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2nd National Iranian Conference on Gas Hydrate (NICGH)
Semnan University
1
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
haghtala@modares.ac.ir
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.
Prediction of methane hydrate equilibrium pressurs…
2
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.
2nd National Iranian Conference on Gas Hydrate (NICGH)
Semnan University
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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
Prediction of methane hydrate equilibrium pressurs…
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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)
2nd National Iranian Conference on Gas Hydrate (NICGH)
Semnan University
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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)
Prediction of methane hydrate equilibrium pressurs…
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
2nd National Iranian Conference on Gas Hydrate (NICGH)
Semnan University
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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.
Prediction of methane hydrate equilibrium pressurs…
8
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)
2nd National Iranian Conference on Gas Hydrate (NICGH)
Semnan University
9
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)
Prediction of methane hydrate equilibrium pressurs…
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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Semnan University
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