Study of Nanoparticle–Surfactant-Stabilized Foam as a Fracturing Fluid

Article pubs.acs.org/IECR

Study of Nanoparticle−Surfactant-Stabilized Foam as a Fracturing Fluid Qichao Lv, Zhaomin Li,* Binfei Li, Songyan Li, and Qian Sun College of Petroleum Engineering, China University of Petroleum, Qingdao 266580, Shandong, China ABSTRACT: The development of hydraulic fracturing has created a huge demand for fracturing fluids with high performance and low formation damage in recent years. In this paper, a foam stabilized by partially hydrophobic modified SiO2 nanoparticles and sodium dodecyl benzenesulfonate (SDBS) was studied as a fracturing fluid. The properties of SiO2/SDBS foam such as rheology, proppant suspension, filtration, and core damage were investigated. The experimental data showed that the stability and thermal adaptability of sodium dodecyl benzenesulfonate (SDBS) foam increased when silica (SiO2) nanoparticles were added. The surface tension of SDBS dispersion almost did not change after SiO2 nanoparticles were added; however, the dilational viscoelasticity of the interface increased, indicating that the SiO2 nanoparticles attached to the interface and formed a stronger viscoelasticity layer to resist the external disturbance. The proppant settling velocity in the SiO2/SDBS foam was found to be 2 orders of magnitude lower than that in a pure SDBS foam. The total leakoff coefficient of the SiO2/SDBS foam was found to be lower than that of an SDBS foam. Although the core damage ratio of the SiO2/SDBS foam was slightly larger than that of an SDBS foam, compared to GEL/SDBS, the core damage caused by the SiO2/SDBS foam remained at a low level. SiO2 nanoparticle−surfactant-stabilized foam is superior to a surfactant-stabilized foam and causes lower core permeability damage than a gel−surfactant-stabilized foam. It is recommended for use in hydraulic fracturing, particularly for fracturing stimulation in tight and shale gas reservoirs.

1. INTRODUCTION The hydraulic fracturing of tight and shale gas reservoirs has increased significantly in recent years, thus creating a huge demand for fracturing fluids with high performance and low formation damage.1−5 Traditional fracturing fluids use water viscosifying agents such as guar gum and its derivatives to support and carry the proppant. However, guar gum forms an insoluble residue in the formation, and these insoluble materials plug pore throats, causing impaired leakoff and formation damage that could be fatal to tight and shale gas reservoirs.6,7 Moreover, the price of guar gum fluctuates a lot depending on the market, costing more to companies worldwide.8,9 Foam fracturing fluids are attracting much attention because the liquid content of a foam fluid is very small, thus reducing the damage potential to sensitive formations. The apparent viscosity of a foam is high; therefore, it has excellent proppant transport ability. Moreover, because of a special microstructure, a foam fluid has less fluid loss to formation than a conventional fracturing fluid.10−14 However, some factors lead to foam instability such as foam drainage, rupture of liquid films, and interbubble gas diffusion. Gas-in-water foams are not stable enough in the presence of a surfactant, particularly in deep reservoirs with high temperatures and high surfactant adsorption. Foams with guar gel and synthetic polymers as the stabilizer have been made. Those foams showed a long halflife; however, the formation damage also increased because of the presence of foam stabilizers. Thus, foam stability with less formation damage is a key factor for the extensive use of foam fracturing fluids. Nanoparticles have been extensively studied as the stabilizer in aqueous foams.15−17 Nanoparticles improve the stability of a foam by two mechanisms. Nanoparticles absorb at the gas− liquid interface and form a dense layer, thus preventing © XXXX American Chemical Society

interbubble gas diffusion and slowing down or halting a complete disproportionation (Ostwald ripening). The interwoven distribution of adsorbed and nonadsorbed nanoparticles increases the flow resistance of water between bubbles and slows down liquid drainage. Gonzenbach and Studart reported a versatile method for the preparation of ultrastable nanoparticle-stabilized foams. The concentration of colloidal particles in the liquid phase was increased by modifying the surface of particles with short-chain amphiphilic molecules, thus enhancing the ability of the gas−liquid interface area against disproportionation, coalescence, and drainage.18 Binks and Kirkland reported the synergism between the surfactant and silica nanoparticles in foam by the cryo-SEM analysis of frozen foams; they showed that the changeover from surfactant to particle dominated bubble surfaces in line similar to a “colloidal armor” that dramatically increased the stability of foam.19 Many studies demonstrated that nanoparticle-stabilized foams can survive for weeks or more, even under extremely harsh conditions.20−22 Ultrastable foams have a good application perspective in the fields of food, cosmetics, and engineering.23−25 Recently, nanoparticle-stabilized foams have been used in the oil and gas industry. Espinosa reported that nanoparticle-stabilized foams have some advantages for applications in enhanced oil recovery.26 Yu et al. reported an excellent performance of nanoparticle-stabilized CO2 foams for oil recovery in Berea sandstone core; the core permeability did not change after foam flooding, indicating no nanoparticle Received: June 16, 2015 Revised: September 3, 2015 Accepted: September 9, 2015

A

DOI: 10.1021/acs.iecr.5b02197 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research plugging.27 After the investigation of foam flooding by using a visual micromodel, Sun and Li reported that SiO2 nanoparticlestabilized foams have a great application in flushing oil from dead end pores, which was attributed to the enhanced foam stability and viscoelasticity caused by the attached particles.28 Despite significant studies on nanoparticle-stabilized foams, the properties and applications of nanoparticle-stabilized foams in hydraulic fracturing have not been reported. In this study, a foam stabilized by SiO2 nanoparticles and sodium dodecyl benzenesulfonate (SDBS) was investigated as the fracturing fluid. The properties of SiO2/SDBS foam such as rheology, proppant suspension, filtration, and core damage were investigated.

Figure 2. Microscopic images of the proppant.

2. MATERIALS SDBS (purity >99.0 wt %), potassium chloride (KCl, purity >99.0 wt %), and FITC fluorescent powder were purchased from Sigma (USA). Nitrogen (purity >99.0 wt %) was supplied by Tianyuan Inc. (China). Deionized water was double distilled from potassium permanganate to remove traces of organic compounds. SiO2 nanoparticles (HDK H18, purity >99.8 wt %) were purchased from Germany Wacker Chemical, Co., Ltd. As shown in the cryo-TEM images (Figure 1), the 0.1 wt % SiO2

3. METHODS 3.1. Preparation of Dispersions. A SiO2/SDBS dispersion was prepared by mixing 1.0 wt % SiO2 nanoparticles and 0.4 wt % SDBS in 1.0 wt % KCl brine containing 0.02 wt % FITC fluorescent powder. KCl brine was used to simulate formation water and enhance the antiswelling ability of the liquid in the core. After the mixture was stirred for 10 h, it was ultrasonicated for 1 h. After the solution appeared slightly hazy, it was used for experiments. 3.2. Preparation and Characterization of Foams. The Warning Blender method was used to prepare the foams. A 100 mL dispersion was stirred for 3 min at 7000 rpm using a blender (GJ-3S, Qingdao Senxin Machinery Equipment Co., Ltd., China). After stirring was stopped, the foam was transferred to a sealed cylinder to record the foam volume. The time taken from the beginning to 50 mL liquid draining from the foam (half-life) was also recorded. The stability experiments were performed using an oven at a constant temperature and under ordinary pressure. The microstructure of the foam was observed using a fluorescence microscope (DMI3000B, Leica, Germany). The surface dilational viscoelasticity of the dispersions was measured using a bubble/drop profile analysis tensiometer (Tracker-H, Teclis, France); the principle of surface dilational viscoelasticity has been described in the literature.29−31 The same setup was used to determine the surface rheology properties. After 40 min of bubble formation, oscillations were performed with a bubble area sinusoidal oscillations of relative amplitude δS/S0 = 15%. The dilatational moduli vs oscillation frequency ranged from 0.05 to 0.2 Hz. The temperature of the measuring cell was kept constant at 30 °C. The apparent viscosity of the foam was measured using an MCR 302 Paar rheometer equipped with a concentric cylinder system. The foams were injected directly from the production device to the cylinder. A rotor with six blades was used in the measuring system, which reduced the disturbance to foam

Figure 1. Cryo-TEM images of 0.1 wt % HDK H18 nanoparticles in a 15 wt % ethanol solution.

nanoparticles are almost monodispersed in a 15 wt % ethanol solution. The particles are almost spherical with an average diameter of ∼12 nm and an average surface area of 200 m2/g. To increase hydrophobicity, the surface of the nanoparticles was modified by coating with dimethylsiloxane, and the density of the silanol groups was slightly less than 0.5 per nm2. Berea sandstone core samples and proppant were kindly provided by Shengli Oilfield, China. Table 1 shows the parameters of the core samples. The proppant was spherical ceramsite with a 380−0.425 μm diameter as shown in Figure 2. Table 1. Core Properties

initial gas permeability (md) core samples

diameter (cm)

length (cm)

high

low

A B C D E

2.54 2.54 2.54 2.54 2.54

5 5 5 5 5

27 27 27 27 27

3 3 3 3 3 B

foam type SDBS SDBS SDBS SDBS SDBS

foam quality (%)

SiO2/SDBS SiO2/SDBS SiO2/SDBS SiO2/SDBS SiO2/SDBS

0 35 50 65 80

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Figure 3. Schematic of core filtration and microscopic filtration experimental apparatus.

and gas in the antifoaming solution were separated. Then, the volume of liquid filtration was recorded using a weighing balance, and the volume of gas filtration was recorded using a gas flowmeter. The shear rate of foam at the core face was estimated from the flow rate and flow-through-slot dimensions (facing the core inlet). Equation 1 shows the shear-rate expression for the foam flowing through the core surface:13

stability by the rheometer. The viscometric response to time was recorded under a constant shear rate of 170 s−1. The temperature of the foam was changed from 30 to 90 °C using a Peltier system. 3.3. Measurement of Proppant-Carrying Fluids. After the foams were generated by the Warning Blender method, they were mixed uniformly with the proppant. The concentration of the proppants in the proppant-carrying fluid was 0.02 g/cm3. The proppant settling velocities were measured using a cuboid colorimeter cell with a 90 mm height and a 6 mm thickness. A water bath was used to control the temperature of the colorimeter cell. A proppant-carrying fluid was injected into the colorimeter cell, and the proppants were monitored using a digital camera (VHX-5000, Keyence, Japan) equipped with a large depth-of-view portable 3-D scanner. The average value of the proppant settling velocity was recorded, and the interaction between proppant and bubbles was also evaluated. Moreover, the bubble surface was scanned by the large depth-of-view portable 3-D scanner and the roughness of bubble surface was automatically analyzed. 3.4. Measurement of Filtration. A laboratory apparatus was designed and built for evaluating the filtration performance of foam fracturing fluids. The setup enabled us to (1) measure the dynamic leakoff rates of both liquid and gas phases, (2) evaluate the rock damage by fracturing fluids, and (3) monitor the microstructure of foam during filtration. A schematic of the system is shown in Figure 3. It includes three main parts: a foam generator cell, a fluid-loss cell, and a micromodel cell. The foam generator cell was used to mix gas and liquid to generate foams and control the foam’s flow rate and foam quality. Dynamic leakoff rates and core damage were measured using a fluid-loss cell. A dynamic filtration core holder was used in the fluid-loss cell. Foam was injected into the core holder and passed through the core surface. As shown in Figure 3, the bule line indicates the flow direction of foam fluid. When the fluid touched the core surface, a part of the liquid and gas leaked off into the core. After the fluid flowed out of the core, the liquid

γ=

0.1 × q 6ν = 2 w w ×h

(1)

where v is the average velocity (in cm/s); q is the volumetric flow rate of foam (in cm3/min); w is the slot width (in cm); h is the slot height (in cm). The slot width of the core holder was 0.1−0.5 cm, and the slot height was 2.54 cm. The shear rate was maintained at 50 s−1 for the foam filtration test. The pressure drop between the core inlet and outlet was 3.5 MPa, which was controlled using an ISCO pump (100DX, ISCO, USA) and a BPV (back-pressure valve). All the experiments were performed for 2 h at 30 °C, which was controlled by a calorstat. The microstructure of foam during filtration was monitored using a micromodel cell. A glass-etched micromodel was prepared by etching a two-dimensional network of pores and throats by a photochemical method. The network imitating pore and throat was patterned from the pore structure of a core from Shengli Oilfield. The size of the network was 8 cm × 8 cm × 6 mm, and the depth and width of the channel were approximately 10 μm and 15−50 μm, respectively. Two slots were designed in the model. One slot faced the network inlet, and the other slot faced the network outlet. The depth and width of the slot were approximately 50 and 300 μm, respectively. First, the foam was injected from inlet ① and passed through the slot facing network inlet, and then most of the foam was removed from outlet ②. The foam leakoff through network was passed into another slot and removed from outlets ③ and ④. Back-pressure regulators (BPR) with an accuracy of C

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foam volume was approximately 25−35% lower than that of the SDBS foam, indicating that a SiO2/SDBS foam is difficult to generate compared to an SDBS foam. The foam volume first increased and then decreased with increasing temperature. The maximum foam volume of the SDBS foam occurred at 60 °C, whereas that of the SiO2/SDBS foam occurred at 80 °C, thus endowing the SiO2/SDBS foam a better thermal adaptability. The foam stability was also studied from the change in microstructure with time. As shown in Figure 5, for SDBS foam, the bubbles became larger and irregular shape with increasing time. All the initial bubble areas were below 1.25 × 103 μm2; 3 h later, half of the bubble areas were above 1.25 × 103 μm2; 7 h later, the distribution range of bubble areas became very large. Some bubble areas were above 100 μm2. The size increased rapidly with time because big bubbles coalesced with adjacent small bubbles driven by the pressure difference due to Young−Laplace. As the drainage progressed, the average thickness of the bubble film changed from 10 μm to less than 2 μm during 7 h, and the film ruptured intermittently, which is a disadvantage to the stability of foam especially in a long-time fracturing operation with a low flow rate. For the SiO2/SDBS foam, the initial average size of bubbles was approximately half of that of the SDBS foam. Although the size increased with time, 3 h later, most of the bubble areas were still below 1.25 × 103 μm2, and 7 h later, the bubble areas were maintained below 2.75 × 103 μm2, indicating better stability of the SiO2/SDBS foam than of the SDBS foam. Moreover, the shape of bubbles was still spherical, mainly because SiO2 nanoparticles that adsorbed on the bubble surface enhanced the capability of film to resist deformation. Although the thickness of the bubble film decreased slightly during the first 3 h, it almost remain unchanged from 3 to 7 h. Seven hours later, the average thickness of the film was about 6 μm, and the film almost did not rupture. Compared to the SDBS foam, the microstructure of the SiO2/SDBS foam was very stable, which is very important for the other excellent properties of the SiO2/ SDBS foam as fracturing fluid as discussed later. 4.2. Rheology of Foam. 4.2.1. Surface Dilational Rheology. The dynamic surface tension of surfactant dispersions before and after adding nanoparticles was studied to determine whether the nanoparticles affected the surface tension. The experimental results are shown in Figure 6. When the balance point of the test arrived, the surface tension of 0.4 wt % SDBS dispersion almost did not change after 1.0 wt % SiO2 nanoparticles were added. This indicates that the effect of

less than 0.001 MPa were used to control the pressure of outlets ②, ③, and ④. Foams produced from the foam generator were measured with an MCR 302 rheometer, equipped with a plate−plate geometry (diameter = 50 mm and gap = 0.3 mm). A smooth surface is used on the bottom plate to provide wall slip. The top plate is rotated at controlled shear rate, varied from 0 to 30 s−1. More details are provided in the literature.32

4. RESULTS AND DISCUSSION 4.1. Stability of Foam. During foam fracturing, first the foam was generated on the surface, and then it was injected into the well and passed into the formation. The temperature of the foam fluid increased with increasing depth of well and reached the highest point under the target formation. Foam stability may deteriorate at a high temperature, which is a disadvantage for fracturing performance. Thus, the half-life of nanoparticle− surfactant-stabilized foam at different temperatures was studied with surfactant-stabilized foam as the control group. As shown in Figure 4, the half-life time of the SiO2/SDBS foam was

Figure 4. Half-life time and foam volume at different temperatures (SDBS foam, 0.4 wt % SDBS solution + N2; SiO2/SDBS foam, 0.4 wt % SDBS + 1.0 wt % SiO2 dispersion + N2).

approximately 4 times that of the SDBS foam at 20 °C. When the temperature was increased to 90 °C, the half-life became 40 times of that of the SDBS foam. Therefore, the thermal stability of the SiO2/SDBS foam is higher than that of the SDBS foam. The initial foam volume was also investigated. The SiO2/SDBS

Figure 5. Microscopic analysis of foams at 60 °C ((a) microstructure of foams as a function of time; (b) bubble size statistical distribution curves as a function of time). D

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interface. If no nanoparticles adsorbed on the air/liquid interface in the dispersion, the dilational viscoelasticity of SDBS bubble film and SiO2/SDBS should remain the same. However, the experimental data show that the dilational viscoelasticity of SiO2/SDBS dispersion was much higher than that of an SDBS solution. It can be concluded that SiO2 nanoparticles adsorbed at the interface along with SDBS and thus enhanced the viscoelasticity of SiO2/SDBS dispersion. The much higher viscoelasticity of SiO2/SDBS dispersion also indicated other possible mechanisms involving the nanoparticles attached at the interface and forming stronger viscoelasticity layers. 4.2.2. Viscosity of Foam. The viscosity behavior is very important to the performance of fracturing fluid, such as proppant-carrying capacity and filtration property. As a special fracturing fluid, a foam consists of micrometer-sized bubbles. The property of the foam is significantly influenced by the scale, volume fraction, and interface property of bubbles, and they are unstable and change over time. The change in the apparent viscosity of foams with time is shown in Figure 8. The test

Figure 6. Dynamic surface tension of different systems: 0.4 wt % SDBS solution/nitrogen interface and 1.0 wt % SiO2 nanoparticles with 0.4 wt % SDBS concentration aqueous dispersion/nitrogen interface.

nanoparticles on the surface tension was negligible. The only difference is that the dynamic surface tension of SiO2/SDBS dispersion required more time to reach the balance point compared to a pure SDBS solution. To understand further the difference, the change in the dynamic surface tension of the dispersions with the sinusoidal variation of area was investigated, and the dilational viscoelasticity of surfaces was measured. The dilational viscoelasticity of a bubble film affects its ability to resist the external disturbances to avoid the bubble coalescence and rupture directly.33,34 This property is very important to foam fracturing fluid, particularly when pressure fluctuations exacerbate external disturbances during stimulation. To evaluate the effect of nanoparticles on the dilational viscoelasticity and verify the adsorption of nanoparticles at the interfacial layer, the viscoelasticity vs oscillation frequency ν (Hz) of the dispersion was compared to a pure SDBS solution. Figure 7 shows that the viscoelasticity of dispersion with nanoparticles was higher in the experimental frequency range. The effect of nanoparticles on the interfacial property in the presence of SDBS can be explained in two ways by considering particle−surfactant interactions: a decrease in the SDBS concentration due to SDBS adsorption on nanoparticles and an increase in the affinity for nanoparticles on air/water

Figure 8. Change in apparent viscosity of foams over time with an initial foam quality 50% (SDBS foam, 0.4 wt % SDBS solution + N2; SiO2/SDBS foam, 0.4 wt % SDBS + 1.0 wt % SiO2 dispersion + N2).

temperature was controlled at 30, 60 and 90 °C. For the SDBS foam at 30 °C, the apparent viscosity first increased and then decreased with time; the maximum apparent viscosity was reached at 360 s. This experimental result can be interpreted as follows: During the test, the foam quality increased because of liquid drainage, and the interactions between gas bubbles increased, thus increasing the internal friction and viscosity of foam. With the passage of time, the foam became more unstable and easily ruptured because of bubble coalescence and liquid drainage. Therefore, the internal friction and viscosity of the foam decreases gradually with time. For the SiO2/SDBS foam at 30 °C, the initial apparent viscosity was approximately 2 times of that of the SDBS foam. Although the viscosity of the SiO2/SDBS dispersion was slightly higher than that of the SDBS solution, it was generally below 2 mPa·s, indicating that SiO2 nanoparticles could not significantly improve the viscosity of the continuous phase, and the small increase in the continuous phase is not sufficient to explain the high viscosity of the SiO2/SDBS dispersion because silica nanoparticles attached to the bubble surface, and the enhanced foam interfacial layer resisted the deformation. More internal friction appeared when the rotor of rheometer deformed the foam

Figure 7. Dilational viscoelasticity vs frequency of systems: 0.4 wt % SDBS solution/nitrogen interface and 1.0 wt % SiO2 nanoparticles with 0.4 wt % SDBS concentration aqueous dispersion/nitrogen interface. E

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Industrial & Engineering Chemistry Research structure. The viscosity of the SiO2/SDBS foam also increased with time. However, as the foam quality increased with time, the interactions of bubbles with the colloidal armor became stronger, and the slope of the viscosity growth curve increased. Compared to the SDBS foam, the SiO2/SDBS foam quality increased more slowly with time because the SiO2/SDBS foam was more stable. The maximum viscosity of the SiO2/SDBS foam was reached at a longer time of 745 s. Figure 8 shows that as the temperature increased from 30 to 90 °C, the apparent viscosity of foams decreased, and the maximum viscosity of foam was reached in less time because the foam was more unstable at a high temperature. Although the maximum viscosity of the SiO2/SDBS foam decreased from 30 to 90 °C, the maximum viscosity of the SiO2/SDBS foam at 90 °C was higher than that of the SDBS foam at 30 °C. Moreover, at a high temperature, the SDBS foam easily ruptured, and the viscosity reached a stable point rapidly in less than 10 mPa·s. For the SiO2/SDBS foam, the decrease in viscosity lasted longer than 3300 s before the viscosity reached a stable point in less than 10 mPa·s at 90 °C, which is three times taken by the SDBS foam. Therefore, in terms of viscosity, a SiO2/SDBS foam also possess a better temperature resistance than an SDBS foam. 4.3. Proppant Suspension. Proppant-carrying ability is an important property of fracturing fluid. Fluid with a higher proppant-carrying ability can transfer more proppant from near-well-bore to far-well-bore and from the main fracture to fractures of small sizes. The static settlement test of proppant was carried out in different fluids to characterize the proppantcarrying ability. As shown in Figure 9, the proppant settling

Figure 9 shows that the proppant settling velocity in the SiO2/SDBS foam was 1 order of magnitude lower than that in the pure SDBS foam and SiO2/SDBS dispersion from 20 to 90 °C. The SiO2/SDBS foam showed excellent proppant-carrying ability compared to the foam without silica nanoparticles. Figure 10 shows the interaction between proppant with bubbles

Figure 10. Interactions between proppant and bubbles (A, SDBS foam; B, SiO2/SDBS foam).

in SDBS foam and SiO2/SDBS foam. First, as mentioned above, the dilational viscoelasticity of the SiO2/SDBS dispersion was much higher than that of an SDBS solution. This indicates that when the proppant settled through the deformed bubbles, SiO2/SDBS bubbles produced more resistance than the SDBS foam. Second, the SiO2/SDBS foam was more stable than the SDBS foam; therefore, the films of the SiO2/SDBS foam lasted longer when they supported proppants. Moreover, as shown in Figure 11, the section profiles of the SDBS bubble surface and SiO2/SDBS bubble surface were measured; this clearly indicated that the surface of SiO2/SDBS bubbles was rougher than the SDBS bubbles. This is because the compression of a nanoparticle layer increases its surface concentration. Because nanoparticles are irreversibly adsorbed, further compression undulate the air−water interface, thus providing a rough bubble surface to the SiO2/SDBS foam;19 Therefore, the proppant did not easily slip on the surface of the SiO2/SDBS bubbles and was suspended by foams as shown in Figure 10. As the temperature increased, the proppant settling velocity of the foams increased. The proppant-carrying ability of SDBS foams was more sensitive to temperature than the SiO2/SDBS foam, and the order of the magnitude of its proppant settling velocity changed from 10−4 to 10−3 m/s with the increase in temperature from 20 to 90 °C. Although the proppant settling velocity in the SiO2/SDBS foams increased with temperature, it varied within a small range. When the temperature reached 90 °C, the proppant settling velocity in the SiO2/SDBS foams was approximately 3.72 × 10−5 m/s, which is lower than the maximum perfect proppant settling velocity (8.3 × 10−5 m/s). 4.4. Multiphase Fluid-Loss Property and Core Damage. 4.4.1. Multiphase Fluid-Loss Property. The leakoff properties of foam have been studied previously as a nonwallbuilding fluid. However, foam is a two-phase-structured fluid. As shown in Figure 12, when the foam flows rapidly through a slot facing the network inlet as indicated by the white arrow, some bubbles entered the rock matrix near the rock surface and blocked the flow path for foam filtration as indicated by the light blue arrow. The effects of those bubbles are similar to the filter cake of a conventional fracturing fluid. Therefore, a leakoff coefficient Cw for wall-building fluids was used in foam leakoff analysis.36 Cw, described by eq 2, represents the flow resistance

Figure 9. Proppant settling velocity vs temperature (SDBS foam, 0.4 wt % SDBS solution + N2; SiO2/SDBS foam, 0.4 wt % SDBS + 1.0 wt % SiO2 dispersion + N2).

velocities in pure SDBS foam and SiO2/SDBS were almost the same, approximately 9 × 10−3 m/s, which is a poor or unacceptable proppant settling velocity (vs > 8.3 × 10−4 m/s).35 The foam improved the proppant-carrying ability of the liquid. Figure 9 shows that the proppant settling velocity in SDBS foam was 1 order of magnitude lower than that in the pure SDBS foam and SiO2/SDBS dispersion. This is because the proppant was supported by the bubbles of the foams, and they did not sink until the bubbles deformed or ruptured. However, the perfect proppant settling velocity (vs < 8.3 × 10−5 m/s) was also not reached in the SDBS foam.35 F

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Figure 11. Microscopic analysis of bubble surfaces (A, micrograph of SDBS foam; B, micrograph of SiO2/SDBS foam; C, sectional profiles of bubble surfaces), blue dotted lines in images A and B are section lines.

shown in Figure 12, the first two mechanisms have been discussed to explain the filtration reduction in the foam with silica nanoparticles, which were Jamin effect and foam slipping in the pore and throat of rock. The first mechanism is that nanoparticles affect the Jamin effect of bubbles, thus increasing the bubble flow resistance FΔP. When the bubbles of a foam leakoff from a pore into a throat in the rock matrix, these bubbles are deformed as marked by the red circle and shown with a corresponding sketch map in Figure 12. Deformed bubbles resist foam filtration as follows:37 Figure 12. Microscopic image of dynamic foam filtration (SiO2/SDBS foam, foam quality 55%); the map on the right was used to illustrate the principle of foam with silica nanoparticles in the reduction of filtration.

ΔP = P1 − P2 =

(3)

where ΔP is the pressure difference, i.e., the resistance to bubbles from pore to throat, Pa; P1 is the pressure at the front of the bubble, pa; P2 is the pressure behind the bubble, pa; δ1 is the surface tension of the deformed bubble film, mN/m; δ0 is the surface tension of the undeformed bubble film, mN/m; r1 is the radius of the curvature of the deformed bubble film; r0 is the radius of the curvature of the undeformed bubble film. Taking the derivative of eq 3:

associated with the complex filtration process occurring at or near the fracture face.

Cw = 0.0164m /Ac

2δ 2δ1 − 0 r1 r0

(2)

where m is the slope of an experimental plot of fluid volume VS. The square root of time is in m3/√min, and Ac is the crosssectional area of the exposed core (in m2). Figure 13 shows the

dP =

2(δ0 + dδ) 2δ − 0 r0 + dr r0

(4)

The relationship between δ1 and δ2 can be derived from the definition of the dilational modulus as follows:38 δ1 − δ0 = dδ = |ε| × dln A

(5)

where ε is the dilational modulus of liquid/air interface, mN/m; A is the interfacial area. Equation 6 can be derived from eqs 4 and 5 as follows: ⎛ 2 2⎞ 2dln A − ⎟ + | ε| dP = δ 0 ⎜ r0 ⎠ r0 + dr ⎝ r0 + dr

(6)

Integrating the function of eq 6: ΔP = δ0

∫r

0

Figure 13. Effect of foam quality on leakoff coefficient.

r1 ⎛

2 2⎞ − ⎟ + | ε| ⎜ r0 ⎠ ⎝ r0 + dr

= δ0 × S1 + |ε| × S2

total leakoff coefficient of SDBS and SiO2/SDBS foams exposed to 3 and 29 md cores under a 3.5 MPa differential pressure. The leakoff coefficient of the SiO2/SDBS foam was lower than that of SDBS foam, especially when the foam quality was above 50%. This indicated that SiO2/SDBS foams have superior fluid-loss-control properties than SDBS foam. As

∫r

0

r1

2dln A r0 + dr (7)

Equation 7 shows the relationship between bubble resistance ΔP with dilational modulus |ε|, surface tension δ0, and the geometry functions S1 and S2 of the bubble. As mentioned above, the surface tension δ0 of SDBS bubbles did not change by adding silica nanoparticles; however, the dilational modulus |ε| of bubbles improved as shown in Figure 7. Therefore, when G

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Industrial & Engineering Chemistry Research the geometry deformations of the bubbles are the same, the pressure difference ΔP of SiO2/SDBS bubbles was higher than that of SDBS bubbles. Because the bubble flow resistance FΔP = ΔP·A, where A is the cross-sectional area of the throat and is a constant, the bubble flow resistance FΔP of SiO2/SDBS bubbles was higher than that of SDBS bubbles. These are the main reason why the leakoff coefficient of the SiO2/SDBS foam is lower than that of the SDBS foam. The second mechanism shows that nanoparticles affect bubble slipping, thus increasing bubble-slipping resistance Fslip in the throat. As discussed above, the silica nanoparticles adsorbed at the interface along with SDBS and thus enhanced the viscoelasticity of the SiO2/SDBS bubble film. Therefore, the bubble film with a colloidal armor tends to be solid-like. When the bubbles flow into the throat, as marked by the green circle and shown with a corresponding map in Figure 12, the SiO2/ SDBS bubbles provide more vertical stress to the wall. Moreover, the surface of the SiO2/SDBS bubbles was rougher than that of the SDBS bubbles. Therefore, a SiO2/SDBS bubble will have a higher slipping resistance Fslip when it flows into the throat. To compare the slipping resistance of SiO2/SDBS and SDBS foams by a quantitive method, the foam slip stress was measured in the gap of two panels, and the results are shown in Figure 14. The slip stress of SiO2/SDBS foam was clearly

Figure 15. Bubble division process. The four images show a continuous process for foam filtration in the porous media. The time delay between the images is 3 s.

Figure 16. Size changes in bubbles during foam filtration (A, SDBS foam, foam quality 55%; B, SiO2/SDBS foam, foam quality 55%).

decreased less than the SDBS bubbles after the same filtration distance. This property of SiO2/SDBS bubbles reduced the volume of foam filtration, which is another reason why the leakoff coefficient of SiO2/SDBS foam is lower than that of SDBS foam. Figures 17 and 18 show the leakoff coefficients for the liquid and gas phases of SDBS and SiO2/SDBS foams, respectively,

Figure 14. Foam slip stress as a function of shear rate measured in the gap of two panels (the gap distance was 0.3 mm, and the temperature was 30 °C).

higher than that of SDBS foam with a shear rate from 0 to 30 s−1. The slip stress increased with shear rate and when the shear rate reached 30 s−1, the slip stress of the SiO2/SDBS foam was 2−3 times higher than that of the SDBS foam. The results indicate that silica nanoparticles increased the foam slipping resistance, thus increaing the flow resisitance. This is the second reason why the leakoff coefficient of the SiO2/SDBS foam was lower than that of the SDBS foam. Moreover, as shown in Figure 15, during the foam leakoff in the network, the bubbles were deformed and divided into small-size bubbles by the throat in the network. Figure 16 shows the size changes in the bubbles during foam filtration (blue arrows are used to denote the filtration direction). As shown in the red circle, the sizes of SDBS bubbles changed from large to small very rapidly, close to the size of the throat. Compared to the large bubbles, the small bubbles easily passed through the throat, thus increasing filtration. During the SiO2/ SDBS foam leakoff in the network, the size of bubbles

Figure 17. Effect of foam quality on gas leakoff coefficient.

under various experimental conditions. As the foam quality increased, both the liquid leakoff coefficients of the two types of foams decreased. However, the liquid leakoff coefficient of the SiO2/SDBS foam was lower than that of the SDBS foam from foam quality 0% to 80%, which shows better liquid loss resistance property of the SiO2/SDBS foam. The gas leakoff coefficient first increased and then decreased with the increase H

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Industrial & Engineering Chemistry Research

to gas. The result indicates that the foam fluid decreased the damage to gas well more than the conventional water base fracturing fluid. The core damage ratio of the SiO2/SDBS foam was slightly higher than that of the SDBS foam. This may be caused by the retention of SiO2/SDBS bubbles in the pore. However, compared to GEL/SDBS, the core damage caused by the SiO2/SDBS foam remained at a low level; thus, a SiO2/ SDBS foam is a relatively clean fluid for formation.

5. CONCLUSION (1) The stability and thermal adaptability of an SDBS foam increased when silica nanoparticles were added, which is an important result for a foam injected from a surface at a normal temperature to the target formation at a high temperature. Although the foam volume decreased slightly, the microstructure of the SiO2/SDBS foam was very stable, which is very important for a high foam viscosity, strong proppant carrying capacity, and low filtration loss. (2) The surface tension of SDBS dispersion had almost no change after SiO2 nanoparticles were added. However, the dilational viscoelasticity of the interface increased, indicating that the nanoparticles attached at the interface and formed stronger viscoelasticity layers to resist the external disturbances. More internal friction appeared when the rotor of rheometer deformed the SiO2/SDBS foam structure. (3) The proppant settling velocity in the SiO2/ SDBS foams is 2 orders of magnitude lower than that in a pure SDBS foam and SiO2/SDBS dispersion from 20 to 90 °C, indicating that the proppant-carrying ability of foam was improved significantly by SiO2 nanoparticles. (4) The total leakoff coefficient of the SiO2/SDBS foam was lower than that of the SDBS foam, and the gas and liquid coefficients of the SiO2/SDBS foam were also lower than those of the SDBS foam. Although the core damage ratio of the SiO2/SDBS foam was slightly higher than that of the SDBS foam, compared to GEL/SDBS, the core damage caused by the SiO2/SDBS foam remained at a low level.

Figure 18. Effect of foam quality on liquid leakoff coefficient.

in foam quality. The maximum gas leakoff coefficient of the SDBS foam occurred at a foam quality of 65% when testing in the rock with a permeability of 27 md, whereas the maximum gas leakoff coefficient of the SiO2/SDBS foam occurred at a foam quality of 35%, which is lower than that of the SDBS foam. The gas leakoff coefficient of the SiO2/SDBS foam was also lower than that of the SDBS foam from foam quality 0% to 80% under the same experimental conditions, indicating a better gas loss resistance property of the SiO2/SDBS foam. 4.4.2. Core Damage. Core damage tests are based on a comparison between the core permeability to N2 before and after the leakoff test. The ratio of the final to the initial permeability was calculated using eq 8:

ηd =

k1 − k 2 × 100% k1

(8)

where ηd is the ratio of the final to the initial core permeability, %; k1 is the initial core permeability, μm2; k2 is the core permeability tested after the leakoff test, μm2. The experimental results of different fracturing fluids are shown in Figure 19. GEL/SDBS foam (0.4 wt % SDBS + 0.5% linear guar gel + N2) was also tested to obtain the contrast data. The common result of the three types of foams is as follows: As the foam quality increased, the ratio of the final to the initial core permeability decreased. One of the reasons for this result is that the gas saturation of core increased and so did the relative permeability

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AUTHOR INFORMATION

Corresponding Author

*Z. Li. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support for this study was received from the projects supported by the National High-tech R&D Program (2013AA064803) and the Fundamental Research Funds for the Central Universities (15CX06023A). We sincerely thank other colleagues in the Foam Fluid Research Center at the China University of Petroleum (East China) for helping in the experimental studies.

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REFERENCES

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Figure 19. Damage rate of core sample permeability by different fracturing fluids (For each foam quality and foam system, there are four data points measured in different core permeabilities (0.4, 3.0, 27.0, 95.0 md). The dash cure was used to fit the average value of the four data points). I

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