Experimental study on rheological properties of nanoparticle-stabilized carbon dioxide foam

Journal Pre-proof Experimental Study on Rheological Properties of Nanoparticle-stabilized Carbon Dioxide Foam Dongxing Du, Xu Zhang, Yingge Li, Di Zhao, Fei Wang, Zhifeng Sun PII:

S1875-5100(19)30392-0

DOI:

https://doi.org/10.1016/j.jngse.2019.103140

Reference:

JNGSE 103140

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 21 September 2019 Revised Date:

28 December 2019

Accepted Date: 28 December 2019

Please cite this article as: Du, D., Zhang, X., Li, Y., Zhao, D., Wang, F., Sun, Z., Experimental Study on Rheological Properties of Nanoparticle-stabilized Carbon Dioxide Foam, Journal of Natural Gas Science & Engineering, https://doi.org/10.1016/j.jngse.2019.103140. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

1

Experimental Study on Rheological Properties of

2

Nanoparticle-stabilized Carbon Dioxide Foam

3

Dongxing Du 1, Xu Zhang 1, Yingge Li 2, *, Di Zhao1, Fei Wang 1, Zhifeng Sun1

4 5 6 7 8 9 10 11

1

12

In relationship with the potential application of nanoparticle (NP) foam technology in CO2

13

enhanced oil recovery (EOR) and greenhouse geological storage in tight reservoirs, the

14

rheological properties of the NP-stabilized CO2 foam with surfactant (α-olefin sulfonate-AOS)

15

solution were experimentally investigated. The foam was treated as a power-law non-Newtonian

16

fluid, and the relationships between the shear stress and shear rate as well as the apparent viscosity

17

of foam and foam quality were determined under influential parameters including the NP additive,

18

internal gas type, salinity, and oil presence. Critical foam quality values in the range 91–96% were

19

observed for the NP-stabilized foam, whereas no such values were obtained for the corresponding

20

AOS-CO2 foam. The results show the NP-AOS-CO2 foam has lower viscosity compared to the

21

NP-AOS-N2 foam, and the solution salinity decreases the viscosity of the NP-AOS-CO2 foam,

22

whereas oil presence has no obvious effect on the foam viscosity.

23 24 25

Keywords: nanoparticle; CO2 foam; non-Newtonian behavior; foam quality

26

In the petroleum industry, the immiscible gas flooding process could result in low oil displacement

27

efficiency, because of gravity stratification and gas channeling in the rock formations. Foam

28

technology shows strong profile control ability through remarkably improving the gas phase

29

viscosity, thereby has been successfully used in enhanced oil recovery (EOR) in tight oil

30

reservoirs [1–5]. With the emerging needs of decreasing carbon dioxide emission, taking CO2 as

31

the foam internal phase has also attracted worldwide attention as an effective technology for the

32

CO2 geological storages in the Carbon Capture Utilization and Storage (CCUS) chain [6–10].

33

Surfactants and/or polymers have been usually used to stabilize the generated foam fluid by

34

decreasing the surface tension between the gas phase and the continuous liquid phase [11–13]. The

35

carbon dioxide foam formed by chemical additives, however, represents a challenge because the

36

foam stability can be adversely affected by the oil presence, high salinity of formation water, and

Geo-Energy Research Institute, College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao, 266061, China 2 College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, China * Corresponding Author. Email: [email protected] Abstract

1. Introduction

1

1

high temperature as typically found in oil reservoirs [14,15]. With the development of

2

nanotechnology, the use of surface-treated nanoparticles (NPs) together with surfactants has been

3

proven to be effective for improving foam stability under high salinity and high temperature

4

reservoir conditions [16–20]. The NPs adsorbed at the gas–liquid interface can increase the film

5

mechanical strength through forming a spatial network structure to reduce the direct contact

6

between the fluids, thereby acting as a barrier to the rate of liquid discharge, reducing the gas

7

diffusion, and preventing membrane cracking and bubble coarsening [21–26]. Because of their

8

small sizes, the NPs can transport with little retention in porous media without plugging the pore

9

throats [18,27]. Roberts et al. [28] showed that 96% of a highly concentrated dispersion (18.7 wt%)

10

of 5 nm silica nanoparticles came out in the effluent water after its injection into a very tight (10

11

mD) limestone core. Yu et al. [29] demonstrated that the equilibrium adsorption of NPs is very

12

low in sandstone, limestone, and dolomite porous media. Rognmo et al. [30] found that a large

13

degree of NPs remains at the CO2-brine interface to stabilize foam when flowing through the

14

porous medium. In fact, as NPS are less prone to adsorption on reservoir rocks and clay minerals

15

during migration compared to surfactants, they have been widely used as the surfactant transport

16

agent to minimize the surfactant adsorption in porous media [26,31–34].

17

In relation to the potential application of NP-stabilized CO2 foam on EOR and CO2 geological

18

storage, extensive laboratory studies have been carried out concerning the foam propagation

19

behaviors in porous media. Rognmo et al. [30] conducted an experimental investigation on the

20

foam generation and flow behavior of hydrophilic silica NP-stabilized liquid CO2 foam in

21

sandstone core plugs and observed significantly decreased critical foam quality values for the

22

NP-stabilized foams. Rognmo et al. [35] presented a comprehensive experimental investigation on

23

the use of NPs as foam stabilizers during the co-injection of supercritical CO2 and brine under

24

reservoir conditions and observed that the NP-stabilized CO2-foam remains stable during the oil

25

displacement and therefore increases the oil recovery by a factor of two. Rahmani et al. [36]

26

carried out laboratory tests with the co-injection of CO2 and a solution of 12-nm methyl-coated

27

SiNPs to generate stable CO2 foam in the cores and found that the SiNPs were able to generate

28

stabilized CO2 foam in both unfractured and fractured limestone cores with the lower critical shear

29

rate for the foam generation. Other representative researchers include Espinoza et al. [37],

30

Aroonsri et al. [38], Yu et al. [39–41], and Singh et al. [42] measured the foam's apparent

31

viscosity in capillary tubes, glass bead-packs, sand-packs, sandstone cores carbonate rock cores,

32

and two-layers heterogeneous 2D sand pack.

33

To understand the mechanism of NP-stabilized foam displacement process in underground

34

formations, detailed investigations on the foam rheological properties are substantial.

35

Non-Newtonian flow index and foam quality regime determination are the two typical rheological 2

1

properties [43–51]. Worthen et al. [52] generated CO2/water foams with either PEG-coated silica

2

or methylsilyl modified silica NPs and measured the apparent viscosity as 120-folds compared to

3

that of a CO2–water mixture without NPs. Xue et al. [26] used a capillary tube viscometer and

4

calculated the apparent viscosity by using the Hagen–Poiseuille equation and found that the

5

combination of surfactant and NPs resulted in a synergistic effect whereby the viscosities were

6

much higher than expected from a combination of each species alone. The NP-stabilized

7

CO2/water foam shows shear thinning behavior with a power-law index of 0.5. Yekeen et al. [33]

8

determined the apparent viscosity of the foam in a 2D Hele–Shaw cell and reported increased

9

foam apparent viscosity along with improved foam quality from 50% to 75%. Xiao et al. [53]

10

determined the in situ shear viscosity of supercritical CO2 foams stabilized by nano-SiO2 in a flow

11

loop apparatus at 40 °C in the pressure range 1140±20 psi. They demonstrated that the foam with

12

80% foam quality has the highest viscosity and stability, and the foams with NPs show

13

shear-thinning and shear-thickening behaviors depending on the foam quality and components.

14

Using the same apparatus, Xiao et al. [54] studied the effects of shear rates, surfactant, foam

15

quality, salinity, and NP size on the in situ shear viscosity of NP-stabilized ScCO2 foam. Verma et

16

al. [55] tested the foam rheology using a rheometer in a cup and bob geometry and obtained the

17

shear-thinning flow behavior index varying from 0.51 to 0.77. As a fundamental study for

18

revealing the mechanism behind the foam flooding behavior in porous media, it is unnecessary to

19

perform foam rheological tests under the exact EOR and storage reservoir conditions. For instance,

20

the effective foam viscosity used in the foam population-balance model [56–57] is classically

21

based on the rheological model of a single bubble [43] and a train of bubbles within a capillary

22

tube [44] under room temperature and atmospheric backpressure conditions. The population

23

balance model explicitly relates the gas mobility reduction to the foam texture as defined by the

24

effective viscosity (µf) represented by Eq. (1) (µg is the gas phase viscosity, nf is the flowing

25

bubble density, and α is the constant).

  

µ f = µ g 1 + α

26

nf   µg u df 

(1)

27

where the power-law exponent of d, which explicitly reveals the non-Newtonian foam rheology, is

28

set to be 1/3 in accordance with Bretherton’s [43] and Hirasaki’s [44] results under the normal

29

conditions. Based on this mechanistic model, lots of foam modeling and numerical studies [58–63]

30

have been performed to reproduce and successfully predict the surfactant foam displacement

31

behavior under realistic reservoir conditions, showing the fact that the laboratory rheology tests

32

under normal conditions could be feasible and essential to guide the foam field applications.

33

The current literature survey indicates that the NP-stabilized CO2 foam is becoming more and

34

more popular relating to its potential applications in CO2 EOR and carbon geological storage 3

1

practices. With solid particles dispersed in the continuous liquid phase, the rheological behavior of

2

NP-stabilized foam is much more sophisticated than the conventional surfactant stabilized foam.

3

At present, however, systematic studies on the rheological properties of NP-stabilized foam are

4

scarce. Researchers have used various apparatus and reported inconsistent and incomplete

5

rheology results. In this study, therefore, the non-Newtonian behavior of the NP-stabilized CO2

6

foam was comprehensively investigated under various foam qualities with special focus on the

7

effects of internal gas phase, salinity, and oil presence.

8

2. Experimental

9

2.1 Materials

10

Silica NPs with an average specific surface area of 300 m2/g and an average primary particle size

11

of 7 nm (model NP300, supplied in powder form by Evonic, Germany) were used as the additive

12

foam stabilizer. The surfactant used was sodium α-olefin sulfonate (AOS, purity ≥99%, provided

13

by Sinolight Chemical Industry Group) in accordance with its wide application in foam displacing

14

oil processes [64–66]. Analytically pure NaCl was dissolved in deionized water to simulate the

15

solution salinity. The n-dodecane component (n-C12H26, with a molecular weight of 170.34,

16

provided by Tianjin Guangfu Fine Chemical Research Institute) was used to simulate an oil

17

presence environment.

18

Table 1 lists five types of foam with various compositions. As a benchmark case, the first type of

19

foam is generated with only AOS surfactant to validate the experimental apparatus and

20

methodology. The 2nd–5th types of foam are all NP-stabilized foams, and their varying

21

compositions could reveal the effects of internal gas type (CO2 versus N2), salinity, and oil

22

presence on the rheological properties of foams. Based on the parameter selection ranges reported

23

in the literature, 0.15 wt% concentration of both NP and surfactant was used [55,67].

24

Table 1 Foam with various compositions No.

25 26 27 28 29

Foam compositions 1

CO2+0.15%AOS

2

CO2+0.15%AOS+0.15%NP300

3

N2+0.15%AOS+0.15%NP300

4

CO2+0.15%AOS+0.15%NP300+2%NaCl

5

CO2+0.15%AOS+0.15%NP300+10%C12H26

To prepare the aqueous solution, the NP together with the desired surfactant solution was placed in a magnetic stirrer for 5 h at a high speed of 1200 RPM, and then was placed in an ultrasonic disperser for 3 h dispersion at a frequency of 40 kHz. By applying the above method, the NP dispersion solution maintained stable state and did not exhibit macroscopic aggregation during the test process. 4

1

2.2 Experimental apparatus and procedure

2

Fig. 1 depicts the schematic diagram of the experimental setup. Bulk foam was generated by

3

mixing CO2 or N2 gas with the NP-surfactant solution in the foam generator and then passed

4

through a straight quartz glass tube, in which the foam morphology was clearly observed. The

5

structure of the quartz tube and the foam generator assembly followed as adopted by Du et al. [50].

6

The dimension of the quartz tube is as follows: length, 300 mm; inner diameter, 3 mm; wall

7

thickness, 10 mm. The body of the foam generator is made of 304 stainless steel, and the filling

8

material is consolidated quartz sand plate. The height, outer diameter, and the inner diameter of

9

the foam generator is 65.8, 46.4, and 32 mm, respectively. Gas injection was carefully

10

manipulated and monitored using a mass flow controller (FL-802 50 mL ± 1%, Shenzhen Flow

11

method measure and control systems Co. Ltd), and the surfactant flow rate was controlled using a

12

high-precision piston pump. The pressure difference between the inlet and outlet was measured

13

using a U-tube differential pressure gauge after foam flow inside the tube reaching the stable

14

condition. All the experiments were carried out at a constant temperature of 20 °C.

15 16 17 18

1- Gas tank, 2-NP-Surfactant solution, 3-Piston pump, 4-Valve, 5-Foam generator, 6-Quartz glass tube, 7-Differential pressure measurement unit, 8- Effluent collector, 9-Gas mass flow controller

Fig. 1 Schematic diagram of the experimental setup

19

2.3 Power-law constitutive equation

20

It is assumed the foam behaves as a non-Newtonian fluid whose shear stress (τ) and shear rate (γ)

21

are in a power function relationship with the constitutive equation (2):

τ =K γ n

22

(2)

23

where K is the flow consistency coefficient, and n is the flow behavior index (with n <1 for

24

shear-thinning fluids, n = 1 for Newtonian fluid and n >1for shear-thickening fluids). Eq. (2) can

25

be rewritten in the same shape as a Newtonian fluid in engineering applications such as,

26

τ =µα γ

27

µ α = K γ n −1

(3)

where µα is the apparent viscosity of the foam fluid and is a function of the shear deformation rate. 5

1

As the pressure difference along the tube is in the range 300–1500 Pa, the foam flow is treated

2

incompressible and the shear stress and shear rates can be calculated as follows:

4

∆p D 8U γ= (4) L 4 D where D is the tube diameter, ∆p is the flow pressure difference, L is the tube length, and U is the

5

average flow rate inside the tube, and its relationship with the volumetric flow rate Q is

6

represented by the following equation.

3

τ=

U = 4Q (π D 2 )

7 8U D

(5)

D∆p curves in a logarithmically scaled graph could 4L

8

Therefore, plotting the measured

9

determine the flow behavior index n and the flow consistency coefficient K, thereby leading to the

and

10

apparent viscosity of the NP-stabilized CO2 foam fluid.

11

As another important rheological property, the effect of foam quality on the foam apparent

12

viscosity is also addressed in detail. Foam quality f is defined as the volume fraction of the gas

13

phase in foam:

14

f=Vg/(Vg+Vl)

(6)

15

where Vg and Vl are the volumes of the gas and liquid phases in the foam, respectively.

16

Consisting of more than 80% volume fraction of the gas phase, the foam used in the EOR

17

practices usually obeys the PVT model of the internal gas phase when operating under different

18

conditions, which has been validated through satisfactory numerical reproducibility based on the

19

experimental studies [56–63].

20

3. Results and Discussion

21

3.1 Rheological properties of the AOS-CO2 foam

22

The rheological properties of the surfactant generated from CO2 foam have been investigated in

23

detail, and therefore the non-Newtonian properties of AOS-CO2 foam were measured in the first

24

case to validate the experimental setup and the data manipulation procedure.

25

Figs. 2(a)–(d) show the logarithmic plots of τ versus γ under the surfactant flow rates of 1.0, 1.5,

26

2.0, and 2.5 mL/min. Error bar for all the data was also plotted in these figures based on the error

27

analysis in Section 3.6. A clear linear relationship was observed between lnτ and lnγ, validating

28

the power-law non-Newtonian assumption for the foam fluid. The fit lines in the figures show that

29

the flow behavior index n varies from 0.603 to 0.686, which is consistent with the

30

Bretherton-based theoretical value of 0.667 [43,44,68] and the empirical values varying from 0.61

31

to 0.77 [50,69,70] for surfactant generated foam, thereby validating the experimental apparatus

32

and procedure used in this study. 6

0.8

Surfactant: 1ml/min lnτ =0.603*lnγ-2.433

1.0

Surfactant: 1.5ml/min lnτ=0.648*lnγ-2.930

0.6

lnτ

lnτ

0.8

0.6

0.4

0.2 0.4

0.0 0.2 4.6

4.8

5.0

5.2

5.4

5.6

4.6

5.8

4.8

5.0

5.2

a

Surfactant rate 1ml/min

b 0.8

Surfactant: 2ml/min lnτ=0.686*lnγ -3.204

0.6

0.6

0.4

0.4

lnτ

lnτ

0.8

0.2

0.2

0.0

0.0 4.6

4.8

5.0

5.2

c

5.6

5.8

5.4

5.6

Surfactant: 2.5ml/min lnτ=0.628*lnγ -2.930

4.6

5.8

Surfactant rate 1.5 ml/min

4.8

5.0

5.2

5.4

5.6

5.8

lnγ

lnγ

3 4 5

5.4

lnγ

lnγ

1 2

Surfactant rate 2ml/min

d

Surfactant rate 2.5 ml/min

Fig.2 Shear stress vs. shear rates for AOS-CO2 foam at different surfactant flow rates

Apparent Viscosity µa(mPa· s)

16

1ml/min 1.5ml/min 2ml/min 2.5ml/min

14

12

10

8

6 78

80

82

84

86

88

90

92

94

96

98

Foam Quality f (%)

6 7

Fig. 3 Apparent viscosity under various foam qualities for AOS-CO2 foam

8

Fig. 3 depicts the foam apparent viscosity under various foam qualities. Notably, four separated

9

lines exist corresponding to the four surfactant rates of 1.0, 1.5, 2.0, and 2.5 mL/min. Based on the

10

foam quality definition as described in Eq. (6), higher gas phase rate is necessary under the case of

11

higher surfactant rate to obtain the same foam quality values. Therefore, under the same f values,

12

the black line for the case of 1 mL/min has the lower total flow rate compared to the other

13

surfactant rate cases, and thereby shows the highest foam apparent viscosity as a shear thinning

14

fluid. Fig. 3 clearly shows the unanimously decreasing foam apparent viscosities with increasing

15

foam quality for all the surfactant rate cases. The foam quality region 80–98%, as revealed in Fig. 7

1

3, is consistent with other reported studies on the foam flooding processes in porous media. [26,

2

51,66,71–73]

3

3.2 Rheological properties of NP-AOS-CO2 foam

4

Figs. 4 (a), (b), (c), and (d) show the relationship between the shear stress and shear rate at various

5

surfactant rates of 1, 1.5, 2, and 2.5 mL/min, respectively. The linear relationship between lnτ and

6

lnγ is still valid; however, the slope varies in different shear rate regions. For example in Fig. 4(a),

7

the value of n is fit to be 0.889 in the range of 4.4< lnγ <5.0, whereas it decreases to 0.616 in the

8

region of 5.0< lnγ <5.8. With detailed error analysis described in Section 3.6, error bars were not

9

put in Fig. 4 for more clearly revealing the slope variation characteristics. The detailed rheological

10

properties are listed in Table 2. 1.4

1.2 1.2

Surfactant: 1ml/min lnτ=0.889*lnγ-3.545 lnτ=0.616*lnγ-2.288

Surfactant: 1.5ml/min lnτ=1.077*lnγ-4.842 lnτ=0.444*lnγ-1.541

1.0 0.8

1.0

lnτ

lnτ

0.6 0.8 0.6

0.4 0.2 0.0

0.4

-0.2 0.2 4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

4.2

5.8

4.4

4.6

4.8

a

Surfactant rate 1ml/min

b

0.8

0.6

Surfactant: 2ml/min lnτ=0.818*lnγ-3.994 lnτ=0.637*lnγ-2.942

0.6 0.4

5.0

5.2

5.4

5.6

5.8

6.0

lnγ

lnγ

11 12

Surfactant rate 1.5ml/min Surfactant: 2.5ml/min lnτ=0.662*lnγ -3.195 lnτ=0.306*lnγ -1.292

0.4 0.2

lnτ

lnτ

0.2 0.0

0.0

-0.2

-0.2

-0.4 -0.4

-0.6 4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

lnγ

lnγ

13 14 15

Fig.4 Shear stress vs. shear rates for NP-AOS-CO2 foam at different surfactant flow rates

16

The reason behind the variation in the flow behavior index could be analyzed based on the foam

17

quality. Accordingly, the data of the foam apparent viscosity versus foam quality is plotted in Fig.

18

5, in which the dependence of the foam viscosity on the foam quality is clearly revealed. Still

19

taking the case of 1.0 mL/min as the example, Fig. 5 shows that the apparent viscosity increases in

20

the foam quality region 91–96% whereas it decreases in the region of f >96% corresponding to the

21

slope change in Fig. 4(a) after lnγ >5. In other surfactant rate cases, the decreased slope between

22

µa and f was also distinctively observed at certain foam quality values, indicating a critical foam

23

quality value in the range 0.92–0.96 for the NP-stabilized surfactant CO2 foam. The clear change

c

8

Surfactant of 2ml/min

d

Surfactant rate of 2.5ml/min

1

in the slope between lnτ and lnγ as well as between ua and f could attribute to the higher capillary

2

pressure pc at larger foam quality values. Capillary pressure is the pressure difference between the

3

flat part of the foam film and the highly curved plateau border and is proportional to (1-f)-0.5. The

4

value of pc could become very high at higher f values, leading to foam coalescence and Ostwald

5

ripening because of rapid lamella drainage [26,44,71,74]. The clear higher critical foam quality in

6

the range 0.92–0.96 for NP-AOS-CO2 foam is in contrast with the AOS-CO2 foam and can be

7

attributed to the improved surface dilational viscoelasticity of the NPs/AOS foam because of the

8

adsorption and accumulation of NPs on the bubble surface and plateau border to prevent the quick

9

liquid drainage [75,76].

Apparent Viscosity µa (mPa· s)

18

1ml/min 1.5ml/min 2ml/min 2.5ml/min

16 14 12 10 8 6 78

80

82

84

86

88

90

92

94

96

98

Foam Quality f (%)

10 11

Fig. 5 Apparent viscosity under various foam qualities for NP-AOS-CO2 foam

12

3.3 Rheological properties of NP-AOS-N2 foam

13

The non-Newtonian flow behavior of NP-AOS-N2 foam at various surfactant rates of 1, 1.5, 2, and

14

2.5 mL/min is displayed in Figs. 6(a), (b), (c), and (d), respectively. Same phenomenon was

15

observed in which the slope of the NP-stabilized foam changes at certain shear rate value. The fit

16

lines in the figures indicate that the flow behavior index varies from 0.787 to 1.103 in the lower

17

shear rate range, whereas it varies in the range 0.261–0.591 at higher shear rates.

18

The foam apparent viscosities under different foam qualities are shown in Fig. 7, from which it

19

could be deduced that the variation in the foam resistance characteristic is closely related to the

20

foam quality. Taking the case of surfactant rate 2.5 mL/min as the example, the foam viscosity

21

values stay in a relatively narrow region at lower foam quality region of 80%< f <92%, while it

22

decreases significantly under the higher f values in the range 92–96%.

23

As listed in Table 2, the critical foam qualities locate within 92% to 96% based on the variation in

24

the flow behavior index and foam apparent viscosity behaviors. Through comparison of the

25

maximum apparent viscosities between NP-AOS-CO2 and NP-AOS-N2 foam, it could be clearly

26

observed that the foam with internal phase of N2 has higher apparent viscosities than the CO2

27

foam and could be attributed to the higher CO2 solubility in the surfactant solution [72,73]. The 9

1

stronger rheological properties of the N2 foam indicate that other than CO2 foam, NP-stabilized N2

2

foam is also worth of further investigation of its potential application in tight reservoir EOR

3

practices. 1.4

1.4

Surfactant: 1ml/min ln τ=0.992*lnγ-3.845 ln τ=0.261*lnγ-0.317

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2 4.2

4.4

4.6

Surfactant: 1.5ml/min lnτ=0.787*ln γ-3.070 lnτ=0.545*ln γ-1.938

1.2

lnτ

lnτ

1.2

4.8

5.0

5.2

5.4

5.6

0.2

5.8

4.4

4.6

4.8

5.0

4 5

5.2

5.4

5.6

5.8

lnγ

lnγ

a Surfactant rate 1ml/min

b

Surfactant rate 1.5ml/min

1.4

1.2

Surfactant: 2ml/min lnτ =1.103*lnγ-4.792 lnτ =0.433*lnγ-1.222

1.2 1.0

0.8

0.6

lnτ

lnτ

0.8

0.6

0.4

0.4

0.2

0.2

0.0 -0.2 4.2

Surfactant: 2.5ml/min lnτ=0.988*lnγ -4.361 lnτ=0.590*lnγ -2.369

1.0

0.0 4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

4.2

6.0

4.4

4.6

4.8

5.0

6 7 8

5.2

5.4

5.6

5.8

6.0

lnγ

lnγ

c Surfactant rate 2ml/min d Surfactant rate 2.5ml/min Fig. 6. Shear stress vs. shear rates for NP-AOS-N2 foam at different surfactant flow rates 22

Apparent Viscosity µa (mPa· s)

20

1ml/min 1.5ml/min 2ml/min 2.5ml/min

18 16 14 12 10 8 78

80

82

84

86

88

90

92

94

96

98

Foam Quality f (%)

9 10 11 12

3.4 Rheological properties of NP-AOS-CO2-NaCl foam

13

Figs. 8(a), (b), (c), and (d) show the plot of the shear stress versus shear rate in logarithmic scale

14

for the NP-stabilized CO2 foam containing 2 wt% anhydrous NaCl at the surfactant flow rates of 1,

Fig. 7 Apparent viscosity for NP-AOS-N2 foam under various foam qualities

10

1

1.5, 2, and 2.5 mL/min, respectively. A clear variation in the slope between lnτ and lnγ was

2

observed in all the four cases. The NP-stabilized foam with salinity effect shows shear thickening

3

behavior with n values varying from 1.088 to 1.409 in the lower shear stress region, specifically

4

4.2< lnγ <5.1, 4.4< lnγ <5.35, 4.3< lnγ <5.45 4.4
5

rate as listed in Table 2, whereas at a higher shear rate region, the NP foam behaves in a shear

6

thinning manner with a flow behavior index of 0.321< n <0.715. 1.0

Surfactant: 1ml/min lnτ =1.429*lnγ-6.603 lnτ =0.565*lnγ-2.146

0.8 0.6 0.4

0.5

0.2

lnτ

lnτ

Surfactant: 1.5ml/min lnτ =1.297*lnγ-6.097 lnτ =0.321*lnγ-0.895

1.0

0.0

0.0

-0.2 -0.4 -0.5

-0.6 4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

4.2

4.4

4.6

4.8

5.0

lnγ

7 8

a

surfactant rate 1ml/min

b

Surfactant: 2ml/min lnτ =1.098*lnγ-5.234 lnτ =0.358*lnγ-1.060

1.0 0.8

5.8

6.0

Surfactant: 2.5ml/min lnτ =1.088*lnγ -5.311 lnτ =0.715*lnγ -3.288

0.6 0.4

0.4

0.2

lnτ

lnτ

5.6

surfactant rate 1.5ml/min

0.8

0.6

0.2

0.0

0.0

-0.2

-0.2

-0.4

-0.4

-0.6

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

4.2

4.4

4.6

lnγ

9

5.4

1.0

1.2

-0.6 4.2

5.2

lnγ

4.8

5.0

5.2

5.4

5.6

5.8

6.0

lnγ

10 11

Fig. 8 Shear stress vs. shear rate for NP-AOS-CO2-NaCl foam at different surfactant flow rates

12

As shown in Fig. 9, the foam rheology transition could be more clearly revealed by plotting the

13

foam apparent viscosity versus foam quality. The detailed results in Table 2 clearly show that

14

before the critical foam quality in the range 93–96%, the foam apparent viscosity increases with

15

foam quality while it shows a decreasing trend after the critical values. Table 2 also shows that the

16

presence of NaCl dramatically decreases the apparent viscosity of the NP-stabilized foam. The

17

maximum apparent viscosity for the NP-foam with salt-containing surfactant solution is 12.7

18

mPa.s, which is much lower than 18 mPa.s in the unsalted case.

19

Fig. 10 comparatively displays the morphologies of the NP-AOS-CO2 foam and the

20

NP-AOS-CO2-NaCl foam and clearly shows that the foam generated in saline solution has a much

21

less bubble population as compared to the salt-free foam. The possible reason for the lower bubble

22

density of the NP-stabilized foam with saline might be lower colloidal stability of silica NPs in the

c surfactant rate 2ml/min

11

d

surfactant rate 2.5ml/min

1

salt-containing solutions, which results in aggregation of the particles and thereby decreases the

2

foam apparent viscosity because of the reduced foam stability [17,27,53–54,77].

Apparent Viscosity(mPa· s )

13

1ml/min 1.5ml/min 2ml/min 2.5ml/min

12 11 10 9 8 7 78

80

82

84

86

88

90

92

94

96

98

Foam Quality(%)

3 4

Fig. 9 Apparent viscosity for NP-AOS-CO2-NaCl foam under various foam qualities

5 6 7 8

3.5 Rheological properties of NP-AOS-CO2-Oil foam

9

In order to understand the effect of the presence of oil on the NP-stabilized CO2 foam rheology, 10

10

wt% of n-C12H26 was mixed in the surfactant solution together with the NPs. Figs. 11(a), (b), (c),

11

and (d) display the rheological relationship between lnτ and lnγ of the NP-AOS-CO2-Oil foam at

12

various surfactant rates of 1, 1.5, 2, and 2.5 mL/min, respectively. Clearly, the relationship

13

between the shear stress and shear rate changes at certain shear rate values in the range 5.1< lnγ

14

<5.25, where the flow behavior index varies from the region 0.989–1.114 (nearly the Newtonian

15

flow) to the shear thinning non-Newtonian behavior of 0.272< n <0.823.

16

The variation in the foam apparent viscosity relating to the foam quality is depicted in Fig. 12 and

17

listed in Table 2, showing clear transition points. In accordance with the results shown in Fig. 11,

18

the foam viscosity shows nearly stable values in the foam quality regions 81–91%, 83–93%,

19

87–95%, and 92–96% corresponding to the surfactant rates of 1, 1.5, 2, and 2.5 mL/min,

20

respectively, whereas above those critical points, the foam apparent viscosity decreases with

Fig. 10 Morphology of the (a) NP-AOS-CO2 foam and the (b) NP-AOS-CO2-NaCl foam

12

1

increasing foam quality, showing the obvious shear thinning rheological behavior.

2

The strength of the NP-stabilized foam in the presence of oil could be obtained based on the

3

maximum apparent viscosity values listed in Table 2. The oil presence does not damage the foam

4

strength as compared to the case without the oil presence (17.9 mPa.s versus 18 mPa.s), indicating

5

that the NP-stabilized foam has great potentials for the CO2 EOR practices. 1.5

1.2

Surfactant: 1ml/min lnτ=1.065*lnγ -4.467 lnτ=0.272*lnγ -0.340

1.0

Surfactant: 1.5ml/min lnτ=1.114*lnγ -5.116 lnτ=0.574*lnγ -2.281

1.0 0.8 0.6

0.2

lnτ

lnτ

0.4 0.5

0.0 -0.2 -0.4

0.0

-0.6 4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

-0.8 4.2

5.8

4.4

4.6

4.8

5.0

6 7

a

5.2

5.4

5.6

5.8

6.0

lnγ

lnγ

Surfactant rate 1ml/min

b

Surfactant rate 1.5ml/min

1.0

1.2

Surfactant: 2ml/min lnτ=1.102*lnγ -5.093 lnτ=0.612*lnγ -2.495

1.0 0.8

Surfactant: 2.5ml/min ln τ=0.989*lnγ -4.724 ln τ=0.823*lnγ -3.827

0.8 0.6

0.6

lnτ

lnτ

0.4 0.4

0.2 0.2

0.0

0.0

-0.2

-0.2 -0.4 4.2

8 9 10

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

-0.4 4.2

6.0

4.4

4.6

4.8

5.0

lnγ

c

5.2

5.4

5.6

5.8

Surfactant rate 2ml/min

d

Surfactant rate 2.5ml/min

Fig.11 Shear stress vs. shear rates for NP-AOS-CO2-Oil foam at different surfactant flow rates

Apparent Viscosity µa(mPa· s)

18

1ml/min 1.5ml/min 2ml/min 2.5ml/min

16

14

12

10

8 80

82

84

86

88

90

92

94

96

98

Foam Quality f (%)

11 12 13 14

6.0

lnγ

Fig. 12 Apparent viscosity under various foam qualities for the NP-AOS-CO2-Oil foam

13

1

Table 2 Detailed rheological properties for the 5 tested foam system Surfactant rate (ml/min)

No.

Foam composition

1

AOS+CO2

1.0 1.5 2.0 2.5

2

NP+ AOS+CO2

1.0 1.5 2.0 2.5

3

NP+ AOS+N2

1.0 1.5 2.0 2.5

4

NP+AOS+CO2+NaCl

1.0 1.5 2.0 2.5

5

NP+ AOS+CO2+Oil

1.0 1.5 2.0 2.5

2

Flow behavior index n

Foam quality f

4.6-5.8 4.6-5.8 4.6-5.8 4.6-5.8 4.4
0.603 0.648 0.686 0.628 0.889 0.616 1.077 0.444 0.818 0.637 0.662 0.306 0.992 0.261 0.787 0.545 1.103 0.433 0.988 0.590 1.429 0.565 1.297 0.321 1.098 0.358 1.088 0.715 1.065 0.272 1.114 0.574 1.102 0.612 0.989 0.823

91%~98% 87%~97% 83%~96% 80%~95% 91%~96% 96%~98% 87%~95% 95%~97% 83%~92% 92%~95% 80%~93% 93%~96% 90%~95% 95%~98% 87%~94% 94%~97% 83%~93% 93%~96% 80%~92% 92%~96% 91%~96% 96%~98% 87%~95% 95%~97% 83%~94% 94%~96% 80%~93% 93%~95% 92%~96% 96%~98% 87%~95% 95%~97% 83%~93% 93%~96% 81%~91% 91%~95%

Maximum apparent viscosity (mPa·s)

16.3 11.8 10.6 10.6 18.0 11.8 8.4 9.4 20.7 18.8 15.4 12.1 12.7 11.0 10.3 8.0 17.9 11.3 10.9 8.9

3.6 Error Analysis

3 4

Shear rate lnγ

Table 3 lists the errors of the measured direct parameters, including pressure drop, tube diameter, tube length, and volumetric flow rate.

5

Table 3 Experimental errors for directly measured parameters

14

Parameters

Absolute error

Minimum data in experiments

Maximum relative accuracy

Pressure p Diameter D Length L Volumetric flow rate Q

10Pa 0.02mm 0.5mm 0.1sccm

300Pa 3.94mm 15.0cm 10sccm

±3.34% ±0.50% ±0.12% ±1.0 %

1 2 3

Based on Table 3, the measurement error for indirectly obtained apparent viscosity can be calculated as follows, The error for the shear rate can be calculated by Eq. (7), ∆ఊ

∆ொ

∆஽

4

Erሺγሻ = ± ቚ ቚ = ± ቀቚ ቚ + 3 ቚ ቚቁ = ±2.5%

5

The error for the shear stress can be determined through Eq. (8),

ఊ

∆ఛ

ொ

∆௣

஽

∆஽

∆௟

6

Erሺ߬ሻ = ± ቚ ቚ = ± ቀቚ ቚ + 3 ቚ ቚ + ቚ ቚቁ = ±4.96%

7

The error in the apparent viscosities was found as 7.46% by Eq. (9).

ఛ

௣

∆ఓೌ

Erሺߤ௔ ሻ = ± ቚ

8

ఓೌ

஽

∆ఛ

௟

∆ఊ

ቚ = ± ቀቚ ቚ + ቚ ቚቁ = ±7.46% ఛ

ఊ

(7)

(8)

(9)

9 10

4 Conclusions

11

Aiming at the great application prospects of nanofoam technology in EOR and the greenhouse

12

geological storage in tight reservoirs, the rheological properties of the NP-stabilized CO2 foam

13

were experimentally investigated. By varying the internal gas type, adding NaCl and oil

14

components, the effect of gas type, salinity, and oil presence on the non-Newtonian foam flow

15

behavior was scrutinized. The main conclusions of this study are as follows.

16

(1) The benchmark case of surfactant (AOS) CO2 foam shows clearly a shear thinning behavior

17

with the flow behavior index n varying from 0.603 to 0.686 and is consistent with the reported

18

theoretical and the empirical values.

19

(2) With dispersed SiO2 NPs in the surfactant solution, the CO2 foam shows a transitional

20

characteristic between the shear stress and the shear rate. When lnγ is greater than a certain

21

value (5.0–5.45 corresponding to various surfactant rates), the shear stress slope decreases.

22

Accordingly, the critical foam quality values within 92–95% were observed based on the foam

23

apparent viscosity results.

24

(3) The NP-stabilized N2 foam also shows the transitional behavior based on the lnτ versus lnγ as

25

well as the µa vs. f results, with quasi Newtonian flow behavior transiting to shear thinning

26

behavior in higher lnγ and foam quality regions. Compared to the NP-stabilized CO2 foam, N2

27

foam shows higher apparent viscosity.

28

(4) The salt-containing NP-stabilized foam also shows rheological transition behaviors, varying

29

from shear thickening to shear thinning non-Newtonian behavior with increasing shear rate

30

and foam quality values. With the less bubble populations in the bulk foam, CO2 foam

31

generated with NP-AOS-NaCl solution shows lower apparent viscosities compared to the

32

salt-free cases.

33

(5) The oil presence does not show negative effects on the NP-stabilized CO2 foam rheology with

34

nearly the same maximum apparent viscosity and the transitional foam quality values,

35

indicating that the NPs foam technology could be potentially used in the CO2 EOR and CCUS

36

applications. 15

1

Acknowledgements

2

The authors would like to thank the financial support from National Natural Science Foundation

3

of the People’s Republic of China (NSFC No.51476081).

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

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Highlights 1. Rheological properties of Nanoparticle (NP) stabilized CO2 foam are comprehensively investigated. 2. Effects of internal gas phase, salinity and oil presence are studied. 3. Critical foam quality is clearly observed. 4. Oil presence doesn’t show negative effect on NP stabilized CO2 foam strength.

Declaration of Interest Statement The authors declared that they have no conflicts of interest to this work.

Credit author statement

As the corresponding author, I ensure that the manuscript descriptions are accurate and agreed by all authors.

The contribution roles for each co-author of the paper are listed in the following Table. Author contributions roles Name of Author

Contributions

Dongxing Du

Conceptualization; Formal analysis; original draft

Xu Zhang

Investigation; Methodology

Yingge LI

Funding acquisition; Project administration; Supervision

Di Zhao

Resources; review & editing

Fei Wang

Resources; review & editing

Zhifeng Sun

Resources; review & editing

Yingge Li

2019-12-28