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Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture
Journal Pre-proof Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture Hussein Hassan, Hassan Pahlavanzadeh PII:
S1875-5100(19)30380-4
DOI:
https://doi.org/10.1016/j.jngse.2019.103128
Reference:
JNGSE 103128
To appear in:
Journal of Natural Gas Science and Engineering
Received Date: 17 July 2019 Revised Date:
20 October 2019
Accepted Date: 16 December 2019
Please cite this article as: Hassan, H., Pahlavanzadeh, H., Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture, Journal of Natural Gas Science & Engineering, https://doi.org/10.1016/j.jngse.2019.103128. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.
Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture Hussein Hassan, Hassan Pahlavanzadeh* Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
Abstract In the current study, the effect of tetra-n-butyl ammonium bromide (TBAB) and cyclohexane mixture on CH4 semi-clathrate hydrate formation was studied. Semi-clathrate dissociation conditions for CH4 + TBAB + cyclohexane+ water were investigated at different concentrations of TBAB (0.05, 0.10, and 0.15) mass fraction in the presence of cyclohexane at the pressure and temperature ranges of 1 - 8 MPa and 275.1 - 295 K, respectively. In addition, a thermodynamic model was suggested to predict the phase equilibria of our system, which is divided into four phases, where the van der Waals–Platteeuw Solid Solution Theory has been used to predict the hydrate phase. For gas phase, The SRK equation of state was applied. For oil phase, the cyclohexane activity coefficient in the organic phase was calculated by the non-random twoliquid model (NRTL). Finally, to determine the activity coefficient of the electrolyte species in the aqueous phase, the semi-empirical electrolyte NRTL (eNRTL) activity model was used. The results showed that the proposed model has an acceptable agreement with the experimental semiclathrate hydrate dissociation data with an approximately average absolute relative deviation of 5.4%. Keywords: Gas Hydrate, Clathrate Hydrate, Semi-clathrate Hydrate, Methane, TBAB, Cyclohexane.
1- Introduction Hydrates or clathrate hydrates are defined as nonstoichiometric crystalline structures that are created through a reaction between water molecules and other small surrounding molecules including methane, ethane, and carbon dioxide [1, 2]. The formation of such crystalline structures takes place under high pressure and low temperature conditions [3]. Previous studies confirmed that hydrate crystalline structures are divided into three types SI, SH, and SII, which are commonly used in the oil and gas industry [4]. The formation of each type of these hydrates is dependent on the molecular diameter of their backbone molecules [5]. For example, CH4, CO2, and H2S are known to form sI hydrates, while other molecules like propane and N2 will form SII hydrates [6]. However, the practicability of using such compounds has been significantly decreased due to the strict formative and dissociative conditions needed by these compounds [7]. For this purpose, some additives or promoters have been used in order to diminish the severity of the formative and dissociative conditions, to reduce energy consumption and enhance hydrate applications [4, 8]. Tetra-n-butyl ammonium bromide (TBAB: (C4H9)4NBr) is one of these additives that belongs to the alkyl ammonium salts [9]. It enhances the enclosure formation through physical combination between TBA+ ions and water molecules connected by the hydrogen bonds. In this process, TBA+ ions fill four big cages (two tetrakaidecahedra and two pentakaidecahedra); however, the small gas molecules fill the dodecahedral small cages [10-12]. TBAB has indispensable characteristics including enhancement of gas storage, improving the selectivity of small dodecahedral cavities for catching the gas molecules, and alleviating the severity of pressure–temperature conditions [13-16]. Hence, semi-clathrate hydrates of TBAB
have been excessively implicated in gas storage and transportation, separation of gas mixtures, and CO2 sequestration [17-19]. Investigations concerning the hydrates of this compound have shown that the phase behavior of binary water + alkyl ammonium salts systems is quite complicated, and thus diverse structures are specified based on the composition of the system [10, 20-23]. The majority of the published work was about studying the phase equilibria between a single gas (CO2, N2 and CH4) and a single promoter such as THF, TBAB or TBAF[24]. However, few studies have investigated the applicability of a mixture of promoters in a single gas for postcombustion. Cyclopentane, cyclohexane, and methyl cyclohexane are known as Heavy Hydrate Formers (HHFs), which can play a significant role in gas hydrate phase equilibria [25, 26]. There is scarcity studies performed on this group, and recently, there is no additional information concerning them [27, 28]. The clathrate hydrate phase equilibria of HHFs have been widely examined in the presence of methane [28]. However, there is still insufficient information regarding the clathrate hydrates of cyclopentane, cyclohexane and methyl cyclohexane in the presence of other gases [4, 29]. In order to gain an overview about the phase equilibria of the mentioned compounds, researchers have made different experimental and theoretical studies. Artificial Neural Networks (ANNs) have been used for convenient illustration of the hydrate dissociation conditions of the systems including H2+TBAB aqueous solutions [30]. Additionally, a thermodynamic model has been introduced and the Statistical Associating Fluid Theory (SAFT-VRE) has been utilized to model the aqueous phase and van der Waals–Platteeuw to study the hydrate phase formed in the carbon dioxide +TBAB aqueous solution system [31, 32]. Another thermodynamic model concerning the phase equilibria of semi-clathrate hydrates of CO2, CH4, or N2 +tetra-n-butyl ammonium
bromide aqueous solution has been proposed [12]. In this model, vander Waals–Platteeuw is used to characterize the hydrate phase, and Peng–Robinson (PR-EoS) equation of state is used to calculate the fugacity of gaseous hydrate former and the mean activity coefficients. Thereafter, a correlation on the basis of an existing osmotic coefficient and activity coefficient values is used. Finally, the Non-Random Two-Liquid (NRTL) activity model is used to determine the activity coefficient of non-electrolyte species in the aqueous phase [33, 34]. In addition, Venkata Ramana Avula et al. have developed a thermodynamic model to predict the phase stability conditions for methane hydrate–ionic liquid (IL)–water system[35]. In this model, the hydrate phase is computed from modified van der Waals–Platteeuw model. The Peng–Robinson equation of state and developed activity model as a combination of Pitzer–Mayorga–Zavitsas-hydration model is used to evaluate the fugacities of gas and liquid phases, respectively. The hydrate phase stability prediction is also computed using the liquid phase activity predicted by NRTL and Pitzer– Mayogra models[35]. In this study, we present a new phase equilibrium data about the semi-clathrate hydrates of CH4 in the presence of a mixture of TBAB and cyclohexane. Secondly, we report the hydrate dissociation conditions for CH4 + cyclohexane + TBAB + water systems at distinct temperatures where there is still limited information regarding them. The isochoric pressure-search method was utilized in order to create our experimental data. In addition, a thermodynamic model is suggested to predict the dissociation conditions of the semi-clathrate hydrates for this system. The hydrate phase properties were predicted by the van der Waals–Platteeuw theory. The aqueous phase properties were evaluated using the e-NRTL electrolyte model and the SoaveRedlich-Kwong equation of state; (SRK EOS) was employed to calculate the gas/vapor phase
properties. Finally, the cyclohexane activity coefficient in the organic phase was calculated by the Non-Random Two-Liquid X (NRTL) model. 2- Experimental section 2.1- Materials Table 1 presents the purities and suppliers of the chemicals used in this study. The aqueous solutions were prepared using an analytical balance with the mass uncertainty of ± 0.0001 g. The CH4 with 99.999% purity purchased from Sabalan Gas Company (Iran), and cyclohexane and TBAB with more than 99.99% purity were obtained from the Sigma-Aldrich chemical company (USA). All chemicals and additives were used as received. Table 1: Purities and suppliers of the chemicals used in this study. Chemical
Formula
Purity
Supplier
CH4
CH4
99.999
Sabalan Gas Company
Cyclohexane
C6H18
99.99
Sigma-Aldrich
TBAB
(C4H9)4NBr
99.999
Sigma-Aldrich
2.2- Experimental apparatus [27, 36-38] The used apparatus was arranged in the processing engineering unit at Tarbiat Modares University (TMU). It includes a jacketed cell made of stain-less steel with the useful volume of 790 cm3. It can stand a high pressure and temperature up to 16 MPa and 323.15 K, respectively. Additionally, the temperature in the inner side of the apparatus is regulated by a circulator water bath, which can provide an adjustable heating rate. Moreover, the vessel consists of an electromagnetic stirrer motor in order to mix the components and the crystalline hydrate formed inside the vessel during the measurements. To measure the
temperature and pressure inside the reactor, two platinum resistance thermometers (Pt100) are used. Finally, in order to record the pressure and temperature of the vessel at 255 time intervals, an in-house software is used. A schematic diagram of the used setup is shown in Fig. 1.
Fig. 1: Schematic diagram of the experimental apparatus used in this work. 3- Experimental procedure To measure the hydrate dissociation conditions, the isochoric pressure-search method was used [39] [37]. At first and before doing the tests, the apparatus was flushed with distilled water for an hour to eliminate every impurity. then, the vessel was evacuated for a 30 min under vacuum condition (pressure down to 10 Pa). Next, it was filled with the desired aqueous solution (30% of the volume of the reactor). After that, the vessel was charged with the desired pressure by adding the desired gas (in our case CH4). Then vigorously we turned on the electromagnetic motor to mix the solution and increase the temperature to heat it for 15 min before doing the cooling step. The temperature was then slowly decreased with a rate of 10 K · h−1 until the hydrate phase was formed. After that, the heating step started where the reactor was heated slowly with a rate of 1 K • h−1 [37, 39]. Thereafter, the temperature was increased slowly at a rate of 0.2 K • h−1. In every step, the temperature was retained constant for enough time until the equilibrium state occured
inside the reactor. Thereafter, the data of each test was sketched to determine the hydrate dissociation point, which is the intersection of the two curves (heating and cooling). 4- Thermodynamic framework The system studied in this work consists of four phases: hydrate, water + TBAB, gas, and cyclohexane. The thermodynamic model is based on the equality of hydrate fugacity and liquid L
fugacity. In the equilibrium condition, the fugacity of water in the liquid ( fw ) and hydrate phases was equal, which is written as follow: ƒ wL = ƒwH
(1)
Where, fwH and fwL are the fugacity of water in the hydrate and liquid phases, respectively. 4.1- Hydrate phase: The fugacity of water in the hydrate phase (fwH) is calculated using the van der Waals-Platteeuw Model [33]: ƒ w H = ƒ w MT exp (( −∆µ w MT − H ) / RT )
(2)
Where, fwMT represents the fugacity of water in the hypothetical empty hydrate lattice, ∆µ wMT-H is the chemical potential difference between the empty hydrate and filled hydrate phases. Regarding the presence of guest molecules, based on the Langmuir absorption theory, the chemical potential is calculated through the following equation: 3
∆µ w MT − H = µ w MT − µ w H = RT ∑ vi ln(1 + Cij ƒ j )
(3)
( i =1)
Where, υi, T, R and Cij are the number of cavities, temperature, the universal gas constant, and the Langmuir constant for types i and j cavity, respectively. We assumed that cyclohexane has a
synergic effect on the TBAB semi-clathrate hydrate [40], so the above equation can be further described as the following equation:
∆μ
+ ƒ ( + , ƒ + , ƒ ) = #
" ( + , "ƒ + , " ƒ )
(4)
To calculate the Langmuir constants, Parrish and Prausnitz (1972) proposed a group of equations expressed as follows: For tetrakaidecahedra cages: Clarge1= × ()
(5)
For pentakaidecahedra cages: Clarge 2= × ( ) %
&
(6)
For the dodecahedral small cages [33]: Csmall=
× ( ) ''
(7)
In the above equations, a, s, d and f are respectively, adjustable parameters for tetrakaidecahedra and pentakaidecahedra cavities, which are obtained through fitting of the experimental data (the optimized values of these parameters are presented in Table 2). Additionally, aa and bb are the parameters recommended by Parrish and Prausnitz (1972) for each gaseous hydrate former encaged in dodecahedral small cages (reported in Table 3) [31]. Table 2: Adjustable parameters for tetrakaidecahedra and pentakaidecahedra cages
Type A
a(K Mpa-1)
s(K)
d(K Mpa-1)
f(K)
1.2412 × 10*
1.2947 × 10+
4.0065× 10,
2.5309 × 10-
2.4544× 10,
Type B
4.816 × 10-
1.297 × 10..
2.3213 × 10.
The below assumptions have been used in order to define the Langmuir constants[12]: 1- We have two types of semi-clathrates with different hydration numbers: type A with 26 hydration number and type B with 38 hydration number. 2- The gas molecules (CH4) are situated in the small cavities. 3- The positive ion TBA+ is captured between two large tetrakaidecahedra and two large pentakaidecahedra. 4- All types of semi-clatrates listed before have: two large cavities and one small cavity. The below equations are used to calculate the number of cages of the specified type per water molecule in a unit hydrate cell:
vl arg e1 =
nl arg e1 N
MT w
; vl arg e 2 =
nl arg e 2 N
MT w
; v small =
(8)
n small N wMT
The calculations showed that / smal=3/38; /large1=1/19; and /large2=1/19. Table 3: Constants aa and bb Gas
aa(K MPa-1)
bb(K)
CH4
0.0037237
2708.8
Equation (9) is used to calculate the fugacity of water in the hypothetical empty hydrate lattice (fwMT):
ƒ wMT=PwMT exp(
0 (11 )
)
(9)
The water molar volume in empty hydrate lattice (VwMT) is calculated according to Equation (10) [41]: VwMT= (11.835+2.217× 23 T + 2.242× 24 T2)
2562 74
NA +1.6155× 28 P – 2.50542"
(10)
P2
Equation (11) is used in order to calculate the vapor pressure of water in vacant hydrate cavities, where pressure (P) is in MPa [14]: PwMT=0.1 exp (17.44 -
4226.8
(11)
)
4.2- Thermodynamic model of the aqueous phase The water fugacity in the aqueous phase is calculated using the following equation: Vw ( P − Pwsat ) fWL = xwLγ wL Pwsatϕ wsat ,V exp RT
(12)
Where, xw is the mole fraction, γ w is the water activity coefficient, Pw L
pressure,
L
sat
is the water vapor
ϕwsat ,V is the fugacity coefficient of pure water, Vw is the molar volume of water, and
the saturation state is indicated by superscript sat. Equation (13) is used to calculate the molar < fraction of water in the aqueous solution phase (:; ) [12]:
= =
− = + 2. 22 × " ×
(13)
Where, m (mol/kg) is the molality of the promoter, TBAB, in the aqueous solution, and Mw (kg/mol) is the molecular weight of water. The relation between molality and molar fraction of TBAB can be derived as follows [31]:
= = =? = = 5
(14)
@. 23=? =( ) 222=
(15)
The pressure/temperature (PT) flash calculation showed that the gas mole fraction in water was negligible, so xBC is considered negligible (:D< = 0). To calculate the activity coefficient of water
in the aqueous phase (γwL), the electrolyte-Non-Random Two-Liquid (e-NRTL) activity
coefficient model is used: for water : lnγi=lnγiLC +lnγi*PDH
(16)
for ions : lnγi*=lnγi*LC +lnγi*PDH
(17)
Where, i represents the cation, anion and water component. The interaction parameters EF,G of eNRTL model between water-TBA+Br- molecules are determined using equation (18): H ,I = ,I +
' ,I & − + J ,I K + K LL &
(18)
Where, MF,G , NF,G MOP QF,G are adjustable parameters, which are fitted from our data at RSTU = 298.15Z and tabulated in Table 4.
Table 4: ai,j, bi,j and ci,j between water-TBA+Br- molecules Components [\,]
^\,] (_) `\,]
TBA+, Br-, water
water, TBA+, Br-
-3.2185
7.5871
-4.2629
5.4443
11.3440
-1.4560
The TBA+ cation is denoted by subscript ca, and its fugacity is determined using Equation (19) as follows: vpL ( P − Ppsat ) fcaL = xpLγ pL Ppsat exp RT
(19)
The hydrate promoter (TBAB) is indicated by subscript p. γpL is determined using the e-NRTL activity coefficient model. To calculate the promoter molar volume (/a b ) and the density data (cp) of TBAB in aqueous solution, Equations (20) and (21) are used [42, 43]: dp= dw + O1(100wp) + O2(100wp)2 + O3(100wp)3
(20)
Oi=qi + ri(T)+ si(T)2
(21)
Where, ri, qi and si for TBAB are obtained from the data available in the literature and reported in Table 5. cp is reported in g cm-3. Table 5: Constants Values in Equations (21) and (22) [37] Constants
s3
s2
s1
r3
r2
r1
q2
q1
Values
-7.091× 10-
5.304× 10+
4.549 × 10+
4.088× 10*
-3.099× 10-
5.693× 10-
4.57× 10e
-1.707 × 2@
Pghij is calculated using Equation (22) [44]:
Ppsat= 2.724[email protected]/(42."8))
(22)
4.3- Oil phase The following equation provides the fugacity of cyclohexane in oil phase:
m2 n ƒ = = γ 1 =o K
11n
L ; q = = − =
(23)
To calculate the CH4 solubility in organic phase (xgoil), the following expression is used [12]:
= =
ƒ r
s∗7 =o u
v (1 −
(24)
1n )
w
∗ Since xyz+ is a function of xgoil, an iterative method is needed to calculate the xgoil from Equation (24).
The Henry’s constant (MPa) of gas in cyclohexane (Hg-CH) is calculated as follows: '
'
= u − K − { L ∗ 2{({"k6.3) w
(25)
Where, a and b are constants and their values is to 6.74545, and 300.6826 K, respectively [45]. Equation (25) is based on the vapor liquid equilibrium of CH4-CH system at the atmospheric }
pressure. Where, xCH4_CH = T |{~ is a function of temperature at the atmospheric pressure[45]. When the total pressure is equal to one bar, the gas solubility is low, and the gas
phase can be assumed to be ideal. The equilibrium equation is written as xCH4∗Hg-CH = yCH4, where yCH4 is calculated from yCH, which is obtained by its corresponding equilibrium equation, yCH = xCH*PCH_sat = (1-xCH4)×PCH_sat. Then Hg_CH = (1-(1-xCH4)×PCH_sat)/xCH4, which is written in the form of Equation (26). In addition, A, B and C are Antoine’s coefficients for cyclohexane (Their values are reported in Table 6). Table 6: Antoine’s coefficients values Constants
A(K)
B(K)
C(K)
Values
6.85146
1206.47
223.136
The saturation pressure of cyclohexane (MPa) is obtained using Equation (26):
(/({("k6.3)))/k42 1n = 2
(26)
Cyclohexane activity coefficient in the oil phase (γCHoil) is calculated by NRTL activity model. The interaction parameters between CH4 and cyclohexane are calculated from Equation (27): H ,I = ,I +
' ,I
(27)
Where, MF,G and NF,G are parameters, which are fitted from our data and their values are reported in Table 7. Table 6: MF,G and NF,G parameters used in this work Parameters
,I (j/mol.k) ' ,I (j/mol.k2)
CH4
Cyclohexane
CH4
0
0.3787
Cyclohexane
0.2455
0
CH4
0
-0.2490
Cyclohexane
0.7387
0
4.4- Thermodynamic model of the gas phase In this study, the SRK equation of state is used to calculate the fugacity of components in the gas phase such as methane. The applied critical properties and acentric factor of methane are listed in Table 8. Table 7: Critical properties and acentric factors of the applied pure gas. Compound
PC (MPa)
TC (K)
CH4
4.61
190.6
0.0114
By placing the above Equations in equation 1, the Relation (28) is obtained:
0 151 n m (151 L =m s 1n =oK
1 =o (
×
(28)
+ ƒ
( + , ƒ + , ƒ ) # − = 2
" ( + , " ƒ + , " ƒ )
The percentage of the Average Absolute Relative Deviation (AARD) in pressure is calculated as follows: = 1 ∑
1 = 1J
1 =
× 22
(29)
Where, N is the number of experimental points, P and PiC denote the experimental and calculated
pressure, respectively. To understand what we have done before, an algorithm is sketched in Fig. 2
that shows the calculation procedure for prediction of hydrate formation pressures at given temperatures.
Imput (ww, Mw,MTBAB,Pwsat,Vw,PTBABsat,VTBAB,PCHSat, VCH, PwMT)
Read T
xw=
/(
~
+
~
)
Guess P
s
L1
CCH4 ,CTBAB ,CTBAB
L2
γTBAB by ENRTL
Guess xCH4 :yz+
D¯°±±
²|< = :yz+
xB =
Calculate g by SRK
oil
Guess γCH4oil
γw by ENRTL
ƒCH4g= ch4g * P
ƒ B
hij υv B (P − P ) HB exp u w RT
e= ¡1 −
¦§¨©©
¢ £¤¥
ª«¬ ¢£¤¥
¡ < 10*
γCH4oil by NRTL
Not satisfied return
hij υ ® (P − P ) hij ƒ w = x γ P exp u RT
Checking Equation (28)
Satisfied
Save T, P
Fig. 2: Calculation procedure for prediction of hydrate formation pressures at given temperatures
Results and discussion The experimental conditions of semi-clathrate hydrate formation for CH4 after the addition of TBAB + cyclohexane (CH) are presented in Table 9 and depicted in Figs. 3-5. In order to ensure that the experimental procedure and setup are valid, some tests for CH4 in the presence of pure water were performed at the pressure and temperature ranges 3.1 - 6 MPa and 274 - 280 K, respectively. The measured data are presented in Table 9 and plotted in Fig. 3. Comparison of the results shown in Fig. 3 revealed that there is consistency between the collected test data and those mentioned in the literature [46] (with small AARD). Figs. 3-5 illustrate the experimental data of hydrate dissociation conditions for (CH4 + TBAB + CH + water) system at the distinct mass fractions (0.05, 0.10, and 0.25) of TBAB in the aqueous phase. As shown, cyclohexane exerted a promoting effect on CH4 + TBAB + CH + water system. Therefore, cyclohexane improved the temperature and reduced the hydrate dissociation pressure in comparison to CH4 + TBAB + water at the same TBAB concentrations. According to these results, it can be concluded that cyclohexane exerts the same or slightly higher promoting effect in comparison to TBAB in the presence of CH4. Hence, CH might modify the hydrate dissociation conditions toward milder conditions. Furthermore, it is seen from Figs. 3-5 that the hydrate dissociation conditions switch to the left side when the TBAB concentration in the aqueous solution and in the presence of CH increases from 0.05 to 0.10 mass fraction. However, such conditions switch to the right side when the TBAB concentration increases to 0.25 mass fraction.
Table 9: Experimental hydrate dissociation conditions of CH4 + TBAB+ CH + water system TBAB mass fraction (w)
T/K
P/MPa
w=0
274.1
2.9
275.2
3.19
276.3
3.49
277.34
3.88
278.2
4.29
283.9
2.014
285.71
3.187
287.53
4.525
288.42
5.487
289.47
6.923
285.9
1.52
288.55
3.375
289.65
4.3
290.24
5.12
291.36
6.254
288.51
1.04
290.05
1.965
292.6
4.5
293.46
5.515
294.03
6.351
w=0.05
w=0.10
w=0.25
Hence, the behavior of the system in the presence of TBAB within the concentration range of 0.05 - 0.10 mass fractions is probably due to the difference in the capability of CH and TBAB promoters for occupying empty cavities. TBAB promoter has more capability to reside in large cavities while all cyclohexane persists in the oil solution. As a result, TBAB acts as an inhibitor in the presence of cyclohexane. Correspondingly, TBAB and CH stabilize the hydrate cages as the TBAB mass fraction increases from 0.10 to 0.25; however, part of the TBAB promoter remains in the aqueous phase. Therefore, the inhibiting effect of TBAB decreases as its concentration changes from 0.10 to 0.25, which is not the case when its mass fraction is in the range of 0.05 - 0.10 or at 0.25. According to the experimental results, combining 0.25 TBAB mass fraction with 40cc CH made the hydrate dissociation conditions more moderate than the (CH4 + CH + water) system. So, it can be concluded that both promoters probably occupy the hydrate cavities, and TBAB's function shifts from inhibitor to promoter at 0.25 TBAB mass fraction. Finally, the thermodynamic model was developed and applied in order to evaluate the hydrate dissociation conditions, while adding the mixed promoters (TBAB+CH) to the water + CH4 system. Initially, 0.05, 0.10, and 0.25 TBAC mass fractions plus 40cc CH data were used to acquire the Langmuir constants using optimization techniques. Additionally, consistency was observed between the predicted and measured experimental data. The results depicted in Fig. 6, show that within the mentioned TBAB concentrations, the suggested thermodynamic model can be used to evaluate the results with an acceptable outcome. The obtained results are shown in Table 10, which demonstrate an acceptable accuracy of the model results in wide ranges of temperature and pressure comparing to the selected experimental data.
8 7 6
P(MPA)
5 4 3 2 1 0 272
274
276
278
280
282
284
286
288
290
292
T(K)
Fig. 3: Hydrate equilibrium data (hydrate dissociation conditions) for the (CH4 + TBAB+ cyclohexane + water) system: □, (pure CH4 + water) system [46]; *,(pure CH4 + water) this work; ∆, (cyclohexane+ CH4 + water) system [47]; ×, CH4 in the presence of 0.05 mass fraction TBAB aqueous solution [48]; ◊, CH4 + CH in the presence of 0.05 mass fraction TBAB aqueous solution (this work).
10 9 8 7
P(MPA)
6 5 4 3 2 1 0 272
274
276
278
280
282
284
286
288
290
292
294
T(K)
Fig. 4: Hydrate equilibrium data (hydrate dissociation conditions) for the (CH4 + TBAB+ cyclohexane + water) system: ◊, (pure CH4 + water) system [46]; □, (cyclohexane+ CH4 + water) [47]; ∆, CH4 in the presence of 0.10 mass fraction TBAB aqueous solution [14]; ×, CH4 + CH in the presence of 0.10 mass fraction TBAB aqueous solution (this work). 12
10
P (MPA)
8
6
4
2
0 270
275
280
285 T(K)
290
295
300
Fig. 5: Hydrate equilibrium data (hydrate dissociation conditions) for the (CH4 + TBAB+ cyclohexane + water) system: ◊, (pure CH4 + water) system [46]; □, (cyclohexane+ CH4 + water) [47]; ∆, CH4 in the presence of 0.25 mass fraction TBAB aqueous solution [14]; ×, CH4 + CH in the presence of 0.25 mass fraction TBAB aqueous solution (this work).
Fig. 6: Comparison between the experimental data and the predicted values of the proposed model. Symbols show the experimental data; solid lines stand for the predictions of the model; *, CH4 + CH in the presence of 0.05, 0.10 and 0.25 mass fraction TBAC aqueous solution (this work). Table 10: Model results for prediction of hydrate dissociation conditions in the presence of CH4, TBAB, cyclohexane and water System
wTBAB
Temperature range
Pressure range
³³´µ
CH4+ water+ TBAB +cyclohexane
(k)
(MPa)
0.05
283.9 - 289.47
20.14 - 69.23
8.7337
0.1
285.9 - 291.36
15.2 - 62.54
3.1543
0.25
288.51 - 294.03
10.4 - 63.51
6.6269
5. Conclusion This paper reports the experimental data of hydrate dissociation conditions for (CH4 + TBAB + CH + water) system. Additionally, we investigated the effectiveness of the mixed promoters (CH + TBAB) on the hydrate dissociation conditions of CH4 gas. Based on the collected experimental results, adding cyclohexane to the CH4 + TBAB + water system exerted a promoting effect on the equilibrium conditions of the formed hydrate, despite that cyclohexane exerted a slight promoting effect on hydrate dissociation conditions during the three series of tests. Furthermore, TBAB exerted a promoting effect on the hydrate dissociation conditions of CH4 + CH + water system. In addition to that, a thermodynamic model was established to evaluate the hydrate dissociation conditions of (CH4 + TBAB + CH + water) system. Fitting model was used to obtain the Langmuir constants in some of the measured experimental data at 0.05, 0.10, and 0.25 TBAB mass fractions plus 40cc CH. Finally, the average absolute relative deviation (AARD %) of the suggested model's results was found to be 5.4%. References 1. 2. 3.
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Research Highlights •
Experimental hydrate dissociation conditions for (CH4 + TBAB + cyclohexane + water) system are reported.
•
A thermodynamic model has been developed and its results are in acceptable agreement with the experimental data.
•
The TBAB exerted an inhibiting effect on the hydrate dissociation conditions of the CH4 + CH + water system.
•
The addition of cyclohexane to the CH4+ TBAB+ water system exerted a promoting effect on the equilibrium conditions of the formed hydrate.
S1875-5100(19)30380-4
DOI:
https://doi.org/10.1016/j.jngse.2019.103128
Reference:
JNGSE 103128
To appear in:
Journal of Natural Gas Science and Engineering
Received Date: 17 July 2019 Revised Date:
20 October 2019
Accepted Date: 16 December 2019
Please cite this article as: Hassan, H., Pahlavanzadeh, H., Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture, Journal of Natural Gas Science & Engineering, https://doi.org/10.1016/j.jngse.2019.103128. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.
Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture Hussein Hassan, Hassan Pahlavanzadeh* Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran
Abstract In the current study, the effect of tetra-n-butyl ammonium bromide (TBAB) and cyclohexane mixture on CH4 semi-clathrate hydrate formation was studied. Semi-clathrate dissociation conditions for CH4 + TBAB + cyclohexane+ water were investigated at different concentrations of TBAB (0.05, 0.10, and 0.15) mass fraction in the presence of cyclohexane at the pressure and temperature ranges of 1 - 8 MPa and 275.1 - 295 K, respectively. In addition, a thermodynamic model was suggested to predict the phase equilibria of our system, which is divided into four phases, where the van der Waals–Platteeuw Solid Solution Theory has been used to predict the hydrate phase. For gas phase, The SRK equation of state was applied. For oil phase, the cyclohexane activity coefficient in the organic phase was calculated by the non-random twoliquid model (NRTL). Finally, to determine the activity coefficient of the electrolyte species in the aqueous phase, the semi-empirical electrolyte NRTL (eNRTL) activity model was used. The results showed that the proposed model has an acceptable agreement with the experimental semiclathrate hydrate dissociation data with an approximately average absolute relative deviation of 5.4%. Keywords: Gas Hydrate, Clathrate Hydrate, Semi-clathrate Hydrate, Methane, TBAB, Cyclohexane.
1- Introduction Hydrates or clathrate hydrates are defined as nonstoichiometric crystalline structures that are created through a reaction between water molecules and other small surrounding molecules including methane, ethane, and carbon dioxide [1, 2]. The formation of such crystalline structures takes place under high pressure and low temperature conditions [3]. Previous studies confirmed that hydrate crystalline structures are divided into three types SI, SH, and SII, which are commonly used in the oil and gas industry [4]. The formation of each type of these hydrates is dependent on the molecular diameter of their backbone molecules [5]. For example, CH4, CO2, and H2S are known to form sI hydrates, while other molecules like propane and N2 will form SII hydrates [6]. However, the practicability of using such compounds has been significantly decreased due to the strict formative and dissociative conditions needed by these compounds [7]. For this purpose, some additives or promoters have been used in order to diminish the severity of the formative and dissociative conditions, to reduce energy consumption and enhance hydrate applications [4, 8]. Tetra-n-butyl ammonium bromide (TBAB: (C4H9)4NBr) is one of these additives that belongs to the alkyl ammonium salts [9]. It enhances the enclosure formation through physical combination between TBA+ ions and water molecules connected by the hydrogen bonds. In this process, TBA+ ions fill four big cages (two tetrakaidecahedra and two pentakaidecahedra); however, the small gas molecules fill the dodecahedral small cages [10-12]. TBAB has indispensable characteristics including enhancement of gas storage, improving the selectivity of small dodecahedral cavities for catching the gas molecules, and alleviating the severity of pressure–temperature conditions [13-16]. Hence, semi-clathrate hydrates of TBAB
have been excessively implicated in gas storage and transportation, separation of gas mixtures, and CO2 sequestration [17-19]. Investigations concerning the hydrates of this compound have shown that the phase behavior of binary water + alkyl ammonium salts systems is quite complicated, and thus diverse structures are specified based on the composition of the system [10, 20-23]. The majority of the published work was about studying the phase equilibria between a single gas (CO2, N2 and CH4) and a single promoter such as THF, TBAB or TBAF[24]. However, few studies have investigated the applicability of a mixture of promoters in a single gas for postcombustion. Cyclopentane, cyclohexane, and methyl cyclohexane are known as Heavy Hydrate Formers (HHFs), which can play a significant role in gas hydrate phase equilibria [25, 26]. There is scarcity studies performed on this group, and recently, there is no additional information concerning them [27, 28]. The clathrate hydrate phase equilibria of HHFs have been widely examined in the presence of methane [28]. However, there is still insufficient information regarding the clathrate hydrates of cyclopentane, cyclohexane and methyl cyclohexane in the presence of other gases [4, 29]. In order to gain an overview about the phase equilibria of the mentioned compounds, researchers have made different experimental and theoretical studies. Artificial Neural Networks (ANNs) have been used for convenient illustration of the hydrate dissociation conditions of the systems including H2+TBAB aqueous solutions [30]. Additionally, a thermodynamic model has been introduced and the Statistical Associating Fluid Theory (SAFT-VRE) has been utilized to model the aqueous phase and van der Waals–Platteeuw to study the hydrate phase formed in the carbon dioxide +TBAB aqueous solution system [31, 32]. Another thermodynamic model concerning the phase equilibria of semi-clathrate hydrates of CO2, CH4, or N2 +tetra-n-butyl ammonium
bromide aqueous solution has been proposed [12]. In this model, vander Waals–Platteeuw is used to characterize the hydrate phase, and Peng–Robinson (PR-EoS) equation of state is used to calculate the fugacity of gaseous hydrate former and the mean activity coefficients. Thereafter, a correlation on the basis of an existing osmotic coefficient and activity coefficient values is used. Finally, the Non-Random Two-Liquid (NRTL) activity model is used to determine the activity coefficient of non-electrolyte species in the aqueous phase [33, 34]. In addition, Venkata Ramana Avula et al. have developed a thermodynamic model to predict the phase stability conditions for methane hydrate–ionic liquid (IL)–water system[35]. In this model, the hydrate phase is computed from modified van der Waals–Platteeuw model. The Peng–Robinson equation of state and developed activity model as a combination of Pitzer–Mayorga–Zavitsas-hydration model is used to evaluate the fugacities of gas and liquid phases, respectively. The hydrate phase stability prediction is also computed using the liquid phase activity predicted by NRTL and Pitzer– Mayogra models[35]. In this study, we present a new phase equilibrium data about the semi-clathrate hydrates of CH4 in the presence of a mixture of TBAB and cyclohexane. Secondly, we report the hydrate dissociation conditions for CH4 + cyclohexane + TBAB + water systems at distinct temperatures where there is still limited information regarding them. The isochoric pressure-search method was utilized in order to create our experimental data. In addition, a thermodynamic model is suggested to predict the dissociation conditions of the semi-clathrate hydrates for this system. The hydrate phase properties were predicted by the van der Waals–Platteeuw theory. The aqueous phase properties were evaluated using the e-NRTL electrolyte model and the SoaveRedlich-Kwong equation of state; (SRK EOS) was employed to calculate the gas/vapor phase
properties. Finally, the cyclohexane activity coefficient in the organic phase was calculated by the Non-Random Two-Liquid X (NRTL) model. 2- Experimental section 2.1- Materials Table 1 presents the purities and suppliers of the chemicals used in this study. The aqueous solutions were prepared using an analytical balance with the mass uncertainty of ± 0.0001 g. The CH4 with 99.999% purity purchased from Sabalan Gas Company (Iran), and cyclohexane and TBAB with more than 99.99% purity were obtained from the Sigma-Aldrich chemical company (USA). All chemicals and additives were used as received. Table 1: Purities and suppliers of the chemicals used in this study. Chemical
Formula
Purity
Supplier
CH4
CH4
99.999
Sabalan Gas Company
Cyclohexane
C6H18
99.99
Sigma-Aldrich
TBAB
(C4H9)4NBr
99.999
Sigma-Aldrich
2.2- Experimental apparatus [27, 36-38] The used apparatus was arranged in the processing engineering unit at Tarbiat Modares University (TMU). It includes a jacketed cell made of stain-less steel with the useful volume of 790 cm3. It can stand a high pressure and temperature up to 16 MPa and 323.15 K, respectively. Additionally, the temperature in the inner side of the apparatus is regulated by a circulator water bath, which can provide an adjustable heating rate. Moreover, the vessel consists of an electromagnetic stirrer motor in order to mix the components and the crystalline hydrate formed inside the vessel during the measurements. To measure the
temperature and pressure inside the reactor, two platinum resistance thermometers (Pt100) are used. Finally, in order to record the pressure and temperature of the vessel at 255 time intervals, an in-house software is used. A schematic diagram of the used setup is shown in Fig. 1.
Fig. 1: Schematic diagram of the experimental apparatus used in this work. 3- Experimental procedure To measure the hydrate dissociation conditions, the isochoric pressure-search method was used [39] [37]. At first and before doing the tests, the apparatus was flushed with distilled water for an hour to eliminate every impurity. then, the vessel was evacuated for a 30 min under vacuum condition (pressure down to 10 Pa). Next, it was filled with the desired aqueous solution (30% of the volume of the reactor). After that, the vessel was charged with the desired pressure by adding the desired gas (in our case CH4). Then vigorously we turned on the electromagnetic motor to mix the solution and increase the temperature to heat it for 15 min before doing the cooling step. The temperature was then slowly decreased with a rate of 10 K · h−1 until the hydrate phase was formed. After that, the heating step started where the reactor was heated slowly with a rate of 1 K • h−1 [37, 39]. Thereafter, the temperature was increased slowly at a rate of 0.2 K • h−1. In every step, the temperature was retained constant for enough time until the equilibrium state occured
inside the reactor. Thereafter, the data of each test was sketched to determine the hydrate dissociation point, which is the intersection of the two curves (heating and cooling). 4- Thermodynamic framework The system studied in this work consists of four phases: hydrate, water + TBAB, gas, and cyclohexane. The thermodynamic model is based on the equality of hydrate fugacity and liquid L
fugacity. In the equilibrium condition, the fugacity of water in the liquid ( fw ) and hydrate phases was equal, which is written as follow: ƒ wL = ƒwH
(1)
Where, fwH and fwL are the fugacity of water in the hydrate and liquid phases, respectively. 4.1- Hydrate phase: The fugacity of water in the hydrate phase (fwH) is calculated using the van der Waals-Platteeuw Model [33]: ƒ w H = ƒ w MT exp (( −∆µ w MT − H ) / RT )
(2)
Where, fwMT represents the fugacity of water in the hypothetical empty hydrate lattice, ∆µ wMT-H is the chemical potential difference between the empty hydrate and filled hydrate phases. Regarding the presence of guest molecules, based on the Langmuir absorption theory, the chemical potential is calculated through the following equation: 3
∆µ w MT − H = µ w MT − µ w H = RT ∑ vi ln(1 + Cij ƒ j )
(3)
( i =1)
Where, υi, T, R and Cij are the number of cavities, temperature, the universal gas constant, and the Langmuir constant for types i and j cavity, respectively. We assumed that cyclohexane has a
synergic effect on the TBAB semi-clathrate hydrate [40], so the above equation can be further described as the following equation:
∆μ
+ ƒ ( + , ƒ + , ƒ ) = #
" ( + , "ƒ + , " ƒ )
(4)
To calculate the Langmuir constants, Parrish and Prausnitz (1972) proposed a group of equations expressed as follows: For tetrakaidecahedra cages: Clarge1= × ()
(5)
For pentakaidecahedra cages: Clarge 2= × ( ) %
&
(6)
For the dodecahedral small cages [33]: Csmall=
× ( ) ''
(7)
In the above equations, a, s, d and f are respectively, adjustable parameters for tetrakaidecahedra and pentakaidecahedra cavities, which are obtained through fitting of the experimental data (the optimized values of these parameters are presented in Table 2). Additionally, aa and bb are the parameters recommended by Parrish and Prausnitz (1972) for each gaseous hydrate former encaged in dodecahedral small cages (reported in Table 3) [31]. Table 2: Adjustable parameters for tetrakaidecahedra and pentakaidecahedra cages
Type A
a(K Mpa-1)
s(K)
d(K Mpa-1)
f(K)
1.2412 × 10*
1.2947 × 10+
4.0065× 10,
2.5309 × 10-
2.4544× 10,
Type B
4.816 × 10-
1.297 × 10..
2.3213 × 10.
The below assumptions have been used in order to define the Langmuir constants[12]: 1- We have two types of semi-clathrates with different hydration numbers: type A with 26 hydration number and type B with 38 hydration number. 2- The gas molecules (CH4) are situated in the small cavities. 3- The positive ion TBA+ is captured between two large tetrakaidecahedra and two large pentakaidecahedra. 4- All types of semi-clatrates listed before have: two large cavities and one small cavity. The below equations are used to calculate the number of cages of the specified type per water molecule in a unit hydrate cell:
vl arg e1 =
nl arg e1 N
MT w
; vl arg e 2 =
nl arg e 2 N
MT w
; v small =
(8)
n small N wMT
The calculations showed that / smal=3/38; /large1=1/19; and /large2=1/19. Table 3: Constants aa and bb Gas
aa(K MPa-1)
bb(K)
CH4
0.0037237
2708.8
Equation (9) is used to calculate the fugacity of water in the hypothetical empty hydrate lattice (fwMT):
ƒ wMT=PwMT exp(
0 (11 )
)
(9)
The water molar volume in empty hydrate lattice (VwMT) is calculated according to Equation (10) [41]: VwMT= (11.835+2.217× 23 T + 2.242× 24 T2)
2562 74
NA +1.6155× 28 P – 2.50542"
(10)
P2
Equation (11) is used in order to calculate the vapor pressure of water in vacant hydrate cavities, where pressure (P) is in MPa [14]: PwMT=0.1 exp (17.44 -
4226.8
(11)
)
4.2- Thermodynamic model of the aqueous phase The water fugacity in the aqueous phase is calculated using the following equation: Vw ( P − Pwsat ) fWL = xwLγ wL Pwsatϕ wsat ,V exp RT
(12)
Where, xw is the mole fraction, γ w is the water activity coefficient, Pw L
pressure,
L
sat
is the water vapor
ϕwsat ,V is the fugacity coefficient of pure water, Vw is the molar volume of water, and
the saturation state is indicated by superscript sat. Equation (13) is used to calculate the molar < fraction of water in the aqueous solution phase (:; ) [12]:
= =
− = + 2. 22 × " ×
(13)
Where, m (mol/kg) is the molality of the promoter, TBAB, in the aqueous solution, and Mw (kg/mol) is the molecular weight of water. The relation between molality and molar fraction of TBAB can be derived as follows [31]:
= = =? = = 5
(14)
@. 23=? =( ) 222=
(15)
The pressure/temperature (PT) flash calculation showed that the gas mole fraction in water was negligible, so xBC is considered negligible (:D< = 0). To calculate the activity coefficient of water
in the aqueous phase (γwL), the electrolyte-Non-Random Two-Liquid (e-NRTL) activity
coefficient model is used: for water : lnγi=lnγiLC +lnγi*PDH
(16)
for ions : lnγi*=lnγi*LC +lnγi*PDH
(17)
Where, i represents the cation, anion and water component. The interaction parameters EF,G of eNRTL model between water-TBA+Br- molecules are determined using equation (18): H ,I = ,I +
' ,I & − + J ,I K + K LL &
(18)
Where, MF,G , NF,G MOP QF,G are adjustable parameters, which are fitted from our data at RSTU = 298.15Z and tabulated in Table 4.
Table 4: ai,j, bi,j and ci,j between water-TBA+Br- molecules Components [\,]
^\,] (_) `\,]
TBA+, Br-, water
water, TBA+, Br-
-3.2185
7.5871
-4.2629
5.4443
11.3440
-1.4560
The TBA+ cation is denoted by subscript ca, and its fugacity is determined using Equation (19) as follows: vpL ( P − Ppsat ) fcaL = xpLγ pL Ppsat exp RT
(19)
The hydrate promoter (TBAB) is indicated by subscript p. γpL is determined using the e-NRTL activity coefficient model. To calculate the promoter molar volume (/a b ) and the density data (cp) of TBAB in aqueous solution, Equations (20) and (21) are used [42, 43]: dp= dw + O1(100wp) + O2(100wp)2 + O3(100wp)3
(20)
Oi=qi + ri(T)+ si(T)2
(21)
Where, ri, qi and si for TBAB are obtained from the data available in the literature and reported in Table 5. cp is reported in g cm-3. Table 5: Constants Values in Equations (21) and (22) [37] Constants
s3
s2
s1
r3
r2
r1
q2
q1
Values
-7.091× 10-
5.304× 10+
4.549 × 10+
4.088× 10*
-3.099× 10-
5.693× 10-
4.57× 10e
-1.707 × 2@
Pghij is calculated using Equation (22) [44]:
Ppsat= 2.724[email protected]/(42."8))
(22)
4.3- Oil phase The following equation provides the fugacity of cyclohexane in oil phase:
m2 n ƒ = = γ 1 =o K
11n
L ; q = = − =
(23)
To calculate the CH4 solubility in organic phase (xgoil), the following expression is used [12]:
= =
ƒ r
s∗7 =o u
v (1 −
(24)
1n )
w
∗ Since xyz+ is a function of xgoil, an iterative method is needed to calculate the xgoil from Equation (24).
The Henry’s constant (MPa) of gas in cyclohexane (Hg-CH) is calculated as follows: '
'
= u − K − { L ∗ 2{({"k6.3) w
(25)
Where, a and b are constants and their values is to 6.74545, and 300.6826 K, respectively [45]. Equation (25) is based on the vapor liquid equilibrium of CH4-CH system at the atmospheric }
pressure. Where, xCH4_CH = T |{~ is a function of temperature at the atmospheric pressure[45]. When the total pressure is equal to one bar, the gas solubility is low, and the gas
phase can be assumed to be ideal. The equilibrium equation is written as xCH4∗Hg-CH = yCH4, where yCH4 is calculated from yCH, which is obtained by its corresponding equilibrium equation, yCH = xCH*PCH_sat = (1-xCH4)×PCH_sat. Then Hg_CH = (1-(1-xCH4)×PCH_sat)/xCH4, which is written in the form of Equation (26). In addition, A, B and C are Antoine’s coefficients for cyclohexane (Their values are reported in Table 6). Table 6: Antoine’s coefficients values Constants
A(K)
B(K)
C(K)
Values
6.85146
1206.47
223.136
The saturation pressure of cyclohexane (MPa) is obtained using Equation (26):
(/({("k6.3)))/k42 1n = 2
(26)
Cyclohexane activity coefficient in the oil phase (γCHoil) is calculated by NRTL activity model. The interaction parameters between CH4 and cyclohexane are calculated from Equation (27): H ,I = ,I +
' ,I
(27)
Where, MF,G and NF,G are parameters, which are fitted from our data and their values are reported in Table 7. Table 6: MF,G and NF,G parameters used in this work Parameters
,I (j/mol.k) ' ,I (j/mol.k2)
CH4
Cyclohexane
CH4
0
0.3787
Cyclohexane
0.2455
0
CH4
0
-0.2490
Cyclohexane
0.7387
0
4.4- Thermodynamic model of the gas phase In this study, the SRK equation of state is used to calculate the fugacity of components in the gas phase such as methane. The applied critical properties and acentric factor of methane are listed in Table 8. Table 7: Critical properties and acentric factors of the applied pure gas. Compound
PC (MPa)
TC (K)
CH4
4.61
190.6
0.0114
By placing the above Equations in equation 1, the Relation (28) is obtained:
0 151 n m (151 L =m s 1n =oK
1 =o (
×
(28)
+ ƒ
( + , ƒ + , ƒ ) # − = 2
" ( + , " ƒ + , " ƒ )
The percentage of the Average Absolute Relative Deviation (AARD) in pressure is calculated as follows: = 1 ∑
1 = 1J
1 =
× 22
(29)
Where, N is the number of experimental points, P and PiC denote the experimental and calculated
pressure, respectively. To understand what we have done before, an algorithm is sketched in Fig. 2
that shows the calculation procedure for prediction of hydrate formation pressures at given temperatures.
Imput (ww, Mw,MTBAB,Pwsat,Vw,PTBABsat,VTBAB,PCHSat, VCH, PwMT)
Read T
xw=
/(
~
+
~
)
Guess P
s
L1
CCH4 ,CTBAB ,CTBAB
L2
γTBAB by ENRTL
Guess xCH4 :yz+
D¯°±±
²|< = :yz+
xB =
Calculate g by SRK
oil
Guess γCH4oil
γw by ENRTL
ƒCH4g= ch4g * P
ƒ B
hij υv B (P − P ) HB exp u w RT
e= ¡1 −
¦§¨©©
¢ £¤¥
ª«¬ ¢£¤¥
¡ < 10*
γCH4oil by NRTL
Not satisfied return
hij υ ® (P − P ) hij ƒ w = x γ P exp u RT
Checking Equation (28)
Satisfied
Save T, P
Fig. 2: Calculation procedure for prediction of hydrate formation pressures at given temperatures
Results and discussion The experimental conditions of semi-clathrate hydrate formation for CH4 after the addition of TBAB + cyclohexane (CH) are presented in Table 9 and depicted in Figs. 3-5. In order to ensure that the experimental procedure and setup are valid, some tests for CH4 in the presence of pure water were performed at the pressure and temperature ranges 3.1 - 6 MPa and 274 - 280 K, respectively. The measured data are presented in Table 9 and plotted in Fig. 3. Comparison of the results shown in Fig. 3 revealed that there is consistency between the collected test data and those mentioned in the literature [46] (with small AARD). Figs. 3-5 illustrate the experimental data of hydrate dissociation conditions for (CH4 + TBAB + CH + water) system at the distinct mass fractions (0.05, 0.10, and 0.25) of TBAB in the aqueous phase. As shown, cyclohexane exerted a promoting effect on CH4 + TBAB + CH + water system. Therefore, cyclohexane improved the temperature and reduced the hydrate dissociation pressure in comparison to CH4 + TBAB + water at the same TBAB concentrations. According to these results, it can be concluded that cyclohexane exerts the same or slightly higher promoting effect in comparison to TBAB in the presence of CH4. Hence, CH might modify the hydrate dissociation conditions toward milder conditions. Furthermore, it is seen from Figs. 3-5 that the hydrate dissociation conditions switch to the left side when the TBAB concentration in the aqueous solution and in the presence of CH increases from 0.05 to 0.10 mass fraction. However, such conditions switch to the right side when the TBAB concentration increases to 0.25 mass fraction.
Table 9: Experimental hydrate dissociation conditions of CH4 + TBAB+ CH + water system TBAB mass fraction (w)
T/K
P/MPa
w=0
274.1
2.9
275.2
3.19
276.3
3.49
277.34
3.88
278.2
4.29
283.9
2.014
285.71
3.187
287.53
4.525
288.42
5.487
289.47
6.923
285.9
1.52
288.55
3.375
289.65
4.3
290.24
5.12
291.36
6.254
288.51
1.04
290.05
1.965
292.6
4.5
293.46
5.515
294.03
6.351
w=0.05
w=0.10
w=0.25
Hence, the behavior of the system in the presence of TBAB within the concentration range of 0.05 - 0.10 mass fractions is probably due to the difference in the capability of CH and TBAB promoters for occupying empty cavities. TBAB promoter has more capability to reside in large cavities while all cyclohexane persists in the oil solution. As a result, TBAB acts as an inhibitor in the presence of cyclohexane. Correspondingly, TBAB and CH stabilize the hydrate cages as the TBAB mass fraction increases from 0.10 to 0.25; however, part of the TBAB promoter remains in the aqueous phase. Therefore, the inhibiting effect of TBAB decreases as its concentration changes from 0.10 to 0.25, which is not the case when its mass fraction is in the range of 0.05 - 0.10 or at 0.25. According to the experimental results, combining 0.25 TBAB mass fraction with 40cc CH made the hydrate dissociation conditions more moderate than the (CH4 + CH + water) system. So, it can be concluded that both promoters probably occupy the hydrate cavities, and TBAB's function shifts from inhibitor to promoter at 0.25 TBAB mass fraction. Finally, the thermodynamic model was developed and applied in order to evaluate the hydrate dissociation conditions, while adding the mixed promoters (TBAB+CH) to the water + CH4 system. Initially, 0.05, 0.10, and 0.25 TBAC mass fractions plus 40cc CH data were used to acquire the Langmuir constants using optimization techniques. Additionally, consistency was observed between the predicted and measured experimental data. The results depicted in Fig. 6, show that within the mentioned TBAB concentrations, the suggested thermodynamic model can be used to evaluate the results with an acceptable outcome. The obtained results are shown in Table 10, which demonstrate an acceptable accuracy of the model results in wide ranges of temperature and pressure comparing to the selected experimental data.
8 7 6
P(MPA)
5 4 3 2 1 0 272
274
276
278
280
282
284
286
288
290
292
T(K)
Fig. 3: Hydrate equilibrium data (hydrate dissociation conditions) for the (CH4 + TBAB+ cyclohexane + water) system: □, (pure CH4 + water) system [46]; *,(pure CH4 + water) this work; ∆, (cyclohexane+ CH4 + water) system [47]; ×, CH4 in the presence of 0.05 mass fraction TBAB aqueous solution [48]; ◊, CH4 + CH in the presence of 0.05 mass fraction TBAB aqueous solution (this work).
10 9 8 7
P(MPA)
6 5 4 3 2 1 0 272
274
276
278
280
282
284
286
288
290
292
294
T(K)
Fig. 4: Hydrate equilibrium data (hydrate dissociation conditions) for the (CH4 + TBAB+ cyclohexane + water) system: ◊, (pure CH4 + water) system [46]; □, (cyclohexane+ CH4 + water) [47]; ∆, CH4 in the presence of 0.10 mass fraction TBAB aqueous solution [14]; ×, CH4 + CH in the presence of 0.10 mass fraction TBAB aqueous solution (this work). 12
10
P (MPA)
8
6
4
2
0 270
275
280
285 T(K)
290
295
300
Fig. 5: Hydrate equilibrium data (hydrate dissociation conditions) for the (CH4 + TBAB+ cyclohexane + water) system: ◊, (pure CH4 + water) system [46]; □, (cyclohexane+ CH4 + water) [47]; ∆, CH4 in the presence of 0.25 mass fraction TBAB aqueous solution [14]; ×, CH4 + CH in the presence of 0.25 mass fraction TBAB aqueous solution (this work).
Fig. 6: Comparison between the experimental data and the predicted values of the proposed model. Symbols show the experimental data; solid lines stand for the predictions of the model; *, CH4 + CH in the presence of 0.05, 0.10 and 0.25 mass fraction TBAC aqueous solution (this work). Table 10: Model results for prediction of hydrate dissociation conditions in the presence of CH4, TBAB, cyclohexane and water System
wTBAB
Temperature range
Pressure range
³³´µ
CH4+ water+ TBAB +cyclohexane
(k)
(MPa)
0.05
283.9 - 289.47
20.14 - 69.23
8.7337
0.1
285.9 - 291.36
15.2 - 62.54
3.1543
0.25
288.51 - 294.03
10.4 - 63.51
6.6269
5. Conclusion This paper reports the experimental data of hydrate dissociation conditions for (CH4 + TBAB + CH + water) system. Additionally, we investigated the effectiveness of the mixed promoters (CH + TBAB) on the hydrate dissociation conditions of CH4 gas. Based on the collected experimental results, adding cyclohexane to the CH4 + TBAB + water system exerted a promoting effect on the equilibrium conditions of the formed hydrate, despite that cyclohexane exerted a slight promoting effect on hydrate dissociation conditions during the three series of tests. Furthermore, TBAB exerted a promoting effect on the hydrate dissociation conditions of CH4 + CH + water system. In addition to that, a thermodynamic model was established to evaluate the hydrate dissociation conditions of (CH4 + TBAB + CH + water) system. Fitting model was used to obtain the Langmuir constants in some of the measured experimental data at 0.05, 0.10, and 0.25 TBAB mass fractions plus 40cc CH. Finally, the average absolute relative deviation (AARD %) of the suggested model's results was found to be 5.4%. References 1. 2. 3.
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Research Highlights •
Experimental hydrate dissociation conditions for (CH4 + TBAB + cyclohexane + water) system are reported.
•
A thermodynamic model has been developed and its results are in acceptable agreement with the experimental data.
•
The TBAB exerted an inhibiting effect on the hydrate dissociation conditions of the CH4 + CH + water system.
•
The addition of cyclohexane to the CH4+ TBAB+ water system exerted a promoting effect on the equilibrium conditions of the formed hydrate.