experimental study on profile control property. In this section, five heterogeneous dual sandpack models (#6–#10) were used to evaluate the effectiveness of the SiO₂/SDS foam for profile control in heterogeneous formation. The parameters of the sandpack models are listed in Table 1. For all of the profile control tests, the liquid mainly came from the high permeability model during waterflooding, resulting in low sweep efficiency in the low permeability model. The initial diversion ratios of high and low permeability models were about 85.0% and 15.0%, respectively. During foam flooding, the diversion ratios of the high permeability model decreased, while the low permeability model increased with increasing foam injection volume. Foam reduced the gas mobility effectively in high permeability formation, causing the subsequent displacing fluid to be diverted from high to low permeability formation.⁴⁵ So the foam could achieve a more uniform injecting distribution in a heterogeneous sandpack model compared to water injection.⁴⁶

During the SDS foam injection process (Fig. 14a), the diversion ratio of the low permeability model increased gradually. At the end of SDS foam injection, the diversion ratio for the low permeability model was about 36.5%. But the diversion ratio for the high permeability model increased rapidly with the following waterflooding, and it reverted to about 85.0% again after 1.0 PV of water was subsequently injected. When nanoparticle-stabilized foams were adopted, the diversionary effect was dramatic (Fig. 14b–e). When the SiO₂ concentration was 1.0 wt%, the diversion ratios of high permeability and low permeability sandpacks were equal at the end of foam flooding. The diversion ratio in the low permeability model was bigger than that of the high permeability model when the SiO₂ concentration was over 1.5 wt%. It meant that more fluid came from the low permeability model than the high permeability model, and the foam in the high permeability model resisted fluid flowing effectively. The diversion ratio of the high permeability model increased slowly as the water was injected. When the SiO₂ concentration was 2.0 wt%, the diversion ratios in the high and low permeability models were still maintained at 50.0%, even after 3.0 PV water was injected. It seemed that the SiO₂/SDS foam had a better resistance to water flushing than the SDS foam.

Fig. 14 Changes in the diversion ratio during foam flooding as a function of SiO₂ concentration (a) SDS foam, C_SDS = 0.5 wt%; (b) SiO₂/SDS foam, C_SiO2 = 0.5 wt%; (c) SiO₂/SDS foam, C_SiO2 = 1.0 wt%; (d) SiO₂/SDS foam, C_SiO2 = 1.5 wt%; (e) SiO₂/SDS foam, C_SiO2 = 2.0 wt%. For SiO₂/SDS dispersions, the relative SDS concentration is fixed at RC = 0.4.

During the foam flooding process, the stable SiO₂/SDS foam first entered into the high permeability path in the sandpack and blocked the sandpack by its high apparent viscosity. The fluid had to shift to the low permeability model as the foam propagated through the high permeability model. Ma et al.⁴⁶ proposed that the better the foam stability, the better the diversion effect would be. The foam stability increased with SiO₂ concentration at the proper SDS concentration. As a result, it could be concluded that the nanoparticles imposed a positive effect on the profile control property. Besides, the enhanced dilational viscoelasticity of SiO₂/SDS foam could improve the plugging performance in the high permeability model, and compel more fluid through the low permeability model.

3.3.3. Experimental study on oil recovery. Five foam flooding tests (#11–#15) were conducted to examine the effect of SiO₂ concentration on oil recovery in homogeneous formations. Fig. 15 showed the pressure drop and oil recovery as a function of the fluid injection. As shown in the figure, during the primary waterflooding, the differential pressure increased and a pressure peak appeared quickly. After that, the differential pressures fell sharply, indicating water breakthrough in the sandpack. And the breakthrough occurred at about 0.25 PV of water injection. From the low value of the breakthrough PV, it could be inferred that the flooding process was unstable and viscous fingering appeared during waterflooding. The oil recovery also increased rapidly at the beginning of waterflooding, and then reached a rather low platform. With foam injection, the differential pressures started to rise and a high pressure peak value was set up at the end of 1.5 PV foam flooding (Fig. 15a–e). The SiO₂/SDS foam injection established higher differential pressure than SDS foam injection. And the final built-up differential pressures increased with SiO₂ concentration. The higher differential pressures suggested that the SiO₂/SDS foam could block the water channels and reduce the mobility of the water phase. As a result, the subsequently injected water was forced to the oil enrichment zone, thereby improving sweep efficiency and increasing the oil recovery.

Fig. 15 Differential pressure and oil recovery during the injection process. (a) SDS foam, C_SDS = 0.5 wt%; (b) SiO₂/SDS foam, C_SiO2 = 0.5 wt%; (c) SiO₂/SDS foam, C_SiO2 = 1.0 wt%; (d) SiO₂/SDS foam, C_SiO2 = 1.5 wt%; (e) SiO₂/SDS foam, C_SiO2 = 2.0 wt%. For SiO₂/SDS dispersions, the relative SDS concentration is fixed at RC = 0.4.

As shown in Table 2, the oil recovery after primary waterflooding was about 34.1–36.3%. There was still a lot of residual oil in the sandpack. When the SDS foam flooding was injected, the enhanced oil recovery was 19.9%, so the final oil recovery was only 54.0%. It can be seen (Fig. 15a) that the peak differential pressure was about 0.65 MPa at the end of SDS foam flooding. The result indicated that the SDS foam could partly block the water channels and increase the sweep volume. Some of the residual oil was displaced after waterflooding, but the oil recovery was still low. Because of the instability of SDS foam in porous media, its bubble rupture caused the separation of gas and liquid. The enhanced oil recovery increased with the SiO₂ concentration and exhibited a significant change when the SiO₂ concentration ranged from 0.5 wt% to 2.0 wt%. It was noted that the peak differential pressure was also a function of SiO₂ concentration, and showed the same trend as the oil recovery. The max peak pressure (1.61 MPa) corresponded to the max enhanced oil recovery (41.2%) at a SiO₂ concentration of 2.0 wt%. When the SiO₂ concentration was 0.5 wt%, the enhanced oil recovery was only a little greater than that of the SDS foam. This was mainly because the bubbles of the foam were not stable enough. After the SiO₂ concentration exceeded 1.0 wt%, there was a significant increase in enhanced oil recovery. From the differential pressure and oil recovery, it could be concluded that the increase in oil recovery showed a good correspondence with the increased pressure drop during foam flooding and a test with a higher differential pressure gave a higher enhanced oil recovery. In addition, the enhanced dilational viscoelasticity of foam might also help to displace the oil on the pore wall.⁴⁷

Table 2 Summary of flooding tests in sandpacks

Model no.	Waterflooding recovery (%)	Foam system	Concentration of SiO2 (wt%)	Enhanced oil recovery^a (%)	Final oil recovery (%)
a Oil displaced by foam flooding and subsequent waterflooding.
#11	34.1	SDS foam	0	19.9	54.0
#12	35.8	SiO2/SDS foam	0.5	21.3	57.1
#13	35.0	SiO2/SDS foam	1.0	28.5	63.5
#14	36.3	SiO2/SDS foam	1.5	33.2	69.5
#15	34.5	SiO2/SDS foam	2.0	41.2	75.7

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4. Conclusions

The properties and applications of aqueous foams prepared by SDS and SiO₂ nanoparticle dispersions were studied. The SiO₂ nanoparticle and SDS led to a synergistic stabilization of foams at the optimal SDS and SiO₂ concentration ratio. And the synergistic effect was more and more obvious with increasing SiO₂ concentration, while the foam volume decreased slightly. Besides, the dilational viscoelasticity was consistent with the foam stability. The adsorption amount of SiO₂ on the bubble surface was crucial to obtain a stable SiO₂/SDS foam. The SiO₂/SDS foam was generally better than the SDS foam at improving the plugging and profile control effects. When water was subsequently injected, the SiO₂/SDS foam showed better resistance to water flushing. In the oil displacement experiments, the SiO₂/SDS foam effectively enhanced oil recovery, and the final oil recovery was as high as 75.7%. The effective displacement in porous media was strengthened with increasing SiO₂ concentration. It was believed that the improved foam stability and enhanced dilational viscoelasticity by SiO₂ nanoparticles were the most important factors leading to the excellent performance in sandpack experiments.

Acknowledgements

This work was financially supported by the Fundamental Research Funds for the Central Universities (13CX05018A), the National Natural Science Foundation of China (51274288), National Natural Science Foundation of Shandong Province (2012ZRE28014), the National Natural Science Foundation of China-Petrochemical Industry Fund (U1262102), the Outstanding Doctoral Dissertation Training Program of the China University of Petroleum (Grant LW130201A), the Special Research Fund for the Doctoral Program of high education (20120133110008). We sincerely thank other colleagues in the Foam Fluid Research Center at the China University of Petroleum (East China) for helping with the experimental research.

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