prediction of methane hydrate equilibrium pressurs in...

2nd National Iranian Conference on Gas Hydrate (NICGH)

Semnan University

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Prediction of methane hydrate equilibrium pressurs in the

presence of aqueous Imidazolium-based ionic liquid solutions

using Electrolyte Cubic Square Well Equation of State

A. Haghtalab* 1, M. Zare1, A. N. Ahmadi2, K. Nazari2,G. Khatinzadeh2

1- Department of Chemical Engineering, Tarbiat Modares University, P.O. Box: 14115-143, Tehran, Iran

2- Center of chemistry and petrochemical, Research Institute of Petroleum Industry, Tehran, Iran

[email protected]

Abstract Electrolyte Cubic Square-Well Equation of State, eCSW EoS, based upon the Helmholtz free

energy consists of the one non-electrolyte term and the two electrolyte terms. The non-electrolyte

term is cubic square-well equation of state (CSW EoS) and the two electrolyte contributions

consist of a Born energy and the mean spherical approximation terms. In this work, eCSW EoS is

coupled with the van der Waals-Platteuw model and applied to predict the hydrate dissociation

pressures of the methane+ ionic liquid+ water systems. Ferthermore, the adjustable paramers of

the imidazolium based ionic liquid solutions calculated by using experimental data in litreture.A

good agreement between the results of the model with the experimental data indicates the

reliability of this model to predict the hydrate equilibrium conditions.

Keywords: eCSW EoS, ionic liquid, hydrate, methane, imidazolium, van der Waals-Platteuw model.

Research Highlights Computation the hydrate dissociation pressures of the methane+ ionic liquid+ water

systems.

Calculation the adjustable paramers of the imidazolium based ionic liquid solutions by

using various experimental data.

Compairing the prediction of the model with the expermental data in litreture.

mailto:[email protected]

Prediction of methane hydrate equilibrium pressurs…

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1. Introduction

Gas or Clathrate hydrates are non-stoichiometric compounds in which the guest molecules

with desirable size and shape are trapped inside the water molecules network so that no

chemical bonding is formed among water and gas molecules [1, 2]. In gas processing and

transmission gas pipelines, gas hydrates are undesirable since it causes blockage of pipelines

[3]. Therefore, various methods can be applied to reduce risk of hydrate formation including

operating outside the hydrate stability zone, removing/reducing both free water and vaporized

water, and injecting inhibitors [2, 4]. One kind of inhibitors which can be applied to prevent

hydrate blockages in oil and gas industries is thermodynamic inhibitors. The aforementioned

inhibitors including alcohols, glycols and inorganic salts effectively shift hydrate equilibrium

phase boundary to the lower temperatures and higher pressures. these inhibitors reduce water

activity and lead to prevent gas hydrates formation [2, 5-7].

Ionic liquids are a type of green electrolytes with low melting points and are composed of

complex ionic species that have specific characteristics including low volatility (low vapor

pressure) and good thermal stability [8-10]. Some studies have been carried out to represent

ionic liquids as the new group of inhibitors because of their specific chemical behavior [11].

Several investigations have been accomplished to model and predict gas hydrate formation

conditions in the presence of the thermodynamic inhibitors [12-17]. Most of these

thermodynamic models are composed of van der Waals-Platteuw model for solid phase and

also equation of states for fluid phases. However, a few works have been devoted to

thermodynamic modeling of the equilibrium hydrate formation conditions in the presence of

aqueous ionic liquid solutions [18]. Mohammadi et al. studied effect of

tributhylmethylphosphonium methylsulfate as an ionic liquid on methane and carbon dioxide

hydrates. In their model , the van der Waals-Platteeuw theory was coupled with Peng-

Robinson equation of state for gas phase and the nonrandom two liquid (NRTL) model for

liquid phase so that the results were in good agreement with experiment [18]. Also, in

previous work, the electrolyte cubic square well equation of state (eCSW EoS) was combined

with the van der Waals-Platteuw model and applied for prediction hydrate formation

conditions of various systems including single gases, mixed gases and natural gases in

presence/absence electrolyte aqueous solutions. Comparing the results of the model with

experiments in literature indicates this model can be predicted the hydrate formation

conditions well [19].

In this work, the electrolyte Cubic Square Well equation of state (eCSW EoS) based upon the

Helmholtz free energy [19- 21] is coupled with the van der Waals-Platteuw model [22] and

applied to predict the hydrate dissociation pressures of the methane +ionic liquid+ water

systems. Moreover, adjustable parameters of the ionic liquid-water systems are calculated

using enthalpy, vapor pressure and osmotic coefficients experimental data in literature so that

the results of the model are compared with experiment.

2.Thermodynamic modeling

The eCSW EoS for fluid phase is coupled with van der Waals-Platteuw model to calculate gas

hydrate formation conditions of the three phase systems (H-L-V) as follows.


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2.1. Thermodynamic framework of gas hydrates

To predict gas hydrate conditions, equaling of the chemical potential of water in the various

phases (liquid water-hydrate-gas/vapor) must be satisfied as

H L

W W

(1)

H L

W W

(2)

where and stand for the difference in chemical potential between empty hydrate

lattice and water in the hydrate and aqueous phases, respectively. The chemical potential of

the hydrate phase is computed based on van der Waals-Platteuw model presented by Parish

and Prausnitz [22]. In this model, the gas molecules with desirable shape and size are

adsorbed in water molecule cavities. H

W based on the Langmuir adsorption theory which is

expressed as [22]

, (1 )H

W m m j

m j

T P R T ln

(3)

where m

denotes for cavity number per water molecules in hydrate structure. The structural

lattice properties of the gas hydrates are taken from reference [23]. m j

is described the

fractional of cavity m which is occupied by guest molecule j so that based on Langmuir

theory is written as

( , )

1 ( , )

mj j

mj

mj jj

C T f T P

C f T P

(4)

where Cmj is Langmuir constant of gas j in a type m cavity. fj (T, P) is the fugacity of gas

species j in the vapor phase. For computing the Langmuir constants a temperature correlation

is used as [22, 24-26]

exp( )mj mj

mj

A B

C

T T

(5)

where Amj and Bmj are the adjustable constants and can be fitted by regression of the

experimental data of the single and mixed gas hydrates. In this work, the Langmuir constants

of methane are considered as a function of temperature and computed in previous work [19]

as shown in Table 1.

Table 1. Langmuir constants of methane gas for structure I and II [19]

Bmj

(K) Amj 103

(K/MPa) Structure Kind of cavity

3187 0.787 I Small cavity 2594 0.4332 II 2621 2.585 I Large cavity 1822 51.98 II


4

The difference in chemical potential between the empty hydrate lattice and the water liquid

phase is presented by Holder [27] so that is expressed as

0 0

0 0

2

0

, ( , )l n ( )

L T PL L

w w w w

w

T P

T P T P h Vd T d P a

R T R T R T R T

(6)

0

0

T

L

w w w

T

h h C p d T

(7)

where the reference parameters are presented by Parrish and Prausnitz [22]. Moreover,

activity of water is calculated as [22]

w w wa x

(8)

where w

a and w

are activity and activity coefficient of water in the liquid phase,

respectively. In this work, the symmetrical activity coefficient of water is calculated [21]

through the fugacity coefficients using eCSW EoS as

0

( , , )

( , , 1)

w

w

w w

T P x

T P x

(9)

where 0

w and

w are the fugacities of pure water and water in the liquid phase, respectively.

To compute solubility of gas or gases in the liquid phase and determining concentration of

components in both liquid and vapor phases, an isothermal flash calculation is performed

through zero setting of the mole fraction of all the ionic species in the gas phase.

2.2. The Cubic Square-Well Equation of State

The electrolyte Cubic Square-Well Equation of State is based on the molar residual Helmholtz

energy function as

, ,re s id

i M S A B o rn C S Wa T v x a a a a a

(10)

where T, v and xi stand for temperature, molar volume and mole fraction respectively. The

subscript CSW and MSA denote cubic square well equation of state and mean spherical

approximation theory, respectively. Description of the non-electrolyte contribution of the

model, cubic square well equation of state (CSW EoS), was presented by Haghtalab and

Mazloumi [28] that is obtained using the GVDW theory and a new coordination number

model. The molar Helmholtz energy of the non-electrolyte contribution is presented as [28]

0

0 0

ln ( )

4 2 1C S W

m wz R Ta R T l n

m m

(11)


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where the first term represents the van der Waals repulsive term and the second part

illustrates the attractive part based on square-well potential. Where T is absolute temperature,

R is gas constant, is molar volume and is constant ( 26

). For a mixture the

mixing rules are expressed as [28]

i j i j

i j

m x x m (12)

( e x p )i j

i j i j i j i j

i j i j

w x x w x x m

k T

(13)

0 0i i

i

x (14)

i i

i

z x z (15)

3

3

4 2 3

4 2 ( 3 )

i j

i j

i j

m

(16)

34 2

1

3i ii

z

(17)

3

0

2

A i

i

N

(18)

and combining rules are expressed as

(1 )i j i j i j

k (19)

i i j j

i j

i j

(20)

where is the square-well potential depth, is a diameter of component, is the

potential range, v0 is the closed packed volume and NA Avogadro’s number, kij is interaction

parameter in which kij=kji.

The explicit simple version of MSA, for long range interaction of ions, is applied in the

Helmholtz energy equation as

3

2 Γ 3(1 Γ )

3 2M S A

A

R Ta

N

(21)


6

2 2

2 2

0

A

i i

io n s

e Nk x Z

D R T

(22)

1Γ 1 2 1

2

k

(23)

where Γ is the MSA screening parameter, k is the Debye screening length, e is the elementary

charge unit,0

is permeability of the free space, v is molar volume, Zi is the charge number of

ions, is the average diameter of ions that is computed by /i i i

x x , where

summation is over ions and D is the dielectric constant of mixed solvents. In this work, the

dielectric constant of water is calculated in terms of temperature [20]. The Born contribution

of the molar residual Helmholtz energy is expressed as

22

0

1(1 )

4

i iA

B o r n

io n s i

x ZN ea

D

(24)

It is noted that for calculating hydrate equilibrium dissociation pressures of the various

systems without any electrolytes, the Born and MSA terms of the eCSW equation are

vanished. Thus, the CSW contribution of equation of state is applied for calculating fugacity

coefficient of the components in the different phases [20, 28].

3. Results and disscution

The proposed hydrate model in this work applied to determine the methane hydrate

dissociation pressurs. As mentioned before, to compute fugacity coefficients in the different

phases, the eCSW EoS was coupled with van der Waals Platteuw model and applied to

predict the hydrate dissociation pressures of the ionic liquid-methane-water systems. To

predict the hydrate dissociation pressures of various systems, the objective function was used

as

1

1% 1 0 0

e x p c a lN p

e x p

i

P P

A A D

N p P

(25)

3.1.Estimation the model parameters

To model the hydrate formation conditions, the three adjustable parameters, i.e k

, and

for pure components and the interaction parameters for mixture must be correlated. The

parameters for pure components are calculated using both saturated vapor pressure and liquid

density data simultaneously as shown in Table 2 [20,28].

Table 2. The parameters of the eCSW EoS for the pure components [20, 28].

λ /ε k 10

10σ .(m) Guests

1.760 122.434 2.928 CH4

1.464 772.657 2.317 H2O


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Because of solubility of the present ionic liquids in liquid phase, thus it was considered, the

ionic liquids to be perfectly ionized in water similar to a stronge aqueous electrolyte solution.

Thus, to correlate the pure experimental data accurately, in addition to the three pure

component paremeters, two extra binary interaction parametrs such

as,

cation w ater

k and,c a tio n a n io n

k were adjusted for the binary aqueous ionic liquid solutions using

enthalpy and osmotic coefficients experimental data in literature. To reduce the adjustable

parameters, their values for a cation and an anion in a binary electrolyte system are considered

to be the same [20], i.e. c

= ,a c a

, c a

. Moreover, since solvation effect of anions

are less than cations, thus, the interaction parameters among the anions and the other

components in the liquid phase are ignored [20]. Thus, the five adjustable parameters of

eCSW EoS per each electrolyte are optimized using the following objective function:

1 0 0%

c a l e x p

i i

e x p

i i

X

A A D

N p X

X

(26)

where Np is the number of data points,. X is the various thermodynamic properties for ionic

liquid/water systems which are taken from literature and AAD is Averaged Absolute

Deviation. The superscripts “exp” and “cal” stand for experimental and calculated properties,

respectively. It should be noted that for computing the adjustable parameters of the

[EMIM][EtSO4], [BMIM][MeSO4] solutions, the osmotic coefficients data of these ionic

liquids [29] were used. Also, the five parameters of the [EMIM][HSO4] solutions were

calculated through excess enthalpy experimental data [30]. The values of the adjustable

parameters of the mentioned ionic liquid solutions are presented in Table 3.

Table 3. The fitted parameters of the ionic liquid solutions by using eCSW EoS.

AAD% cation,water k cation,anionk λ /ε k 10

10σ .(m) Ionic Liquid

3.86 0.224 0.086 1.49 1671.2 4.00 ]4[EMIM][EtSO

1.12 -0.288 0.207 1.61 342.1 4.16 ]4[EMIM][HSO

4.16 -0.292 -0.166 1.54 1360.8 4.50 ]4[BMIM][MeSO

3.2.Methane hydrate in the presence of ionic liquid solutions

In this section, reliability of the present model in prediction of the hydrate dissociation

pressures of methane in presence of the ionic liquid solutions is investigated.It should be

noted that the experimental data are taken from pervious work [31].

Fig. 1 shows the predictive capability of this model for methane+[EMIM][EtSO4]+water,

methane+[BMIM][MeSO4]+water and methane +water systems that are compared with the

experimental data [31]. The predictions are in excellent agreement with the experimental data.

The AAD% of the methane+ [EMIM][EtSO4]+water, methane+[BMIM][MeSO4]+water and

methane +water systems are 1.29, 1.05 and 2.07, respectively.


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Fig.1. Comparing the calculated hydrate dissociation pressures of methane+ionic liquid+water systems

with the measured experimental data of this work. Symbols present the measured experimental data and

the concentration of ionic liquids is 10 w%. , methane+water; □, methane+[EMIM][EtSO4]+water; ●,

methane+[BMIM][MeSO4]+water, ―, model.

In Fig. 2, predictions of methane hydrate in presence of the 10w% [EMIM][HSO4] solution

and pure water are demonstrated so that the calculated results are in very good agreement

with the experiment and the maximum deviation between the experimental and predicted

values for the methane+[EMIM][HSO4] +water system is 2.27%.

6.5

7.5

8.5

9.5

10.5

11.5

12.5

13.5

14.5

281 283 285 287 289

p(M

Pa)

T(K)


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Fig.2. Comparing the calculated hydrate dissociation pressures of methane+ionic liquid+water systems

with the measured experimental data of this work. Symbols present the measured experimental data. ,

methane+water; ▲, methane+water+[EMIM][HSO4] (10w%), ―, model.

Comparing the prediction of the present model with the expermints shows this model can be

applied to predict the hydrate dissociation pressures of methane in presence of the ionic liquid

solutions accurately.

4. Conclusions

The eCSW equation of state was coupled with the van der Waals-Platteuw model and applied

to predict the hydrate equilibrium dissociation pressures for the methane+ ionic liquid+ water

systems. In addition, the adjustble paramers of the imidazolium based ionic liquid solutions

calculated by using variuos experimental data in litreture. It was found that the results of the

present model were generally in good agreement with the experiments.

Nomenclature

Amj, Bmj fitted parameters,(K/MPa), (K)

wa

activity of water

Cmj Langmuir constant

WP

C molar capacity difference between liquid water and ice

D the dielectric constant of mixed solvents

,j wH Henry constants

]4[]3[]2[]1[

,,,iiii

HHHH constants in Henry constant eq.

wh enthalpy difference between empty hydrate lattice and liquid water

0

wh at 273.15 K and 0 KPa

k Boltzmann’s constant (1.38066 10-23Jk-1)

kij binary interaction parameter between i and j companents

m orientational parameter

NA Avogadro’s number(6.02205 1023/mol)

R gas constant (8.314 Jmol-1. K -1)

P system pressure (MPa)

T system temperature(K)


10

v molar volume(m3/mol)

V volume(m3)

vdWP van der Waals-Platteuw model

wt% weight percent

x, y mole fraction liquid and gas

Zi charge number of ion i

z coordination number

zm maximum coordination number

Greek letters

Г

the MSA screening parameter

m cavity number per water molecules in the hydrate structure

0 0( , )

WT P chemical potential reference at 273.15 K and 0 KPa

square-well potential depth (J) ,characteristic energy

0

permeability of the free space

ij Interaction energy between molecules i , j

constant (0.7405)

size parameter(m)

ξ

reduced density

λ

square-well potential parameter

activity coefficient

the potential range

v0 closed packed volume

fugacity coefficient

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“,14thIranian National Chemical Engineering Congress, Sharif University of Technology, Tehran,

Iran, 16-18 October, 2012.

prediction of methane hydrate equilibrium pressurs in...

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