Experimental study on CO2 diffusion in bulk n-decane and n-decane saturated porous media using micro-CT

Accepted Manuscript Experimental study on CO2 diffusion in bulk n-decane and n-decane saturated porous media using micro-CT Yu Liu, Ying Teng, Guohuan Lu, Lanlan Jiang, Jiafei Zhao, Yi Zhang, Yongchen Song PII:

S0378-3812(16)30099-1

DOI:

10.1016/j.fluid.2016.02.034

Reference:

FLUID 11023

To appear in:

Fluid Phase Equilibria

Received Date: 2 November 2015 Revised Date:

16 February 2016

Accepted Date: 21 February 2016

Please cite this article as: Y. Liu, Y. Teng, G. Lu, L. Jiang, J. Zhao, Y. Zhang, Y. Song, Experimental study on CO2 diffusion in bulk n-decane and n-decane saturated porous media using micro-CT, Fluid Phase Equilibria (2016), doi: 10.1016/j.fluid.2016.02.034. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

ACCEPTED MANUSCRIPT

Experimental study on CO2 diffusion in bulk n-decane and n-decane saturated

2

porous media using micro-CT

3

Yu Liu, Ying Teng, Guohuan Lu, Lanlan Jiang*, Jiafei Zhao, Yi Zhang, and Yongchen Song*

4

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of

5

Education, Dalian University of Technology, 116024 Dalian, China

6

(*For correspondence: [email protected]; [email protected])

7

RI PT

1

Abstract: Molecular diffusion has been considered to be an underlying mechanism for

9

many oil recovery processes. Reliable estimation of the molecular diffusion

10

coefficient as a transport property is therefore important for CO2-enhanced oil

11

recovery. In the present work, the dynamic processes of CO2 diffusion in bulk

12

n-decane and n-decane saturated porous media were investigated using the

13

micro-focus X-ray CT (micro-CT) scanning technique. CO2 diffusion was visually

14

and quantitatively analyzed by interpreting the CO2 concentration with grayscale CT

15

images. Next, local CO2 diffusion coefficients, varying with time and position, were

16

calculated from concentration profiles based on Fick’s second law. The results showed

17

that the local diffusion coefficients in bulk n-decane demonstrate an exponential

18

function of diffusion distance and time. The total diffusion coefficients in bulk oil

19

under pressure from 1 to 6 MPa and temperature at 29 oC and 35 oC were calculated.

21 22

M AN U

TE D

EP

AC C

20

SC

8

The results showed that the initial pressure has a strong influence on the diffusion coefficient, i.e., high CO2 initial pressure leads to high CO2 diffusivity in oil. Experiment results in n-decane saturated porous media showed that the CO2 local

23

diffusion coefficient decreases gradually along the diffusion path with time until

24

reaching a stable state. The total diffusion coefficients in n-decane saturated porous

25

media were smaller than those in bulk oil under the same pressure and temperature

26

conditions because the diffusion path is more complicated than in bulk oil. It is -1-

ACCEPTED MANUSCRIPT

1

demonstrated that the pathways of porous media impede CO2 mass transfer and

2

decrease the diffusion coefficient.

3

Keywords: carbon dioxide; diffusion coefficient; porous media; micro-CT

5

RI PT

4

1. Introduction

Increased focus on anthropogenic climatic change and greenhouse gas emissions

7

has led to the study of the geological storage of CO2 [1]. CO2 injection into oil fields

8

to improve oil production, i.e., CO2-enhanced oil recovery (CO2-EOR), has been able

9

to sequestrate large amounts of CO2 and offset the extra cost of storage [2]. Although

10

injection of some light hydrocarbon may also improve the oil production, it leads to

11

asphaltene deposits in the crude oil, and the bitumen in the reservoir may block the

12

flow path and production facilities, seriously affecting normal operation of oilfields.

13

CO2 has better fluid properties than other oil-displacing agents, such as light

14

hydrocarbon [3]. CO2 dissolution into oil results in volumetric expansion and

15

viscosity reduction of the under-saturated crude oil in the reservoir, which

16

significantly decreases oil flow resistance and enhances the flow properties [4, 5]. For

17

the actual production conditions beyond the critical point of CO2 (Tc = 31.1℃ and Pc

18

= 7.38 MPa) [6], supercritical CO2 achieves strong dissolution ability and reduces the

19

interfacial tension between oil and CO2. Displacement efficiency during CO2 injection

21 22

M AN U

TE D

EP

AC C

20

SC

6

is strongly influenced by achieving miscibility of CO2 with oil. Molecular diffusion has been shown to be a major factor influencing CO2 solubility and miscibility. The determination of the diffusion coefficient in CO2-EOR engineering design, risk

23

assessment and economic evaluation is necessary. Thus, it is of importance to study

24

the CO2 diffusion coefficient in oil and the influence of porous media on CO2

25

diffusivity. -2-

ACCEPTED MANUSCRIPT

As is known, diffusion is the process of one fluid mixing spontaneously with

2

another. The typical mathematical expression for the molecular diffusion process is

3

Fick`s Law [7]. Fick`s Law can be used to solve the diffusion coefficient, D. Fick’s

4

first law ( J = −D∇C ) can be applied to steady state systems when the concentration

5

remains constant. However, in many cases of diffusion, the concentration changes

6

with time. Fick’s second Law ( ∂C / ∂t = −∂J / ∂x ) can be used to describe the

7

diffusion kinetics.

SC

RI PT

1

Several researchers have conducted massive research since the beginning of the

9

1930s about the diffusion coefficient, and they have obtained plentiful research results.

10

Pomeroy et al. [8] calculated the diffusion coefficient and the solubility of methane in

11

the process of dissolution in static light oil. It was concluded that the diffusion

12

coefficient was not affected by the system pressure and methane concentration when

13

the pressure is less than 2 MPa. Reamer et al. [9] conducted experimental research of

14

methane diffusion in butane and discussed the influence of temperature on the

15

diffusion coefficient. However, the system pressure and temperature fluctuations

16

generate a great influence on the results and can easily cause error. The pressure

17

decay method was first introduced by Newitt and Weale [10] and was used to study

18

the gas solubility in polystyrene. Lundberg et al. [11] extended the method to measure

19

diffusion coefficients. The standard dual-chamber pressure decay proposed by Koros

21 22

TE D

EP

AC C

20

M AN U

8

and Paul [12] greatly improved the reliability and accuracy of such technology. It is convenient to obtain the initial gas density, but the system is prone to leakage. Riazi [13] measured the dissolution processes of methane in n-pentane using a PVT cell. He

23

first proposed the pressure-decay method and established a semi-analytical model.

24

The rate of pressure change was a function of time and related to the diffusion process.

25

Zhang et al. [14] used a similar experimental method and developed a nonlinear -3-

ACCEPTED MANUSCRIPT

regression model for diffusivity measurement. Yang and Gu [15] obtained the droplet

2

dynamic interfacial tension using image acquisition technology and calculated the

3

diffusion coefficients. They reported a dynamic interfacial method by which the CO2

4

diffusion coefficient can be measured at high temperature and pressure both quickly

5

and conveniently. However, the complicated data processing requires a high accuracy

6

facility. Recently, it was common to use model studies on gas diffusion coefficient.

7

Loskutov [16] proposed a new method of finding experimental time dependence of

8

the self-diffusion coefficient for fluid in the porous media. Zheng et al. [17] presented

9

a theoretical model for the relative gas diffusion coefficient in dry porous media. Ma

10

and Chen [18] simulated the diffusion process in stochastic fractal porous media using

11

lattice Boltzmann model. Zhao et al. [19] developed an MRI experimental method

12

along with a mathematical model to measure the CO2 effective diffusivity in

13

liquid-saturated porous media.

M AN U

SC

RI PT

1

Furthermore, some new methods have been proposed in recent years. X-ray CT

15

scanning techniques in the oil industry have shown revolutionary advancements. As a

16

type of noninvasive visualization research technique, the X-ray CT scanning

17

technique has already been applied in the field of fluid distribution of porous media

18

[20]. Salama and Kantzas [21] obtained CO2 concentration distribution profiles in

19

diffusion experiments using X-ray CT imaging. Luo et al. [22, 23] measured the

21 22

EP

AC C

20

TE D

14

hydrocarbon solvent diffusion coefficient in heavy oil; the concentration distribution curves of the solvent and heavy oil were acquired through X-ray CT. A numerical computation method was developed by Guerrero et al. [24] for the calculation of

23

diffusion coefficients from concentration profiles obtained from an X-ray CT scan.

24

Determination of CO2 effective diffusion coefficients in oil-saturated porous media is

25

essential to understand and evaluate the CO2 dissolution process in a reservoir during -4-

ACCEPTED MANUSCRIPT

1

an enhanced oil recovery project [25]. Song et al. [26] investigated the CO2 diffusion

2

process in heavy oil using CT imaging technology combined with a non-iterative

3

finite volume mathematical model. To date, little research has been performed in terms of investigating the diffusion

5

process in the oil system or porous media. In this study, an accurate processing

6

method using X-ray CT technology to determine the diffusion coefficients of CO2 was

7

reported. CO2 diffusion processes in pure oil and oil-saturated porous media were

8

visually and quantitatively analyzed.

9

2. Experimental Section 2.1 Apparatus and materials

SC

M AN U

10

RI PT

4

Figure 1 shows the simplified schematic diagram of the experimental setup used to

12

investigate the CO2 diffusion coefficient. The whole experimental setup mainly

13

consisted of three parts. The first part is the CT scan system, including a micro-CT

14

scanner (InspeXio SMX-225CT, Shimadzu, Japan) and a data processor. The CT

15

scanner has a spatial resolution of approximately 4 µm and a maximum X-ray tube

16

voltage of 225 keV. A self-designed pressure vessel (as shown in Fig. 2) was used as

17

the sample holder. It consists of the following components: a sample container made

18

of a PEEK tube, two end caps made of titanium alloy, and two inlet and outlet

19

connectors. The outlet was blocked in the present experiments. The PEEK tube has a

21 22

EP

AC C

20

TE D

11

15 mm inner diameter. The pressure vessel was placed in the vertical position on the stage of the CT scanner. The maximum working pressure of the imaging vessel was 15 MPa. The second part is the injection system, including a syringe pump (model

23

260D, Teledyne ISCO. Inc., USA) connected to a gas cylinder, a digital pressure

24

gauge (Rosemount 3051, Emerson Inc., USA) for recording the pressure of the system

25

during the experiment, and a vacuum pump. The maximum capacity of the syringe -5-

ACCEPTED MANUSCRIPT

pump is 266 ml, which can achieve constant-pressure or constant-injection rate mode.

2

The last part is the temperature control system. The cylinder of the syringe pump was

3

equipped with a temperature control chamber. The chamber was warmed with

4

circulating water and the temperature was controlled by a heating circulator (F-25ME,

5

Julabo, Inc., Germany), with a temperature control range of -45 to 200 oC and

6

precision of±0.5 oC. An electric heating film for the temperature control was wrapped

7

around the pressure vessel. The electric heating film was made of graphite material to

8

guarantee the image quality of the X-ray CT scan. A digital temperature controller

9

was used to measure and control the temperature at the inlet of the tube. The

10

temperature and pressure data were transferred to a local computer. The whole

11

experimental setup was connected via 1/16 inch stainless steel tubes.

M AN U

SC

RI PT

1

CO2 with 99.99% purity (Dalian Da-te Gas, Ltd., China) was used as the gas phase,

13

and n-decane with 99% purity (TCI, Shanghai Development Co., Ltd., China) was

14

used as the liquid phase in the experiments. Spherical glass beads (BZ02, As-One Co.,

15

Ltd., Japan) with the diameter ranging from 0.177 to 0.250 mm were packed in the

16

vessel as the porous media. The porosity of the glass bead packs was measured to be

17

36.8% according to the weighing method. The absolute permeability was 13.8 Darcy

18

based on a water injection Darcy experiment. The tortuosity of the BZ02 glass beads

19

was calculated to be 3.27, with a pore structure analysis based on the CT scanned

21 22

EP

AC C

20

TE D

12

images.

2.2 Experimental procedures The flat bottom glass test tubes, 1.5 cm in length and 1.0 cm in diameter, were

23

filled with an amount of n-decane or saturated porous media, and then placed at the

24

bottom of the pressure vessel, as shown in Fig. 1. Then, the first CT scan was

25

performed for bulk n-decane or n-decane saturated porous media, which we called the -6-

ACCEPTED MANUSCRIPT

initial scan. The pressure vessel was vacuumized for 2 hours before CO2 injection.

2

Temperature was controlled at 29 ◦C or 35 ◦C using the electric heating film. Finally

3

CO2 was injected into the pressure vessel. The pressure of the CO2 pump was set to

4

the desired value from 1 to 6 MPa. In the tube, CO2 was injected continually to offset

5

the pressure depletion as CO2 diffusion slowly occurred. Scans were performed every

6

30 minutes using the X-ray CT, and the total injection volume of CO2 was recorded

7

automatically by the syringe pump. Meanwhile, the pressure of the whole dynamic

8

process was recorded by the pressure transmitter. The X-ray tube voltage and the

9

current were set to be 180 kV and 40 µA, respectively. The CT scanner provided an

10

image size of 512 × 512 pixels and a resolution of 0.086 mm/pixel corresponding to a

11

field of view of 44.0×44.0 mm.

12

2.3 Data analysis

M AN U

SC

RI PT

1

We conducted a series of tests to calibrate the linear relationship between the

14

grayscale and density. We used air and several liquids, with density ranging from 0 to

15

1.11. As can be observed in Fig. 3, the results showed that the grayscale value of the

16

scanned CT image is consistent with the density of gas and oil. Thus, the grayscale

17

value is appropriate for the evaluation of concentration in our experiments.

20

21

EP

19

Based on the CT grayscale images, the normalized dimensionless concentration profiles could be calculated as follows [27]:

AC C

18

TE D

13

C ρCO 2 + oil − ρ oil CTCO 2+ oil − CToil = = C0 ρ0 − ρoil CT0 − CToil

(1)

where ρ0 is the mixture density at the interface and ρCO2+oil is the mixture density at

22

any position along the distance, and CT0 is the grayscale value of the CT image at the

23

interface. CTCO2+oil is the grayscale value of CO2 and the n-decane mixture at any

24

position along the distance and CToil is the grayscale value of bulk n-decane.

-7-

ACCEPTED MANUSCRIPT

1 2

As a result of the linear relationship [21, 28] between density and the CT grayscale value, Eqs. 2 through 4 are valid in the case of porous media [29]: CTsand + CO2 = (1 − φ )CTsand + φ CTCO2

(2)

4

CTsand + oil = (1 − φ )CTsand + φ CToil

(3)

5

CTsand +CO2 + oil = (1 − φ )CTsand + φ CTCO2 + oil

RI PT

3

(4)

where φ is the porosity of the porous media, and CT refers to the grayscale value of

7

the CT images. The subscript CO2 is for bulk CO2, sand is for dried bead packs,

8

sand+CO2 is for CO2 saturated bead packs, sand+oil is for n-decane saturated bead

9

packs, and sand+CO2+oil is for CO2 diffused in n-decane saturated bead packs. By

M AN U

10

SC

6

substituting Eqs. 2 to 4 into Eq. 1, Eq. 5 can be obtained:

C φ0 (CT( sand + CO2 + oil )1 − CT( sand + oil )1 ) = C0 φ1 (CT( sand +CO2 + oil )0 − CT( sand + oil )0 )

11

12

(5)

The subscript 0 represents the position at the interface, and subscript 1 represents a position along the diffusion path.

14

3. Mathematical Analysis

TE D

13

Figure 4a shows the region of interest (ROI) of the CT images for the diffusion

16

experiments. As shown in Fig. 4b, the CO2-oil interface is located at x=0 (boundary

17

A), whereas the original height of the n-decane is x=L (boundary B). To analyze the

18

diffusion process, the following assumptions should be taken into account:

20 21 22 23 24

AC C

19

EP

15

1). No chemical reaction occurs. 2). The CO2 effective diffusion coefficient (D) is constant during the measurement

process.

3). The swelling of the n-decane is non-negligible, the volatilization of n-decane is negligible, and the amount of n-decane evaporated into the CO2 is neglected. 4). The natural convection effect is negligible. -8-

ACCEPTED MANUSCRIPT

According to Fick’s second law:

∂C ( x, t ) ∂  ∂C ( x, t )  = D  ∂t ∂x  ∂x 

2

3 4

(6)

The hypotheses for the boundary and initial conditions applicable to the system shown in Fig. 5 are as follows: C ( x, t )t = 0 = 0

6

C ( x, t ) x =0 = Ceq

(0 ≤ x ≤ L) (t > 0)

(7a)

(7b)

SC

5

RI PT

1

Equation 7a suggests that the initial CO2 concentration along the diffusion path is

8

zero at the beginning of the diffusion. Equation 7b suggests that CO2 diffusion is

9

sufficiently rapid at the interface. Its concentration reaches equilibrium (Ceq)

10 11

M AN U

7

immediately at the interface (x=0) at any time after the diffusion begins. In this study, a one-dimensional interpretation method was used. As shown in Fig. 5, by selecting the appropriate spatial grids and time iteration step size, xi = i × ∆x

13

(i=0,1,...,N, N × ∆x = 1 ), tn = n × ∆t (n=0,1,2,…), the multiple integrals over time and

14

space step will be

TE D

12

∂ 

t +∆t

∂C 

t +∆t

t

t

18

21

 ∂C   ∂C   ∂C  D  1 −D  1 =  ∆x  ∂x i +  ∂x i −  ∂t i n

n

2

n

(9)

2

Through computing the forward difference in time, Equation 9 can be written as

Di +1/2

19

20

(8)

Combining the mean value theorem in explicit form yields the volume integral:

AC C

17

EP

cv

16

∂C dVdt ∂t cv

∫ ∫ ∂x  D ∂x dVdt = ∫ ∫

15

Cin+1 − Cin C n − Cin−1 Cin +1 − Cin − Di −1/ 2 i = ∆x ∆x ∆x ∆t

(10)

Hence, the discretized equations for the diffusion coefficient of internal points can be further written as -9-

ACCEPTED MANUSCRIPT

−(Cin − Cin−1 ) Din−1/ 2 + (Cin+1 − Cin ) Din+1/ 2 =

1

(11b)

−(CNn − CNn −1 ) DNn −1/2 + 2(CBn − C Nn ) DBn =

RI PT

n −2(C0n − C An ) DAn + (C1n − C0n ) D1/2 =

4

∆x 2 n +1 (CN − C Nn ) ∆t

(11c)

Combining the discretized equations for internal points and boundary A, B, a matrix is formed as ND = b

7

SC

6

∆x 2 n +1 (C0 − C0n ) ∆t

Similarly, it can be applied to boundary A and B:

3

5

(11a)

(12)

M AN U

2

∆x 2 n +1 (Ci − Cin ) ∆t

The dimensionless concentration distribution of vector b the matrix N can be

9

measured directly. Vector D is the unknown diffusion coefficient. The diffusion

10

coefficient of each grid point can be obtained by solving the linear system of

11

equations.

12

4. Results and Discussion

13

4.1 CO2 concentration

TE D

8

Figure 6 gives two examples of the time-series images of CO2 diffusion for the

15

n-decane solution at 2 MPa and 4 MPa. From the images, it can be observed that the

16

interface moves upward because of the volumetric expansion of n-decane at the initial

17

moment. Then, the phenomena of expansion weaken as time passes. This

19 20

AC C

18

EP

14

demonstrates that diffusion slows down with time. At the beginning, CO2 sufficiently diffuses into n-decane at the interface. A higher concentration difference yields more rapid diffusion. Meanwhile, the grayscale of the images gradually became brighter

21

along the diffusion direction, indicating that a CO2 concentration gradient existed

22

along the diffusion direction. Once CO2 was in sufficient contact with n-decane at the

23

interface, a thin film was generated, which further prevented CO2 diffusion. Thus, -10-

ACCEPTED MANUSCRIPT

1

CO2 diffused into n-decane slowly below the interface. The region of interest (ROI) was chosen for the diffusion coefficient analysis (Fig.

3

4a). Based on Eq. 1, CO2 concentration profiles were determined based on the

4

obtained CT grayscale value. Figure 7 shows the CO2 normalized dimensionless

5

concentration profiles along the diffusion direction at 4 MPa at different times (30

6

min, 90 min, and 180 min). The CO2 concentration was a function of time and

7

distance, and the uncertainties associated with the position were related to the CT

8

grayscale values. The CO2 concentration was higher near the interface and decreased

9

in magnitude as it approached the vessel bottom. 4.2 CO2 diffusion coefficient

SC

M AN U

10

RI PT

2

The diffusion coefficients were calculated from the concentration profiles directly

12

from the non-iterative finite volume method given by Eqs. 11 and 12. Through the

13

matrix calculation for the CO2 concentration profiles, the CO2 diffusion in any

14

position of ROI and time can be obtained.

TE D

11

Figure 8 shows the evolution of the CO2 diffusion coefficient profile varying with

16

time at 2 MPa (8a), 3 MPa (8b) and 4 (8c) MPa, respectively. The CO2 diffusion

17

coefficient decreased along the diffusion direction. Next, it became stable until there

18

was no change in the concentration profile. This behavior can be attributed the driving

19

force slightly vanishing at the near-bottom boundaries, except for molecular diffusion.

21 22

AC C

20

EP

15

In addition, the CO2 diffusion coefficients were reduced at the same location with over time, which reflects the decreasing influence of the concentration gradient on convection and that of the incubation period. At the beginning of the CO2 diffusion,

23

the great concentration gradient leads to rapid diffusion with high diffusion

24

coefficients. With continuous diffusion, the CO2 concentration gradient decreases, and

25

the diffusion process slows down along the diffusion direction with decreasing CO2 -11-

ACCEPTED MANUSCRIPT

1

diffusion coefficients. The experimental results show that the diffusion coefficient curve has the same

3

evolution at various pressures; the results are in accordance with previous

4

experimental results [30]. Regardless of time and position, the results showed that the

5

diffusion coefficients increased with operating pressure. This was mainly attributed to

6

the fact that the CO2 concentration was proportional to the CO2 pressure. Under the

7

same temperature, the CO2 concentration gradient and the free energy of the CO2

8

molecular increased with increasing pressure. Thus, the CO2 pressure controlled the

9

number of CO2 molecules in contact with the oil interface. The trend reflected that the

10

initial pressure has a great influence on the diffusion coefficient and highlighted the

11

importance of reservoir conditions for diffusion.

M AN U

SC

RI PT

2

Figure 9 shows the CO2 bulk diffusion coefficient profile as a function of time at

13

various pressures at 29 ◦C (9a) and 35 ◦C (9b). The bulk diffusion coefficient

14

exponentially decreased with increasing diffusion time at the same temperature, and

15

then tended to be stable. According to Fick’s second law, with a constant

16

concentration at the boundary, the rate of diffusion is proportional to the square root

17

of time. The rate of diffusion significantly decreases as a solvent diffuses further into

18

a solute, which suggests the concentration is related to the square root of time [31].

20 21 22

EP

The bulk diffusion coefficients at different times are listed in Tab. 1. The results are

AC C

19

TE D

12

in agreement with the experimental results of previous studies [32]. They have the same order of magnitude (10-9 m2/s) compared to the results obtained using the conventional pressure decay method [33]. In addition, compared to the pressure decay

23

method, the CT scan method is able to provide the dynamics diffusion process and

24

local diffusion profile along the diffusion direction with time. As a result, the

25

diffusion in the CO2-oil system is expected to be more reliable. -12-

ACCEPTED MANUSCRIPT

1

4.3 CO2 effective diffusion coefficient The molecular diffusion coefficient in porous media is called the effective diffusion

3

coefficient. CO2 effective diffusion in porous media depends on the contact time, the

4

length of diffusion and the diffusion rate. The diffusion rate is determined by the

5

diffusion coefficient.

RI PT

2

The data processing procedure of the effective diffusion coefficient in porous media

7

is similar to the procedure of the diffusion coefficient in pure oil. In Fig. 10, the CO2

8

effective diffusion coefficients along the diffusion direction at different times were

9

calculated in oil-saturated BZ02. Similar to the CO2/oil system, the effective diffusion

10

coefficient in porous media is a function of time and distance. The CO2 effective

11

diffusion coefficient gradually decreases with increasing diffusion time and distance

12

until reaching a stable state. The CO2 effective diffusion coefficients in porous media

13

increased with pressure, which is consistent with the phenomenon in pure oil. Finally,

14

we processed the bulk CO2 effective diffusion of porous media in the same way as in

15

pure oil, and obtained bulk CO2 effective diffusion coefficients in porous media at 2

16

MPa and 4 MPa of 1.35×10-9 m2/s, 5.11×10-9 m2/s, respectively.

TE D

M AN U

SC

6

In contrast to the CO2 diffusion coefficient in the pure oil solution, we can

18

determine that the CO2 effective diffusion coefficient in oil saturated porous media

19

was significantly smaller. The diffusion coefficient is lower in porous media

21 22

AC C

20

EP

17

compared to the bulk volume because of the variable area of contact between the two fluids, however, the diffusion mechanism remains the same. The diffusive molecules have to travel a longer path through a tortuous pore network; the diffusion length is

23

affected by pore-space geometry, microscopic and macroscopic heterogeneities and

24

determines how far the concentration propagates by diffusion in a given time [34, 35].

25

Hence, the diffusion rates become slower. In a porous media, the diffusion coefficient -13-

ACCEPTED MANUSCRIPT

depends on the tortuosity factor and porosity [36]. With decreasing porosity and

2

increasing tortuosity, the CO2 diffused more sufficiently. In n-decane saturated porous

3

media, the CO2 diffusive transport is constrained within the porous media pore spaces,

4

which are connected along tortuous pathways [37]. Because of the existence of porous

5

structure, the CO2 molecular diffusion is restricted, which diminishes the diffusion

6

distance compared to the direct pathways that occur in pure oil. A greater porosity

7

distribution and less even pore size decrease the CO2 diffusion coefficient.

8

5. Conclusions

SC

RI PT

1

A visualization method using the X-ray CT technique for investigating the diffusion

10

process of CO2 in pure oil and oil-saturated porous media was reported. The CO2

11

diffusion coefficient was determined visually and quantitatively with CT grayscale

12

images. The diffusion coefficients at different locations and time under experimental

13

pressure were obtained. The effective diffusion coefficient of gas in oil-saturated

14

porous media was also investigated. From the experimental results, the following

15

conclusions can be drawn.

TE D

M AN U

9

The diffusion coefficients decrease along the diffusion path and show an

17

exponential relationship of distance at different time steps, and increase with the

18

system pressure at a constant temperature. The initial pressure has a great influence on

19

the diffusion coefficient, which means that increasing the initial CO2 pressure results

21 22 23

AC C

20

EP

16

in higher CO2 diffusivity in oil. The CO2 diffusion coefficient in the oil-saturated porous media was much lower than that in bulk oil. This indicates that the diffusion was suppressed by the tortuous diffusion path of the porous media.

Acknowledgment

24

This study has been supported by the National Natural Science Foundation of

25

China (Grant No.51506024,51436003), the National Basic Research Program of -14-

ACCEPTED MANUSCRIPT

1

China (973) Program (Grant No. 2011CB707300). It has been also supported by the

2

Fundamental Research Funds for the Central Universities (DUT13LAB01).

3

References

EP

TE D

M AN U

SC

RI PT

[1] J.T. Houghton, Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell, C. Johnson, Climate change 2001: the scientific basis, (2001). [2] C. Chang, Q. Zhou, L. Xia, X. Li, Q. Yu, Dynamic displacement and non-equilibrium dissolution of supercritical CO 2 in low-permeability sandstone: An experimental study, International Journal of Greenhouse Gas Control, 14 (2013) 1-14. [3] F. Moeini, A. Hemmati-Sarapardeh, M.-H. Ghazanfari, M. Masihi, S. Ayatollahi, Toward mechanistic understanding of heavy crude oil/brine interfacial tension: The roles of salinity, temperature and pressure, Fluid Phase Equilibria, 375 (2014) 191-200. [4] D.B. Bennion, The use of carbon dioxide as an enhanced recovery agent for increasing heavy oil production, in: Paper for Presentation at the Joint Canada/Romanla Heavy Oil Symposium, March, 1993, pp. 7-13. [5] C. Yang, Y. Gu, Diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil, Fluid Phase Equilibria, 243 (2006) 64-73. [6] R. Span, W. Wagner, A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa, Journal of Physical and Chemical Reference Data, 25 (1996) 1509. [7] E.L. Cussler, Diffusion: mass transfer in fluid systems, Cambridge university press, 2009. [8] R.D. Pomeroy, W.N. Lacey, N.F. Scudder, F.P. Stapp, Rate of solution of methane in quiescent liquid hydrocarbons, Industrial & Engineering Chemistry, 25 (1933) 1014-1019. [9] H. Reamer, J. Opfell, B. Sage, Diffusion coefficients in hydrocarbon systems methane-decane-methane in liquid phase-methane-decane-methane in liquid phase, Industrial & Engineering Chemistry, 48 (1956) 275-282. [10] D. Newitt, K. Weale, 310. Solution and diffusion of gases in polystyrene at high pressures, J. chem. Soc., (1948) 1541-1549. [11] J.L. Lundberg, M.B. Wilk, M.J. Huyett, Sorption studies using automation and computation, Industrial & Engineering Chemistry Fundamentals, 2 (1963) 37-43. [12] W.J. Koros, D. Paul, Design considerations for measurement of gas sorption in polymers by pressure decay, Journal of Polymer Science: Polymer Physics Edition, 14 (1976) 1903-1907. [13] M.R. Riazi, A new method for experimental measurement of diffusion coefficients in reservoir fluids, Journal of Petroleum Science and Engineering, 14 (1996) 235-250. [14] Y. Zhang, C. Hyndman, B. Maini, Measurement of gas diffusivity in heavy oils, Journal of Petroleum Science and Engineering, 25 (2000) 37-47. [15] C. Yang, Y. Gu, A new method for measuring solvent diffusivity in heavy oil by dynamic pendant drop shape analysis (DPDSA), SPE journal, 11 (2006) 48-57. [16] V.V. Loskutov, Empirical time dependence of liquid self-diffusion coefficient in porous media, Journal of magnetic resonance, 216 (2012) 192-196. [17] Q. Zheng, J. Xu, B. Yang, B. Yu, Research on the effective gas diffusion coefficient in dry porous media embedded with a fractal-like tree network, Physica A:

AC C

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 42 43 44 45 46 47

-15-

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

Statistical Mechanics and its Applications, 392 (2013) 1557-1566. [18] Q. Ma, Z. Chen, Numerical study on gas diffusion in isotropic and anisotropic fractal porous media (gas diffusion in fractal porous media), International Journal of Heat and Mass Transfer, 79 (2014) 925-929. [19] Y. Zhao, J. Chen, M. Yang, Y. Liu, Y. Song, A rapid method for the measurement and estimation of CO diffusivity in liquid hydrocarbon-saturated porous media using MRI, Magnetic resonance imaging, (2015). [20] L. Jiang, Y. Liu, Y. Song, M. Yang, Z. Xue, Y. Zhao, J. Zhao, Y. Zhang, T. Suekane, Z. Shen, Application of X-ray CT investigation of CO2–brine flow in porous media, Experiments in Fluids, 56:91 (2015). [21] D. Salama, A. Kantzas, Monitoring of diffusion of heavy oils with hydrocarbon solvents in the presence of sand, in: SPE International Thermal Operations and Heavy Oil Symposium, Society of Petroleum Engineers, 2005. [22] H. Luo, A. Kantzas, Investigation of diffusion coefficients of heavy oil and hydrocarbon solvent systems in porous media, in: SPE Symposium on Improved Oil Recovery, Society of Petroleum Engineers, 2008. [23] H. Luo, S. Kryuchkov, A. Kantzas, The effect of volume changes due to mixing on diffusion coefficient determination in heavy oil and hydrocarbon solvent system, in: SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, 2007. [24] U.E. Guerrero Aconcha, A. Kantzas, Diffusion of hydrocarbon gases in heavy oil and bitumen, in: Latin American and Caribbean Petroleum Engineering Conference, Society of Petroleum Engineers, 2009. [25] Z. Li, M. Dong, Experimental study of diffusive tortuosity of liquid-saturated consolidated porous media, Industrial & Engineering Chemistry Research, 49 (2010) 6231-6237. [26] L. Song, A. Kantzas, J.L. Bryan, Investigation of CO2 diffusivity in heavy oil using X-ray computer-assisted tomography under reservoir conditions, in: SPE International Conference on CO2 Capture Storage and Utilization, Society of Petroleum Engineers, 2010. [27] L.Y. Tang, Y. Liu, Y.C. Song, Z.J. Shen, X.H. Zhou, Investigation of CO2 Diffusion in Oil-Saturated Porous Media by Using X-Ray Computer-Assisted Tomography, Advanced Materials Research, 807-809 (2013) 2498-2502. [28] A. Kantzas, Investigation of physical properties of porous rocks and fluid flow phenomena in porous media using computer assisted tomography, In Situ;(USA), 14 (1990). [29] H. Luo, A. Kantzas, Study of diffusivity of hydrocarbon solvent in heavy-oil saturated sands using X-ray computer assisted tomography, Journal of Canadian Petroleum Technology, 50 (2011) 24. [30] A. Kavousi, F. Torabi, C.W. Chan, E. Shirif, Experimental measurement and parametric study of CO2 solubility and molecular diffusivity in heavy crude oil systems, Fluid Phase Equilibria, 371 (2014) 57-66. [31] A.A. Asfour, Diffusion: Mass transfer in fluid systems By E. L. Cussler, Cambridge University Press, 1984, 525 pp., $49.50, Aiche Journal, 31 (1985) 523-523. [32] L.Y. Tang, Y. Liu, Y.C. Song, Z.J. Shen, X.H. Zhou, Investigation of CO2 Diffusion in Oil-Saturated Porous Media by Using X-Ray Computer-Assisted Tomography, in: Advanced Materials Research, Trans Tech Publ, 2013, pp. 2498-2502. [33] Y. Song, M. Hao, Y. Liu, Y. Zhao, B. Su, L. Jiang, CO2 diffusion in

AC C

1 2 3 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 42 43 44 45 46 47 48 49 50

-16-

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

n-hexadecane investigated using magnetic resonance imaging and pressure decay measurements, RSC Advances, 4 (2014) 50180-50187. [34] A.T. Grogan, V.W. Pinczewski, G.J. Ruskauff, F.M. Orr, Diffusion of CO2 at Reservoir Conditions: Models and Measurements, Spe Reservoir Engineering, 3 (1988) 93-102. [35] R.B. Bird, Transport Phenomena, Journal of Applied Mechanics, 28 (2001) 235-252. [36] G.R. Darvish, Physical Effects Controlling Mass Transfer in Matrix Fracture System during CO2 Injection Into Chalk Fractured Reservoirs, in: Department of Petroleum Engineering & Applied Geophysics, Fakultet for ingeniørvitenskap og teknologi, Fakultet for ingeniørvitenskap og teknologi, 2007. [37] F. Marica, S.A.B. Jofré, K.U. Mayer, B.J. Balcom, T.A. Al, Determination of spatially-resolved porosity, tracer distributions and diffusion coefficients in porous media using MRI measurements and numerical simulations, Journal of contaminant hydrology, 125 (2011) 47-56.

AC C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

-17-

SC

RI PT

ACCEPTED MANUSCRIPT

2

M AN U

1

Fig. 1. Schematic diagram of the CT scan experimental setup.

AC C

EP

TE D

3

-1-

1 2

Fig. 2. The design of the pressure vessel for the X-ray CT scan.

AC C

EP

TE D

M AN U

SC

3

RI PT

ACCEPTED MANUSCRIPT

-2-

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

1 2

Fig. 3. The linear relation between the grayscale value of the CT image and density of

3

the air and liquids.

4

AC C

EP

TE D

5

-3-

1 2

(b)

SC

(a)

RI PT

ACCEPTED MANUSCRIPT

Fig. 4. Image sample with ROI (a) and a schematic diagram of the diffusion process

4

system (b).

M AN U

3

AC C

EP

TE D

5

-4-

ACCEPTED MANUSCRIPT

1 2

Fig. 5. Medium domain of one-dimensional diffusion.

AC C

EP

TE D

M AN U

SC

3

RI PT

∆x

-5-

ACCEPTED MANUSCRIPT

SC

RI PT

1

Fig. 6. Images of CO2 diffusion in n-decane solution under conditions of 2 MPa and 4

4

MPa.

M AN U

2 3

5 6 7

11 12 13

EP

10

AC C

9

TE D

8

-6-

SC

RI PT

ACCEPTED MANUSCRIPT

M AN U

1 2

Fig. 7. The CO2 normalized dimensionless concentration along the diffusion direction

3

at 4 MPa (30 min, 90 min, and 180 min).

4 5

9 10 11

EP

8

AC C

7

TE D

6

-7-

1 2 3

M AN U

SC

(a) 2 MPa

RI PT

ACCEPTED MANUSCRIPT

TE D

4 5 6

7 8 9 10

AC C

EP

(b) 3 MPa

(c) 4 MPa Fig. 8. The relationship between the CO2 diffusion coefficient in n-decane solution and diffusion time.

11

-8-

SC

RI PT

ACCEPTED MANUSCRIPT

(a) T= 29 ◦C

3 4 5

(b) T=35 ◦C Fig. 9. The relationship between the CO2 diffusion coefficient in n-decane solution

6

and diffusion time.

EP

AC C

7

TE D

M AN U

1 2

-9-

1 2

M AN U

SC

(a) 2 MPa

RI PT

ACCEPTED MANUSCRIPT

(b) 4 MPa Fig. 10. The CO2 effective diffusion coefficient in oil-saturated BZ02 glass sand along

6

the diffusion direction with time.

EP AC C

7

TE D

3 4 5

-10-

ACCEPTED MANUSCRIPT

Tab. 1. The CO2 bulk diffusion coefficient at different diffusion times. Bulk diffusion coefficient (10-9m2/s)

Time(min) 30 60 90 120 150 180 30 60 90 120 150 180

29

35

2 Mpa 5.52 3.44 2.06 1.12 0.95 0.69 13.97 5.84 3.56 1.79 1.23 0.98

3 Mpa 11.12 4.68 2.05 1.66 1.13 0.83 24.26 8.97 5.47 4.76 2.83 1.21

4 Mpa 20.68 8.323 6.72 2.93 1.84 1.23 31.23 15.72 9.82 6.28 3.90 2.09

M AN U

2 3

1 Mpa 2.69 1.85 1.27 0.97 0.53 0.38 5.89 2.47 1.59 1.04 0.86 0.56

AC C

EP

TE D

4

-11-

5 Mpa 34.89 16.87 10.27 5.54 2.35 1.99 45.56 21.67 13.45 9.35 4.67 2.56

6 Mpa 43.35 25.98 15.97 7.38 3.84 2.29 64.45 38.55 19.35 13.66 7.56 4.58

RI PT

Temperature(℃)

SC

1