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Experimental measurement and thermodynamic modeling of hydrate dissociation conditions for (CO2 + TBAC + cyclopentane + water) system
Journal Pre-proofs Experimental Measurement and Thermodynamic Modeling of Hydrate Dissociation Conditions for (CO2 + TBAC + Cyclopentane + Water) system Hassan Pahlavanzadeh, Samira Mohammadi, Amir H. Mohammadi PII: DOI: Reference:
S0021-9614(19)30221-6 https://doi.org/10.1016/j.jct.2019.105979 YJCHT 105979
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
8 March 2019 15 September 2019 12 October 2019
Please cite this article as: H. Pahlavanzadeh, S. Mohammadi, A.H. Mohammadi, Experimental Measurement and Thermodynamic Modeling of Hydrate Dissociation Conditions for (CO2 + TBAC + Cyclopentane + Water) system, J. Chem. Thermodynamics (2019), doi: https://doi.org/10.1016/j.jct.2019.105979
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© 2019 Published by Elsevier Ltd.
Experimental Measurement and Thermodynamic Modeling of Hydrate Dissociation Conditions for (CO2 + TBAC + Cyclopentane + Water) system
Hassan Pahlavanzadeha*1, Samira Mohammadia, Amir H. Mohammadib
a
Faculty of Chemical Engineering, Tarbiat Modares University, Tehran
b
Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V, Avenue, Durban, South Africa
Abstract - In this communication, experimental data of hydrate dissociation conditions for (CO2 + tetra n-butylammonium chloride (TBAC) + cyclopentane (CP) + water) system is reported in the temperature range of (286 to 293) K, the pressure range of (0.97 to 3.51) MPa, and at various concentrations of TBAC (0.05, 0.10, 0.18 and 0.25 mass fractions). The experiments were carried out using an isochoric pressure-search method to obtain the experimental data and the method validity was checked by re-generating (CO2 + TBAC) hydrate data reported in literature. A thermodynamic model was developed to estimate the experimental hydrate dissociation conditions, which employs e-NRTL activity coefficient model and PR equation of state to model the liquid and the vapor/gas phases and van der Waals – Platteeuw (vdW-P) theory to model the hydrate phase. Experimental hydrate dissociation conditions at 0.05, 0.10 and 0.25 TBAC mass fractions were used to obtain the parameters of the thermodynamic model. Using the obtained parameters, the hydrate dissociation conditions at 1
Corresponding author. Tel.: +98 2182883312; fax: +98 2182883381. E-mail address: [email protected] (H. Pahlavanzadeh).
1
0.18 mass fraction of TBAC were predicted. The predicted values are in a reasonable agreement with the experimental data demonstrating the success of modeling. The average absolute relative deviation (AARD %) for the model is about 3.5%.
Keywords - Gas Hydrate; Clathrate Hydrate; Semi-clathrate Hydrate; Carbon Dioxide; TBAC; Cyclopentane.
2
1. Introduction
Gas hydrates (or clathrate hydrates) are crystalline solids physically similar to ice or snow. Low temperatures and/or high pressures are required for the gas hydrate to form. Water cavities formed by hydrogen-bonds function as a host and trap the gas and/or some volatile liquid molecules as guest molecules. Guest molecules and water cavities have the interaction which stabilizes the hydrate structure through van der Waals (vdW) forces. Guest molecules with different sizes and types can determine the structure of hydrate cages that typically include structure I (sI), structure II (sII) and structure H (sH) [1]. Applications of gas hydrates in industry may include gas storage [2; 3], separation [4], transportation of natural gas [5], cold storage [6], water desalination [7; 8], etc. The addition of promoters to the hydrate systems in order to overcome the thermodynamic and kinetic limitations of the hydrate formation process may facilitate adaptation of the hydrate formation technology for various applications such as CO2 capturing. In this regard, thermodynamic promoters may change the formation conditions of hydrate toward higher temperatures and/or lower pressures. The experimental data of hydrate dissociation/equilibrium conditions for a system of (CO2+ water) in the presence of insoluble water promoters such as cyclopentane, cyclohexane, methyl cyclohexane, methyl cyclepentane, and tetrahydrofuran have been reported in the literature [9; 10]. According to the obtained results, among the aforementioned insoluble water promoters, cyclopentane is the most effective promoter. It was further found that quaternary ammonium salts, for example, tetra-nbutylammonium bromide (TBAB), and tetra-n-butylammonium chloride (TBAC), when added to hydrate systems, may lead to formation of semi-clathrate hydrates even at atmospheric pressure. The hydrate cages in a semi-clathrate structure are formed by hydrogen bounds between water molecules and halide anions (Br- and Cl-), which encapsulate tetra-n-butylammonium cations 3
(TBA+) [11]. Recently, researchers have reported the application of semi-clathrate hydrates for gas separation and storage, and cold storage [12; 13; 14; 15; 16]. The experimental data of semiclathrate hydrates dissociation conditions for (methane + TBAC) system with different TBAC mass fractions (0.05 to 0.30) have been reported in the temperature range of 281.65 to 292.85 K [17]. The results indicate that the dissociation pressures of methane hydrate are reduced by 5 MPa in the presence of TBAC. Other researchers [18; 19; 20; 21; 22] have reported that TBAB, TBAF, TBAC, and TBPB may moderate the hydrate dissociation conditions. The measurements of dissociation conditions for TBAB semi-clathrate hydrate + different gases (CO2, N2, CH4 or H2) at different temperatures ranging from 277.7 K to 294.7 K and pressures of at most 15.49 MPa have been conducted [23]. The reported experimental results [23] show that beyond the stoichiometric concentration of TBAB, i.e., 0.35 mass fraction, an inhibition effect is observed. In recent years, the thermodynamic promotion effects of mixed promoters (THF and CP) on CO2-clathrate hydrate have been investigated [24; 25]. It has been reported that the hydrate dissociation pressure of (CO2 + THF + CP + H2O) system decreases in comparison with the hydrate dissociation pressure of (CO2 + THF + H2O) system. According to studies conducted on the (CO2 + N2 + TBAB + CP) system, combination of TBAB with (1.38 mole %) and CP with (5 vol %) has promoting effects compared to (CO2 + N2 + TBAB) system. On the other hand, there is no promoting effect for the mixture of TBAB (0.62 mole%) and CP (5 vol%) [26]. In addition, it has been shown that the CP has a better promoting effect than TBAB due to the formation of different hydrate structure [26]. To the extent of our knowledge, no hydrate equilibrium data has been reported for the system of (CO2 + TBAC + CP). Thus, experimental measurement of (CO2
+
TBAC + CP + H2O) hydrate dissociation pressure at different
concentrations of TBAC using a reliable method seems to be necessary.
4
In this study, first, the experimental hydrate dissociation conditions of (CO2 + H2O) and (CO2 + TBAC + H2O) systems were measured and then the obtained data were compared to the experimental results reported in the literature. Finally, the hydrate incipient conditions of (CO2 + TBAC + CP + H2O) system were measured and modeled at different concentrations of TBAC (0.05, 0.1, 0.18, and 0.25 mass fractions).
2. Experimental Section 2.1. Chemicals Specifications of the utilized chemicals in the current study are presented in Table 1. An accurate analytical balance (mass uncertainty: ± 0.0001g) with a gravimetric method was used to prepare the aqueous solutions. Aqueous solutions of TBAC were prepared utilizing deionized distilled water.
Table 1. Purities and suppliers of the chemicals used in this study.
2.2. Apparatus Fig. 1 illustrates a schematic representation of the used apparatus in this work. A cylindrical reactor was utilized in this work that has a volume of 790 cm3 which can withstand pressures up to 10 MPa. The reactor is a stainless steel vessel with two valves that may be utilized for introducing and draining aqueous solution/liquid and a valve for injecting and releasing a hydrate forming gas. A stirrer is utilized in the reactor to mix the existening contents 5
in the reactor and to ensure an effective contact between the hydrate forming gas, the aqueous/ liquid phase, and the hydrate phase. A programmable coolant circulator and a thermometer are used to fix and control the reactor temperature. To measure the temperature and pressure of the reactor, a platinum thermometer (Pt 100) and a pressure transducer (type 26-600G for pressure values up to 10MPa) are used, respectively. The calibration of temperature against a 25 reference platinum thermometer resistance is employed to estimate the maximum uncertainty of the temperature measurement, which is about ± 0.1 K. The calibration of pressure against a dead weight balance (Desgranges and Huot, model 520) is used to estimate the pressure measurement uncertainty which is about ± 5 kPa. A vacuum pump is utilized for evacuating the reactor. A data acquisition system receives and records the data (time, temperature and pressure) of the reactor in 20 seconds periods of time. Figure 1. Schematic diagram of the experimental apparatus.
2.3. Experimental Procedure An isochoric pressure search method with a step-heating approach was used to measure the hydrate dissociation conditions for (CO2 + TBAC + CP + water) system [27]. In comparison to conventional continuous-heating approach, the step-heating approach is more reliable and accurate, because, in this method, the system temperature is changed through steps and the system has adequate time in each step to get the equilibrium state [28; 29]. After rinsing the system with deionized-distillated water, the reactor was purged with the gas and evacuated using vacuum pump down to 1 kPa and then TBAC aqueous solution (100 cm3) and organic phase of
6
cyclopentane (50 cm3) were added to the reactor. After introducing the gas into the system up to a specific pressure, i.e., higher than the hydrate formation pressure, the temperature was reduced with 3 K steps to get to a set-point temperature in the proximity of the corresponding hydrate dissociation temperature. Each 3 K step has a 45 min length to provide adequate time for the system to get an equilibrium state. Finally, the cooling line can be provided by plotting the pressures versus the temperatures obtained from each step of cooling. The hydrate is formed in the system, when at the set-point temperature a sudden pressure drop is achieved. The temperature and pressure are observable on a display connected to the data acquisition system, which receives and records the data. The heating rate in this work is 0.5 K and adequate time to get the equilibrium state after each step is 6 h. In order to achieve the hydrate dissociation point, heating curve obtained from polynomial fitted with the equilibrium data is intersected with the cooling rate and the intersection point is the hydrate dissociation point.
3. Thermodynamic model The equality of water fugacity in the aqueous phase ( f wL ) and in the hydrate as four phase (L-Lo-G-H) equilibrium condition for the system of ( CO2 + TBAC + CP + water), is written as follow: f wH f wL
(1)
where f denotes fugacity, subscript w stand for water, and L, Lo, H and G represent the aqueous solution, organic solution, hydrate, and gas phases, respectively. 7
The water fugacity in the aqueous phase may be expressed by the following equation:
f x P L W
L L sat w w w
sat ,V w
Vw P Pwsat exp RT
(2)
where xwL is the mole fraction, wL is the water activity coefficient, Pwsat is the water vapor pressure,
wsat ,V is the fugacity coefficient of pure water, Vw is the molar volume of water, and the saturation state is indicated by superscript sat. A PT flash calculation shows that water mole fraction in cyclopentane, cyclopentane mole fraction in aqueous solution, and water and cyclopentane mole fractions are negligible in vapor phase. The mole fraction of water ( xwL ), cation (TBA+) ( xcL ) and anion (Cl-) ( xaL ) in aqueous solution are calculated as follows: 1 xgL x nw n n n w a c
1 xgL x nc n n n c w a
(4)
1 xgL xaL na n n n c w a
(5)
L w
L c
(3)
where nc, na and nw stand for cation moles, anion moles and water moles, respectively, which are calculated as follows:
nc Z c m; na Z a m; nw 55.5
(6)
8
m
1000 wp
(7)
277.92 1 wp
Z a , Z c , m and wp stand for the charge number of anion, cation, molality and weight fraction of TBAC, respectively. CO2 mole fraction in the aqueous phase, which is denoted by xgL may be derived from the equality of fugacities:
x L g
f gG
vg P Pwsat H g w exp RT
(8)
where Hg-w denotes the Henry constant of CO2 in water, fgG is the CO2 fugacity coefficient in the gas phase, vg∞ represents the CO2 molar volume at infinite dilution, P is the total pressure, Pwsat is the saturation vapor pressure of water, R and T are the universal gas constant and the temperature, respectively. Peng-Robinson equation of state (PR-EoS) is applied to calculate the fugacity of CO2 in the gas phase. The Hg-w and Pwsat are calculated as follows [30]: Ln H g w 11.981
Ln Pwsat 62.136
2028 T
(9)
-7258.2 -7.304Ln T +4.17 106 T 2 T
(10)
where T is in K, Hg-w and Pwsat are in bar. CO2 molar volume at infinite dilution is considered to be 33.9 cm3/mol. Molar volume of water (Vm) is calculated as follow [30]:
9
1000
Vm
2 3
17.863 58.606t 213.890t 141.260t
4 3
, t 1
T 273.15 373.98
(11)
Using the electrolyte-Non-Random Two-Liquid (e-NRTL) activity coefficient model, the activity coefficient of water in aqueous phase, γwL, is calculated. The interaction parameters of eNRTL model between water-TBA+Cl- and TBA+Cl--water are determined using mean activity coefficient and osmotic coefficient of tetra-n-butylammonium chloride-water solution [31]. Table 2 shows the interaction parameters. Table 3 reports the acentric factors, critical temperature and pressure of CO2 gas.
Table 2. Optimized parameters of e-NRTL model for tetra-n-butylammonium chloride (ca)water (m) [31].
Table 3. Critical properties and acentric factor of CO2 gas [30].
Equation (12) is applied to determine the water fugacity in the hydrate phase.
f
H w
f
MT w
wMT H exp RT
(12)
In Equation (12), the superscript MT indicates an empty hydrate lattice, f wMT and wMT H stand for the fugacity of the empty hydrate lattice and the water chemical potential
difference between empty and filled hydrate lattice. f wMT is presented by Equation (13):
10
f
MT w
P
MT w
VmMT P PwMT exp RT
(13)
As an assumption, water molar volume (m3/mol) of hydrate structure I (As dodecahedral cages are the host of gaseous molecules) [32; 33] which is expressed by Eq (14), is used to determine water molar volume (m3/mol) of the empty hydrate lattice VmMT . The saturated vapor pressure of water in empty hydrate lattice ( PwMT ) [33] is calculated by Eq (15): VwMT T , P 11.835 2.217 105 T 2.242 106 T 2
3
1030 N A 8.006 109 P 5.448 1012 P 2 NW
(14)
(15)
6003.9 h wp PwMT 0.1exp 17.44 T
where Avogadro’s number is indicated by
and the number of water molecules per unit
hydrate cell is represented by NwMT. In Eq (14), the units of pressure and temperature are MPa and K, respectively. wp in Eq (15) is the weight fraction of TBACl in aqueous phase and h is an adjustable parameter whose the optimized value is presented in Table 4. The vdW–P model is employed to determine ΔμwMT-H [34]:
Table 4. The optimized values of parameters.
3
wMT H wMT wH RT vi ln 1 Cij f j
(16)
i 1
where, Cij is Langmuir constant, fj is the hydrate former fugacity and vi is the number of cages of type i per water molecule in a unit hydrate cell. Based on x-ray diffraction studies [35], TBAC
11
semi-clathrate hydrate has structures of type I, II and III with hydration numbers 32, 30 and 24, respectively. All the three structures have tetragonal structure 1 (TS-1) with unit cell formula 16T.4P.10D, in which the number of (3T.P), 4T and D type cavities are 4, 1 and 10, respectively. Also, studies conducted on structures of TBAC hydrates indicate that 4T and 3T.P type cavities are the structures around TBA+ cation and one type of small D cavities trap guest molecules. Based on the assumption that tetragonal structure (TS-1) is formed in the presence of mixed promoters, two large cages of tetragonal structure (3T.P and 4T) may include cyclopentane molecule. Thus Eq. (16) could be described as the following equation:
v small vl arg e 1 vl arg e 2 H ln 1 C s f gG ln 1 C la1 f caL ln 1 C la 2 f caL RT
ln 1 C cyclo1 f
Lo cp
vl arg e 1
ln 1 C cyclo 2 f
Lo cp
vl arg e 2
(17)
where, the TBA+ cation is denoted by subscript ca, and its fugacity is determined using the Eq.(18):
v pL P Ppsat f x P exp RT L ca
L p
L p
sat p
(18)
where the hydrate promoter (TBAC) is indicated by subscript p. γpL is determined using e-NRTL activity coefficient model. For the calculation promoter molar volume, vpL , the density of TBAC solutions is used [36; 37]. The following equation provides the fugacity of cyclopentane in organic phase:
f
Lo cp
vcpLo P Pcpsat ; xcpLo 1 xgLo x P exp RT Lo Lo sat cp cp cp
12
(19)
For the calculation of solubility of CO2 in organic phase (xgLo), the following expression is used:
x
Lo g
f gG
vg P Pcpsat H g cp exp RT
(20)
The Henry’s constant (MPa) of gas in cyclopentane (Hg-cp) is calculated as follow [30]: 9972.345 H g cp 0.1exp 357.257 62.466 ln T 0.0915 T T
(21)
The saturation pressure of cyclopentane (MPa) is obtained using equation (22) [30]: 2839 Pcpsat 0.1exp 35.5041 3.8639 Ln T 2.8 1016 T 6 T
(22)
Cyclopentane activity coefficient in organic phase (γcpLo) is calculated by NRTL activity model. The interaction parameters between CO2-cyclopentane, which are given in Table 5, are obtained from isobar vapor-liquid equilibrium data regression [38].
Table 5. NRTL activity coefficient interaction parameters between cyclopentane and CO2.
For Langmuir constants related to (3T.P), 4T and D type cavities, the recommended correlations by Shi and Liang [39] are employed which are functions of temperature and TBAC
13
mass fraction. The equation of Langmuir constant for large cages of 4T can be expressed as follows: Cl arg e1
1 c exp d exp 75.688w3p 136.33w2p 91.395wp 17.485 T T
(23)
For 3T.P type cages: Cl arg e 2
1 e exp f exp 19.232 w2p 24.936 wp 1.1264 T T
(24)
Parameters c, d, e and f are obtained through fitting the model to the experimental data, which the optimized values of these parameters are presented in Table 4. CO2 gas molecules are encaged in dodecahedral cavities, which Langmuir constants for small D cages are presented as follows:
Csmall
0.000566 4182.53 44770 exp T T 2 T
2.35
(25)
For the Langmuir constant of cyclopentane molecule, the following correlations are suggested:
qq bb dd Ccyclo1 exp 2 T T T
Ccyclo 2
ss
ww rr vv exp 2 T T T
(26)
(27)
ll
The optimized values are demonstrated in Table 4. The numbers of 4T (nlarge1), 3T.P (nlarge2) and D (ns) cavities per unit semi-clathrate hydrate cell are calculated as follow: 14
vl arg e1
nl arg e1 N
MT w
; vl arg e 2
nl arg e 2 N
MT w
; vsmall
nsmall N wMT
(28)
For tetragonal structure (TS-1), the values of nlarge1, nlarge2, nsmall and
are 1, 4, 10 and
64, respectively. Equation (29) is obtained by replacing the preceding equations in Eq. (1) which the hydrate dissociation pressure of the CO2 + TBAC + CP + H2O system can be determined: VmMT P PwMT PwMT exp vl arg e1 vl arg e 2 1 C f G vsmall 1 C RT 1 Cl arg e 2 f caL f caL e l g s 1 arg 1 0 sat Lo vl arg e1 Lo vl arg e 2 V P P L L sat sat ,V 1 Ccyclo1 f cp 1 Ccyclo 2 f cp w w P x exp w w w w RT
(29)
3.1. Regression Method The objective function (30) may be defined for the optimization of parameters of the Langmuir constants ( Ccyclo1 , Ccyclo 2 , Cl arg e1 , Cl arg e 2 ):
OF
100 NP Pexp(i ) Pcal (i ) P NP i 1 exp( i )
(30)
where NP is the total number of data points. P shows the hydrate dissociation pressure and subscript exp(i) and cal(i) stand for ith experimental values, and calculated hydrate dissociation pressure, respectively. The above objective function or the average absolute relative deviation (AARD %) was minimized by the fminsearch function in the optimization toolbox of MATLAB
15
software. The first guesses for fitted parameters (Table 4) were determined using the genetic algorithm. Fig. 2 shows the flow chart applied to determine the model parameters (Table 4).
Figure 2. Flow chart for calculation of the model parameters.
4. Results and discussion
Table 6 presents the experimental hydrate dissociation data for (CO2 + TBAC + CP + water system). To evaluate the step-heating method employed in the current study, the dissociation conditions of hydrate were measured for the systems of (CO2 + water) and (CO2 + TBAC + water), as reported in Table 6. The obtained data together with the data of other researchers [20; 40] are presented in Fig. 3. The good agreement of the measured experimental data with the data reported in the previous studies validates the step-heating method applied in the current study. The experimental data of hydrate dissociation conditions for (CO2 + TBAC + CP + water) system at various mass fractions of TBAC in the aqueous phase, i.e., 0.05, 0.10, 0.18 and 0.25 mass fractions are shown in Fig. 4. According to this figure, for CO2 + TBAC + CP + water system, cyclopentane has the promotion role. Hence, this promoter enhances the temperature and decreases the pressure of hydrate dissociation compared to CO2 + TBAC + water at the same TBAC concentrations. It can be likely attributed to the fact that cyclopentane has more promotion effect compared to TBAC in the presence of CO2, Therefore, CP may change the hydrate dissociation conditions in the direction of milder conditions.
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Table 6. Experimental hydrate dissociation conditions of CO2 + TBAC+ CP + water system.
Figure 3. Experimental hydrate dissociation conditions for the (CO2 + water) and (CO2 + TBAC + water) systems. ◊ ,(CO2 + water) system [40]: ▲,(CO2 + water) system (This work): + , CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]: ○, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution (This work).
Figure 4: Dissociation conditions of clathrate/semi-clathrate hydrates for the (CO2 + TBAC + CP +water) systems. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 + CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ● , CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work); +, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]; □, CO2 in the presence of 0.10 mass fraction TBAC aqueous solution [27]; Δ ,CO2 in the presence of 0.15 mass fraction TBAC aqueous solution [20]; × ,CO2 in the presence of 0.22 mass fraction TBAC aqueous solution [20]; ◊ , CO2 + CP + water [9]; ►, CO2 + water [40].
Also, the obtained results show that, as the TBAC concentration in the aqueous solution in the presence of CP increases from 0.05 to 0.10 mass fraction, the hydrate dissociation conditions shift to the left side, while at the concentrations of higher than 0.10 mass fraction of TBAC, these conditions go towards the right side. Finally, at 0.25 TBAC mass fraction, the synergetic effect of mixed promoters (CP + TBAC) is higher than other concentrations. One of the possible reasons for the behavior of the system in the presence of TBAC with concentrations between 0.05 to 0.10 mass fraction is that the capability of CP and TBAC promoters for filling empty cavities are different, so, one of the promoters (i.e., CP) is more likely to occupy the large cavities and all of TBAC remains in the aqueous solution. Therefore, TBAC in the presence of CP acts as an inhibitor. Accordingly, with increasing TBAC mass fraction from 0.10 to 0.25, TBAC and CP stabilize the hydrate cages, but some of TBAC promoter remains in the aqueous phase. Hence, with concentration changes from 0.10 to 0.25 TBAC mass fraction, the inhibition 17
effect decreases in comparison to 0.05 to 0.10 mass fractions and at the concentration of 0.25 mass fraction, the inhibition role of TBAC vanishes. According to the experimental data, the hydrate dissociation conditions for the combination of 0.25 TBAC mass fraction and 50cc CP are more moderate than (CO2 + CP + water) system. It can be related to the fact that, at 0.25 TBAC mass fraction, both promoters probably fill the hydrate cavities and TBAC role changes from inhibitor to promoter in the presence of CP. Also, the presence of mixed promoters (TBAC+CP) in the CO2 + water system promotes the formation conditions of hydrate and changes the dissociation curve of the hydrate toward the right side. Finally, the thermodynamic model was developed and utilized to estimate the hydrate dissociation conditions, when the mixed promoters (TBAC+CP) are added to water + CO2 system. First, the parameters of Langmuir constants were obtained using 0.05, 0.10, and 0.25 TBAC mass fraction (plus 50cc CP) data (through optimization techniques). To investigate the predictive power of the proposed thermodynamic model, hydrate dissociation conditions for the system of 0.18 TBAC mass fraction (plus 50cc CP) were predicted and compared to the experimental data. An acceptable agreement is found between the predicted and measured experimental data. These findings suggest that, at least at these TBAC concentrations, the proposed thermodynamic model can estimate the results with an acceptable agreement. The results are presented in Fig. 5.
Figure 5. The comparison between experimental data and the predicted values of the proposed model. Symbols show the experimental data; solid lines stand for the predictions of the model. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 18
+ CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ●, CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work).
5. Conclusion The experimental data of hydrate dissociation conditions for (CO2 + TBAC + CP + water) system are reported. The effect of (CP + TBAC) mixed promoters on the hydrate dissociation conditions of CO2 gas was investigated. According to the experimental results of this work, the addition of TBAC to the system of (CO2+CP+water) has an inhibition effect on equilibrium conditions of the formed hydrate, however at 0.25 TBAC mass fraction, the promotion impact on hydrate dissociation conditions is observable. Also, the presence of CP in the (CO2 + TBAC + water) system has a promotion impact on the hydrate dissociation conditions of this system. The results show that (CP + TBAC) mixed promoters can remarkably decrease the hydrate dissociation conditions of CO2 gas. For example, under the tested conditions, the hydrate dissociation conditions of CO2 gas is decreased by 13 K at a given temperature. Furthermore, a thermodynamic model was developed to estimate the hydrate dissociation conditions of (CO2 + TBAC + CP + water) system. Langmuir constants were obtained by fitting model to some of the experimental data measured in this study (0.05, 0.10, and 0.25 TBAC mass fraction (plus 50cc CP)). Good agreement of predicted hydrate dissociation conditions for the system of 0.18 TBAC mass fraction (plus 50cc CP) with experimental data confirm the validity of the model results. The average absolute relative deviation (AARD %) for the results of the proposed model is found to be 3.5%.
19
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[11] D.L. Fowler, W.V. Loebenstein, D.B. Pall, C.A. Kraus, Journal of the American Chemical Society 62 (1940) 1140-1142. [12] S. Li, S. Fan, J. Wang, X. Lang, D. Liang, Journal of Natural Gas Chemistry 18 (2009) 15-20. [13] K. Shin, Y. Kim, T.A. Strobel, P. Prasad, T. Sugahara, H. Lee, E.D. Sloan, A.K. Sum, C.A. Koh, The Journal of Physical Chemistry A 113 (2009) 6415-6418. [14] S. Wenji, X. Rui, H. Chong, H. Shihui, D. Kaijun, F. Ziping, international journal of refrigeration 32 (2009) 1801-1807. [15] J. Deschamps, D. Dalmazzone, Journal of Chemical & Engineering Data 55 (2010) 3395-3399. [16] S. Kim, I.-H. Baek, J.-K. You, Y. Seo, Applied Energy 140 (2015) 107-112. [17] Z.-G. Sun, C.-G. Liu, Journal of Chemical & Engineering Data 57 (2012) 978-981. [18] A. Fukumoto, P. Paricaud, D. Dalmazzone, W. Bouchafaa, T.T.-S. Ho, W. Fürst, Journal of Chemical & Engineering Data 59 (2014) 3193-3204. [19] A. Kamran-Pirzaman, A.H. Mohammadi, H. Pahlavanzadeh, Chemical Engineering Communications 202 (2015) 806-814. [20] A. Mohammadi, M. Manteghian, A.H. Mohammadi, Fluid Phase Equilibria 381 (2014) 102-107. [21] X. Wang, M. Dennis, Journal of Chemical & Engineering Data 62 (2017) 1083-1093. [22] T. Suginaka, H. Sakamoto, K. Iino, Y. Sakakibara, R. Ohmura, Fluid Phase Equilibria 344 (2013) 108-111. [23] A.H. Mohammadi, A. Eslamimanesh, V. Belandria, D. Richon, Journal of Chemical & Engineering Data 56 (2011) 3855-3865. [24] P.J. Herslund, K. Thomsen, J. Abildskov, N. von Solms, A. Galfré, P. Brântuas, M. Kwaterski, J.-M. Herri, International Journal of Greenhouse Gas Control 17 (2013) 397-410. [25] P.J. Herslund, N. Daraboina, K. Thomsen, J. Abildskov, N. von Solms, Fluid Phase Equilibria 381 (2014) 20-27. [26] F. Tzirakis, P. Stringari, N. von Solms, C. Coquelet, G. Kontogeorgis, Fluid Phase Equilibria 408 (2016) 240-247. [27] A. Kamran-Pirzaman, H. Pahlavanzadeh, A.H. Mohammadi, The Journal of Chemical Thermodynamics 64 (2013) 151-158. [28] B. Tohidi, R.W. Burgass, A. Danesh, K.K. Østergaard, A.C. Todd, Improving the accuracy of gas hydrate dissociation point measurements, Annals of the New York Academy of Sciences, New York Academy of Sciences, 2000, pp. 924-931. [29] R. Masoudi, B. Tohidi, R. Anderson, R.W. Burgass, J. Yang, Fluid Phase Equilibria 219 (2004) 157163. [30] A.P. Aspen, Version 8.6. [31] L.S. Belvèze, J.F. Brennecke, M.A. Stadtherr, Industrial & Engineering Chemistry Research 43 (2004) 815-825. [32] J.B. Klauda, S.I. Sandler, Industrial & engineering chemistry research 39 (2000) 3377-3386. [33] A. Eslamimanesh, A.H. Mohammadi, D. Richon, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 46 (2012) 62-71. [34] J.C. Platteeuw, J.H. van der Waals, Recueil des Travaux Chimiques des Pays-Bas 78 (1959) 126133. [35] T.V. Rodionova, V.Y. Komarov, G.V. Villevald, T.D. Karpova, N.V. Kuratieva, A.Y. Manakov, The Journal of Physical Chemistry B 117 (2013) 10677-10685. [36] V. Belandria, A.H. Mohammadi, D. Richon, The Journal of Chemical Thermodynamics 41 (2009) 1382-1386. [37] L.-F. Chen, A.N. Soriano, M.-H. Li, The Journal of Chemical Thermodynamics 41 (2009) 724-730. [38] N.N. Shah, J.A. Zollweg, W.B. Streett, Journal of Chemical & Engineering Data 36 (1991) 188-192. [39] L.-l. Shi, D.-q. Liang, Fluid Phase Equilibria 386 (2015) 149-154. 21
[40] 71.
S. Adisasmito, R.J. Frank III, E.D. Sloan Jr, Journal of Chemical and Engineering Data 36 (1991) 68-
22
Figure 1. Schematic diagram of the experimental apparatus.
23
Guess adjusted parameters (table. 4)
Change parameters
Input T and P ranges
Calculate
(Eq.2)
Calculate
(Eq.18)
Calculate
(Eq.19)
Is abs equation (29) ˂ 10-5
No Yes Display parameters
Figure 2. Flow chart for calculation of the model parameters.
24
5 4.5 4
P/MPa
3.5 3 2.5 2 1.5 1 0.5 272
274
276
278
280 T/K
282
284
286
288
Figure 3. Experimental hydrate dissociation conditions for the (CO2 + water) and (CO2 + TBAC + water) systems. ◊ ,(CO2 + water) system [40]: ▲,(CO2 + water) system (This work): + , CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]: ○, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution (This work).
25
5 4.5 4 3.5
P/MPa
3 2.5 2 1.5 1 0.5 0 274
276
278
280
282
284 T/K
286
288
290
292
294
Figure 4: Dissociation conditions of clathrate/semi-clathrate hydrates for the (CO2 + TBAC + CP +water) systems. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 + CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ● , CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work); +, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]; □, CO2 in the presence of 0.10 mass fraction TBAC aqueous solution [27]; Δ ,CO2 in the presence of 0.15 mass fraction TBAC aqueous solution [20]; × ,CO2 in the presence of 0.22 mass fraction TBAC aqueous solution [20]; ◊ , CO2 + CP + water [9]; ►, CO2 + water [40].
26
9 8 7
P/MPa
6 5 4 3 2 1 0 286
287
288
289
290
291
292
293
294
T/K
Figure 5. The comparison between experimental data and the predicted values of the proposed model. Symbols show the experimental data; solid lines stand for the predictions of the model. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 + CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ●, CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work).
27
Table 1. Purities and suppliers of the chemicals used in this study. Chemical
Supplier
Purity (stated by supplier)
carbon dioxide
Air Liquide
0.999 mole fraction
tetra-n-buthylammonium chloride (TBAC)
Merck Company
0.99 mass fraction
cyclopenthane
Merck Company
0.999 mole fraction
28
Table 2. The results of VLLE calculations for the determination of water, cyclopentane and CO2 mole fractions in the three phases at the temperatures and pressures of the hydrate equilibrium points for (CO2 + TBAC+ CP + water) system. Aqueous Organic phase Component CO2 (Vapor phase) phase 0.0008 Water 0.0014 0.9998 0.9339 Cyclopentane 0.0280 0.000001 CO2 0.9716 0.0001 0.653
29
Table 3. Optimized parameters of e-NRTL model for tetra-nbutylammonium chloride (ca)-water (m) [31]. τm,ca
τca,m
α
7.8229
-4.0247
0.2000
30
Table 4. Critical properties and acentric factor of CO2 gas [30]. Compound CO2 a
Critical pressure.
b
Critical temperature.
c
Acentric factor.
(MPa)
(K)
7.377
304.13
31
0.2239
Table 5. The optimized values of the parameters. Parameter Optimized value Parameter Optimized value
qq (K) 4796.11 ll -32.16
bb (K) -62.93 c (K) 11.83
dd (K2) ss ww (K) -69.60 -15.00 193.96 d e (K) f 3.28 1.23 19.00
K: Kelvin
32
rr (K) -48.72 h -0.29
vv (K2) 83.68
Table 6. NRTL activity coefficient interaction parameters between cyclopentane and CO2 in organic phase on TBAC- water free basis
cyclopentane CO2 ij aij
bij T
aij cyclopentane 0 -4.459
CO2 -7.25 0
, ij 0.3
33
bij cyclopentane CO2 0 2319.35 2333.42 0
Table 7. Experimental hydrate dissociation conditions of CO2 + TBAC+ CP + water system. (CO2 gas/vapor phase on CP- water- TBAC free (CO2 gas/vapor phase on CP- water- TBAC basis + 0.05 TBAC mass fractiona in aqueous free basis + 0.1 TBAC mass fractiona in solution on CP-CO2 free basis )+ CP organic aqueous solution on CP-CO2 free basis )+ CP phase (50 cm3) on TBAC- water free basis) organic phase (50 cm3) on TBAC- water free basis) b b Temperaturec (K) Temperaturec (K) Pressure (MPa) Pressure (MPa) 1.04 286.9 1.60 287.2 1.54 288.6 2.09 288.5 1.87 289.4 2.58 289.2 2.67 291.1 2.95 289.7 3.34 292.1 3.51 290.4 (CO2 gas/vapor phase on CP- water- TBAC free (CO2 gas/vapor phase on CP- water- TBAC basis + 0.18 TBAC mass fractiona in aqueous free basis + 0.25 TBAC mass fractiona in solution on CP-CO2 free basis )+ CP organic aqueous solution on CP-CO2 free basis )+ CP phase (50 cm3) on TBAC- water free basis) organic phase (50 cm3) on TBAC- water free basis) b b Temperaturec (K) Temperaturec (K) Pressure (MPa) Pressure (MPa) 1.72 288.3 0.97 288.4 2.07 289.1 1.31 289.5 2.44 289.9 1.71 290.6 3.01 290.7 2.3 292.1 3.50 291.4 2.9 293.1 (CO2 gas/vapor phase + 0.05 TBAC mass 3 (CO2 gas/vapor phase + 100 cm water) fractiona in aqueous solution on CO2 free basis) b b Temperaturec (K) Temperaturec (K) Pressure (MPa) Pressure (MPa) 1.88 276.8 1.5 282.1 2.39 278.5 2.33 283.4 3.5 284.9
34
Research Highlights
Experimental hydrate dissociation conditions for (CO2 + TBAC + Cyclopentane + Water) system are reported.
A thermodynamic model has been developed and its results are in acceptable agreement with the experimental data.
The addition of low-medium concentration TBAC to the system of (CO2 + CP + water) has an inhibition effect.
The addition of high TBAC concentration to the system of (CO2 + CP + water) has a promotion effect.
The addition of CP in the (CO2 + TBAC + water) system has a promotion impact.
35
S0021-9614(19)30221-6 https://doi.org/10.1016/j.jct.2019.105979 YJCHT 105979
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
8 March 2019 15 September 2019 12 October 2019
Please cite this article as: H. Pahlavanzadeh, S. Mohammadi, A.H. Mohammadi, Experimental Measurement and Thermodynamic Modeling of Hydrate Dissociation Conditions for (CO2 + TBAC + Cyclopentane + Water) system, J. Chem. Thermodynamics (2019), doi: https://doi.org/10.1016/j.jct.2019.105979
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© 2019 Published by Elsevier Ltd.
Experimental Measurement and Thermodynamic Modeling of Hydrate Dissociation Conditions for (CO2 + TBAC + Cyclopentane + Water) system
Hassan Pahlavanzadeha*1, Samira Mohammadia, Amir H. Mohammadib
a
Faculty of Chemical Engineering, Tarbiat Modares University, Tehran
b
Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V, Avenue, Durban, South Africa
Abstract - In this communication, experimental data of hydrate dissociation conditions for (CO2 + tetra n-butylammonium chloride (TBAC) + cyclopentane (CP) + water) system is reported in the temperature range of (286 to 293) K, the pressure range of (0.97 to 3.51) MPa, and at various concentrations of TBAC (0.05, 0.10, 0.18 and 0.25 mass fractions). The experiments were carried out using an isochoric pressure-search method to obtain the experimental data and the method validity was checked by re-generating (CO2 + TBAC) hydrate data reported in literature. A thermodynamic model was developed to estimate the experimental hydrate dissociation conditions, which employs e-NRTL activity coefficient model and PR equation of state to model the liquid and the vapor/gas phases and van der Waals – Platteeuw (vdW-P) theory to model the hydrate phase. Experimental hydrate dissociation conditions at 0.05, 0.10 and 0.25 TBAC mass fractions were used to obtain the parameters of the thermodynamic model. Using the obtained parameters, the hydrate dissociation conditions at 1
Corresponding author. Tel.: +98 2182883312; fax: +98 2182883381. E-mail address: [email protected] (H. Pahlavanzadeh).
1
0.18 mass fraction of TBAC were predicted. The predicted values are in a reasonable agreement with the experimental data demonstrating the success of modeling. The average absolute relative deviation (AARD %) for the model is about 3.5%.
Keywords - Gas Hydrate; Clathrate Hydrate; Semi-clathrate Hydrate; Carbon Dioxide; TBAC; Cyclopentane.
2
1. Introduction
Gas hydrates (or clathrate hydrates) are crystalline solids physically similar to ice or snow. Low temperatures and/or high pressures are required for the gas hydrate to form. Water cavities formed by hydrogen-bonds function as a host and trap the gas and/or some volatile liquid molecules as guest molecules. Guest molecules and water cavities have the interaction which stabilizes the hydrate structure through van der Waals (vdW) forces. Guest molecules with different sizes and types can determine the structure of hydrate cages that typically include structure I (sI), structure II (sII) and structure H (sH) [1]. Applications of gas hydrates in industry may include gas storage [2; 3], separation [4], transportation of natural gas [5], cold storage [6], water desalination [7; 8], etc. The addition of promoters to the hydrate systems in order to overcome the thermodynamic and kinetic limitations of the hydrate formation process may facilitate adaptation of the hydrate formation technology for various applications such as CO2 capturing. In this regard, thermodynamic promoters may change the formation conditions of hydrate toward higher temperatures and/or lower pressures. The experimental data of hydrate dissociation/equilibrium conditions for a system of (CO2+ water) in the presence of insoluble water promoters such as cyclopentane, cyclohexane, methyl cyclohexane, methyl cyclepentane, and tetrahydrofuran have been reported in the literature [9; 10]. According to the obtained results, among the aforementioned insoluble water promoters, cyclopentane is the most effective promoter. It was further found that quaternary ammonium salts, for example, tetra-nbutylammonium bromide (TBAB), and tetra-n-butylammonium chloride (TBAC), when added to hydrate systems, may lead to formation of semi-clathrate hydrates even at atmospheric pressure. The hydrate cages in a semi-clathrate structure are formed by hydrogen bounds between water molecules and halide anions (Br- and Cl-), which encapsulate tetra-n-butylammonium cations 3
(TBA+) [11]. Recently, researchers have reported the application of semi-clathrate hydrates for gas separation and storage, and cold storage [12; 13; 14; 15; 16]. The experimental data of semiclathrate hydrates dissociation conditions for (methane + TBAC) system with different TBAC mass fractions (0.05 to 0.30) have been reported in the temperature range of 281.65 to 292.85 K [17]. The results indicate that the dissociation pressures of methane hydrate are reduced by 5 MPa in the presence of TBAC. Other researchers [18; 19; 20; 21; 22] have reported that TBAB, TBAF, TBAC, and TBPB may moderate the hydrate dissociation conditions. The measurements of dissociation conditions for TBAB semi-clathrate hydrate + different gases (CO2, N2, CH4 or H2) at different temperatures ranging from 277.7 K to 294.7 K and pressures of at most 15.49 MPa have been conducted [23]. The reported experimental results [23] show that beyond the stoichiometric concentration of TBAB, i.e., 0.35 mass fraction, an inhibition effect is observed. In recent years, the thermodynamic promotion effects of mixed promoters (THF and CP) on CO2-clathrate hydrate have been investigated [24; 25]. It has been reported that the hydrate dissociation pressure of (CO2 + THF + CP + H2O) system decreases in comparison with the hydrate dissociation pressure of (CO2 + THF + H2O) system. According to studies conducted on the (CO2 + N2 + TBAB + CP) system, combination of TBAB with (1.38 mole %) and CP with (5 vol %) has promoting effects compared to (CO2 + N2 + TBAB) system. On the other hand, there is no promoting effect for the mixture of TBAB (0.62 mole%) and CP (5 vol%) [26]. In addition, it has been shown that the CP has a better promoting effect than TBAB due to the formation of different hydrate structure [26]. To the extent of our knowledge, no hydrate equilibrium data has been reported for the system of (CO2 + TBAC + CP). Thus, experimental measurement of (CO2
+
TBAC + CP + H2O) hydrate dissociation pressure at different
concentrations of TBAC using a reliable method seems to be necessary.
4
In this study, first, the experimental hydrate dissociation conditions of (CO2 + H2O) and (CO2 + TBAC + H2O) systems were measured and then the obtained data were compared to the experimental results reported in the literature. Finally, the hydrate incipient conditions of (CO2 + TBAC + CP + H2O) system were measured and modeled at different concentrations of TBAC (0.05, 0.1, 0.18, and 0.25 mass fractions).
2. Experimental Section 2.1. Chemicals Specifications of the utilized chemicals in the current study are presented in Table 1. An accurate analytical balance (mass uncertainty: ± 0.0001g) with a gravimetric method was used to prepare the aqueous solutions. Aqueous solutions of TBAC were prepared utilizing deionized distilled water.
Table 1. Purities and suppliers of the chemicals used in this study.
2.2. Apparatus Fig. 1 illustrates a schematic representation of the used apparatus in this work. A cylindrical reactor was utilized in this work that has a volume of 790 cm3 which can withstand pressures up to 10 MPa. The reactor is a stainless steel vessel with two valves that may be utilized for introducing and draining aqueous solution/liquid and a valve for injecting and releasing a hydrate forming gas. A stirrer is utilized in the reactor to mix the existening contents 5
in the reactor and to ensure an effective contact between the hydrate forming gas, the aqueous/ liquid phase, and the hydrate phase. A programmable coolant circulator and a thermometer are used to fix and control the reactor temperature. To measure the temperature and pressure of the reactor, a platinum thermometer (Pt 100) and a pressure transducer (type 26-600G for pressure values up to 10MPa) are used, respectively. The calibration of temperature against a 25 reference platinum thermometer resistance is employed to estimate the maximum uncertainty of the temperature measurement, which is about ± 0.1 K. The calibration of pressure against a dead weight balance (Desgranges and Huot, model 520) is used to estimate the pressure measurement uncertainty which is about ± 5 kPa. A vacuum pump is utilized for evacuating the reactor. A data acquisition system receives and records the data (time, temperature and pressure) of the reactor in 20 seconds periods of time. Figure 1. Schematic diagram of the experimental apparatus.
2.3. Experimental Procedure An isochoric pressure search method with a step-heating approach was used to measure the hydrate dissociation conditions for (CO2 + TBAC + CP + water) system [27]. In comparison to conventional continuous-heating approach, the step-heating approach is more reliable and accurate, because, in this method, the system temperature is changed through steps and the system has adequate time in each step to get the equilibrium state [28; 29]. After rinsing the system with deionized-distillated water, the reactor was purged with the gas and evacuated using vacuum pump down to 1 kPa and then TBAC aqueous solution (100 cm3) and organic phase of
6
cyclopentane (50 cm3) were added to the reactor. After introducing the gas into the system up to a specific pressure, i.e., higher than the hydrate formation pressure, the temperature was reduced with 3 K steps to get to a set-point temperature in the proximity of the corresponding hydrate dissociation temperature. Each 3 K step has a 45 min length to provide adequate time for the system to get an equilibrium state. Finally, the cooling line can be provided by plotting the pressures versus the temperatures obtained from each step of cooling. The hydrate is formed in the system, when at the set-point temperature a sudden pressure drop is achieved. The temperature and pressure are observable on a display connected to the data acquisition system, which receives and records the data. The heating rate in this work is 0.5 K and adequate time to get the equilibrium state after each step is 6 h. In order to achieve the hydrate dissociation point, heating curve obtained from polynomial fitted with the equilibrium data is intersected with the cooling rate and the intersection point is the hydrate dissociation point.
3. Thermodynamic model The equality of water fugacity in the aqueous phase ( f wL ) and in the hydrate as four phase (L-Lo-G-H) equilibrium condition for the system of ( CO2 + TBAC + CP + water), is written as follow: f wH f wL
(1)
where f denotes fugacity, subscript w stand for water, and L, Lo, H and G represent the aqueous solution, organic solution, hydrate, and gas phases, respectively. 7
The water fugacity in the aqueous phase may be expressed by the following equation:
f x P L W
L L sat w w w
sat ,V w
Vw P Pwsat exp RT
(2)
where xwL is the mole fraction, wL is the water activity coefficient, Pwsat is the water vapor pressure,
wsat ,V is the fugacity coefficient of pure water, Vw is the molar volume of water, and the saturation state is indicated by superscript sat. A PT flash calculation shows that water mole fraction in cyclopentane, cyclopentane mole fraction in aqueous solution, and water and cyclopentane mole fractions are negligible in vapor phase. The mole fraction of water ( xwL ), cation (TBA+) ( xcL ) and anion (Cl-) ( xaL ) in aqueous solution are calculated as follows: 1 xgL x nw n n n w a c
1 xgL x nc n n n c w a
(4)
1 xgL xaL na n n n c w a
(5)
L w
L c
(3)
where nc, na and nw stand for cation moles, anion moles and water moles, respectively, which are calculated as follows:
nc Z c m; na Z a m; nw 55.5
(6)
8
m
1000 wp
(7)
277.92 1 wp
Z a , Z c , m and wp stand for the charge number of anion, cation, molality and weight fraction of TBAC, respectively. CO2 mole fraction in the aqueous phase, which is denoted by xgL may be derived from the equality of fugacities:
x L g
f gG
vg P Pwsat H g w exp RT
(8)
where Hg-w denotes the Henry constant of CO2 in water, fgG is the CO2 fugacity coefficient in the gas phase, vg∞ represents the CO2 molar volume at infinite dilution, P is the total pressure, Pwsat is the saturation vapor pressure of water, R and T are the universal gas constant and the temperature, respectively. Peng-Robinson equation of state (PR-EoS) is applied to calculate the fugacity of CO2 in the gas phase. The Hg-w and Pwsat are calculated as follows [30]: Ln H g w 11.981
Ln Pwsat 62.136
2028 T
(9)
-7258.2 -7.304Ln T +4.17 106 T 2 T
(10)
where T is in K, Hg-w and Pwsat are in bar. CO2 molar volume at infinite dilution is considered to be 33.9 cm3/mol. Molar volume of water (Vm) is calculated as follow [30]:
9
1000
Vm
2 3
17.863 58.606t 213.890t 141.260t
4 3
, t 1
T 273.15 373.98
(11)
Using the electrolyte-Non-Random Two-Liquid (e-NRTL) activity coefficient model, the activity coefficient of water in aqueous phase, γwL, is calculated. The interaction parameters of eNRTL model between water-TBA+Cl- and TBA+Cl--water are determined using mean activity coefficient and osmotic coefficient of tetra-n-butylammonium chloride-water solution [31]. Table 2 shows the interaction parameters. Table 3 reports the acentric factors, critical temperature and pressure of CO2 gas.
Table 2. Optimized parameters of e-NRTL model for tetra-n-butylammonium chloride (ca)water (m) [31].
Table 3. Critical properties and acentric factor of CO2 gas [30].
Equation (12) is applied to determine the water fugacity in the hydrate phase.
f
H w
f
MT w
wMT H exp RT
(12)
In Equation (12), the superscript MT indicates an empty hydrate lattice, f wMT and wMT H stand for the fugacity of the empty hydrate lattice and the water chemical potential
difference between empty and filled hydrate lattice. f wMT is presented by Equation (13):
10
f
MT w
P
MT w
VmMT P PwMT exp RT
(13)
As an assumption, water molar volume (m3/mol) of hydrate structure I (As dodecahedral cages are the host of gaseous molecules) [32; 33] which is expressed by Eq (14), is used to determine water molar volume (m3/mol) of the empty hydrate lattice VmMT . The saturated vapor pressure of water in empty hydrate lattice ( PwMT ) [33] is calculated by Eq (15): VwMT T , P 11.835 2.217 105 T 2.242 106 T 2
3
1030 N A 8.006 109 P 5.448 1012 P 2 NW
(14)
(15)
6003.9 h wp PwMT 0.1exp 17.44 T
where Avogadro’s number is indicated by
and the number of water molecules per unit
hydrate cell is represented by NwMT. In Eq (14), the units of pressure and temperature are MPa and K, respectively. wp in Eq (15) is the weight fraction of TBACl in aqueous phase and h is an adjustable parameter whose the optimized value is presented in Table 4. The vdW–P model is employed to determine ΔμwMT-H [34]:
Table 4. The optimized values of parameters.
3
wMT H wMT wH RT vi ln 1 Cij f j
(16)
i 1
where, Cij is Langmuir constant, fj is the hydrate former fugacity and vi is the number of cages of type i per water molecule in a unit hydrate cell. Based on x-ray diffraction studies [35], TBAC
11
semi-clathrate hydrate has structures of type I, II and III with hydration numbers 32, 30 and 24, respectively. All the three structures have tetragonal structure 1 (TS-1) with unit cell formula 16T.4P.10D, in which the number of (3T.P), 4T and D type cavities are 4, 1 and 10, respectively. Also, studies conducted on structures of TBAC hydrates indicate that 4T and 3T.P type cavities are the structures around TBA+ cation and one type of small D cavities trap guest molecules. Based on the assumption that tetragonal structure (TS-1) is formed in the presence of mixed promoters, two large cages of tetragonal structure (3T.P and 4T) may include cyclopentane molecule. Thus Eq. (16) could be described as the following equation:
v small vl arg e 1 vl arg e 2 H ln 1 C s f gG ln 1 C la1 f caL ln 1 C la 2 f caL RT
ln 1 C cyclo1 f
Lo cp
vl arg e 1
ln 1 C cyclo 2 f
Lo cp
vl arg e 2
(17)
where, the TBA+ cation is denoted by subscript ca, and its fugacity is determined using the Eq.(18):
v pL P Ppsat f x P exp RT L ca
L p
L p
sat p
(18)
where the hydrate promoter (TBAC) is indicated by subscript p. γpL is determined using e-NRTL activity coefficient model. For the calculation promoter molar volume, vpL , the density of TBAC solutions is used [36; 37]. The following equation provides the fugacity of cyclopentane in organic phase:
f
Lo cp
vcpLo P Pcpsat ; xcpLo 1 xgLo x P exp RT Lo Lo sat cp cp cp
12
(19)
For the calculation of solubility of CO2 in organic phase (xgLo), the following expression is used:
x
Lo g
f gG
vg P Pcpsat H g cp exp RT
(20)
The Henry’s constant (MPa) of gas in cyclopentane (Hg-cp) is calculated as follow [30]: 9972.345 H g cp 0.1exp 357.257 62.466 ln T 0.0915 T T
(21)
The saturation pressure of cyclopentane (MPa) is obtained using equation (22) [30]: 2839 Pcpsat 0.1exp 35.5041 3.8639 Ln T 2.8 1016 T 6 T
(22)
Cyclopentane activity coefficient in organic phase (γcpLo) is calculated by NRTL activity model. The interaction parameters between CO2-cyclopentane, which are given in Table 5, are obtained from isobar vapor-liquid equilibrium data regression [38].
Table 5. NRTL activity coefficient interaction parameters between cyclopentane and CO2.
For Langmuir constants related to (3T.P), 4T and D type cavities, the recommended correlations by Shi and Liang [39] are employed which are functions of temperature and TBAC
13
mass fraction. The equation of Langmuir constant for large cages of 4T can be expressed as follows: Cl arg e1
1 c exp d exp 75.688w3p 136.33w2p 91.395wp 17.485 T T
(23)
For 3T.P type cages: Cl arg e 2
1 e exp f exp 19.232 w2p 24.936 wp 1.1264 T T
(24)
Parameters c, d, e and f are obtained through fitting the model to the experimental data, which the optimized values of these parameters are presented in Table 4. CO2 gas molecules are encaged in dodecahedral cavities, which Langmuir constants for small D cages are presented as follows:
Csmall
0.000566 4182.53 44770 exp T T 2 T
2.35
(25)
For the Langmuir constant of cyclopentane molecule, the following correlations are suggested:
qq bb dd Ccyclo1 exp 2 T T T
Ccyclo 2
ss
ww rr vv exp 2 T T T
(26)
(27)
ll
The optimized values are demonstrated in Table 4. The numbers of 4T (nlarge1), 3T.P (nlarge2) and D (ns) cavities per unit semi-clathrate hydrate cell are calculated as follow: 14
vl arg e1
nl arg e1 N
MT w
; vl arg e 2
nl arg e 2 N
MT w
; vsmall
nsmall N wMT
(28)
For tetragonal structure (TS-1), the values of nlarge1, nlarge2, nsmall and
are 1, 4, 10 and
64, respectively. Equation (29) is obtained by replacing the preceding equations in Eq. (1) which the hydrate dissociation pressure of the CO2 + TBAC + CP + H2O system can be determined: VmMT P PwMT PwMT exp vl arg e1 vl arg e 2 1 C f G vsmall 1 C RT 1 Cl arg e 2 f caL f caL e l g s 1 arg 1 0 sat Lo vl arg e1 Lo vl arg e 2 V P P L L sat sat ,V 1 Ccyclo1 f cp 1 Ccyclo 2 f cp w w P x exp w w w w RT
(29)
3.1. Regression Method The objective function (30) may be defined for the optimization of parameters of the Langmuir constants ( Ccyclo1 , Ccyclo 2 , Cl arg e1 , Cl arg e 2 ):
OF
100 NP Pexp(i ) Pcal (i ) P NP i 1 exp( i )
(30)
where NP is the total number of data points. P shows the hydrate dissociation pressure and subscript exp(i) and cal(i) stand for ith experimental values, and calculated hydrate dissociation pressure, respectively. The above objective function or the average absolute relative deviation (AARD %) was minimized by the fminsearch function in the optimization toolbox of MATLAB
15
software. The first guesses for fitted parameters (Table 4) were determined using the genetic algorithm. Fig. 2 shows the flow chart applied to determine the model parameters (Table 4).
Figure 2. Flow chart for calculation of the model parameters.
4. Results and discussion
Table 6 presents the experimental hydrate dissociation data for (CO2 + TBAC + CP + water system). To evaluate the step-heating method employed in the current study, the dissociation conditions of hydrate were measured for the systems of (CO2 + water) and (CO2 + TBAC + water), as reported in Table 6. The obtained data together with the data of other researchers [20; 40] are presented in Fig. 3. The good agreement of the measured experimental data with the data reported in the previous studies validates the step-heating method applied in the current study. The experimental data of hydrate dissociation conditions for (CO2 + TBAC + CP + water) system at various mass fractions of TBAC in the aqueous phase, i.e., 0.05, 0.10, 0.18 and 0.25 mass fractions are shown in Fig. 4. According to this figure, for CO2 + TBAC + CP + water system, cyclopentane has the promotion role. Hence, this promoter enhances the temperature and decreases the pressure of hydrate dissociation compared to CO2 + TBAC + water at the same TBAC concentrations. It can be likely attributed to the fact that cyclopentane has more promotion effect compared to TBAC in the presence of CO2, Therefore, CP may change the hydrate dissociation conditions in the direction of milder conditions.
16
Table 6. Experimental hydrate dissociation conditions of CO2 + TBAC+ CP + water system.
Figure 3. Experimental hydrate dissociation conditions for the (CO2 + water) and (CO2 + TBAC + water) systems. ◊ ,(CO2 + water) system [40]: ▲,(CO2 + water) system (This work): + , CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]: ○, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution (This work).
Figure 4: Dissociation conditions of clathrate/semi-clathrate hydrates for the (CO2 + TBAC + CP +water) systems. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 + CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ● , CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work); +, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]; □, CO2 in the presence of 0.10 mass fraction TBAC aqueous solution [27]; Δ ,CO2 in the presence of 0.15 mass fraction TBAC aqueous solution [20]; × ,CO2 in the presence of 0.22 mass fraction TBAC aqueous solution [20]; ◊ , CO2 + CP + water [9]; ►, CO2 + water [40].
Also, the obtained results show that, as the TBAC concentration in the aqueous solution in the presence of CP increases from 0.05 to 0.10 mass fraction, the hydrate dissociation conditions shift to the left side, while at the concentrations of higher than 0.10 mass fraction of TBAC, these conditions go towards the right side. Finally, at 0.25 TBAC mass fraction, the synergetic effect of mixed promoters (CP + TBAC) is higher than other concentrations. One of the possible reasons for the behavior of the system in the presence of TBAC with concentrations between 0.05 to 0.10 mass fraction is that the capability of CP and TBAC promoters for filling empty cavities are different, so, one of the promoters (i.e., CP) is more likely to occupy the large cavities and all of TBAC remains in the aqueous solution. Therefore, TBAC in the presence of CP acts as an inhibitor. Accordingly, with increasing TBAC mass fraction from 0.10 to 0.25, TBAC and CP stabilize the hydrate cages, but some of TBAC promoter remains in the aqueous phase. Hence, with concentration changes from 0.10 to 0.25 TBAC mass fraction, the inhibition 17
effect decreases in comparison to 0.05 to 0.10 mass fractions and at the concentration of 0.25 mass fraction, the inhibition role of TBAC vanishes. According to the experimental data, the hydrate dissociation conditions for the combination of 0.25 TBAC mass fraction and 50cc CP are more moderate than (CO2 + CP + water) system. It can be related to the fact that, at 0.25 TBAC mass fraction, both promoters probably fill the hydrate cavities and TBAC role changes from inhibitor to promoter in the presence of CP. Also, the presence of mixed promoters (TBAC+CP) in the CO2 + water system promotes the formation conditions of hydrate and changes the dissociation curve of the hydrate toward the right side. Finally, the thermodynamic model was developed and utilized to estimate the hydrate dissociation conditions, when the mixed promoters (TBAC+CP) are added to water + CO2 system. First, the parameters of Langmuir constants were obtained using 0.05, 0.10, and 0.25 TBAC mass fraction (plus 50cc CP) data (through optimization techniques). To investigate the predictive power of the proposed thermodynamic model, hydrate dissociation conditions for the system of 0.18 TBAC mass fraction (plus 50cc CP) were predicted and compared to the experimental data. An acceptable agreement is found between the predicted and measured experimental data. These findings suggest that, at least at these TBAC concentrations, the proposed thermodynamic model can estimate the results with an acceptable agreement. The results are presented in Fig. 5.
Figure 5. The comparison between experimental data and the predicted values of the proposed model. Symbols show the experimental data; solid lines stand for the predictions of the model. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 18
+ CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ●, CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work).
5. Conclusion The experimental data of hydrate dissociation conditions for (CO2 + TBAC + CP + water) system are reported. The effect of (CP + TBAC) mixed promoters on the hydrate dissociation conditions of CO2 gas was investigated. According to the experimental results of this work, the addition of TBAC to the system of (CO2+CP+water) has an inhibition effect on equilibrium conditions of the formed hydrate, however at 0.25 TBAC mass fraction, the promotion impact on hydrate dissociation conditions is observable. Also, the presence of CP in the (CO2 + TBAC + water) system has a promotion impact on the hydrate dissociation conditions of this system. The results show that (CP + TBAC) mixed promoters can remarkably decrease the hydrate dissociation conditions of CO2 gas. For example, under the tested conditions, the hydrate dissociation conditions of CO2 gas is decreased by 13 K at a given temperature. Furthermore, a thermodynamic model was developed to estimate the hydrate dissociation conditions of (CO2 + TBAC + CP + water) system. Langmuir constants were obtained by fitting model to some of the experimental data measured in this study (0.05, 0.10, and 0.25 TBAC mass fraction (plus 50cc CP)). Good agreement of predicted hydrate dissociation conditions for the system of 0.18 TBAC mass fraction (plus 50cc CP) with experimental data confirm the validity of the model results. The average absolute relative deviation (AARD %) for the results of the proposed model is found to be 3.5%.
19
References [1] E.D. Sloan Jr, C. Koh, Clathrate hydrates of natural gases, CRC press, 2007. [2] Z. Taheri, m.r. Shabani, K. Nazari, A. Mehdizaheh, Natural gas transportation and storage by hydrate technology: Iran case study, 2014. [3] H. Veluswamy, A. Kumar, R. Kumar, P. Linga, An innovative approach to enhance methane hydrate formation kinetics with leucine for energy storage application, 2017. [4] E. Kim, G. Ko, Y. Seo, ACS Sustainable Chemistry & Engineering 5 (2017) 5485-5492. [5] H. Shirota, I. Aya, S. Namie, P. Bollavarum, D. Turner, E. Dendy Sloan, Measurement of methane hydrate dissociation for application to natural gas storage and transportation, 2002. [6] H. Hashemi, S. Babaee, A.H. Mohammadi, P. Naidoo, D. Ramjugernath, International Journal of Refrigeration (2018). [7] P. Ngema, C. Petticrew, P. Naidoo, A. Mohammadi, D. Ramjugernath, Experimental measurements of the dissociation conditions of clathrate hydrates for (refrigerant + salt +water) system: Application to water desalination, 2012. [8] P. Babu, A. Nambiar, T. He, I.A. Karimi, J.D. Lee, P. Englezos, P. Linga, ACS Sustainable Chemistry & Engineering 6 (2018) 8093-8107. [9] A.H. Mohammadi, D. Richon, Chemical Engineering Science 64 (2009) 5319-5322. [10] H. Pahlavanzadeh, M. Khanlarkhani, A.H. Mohammadi, The Journal of Chemical Thermodynamics 92 (2016) 168-174. 20
[11] D.L. Fowler, W.V. Loebenstein, D.B. Pall, C.A. Kraus, Journal of the American Chemical Society 62 (1940) 1140-1142. [12] S. Li, S. Fan, J. Wang, X. Lang, D. Liang, Journal of Natural Gas Chemistry 18 (2009) 15-20. [13] K. Shin, Y. Kim, T.A. Strobel, P. Prasad, T. Sugahara, H. Lee, E.D. Sloan, A.K. Sum, C.A. Koh, The Journal of Physical Chemistry A 113 (2009) 6415-6418. [14] S. Wenji, X. Rui, H. Chong, H. Shihui, D. Kaijun, F. Ziping, international journal of refrigeration 32 (2009) 1801-1807. [15] J. Deschamps, D. Dalmazzone, Journal of Chemical & Engineering Data 55 (2010) 3395-3399. [16] S. Kim, I.-H. Baek, J.-K. You, Y. Seo, Applied Energy 140 (2015) 107-112. [17] Z.-G. Sun, C.-G. Liu, Journal of Chemical & Engineering Data 57 (2012) 978-981. [18] A. Fukumoto, P. Paricaud, D. Dalmazzone, W. Bouchafaa, T.T.-S. Ho, W. Fürst, Journal of Chemical & Engineering Data 59 (2014) 3193-3204. [19] A. Kamran-Pirzaman, A.H. Mohammadi, H. Pahlavanzadeh, Chemical Engineering Communications 202 (2015) 806-814. [20] A. Mohammadi, M. Manteghian, A.H. Mohammadi, Fluid Phase Equilibria 381 (2014) 102-107. [21] X. Wang, M. Dennis, Journal of Chemical & Engineering Data 62 (2017) 1083-1093. [22] T. Suginaka, H. Sakamoto, K. Iino, Y. Sakakibara, R. Ohmura, Fluid Phase Equilibria 344 (2013) 108-111. [23] A.H. Mohammadi, A. Eslamimanesh, V. Belandria, D. Richon, Journal of Chemical & Engineering Data 56 (2011) 3855-3865. [24] P.J. Herslund, K. Thomsen, J. Abildskov, N. von Solms, A. Galfré, P. Brântuas, M. Kwaterski, J.-M. Herri, International Journal of Greenhouse Gas Control 17 (2013) 397-410. [25] P.J. Herslund, N. Daraboina, K. Thomsen, J. Abildskov, N. von Solms, Fluid Phase Equilibria 381 (2014) 20-27. [26] F. Tzirakis, P. Stringari, N. von Solms, C. Coquelet, G. Kontogeorgis, Fluid Phase Equilibria 408 (2016) 240-247. [27] A. Kamran-Pirzaman, H. Pahlavanzadeh, A.H. Mohammadi, The Journal of Chemical Thermodynamics 64 (2013) 151-158. [28] B. Tohidi, R.W. Burgass, A. Danesh, K.K. Østergaard, A.C. Todd, Improving the accuracy of gas hydrate dissociation point measurements, Annals of the New York Academy of Sciences, New York Academy of Sciences, 2000, pp. 924-931. [29] R. Masoudi, B. Tohidi, R. Anderson, R.W. Burgass, J. Yang, Fluid Phase Equilibria 219 (2004) 157163. [30] A.P. Aspen, Version 8.6. [31] L.S. Belvèze, J.F. Brennecke, M.A. Stadtherr, Industrial & Engineering Chemistry Research 43 (2004) 815-825. [32] J.B. Klauda, S.I. Sandler, Industrial & engineering chemistry research 39 (2000) 3377-3386. [33] A. Eslamimanesh, A.H. Mohammadi, D. Richon, P. Naidoo, D. Ramjugernath, The Journal of Chemical Thermodynamics 46 (2012) 62-71. [34] J.C. Platteeuw, J.H. van der Waals, Recueil des Travaux Chimiques des Pays-Bas 78 (1959) 126133. [35] T.V. Rodionova, V.Y. Komarov, G.V. Villevald, T.D. Karpova, N.V. Kuratieva, A.Y. Manakov, The Journal of Physical Chemistry B 117 (2013) 10677-10685. [36] V. Belandria, A.H. Mohammadi, D. Richon, The Journal of Chemical Thermodynamics 41 (2009) 1382-1386. [37] L.-F. Chen, A.N. Soriano, M.-H. Li, The Journal of Chemical Thermodynamics 41 (2009) 724-730. [38] N.N. Shah, J.A. Zollweg, W.B. Streett, Journal of Chemical & Engineering Data 36 (1991) 188-192. [39] L.-l. Shi, D.-q. Liang, Fluid Phase Equilibria 386 (2015) 149-154. 21
[40] 71.
S. Adisasmito, R.J. Frank III, E.D. Sloan Jr, Journal of Chemical and Engineering Data 36 (1991) 68-
22
Figure 1. Schematic diagram of the experimental apparatus.
23
Guess adjusted parameters (table. 4)
Change parameters
Input T and P ranges
Calculate
(Eq.2)
Calculate
(Eq.18)
Calculate
(Eq.19)
Is abs equation (29) ˂ 10-5
No Yes Display parameters
Figure 2. Flow chart for calculation of the model parameters.
24
5 4.5 4
P/MPa
3.5 3 2.5 2 1.5 1 0.5 272
274
276
278
280 T/K
282
284
286
288
Figure 3. Experimental hydrate dissociation conditions for the (CO2 + water) and (CO2 + TBAC + water) systems. ◊ ,(CO2 + water) system [40]: ▲,(CO2 + water) system (This work): + , CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]: ○, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution (This work).
25
5 4.5 4 3.5
P/MPa
3 2.5 2 1.5 1 0.5 0 274
276
278
280
282
284 T/K
286
288
290
292
294
Figure 4: Dissociation conditions of clathrate/semi-clathrate hydrates for the (CO2 + TBAC + CP +water) systems. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 + CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ● , CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work); +, CO2 in the presence of 0.05 mass fraction TBAC aqueous solution [20]; □, CO2 in the presence of 0.10 mass fraction TBAC aqueous solution [27]; Δ ,CO2 in the presence of 0.15 mass fraction TBAC aqueous solution [20]; × ,CO2 in the presence of 0.22 mass fraction TBAC aqueous solution [20]; ◊ , CO2 + CP + water [9]; ►, CO2 + water [40].
26
9 8 7
P/MPa
6 5 4 3 2 1 0 286
287
288
289
290
291
292
293
294
T/K
Figure 5. The comparison between experimental data and the predicted values of the proposed model. Symbols show the experimental data; solid lines stand for the predictions of the model. ■, CO2 + CP in the presence of 0.05 mass fraction TBAC aqueous solution (this work); ▼, CO2 + CP in the presence of 0.10 mass fraction TBAC aqueous solution (this work); ●, CO2 + CP in the presence of 0.18 mass fraction TBAC aqueous solution (this work); * , CO2 + CP in the presence of 0.25 mass fraction TBAC aqueous solution (this work).
27
Table 1. Purities and suppliers of the chemicals used in this study. Chemical
Supplier
Purity (stated by supplier)
carbon dioxide
Air Liquide
0.999 mole fraction
tetra-n-buthylammonium chloride (TBAC)
Merck Company
0.99 mass fraction
cyclopenthane
Merck Company
0.999 mole fraction
28
Table 2. The results of VLLE calculations for the determination of water, cyclopentane and CO2 mole fractions in the three phases at the temperatures and pressures of the hydrate equilibrium points for (CO2 + TBAC+ CP + water) system. Aqueous Organic phase Component CO2 (Vapor phase) phase 0.0008 Water 0.0014 0.9998 0.9339 Cyclopentane 0.0280 0.000001 CO2 0.9716 0.0001 0.653
29
Table 3. Optimized parameters of e-NRTL model for tetra-nbutylammonium chloride (ca)-water (m) [31]. τm,ca
τca,m
α
7.8229
-4.0247
0.2000
30
Table 4. Critical properties and acentric factor of CO2 gas [30]. Compound CO2 a
Critical pressure.
b
Critical temperature.
c
Acentric factor.
(MPa)
(K)
7.377
304.13
31
0.2239
Table 5. The optimized values of the parameters. Parameter Optimized value Parameter Optimized value
qq (K) 4796.11 ll -32.16
bb (K) -62.93 c (K) 11.83
dd (K2) ss ww (K) -69.60 -15.00 193.96 d e (K) f 3.28 1.23 19.00
K: Kelvin
32
rr (K) -48.72 h -0.29
vv (K2) 83.68
Table 6. NRTL activity coefficient interaction parameters between cyclopentane and CO2 in organic phase on TBAC- water free basis
cyclopentane CO2 ij aij
bij T
aij cyclopentane 0 -4.459
CO2 -7.25 0
, ij 0.3
33
bij cyclopentane CO2 0 2319.35 2333.42 0
Table 7. Experimental hydrate dissociation conditions of CO2 + TBAC+ CP + water system. (CO2 gas/vapor phase on CP- water- TBAC free (CO2 gas/vapor phase on CP- water- TBAC basis + 0.05 TBAC mass fractiona in aqueous free basis + 0.1 TBAC mass fractiona in solution on CP-CO2 free basis )+ CP organic aqueous solution on CP-CO2 free basis )+ CP phase (50 cm3) on TBAC- water free basis) organic phase (50 cm3) on TBAC- water free basis) b b Temperaturec (K) Temperaturec (K) Pressure (MPa) Pressure (MPa) 1.04 286.9 1.60 287.2 1.54 288.6 2.09 288.5 1.87 289.4 2.58 289.2 2.67 291.1 2.95 289.7 3.34 292.1 3.51 290.4 (CO2 gas/vapor phase on CP- water- TBAC free (CO2 gas/vapor phase on CP- water- TBAC basis + 0.18 TBAC mass fractiona in aqueous free basis + 0.25 TBAC mass fractiona in solution on CP-CO2 free basis )+ CP organic aqueous solution on CP-CO2 free basis )+ CP phase (50 cm3) on TBAC- water free basis) organic phase (50 cm3) on TBAC- water free basis) b b Temperaturec (K) Temperaturec (K) Pressure (MPa) Pressure (MPa) 1.72 288.3 0.97 288.4 2.07 289.1 1.31 289.5 2.44 289.9 1.71 290.6 3.01 290.7 2.3 292.1 3.50 291.4 2.9 293.1 (CO2 gas/vapor phase + 0.05 TBAC mass 3 (CO2 gas/vapor phase + 100 cm water) fractiona in aqueous solution on CO2 free basis) b b Temperaturec (K) Temperaturec (K) Pressure (MPa) Pressure (MPa) 1.88 276.8 1.5 282.1 2.39 278.5 2.33 283.4 3.5 284.9
34
Research Highlights
Experimental hydrate dissociation conditions for (CO2 + TBAC + Cyclopentane + Water) system are reported.
A thermodynamic model has been developed and its results are in acceptable agreement with the experimental data.
The addition of low-medium concentration TBAC to the system of (CO2 + CP + water) has an inhibition effect.
The addition of high TBAC concentration to the system of (CO2 + CP + water) has a promotion effect.
The addition of CP in the (CO2 + TBAC + water) system has a promotion impact.
35