Dynamic Filtration Behavior of Dry Supercritical CO2 Foam with

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Thermodynamics, Transport, and Fluid Mechanics

Dynamic filtration behavior of dry supercritical CO2 foam with nanoparticles in porous media Qichao Lv, Tongke Zhou, Xing Zhang, Rong Zheng, Chao Zhang, Binfei Li, and Zhaomin Li Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b02783 • Publication Date (Web): 18 Jul 2019 Downloaded from pubs.acs.org on July 21, 2019

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Industrial & Engineering Chemistry Research

Dynamic filtration behavior of dry supercritical CO2 foam with nanoparticles in porous media Qichao Lv1*, Tongke Zhou1, 2, Xing Zhang3, Rong Zheng2, Chao Zhang2, Binfei Li2, Zhaomin Li2 1

Unconventional Petroleum Research Institute, China University of Petroleum (Beijing), Beijing 102249, China; 2 College of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, Shandong, China; 3 Petroleum Engineering Research Institute of Shengli Oil Field, Sinopec, Dongying 257017, Shandong Province, China Abstract: The use of CO2 as a fracturing fluid for reservoir stimulation to enhance oil and gas recovery in low-permeability formations is widespread. However, during the CO2 injection process, the low viscosity of supercritical CO2 (SC-CO2) at high temperature and pressure conditions usually causes serious fluid loss in porous media, thus restricting its efficient utilization. In this work, the dynamic filtration control properties of nanoparticle-enhanced dry SC-CO2 foams in porous media were explored, and the effects of nanoparticle and surfactant concentration, foam quality, pressure drop, temperature, and permeability were systematically studied. The results showed that the SC-CO2/liquid interfacial viscoelasticity modulus and the corresponding foam viscosity were improved by the adsorption of silica nanoparticles at the SC-CO2/liquid interface. At high foam quality (≥ 90%), The nanoparticles reduced the amount of coarse bubbles and prevented bubble disproportionation, both of which helped to maintain a higher viscosity in the ultra-dry foam. The nanoparticles also significantly enhanced the foam filtration control performance; compared to bare dioctyl sodium sulfosuccinate (AOT) foam, the total filtration coefficient of CO2 was decreased by a factor of about 2.2–6.5 with an increase in SiO2 nanoparticle concentration from 0.5 wt% to 1.5 wt%. The effect of surfactant concentration on the filtration of foam with nanoparticles also correlates well with its effect on interfacial viscoelastic modulus and foam viscosity. Increasing the foam quality from 80% to 97% only increases the filtration control performance to a certain extent, as the foams become ultra-dry and unstable if the foam quality is too high (≥ 90%); thereafter, a continuing increase in foam quality caused by CO2 expansion at high pressure drop values leads to low flow resistance and weakens the filtration control performance. The addition of silica nanoparticles reduces the temperature dependence of the foam filtration coefficient. The permeability and total filtration coefficient follow a power law relationship, with the addition of nanoparticles causing a decrease in the power law exponent. Return permeability tests after filtration result confirmed that nanoparticle-enhanced dry SC-CO2 foams are relatively clean fluids for porous media. Keywords: dynamic filtration; dry foam; supercritical CO2; nanoparticle; porous media

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Introduction Carbon capture, utilization, and storage (CCUS) plays an increasingly important role in the reduction of CO2 emissions worldwide [1-4]. The technology has attracted considerable interest in the oil and gas industry [5-7], where CO2 is widely used as a fracturing fluid for reservoir stimulation to enhance oil and gas recovery [8-10]. During the injection of CO2 into the reservoir, the high temperature and pressure conditions in the subsurface cause it to become supercritical [11, 12]; this is often undesirable, as the low viscosity of supercritical CO2 can cause serious fluid loss in porous media and restrict its efficient utilization [13, 14]. To mitigate this problem, CO2-in-water foams are of great interest for the viscosity enhancement and filtration control of SC-CO2 [15, 16]. However, the presence of water in the foam can lead to the production of waste water and the invasion of liquid filtrate into the formation; thus, it would be advantageous to lower the water content and establish a nearly waterless “dry” CO2 foam. For dry CO2 foams with low water content (foam quality > 90%), the aqueous thin lamellar foam film [17] is fragile and sensitive to disturbances such as pressure and temperature fluctuations. In addition, it is difficult for the aqueous lamella to resist the diffusion of supercritical CO2 and prevent Ostwald ripening [18]. Moreover, the high capillary pressure induces rapid liquid drainage from foam the and aggravates the thinning of lamellar structures [19]. To enhance the stability of dry CO2 foams, various additives such as plant gums, synthetic polymers, and worm-like micelles have been used to increase the viscosity of the continuous aqueous phase [18, 20]. Fig. 1 showed the relationship between foam stability with the addition of conventional stabilizers (thickeners) and the damage done to porous media. While the presence of stabilizers is indeed effective in prolonging the half-life of dry foams, their use may not be ideal for subsurface applications where the presence of a highly viscous aqueous phase risks damaging the permeability of the formation.

Figure 1. The relationship between foam stability with the addition of conventional stabilizers (thickeners) and the damage done to porous media.

The use of nanoparticles to stabilize CO2 foam at elevated temperatures and pressures is seen as a feasible alternative to conventional stabilizers. Over the past decade, the characteristics of aqueous foams with nanoparticles have attracted considerable attention owing to their potential industrial applications in fields such as cosmetics, engineering, food, and medicine [21-24]. While conventional foam stabilizers work by decreasing the surface tension and enhancing the viscosity of the continuous phase, nanoparticles work differently—by adsorbing on the surface of foam 2


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films and forming a particle barrier around the bubbles, thus preventing interbubble gas diffusion and enhancing the strength of the films [25]. The liquid flow resistance in aqueous films is increased by the inter-woven distribution of both adsorbed and nonadsorbed nanoparticles, thus slowing down the drainage of liquid from the foam [26]. Horozov [22] reported that the survival time of aqueous foams (either with nanoparticles alone or in the presence of both nanoparticles and surfactant mixture) can extend to weeks or more, even under extremely harsh conditions. Only very recently, Xue et al. [27] investigated the stability of dry CO2 foams (foam quality of 90–98%) with added SiO2 nanoparticles and surfactant, concluding that adsorbed nanoparticles at the film surface clearly inhibited Ostwald ripening and enhanced the stability of the foam. In recent years, the use of nanoparticle-stabilized CO2 foams for mobility control and enhanced oil recovery in porous media has also been the subject of a number of studies. Espinosa et al. [28] reported a stable SC-CO2 foam with 5 nm SiO2 nanoparticles modified with short-chain polyethylene glycol, which was generated in-situ in a model porous medium (glass bead pack) through co-injecting CO2 and an aqueous dispersion of nanoparticles. Their results showed that the flow resistance of the foam with nanoparticles was between 2 to 18 times higher than that without nanoparticles. Mo and Yu [29] investigated the mobility of SC-CO2 foam with nanoparticles in sandstone core, and found that the foam mobility decreased and the foam resistance factor increased with increasing nanoparticle concentration. In addition, their study [30] showed that the sandstone core permeability did not change after flooding with the CO2/nanoparticle dispersion, indicating that no particle plugging took place. Li et al. [26] used a two-dimensional micromodel of reservoir rock to demonstrate the synergistic effect between hydrophobic nanoparticles and surfactant towards stabilizing CO2 foam in porous media containing crude oil. Their results showed that the addition of nanoparticles increased the flooding pressure of foam and markedly improved the oil recovery. Rognmo et al. [31] used hydrophilic nanoparticle-stabilized CO2 foam to reduce CO2 mobility and investigated nanoparticle retention in sandstone core samples, finding that the nanoparticle retention was about 401 μg/g which is in the lower range of reported retention values for conventional aqueous surfactants. Moreover, 20% of the retained nanoparticles were extracted by re-mobilization. In addition, Ramin and Abdolhossein [32] found that the use of silica nanoparticles mixed with sand proppant can effectively reduce fines migration and enhance the hydraulic performance of fracturing operations. However, even though significant research has been conducted on nanoparticle stabilized CO2 foams in porous media, there have been few studies to date on the filtration control performance of dry SC-CO2 foams with nanoparticles. However, these materials are quite promising as they offer a potentially attractive method for reducing fluid loss during CO2 fracturing operations, which is conducive to the formation of hydraulically induced fractures and stabilization of the proppant-carrying capacity of fracturing fluid. Against this backdrop, therefore, the present study explores the dynamic filtration control properties of dry SC-CO2 foam with nanoparticles in porous media, as follows: first, the effect of nanoparticles on the SC-CO2/liquid interfacial viscoelasticity and corresponding foam viscosity were ascertained. Next, the factors affecting dynamic foam filtration, i.e., nanoparticle and surfactant concentration, foam quality, pressure drop, temperature, and permeability, were investigated. Finally, return permeability tests after filtration were used to assess the permeability damage to porous media.

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2. Experimental Section 2.1. Materials SiO2 nanoparticles (NP) (ρ = 2200 g/L, purity > 99.8 wt%) with an average particle diameter of 12 nm and a specific surface area of approximately 200 m2/g were supplied by Wacker Chemie AG, Germany. They were prepared using a flame hydrolysis deposition (FHD) method and were received as a white powder. The nanoparticle surface was modified with polydimethylsiloxane by Wacker to enhance its hydrophobicity. The surface density of the silanol groups was < 0.5 per nm2 and the weight loss of the particles on drying at 105 °C for 2 h was < 0.6 wt%. Ethanol with a purity of 99.7 wt% was supplied by Shanghai Titan Scientific Co., Ltd., China, and used as the cosolvent for the SiO2 nanoparticles. CO2 (purity > 99.999 %) and N2 (purity > 99.99%) were purchased from Tianyuan Inc., China and used as received. Dioctyl sodium sulfosuccinate (a.k.a. AOT) purchased from Sigma, USA with 99 wt% purity was used as the surfactant. Deionized (DI) water obtained using a Milli-Q purification system (Millipore, USA) was used to prepare the liquid phase of the foam. All glassware used in the experiments was cleaned with a surfactant-free cleaning agent (67 wt% sulfuric acid and 12 wt% potassium dichromate) to remove organic compounds prior to use. 2.2. Preparation of AOT/NP dispersions To disperse the hydrophobic SiO2 nanoparticles in water, ethanol was used to wet the SiO2 powder before adding DI water. The mass ratio of nanoparticles and ethanol in the mixture was 1:2. After the nanoparticles were dispersed, the ethanol was removed through repeated sedimentation-redispersion cycles. The aqueous nanoparticle suspension with a residual ethanol concentration < 10−3 wt% was then mixed with AOT. To prepare well-dispersed AOT/NP mixtures, the mixtures were first stirred for 3 hours and then sonicated using a YPS17B ultrasonic processor (Success Ultrasonic Equipment Co., Ltd., China). The ultrasonication frequency was set at 20 kHz for 25 min. To avoid foaming and overheating, the ultrasonication was done in cycles of 15 s, following by 20 s of rest. The temperature of the aqueous dispersion was maintained at 25 °C using an F12-EH water circulator (JULABO GmbH, Germany). Finally, the AOT/NP dispersions were visually inspected, and those appearing slightly hazy were used for the experiments. 2.3. Measurement of interfacial rheology A Tracker-H dynamic tensiometer (TECLIS Instruments, France) was used to assess the interfacial properties between the AOT/NP dispersions and CO2, and the drop profile analysis method was employed to measure the interfacial tension and interfacial dilational viscoelasticity. This method has been successfully applied to the rheological study of gas-liquid and liquid-liquid interfaces [33-35], and was conducted as follows: a view cell was filled with SC-CO2 at the test temperature and pressure conditions and a drop of the AOT/NP dispersion was generated in the cell using a syringe. Sinusoidal volume oscillations with a frequency of 0.2 Hz and a volume amplitude of 10% were loaded at the drop. The drop profile was then photographed, and the interfacial tension was obtained by axisymmetric shape analysis via the Laplace-Young equation. The dynamic interfacial tension and corresponding drop geometry were combined to calculate the interfacial dilational viscoelasticity modulus, E, according to Eq. 1:

E=

d d  dA / A d ln A 4


(1)

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where γ is the interfacial tension between the AOT/NP dispersion and SC-CO2 (mN/m), and A is the interfacial area (m2). The interfacial dilational viscoelasticity modulus reflects the interfacial resistance forces towards changes in volume or area, which directly affects the foam viscosity and flow behavior in porous media. 2.4 Measurement of viscosity and dynamic filtration The viscosity and dynamic filtration behavior of the dry SC-CO2 foams were investigated in a special laboratory apparatus under pressure and temperature ranges of 8–16 MPa and 40–80 °C, respectively. Fig. 2 shows a schematic diagram of the high-temperature, high-pressure (HTHP) apparatus, which included four main sections: a dry foam generator, a visual crack cell, a tube viscometer, and a dynamic filtration test cell. The apparatus allowed for: (1) generating dry SC-CO2 foam and monitoring its microstructure, (2) measuring the viscosity of the foam in a tube, and (3) studying the dynamic filtration behavior of the liquid and gas phases in porous media. The dry foam was generated by mixing CO2 and AOT/NP dispersion in a foam generator filled with silica sand of diameter ~120–150 μm. The temperature of the foam generator and the pipeline were controlled using the F12-EH circulator. A booster pump was used to increase the pressure of CO2, and the flowrates of the CO2 and AOT/NP dispersion were controlled using a high-pressure mass flow meter and an ISCO pump, respectively. The foam quality was adjusted by changing the flowrates of the two phases. After the foam generation, its microstructure was monitored in a visual crack cell as shown in Fig. 2. To decrease the overlay of bubbles and clearly visualize the foam structure, two stalinite plates were combined to obtain a foam flow channel with a gas thickness of approximately 100 μm.

Figure 2. Schematic diagram of the HTHP dynamic filtration and viscosity measurement apparatus for dry SC-CO2 foam.

The viscosities of the dry CO2 foams were measured in a tube viscometer with diameter 2 × 10−3 m and length 8 m, as shown in Fig. 2. The temperature of the tube was controlled via a circulating water bath. During the tests, the pressure loss of foam in the tube was recorded using a 5



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pressure difference transducer under constant flowrate. The shear rate in the tube was about 170 s−1. The effective viscosity, ηe, of the foams was calculated as per Eq. 2 [36]:

e 

DP / (4 L) 8v / D

(2)

where D is tube diameter (m), L is the tube length (m), △P is the pressure drop (Pa), and v is the foam flowrate (m/s). The porous media used in this study were artificial sandstone cores supplied by Bangda Co. Ltd., China. These cores are characterized by high compressive strength and quite homogeneous compositions. The permeabilities of the cores ranged from 5.9 mD to 210.3 mD, measured using a HK-4 nitrogen gas permeameter (Hongbo Co. Ltd., China). The detailed core permeability data are shown in Table 1. The dimensions of the cuboid-shaped cores were approximately 20 mm × 20 mm × 300 mm. To maintain the relative stability of the dry foam, a special core holder was designed to facilitate the dynamic filtration tests. To avoid leakage of the injected fluids, the cores were wrapped in a sealing sleeve in the core holder. The dry CO2 foam was injected into a slot with one side facing the core inlet surface (filtration surface). Thus, part of the foam entered into the porous core and the rest flowed out through the slot as shown by the arrow marks in Fig. 2. The filtrate from the outlet of the core was collected in a vessel containing a defoaming solution. After defoaming the filtrate, the accumulative volumes of the separated CO2 and liquid were recorded. The filtration pressure drop was controlled by adjusting the pressures at the filtration surface and the outlet via two back-pressure valves (BPV). A heating jacket was used to increase the temperature of the cuboid core. To record the pressure and temperature distributions in the porous media, five equidistant pressure and temperature sensors were installed in the core holder at intervals of around 6 cm, as shown in Fig. 2. The detailed test conditions for the dynamic filtration experiments are shown in Table 1. The pressures and temperatures of the foam fluids in all the tests were above the critical point of CO2 (31.2 °C, 7.38 MPa). Table 1. Dynamic filtration test conditions for dry CO2 foams.

Figure

6,7

8,9

Foam quality Г (%)

AOT Concentr ation (×10−3M )

90

Pressure (MPa)

NP Concentr ation (wt%)

Filtration surface

0.25, 3, 8

0

90

0.25, 3, 8

90

Outlet

Temperatur e (°C)

Permeability (mD)

16

13

40

26.1±0.2

0.5

16

13

40

26.8±0.4

0.25, 3, 8

1.0

16

13

40

28.6±0.4

90

0.25, 3, 8

1.5

16

13

40

29.3±0.5

80–97

3

0

16

13

40

26.1±0.2

80–97

3

0.5

16

13

40

26.8±0.4

6


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10

11

12

80–97

3

1.0

16

13

40

28.6±0.4

80– 97

3

1.5

16

13

40

29.3±0.5

80–97

3

1.5

16

8, 10 13

40

28.6±0.4

90

3

0

16

13

40, 60, 80

26.1±0.2

90

3

0.5

16

13

40, 60, 80

26.8±0.4

90

3

1.0

16

13

40, 60, 80

28.6±0.4

90

3

1.5

16

13

40, 60, 80

29.3±0.5

90

3

1.5

16

13

40

5.9–120.2

90

3

1.5

16

13

40

6.1–193.5

90

3

1.5

16

13

40

6.6–210.3

90

3

1.5

16

13

40

7.1–201.2

3. Results and Discussion 3.1 Effect of nanoparticles on interfacial rheology and dry foam viscosity Foam filtration is a type of spontaneous two-phase flow in porous media. According to Darcy’s law, the viscosity of a fluid is crucial to its flow behavior in porous media [37, 38]. As SC-CO2/liquid foam fluids have large interfacial surface areas, their viscosity is closely correlated with their interfacial properties. Thus, the interfacial rheology and the corresponding dry foam viscosity of SC-CO2/liquid were measured as a function of bulk AOT concentration both with and without of SiO2 nanoparticles. The results for the interfacial viscoelasticity modulus of SC-CO2/liquid and the corresponding foam viscosity are shown in Fig. 3. The same general trend was observed for each system, wherein the values of E and the foam viscosity showed maximum values at moderate AOT concentration. The curves may be divided into three regions, I, II and II, as indicated on Fig. 3. A schematic illustration of the interactions between the SiO2 nanoparticles and the AOT near the SC-CO2/liquid interface in each region is shown in Fig. 4.

Figure 3. (a) Interfacial viscoelastic modulus of SC-CO2/liquid interface and (b) the corresponding foam viscosity as functions of AOT concentration at 40 °C and 16 MPa. Other conditions were as follows: foam quality was 90%, the amounts of SiO2 nanoparticles added to the dispersions were 0.5 wt%, 1.0 wt%, and 1.5 wt%, and the apparent viscosity of foam was measured at the shear rate of 170 s-1. 7



Figure 4. Schematic illustration of the adsorption behavior of nanoparticles on the SC-CO2/liquid interface at different AOT concentration.

In region Ⅰ, the concentration of AOT was below the critical micelle concentration (CMC). A small fraction of the AOT was adsorbed on the SiO2 nanoparticles via the hydrophobic attractive interactions between the twin hydrocarbon tails of the AOT monomers and the modified nonpolar groups of the nanoparticles. Thus, the adsorption of AOT at the SC-CO2/liquid interface decreases, leading to the rising of interfacial tension with increasing SiO2 nanoparticle concentration as shown in the insert in Fig. 3(a). However, at lower AOT concentrations the SiO2 nanoparticles are still too hydrophobic and tend to flocculate in the liquid phase. Thus, the effect of nanoparticles on the interfacial viscoelasticity is not very pronounced in region I (Fig. 3(a)). Correspondingly, the difference between the viscosities of SC-CO2 foams with and without nanoparticles is small (Fig. 3(b)). In region Ⅱ, the higher concentration of AOT resulted in more AOT monomers being adsorbed on the nanoparticle surfaces and exposing their hydrophilic groups outward, decreasing the overall hydrophobicity of the nanoparticles. According to previous studies by Tang et al. [39] and Zhang et al. [25], surfactant adsorption can cause the nanoparticles to gradually shift from the liquid to the interface. With increasing AOT concentration, the nanoparticles cause the SC-CO2/liquid interface to become solid-like, and thus show a much higher interfacial viscoelasticity modulus (Fig. 3(a)). The value of E also increased with the increasing nanoparticle concentration from 0.5 wt% to 1.5 wt%, indicating a much higher interfacial intensity of foam films. This causes more internal friction to appear when the foam flows in the tube. Correspondingly, the viscosity of the foam was enhanced with the increasing concentration of AOT and SiO2 nanoparticles in this region, as shown in Fig. 3(b). In addition, the viscosities of the dispersions were also increased by the addition of nanoparticles (Fig. 3(b) inset), but these were still relatively low (< 7 mPa·s). The small viscosity increases seen in the dispersions are not sufficient to explain the high apparent viscosity of the SC-CO2 foams with nanoparticles. In region Ⅲ, with the continuing increase of AOT concentration above the CMC, the surface nanoparticles are more completely surrounded by AOT monomers and become hydrophilic. Simultaneously, free AOT monomers are adsorbed competitively on SC-CO2/liquid interface. Thus, the nanoparticles gradually migrate away from the interface back to the liquid phase and the interfacial viscoelastic modulus decreases (Fig. 3(a)), indicating that the SC-CO2/liquid interface becomes less solid-like. The foam films with less interfacial intensity are easily deformed and the foam viscosity decreases accordingly, as shown in Fig. 3(b). 8


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For the dry SC-CO2 foams used in this study, the foam quality was varied between 80% (dry) to 97% (ultra-dry). Based on the experimental results shown earlier in Fig. 3, the high viscosity SC-CO2 foams with nanoparticles in region Ⅱ were selected to study the relationship between viscosity and foam quality. The results are shown in Fig. 5(a). As the foam quality increases, the viscosity of each foam system increases at first due to enhanced interactions between bubbles, which increases the internal friction. The viscosity eventually reaches a maximum before decreasing at higher foam quality values due to the instability of the foam. This result is in agreement with previous studies on CO2 and N2 foams [19, 40]. In addition, with the nanoparticle concentration increasing from 0 to 1.5 wt%, the foam viscosity noticeably increased and the position of the maximum viscosity value (indicated by the star in Fig. 5(a)) shifted towards higher foam quality values. This is because the addition of nanoparticles enhances the stability of flowing dry foam. The microstructure images of the foams are shown in Fig. 5(b). As the figure shows, for bare AOT foam, the bubbles were coarse and relatively large in size. With the foam quality increasing from 85% to 95%, the bubble film became unstable and bubble disproportionation was more evident. For the foams containing nanoparticles, the bubbles became smaller and more homogeneous with increasing nanoparticle concentration. Moreover, at the high foam quality of 95%, the foam films with higher nanoparticle content were relatively stable, with the presence of the nanoparticles largely preventing disproportionation from occurring.

Figure 5. (a) Apparent viscosity of foams as a function of foam quality; (b) microstructure images of foams with different foam quality and nanoparticle concentrations (the scale of the yellow lines is 400 μm). Other conditions were as follows: the temperature and pressure were 40 °C and 16 MPa, respectively, and the AOT concentration was 3 × 10−3 M.

3.2 Dynamic filtration of dry foam 3.2.1 Effect of the nanoparticle and surfactant concentrations on filtration The dynamic filtration behavior of dry foam was investigated using the special HTHP laboratory apparatus (Fig. 2); to this end, the filtrate volumes of CO2 and liquid were recorded as functions of time to evaluate the filtration control performance of dry foams with different nanoparticle concentrations. The initial foam quality at the core inlet was set at 90%, the pressure and temperature were maintained above the critical point of CO2, and the pressure drop across the core sample was set at 3 MPa. Fig. 6(a) shows the CO2 filtrate volume, VCO2, (expressed at the pressure and temperature conditions of the filtration surface) as a function of the square root of 9



time. As the figure shows, for the foam without nanoparticles, the CO2 filtration curve is unstable at first, and the filtration rate is relatively high. The slope of the curve deceases before reaching a steady value at around 5 min. This filtration curve is similar to that of conventional wall-building fracturing fluid [15], which can be explained by the filtration and plugging of aqueous foam films. For the foams with SiO2 nanoparticles, a similar trend was observed, with VCO2 decreasing with increasing nanoparticle concentration; this indicates that the use of nanoparticles enhances the CO2 filtration control capacity of the dry foam.

Figure 6. Effect of nanoparticle concentration on the (a) CO2, (b) liquid, and (c) total filtrate of the dry foam; (d) the filtration coefficient as a function of nanoparticle concentration. The pressures at the filtration surface and the outlet of the porous media were controlled at 16 MPa and 13 MPa, respectively, the temperature of the foam and porous media was 40 °C, the AOT concentration in the liquid was 3 × 10−3 M, and the foam quality was 90%.

Similar results were observed for the liquid filtration curves as shown in Fig. 6(b), both with and without the addition of SiO2 nanoparticles. The liquid filtrate volume, VL, was lower than VCO2 due to the high foam quality leading to less liquid invasion into the porous media. To analyze the effect of nanoparticles on the filtration of dry foam as a whole, the total filtration volume, VT, (which is the sum of VCO2 and VL) is shown in Fig. 6(c). As the stable (i.e. constant slope) filtration stage played the dominant role in the filtration process, the filtration control capacity was assessed by calculating the filtration coefficient, C, from the slope of the stable stage, as follows [41]:

10


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C  0.005 

m A

(3)

where m is the slope of the filtration curve (mL/min0.5) and A is the area of the filtration surface (cm2). The correlation coefficient values for the linear fits to the CO2, liquid, and total filtrate curves in the stable filtration stage were generally > 0.95, confirming strong linear correlation. Fig. 6(d) shows the filtration coefficients (CCO2, CL, and CT) as functions of nanoparticle concentration. For each dry foam system, the CCO2 contributes the largest share to CT. Therefore, the filtration control of SC-CO2 is crucial to the leakoff of foam in porous media. The addition of nanoparticles significantly reduced the filtration coefficients of the foam; compared to bare AOT foam, the CT value decreased by a factor of about 2.2–6.5 with the SiO2 nanoparticle concentration increasing from 0.5 wt% to 1.5 wt%. As discussed earlier (section 3.1), the adsorption of SiO2 nanoparticles on the SC-CO2/liquid interface enhances the interfacial viscoelastic modulus and apparent viscosity, which in turn increases the flow resistance and filtration control capacity of dry foam in porous media. The filtration performance of the dry CO2 foams as a function of AOT concentration was also investigated, with the results shown in Fig. 7. The effect of surfactant concentration on the filtration coefficients correlates well with its effect on the interfacial viscoelastic modulus and foam viscosity as shown in Fig. 3. For dry foam without nanoparticles, the value of CT decreases with increasing AOT concentration, which may be explained with reference to the foamability and stability enhancements brought about by increasing the surfactant. For dry foam with nanoparticles, when the AOT concentration was low (2.5 × 10−4 M), the properties of the foam corresponded to region Ⅰ in Fig. 3. The SC-CO2/liquid interfacial viscoelastic modulus and foam viscosity were low, resulting in the dry CO2 foam having high mobility in porous media. Thus, the foam leakoff was relatively uncontrolled in this region, and CT was high. As the AOT concentration was increased to 3.0 × 10−3 M (region Ⅱ in Fig. 3, corresponding to strong nanoparticle adsorption on the SC-CO2/liquid interface), the interfacial viscoelastic modulus and foam viscosity increased rapidly, which tends to enhance resistances such as foam film slipping and the Jamin effect in pores and pore throats [34, 42]. Thus, the flowability of the foam in the porous media, and hence CT, was decreased. When the AOT concentration was increased to a relatively high value (8.0 × 10-4 M, corresponding to region Ⅲ in Fig. 3), the interfacial viscoelastic modulus and foam viscosity were decreased due to the desorption of nanoparticles, resulting in uncontrollable leakoff of the dry foam in porous media and markedly increasing CT as shown in Fig. 7.

11



Figure 7. Effect of AOT concentration on the total filtration coefficient of dry foam. The pressures at the filtration surface and the outlet of the porous media were controlled at 16 MPa and 13 MPa, respectively, the temperature of the foam and porous media was 40 °C, and the foam quality was 90%.

3.2.2 Effect of foam quality on filtration For the filtration of dry CO2 foams, the effect of high levels of initial foam quality, Γ, on the filtration control performance was investigated, with Γ varied between 80–97%. The experimental conditions are listed in Table 1, with the CO2 maintained in the supercritical state during the tests. Fig. 8(a) shows the total filtration volume curves of foams with a nanoparticle concentration of 1.0 wt%. With Γ increasing from 80% to 90%, VT was reduced due to the increased foam internal phase enhancing the bubble interactions and increasing the internal friction and foam viscosity (as shown in Fig. 5(a)). Thus, the foam flow resistance in porous media was increased. With the continuing increase of Γ from 90% to 97%, however, the total filtration volume increased, as the reduction of liquid content in the thin films of the dry foam aggravated its instability. This leads to a lower apparent viscosity (Fig. 5(a)), which is disadvantageous to the mobility control of foam in porous media, thereby resulting in higher CT values.

Figure 8.(a) Total filtration volume curve of foams with different initial foam quality values (the nanoparticle concentration in liquid was 1.0 wt%); (b) total filtration coefficient as a function of initial foam quality (the AOT concentration in the liquid was 3 × 10−3 M). 12


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The filtration coefficients obtained from the stable filtration stage are shown in Fig. 8(b). A decrease in CT over this stage indicates an enhancement in the filtration control performance. The curves for foams with different nanoparticle concentrations (Fig. 8(b)) all show similar trends. Compared to the bare AOT foam, the turning point of the filtration coefficient curves for the foams with nanoparticles appeared at a higher Γ value (~90%), corresponding to the viscosity variation from Fig. 5(a). This phenomenon is due to foam stability enhancements caused by the nanoparticles. As shown in Fig. 5(b), the rupture of the foam film and the gas-liquid separation were weakened by the addition of nanoparticles, which helps to maintain a high level of viscosity and inhibits the channeling of CO2 in porous media. Following the dynamic filtration of the dry foam (after about 110 min), the accumulated VCO2 and VL values were recorded. The filtrate composition was compared with that of the initial CO2 foam. Fig. 9 shows the filtrate volume fraction of SC-CO2 as function of Γ. For Γ < 90%, the SC-CO2 fraction of the filtrate was lower than that of the initial foam, which is in agreement with a previous study on aqueous foam filtration [15]. As SC-CO2 is the internal phase of the foam, it was trapped in the foam film during filtration, with flow resistances such as the Jamin effect and film slipping reducing its mobility in porous media. On the other hand, the external liquid phase of the foam was continuous and its flow in porous media was therefore relatively smooth and easy. Hence, the filtration of CO2 foam in porous media is a heterogeneous flow process. However, for the bare AOT foam at higher Γ values (95% and 97%), the filtrate volume fraction of SC-CO2 was above that in the initial foam. This is because the instability of the foam at high quality can lead to a continuous CO2 phase in porous media (i.e. gas channeling). However, once the SiO2 nanoparticles were added, the foam stability was enhanced, thereby improving the CO2 filtration control performance and decreasing the volume fraction of SC-CO2 in the filtrate.

Figure 9. Filtrate volume fraction of SC-CO2 as function of corresponding initial foam quality (the AOT concentration in the liquid was 3 × 10−3 M).

3.2.3 Effect of pressure drop on filtration Here, the relationship between the total filtration coefficient of the foam, CT, and the system pressure drop, ΔP, (i.e. the pressure difference between the filtration surface and the outlet of the 13



core) was investigated, with the results shown in Fig. 10(a). The value of Γ at the filtration surface was varied between 80% and 97%. As the figure shows, higher ΔP values lead to larger leakoff rates, thus increasing the CT values of the foams. However, the relationship between the foam filtration control performance and Γ reveals some interesting phenomena. When Δ P is low (3 MPa), CT shows a minimum value at Γ = 90%, whereas when Δ P increases to 8 MPa, the minimum value of CT now occurs at Γ = 85%.

Figure 10. (a) Total filtration coefficient of foams as a function of pressure drop (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10−3 M, respectively); (b) pressure profiles in the core sample (with a total pressure drop of 8 MPa) as a function of initial foam quality.

To further analyze the variation of CT at the high pressure drop of ΔP = 8 MPa, the 1D spatial pressure distributions along the core sample axis at different Γ are shown in Fig. 10(b). As the figure shows, the shapes of the pressure profiles changed from a convex to a concave shape with increasing Γ. This phenomenon is caused by CO2 expansion occurring closer to the sample inlet as Γ increases, resulting in a higher local pressure drop in the area near the inlet. This phenomenon indicates a weakening of filtration control performance with higher Γ as shown in Fig. 8 earlier. As most of the pressure loss is distributed in the area near the inlet, the flow resistance and mobility control capacity further along the core is decreased. However, for the foams with relatively low Γ (80–85%), the convex profile shape indicates that moderate increases in Γ may actually enhance the foam flow resistance and mobility control capacity, with most of the pressure loss being distributed in the area near the outlet of the core.

3.2.4 Effect of temperature on filtration Here, the effect of temperature on the filtration performance of dry foams was studied, with the results shown in Fig. 11(a). As the figure shows, CT was positively correlated with temperature for all the foams, with the bare surfactant foam showing the strongest temperature dependence due to 14


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the instability and viscosity reduction of the foams at high temperatures in porous media [43, 44]. To specifically analyze the SC-CO2 filtration control performance, the compositions of the accumulated filtrates at the different temperature values (40 °C, 60 °C, and 80 °C) are shown in Fig. 11(b). As the figure shows, for the bare AOT foam, the filtrate volume fraction of SC-CO2 increased from 88% to 94% (which is higher than the Γ value of 90%). The aggravated leakoff of CO2 indicates that the filtration control performance of dry foam was weakened at high temperature. For the foams with nanoparticles, the temperature dependence decreased at higher nanoparticle concentrations. For example, for the foams with 1.0 wt% and 1.5 wt% nanoparticle concentrations, the filtrate volume fraction of SC-CO2 at 80 °C were 89% and 86%, respectively, both of which were lower than the initial foam quality. This result indicates that in terms of filtration control performance, nanoparticle enhanced dry foams possess a better temperature resistance than that of the bare surfactant foam.

Figure 11. (a) Total filtration coefficients of foams as a function of temperature (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10−3 M, respectively, and the initial foam quality was 90%); (b) filtrate volume fractions of SC-CO2 at different temperatures.

3.2.5 Effect of permeability on filtration Here, the effect of the permeability of the porous rock on the filtration of dry SC-CO2 foam (Γ = 90%) was evaluated, with the results shown in Fig. 12. As the figure shows, there is a positive linear relationship between CT and permeability on the log-log plot, meaning that a power law relationship exists between the two variables. Indeed, high permeability rocks with larger pores and pore throats exert lower capillary forces to resist fluid flow, thus leading to a higher foam filtration rate. Here, CT goes up by about two orders of magnitude for every three orders of magnitude of permeability increase, regardless of whether nanoparticles are present in the dry CO2 foam. The fitted power law exponents are shown in Fig. 12, whence it can be seen that with the increase of nanoparticle concentration from 0 to 1.5 wt%, the exponent decreased from 0.76 to 0.52. These results indicate that dry foams with higher nanoparticle concentrations show better filtration control performance in high permeability rocks.

15



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Figure 12. Total filtration coefficients of foams as a function of the permeability of porous media (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10−3 M, respectively, and the initial foam quality was 90%).

3.2.6 Return permeability after filtration After the filtration of dry SC-CO2 foam (Γ = 90%), the return gas permeability, kReturn, of the cores was measured in the direction opposite to the effluent. The return permeability ratio, ηR, is defined as the ratio between the initial permeability, kInitial, and kReturn, i.e.:

R 

kReturn 100% kInitial

(4)

The results are shown in Fig. 13. Compared to the bare surfactant foam, the return permeability ratios were lower in the foams with nanoparticles. Generally, lower initial permeability and higher nanoparticle concentration corresponded to lower return permeability ratios. This might be caused by the retention of nanoparticles in the pores and pore throats of the rock. Nevertheless, the small permeability reduction in porous media is not sufficient to explain the dramatically low filtration coefficients of dry foam with nanoparticles seen in this study. For dry CO2 foam with 1.5 wt% SiO2 nanoparticles, the return permeability ratios in the tested core were between 86% and 92%. This value is relatively high compared to previous filtration studies of foam with gel or nanoparticles at lower foam qualities [43]. A likely reason for this result is that the liquid and nanoparticle penetration into porous media from the dry foams is small, leading to a high relative permeability to gas. This result confirms that the nanoparticle-enhanced dry foams used in this study are relatively clean fluids for porous media. However, the damage of nanoparticle to porous media can not be ignored completely. The adsorption and retention of nanoparticle during the dry foam filtration need to be carefully studied, especially when the foam was used in formation with ultra-low permeability.

16


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Figure 13. Return permeability ratio after filtration as a function of initial permeability (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10−3 M, respectively, and the initial foam quality was 90%).

4. Conclusions In this study, a systematic investigation was conducted into the dynamic filtration behavior of dry SC-CO2 foams with nanoparticles in porous media. The main conclusions which can be drawn from the results presented herein are as follows: (1) The interfacial viscoelasticity modulus of SC-CO2/liquid and corresponding foam viscosity were improved by the adsorption of silica nanoparticles at the SC-CO2/liquid interface. An optimum range for AOT concentration exists above or below which the interfacial adsorption of nanoparticles is not favored. The addition of nanoparticles at high foam quality reduces the coarse bubbles and prevents bubble disproportionation, which helps maintain higher viscosities in the ultra-dry foams. (2) For dry SC-CO2 foams, the CO2 makes the largest contribution towards the total filtrate volume. The foam filtration control performance is enhanced significantly by the presence of silica nanoparticles. Compared to bare AOT foam, the total filtration coefficient of CO2 was decreased by a factor of about 2.2–6.5 with an increase in SiO2 nanoparticle concentration from 0.5 wt% to 1.5 wt%. (3) For dry SC-CO2 foam with nanoparticles, the effect of surfactant concentration on the filtration coefficients correlates well with its effect on interfacial viscoelastic modulus and foam viscosity. A lower filtration coefficient was obtained at higher interfacial viscoelastic modulus and foam viscosity. (4) With the foam quality increasing from 80% to 97%, The foam filtration coefficients first decreased to a minimum, and then increased as the foam became ultra-dry. Compared to bare surfactant foam, the turning point of the filtration coefficient for foams with nanoparticles appeared at a relatively high foam quality, which may be explained by the inhibition effects of dry foam film rupture and gas-liquid separation in porous media caused by nanoparticles. (5) At high filtration pressure drop, the shapes of the pressure profiles along the core sample axis varied with initial foam quality, which was due to CO2 expansion closer to the inlet as foam quality increased. For foams with relatively high initial quality (90–97%), a continued 17



increase in foam quality lead to a low flow resistance and weakened the filtration control performance. (6) The addition of silica nanoparticles lowers the temperature dependence of the foam filtration coefficient compared to the bare surfactant foam and reduces the filtrate volume fraction of SC-CO2. (7) For dry SC-CO2 foam, the permeability and total filtration coefficient follow a power law relationship, with an increase of three orders of magnitude in the former causing an increase of about two orders of magnitude in the latter. The addition of nanoparticles caused a decrease in the power law exponent. The return permeability tests after filtration confirmed that dry SC-CO2 foams with nanoparticles are relatively clean fluids for porous media.

Author information Corresponding author Qichao Lv *Email: [email protected] Notes The authors declare no competing financial interest.

Acknowledgements This study was financially supported by Science Foundation of China University of Petroleum, Beijing (No.2462018YJRC025) and National Natural Science Foundation (51574264). We sincerely thank Foam Fluid Enhanced Oil & Gas Production Engineering Research Center in Shandong province and colleagues at Unconventional Petroleum Research Institute of China University of Petroleum (Beijing) for their kind help in this work.

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Table 1. Dynamic filtration test conditions for dry CO2 foams.

Figure

6,7

8,9

10

11

12

Foam quality Г (%)

AOT Concentr ation (×10−3M )

90

Pressure (MPa)

NP Concentr ation (wt%)

Filtration surface

0.25, 3, 8

0

90

0.25, 3, 8

90

Outlet

Temperatur e (°C)

Permeability (mD)

16

13

40

26.1±0.2

0.5

16

13

40

26.8±0.4

0.25, 3, 8

1.0

16

13

40

28.6±0.4

90

0.25, 3, 8

1.5

16

13

40

29.3±0.5

80–97

3

0

16

13

40

26.1±0.2

80–97

3

0.5

16

13

40

26.8±0.4

80–97

3

1.0

16

13

40

28.6±0.4

80– 97

3

1.5

16

13

40

29.3±0.5

80–97

3

1.5

16

8, 10 13

40

28.6±0.4

90

3

0

16

13

40, 60, 80

26.1±0.2

90

3

0.5

16

13

40, 60, 80

26.8±0.4

90

3

1.0

16

13

40, 60, 80

28.6±0.4

90

3

1.5

16

13

40, 60, 80

29.3±0.5

90

3

1.5

16

13

40

5.9–120.2

90

3

1.5

16

13

40

6.1–193.5

90

3

1.5

16

13

40

6.6–210.3

90

3

1.5

16

13

40

7.1–201.2

21



Figure 1. The relationship between foam stability with the addition of conventional stabilizers (thickeners) and the damage done to porous media.

Figure 2. Schematic diagram of the HTHP dynamic filtration and viscosity measurement apparatus for dry SC-CO2 foam.

22


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Figure 3. (a) Interfacial viscoelastic modulus of SC-CO2/liquid interface and (b) the corresponding foam viscosity as functions of AOT concentration at 40 °C and 16 MPa. Other conditions were as follows: foam quality was 90%, the amounts of SiO2 nanoparticles added to the dispersions were 0.5 wt%, 1.0 wt%, and 1.5 wt%, and the apparent viscosity of foam was measured at the shear rate of 170 s-1.

Figure 4. Schematic illustration of the adsorption behavior of nanoparticles on the SC-CO2/liquid interface at different AOT concentration.

Figure 5. (a) Apparent viscosity of foams as a function of foam quality; (b) microstructure images of foams with different foam quality and nanoparticle concentrations (the scale of the yellow lines is 400 μm). Other conditions were as follows: the temperature and pressure were 40 °C and 16 MPa, respectively, and the AOT concentration was 3 × 10−3 M. 23



Figure 6. Effect of nanoparticle concentration on the (a) CO2, (b) liquid, and (c) total filtrate (c) of the dry foam; (d) the filtration coefficient as a function of nanoparticle concentration. The pressures at the filtration surface and the outlet of the porous media were controlled at 16 MPa and 13 MPa, respectively, the temperature of the foam and porous media was 40 °C, the AOT concentration in the liquid was 3 × 10−3 M, and the foam quality was 90%.

24


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Figure 7. Effect of AOT concentration on the total filtration coefficient of dry foam. The pressures at the filtration surface and the outlet of the porous media were controlled at 16 MPa and 13 MPa, respectively, the temperature of the foam and porous media was 40 °C, and the foam quality was 90%.

Figure 8.(a) Total filtration volume curve of foams with different initial foam quality values (the nanoparticle concentration in liquid was 1.0 wt%); (b) total filtration coefficient as a function of initial foam quality (the AOT concentration in the liquid was 3 × 10-3 M).

25



Figure 9. Filtrate volume fraction of SC-CO2 as function of corresponding initial foam quality (the AOT concentration in the liquid was 3 × 10-3 M).

Figure 10. (a) Total filtration coefficient of foams as a function of pressure drop (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10-3 M, respectively); (b) pressure profiles in the core sample (with a total pressure drop of 8 MPa) as a function of initial foam quality.

26


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Figure 11. (a) Total filtration coefficients of foams as a function of temperature (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10-3 M, respectively, and the initial foam quality was 90%); (b) filtrate volume fractions of SC-CO2 at different temperatures.

Figure 12. Total filtration coefficients of foams as a function of the permeability of porous media (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10-3 M, respectively, and the initial foam quality was 90%).

27



Figure 13. Return permeability ratio after filtration as a function of initial permeability (the nanoparticle and AOT concentrations in the liquid were 1.0 wt% and 3 × 10-3 M, respectively, the initial foam quality was 90%).

28


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Dynamic Filtration Behavior of Dry Supercritical CO2 Foam with

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