# Experimental and Modeling Studies on the Prediction of Gas Hydrate Formation

Authors: Jian-Yi Liu; Jing Zhang; Yan-Li Liu; Xiao-Hua Tan; Jie Zhang
Journal: Journal of Chemistry
 (2015)

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## Abstract

On the base of some kinetics model analysis and kinetic observation of hydrate formation process, a new prediction model of gas hydrate formation is proposed. The analysis of the present model shows that the formation of gas hydrate not only relevant with gas composition and free water content but also relevant with temperature and pressure. Through contrast experiment, the predicted result of the new prediction method of gas hydrate crystallization kinetics is close to measured result, it means that the prediction method can reflect the hydrate crystallization accurately.


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## Body

## 1. Introduction

During the exploitation process, the gas well sometimes closed because of plugging in wellbore or surface pipeline which is caused by gas hydrate [1–4]. In order to solve a series of plugging problems caused by hydrate in oil field and develop natural gas hydrate resources more effectively and utilize hydrate technology more reasonably, the research on natural gas hydrate crystallization kinetics mechanism becomes very necessary [5, 6].An operation step of crystal nucleus growth process is an important factor need to research in the study of crystallization kinetics [7]. In different system, many factors can be used to control crystal nucleus growth process, such as diffusion, heat transfer, stirring rate, reaction kinetics, and heat exchange rate on surface of crystal [8–10]. In view of the above factors, many researchers propose the crystallization kinetics model which describes the nucleation based on mass transfer theory, crystallization theory, and two-film gas-liquid mass transfer theory [11, 12].The generation of hydrate is actually the nucleation and crystal growth process. Kinetics of hydrate formation is related to generation rate, pressure, temperature, and so forth. The process can be clearly divided into three steps: at first the generation of crystal nucleus with critical radius, then solid crystal nucleus growth, and at last the components transfer to solid-liquid interface of nuclear at aggregation state [13–15].Many factors affect the generation of natural gas hydrate; there are three main points. (1) When the gas temperature is equal to or lower than the water dew point and is accompanied with free water or liquid water, then hydrate formed. (2) In condition of certain pressure and gas composition, the temperature is lower than the hydrate formation temperature; then hydrate formed. (3) The high operating pressure will rise the hydrate formation temperature [16].This paper developed a new prediction method of gas hydrate crystallization kinetics according to the shrinkage bubble model and considering the variation of pressure with time at the same time, to establish a new method for the prediction of natural gas hydrate.


## 2. Model

### 2.1. Hydrate Growth Dynamic

During the hydrate formation process there is transfer phenomena in the hydrate-gas-water [17–19]. The kinetic observation of hydrate formation process is shown in Figure 1. From the figure we can know that at first hydrate mainly gathered at the air-water interface layer; when the temperature is lower than the hydrate phase equilibrium temperature, hydrate nucleation formed quickly by gas and water molecules inside the bubble [20, 21]. The generation process of crystal nucleus is the process that water diffuse into a bubble and gas in bubble diffuse out of bubble; finally the bubble in hydrate gradually reduced and even disappeared then hydrate crystals formed. Experiments show that the hydrate formation process is controlled by the transmission rate of gas and water molecules, through the establishment of hydrate formation kinetics method can describe the generation process [22].Figure 1
Kinetic observation of hydrate formation process.


### 2.2. Shrinkage Bubble Kinetics

Through the hydrate growth kinetic observation we can know that during the growth process of hydrate crystals the bubbles transform into hydrate; the process is shown in Figure2. In Figure 2, the exterior is water, the internal is gas, and the ring is hydrate.Figure 2
Process of a bubble transforming into hydrate.Hydrate volume in hydrate crystals is(1)
V
h
=
4
3
π
r
h
3
-
r
b
3
,where r
h is outer radius of hydrate, r
b is bubble radius, and V
h is hydrate volume in hydrate crystals.The growth rate of hydrate is(2)
d
V
h
d
t
=
4
π
r
h
2
d
r
h
d
t
-
r
b
2
d
r
b
d
t
.During the formation process of hydrates, the chemical potential in phase equilibrium systemization is equal. According to gas adsorption model and the law of diffusion, the hydrate formation rate equation is obtained as follows(3)
d
V
h
d
t
=
4
π
D
r
b
r
h
r
h
-
r
b
p
b
-
p
d
p
b
,where p
b is inner air pressure of bubble and p
d is decomposition pressure. D is the mass transfer coefficient and it can be expressed as(4)
D
=
1
-
y
d
D
h
a
y
d
+
v
c
d
D
h
w
,where y
d is lattice occupancy, v is vacant hole numbers of each water molecule, c
d is water solution concentration under the decomposition pressure of hydrate, D
h
a is mass transfer coefficient between hydrate and gas, and D
h
w is mass transfer coefficient between hydrate and water.Supposing the gas in bubble and hydrate is ideal gas, then(5)
V
b
p
b
+
V
h
p
h
a
ϕ
=
V
b
0
p
b
0
,where ϕ is porosity and V
b is bubble volume. p
h
a is the pressure when the gas density in bubble is equal to the gas density in hydrate, ρ
h
a, which can be expressed as(6)
p
h
a
=
ρ
h
a
R
g
T
M
.Because the reaction is controlled by mass transfer, so the change rate of hydrate volume is(7)
ω
h
=
-
d
V
b
/
d
t
+
1
-
d
h
a
d
V
b
/
d
t
V
b
+
V
h
.From the experiment we can know that hydrate is plastic materials, so(8)
p
1
-
p
b
=
4
3
K
c
ω
-
c
ω
,where ω is compressibility of vacant hole.Then forward formula becomes(9)
p
1
-
p
b
=
4
3
K
c
ω
h
r
h
3
-
r
b
3
r
h
3
,
d
V
b
d
t
=
-
V
b
p
b
d
p
b
d
t
+
p
h
a
ϕ
p
b
d
V
h
d
t
.By comprehensive analysis(10)
r
h
=
3
V
b
0
p
b
0
-
V
b
p
b
4
π
p
h
a
ϕ
+
r
b
3
1
/
3
.Dividing the formation process of gas hydrate into many small blocks of time and assuming that the pressure in bubbles is unchanged mean thatp
b is a constant. From the above formulas the relationship that r
b changes with time can be known; then the rate of hydrate formation can be known, finally:(11)
p
1
-
p
b
=
4
3
K
c
r
h
3
-
r
b
3
r
h
3
×
p
b
p
h
a
ϕ
/
p
b
-
1
+
d
h
a
4
π
D
r
b
r
h
r
h
-
r
b
p
b
-
p
d
/
p
h
×
V
h
p
b
+
V
b
0
p
b
0
-
V
h
p
h
a
ϕ
-
1
.From the above formulasr
h and r
b can be calculated. r
h and r
b are corresponding to p
b, and p
b is corresponding to t, so the relationship between t
-
p
b, r
h, and r
b at the whole reaction time can be calculated.Through shrinkage bubble kinetics model the relationship between inner air pressure of bubble, outer radius of hydrate, bubble radius, and time can be known. But in the actual conditions, only environmental pressure can be detected, so it is necessary to consider relationship between environmental pressure and time to improve the shrinkage bubble kinetics.


### 2.3. Improvement of Shrinkage Bubble Kinetics Model

According to the constant volume substance equilibrium rule the alternation law of pressure with time can be known. In the experiments, the volume is constant which is equal to the volume of natural gas and water before hydrate formation and equal to the volume of residual gas, water, and hydrate after hydrate formation; then the pressure change. The process is shown in Figure3.Figure 3
Chart of hydrate formation.According to the principle of material balance, before hydrate formation there are(12)
V
sum
=
V
g
+
V
w
,
V
g
=
Z
T
p
sc
V
g
sc
p
1
T
sc
,
V
w
=
B
w
V
w
sc
,where V
g is gas volume in the vessel, m3. V
w is water volume in the vessel, m3. Z is Z-factor at the vessel pressure, dimensionless. T is temperature in vessel, K. p
1 is the pressure in vessel before hydrate formation, MPa. T
sc is the temperature at standard state, K. p
sc is the pressure at standard state, MPa. V
g
sc is the injected gas volume at standard state, m3. V
w
sc is the injected water volume at standard state, m3. B
w is the volume coefficient of water, dimensionless.After hydrate formation there are(13)
V
sum
=
V
g
′
+
V
w
′
+
V
h
,
V
w
′
=
V
w
-
V
w
c
,
p
2
=
N
h
R
Z
T
V
sum
-
V
w
′
-
V
h
,
V
w
c
=
K
N
h
M
w
ρ
w
,
N
h
=
V
h
ρ
h
M
h
,
V
h
=
n
v
h
,
n
≤
S
G
W
π
3
v
h
/
4
π
2
/
3
,where V
g
′ is gas volume in the vessel, m3. V
w
′ is water volume in the vessel, m3. V
h is hydrate volume in the vessel, m3. V
w
c is consumption water volume in the vessel, m3. p
2 is the pressure in the vessel after hydrate formation, MPa. N
h is molar of generated hydrate, K is molar of water when generate 1 mole hydrate. M
w is hydrate molecular weight, g/mol. ρ is hydrate density, kg/m3. n is number of generated bubbles. v
h is hydrate volume of each generated bubbles, m3. S
G
W is interface area between gas and water, m2.


## 2.1. Hydrate Growth Dynamic

During the hydrate formation process there is transfer phenomena in the hydrate-gas-water [17–19]. The kinetic observation of hydrate formation process is shown in Figure 1. From the figure we can know that at first hydrate mainly gathered at the air-water interface layer; when the temperature is lower than the hydrate phase equilibrium temperature, hydrate nucleation formed quickly by gas and water molecules inside the bubble [20, 21]. The generation process of crystal nucleus is the process that water diffuse into a bubble and gas in bubble diffuse out of bubble; finally the bubble in hydrate gradually reduced and even disappeared then hydrate crystals formed. Experiments show that the hydrate formation process is controlled by the transmission rate of gas and water molecules, through the establishment of hydrate formation kinetics method can describe the generation process [22].Figure 1
Kinetic observation of hydrate formation process.


## 2.2. Shrinkage Bubble Kinetics

Through the hydrate growth kinetic observation we can know that during the growth process of hydrate crystals the bubbles transform into hydrate; the process is shown in Figure2. In Figure 2, the exterior is water, the internal is gas, and the ring is hydrate.Figure 2
Process of a bubble transforming into hydrate.Hydrate volume in hydrate crystals is(1)
V
h
=
4
3
π
r
h
3
-
r
b
3
,where r
h is outer radius of hydrate, r
b is bubble radius, and V
h is hydrate volume in hydrate crystals.The growth rate of hydrate is(2)
d
V
h
d
t
=
4
π
r
h
2
d
r
h
d
t
-
r
b
2
d
r
b
d
t
.During the formation process of hydrates, the chemical potential in phase equilibrium systemization is equal. According to gas adsorption model and the law of diffusion, the hydrate formation rate equation is obtained as follows(3)
d
V
h
d
t
=
4
π
D
r
b
r
h
r
h
-
r
b
p
b
-
p
d
p
b
,where p
b is inner air pressure of bubble and p
d is decomposition pressure. D is the mass transfer coefficient and it can be expressed as(4)
D
=
1
-
y
d
D
h
a
y
d
+
v
c
d
D
h
w
,where y
d is lattice occupancy, v is vacant hole numbers of each water molecule, c
d is water solution concentration under the decomposition pressure of hydrate, D
h
a is mass transfer coefficient between hydrate and gas, and D
h
w is mass transfer coefficient between hydrate and water.Supposing the gas in bubble and hydrate is ideal gas, then(5)
V
b
p
b
+
V
h
p
h
a
ϕ
=
V
b
0
p
b
0
,where ϕ is porosity and V
b is bubble volume. p
h
a is the pressure when the gas density in bubble is equal to the gas density in hydrate, ρ
h
a, which can be expressed as(6)
p
h
a
=
ρ
h
a
R
g
T
M
.Because the reaction is controlled by mass transfer, so the change rate of hydrate volume is(7)
ω
h
=
-
d
V
b
/
d
t
+
1
-
d
h
a
d
V
b
/
d
t
V
b
+
V
h
.From the experiment we can know that hydrate is plastic materials, so(8)
p
1
-
p
b
=
4
3
K
c
ω
-
c
ω
,where ω is compressibility of vacant hole.Then forward formula becomes(9)
p
1
-
p
b
=
4
3
K
c
ω
h
r
h
3
-
r
b
3
r
h
3
,
d
V
b
d
t
=
-
V
b
p
b
d
p
b
d
t
+
p
h
a
ϕ
p
b
d
V
h
d
t
.By comprehensive analysis(10)
r
h
=
3
V
b
0
p
b
0
-
V
b
p
b
4
π
p
h
a
ϕ
+
r
b
3
1
/
3
.Dividing the formation process of gas hydrate into many small blocks of time and assuming that the pressure in bubbles is unchanged mean thatp
b is a constant. From the above formulas the relationship that r
b changes with time can be known; then the rate of hydrate formation can be known, finally:(11)
p
1
-
p
b
=
4
3
K
c
r
h
3
-
r
b
3
r
h
3
×
p
b
p
h
a
ϕ
/
p
b
-
1
+
d
h
a
4
π
D
r
b
r
h
r
h
-
r
b
p
b
-
p
d
/
p
h
×
V
h
p
b
+
V
b
0
p
b
0
-
V
h
p
h
a
ϕ
-
1
.From the above formulasr
h and r
b can be calculated. r
h and r
b are corresponding to p
b, and p
b is corresponding to t, so the relationship between t
-
p
b, r
h, and r
b at the whole reaction time can be calculated.Through shrinkage bubble kinetics model the relationship between inner air pressure of bubble, outer radius of hydrate, bubble radius, and time can be known. But in the actual conditions, only environmental pressure can be detected, so it is necessary to consider relationship between environmental pressure and time to improve the shrinkage bubble kinetics.


## 2.3. Improvement of Shrinkage Bubble Kinetics Model

According to the constant volume substance equilibrium rule the alternation law of pressure with time can be known. In the experiments, the volume is constant which is equal to the volume of natural gas and water before hydrate formation and equal to the volume of residual gas, water, and hydrate after hydrate formation; then the pressure change. The process is shown in Figure3.Figure 3
Chart of hydrate formation.According to the principle of material balance, before hydrate formation there are(12)
V
sum
=
V
g
+
V
w
,
V
g
=
Z
T
p
sc
V
g
sc
p
1
T
sc
,
V
w
=
B
w
V
w
sc
,where V
g is gas volume in the vessel, m3. V
w is water volume in the vessel, m3. Z is Z-factor at the vessel pressure, dimensionless. T is temperature in vessel, K. p
1 is the pressure in vessel before hydrate formation, MPa. T
sc is the temperature at standard state, K. p
sc is the pressure at standard state, MPa. V
g
sc is the injected gas volume at standard state, m3. V
w
sc is the injected water volume at standard state, m3. B
w is the volume coefficient of water, dimensionless.After hydrate formation there are(13)
V
sum
=
V
g
′
+
V
w
′
+
V
h
,
V
w
′
=
V
w
-
V
w
c
,
p
2
=
N
h
R
Z
T
V
sum
-
V
w
′
-
V
h
,
V
w
c
=
K
N
h
M
w
ρ
w
,
N
h
=
V
h
ρ
h
M
h
,
V
h
=
n
v
h
,
n
≤
S
G
W
π
3
v
h
/
4
π
2
/
3
,where V
g
′ is gas volume in the vessel, m3. V
w
′ is water volume in the vessel, m3. V
h is hydrate volume in the vessel, m3. V
w
c is consumption water volume in the vessel, m3. p
2 is the pressure in the vessel after hydrate formation, MPa. N
h is molar of generated hydrate, K is molar of water when generate 1 mole hydrate. M
w is hydrate molecular weight, g/mol. ρ is hydrate density, kg/m3. n is number of generated bubbles. v
h is hydrate volume of each generated bubbles, m3. S
G
W is interface area between gas and water, m2.


## 3. Experiment

### 3.1. Gas Sample

In this experiment using the gas sample, the content of main gas components is measured by gas chromatography, and the components are shown in Table1.Table 1
Gas components.
Components
N2
CO2
C1
C2
C3
iC4
nC4
iC5
nC5
C6
Content(mol%)
2.012
0.2659
82.9622
9.6578
3.5692
0.3044
0.6639
0.1687
0.2064
0.1894


### 3.2. Water Sample

In this experiment using the field water, the salinity of formation water is 14477 mg/L and pH value is 5.4. The analysis data of water is shown in Table2.Table 2
Water analysis.
Item
K+
Na+
Ca2+
Mg2+
Cl−
SO
4
2
-
HCO
3
-
Total salinity
Content(mg/L)
365
4602
412
96
8007
535
460
14477Injecting 10 mL formation water into vessel, then injecting gas until the pressure of vessel up to 14.7 MPa, and keeping the temperature at 20°C. It has been known that the temperature of hydrate formation is 18°C when the pressure is 14.7 MPa. By decreasing the temperature to 9°C we can obtain the supercooled degree, that is, 9°C. We observe and record the change of the pressure in the vessel.


## 3.1. Gas Sample

In this experiment using the gas sample, the content of main gas components is measured by gas chromatography, and the components are shown in Table1.Table 1
Gas components.
Components
N2
CO2
C1
C2
C3
iC4
nC4
iC5
nC5
C6
Content(mol%)
2.012
0.2659
82.9622
9.6578
3.5692
0.3044
0.6639
0.1687
0.2064
0.1894


## 3.2. Water Sample

In this experiment using the field water, the salinity of formation water is 14477 mg/L and pH value is 5.4. The analysis data of water is shown in Table2.Table 2
Water analysis.
Item
K+
Na+
Ca2+
Mg2+
Cl−
SO
4
2
-
HCO
3
-
Total salinity
Content(mg/L)
365
4602
412
96
8007
535
460
14477Injecting 10 mL formation water into vessel, then injecting gas until the pressure of vessel up to 14.7 MPa, and keeping the temperature at 20°C. It has been known that the temperature of hydrate formation is 18°C when the pressure is 14.7 MPa. By decreasing the temperature to 9°C we can obtain the supercooled degree, that is, 9°C. We observe and record the change of the pressure in the vessel.


## 4. The Results and Discussions

As shown in Figure4, at first the pressure in the vessel declined rapidly; then the decrease rate become slow and steady gradually. The predicted pressure is close to measured pressure. But in the actual conditions, only environmental pressure can be detected, so it is just considered relationship between environmental pressure and time to improve the shrinkage bubble kinetics.Figure 4
Comparison of the results of prediction method with experiment.


## 5. Conclusion

The predicted result of the new prediction method of gas hydrate crystallization kinetics is close to measured result; it means that the prediction method can reflect the hydrate crystallization accurately. In actual application the various parameters should be modified according to the practical situation.



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*Source: 198176-2015-03-19.xml*