Estimation of Low-Temperature Mass-Transfer Properties of Methane

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Estimation of Low-Temperature Mass Transfer Properties of Methane and Carbon Dioxide in n-Decane, Hexadecane and Bitumen using the Pressure Decay Technique Francisco Javier Pacheco-Roman, S. Hossein Hejazi, and Brij B. Maini Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b00112 • Publication Date (Web): 14 Jun 2016 Downloaded from http://pubs.acs.org on June 14, 2016

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Estimation of Low-Temperature Mass Transfer Properties of Methane and Carbon Dioxide in nDecane, Hexadecane and Bitumen using the Pressure Decay Technique Francisco J. Pacheco-Roman‡*, S. Hossein Hejazi‡, and Brij Maini‡ Department of Chemical and Petroleum Engineering, University of Calgary, AB, T2N 1N4, Canada KEYWORDS: Diffusion coefficient, Henry’s Constant, Pressure-Decay Experiments, Liquid hydrocarbons, Gaseous Solvents

ABSTRACT

The pressure-decay technique is used to determine the diffusivity and solubility of methane and carbon dioxide in pure hydrocarbons and bitumen at temperatures of 0, 15, 20 and 25 °C and pressure of 3.5 MPa. An analytical-graphical technique is implemented to extract the related mass-transfer parameters, i.e., diffusion coefficient and Henry’s constant, from the pressuredecay data. The results reveal that the diffusion coefficient of methane and carbon dioxide in both, pure hydrocarbons and bitumen, decreases as the temperature decreases. On the basis of the

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estimated Henry’s constants, the effect of the temperature on the solubility of the gaseous solvents in bitumen and pure hydrocarbons is also determined. As expected, the solubility of both gases in the studied pure hydrocarbons increases as the temperature decreases. In addition to confirming the known trends, this study provides new experimental data for low temperature gas-hydrocarbon diffusion process.

1. INTRODUCTION Heavy oil and bitumen represent an important energy resource. According to the International Energy Agency heavy oil and bitumen account for almost 1.5 trillion barrels of the remaining recoverable resources.1 However, one of the main challenges associated with the recovery of these resources is the high viscosity and consequently low mobility of oil under reservoir conditions. For instance, these hydrocarbon resources can be found in reservoirs at temperatures ranging from 10 to 20 °C and pressures of 0.5 to 4 MPa.2 Therefore, understanding the behavior of the reservoirs’ fluids at these conditions is essential for the implementation of any recovery technique. Certainly, heavy oil recovery processes require the estimation of properties inherent to its operating mechanism. For instance, the design of thermal recovery methods utilize properties such as steam enthalpy, saturation temperature, and rock’s effective thermal conductivity. Similarly, solubility and diffusivity of gases in crude oils are key properties to design and model recovery processes that involve mass transport between these two phases such as non-thermal and hybrid steam-solvent injection methods. Nevertheless, experimental solubility and diffusivity data of gases in heavy oils at low temperatures is scarce in the literature. In general, the effort required to determine these properties is extensive, particularly for estimating diffusivity, due to the difficulties associated with its measurement.3-6 This fact has been the


2

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driving force in the development of diverse experimental techniques to accurately estimate diffusivity of gases in crude oils. Diffusivity, as quantified by the diffusion coefficient (), is experimentally determined using direct or indirect techniques. Direct techniques measure the composition profile as diffusion occurs whereas indirect techniques measure some other property correlated to diffusivity; for example, the Nuclear Magnetic Resonance (NMR) spectra, density profile, volume and pressure. Among all the available indirect methods, the pressure-decay technique (PDT) has been widely used to determine the diffusion coefficient of gases in pure liquid hydrocarbons or their mixtures (crude oils). This experimental technique is non-intrusive, simple, reliable and relatively inexpensive when compared to composition measurement techniques such as chromatography or other analytical tools. In addition, solubility can also be determined from the same experiment. Therefore, we use this experimental technique in our study. The PDT measures the changes in pressure as a gas diffuses into a liquid inside a pressure/volume/temperature (PVT) cell. Then, the diffusion coefficient and other mass transport properties are inferred from the recorded changes in pressure. This technique has been used in several reported studies and Table 1 summarizes the diffusion coefficients of gases in heavy oil/bitumen reported in previous experimental works that utilized the PDT. Table 1 Bulk diffusion coefficient of gases in heavy oils/bitumen using the PDT Reference

Method

Conventional PDT 7

Zhang et. al.

Calculation: Numerical method

Diffusivity

Pressure

Temperature

(x109)m2/s

(MPa)

(°C)

CH4 Venezuelan heavy oil

8.6

3.47

CO2 Venezuelan

4.8

System

21 3.5


3

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Reference

Method

System

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Diffusivity

Pressure

Temperature

(x109)m2/s

(MPa)

(°C)

heavy oil 25

0.190 0.241 CO2-Suncor Coker Feed (SCF) bitumen

50 4

0.383

75

0.433

90

0.592

Conventional PDT

50 8


0.102

90

0.134

25

0.237

50 4

CO2-Syncrude bitumen

Upreti al.*8,9

et

0.374

75

0.428

90

0.398

50

0.794

75

0.932

90

0.0811

25

0.293

CH4-Syncrude bitumen

8

4

75

0.432

90

0.0582

25

0.152

50 8

Conventional PDT Calculation: Numerical method

C2H6-SCF bitumen C2H6-Syncrude bitumen

0.203

75

0.867

90

0.287

4

0.254

25 25

4 0.420

75


4

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Reference

Method

System

Diffusivity

Pressure

Temperature

(x109)m2/s

(MPa)

(°C)

0.608

90

0.492

75 8

0.692 N2-SCF bitumen

0.020

90 4

0.0180

25 25

0.0513

50 4

N2-Syncrude bitumen

0.234

75

0.496

90

0.0555

25

0.172

50 8

Conventional PDT Tharanivasan et al.**10



75

0.746

90

CO2Lloydminster heavy oil

0.56

4.18

CH4Lloydminster heavy oil

0.21

5.06

C3H8Lloydminster heavy oil

1.76

0.76

0.654

2.369

0.801

6.518

0.598

4.416

0.640

5.015

0.795

5.850

Conventional PDT Li et al.11

0.465

CO2-Oilsaturated rocks

23.9

40


5

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Reference

Unatrakarna et al.12

Method

Conventional Calculation: Numerical method

System

Diffusivity

Pressure

Temperature

(x109)m2/s

(MPa)

(°C)

0.690

3.175

CO2-Heavy oil: 21285 cP

2.6-3.1

34.0-35.5

CH4-Heavy oil: 21285 cP

1.3-3.5

11.0-15.0

CO2-Heavy oil: 8154 cP

2.4-2.8

58.0-68.0

CH4-Heavy oil: 8154 cP

1.3-1.5

31.0-41.0

CO2-Heavy oil saturated sand:21285 cP

2.8-3.2

18.0-24.1

64.80

3.2

137.06

4.4

130.89

5.4

134.18

6.33

68.68

7.15

179.13

7.45

61.35

7.87

130.39

8.28

CO2 -Bitumen

0.1339

3.5299

23.9

CH4-Bitumen

0.07667

5.5459

30

38.0

1.7258

21.85

45.3

1.7305

24.85

51.0

1.7278

27.85

Conventional PDT Wang et al.13

Calculation: Graphical method

Conventional PDT Etminan et al.14

Kavousi et al.15


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CO2-Daqing oil

30-55

45


6

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Reference

Method

System

Conventional PDT

CO2-Heavy oil (5000 cP)


Diffusivity

Pressure

Temperature

(x109)m2/s

(MPa)

(°C)

58.9

1.7205

31.85

40.4

3.1047

21.85

51.21

3.1097

24.85

58.1

3.1044

27.85

65.63

3.1067

31.85

44.6

4.4857

21.85

55.71

4.4888

24.85

65.82

4.4886

27.85

75.83

4.4871

31.85

36.3

1.7308

21.85

41.26

1.7225

24.85

50.29

1.7278

27.85

56.91

1.7298

31.85

41.5

3.1062

21.85

47.34

3.1055

24.85

56.82

3.1035

27.85

68.03

3.1075

31.85

43.0

4.4874

21.85

54.16

4.4883

24.85

63.22

4.4877

27.85

75.93

4.4881

31.85

0.493

2.423

0.755

4.034

0.731

2.311

Conventional Calculation: Numerical method

Behzadfar et al.16

CO2-Heavy oil (5000 cP)

Conventional PDT combined with rheometry Calculation:

30 CO2-Bitumen

50


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Reference

Method

System

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Diffusivity

Pressure

Temperature

(x109)m2/s

(MPa)

(°C)

1.080

5.008

0.928

2.244

Numerical method

70 1.162

4.794

*Represents the reported average diffusivity from their concentration dependent-diffusion coefficients **The reported diffusivity is under the equilibrium boundary condition and the whole length of experiment

Other techniques have also been used for measuring diffusivity of gases in heavy oil. Table 2 presents a summary of diffusion coefficients of gases in heavy oils/bitumen determined experimentally using techniques other than the PDT. It includes the technique used, the gas/heavy oil system, the experimental conditions and reported value of the diffusion coefficient. Table 2. Bulk diffusion coefficient of gases in heavy oils/bitumen using techniques different from pressure-decay Diffusivity Pressure Temperature Reference

Method

System

(x109)m2/s

(MPa)

66

3 Denoyelle et. al.17

Schmidt et al.18

Indirect: gas volume dissolved

Direct: analysis of dissolved gas

CO2-Stock Tank Oil

CO2-Athabasca bitumen

8.5-9.2

(°C)

15

75

4.6

80

0.28

20

0.50

50

0.71

75

0.92

5

100

1.15

125

1.41

150

1.55

175


8

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Diffusivity Pressure Temperature Reference

Method

System

Das et al.20

Nguyen et al.21

Yang et al.22

Jamialhlamadi

Indirect: motion of interface

(MPa)

(°C)

1.75

200

0.175

20

0.174

50

0.337

75

C2H6-Athabasca bitumen

0.4-0.75

50

CO2-Maljamar oil

2.1

5

25

C3H8-Peace River bitumen

1.306

0.8-1.2

21-35

C4H10-Peace River bitumen

0.413

0.3

35

CO2-Aberfeldy heavy oil

6

1

50

CH4-Athabasca bitumen

Grogan et al.19

(x109)m2/s

Indirect

Direct: composition analysis

Indirect: Dynamic Pendant Drop Shape Analysis (volume of a drop)

Indirect: Constant

Impure CO2Aberfeldy heavy oil

2.5

0.9

1.2

0.8

0.4

0.7

CO2Lloydminster heavy oil

0.20-0.55

2-6

CH4Lloydminster heavy oil

0.12-0.19

6-14

23

23.9 C2H6Lloydminster heavy oil

0.13-0.77

1.5-3.5

C3H8Lloydminster heavy oil

0.09-0.68

0.4-0.9

CH4-Iranian

8.0-13.6

3.6-28

25


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Diffusivity Pressure Temperature Reference et al.23

GuerreroAconcha et al.24

Method

System

pressure Dissolving gas volume (CPDGV) Indirect: CT number with Computed Assisted Tomography

Indirect: gas volume with constant pressure

Fadaei et al.26

Indirect: oil swelling (microfluidic experiments)

(MPa)

(°C)

crude oil 9.0-16.2

C3H8-bitumen

Etminan et al.25

(x109)m2/s



50

0.05-0.7

0.62

NS

0.5

3.2

75

0.36

3.8

50

0.12

3.1

0.17

4.1

0.21

5.6

21

NS: Not specified

In summary, most experimental data are reported at temperatures above 25 °C and there are very few experiments dealing with the gas-oil diffusion properties at temperatures lower than 25 °C. In fact running such experiments for heavy oil and bitumen at low temperatures becomes lengthy and requires special attention to eliminate leakage. In this study, we aim to investigate the solubility and diffusivity of methane and carbon dioxide in hydrocarbon liquids such as dodecane, hexadecane and heavy oil at temperatures lower than 25 °C. A recently proposed analytical-graphical method is implemented to get the estimation of these properties. Based on


10

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the experimental results the effect of low temperatures in gas diffusion and solubility is discussed. The outline of the paper is as follows. First, we present the technical details of the experimental setup together with the experimental procedure and materials. We briefly present the analytical-graphical technique to extract the diffusion coefficient and Henry’s constant from the pressure-decay data. Then, we present and discuss the experimental results followed by the main conclusions.

2. EXPERIMENTAL SECTION 2.1. Apparatus An experimental apparatus, based on pressure decay technique, is designed and constructed to estimate the diffusivity and solubility of gases in liquid hydrocarbons at low temperatures. Figure 1 presents a schematic of the pressure-decay set-up that works in the temperature range of -10 to 100 °C and pressures from 0 to 6.893 MPa.


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Figure 1. Schematic of the experimental apparatus to measure the mass transport properties of gases in heavy oils This experimental rig consists of a stainless steel cylindrical vessel with an inner diameter of 6.35 cm, outer diameter of 10.2 cm, and height of 5.71 cm. This vessel is closed with a lid through six threaded bolts. A Viton® O-ring between the base of the lid and the vessel seals the vessel and assures the system is leak-proof. The top of the lid has one orifice for a thermocouple to measure the temperature inside the PVT cell and another to inject the gas into the vessel through a preheating coil. A direct discharge of gas into the liquid is avoided by using a small deflector welded at the base of the lid at the gas entry point. A gas cylinder supplies the gas that is injected into the PVT cell at the desired pressure by the means of a pressure regulator. The accuracy in the injection pressure is verified with a high resolution pressure transducer. Actually, the system utilizes two Paroscientific® Digiquartz 31K-101 pressure transducers that can measure pressures up to 6.893 MPa with a resolution of 0.0001%, and precision of 6.89 Pa. The first one measures the gas injection pressure and the other measures the decaying pressure inside


12

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the PVT cell. The PVT cell along with the preheating coil are submerged in a water bath maintained at a constant temperature with a Haake temperature controller/circulator. Finally, the pressure sensors and thermocouples are connected with a computer that displays the data online. This data-acquisition system also records the temperature and pressure inside the PVT cell periodically. The previous experimental set up uses a completely opaque PVT cell. So, we refer to this cell as blind PVT cell. However, experiments are also conducted in the same set up with a visual PVT cell whose interior can be seen through a window on the vessel’s wall. This visual PVT cell is also a stainless steel cylindrical vessel with an inner diameter of 5.22 cm and height of 9.47 cm. In this case, the cell is sealed with a threaded stainless steel screw lid with a Viton® O-ring on the base. The purpose of using the visual PVT cell is to verify the assumption of negligible swelling of heavy oil by tracking the movement of the gas heavy oil interface with the aid of a high precision cathetometer (±0.01 of mm).

2.2. Procedure The systems is first tested for leakage several times before starting experiments. The leakage test consists in pressurizing the system (PVT cell and all connections) with the diffusing gas and monitoring the pressure for at least 24 hours. Once the system is leak-free, diffusion-pressuredecay experiments are carried out following this procedure. (1) A measured mass of liquid sample is carefully poured inside the PVT cell without trapping any air bubbles. (2) Silicon highvacuum grease is applied on the O-ring located on the lid which is then bolted to the vessel. (3) The water bath is set at the desired temperature and the PVT cell is set inside the bath allowing it to reach an equilibrium temperature. (4) The preheating coil and thermocouple attached to the lid


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of the PVT cell are respectively connected to the main gas supply valve and the computer. (5) The temperature and pressure data are monitored through the computer. (6) The gas cylinder is opened and the pressure regulator adjusted to the desired pressure as measured by the pressure transducer. (7) Once the desired pressure is achieved the valve connecting the PVT cell and the injection line is opened and the recording of pressure is started. After reaching the desired pressure in the cell, the valve between the preheating coil and the cell is closed, thus isolating the cell from gas supply. (8) The experiment is completed when the system reaches the equilibrium (i.e. pressure is practically constant) or the pressure decay is less than the resolution of the pressure sensor. (9) The vent line is opened and the PVT cell depressurized to atmospheric pressure. (10) The PVT cell is disconnected from the gas line and thermocouple sensor, taken out from the water bath, and opened. (11) Finally, the PVT cell is heated up in a water bath to easily remove the bitumen and residues cleaned with toluene inside a fume hood. 2.3. Materials and Experiments Diffusion experiments are conducted using carbon dioxide and methane of 99.9% and 99.0% purity, respectively as the gas phase. The liquid hydrocarbons are anhydrous dodecane ≥99%, hexadecane 99%, and a heavy crude oil. The heavy oil is from a Canadian reservoir. The density and viscosity of the heavy oil are 965.9 kg/m3 and 54,200 cP respectively at 50 °C. The experiments are carried out at different temperatures in the range of 0 to 25 C. Table 3 presents the detailed experimental conditions of the pressure-decay tests conducted for each gas/hydrocarbon system. Additionally, the pressure decay curves for methane/dodecane and methane/hexadecane; carbon dioxide/dodecane and carbon dioxide /hexadecane; and methane/bitumen and carbon dioxide/bitumen are shown respectively in Figure 2, Figure 3 and Figure 4.


14

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Table 3. Experimental pressure-decay tests of methane and carbon dioxide in dodecane, hexadecane and bitumen

Gas/ hydrocarbon system

Temperature (), ⁰C

Compressibility factor*, () dimensionless

Initial pressure ( )

Pressure decay (%)

MPa

Thickness of bitumen layer, (ℎ) m

0

0.9003

3.535

16.4

15

0.9179

3.500

16.0

25

0.9269

3.512

16.3

CH4/

20

0.9219

3.540

14.1

hexadecane

25

0.9269

3.512

13.9

0

0.6737

3.595

31.2

15

0.7441

3.583

31.0

25

0.7808

3.536

31.0

CO2/

20

0.7632

3.563

27.9

hexadecane

25

0.7752

3.612

25.9

CH4/

15

0.9188

3.457

bitumen

25

0.9280

CO2/

0

bitumen

25

Gas zone in cell () m

CH4/ dodecane 0.016

0.0357

0.016

0.0357

2.8

0.0174

0.0773

3.591

2.7

0.0174

0.0343

0.6915

3.458

10.0

0.0118

0.0399

0.7871

3.449

7.3

0.0174

0.0773

CO2/ dodecane

*Calculated with the Peng-Robinson EOS at the initial pressure27

3. THEORETICAL BASIS Experimental data from the pressure-decay tests is utilized to calculate and with a graphical method derived from the solution of Fick’s second law28 derived with the Integral Method.29 This method is shown concisely as further details are found elsewhere.30 The


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technique is developed based on the assumption of constant diffusion coefficient, constant gas compressibility factor, isothermal conditions, no chemical reactions, negligible swelling of heavy oil and liquid hydrocarbons, existence of thermodynamic equilibrium with no resistance to mass transfer at the gas/hydrocarbon interface. Steps in evaluating and are (1) to distinguish finite-acting and infinite-acting data and (2) to plot pressure and time derivative of pressure vs. time. We use the central-difference formula of fourth order to numerically differentiate the data. However, because numerical differentiation can amplify the noise associated with measurements, we smooth the PD data before differentiating the data. Specifically, a robust local regression method is implemented, in which each smoothed value is calculated by using a regression weight function defined for the data points. 4. RESULTS In this study, we only focus on the diffusion process of gaseous solvents in pure liquid hydrocarbons and bitumen. Therefore, we only present the PD curves at temperatures at which the hydrocarbons are still liquid. This is noteworthy because hexadecane becomes solid below 18 °C, which is its freezing temperature. Although we ran some experiments with methane and carbon dioxide in solid hexadecane at 15 °C, we observed that the gas-phase pressure did not decay much as a result of the slow diffusion process occurring in a solid medium. Hence, we did not conduct experiments with hexadecane at temperatures lower than 18 °C.

4.1. Methane and Carbon dioxide in Pure Hydrocarbons Figure 2a and Figure 2b present the pressure-decay curves at different temperatures for the systems methane/dodecane and methane/hexadecane, respectively.


16

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(a

3.60

3.60 Methane/hexadecane: 20 C

3.50

Methane/dodecane: 15 C

Methane/hexadecane: 25 C


3.40 Pressure, MPa

3.40 Pressure, MPa

(b


3.50

3.30 3.20

3.30 3.20

3.10

3.10

3.00

3.00

2.90

2.90 0

10

20

30

40

50

0

10

20

Time, hr

30

40

50

Time, hr

Figure 2. PD curves at different temperatures of (a) CH4/dodecane and (b) CH4/hexadecane Figure 3 presents the experimental pressure-decay curves for the systems carbon dioxide/dodecane and carbon dioxide/hexadecane at different temperatures.

(a 3.60

Carbon dioxide/dodecane: 0 C

(b 3.60

Carbon dioxide/hexadecane: 20 C

3.40

Carbon dioxide/hexadecane: 25 C


3.40


3.20

Pressure, MPa

Pressure, MPa

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 51 52 53 54 55 56 57 58 59 60

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3.00 2.80

3.20 3.00 2.80

2.60

2.60

2.40

2.40

2.20

2.20 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

1.0

Time, hr

1.5

2.0

2.5

3.0

Time, hr

Figure 3. Pressure-decay curves at different temperatures of (a) carbon dioxide/dodecane and (b) carbon dioxide/hexadecane Using the procedure described in30, the diffusion coefficient and Henry’s constant are evaluated. Table 4 and 5 shows the estimated mass-transfer parameters of CH4 and CO2 in dodecane and hexadecane at the different experimental temperatures, respectively.


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Table 4. Estimated diffusion coefficients and Henry’s constants of methane in dodecane and hexadecane at different temperatures Gas/hydrocarbon Temperature, ⁰C Estimated Hij, Pa·m3/kg Estimated D, m2/s

CH4/dodecane

0

287161

2.34x10-9

15

321738

3.11x10-9

25

330858

3.75x10-9

20

378123

2.20x10-9

25

394566

2.28x10-9

CH4/hexadecane

Table 5. Estimated diffusion coefficients and Henry’s constants of carbon dioxide in dodecane and hexadecane at different temperatures Gas/hydrocarbon Temperature, °C Estimated Hij, Pa·m3/kg Estimated D, m2/s

CO2/dodecane

0

34220

2.60x10-8

15

40330

3.14x10-8

25

43832

3.71x10-8

20

48765

3.12x10-8

25

55701

3.37x10-8

CO2/hexadecane

4.2. Methane and Carbon Dioxide in bitumen Figure 4 shows the pressure-decay curves of methane and carbon dioxide in bitumen. We expect to find a trend in the diffusion and solubility values on the basis of experimental data at higher temperatures reported in the literature. Table 6 shows the estimated Henry’s constant and diffusion coefficient of the system methane/bitumen at each temperature.


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(a)

(b)

3.50

3.50 Carbon dioxide/bitumen: 0 C

Methane/Bitumen @ 15 C

3.45

Methane/Bitumen @ 25 C

3.40

Carbon dioxide/bitumen: 25 C

Pressure, MPa

3.45 Pressure, MPa

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 51 52 53 54 55 56 57 58 59 60

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3.40

3.35

3.35 3.30 3.25 3.20 3.15 3.10 3.05

3.30 0

20

40

60

80

100

0

20

40

60

80

100

Time, hr

Time, hr

Figure 4. Experimental pressure-decay curves for methane and carbon dioxide in bitumen Table 6. Estimated diffusion coefficients and Henry’s constants of methane in bitumen at 25 and 15 °C. Gas/bitumen system

Temperature, °C Estimated Hij, Pa·m3/kg Estimated D, m2/s 15

1 868 669.7

2.71x10-10

25

2 075 489.9

3.22x10-10

0

52 078.7

7.87x10-11

25

86 798.9

3.05x10-10

Methane/bitumen

Carbon dioxide/bitumen

5. DISCUSSIONS 5.1. Methane and carbon dioxide in pure hydrocarbons Figure 5 shows the effect of temperature on the diffusion coefficient for the gases methane and carbon dioxide in the liquid hydrocarbons dodecane and hexadecane.


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Diffussion coefficient x10-9, m2/s

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Methane/dodecane

Methane/hexadecane

Carbon dioxide/dodecane

Carbon dioxide/hexadecane

40

37.1

35

31.4

30

33.7

26.0

31.2

25 20 15 10 5

3.75

3.11

2.34

2.2

0 0

15

2.28

30

Temperature, ⁰C

Figure 5. Effect of temperature on diffusion coefficient of gases in hydrocarbons Figure 5 indicates that as the temperature decreases the diffusion coefficients of the gases methane and carbon dioxide in the liquid hydrocarbons also decrease. This trend suggests that the diffusion process is slow at low temperatures. This effect of temperature on the diffusion coefficient coincides with the one reported in other works, but conducted at higher temperatures.16, 23, 31 The values of the diffusion coefficient in the liquid hydrocarbons is one order of magnitude higher for the gas CO2 than for the gas CH4. This fact explains the difference in the length of the PD curves shown in Figure 2 and Figure 3. Therefore, reaching the equilibrium pressure takes only 3 hours for the experiments of CO2 in the liquid hydrocarbons, whereas for methane the experiments take more than 40 hours. Figure 5 also reveals that the diffusivity for both gases is slightly higher in dodecane than in hexadecane. Figure 6 shows that Henry’s law constant of CH4 and CO2 in both hydrocarbons follow a similar behavior. In both cases, as the temperature of the gas/hydrocarbon decreases the value of decreases and consequently solubility increases.


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Energy & Fuels

Henry's constant x105, Pa m2/kg

Page 21 of 26

Methane/dodecane

Methane/hexadecane

Carbon dioxide/dodecane

Carbon dioxide/hexadecane

4.50 3.78123

4.00

3.94566

3.50 3.00 2.50

3.21738

3.30858

0.40330

0.43832

2.87161

2.00 1.50 1.00 0.34220

0.50 0.48765

0.00 0

15

0.55701

30

Temperature, ⁰C

Figure 6. Effect of the temperature on Henry’s constant of gases in hydrocarbons In general, the solubility of the gaseous solvents in dodecane and hexadecane is higher for carbon dioxide than for methane. Also, the solubility of both gases is higher in dodecane than in hexadecane. 5.2. Methane and carbon dioxide in bitumen Figure 7a and Table 6 indicate that the effect of temperature on the diffusion coefficient of carbon dioxide in bitumen is similar as for the case of pure hydrocarbons. The diffusion coefficient decreases as the temperature decreases. It is noteworthy that the value of the diffusion coefficient of CH4 and CO2 in bitumen at 25 °C is in the same order of magnitude as the values reported in the literature, this can be compared at least for the existent data reported at this temperature. The trend in the diffusivity of methane is similar to the one observed for carbon dioxide, i.e., diffusivity of methane in bitumen decreases as the temperature decreases. The values of Henry’s constant in Figure 7b indicate that the solubility of methane and carbon dioxide in bitumen is higher as the temperature is lower. This trend is similar as the one observed for the pure hydrocarbons.


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Energy & Fuels

(a)

4

(b) Henry's constant x105, Pa m2/kg

3

3.05

2.71

2

Methane/bitumen

1 0.79

20.75489

20

3.22 Diffussion coefficient x10-10, m2/s

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 51 52 53 54 55 56 57 58 59 60

Page 22 of 26

Carbon dioxide/bitumen

18.68669

15 Methane/bitumen Carbon dioxide/bitumen

10

5 0.52079

0

0.86799

0 0

15

30

0

Temperature, ⁰C

15

30

Temperature, ⁰C

Figure 7. Effect of the temperature on (a) the diffusion coefficient and (b) Henry’s constant of gas methane and carbon dioxide in bitumen It is important to note that the pressure sensitivity can be increased by decreasing the ratio of the thickness of the liquid sample (L) to the diameter of the cell (D). Decreasing the ratio L/D would provide more surface area for the gas to penetrate the fluid and lead to more gas absorption and more drop in pressure. Future work on analyzing the effect of the ratio L/D in the calculated mass transfer parameters from the pressure-decay data is underway. 6. CONCLUSIONS In this study, the PDT is used to determine the diffusion coefficient and Henry’s constant of methane and carbon dioxide in dodecane, hexadecane and bitumen at temperatures of 0, 15, 20 and 25 °C and pressure of 3.5 MPa. The analysis of the estimated diffusion coefficients at the different temperatures for all of the gaseous-solvents/hydrocarbon systems verify that the value of diffusivity decreases as the temperature decreases. Similarly, the effect of the temperature on the solubility of the gaseous solvents in bitumen and pure hydrocarbons is determined; finding that the solubility increases as the temperature decreases for both bitumen and pure hydrocarbons. This study provides new useful experimental data and corroborates the effect of


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low temperatures in the solubility and diffusivity of gaseous solvents in pure hydrocarbons and bitumen. AUTHOR INFORMATION Corresponding Author * Phone: (+52) 556-773-0268 E-mail address: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally. ACKNOWLEDGMENT The first author expresses his gratitude to the Mexican National Council for Science and Technology (CONACYT) (Grant 217244), the Secretariat of Public Education (SEP) (Grant BC1462) and the Mexican Government for the awarded scholarships to pursue his graduate studies. ABBREVIATIONS NMR, Nuclear Magnetic Resonance; PDT, pressure-decay technique; PVT, pressure/volume/temperature. REFERENCES (1) International Energy Agency. Resources to Reserves, IEA Publications, Paris, France, 2013 (2) Rankin, K.; Bradley, N.; van Dorp, J.; Verlaan, M.; Castellanos-Diaz, O.; Nguyen, Q. P. Energy Fuels 2014, 28(7). (3) Hill, E. S.; Lacey, W. N. Ind. Eng. Chem. 1934, 26(12), 1327–1331.


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(4) Reamer, H. H.; Duffy, C. H.; Sage, B. H. AIChE J. 1957, 3, 54-59. (5) Woessner, D. E.; Snowden, B. S.; George, R. A.; Melrose, J. C. Ind. Eng. Chem. Fundamen. 1969, 8(4), 779-786. (6) McKay, W. N. J. Can. Pet. Technol 1971, 10(02), 25-32. (7) Zhang, Y. P.; Hyndman, C. L.; Maini, B. B. Journal of Petroleum Science and Engineering 2000, 25(1-2), 37-47. (8) Upreti, S. R.; Mehrotra, A. K. Ind. Eng. Chem. Res. 2000, 39(4), 1080-1087. (9) Upreti, S. R.; Mehrotra, A. K. Can. J. Chem. Eng. 2002, 80(1), 116-125. (10) Tharanivasan, A. K., Gu, Y., & Chaodong, Y. Energy Fuels 2006, 20(6), 2509-2517. (11) Li, Z.; Mingzhe, D. Ind. Eng. Chem. Res. 2009, 48(20), 9307-9317. (12) Unatrakarna, D.; Asgharia, K.; Condor, J. Energy Procedia 2011, 4, 2170-2177. (13) Wang, S.; Hou, J., Liu, B.; Zhao, F.; Yuan, G.; Liu, G. Energy Sources 2013, 35(6), 538545. (14) Etminan, S. R.; Maini, B. B.; Chen, Z. Fuel 2014, 120(15 March), 218-232. (15) Kavousi, A.; Torabia, F.; Chan, C. W.; Shirif, E. Fluid Phase Equilibria 2014, 371, 57-66. (16) Behzadfar, E.; Hatzikiriakos, S. G. Energy Fuels 2014, 28(2), 1304-1311. (17) Denoyelle, L.; Bardon, C. 86 Annual Meeting, Canadian Institute of Mining and Metallurgy 1984. Ottawa, ON.


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(18) Schmidt, T. Technical Handbook on Oil Sands. Bitumens and Heavy Oils. Technical Publications Series No. 6. AOSTRA, 1989. (19) Grogan, A. T.; Ruskauff, G. J.; Pinczewski, V. W.; Orr, F. M. SPE Res. Eng.1988, 3(1), 93-102. (20) Das, S. K.; Butler, R. M. Can. J. of Chem. Eng. 1996, 74(6), 985-992. (21) Nguyen, T. A.; S. M., F. A. J. Can. Pet. Tech. 1998, 37(2), 24-31. (22) Yang, C.; Gu, Y. Fluid Phase Equilib. 2006, 243(1-2), 64-73. (23) Jamialahmadi, M.; Emadi, M.; Müller-Steinhagen, H. Journal of Petroleum Science and Engineering 2006, 53(1-2), 47-60. (24) Guerrero-Aconcha, U. E., & Kantzas, A. Latin American and Caribbean Petroleum Engineering Conference, Society of Petroleum Engineers. 2009. Cartagena de Indias, Colombia (25) Etminan, S. R.; Maini, B. B., Chen, Z.; Hassanzadeh, H. Fuels 2010, 24(1), 533-549. (26) Fadaei, H., Scarff, B., & Sinton, D. Energy Fuels 2011, 25(10), 4829-4835. (27) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundamen. 1976, 15(1), 59–64. (28) Fick, A. On Liquid Diffusion. Philosophical Magazine Series 4 1855, 10(63), 30-39. (29) Goodman, T. R. Advances in Heat Transfer 1964, 1, 51-122. (30) Pacheco-Roman, F.J.; Hejazi, S. H. SPE Journal 2015, Vol. Preprint, pp. 1-12. (31) Upreti, S. PhD thesis, University of Calgary, 2000.


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Estimation of Low-Temperature Mass-Transfer Properties of Methane

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