Reaction Kinetic Characteristics and Model of Methane Hydrate

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Reaction Kinetic Characteristics and Model of Methane Hydrate Formation in Porous Media Liang Zhang, Sudan Xu, Xin Li, Yin Zhang, Ruohan Yang, Qian Ouyang, and Shaoran Ren Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b00958 • Publication Date (Web): 11 Jul 2017 Downloaded from http://pubs.acs.org on July 16, 2017

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Reaction Kinetic Characteristics and Model of Methane Hydrate Formation in Porous Media

2

Liang Zhang1*, Sudan Xu1, Xin Li1, Yin Zhang2, Ruohan Yang1, Qian Ouyang1, Shaoran Ren1

3

1 School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, 266580, China

4

2 Petroleum Engineering, College of Engineering and Mines, University of Alaska Fairbanks, Fairbanks,

5

USA

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*Corresponding author: [email protected]

7 8

Abstract: Most of natural gas hydrates on the earth are buried in the shallow formation under the

9

deep water. Comprehensively understanding the reaction kinetic characteristics of gas hydrate in

10

porous media is very beneficial to the deep exploration of the hydrate accumulation in nature. In

11

this paper, the formation process of CH4 hydrate in porous media was simulated physically using a

12

high-pressure and low-temperature reactor. The hydrate phase equilibrium and reaction kinetic

13

characteristics at different temperatures, pressures, sand grain sizes and clay contents were assessed.

14

Based on the determination of relevant hydrate kinetic parameters, a novel mixing-flux hydrate

15

reaction model was proposed, which can be used for numerical simulation of gas hydrate

16

accumulation. The experimental results show that the porous media can make the phase equilibrium

17

of CH4 hydrate shift to the right under the capillary effects on the gas and hydrate phases. Low

18

temperature and high pressure can provide large driving force for hydrate formation, but large clay

19

content and small sand grain size usually give a negative effect on the CH4 transfer in the porous

20

media. It often leads to a slow hydrate formation rate and hard distinction of pressure drop between

21

hydrate nucleation and growth stages. Based on the experimental results of cases 1 to 6, the hydrate

22

nucleation kinetic parameters were regressed, and the activation energy Ea as well as the reaction

23

frequency factor kfo of hydrate growth were fitted to be 75.45-90.85 kJ/mol and 8.72×108-6.02×1011

24

mol/(m2 kPa day), respectively. In the numerical simulation of hydrate accumulation, the hydrate

25

formation process can be described by coupling the low-flux reaction and the high-flux reaction

26

which consume the CH4 dissolved in water and the free CH4 gas in pores, respectively. This novel

27

mixing-flux hydrate formation model is suitable for the flexible and practical hydrate accumulation

28

simulation, which can consider various gas sources and transfer states in the hydrate reservoir.

29

Key words: phase equilibrium; reaction kinetics; influencing factor; gas transfer; accumulation

30

simulation

31 32

1 INTRODUCTION

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Natural gas hydrate is a kind of high efficient and clean energy. 46 water molecules and at

34

most 8 guest molecules can generate one CH4 hydrate molecule (see equation 1, n=5.75). 1 m3 of

35

hydrate can release 164-180 Sm3 of natural gas. The high-pressure and low-temperature condition is

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the prerequisite for gas hydrate formation. Most of natural gas hydrate resources are buried in the

2

shallow sediments with a thickness of 300-1000 m (hydrate stability zone) under 300-4000 m deep

3

water (Wei et al, 2010). Only when the natural gas leaks into the hydrate stability zone, the gas

4

hydrate can form. Generally, the natural gas sources for hydrate accumulation can be classified into

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biogenic gas and pyrolysis gas. The former refers to the CH4 gas produced by the organic matter

6

degradation under the biological effect, while the latter mainly comes from the deep hydrocarbon

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reservoirs, which migrates into the shallow formation along faults. The biogenic gas often forms

8

diffusion-type hydrate reservoir in situ with low abundance (Su and Chen, 2006). Deep-water

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basins with rich oil and gas resources are more likely to form the promising seepage-type hydrate

10 11

deposits in large scale. CH4(g) + nH2O(w) CH4•nH2O(s) ± heat

（1）

12

In the past 20 years, researchers have conducted a lot of studies on the hydrate phase

13

equilibrium and reaction kinetics in porous media (Li et al, 2006; Chen et al, 2007; Maddena, 2009;

14

Jiang et al, 2011; Chuvilia et al, 1999; Anderson et al, 2003; Wu et al, 2004; Zhang et al, 2011; Yang

15

et al, 2011; Spangenberg et al, 2005; Zatsepina et al, 2000, 2007). However, to date, the effect of

16

porous media on hydrate thermodynamic and kinetic characteristics is still not clear. Zang et al

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(2015) regarded that one of the key reasons to cause this issue was the lack of explicit classification

18

of porous media. According to the classification standard of IUPAC (International Union of Pure

19

and Applied Chemistry), pores can be divided into micropore (diameter < 2 nm), mesopore

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(diameter between 2-50 nm) and macropore (diameter > 50 nm). There are few studies on the

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hydrate kinetics in micropores. A large number of experiments have shown that mesopore can shift

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the phase equilibrium condition of hydrate to the left because of its significant effect on the water

23

activity as well as the remarkable capillary force between gas and water (Anderson et al, 2003;

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Zhou et al, 2005; Aladko et al, 2004; Zhang et al, 2011; Maddena et al, 2009; Prasad et al, 2012;

25

Zang et al, 2013). In the macropores, the pore has no obvious effect on the hydrate phase

26

equilibrium, especially when the pore size is at µm-mm scale (Zang et al., 2013), but the influence

27

of pore properties on the hydrate reaction kinetics is still not negligible.

28

The prospective seepage-type gas hydrate reservoir is usually a thermodynamic

29

non-equilibrium system in which water, hydrate, and free gas coexist. The characteristics of hydrate

30

phase equilibrium and reaction kinetics are influenced by the porous media of the subsea

31

depositional environment, which will further affect the hydrate accumulation process in the shallow

32

formation under the sea. Most of sediments for gas hydrate accumulation belong to macroporous

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media. Hence, the gas hydrate reaction kinetics in macroporous media has been studied widely.

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Many factors influencing hydrate formation and deposition have been assessed through lab

35

experiments (Handa et al, 1992; Melnikov et al, 1996; Clarke et al, 1996; Chuvilia et al, 1998; Chen ACS Paragon Plus Environment

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et al, 2006; Fan et al, 2007; Ren et al 2009; Jiang et al, 2011; Zang et al, 2013). These studies

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indicate that sediments can promote the gas hydrate nucleation and growth. Coarse-grained

3

sediments are more favorable for hydrate formation than fine-grained sediments due to its larger

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pore size. Nevertheless, in nature, many gas hydrates are buried in muddy sediments with high clay

5

content. The pore size is small even close to mesopore scale. In this case, the clay in sediments

6

tends to make gas hydrate form difficultly. Hence, it is meaningful to conduct more studies to

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comprehensively reveal the influence of clay on the pore characteristics and the hydrate formation

8

kinetics in sediments. Moreover, hydrate kinetic model in porous media is the basis of hydrate

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accumulation numerical simulation, but most of the current kinetic models for hydrate accumulation

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are less concerned with the complexity of gas transfer state and the coexistence of different gas

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sources (Ribeiro et al, 2008; Shi et al, 2010). This limits the accurate numerical simulation of

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hydrate accumulation (Ye et al, 2013).

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In this paper, the formation kinetics of CH4 hydrate in porous composed of natural sand and

14

clay was studied experimentally using a high-pressure and low-temperature reactor. The effect of

15

porous media on the phase equilibrium of CH4 hydrate was assessed. The effects of driving force (T

16

and P) and pore features (sand grain size and clay content) on hydrate formation kinetic

17

characteristics in porous media were investigated. A novel mixing-flux model for hydrate formation

18

in porous media was proposed for the numerical simulation of hydrate accumulation, which can

19

consider different gas sources and transfer states in the hydrate reservoir.

20 21

2 EXPERIMENTAL SECTION

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2.1 Equipment

23

The experimental apparatus used to simulate the formation and decomposition of gas hydrate

24

in porous media is shown in Figure 1. The apparatus consists of a high-pressure reactor, a fluid

25

supply system, a low-temperature water bath, and a data acquisition system. The high-pressure

26

reactor has a fixed volume of 1 L, which can bear a pressure up to 25 MPa. The pressure and

27

temperature in the reactor can be acquired and transferred to the computer in real time by the

28

sensors installed on the top of the reactor. The measurement range of the pressure sensor is from 0

29

to 30 MPa with an accuracy of ±0.1%, while the temperature sensor can detect temperature from

30

-20 to 120 oC with an accuracy of ±0.1 oC. The water bath uses MEG solution as the circulating

31

agent, which can cool and warm the reactor, and keep the reactor at a steady temperature between

32

-20 oC and 90 oC with an accuracy of ±1 oC.

33

2.2 Materials

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99.999 mol% CH4 supplied by Taiyuan Gas Ltd; natural sand collected from Qingdao

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Jinshatan beach (40-60 mesh sand with a grain size of 0.25-0.425 mm, 80-100 mesh sand with a ACS Paragon Plus Environment

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grain size of 0.15-0.18 mm); clay (bentonite) purchased from Weirun New Material Ltd; distilled

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water and 3.5wt% NaCl aqueous solution.

3

4 5 6 7 8 9 10

Figure 1 High-pressure and low-temperature hydrate experimental apparatus (1) gas cylinder; (2) CH4 gas in container; (3) 3.5wt%NaCl water in container; (4,5) constant-flux pump; (6) main reactor; (7) water bath; (8) sand and clay filled in reactor; (9, 10) inlet valve; (11) outlet valve; (12) pressure meter; (13) pressure sensor; (14) temperature sensor; (15) data collection box; (16) computer.

2.3 Procedures

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Hydrate phase equilibrium point test: 1) fill the reactor with natural sand, and saturate it with

12

3.5wt% NaCl water; 2) inject CH4 into the reactor at the top to displace 200 ml water out of the

13

reactor, then continue injecting CH4 into the reactor to enhance the pressure to 4-8 MPa; 3) use the

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water bath to cool down the reactor to -10 oC at a rate of 0.5-1 oC/h, to make the gas hydrate form in

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the reactor; 4) after the pressure in the reactor declines and maintains stable for 3 h, heat the reactor

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to the room temperature at a rate of 0.5-1 oC/h to let the hydrate decomposition; 5) record the P and

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T changes in the reactor, plot the P-T relation curve, the intersection point of the cooling and

18

heating curves is the hydrate phase equilibrium point (Figure 2a).

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a. Determination of hydrate phase equilibrium point b. Typical pressure drop curve of hydrate formation Figure 2 Schematic diagram of hydrate experimental results

Hydrate formation kinetics experiment: 1) fill the reactor with natural sand and clay, and ACS Paragon Plus Environment

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saturate them with 3.5wt% NaCl water; 2) using the water bath to cool down the reactor and

2

maintain the temperature at a constant level between 3-13 oC; 3) inject CH4 into the reactor at the

3

top to displace 200 ml water out of the reactor, and then continue injecting CH4 into the reactor to

4

enhance the pressure to 6-12 MPa to ensure the reactor at the hydrate stability conditions; 4) let the

5

gas hydrate form in the reactor, and record the time t and the P-T changes in the reactor until the

6

pressure in the reactor become stable; 5) divide the hydrate formation stages according to the

7

pressure drop in the reactor (typically including CH4 dissolution, hydrate nucleation and growth, see

8

Figure 2b), and calculate the hydrate formation rate and saturation. The cumulative hydrate

9

formation in the reactor at time t can be calculated using the equations (2)-(3). The instantaneous

10

and stage hydrate formation rates can be calculated using the equation (4), while the saturations of

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various phases in the reactor can be calculated using the equations (5)-(7). ௉ ௏

௉௏

೒೚ ೒೟ ݊௛௧ = ∆݊௚௧ = ݊௚௢ − ݊௚௧ = ௓೚ோ் − ௓೟ோ்

12

೚

೚

೟

೟

‫ܥ‬௛௧ = ݊௛௧ /ܸோ

13

ௗ஼೓೟

14

ௗ௧

=

(2) (3)

௡೓೟శ౴೟ ି௡೓೟ ୼௧௏ೃ

௡೓೟ ఘ೓

15

ܵ௛௧ =

16

ܵ௪௧ =

17

ܵ௚௧ = 1 − ܵ௛௧ − ܵ௪௧

(4) (5)

௏ೃ ఝ

௏ೢ೚ ିହ.଻ହ×ଵ଼×௡೓೟ ×ଵ଴షల ௏ೃ ఝ

(6) (7)

18

where t is the reaction time, min; nht is the total hydrate amount formed in the reactor at time t, mol;

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∆ngt is the total CH4 amount consumed at time t, mol; ngo and ngt are the CH4 amounts in the reactor

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at the beginning (t=0) and time t, respectively, mol; Po and Pt are the pressures in the reactor at the

21

beginning and time t, respectively, Pa; To and Tt are the temperatures in the reactor at the beginning

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and time t, respectively, K; Zo and Zt are the CH4 compressibility factor at Po-To and Pt-Tt

23

conditions, respectively; Vgo and Vgt are the initial gas volume and the gas volume at time t in the

24

reactor, m3, Vgo=200×10-6 m3 (200 ml) in this study, for simplicity, Vgt=Vgo with neglecting the

25

change of total volume of hydrate and water during reaction in the reactor; R is the gas constant,

26

8.314 J/mol/K; Cht is the total hydrate amount formed in unit volume at time t, mol/m3; VR is the

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reactor volume, m3, VR=1000×10-6 m3 in this study; dCht/dt is the instantaneous or stage hydrate

28

formation rate, mol/m3/min; ∆t is the time interval, min; Sht, Swt, Sgt are the hydrate, water and gas

29

saturations in the reactor at time t, fraction, the calculation error can be controlled within ± 0.1%; ρh

30

is the molar volume of hydrate, m3/mol, ρh=129.97×10-6 m3/mol was used in this study; φ is the

31

porosity of the sand in the reactor, fraction; Vwo is the initial water volume in the reactor, m3, Vwo=

32

VRφ –Vgo.

33


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2.4 Schemes

2

A set of experimental schemes were designed to investigate the effects of temperature, pressure,

3

clay content and sand grain size on the gas hydrate formation kinetics, such as the hydrate

4

nucleation and growth rate, gas consumption and hydrate saturation. As shown in Table 1, the cases

5

1 to 6 were used to explore the effects of temperature and pressure, and the cases 4, 7, 8 were used

6

to explore the effect of clay content, while the cases 4 and 9 were used to explore the effects of sand

7

grain size. Moreover, three additional cases 10, 11 and 12 were designed to analyze the influence of

8

porous media on the hydrate phase equilibrium.

9 10

Table 1 Experimental schemes of gas hydrate formation kinetics Parameter

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Initial temperature To, oC

3.6

7.2

12.3

3.2

3.6

3.5

Initial pressure Po, MPa

10.50

10.60

10.90

6.01

9.20

11.20

Grain size, mesh number

40-60

40-60

40-60

40-60

40-60

40-60

Clay content, wt%

0

0

0

0

0

0

Porosity φ, %

45

45

45

45

45

45

Volume of reactor VR, ml

1000

1000

1000

1000

1000

1000

Swo, %

55.56

55.56

55.56

55.56

55.56

55.56

Sgo, %

44.44

44.44

44.44

44.44

44.44

44.44

Initial CH4 amount ngo, mol

1.113

1.109

1.223

0.633

0.966

1.171

Parameter

Case 7

Case 8

Case 9

Case 10

Case 11

Case 12

Initial temperature To, oC

3.6

3.5

3.5

20

20

20


6.01

6.08

6.07

4

6

8

Grain size, mesh number

40-60

40-60

80-100

40-60

40-60

40-60

Clay content, wt%

10

30

0

0

0

0

Porosity φ, %

45

45

45

45

45

45

Volume of reactor VR, ml

1000

1000

1000

1000

1000

1000

Swo, %

55.56

55.56

55.56

55.56

55.56

55.56

Sgo, %

44.44

44.44

44.44

44.44

44.44

44.44

Initial CH4 amount ngo, mol

0.637

0.645

0.644

0.400

0.600

0.801

11 12

3 EXPERIMENTAL RESULTS AND DISCUSSION

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3.1 Characteristics of hydrate phase equilibrium

14

It is generally recognized that the effect of macroporous media on CH4 hydrate phase

15

equilibrium curve can be neglected (Zang et al, 2015). However, in this study, compared with the

16

predicted phase equilibrium curve of CH4 hydrate at bulk, the hydrate phase equilibrium points

17

shifting to the right by about 4-5 oC was observed, although the porous media used is composed of

18

40-60 mesh sand, and has an average pore diameter of about 0.039 mm (see Figure 3a).

19

To date, many experiments have shown that the nanopore can make the hydrate phase

20

equilibrium curve move to the left. There exists a critical pore radius, such as the 58.68 nm given by


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1

Chen et al (2007). When the pore size is smaller than the critical value, the effect of porous media

2

on the phase equilibrium of hydrate cannot be ignored. As shown in Figure 3b, the published

3

experimental results based on the pore size between 6-30 nm show that as the pore size decreases,

4

the phase equilibrium curve of gas hydrate shifts to the left more serious. However, it should be

5

noted that most of these experiments were conducted using the silica gel grains. These gel grains

6

have nanopores inside and should be saturated with water in advance before experiments, while the

7

space between grains is filled with free CH4 gas. Gas hydrate will form in the nanopores of the

8

silica gel grains, where a capillary force exists between the hydrate and water phases (Zang et al,

9

2015). Due to the effect of capillary force, the critical CH4 solubility in the hydrate-water two-phase

10

system will increase. Hence, accordingly, a larger pressure is needed to reach the hydrate phase

11

equilibrium state.

12

Pressure, MPa

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0wt%NaCl at bulk 3.5wt%NaCl at bulk Experimental result in this study

-15

13 14

15 16 17 18

-10

-5

0 5 Temperature, oC

a. Experimental results in this study

10

15

20

b. Experimental results from literature (Zang et al, 2015)

c. The predicted hydrate phase curves considering different capillary effects (Liu et al, 2011) Figure 3 CH4 hydrate phase equilibrium curves in porous media

19

Liu et al (2011) has comprehensively analyzed the influence of various capillary effects on gas

20

hydrate phase equilibrium. As shown in Figure 3c, when only the capillary effect on hydrate phase

21

is considered, the hydrate phase equilibrium curve will shift to the left by about 1-5 oC. This result

22

agrees with the experimental results in Figure 3b. When only the capillary effect on gas phase is

23

considered, the hydrate phase equilibrium curve will shift to the right by about 3-8 oC.

24

Comparatively, the capillary effect on gas phase is more significant than that on hydrate phase,

25

which will result in the hydrate phase equilibrium moving to the right by 1-6 oC when the capillary ACS Paragon Plus Environment

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effects on both gas and hydrate phases are considered. In this case, the shift direction of hydrate

2

phase equilibrium relies on the relative size of the CH4 solubility in the water-hydrate system and

3

the CH4 solubility in the gas-water system. Both of these two CH4 solubilities are decided by the

4

pore size and the interfacial tension (IFT) between the water and gas/hydrate phases, but they have

5

different sensitivity to these factors. As a result, under the capillary effects on gas and hydrate

6

phases, a right shift of hydrate phase equilibrium curve is expected in the homogeneous porous

7

media. However, in the heterogeneous porous media, the effect of porous media on hydrate phase

8

equilibrium is more complex, depending on the specific conditions. For the experiments in this

9

study, the reactor was filled up with uniform sands, involving the capillary effects on both hydrate

10

and gas phases. Hence, to some extent, the right shift of the hydrate phase equilibrium curve can be

11

explained according to the above mechanisms.

12 13

3.2 Characteristics of hydrate formation kinetics

14

3.2.1 Hydrate formation rate and saturation

15

The main experimental results of cases 1 to 9 are shown in Table 2, and Figure 4. Table 2 lists

16

the time, the pressure drop, and the amount of CH4 consumed in each stage of hydrate formation in

17

porous media. The final saturation of each phase and the average hydrate growth rate are also

18

presented. However, not all of the experiments can clearly show the typical three stages of hydrate

19

formation in terms of the pressure drop in the reactor. Especially in the cases 5 and 6, the hydrate

20

nucleation stage was not observed (Figure 4b), but case 6 contributes the maximum pressure drop of

21

8.84 MPa, the highest hydrate saturation of 29.32% as well as the largest average hydrate growth

22

rate of 2593.81 mol/m3/day. In addition, the pressure drop induced by hydrate growth from hydrate

23

nucleation in cases 8 and 9 is hard to be distinguished (Figures 4c and 4d).

24 25

Table 2 Experimental results of CH4 hydrate formation kinetics Parameter tdissolution, min

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

Case 7

Case 8

Case 9

95

70

40

40

0

0

80

108

40

tnucleation, min

250

350

260

560

0

0

2516

2680

2960

tgrowth, min

1030

900

600

2400

1790

1140

2984

4010

6425


10.50

10.60

10.90

6.01

9.20

11.20

6.01

6.08

6.07

∆Pdissolution, MPa

0.31

0.21

0.42

0.14

0

0

0.38

0.51

0.18

∆Pnucleation, MPa

0.28

0.36

0.40

0.24

0

0

0.61

1.6

0.74

∆Pgrowth, MPa

6.16

3.60

0.50

2.35

5.93

8.84

1.45

0.7

0.7

Final pressure Pf, MPa

3.75

6.43

9.58

3.28

3.27

2.36

3.57

3.27

4.45

Gas consumed by dissolution,

0.033

0.022

0.043

0.015

0.000

0.000

0.040

0.054

0.019

Gas consumed by nucleation, mol

0.030

0.038

0.041

0.025

0.000

0.000

0.065

0.170

0.078

Gas consumed by growth, mol

0.653

0.377

0.051

0.248

0.623

0.924

0.154

0.074

0.074

mol


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Total gas consumed, mol

0.716

0.436

0.136

0.288

0.623

0.924

0.259

0.298

0.172

Finial hydrate saturation Shf, %

22.70

13.85

4.30

9.13

19.77

29.32

8.21

9.45

5.45

Residual water saturation Swf, %

36.52

43.95

51.95

47.90

38.98

30.98

48.68

47.63

50.99

Residual gas saturation Sgf, %

40.78

42.20

43.75

42.97

41.25

39.70

43.11

42.92

43.56

837.14

114.19

550.19

1384.3

2053.4

8

3

341.57

164.95

164.95

0.72

0.63

0.42

1.67

2.07

2.78

4.46

2028.6

1339.4

7

2

274.06

330.12

164.83

59.24

36.97

Hydrate concentration formed in growth stage Ch, mol/m3

1451.0 6

tgrowth, day Average hydrate growth rate dCh/dt, mol/m3/day

1.24

0.79

1113.6

2593.8

9

1

1 12

12 a. Initial temperature

Pressure MPa

Pressure, MPa

10 8 6 Case1: 3.6 ℃

4

Case2: 7.2 ℃

2

10

Case4: 6.0 MPa

8

Case5: 9.2 MPa

b. Initial Pressure

Case6: 11.2 MPa

6 4 2

Case3: 12.3 ℃

0

0 0

300

2

600 900 Time, min

1200

1500

0

500

1000

1500 Time, min

2000

2500

3000

7

6

c. Clay content Pressure, MPa

4 3 Case4: 0wt%Clay

2

Case7: 10wt%Clay

1

d. Sand grain size

6

5 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

Energy & Fuels

5 4 3 2

Case4: 40-60mesh Case9: 80-100mesh

1

Case8: 30wt%Clay

0

0

0

2000

4000 Time, min

6000

8000

0

2000

4000 6000 Time, min

8000

10000

3 4 5 6

Figures 5 and 6 presents the instantaneous hydrate formation rates and the hydrate saturations

7

in the reactor at different conditions. The cases 1-6 with large sand grain usually reach a large

8

hydrate formation rate and a large hydrate saturation. Corresponding to the clear distinction

9

between hydrate nucleation and growth, the instantaneous hydrate formation rates in cases 1-6 are

10

generally small at the beginning, but after a certain time, they start to increase sharply and then

11

decrease to a very low level which will last for a long time. The largest instantaneous hydrate

12

formation rate can be up to 1.5-3.0 mol/m3/min. Relatively, the cases 7-9 with small sand grain and

13

high clay content can only achieve small hydrate formation rate and saturation. In most of the time,

14

the hydrate formation rate usually keeps at a stable and small level below 0.15 mol/m3/min.

Figure 4 Pressure drop curves monitored in the reactor at different conditions

15


Energy & Fuels

35

3.0

Case1: 3.6 ℃

2.5

Case3: 12.3 ℃ Case5: 9.2 MPa

Case2: 7.2 ℃ Case4: 6.0 MPa Case6: 11.2 MPa

2.0 1.5 1.0

Case3: 12.3 ℃ Case6: 11.2 MPa

25 20 15 10

0

0.0 0

300

600

900

1200

0

1500

300

600

900

1200

1500

Time, min

Time, min

Figure 5 Instantaneous hydrate formation rates and hydrate saturations with time (cases 1-6) 1.5

10 9

Case7: 40-60mesh+10wt%clay

8

Hydrate saturation, %

1.2

Case4: 40-60mesh+0wt%Clay

Case8: 40-60mesh+30wt%clay 0.9

Case9: 80-100mesh+0wt%clay

0.6

0.3

7 6 5 4 3

Case4: 40-60mesh+0wt%clay Case7: 40-60mesh+10wt%clay Case8: 40-60mesh+30wt%clay Case9: 80-100mesh+0wt%clay

2 1

0.0

0

0

3 4 5 6

Case2: 7.2 ℃ Case5: 9.2 MPa

5

0.5

1 2

Case1: 3.6 ℃ Case4: 6.0 MPa

30

Hydrate saturation, %

Hydrate formatiion rate, mol/m3/min

3.5

Hydrate formation rate, mol/m3/min

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 10 of 23

1000

2000

3000 Time, min

4000

5000

6000

0

1000

2000

3000 Time, min

4000

5000

6000

Figure 6 Instantaneous hydrate formation rates and hydrate saturations with time (cases 4, 7-9)

3.2.2 Effects of initial temperature and pressure

7

8

The pressure drop curves of hydrate formation at different initial temperatures (based on cases

9

1 to 3) are shown in Figure 4a. The correlation of initial temperature with hydrate nucleation and

10

growth times, pressure drop, hydrate saturation, and hydrate growth rate have been analyzed and

11

shown in Figure 7. It can be seen that the hydrate nucleation time varies in a range of 250-350 min

12

while the corresponding pressure drop is between 0.28-0.40 MPa. Overall, the initial temperature

13

has a weak effect on the hydrate nucleation. Comparatively, a strong correlation between hydrate

14

growth and initial temperature can be observed. As the initial temperature decreases from 12.3 to

15

3.6 oC, the pressure drop of hydrate growth stage increases from 0.5 to 6.16 MPa, while the pressure

16

in the reactor needs more time to reach stable (from 600 to 1030 min). Accordingly, the final

17

hydrate saturation and the hydrate growth rate increase from 4.30% to 22.70%, and from 274.06 to

18

2028.67 mol/m3/day, respectively with the decline of initial temperature in the reactor. Low

19

temperature is beneficial to achieving a large hydrate growth rate and a large final hydrate

20

saturation.

Effect of initial temperature

21


0.4

1000

0.2 t_nucleation 0.1

∆P_nucleation 6

9

12

800

t_growth

600

∆P_growth

400 y = -0.6477x + 8.4075 R² = 0.998

200 0

0 3

0

15

3

6

9

T, oC

1

c. Final hydrate saturation dCh/dt, mol/m3/day

Shf, %

15

d. Average hydrate growth rate

2500

20 15 y = -2.0985x + 29.776 R² = 0.994

5

12

T, oC

25

10

7 6 5 4 3 2 1 0

y = -50.052x + 1228.7 R² = 0.9844

∆Pgrowth, MPa

1200

0.3 y = 0.0134x + 0.2435 R² = 0.9186

b. Hydrate growth time and pressure drop

0.5

tgrowth, min

y = -0.1047x + 287.47 R² = 7E-05

∆Pnucleation, MPa

a. Hydrate nucleation time and pressure drop

400 350 300 250 200 150 100 50 0 0

0

2000 1500 1000 y = -202.16x + 2770.7 R² = 0.9994

500 0

0

3

6

9 T,

2 3

12

15

0

3

6

oC

9

12

15

T, oC

Figure 7 Effect of initial temperature on CH4 hydrate formation in porous media

4 5

6

Figure 4b and Figure 8 show the gas hydrae formation characteristics at different initial

7

pressures (based on cases 4, 5 and 6). It can be seen that at the initial pressure of 6.01 MPa (case 4),

8

a typical hydrate formation process can be observed. The stages of hydrate nucleation and growth

9

can be easily distinguished according to the pressure drop. However, as the initial pressure increases

10

to 9.20-11.20 MPa, the hydrate nucleation and growth nearly proceed at the same time due to the

11

great driving force for hydrate formation. A sharp pressure drop without hydrate nucleation stage

12

was observed at the beginning of the experiment. These results are in accordance with the studies

13

from Zang et al (2013) and Liu et al (2016). In addition, as seen in Figure 8, with the increase of the

14

initial pressure in the reactor, the pressure drop during hydrate growth stage increases from 2.35 to

15

8.84 MPa along with the growth time of hydrate declining from 2400 to 1140 min. The final hydrate

16

saturation and hydrate growth rate increase from 9.13% to 29.32%, and from 330.12 to 2593.81

17

mol/m3/day, respectively. High pressure is also beneficial to achieving a large hydrate growth rate

18

and a large final hydrate saturation.

Effect of initial pressure

∆P_nucleation

400

200

0.10

0 4

19

6

8 P, MPa

3000

0.15

y = -0.0489x + 0.5107 R² = 0.8541

100

0.25 0.20

y = -114.15x + 1191.5 R² = 0.8541

300

3500

10

12

10 y = 1.2386x - 5.1975 R² = 0.9948

2500 2000

6

y = -238.01x + 3872 R² = 0.9777

1500

4 t_growth

1000

0.05

500

0.00

0

8

2

∆P_growth

0 4

6


8 P, MPa

10

12

∆Pgrowth, MPa

500


0.30

tgrowth, min

t_nucleation

∆Pnucleation, MPa


600

tnucleation, min

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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tnucleation, min

Page 11 of 23

Energy & Fuels


c. Final hydrate saturation

3000

30

y = 3.8395x - 14.397 R² = 0.9899

25

Shf, %

dCh/dt，mol/m3/day

35

20 15 10 5

2500 2000

y = 418.57x - 2339 R² = 0.9084

1500 1000 500 0

0 4

1 2 3

6

8 P, MPa

10

4

12

6

8 P, MPa

10

12

Figure 8 Effect of initial pressure on CH4 hydrate formation in porous media

4

5

The difference between gas pressure and hydrate phase equilibrium pressure at the same

6

temperature (pg-pe) is defined as the reaction driving force of hydrate formation. The gas hydrate

7

formation characteristics at different driving forces are shown in Figure 9 (based on cases 1-6). It

8

can be seen that the driving forces for hydrate formation in this study are mainly distributed

9

between 0.2 and 6 MPa. As the driving force increases, the hydrate nucleation time becomes shorter

10

and shorter, and the time of hydrate growth also declines slightly. However, overall, the correlation

11

between driving force and nucleation/growth time is weak. Comparatively, both of the final hydrate

12

saturation and hydrate formation rate have a strong correlation with the driving force. The former

13

fits the linear curve of y = 0.0036x + 3.7527 with a correlation coefficient R2 = 0.9909, while the

14

latter matches the equation y = 0.3313x + 93.116 with an R2 of 0.8584.

Effect of reaction driving force

15 a. Hydrate nucleation time

600

b. Hydrate growth time 3000

300 200 100

2000 1500 1000 500

0 0

2000

16

4000 pg -pe, kPa

6000

0

8000

0

c. Final hydrate saturation

35

2000

dCh/dt, mol/m3/day

20 15 10 5 0

2500 y = 0.3313x + 93.116 R² = 0.8584

2000 1500 1000 500

2000

4000 pg-pe, kPa

6000

8000

0

2000

4000 pg-pe, kPa

6000

Figure 9 Effect of driving force on CH4 hydrate formation in porous media

19

3.2.3 Effects of clay content and sand grain size

8000

0

0

21

6000


y = 0.0036x + 3.7527 R² = 0.9909

25

20

4000 pg-pe, kPa

3000

30

17 18

y = -0.003x + 1320.8 R² = 0.0001

2500 y = -0.0584x + 445.96 R² = 0.4909

400

tgrowth, min

tnucleation, min

500

Shf, %

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 12 of 23

Effect of clay content ACS Paragon Plus Environment

8000

Page 13 of 23

1

The effect of clay content on the gas hydrate formation characteristics has been indicated in

2

Figure 4c and Figure 10 (based on cases 4, 7, 8). As the clay content in the sand increases from 0wt%

3

to 30wt%, the induction time of hydrate nucleation increases from 560 to 2680 min along with the

4

pressure drop in the reactor increasing from 0.24 to1.6 MPa. It can also be seen that when the clay

5

content in the sand is larger than 10wt%, the induction time of hydrate nucleation is almost

6

unchanged, but the linear increase of pressure drop in hydrate nucleation stage with clay content

7

increase can still be observed in the reactor. For the hydrate growth stage, with the increase of clay

8

content, the pressure drop induced by hydrate growth becomes smaller and smaller, but more and

9

more time is needed for the pressure in the reactor to reach stable. As the result of the rich clay

10

contained in the sand, the contact between gas and water in the reactor is often restricted, which will

11

further affect the hydrate growth. Hence, a significant decrease of hydrate growth rate from 330.12

12

to 59.24 mol/m3/day was observed as the clay content increases. However, because the total

13

pressure drops monitored in cases 4, 7 and 8 during experimental time are close, the final hydrate

14

saturations formed in these cases are very similar, varying from 8.21% to 9.45%, of which case 7

15

with 10wt% clay gives the smallest one.

16

2500

1.5

2000

t_nucleation

1500

1.0

∆P_nucleation

1000

0.5

y = 0.0459x + 0.2043 R² = 0.9955

500 0

5000 ∆Pnucleation, MPa tgrowth, min

tnucleation, min

3000


2.0

y = 61.743x + 1095.4 R² = 0.6394

4000

10

17

20 Clay content, wt%

30

2000

0

18 19 20

10


30

0.5

∆P_growth

0.0 0

mol/m3/day dCh/dt,

40

1.0

0

40

y = 0.0183x + 8.685 R² = 0.1868

1.5

t_growth

1000

c. Final hydrate saturation 9.6 9.4 9.2 9.0 8.8 8.6 8.4 8.2 8.0

2.0 y = -0.0525x + 2.2 R² = 0.9423

3000

0.0 0

2.5 y = 53.329x + 2420.3 R² = 0.9989

∆Pgrowth, MPa


3500

Shf, %

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

Energy & Fuels

10


30

40


350 300 250 200 150 100 50 0

y = -8.4937x + 297.98 R² = 0.903

0

10


30

40

Figure 10 Effect of clay content on CH4 hydrate formation in porous media

21

In addition, an obvious phenomenon should be noted that as the clay content in the sand

22

increases, to distinguish the stages of hydrate nucleation and growth becomes more and more

23

difficult in terms of the pressure drop monitored in the reactor. Especially in the case 8 where the

24

clay content is up to 30wt%, only a weak pressure decline was observed between the hydrate

25

nucleation and growth stages. According to the linear correlation between the clay content and the


Energy & Fuels

1

pressure drop of hydrate growth, it is speculated that clear pressure decline between hydrate

2

nucleation and growth in the reactor will disappear if the clay content is more than 41.9wt%. The

3

hydrate nucleation will contribute a remarkable pressure drop at the early stage of hydrate formation.

4

These results indicate that the clay content in sediments has an important effect on the hydrate

5

formation kinetics.

6

7

The effect of sand grain size on the hydrate formation characteristics has been shown in Figure

8

4d and Figure 11 (based on cases 4 and 9 with sand grain sizes of 40-60 mesh and 80-100 mesh,

9

respectively). It can be seen that as the sand grain size decreases (namely, as the pore diameter

10

decreases from 0.039 to 0.023 mm), both of the lasting time and pressure drop of hydrate nucleation

11

increase, but the pressure drop in the hydrate growth stage decreases from 2.35 to 0.7 MPa. More

12

time is needed for hydrate growth to reach the stable pressure in the reactor (from 2400 to 6425

13

min). Especially when the sand grain size is 80-100 mesh, it is hard to distinguish the hydrate

14

nucleation and growth stages according to the pressure drop. This is similar to the effect of clay

15

content above. Small pore size due to small sand grain is not beneficial to the sufficient contact

16

between gas and water in the reactor. The formed hydrate will further block the pores and lower the

17

hydrate growth rate. Hence, as a result, when the sand grain size decreases from 40-60 to 80-100

18

mesh, the hydrate saturation decreases from 9.13% to 5.45%, while the hydrate growth rate is

19

reduced from 330.12 to 36.97 mol/m3/day.

Effect of sand grain size

20 b. Hydrate growth time and pressure drop

0.4 t_nucleation ∆P_nucleation

0.2 0

c. Final hydrate saturation 350

dCh/dt, mol/m3/day

10 8 6 4 2 0

∆P_growth

1.5 1.0 0.5 0.0


300 250 200 150 100 50 0

40-60

23 24 25

2.0 t_growth

40-60 80-100 Sand grain size, mesh no.


21 22

2.5

7000 6000 5000 4000 3000 2000 1000 0

∆Pgrowth, MPa

0.6

tgrowth, min

0.8

∆Pnucleation, MPa

tnucleation, min

a. Hydrate nucleation time and pressure drop 3500 3000 2500 2000 1500 1000 500 0

Shf, %

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 14 of 23

80-100 Sand grain size, mesh no.


Figure 11 Effect of sand grain size on CH4 hydrate formation in porous media

26

27

At the ideal conditions when gas and water are distributed evenly in porous media, the gas and

Effect of contact between gas and water


Page 15 of 23

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

Energy & Fuels

1

water for hydrate formation can contact each other adequately. Rock particles and minerals in

2

sediments can be used as the crystal nucleus for hydrate nucleation. The capillary force can drive

3

the water to the gas-water interface to promote the hydrate formation. In this case, smaller sand

4

grain can provide more contact area for gas and water as well as larger capillary pressure for faster

5

water supply. Hence, from this point of view, it seems reasonable that the hydrate formation rate

6

will increase as the sand grain size decreases (Zhang et al, 2011).

7

However, under most real conditions of gas hydrate accumulation, the gas and water in

8

sediments cannot contact each other uniformly. In the reactor of this study, the injected CH4 gas will

9

accumulate at the top of the reactor. The middle zone of the reactor is a gas-water transition belt,

10

while the bottom of the reactor is only filled with water in pores. The gas-water transition belt is the

11

ideal zone where gas and water can contact each other sufficiently and form gas hydrate at a fast

12

rate. However, as more and more hydrates form, the solid gas hydrate will block the pores, and

13

restrict the contact between the gas at the top and the water at the bottom of the reactor. Especially

14

when the clay content is high, or the sand grain size is small, the small-size pore is more easily

15

plugged by the solid hydrate. In this case, the effective contact between gas and water will mainly

16

rely on the capillary force driving the bottom water to the top as well as the dissolved gas in water

17

diffusing to the bottom of the reactor. This process can present a very slow apparent hydrate

18

formation rate, and further reach a low hydrate saturation. In addition, the nucleation process of the

19

hydrate is more likely to occur on the weak hydrophilic surface (Bai, 2013), but the presence of clay

20

minerals in the reactor will significantly enhance the hydrophilicity of the pore surface, which tends

21

to increase the hydrate nucleation time. All of these factors can cause the difficult judgment of the

22

hydrate nucleation and growth stages according to the pressure variation in the reactor.

23 24

3.3 Reaction kinetic model of hydrate formation

25

3.3.1 Reaction kinetic model of hydrate nucleation

26

Natural gas hydrate nucleation rate (J) can be calculated using the model proposed by

27

(Natarajan et al, 1994), as shown in the following equation (8). It is an expression relevant to the

28

oversaturation factor of CH4 in water (S). The induction time of hydrate nucleation (t) can be

29

further predicted using the empirical equation (9).

30

‫ ܵ(݇ = ܬ‬− 1)௡

（ 8）

31

‫ߙ = ݐ‬/‫ܬ‬௥

（9）

32

where J is the hydrate nucleation rate, mol/m3/day; S is the oversaturation factor of CH4 in water; t

33

is the induction time of hydrate nucleation, day; k, n, α, and r are constant coefficients.

34

The oversaturation factor S can be calculated using the apparent CH4 concentration in water ACS Paragon Plus Environment

Energy & Fuels

1

divided by the CH4 solubility in water at the same temperature and pressure. The apparent CH4

2

concentration in water can be estimated based on the pressure drop in the gas dissolution stage at

3

the beginning of the experiment, while the CH4 solubility in water can be predicted using the

4

Duan’s model (Duan et al, 1992). Based on the experimental results of the first 4 cases (cases 5 and

5

6 were not used because no obvious hydrate nucleation stage was observed), the parameters S-1 and

6

J were calculated and listed in Table 3. Through parameter regression, the constants k=784.16,

7

n=0.4644, α=14.599, and r=-0.653 were obtained (see Figure 12). It can be seen that the rate of

8

hydrate nucleation strongly depends on the CH4 oversaturation in porous water. As the CH4

9

oversaturation in water increases, the hydrate nucleation rate rises from 260 to 911 mol/m3/day,

10

while the induction time of hydrate crystallization declines from 0.389 to 0.181 day. However, the

11

correlation between the hydrate nucleation rate and the P-T conditions is not obvious in this study.

12 13 Parameter

Table 3 Main hydrate nucleation parameters calculated Case 1 Case 2 Case 3

Case 4

t, day

0.174

0.243

0.181

0.389

S-1

0.753

0.256

1.530

0.195

684

620

911

260

3

J, mol/m /day 14

hyrate induction time t, day

1200 Hydrate nucleation rate J, mol/m3/day

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 16 of 23

a. J-(S-1)

1000 800 600

y = 784.16x0.4644 R² = 0.6803

400 200 0 0.0

15 16 17 18

0.5

1.0 S-1

1.5

2.0

0.50

b. t-J

y = 14.599x-0.653 R² = 0.8976

0.40 0.30 0.20 0.10 0.00 0

200

400 600 J, mol/m3/day

800

1000

Figure 12 Parameter fitting results of hydrate nucleation kinetic model

3.3.2 Reaction kinetic model of hydrate growth

19

As mentioned above, the difference between the CH4 gas pressure (pg) and the three-phase

20

(gas-water-hydrate) equilibrium pressure (pe) is the driving force for hydrate growth. When pg>pe,

21

gas hydrate forms, when pg

Reaction Kinetic Characteristics and Model of Methane Hydrate

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