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Amino acids as kinetic inhibitors for tetrahydrofuran hydrate formation: Experimental study and kinetic modeling
Journal of Natural Gas Science and Engineering 21 (2014) 64e70
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Amino acids as kinetic inhibitors for tetrahydrofuran hydrate formation: Experimental study and kinetic modeling Parisa Naeiji, Akram Arjomandi, Farshad Varaminian* School of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 June 2014 Received in revised form 23 July 2014 Accepted 24 July 2014 Available online
In this work, a series of natural amino acids which are environmentally friendly and biodegradable have been tested as hydrate crystal growth kinetics inhibitors for THF (tetrahydrofuran) hydrate formation. Also the thermodynamic natural path has been used for modeling of the hydrate formation rate in a constant volume process. The used amino acids consist of glycine and L-leucine at varying concentrations (0.05e1.5 wt%) and the experiments have been conducted in a batch reactor under atmospheric pressure, with and without the presence of acetone. Induction time and equilibrium temperature of hydrate formation have been measured and compared. Amino acids with lower hydrophobicity have been found to be better KHIs to delay nucleation and reduce growth. The results also have shown that glycine has better inhibition performance than L-leucine because of lower hydrophobicity. While, it has been known when acetone is present, inhibition performance of amino acids improves and L-leucine is also more suitable than glycine, because of its nonpolar side chain and insolubility in acetone. The results of modeling show that there is good agreement between model prediction and experimental data with average error of 0.9% and this model can well predict constant volume experimental data of THF hydrate formation in the presence of amino acids. © 2014 Elsevier B.V. All rights reserved.
Keywords: Amino acids Acetone Kinetics hydrate inhibitor Induction time Kinetic modeling Tetrahydrofuran hydrate
1. Introduction Gas clathrate hydrate is non-stoichiometric solid compound that formed by water molecules as hosts and gas molecules as guests. Small guests molecules are trapped in the cavities formed by hydrogen bonded water clusters and stabilized in the cavities via van der Waal interaction forces at conditions of low temperature and/or high pressure. Gas hydrates are classified into three distinct structures according to the difference in cavity shape and size: sI, sII, sH. Small molecules like methane, ethane and some refrigerants can form hydrate crystal (Carroll, 2002; Sloan, 2003; Sun et al., 2011). Hydrate formation conditions are also common in oil and gas transmission and so gas hydrate formation is a major potential reason of pipeline occlusion. Thus, a lot of researches have been performed for prevention of hydrate formation (Kelland, 2011). Nowadays, the most suitable way of avoiding hydrate blockages in oil and gas pipelines is to use chemical inhibitors that may be of two kinds: thermodynamic (TIs) or low dosage (LDIs) inhibitors
* Corresponding author. Tel.: þ98 2313354120; fax: þ98 2313354280. E-mail address: [email protected] (F. Varaminian). http://dx.doi.org/10.1016/j.jngse.2014.07.029 1875-5100/© 2014 Elsevier B.V. All rights reserved.
(Niang et al., 2010; Tang et al., 2010). The thermodynamic inhibitors include compounds such as methanol or glycols that act by shifting the hydrate three-phase equilibrium line. They are required at very high concentrations (up to 50 wt% water) and mostly are expensive (Valberg, 2006). The LDIs can also divide into two groups: kinetics inhibitors (KIs) and anti-agglomerants (AAs). Both are active at concentrations below 1 wt% water. The KIs delay the onset of nucleation or slow the growth rate of crystals that form, while AAs do not prevent hydrate formation, but ensure that hydrates form a finely suspended slush, so that fluid flow is not prevented. The successful KIs are polymeric such as pyrrolidone and quaternary ammonium ions have often been used as AAs (Kelland et al., 2012; Storr et al., 2004). One of the simplest and most effective methods includes measuring the growth rate of THF hydrate crystals in the presence of LDIs. THF hydrate has been widely used for screening natural gas hydrate inhibitors because THF is a liquid entirely miscible with water and forms hydrate with it at 4 C and atmospheric pressure at a molar ratio of 1:17 (THFewater) (Karamoddin and Varaminian, 2014a; York and Firoozabadi, 2008). THF can form a sII structure of hydrate that is the same structure formed by natural gas and it can be used as an analog to study the gas hydrates without the requirement of high pressures (Ding et al., 2010).
P. Naeiji et al. / Journal of Natural Gas Science and Engineering 21 (2014) 64e70
Ding et al. (2010) studied two LDIs, namely Luvicap EG and Gaffix VC-713, in a THFeNaCl hydrate formation solution to determine the inhibition efficiency. They found that the performance of LDIs is affected significantly by the concentration of the inhibitors and reliable information is also provided only if the concentration of the inhibitor is above a critical concentration. Kelland et al. (2013) tested a series of tetraalkylphosphonium bromide salts as THF hydrate crystal growth inhibitors at varying concentrations. They indicated that the inhibition performance is better than that of tetraalkylammonium bromide salts and the best performance for this series also obtained when the alkyl group was iso-hexyl. Hu et al. (2012) investigated a novel kind of KHI copolymer poly (N-vinyl-2-pyrrolidone-co-2-vinyl pyridine)s (HGs) in conjunction with tetrabutylammonium bromide (TBAB) to show its high performance on THF hydrate inhibition. They showed that at the concentration of 1 wt%, the induction time of 19 wt% THF solution could be prolonged to 8.5 h at a high subcooling of 6 C. New class of kinetic inhibitor for gas hydrate formation has been introduced by Sa et al. (2013). They studied natural hydrophobic amino acids as KHIs on CO2 hydrate inhibition, because there is a need for development of environmentally friendly KHIs with enhanced biodegradability due to the potential environmental risks. They found that amino acids with lower hydrophobicity to be better KHIs to delay nucleation and retard growth. In this work, the effect of glycine and L-leucine amino acids on THF hydrate inhibition has been investigated. To enhance inhibition performance, acetone as synergist for amino acids has been used. Also, chemical affinity has been used for modeling of hydrate formation rate in a constant volume. This is a macroscopic model and only needs the initial and final information of the process (Garfinkle, 1999). In contrast with other kinetics models which define microscopic driving force and need parameters such as mass transfer coefficients or heat transfer coefficients, this model didn't have the limitation of microscopic models and determination of its parameters is easier (Garfinkle, 1999). Several studies have been previously reported to model gas hydrate formation rate using chemical affinity method (Karamoddin et al., 2014; Naeiji and Varaminian, 2013; Varaminian and Izadpanah, 2010). Karamoddin and Varaminian (2014b) used this method for modeling of R141b hydrate formation kinetics. They obtained good agreement between predicted and actual data. In this study, it first has been applied to predict the kinetics of THF hydrate formation. 2. Experimental apparatus and procedure 2.1. Experimental apparatus The schematic of used setup is shown in Fig. 1. It consists a reactor of 500 cm3, which made up of Pyrex glass with height of 12 cm and diameter of 6 cm, a jacket for heating and cooling of system by flowing the ethylene glycol solution of 50 mol% and a cooling bath. A magnetically stirrer with a stirring speed controller has been applied for mixing and homogeneity of solution in the reactor. Temperatures of solution within the reactor and ethylene glycol in the jacket are measured by PT100 thermometers (±0.1 K) and recorded by a data acquisition system. Here, process of hydrate formation is performed in atmospheric pressure. 2.2. Materials Amino acids of glycine, L-leucine (Table 1) and THF liquid with a normal purity of 99.5% from Merck, acetone with a purity of 99.0% from Iran Dr. Mojallali Co. with deionized and distilled water have been used to form hydrate.
65
Fig. 1. Experimental setup.
2.3. Experimental procedure THF forms structure II hydrate in molar composition of THF.17H2O and at about 4.4 C under atmospheric pressure. 200 mL of the aqueous THF/H2O solution is prepared and then amino acid of 0.05e1.5 wt% is added. Experiments with the presence of acetone are conducted in acetone of 7.5 vol%. Final solution is placed on a shaker-heater system to get homogeny solution with initial temperature of 20 C. Afterward, the solution of THF/H2O/amino acid is injected into the reactor when the temperature of cooling bath is fixed so that the temperature of inside wall of the reactor is set at 0 C, which represents about 4.4 C subcooling. The stirrer is started and it is allowed to cool the solution. The temperature suddenly increases whilst hydrate forms because of heat generation, until to reach the equilibrium temperature of THF hydrate. Time and temperature of solution during process are recorded. 3. Kinetics modeling of THF hydrate formation In this study, a conceptual model has been served to study THF hydrate formation rate that defines a macroscopic driving force and uses only the initial conditions and final conditions (equilibrium conditions). The model is based on that there is only a unique path for each experiment which on this path decays the chemical affinity. The chemical reaction rate can correlate to the chemical affinity decay rate using the thermodynamic functions (Garfinkle, 1999). Considering the homogeneous stoichiometric chemical reaction proceeding in a closed system at constant volume V, the chemical affinity as a generalized force is defined as:
Table 1 The physicochemical properties of used amino acids (Sa et al., 2013). Glycine (Gly)
L-leucine (L-leu)
eH 2.41 88.3%
eCH2CH(CH3) 2.39 88.9%
10.32 100.0%
10.33 100.0%
0.4
3.8
Molecular structure
Side chain pKa1 (eCOOH) at 273.15 K Degree of ionization (eCOOH) at pH 3.29 pKa2 (eNH2) at 273.15 K Degree of ionization (eNH2) at pH 3.29 Hydrophobicity
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P. Naeiji et al. / Journal of Natural Gas Science and Engineering 21 (2014) 64e70
zQ ¼
nA ni nA nB
(3)
where ni is the mole of THF in the system at ith time. Karamoddin and Varaminian (2014b) suggested a relation to calculate the extent of reaction in constant pressure systems. They expressed that it is equivalent to temperature variation along time, as follows:
zQ ¼
X
ln zQi
(1)
where R is the universal gas constant, T is the temperature of system and zQ is a dimensionless measure of the extent of reaction on range of 0 zQ 1. Since the decay of the chemical affinity along a reaction path independently of reaction mechanism is described, natural path has been denoted by Garfinkle as follows (Garfinkle, 1999):
Ai ¼ Ar ln zti $exp 1 zti
(4)
where TA and TB indicate the initial and equilibrium temperature of hydrate formation, respectively, and Ti is the temperature of system at ith time. After the model parameters, Ar and tk, have been determined, the actual values of Ai and zQ are calculated by using of Eq. (2) and Eq. (1), respectively. Then Ti is obtained by Eq. (4) of the model and it is compared to experimental temperature.
Fig. 2. THF hydrate formation condition at constant pressure.
Ai ¼ RT
nA ni TA Ti ≡ nA nB TA TB
4. Results and discussion The experiments of THF hydrate inhibition have been carried out with amino acids and with or without acetone. The aqueous solutions of amino acids with concentration of 0.05e1.5 wt% and acetone with 7.5 vol% have been used. The model based on chemical affinity has been also used for modeling of THF hydrate formation rate in an isobaric system.
(2) 4.1. THF hydrate formation process
where Ar is the affinity rate constant and zti ¼ ðti =tk Þ on range of 0 zti 1 that tk is the expected time to attain equilibrium. By means of Eq. (2) can be calculated chemical affinity at every time. In order to determine the model parameters of Ar and tk, first chemical affinity from Eq. (1) is calculated, then Ai versus ln½zti $expð1 zti Þ is plotted. But first of all, extent of reaction should be indicated at specific system. As shown in Fig. 2, the experimental conditions for hydrate formation must be below the equilibrium temperature of THF hydrate. In constant pressure experiments, after the formation of hydrate crystals (point A), temperature increases suddenly because of heat generation, until to reach the equilibrium temperature of THF hydrate (point B). At this point, hydrate formation is stopped. The total amount of consumed THF during hydrate formation is equal to (nA nB) and the extent of reaction can be obtained from:
After the solution was enough cooled, the initial crystal nucleuses appeared on the inside wall of reactor and simultaneously the temperature of solution suddenly increased. The formed hydrate crystals grew and continued in the bulk solution when the temperature of solution remained on the equilibrium temperature. The un-hydrate solution remained in the middle of reactor. The stages of growth of THF hydrate are shown in Fig. 3. These images have been obtained during one of processes of THF formation in this study. 4.1.1. Delay time measurement for THF hydrate formation The THF/H2O hydrate equilibrium diagram for the systems that contained 8e50 wt% THF is shown in Fig. 4 (Zanota et al., 2005). According to this, if the temperature of solution (starting from
Fig. 3. The sequences of THF hydrate growth in this study.
P. Naeiji et al. / Journal of Natural Gas Science and Engineering 21 (2014) 64e70
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Table 2 Amino acids results on THF hydrate formation. Solution (wt%) THF THF THF THF THF THF THF THF THF
þ þ þ þ þ þ þ þ þ
pure water Gly 0.05% Gly 0.5% Gly 1% Gly 1.5% L-leu 0.05% L-leu 0.5% L-leu 1% L-leu 1.5%
Equilibrium temperature ( C)
Delay time (min)
4.4 4.3 4.3 4.1 3.7 4.3 4.2 4.1 4.1
4 4.5 7 4 10 4 7 5.5 4
(suddenly increase the temperature of system) has been indicated as delay time for hydrate formation. 4.2. Effect of amino acids on THF hydrate formation
Fig. 4. THF/H2O hydrate equilibrium diagram at atmospheric pressure (Zanota et al., 2005).
20 C) reaches to below the equilibrium temperature of THF hydrate (about 4.4 C), it would be exist enough driving force for hydrate formation. In this study, therefore, elapsed time from the solution temperature of 4.4 C up to hydrate formation moment
THF hydrate formation with and without amino acids at concentrations of 0.05e1.5 wt% is shown in Fig. 5 and also given in Table 2. As shown in Fig. 5, THF solution without any additive firstly formed hydrate at 1.9 C, while THF solution with amino acids turned to hydrate 0.4e2 C. According to Table 2, amino acids can inhibit THF hydrate formation for 10 min, which is the longest one among the solutions. The solution of Gly 1.5 wt% has higher subcooling and longer delay time than other solutions. It can be also said that by enhancing concentration of glycine in the solution,
Fig. 5. THF hydrate formation in the presence of amino acids (glycine and L-leucine) at different concentration.
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Fig. 6. THF hydrate formation in the presence of acetone (7.5 v/v%) and amino acids (glycine and L-leucine) at different concentration.
subcooling and delay time of hydrate formation is increased and equilibrium temperature is reduced. While, in the presence of Lleucine, the solution of L-leu 0.5 wt% has the highest delay time. It can be found that glycine has better inhibition performance on THF hydrate formation than L-leucine. Glycine, having a hydrogen substituent as its side chain with the formula NH2CH2COOH, is the smallest of the 20 amino acids commonly found in protein. Due to its minimal side chain of only one hydrogen atom, it can fit into hydrophilic or hydrophobic environments. While L-leucine is a branched chain a-amino acids with the chemical formula HO2CCH(NH2)CH2CH(CH3)2. It is classified as a hydrophobic amino acid due to its aliphatic isobutyl side chain (Plimmer and Hopkins, 2010). The physical and chemical
properties of amino acids are strongly dependent on the particular side chain. When investigating hydrophobic amino acids as KHIs, an important consideration is their perturbation of the local water structure. It has been demonstrated that the hydrogen bond network between water molecules around hydrophilic moieties of hydrophobic amino acids has been disrupted, while that around hydrophobic alkyl chains has been strengthened. The extent of
Table 3 Amino acids/acetone results on THF hydrate formation. Solution (wt%) THF THF THF THF THF THF THF THF THF THF
þ þ þ þ þ þ þ þ þ þ
pure water Acetone Acetone þ Gly 0.05% Acetone þ Gly 0.5% Acetone þ Gly 1% Acetone þ Gly 1.5% Acetone þ L-leu 0.05% Acetone þ L-leu 0.5% Acetone þ L-leu 1% Acetone þ L-leu 1.5%
Equilibrium temperature ( C)
Delay time (min)
4.4 2.1 2 2 1.8 1.6 1.8 1 1.4 1.1
4 9 11 8 13 7 11 20 23 13
Fig. 7. Affinity versus ln½zti $expð1 zti Þ for THF hydrate formation with the presence of amino acids.
P. Naeiji et al. / Journal of Natural Gas Science and Engineering 21 (2014) 64e70
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Table 4 The results of modeling (referred to Eq. (2)) for THF hydrate formation with the presence of amino acids and acetone. Solution (wt%)
Ar (kJ/mol)
tk (s)
Solution (wt%)
THF THF THF THF THF THF THF THF THF
1.76 1.77 1.99 1.66 1.73 1.68 2.42 2.19 0.98
204.78 207.68 162.79 227.51 111.63 182.53 77.69 98.43 319.52
THF THF THF THF THF THF THF THF THF
þ þ þ þ þ þ þ þ
Gly 0.05% Gly 0.5% Gly 1% Gly 1.5% L-leu 0.05% L-leu 0.5% L-leu 1% L-leu 1.5%
these perturbations is depended on the hydrophobicity of the amino acids (Hecht et al., 1993). It has been previously demonstrated that amino acids with lower hydrophobicity are better KHIs to delay nucleation and retard growth (Sa et al., 2013). The hydrophobicity of glycine is 0.4, while its value for L-leucine is 3.8. Therefore, according to above statements, glycine is more efficient KHIs than L-leucine and it has been observed in our work. 4.3. Effect of amino acids/acetone on THF hydrate formation THF hydrate formation with and without acetone of 7.5 vol% and amino acids at concentrations of 0.05e1.5 wt% is shown in Fig. 6 and also given in Table 3. In the presence of acetone, the solution formed hydrate at 0e1.1 C and prolonged about 23 min, which is the longest one among these solutions. In other words, acetone can enhance subcooling and delay time of the processes. Besides, the equilibrium temperatures of THF hydrate formation reduced significantly by about 1e2.1 C. It can be observed that the solutions of amino acids 1 wt% with the presence of acetone have the best performance. Although, on the contrary to previous section, the solutions included L-leucine have better inhibition performance on THF hydrate formation than glycine. Acetone is the simplest ketone with the formula (CH3)2CO. It is polar and miscible with water and serves as an important solvent in its own right (Sifniades and Levy, 2005). Acetone can form sII hydrate with water as a single guest. Also, promoting and inhibiting effect of acetone on hydrate formation/dissociation has been reported in the literature. Instances, it has been found that the presence of 0.0556 mole fraction acetone in aqueous solution reduces the hydrate dissociation pressure of the methane þ water system by approximately 11 MPa at given temperatures (KamranPirzaman et al., 2013). According to other work, acetone has an inhibiting effect on methane hydrate formation at high acetone concentrations of 0.75 and 0.90 mass fractions (Ng and Robinson, 1994). Some of researchers showed that acetone suppresses R22 hydrate formation for all the studied acetone concentrations of 0.02, 0.04 and 0.06 mole fractions (Javanmardi et al., 2004). Considering these results, the inhibiting or promoting effect of acetone on hydrate formation depends on its concentration in solution. In our work, it acts as an inhibitor on THF hydrate formation and reduces the water activity at concentration of 7.5 vol% with the presence of water and amino acids. Besides, acetone next to Lleucine has been known that it is better synergist than glycine. The reason for this performance might be that amino acids are almost soluble in water but insoluble in acetone and insolubility of Lleucine in acetone, because of its nonpolar side chain, and thereupon more dissolving in water overcomes low hydrophobicity effect of glycine on hydrate formation inhibition.
þ þ þ þ þ þ þ þ þ
Acetone Acetone Acetone Acetone Acetone Acetone Acetone Acetone Acetone
þ þ þ þ þ þ þ þ
Gly 0.05% Gly 0.5% Gly 1% Gly 1.5% L-leu 0.05% L-leu 0.5% L-leu 1% L-leu 1.5%
Ar (kJ/mol)
tk (s)
0.55 1.075 1.073 0.33 0.96 0.91 0.69 0.89 0.97
2096.22 413.74 735.10 3978.15 642.23 613.10 3673.71 2260.92 1299.42
the experiments, the temperature variations with time after the hydrate formation have been modeled. Fig. 7 shows chemical affinity versus ln½zti $expð1 zti Þ for this system. As seen, there is a linear relation between data and therefore the model parameters can be obtained in accord with Eq. (2). The variation of reactor temperature with time during hydrate formation has been calculated using averaged Ar and tk for each experiment. The results of modeling (the values of model parameters) are given in Table 4 and some of their plots are shown in Figs. 8 and 9. It can be seen that there is good agreement between calculated results and experimental data with average error of 0.9%. According to Table 4, Ar values in related to THF and glycine solutions are averagely lower than THF and L-leucine solutions. As previously said, Ar is the affinity rate constant and it can be considered as a kinetic parameter. Thus, the process of THF hydrate formation is slowed in the presence of glycine. Opposite of this statement is observed in the presence of acetone so that THF and L-leucine solutions have slower processes. Generally, when acetone is added to the solution, Ar decreases and tk considerably increases. In other words, acetone helps amino acids for inhibition of THF hydrate formation. 5. Conclusions In this study, inhibition performance of amino acids, glycine and on THF hydrate formation with and without the presence of acetone has been investigated. The thermodynamic natural path in chemical reaction kinetics has been also used to study the kinetics of THF hydrate formation. Although amino acids inhibition performance may be not better than that of chemical inhibitors such as poly(N-vinylpyrrolidone) and poly(N-vinylcaprolactam), but they are environmentally friendly and biodegradable. Glycine, with lower hydrophobicity, is better KHIs to delay nucleation and L-leucine,
4.4. Results of kinetics modeling of THF hydrate formation The thermodynamic natural path in chemical reaction kinetics has been used to study the kinetics of THF hydrate formation. In
Fig. 8. Experimental and calculated results for THF hydrate formation with the presence of amino acids.
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Fig. 9. Experimental and calculated results for THF hydrate formation with the presence of amino acids and acetone.
reduce growth. While, in the presence of acetone, L-leucine has better inhibition performance than glycine, because of its nonpolar side chain. Acetone as an inhibitor helps amino acids to increase their inhibitor capability and reduce the water activity. The results of modeling show that there is good agreement between model prediction and experimental data with average error of 0.9% and this model can well validate experimental data of THF hydrate formation in the presence of amino acids. Nomenclature A Ar n R t tk T V
chemical affinity constant of proportionality number of moles universal gas constant time time required to obtain equilibrium conditions temperature volume
Greek letters zQ extent of reaction based on mole zt extent of reaction based on time Subscripts A initial condition of hydrate formation B final condition of hydrate formation i index of time References Carroll, J., 2002. Natural Gas Hydrate. Elsevier Science & Technology Books.
Ding, A., Wang, S., Pelemis, T., Crisafio, C., Lou, X., 2010. Specific critical concentrations of low dosage hydrate inhibitors in a THFeNaCl hydrate formation solution. Asia-Pac. J. Chem. Eng. 5, 577e584. Garfinkle, M., 1999. The thermodynamic natural path in chemical reaction kinetics. Discrete Dyn. Nat. Soc. 4, 145e164. Hecht, D., Tadesse, L., Walters, L., 1993. Correlating hydration shell structure with amino acid hydrophobicity. J. Am. Chem. Soc. 115, 3336e3337. Hu, J., Li, S., Wang, Y., Lang, X., Li, Q., Fan, S., 2012. Kinetic hydrate inhibitor performance of new copolymer poly(N-vinyl-2-pyrrolidone-co-2-vinyl pyridine)s with TBAB. J. Nat. Gas Chem. 21, 126e131. Javanmardi, J., Ayatollahi, S., Motealleh, R., Moshfeghian, M., 2004. Experimental measurement and modeling of R22 (CHClF2) hydrates in mixtures of acetone þ water. J. Chem. Eng. Data 49, 886e889. Kamran-Pirzaman, A., Pahlavanzadeh, H., Mohammadi, A.H., 2013. Hydrate phase equilibria of furan, acetone, 1,4-dioxane, TBAC and TBAF. J. Chem. Thermodyn. 64, 151e158. Karamoddin, M., Varaminian, F., 2014a. Performance of hydrate inhibitors in tetrahydrofuran hydrate formation by using measurement of electrical conductivity. J. Ind. Eng. Chem. 20, 3815e3820. Karamoddin, M., Varaminian, F., 2014b. Study on the growth process of HCFC141b hydrate in isobaric system by a macroscopic kinetic model. Int. J. Refrigeration. 44, 66e72. Karamoddin, M., Varaminian, F., Daraee, M., 2014. Kinetic study on the process of CHClF2 (R22) hydrate formation in the presence of SDS surfactant based on chemical affinity. J. Nat. Gas Sci. Eng. 19, 46e51. Kelland, M.A., 2011. A review of kinetic hydrate inhibitors: tailor-made water-soluble polymers for oil and gas industry applications. In: Advances in Materials Science Research. Nova Science Publishers Inc., New York. Kelland, M.A., Kvæstad, A.H., Astad, E.L., 2012. Tetrahydrofuran hydrate crystal growth inhibition by trialkylamine oxides and synergism with the gas kinetic hydrate inhibitor poly(N-vinyl caprolactam). Energy Fuel 26, 4454e4464. Kelland, M.A., Gausland, F., Tsunashima, K., 2013. Inhibition of tetrahydrofuran hydrate crystal growth by tetraalkylphosphonium salts e superior performance to equivalent tetraalkylammonium salts. Chem. Eng. Sci. 98, 12e16. Naeiji, P., Varaminian, F., 2013. Experimental study and kinetics modeling of gas hydrate formation of methaneeethane mixture. J. Non-Equilib. Thermodyn. 38, 273e286. Ng, H.J., Robinson, D.B., 1994. New developments in the measurement and prediction of hydrate formation for processing needs. Ann. Acad. Sci. 715, 450e462. Niang, F., Zhang, L., Tu, Y., Jiang, G., Shi, M., 2010. Gas-hydrate formation, agglomeration and inhibition in oil-based drilling fluids for deep-water drilling. J. Nat. Gas Chem. 19, 234e240. Plimmer, R.H.A., Hopkins, F.G., 2010. The chemical composition of the proteins. In: Monographs on Biochemistry. Part I. Analysis, second ed. Longmans, Green and Co., London, p. 82. Sa, J.H., Kwak, G.H., Lee, B.R., Park, D.H., Han, K., Lee, K.H., 2013. Hydrophobic amino acids as a new class of kinetic inhibitors for gas hydrate formation. Sci. Rep. 3, 2428. Sifniades, S., Levy, A.B., 2005. Acetone in Ullmann's Encyclopedia of Industrial Chemistry. Wiley-VCH, Weinheim. Sloan, E.D., 2003. Clathrate hydrate measurements: microscopic, mesoscopic, and macroscopic. J. Chem. Thermodyn. 35, 41e53. Storr, M.T., Taylor, P.C., Monfort, J.P., Rodger, P.M., 2004. Kinetic inhibitor of hydrate crystallization. J. Am. Chem. Soc. 126, 1569e1576. Sun, C., Li, W., Yang, X., Li, F., Yuan, Q., Mu, L., Chen, J., Liu, B., Chen, G., 2011. Progress in research of gas hydrate. Chin. J. Chem. Eng. 19, 151e162. Tang, C., Dai, X.X., Du, J.W., Li, D.L., Zang, X.Y., Yang, X.Y., Liang, D., 2010. Kinetic studies of gas hydrate formation with low-dosage hydrate inhibitors. Sci. China Chem. 53, 2623. Valberg, T., 2006. Efficiency of Thermodynamic Inhibitors for Melting Gas Hydrates (Master thesis of NTNU). Varaminian, F., Izadpanah, A.A., 2010. Modeling of methane and propane hydrate formation kinetics based on chemical affinity. Iran. J. Chem. Chem. Eng. 17, 158e167. York, J.D., Firoozabadi, A., 2008. Comparing effectiveness of rhamnolipid biosurfactant with a quaternary ammonium salt surfactant for hydrate antiagglomeration. J. Phys. Chem. B 112, 845e851. Zanota, M.L., Dicharry, C., Graciaa, A., 2005. Hydrate plug prevention by quaternary ammonium salts. Energy Fuel 19, 584e590.
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Amino acids as kinetic inhibitors for tetrahydrofuran hydrate formation: Experimental study and kinetic modeling Parisa Naeiji, Akram Arjomandi, Farshad Varaminian* School of Chemical, Gas and Petroleum Engineering, Semnan University, Semnan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 June 2014 Received in revised form 23 July 2014 Accepted 24 July 2014 Available online
In this work, a series of natural amino acids which are environmentally friendly and biodegradable have been tested as hydrate crystal growth kinetics inhibitors for THF (tetrahydrofuran) hydrate formation. Also the thermodynamic natural path has been used for modeling of the hydrate formation rate in a constant volume process. The used amino acids consist of glycine and L-leucine at varying concentrations (0.05e1.5 wt%) and the experiments have been conducted in a batch reactor under atmospheric pressure, with and without the presence of acetone. Induction time and equilibrium temperature of hydrate formation have been measured and compared. Amino acids with lower hydrophobicity have been found to be better KHIs to delay nucleation and reduce growth. The results also have shown that glycine has better inhibition performance than L-leucine because of lower hydrophobicity. While, it has been known when acetone is present, inhibition performance of amino acids improves and L-leucine is also more suitable than glycine, because of its nonpolar side chain and insolubility in acetone. The results of modeling show that there is good agreement between model prediction and experimental data with average error of 0.9% and this model can well predict constant volume experimental data of THF hydrate formation in the presence of amino acids. © 2014 Elsevier B.V. All rights reserved.
Keywords: Amino acids Acetone Kinetics hydrate inhibitor Induction time Kinetic modeling Tetrahydrofuran hydrate
1. Introduction Gas clathrate hydrate is non-stoichiometric solid compound that formed by water molecules as hosts and gas molecules as guests. Small guests molecules are trapped in the cavities formed by hydrogen bonded water clusters and stabilized in the cavities via van der Waal interaction forces at conditions of low temperature and/or high pressure. Gas hydrates are classified into three distinct structures according to the difference in cavity shape and size: sI, sII, sH. Small molecules like methane, ethane and some refrigerants can form hydrate crystal (Carroll, 2002; Sloan, 2003; Sun et al., 2011). Hydrate formation conditions are also common in oil and gas transmission and so gas hydrate formation is a major potential reason of pipeline occlusion. Thus, a lot of researches have been performed for prevention of hydrate formation (Kelland, 2011). Nowadays, the most suitable way of avoiding hydrate blockages in oil and gas pipelines is to use chemical inhibitors that may be of two kinds: thermodynamic (TIs) or low dosage (LDIs) inhibitors
* Corresponding author. Tel.: þ98 2313354120; fax: þ98 2313354280. E-mail address: [email protected] (F. Varaminian). http://dx.doi.org/10.1016/j.jngse.2014.07.029 1875-5100/© 2014 Elsevier B.V. All rights reserved.
(Niang et al., 2010; Tang et al., 2010). The thermodynamic inhibitors include compounds such as methanol or glycols that act by shifting the hydrate three-phase equilibrium line. They are required at very high concentrations (up to 50 wt% water) and mostly are expensive (Valberg, 2006). The LDIs can also divide into two groups: kinetics inhibitors (KIs) and anti-agglomerants (AAs). Both are active at concentrations below 1 wt% water. The KIs delay the onset of nucleation or slow the growth rate of crystals that form, while AAs do not prevent hydrate formation, but ensure that hydrates form a finely suspended slush, so that fluid flow is not prevented. The successful KIs are polymeric such as pyrrolidone and quaternary ammonium ions have often been used as AAs (Kelland et al., 2012; Storr et al., 2004). One of the simplest and most effective methods includes measuring the growth rate of THF hydrate crystals in the presence of LDIs. THF hydrate has been widely used for screening natural gas hydrate inhibitors because THF is a liquid entirely miscible with water and forms hydrate with it at 4 C and atmospheric pressure at a molar ratio of 1:17 (THFewater) (Karamoddin and Varaminian, 2014a; York and Firoozabadi, 2008). THF can form a sII structure of hydrate that is the same structure formed by natural gas and it can be used as an analog to study the gas hydrates without the requirement of high pressures (Ding et al., 2010).
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Ding et al. (2010) studied two LDIs, namely Luvicap EG and Gaffix VC-713, in a THFeNaCl hydrate formation solution to determine the inhibition efficiency. They found that the performance of LDIs is affected significantly by the concentration of the inhibitors and reliable information is also provided only if the concentration of the inhibitor is above a critical concentration. Kelland et al. (2013) tested a series of tetraalkylphosphonium bromide salts as THF hydrate crystal growth inhibitors at varying concentrations. They indicated that the inhibition performance is better than that of tetraalkylammonium bromide salts and the best performance for this series also obtained when the alkyl group was iso-hexyl. Hu et al. (2012) investigated a novel kind of KHI copolymer poly (N-vinyl-2-pyrrolidone-co-2-vinyl pyridine)s (HGs) in conjunction with tetrabutylammonium bromide (TBAB) to show its high performance on THF hydrate inhibition. They showed that at the concentration of 1 wt%, the induction time of 19 wt% THF solution could be prolonged to 8.5 h at a high subcooling of 6 C. New class of kinetic inhibitor for gas hydrate formation has been introduced by Sa et al. (2013). They studied natural hydrophobic amino acids as KHIs on CO2 hydrate inhibition, because there is a need for development of environmentally friendly KHIs with enhanced biodegradability due to the potential environmental risks. They found that amino acids with lower hydrophobicity to be better KHIs to delay nucleation and retard growth. In this work, the effect of glycine and L-leucine amino acids on THF hydrate inhibition has been investigated. To enhance inhibition performance, acetone as synergist for amino acids has been used. Also, chemical affinity has been used for modeling of hydrate formation rate in a constant volume. This is a macroscopic model and only needs the initial and final information of the process (Garfinkle, 1999). In contrast with other kinetics models which define microscopic driving force and need parameters such as mass transfer coefficients or heat transfer coefficients, this model didn't have the limitation of microscopic models and determination of its parameters is easier (Garfinkle, 1999). Several studies have been previously reported to model gas hydrate formation rate using chemical affinity method (Karamoddin et al., 2014; Naeiji and Varaminian, 2013; Varaminian and Izadpanah, 2010). Karamoddin and Varaminian (2014b) used this method for modeling of R141b hydrate formation kinetics. They obtained good agreement between predicted and actual data. In this study, it first has been applied to predict the kinetics of THF hydrate formation. 2. Experimental apparatus and procedure 2.1. Experimental apparatus The schematic of used setup is shown in Fig. 1. It consists a reactor of 500 cm3, which made up of Pyrex glass with height of 12 cm and diameter of 6 cm, a jacket for heating and cooling of system by flowing the ethylene glycol solution of 50 mol% and a cooling bath. A magnetically stirrer with a stirring speed controller has been applied for mixing and homogeneity of solution in the reactor. Temperatures of solution within the reactor and ethylene glycol in the jacket are measured by PT100 thermometers (±0.1 K) and recorded by a data acquisition system. Here, process of hydrate formation is performed in atmospheric pressure. 2.2. Materials Amino acids of glycine, L-leucine (Table 1) and THF liquid with a normal purity of 99.5% from Merck, acetone with a purity of 99.0% from Iran Dr. Mojallali Co. with deionized and distilled water have been used to form hydrate.
65
Fig. 1. Experimental setup.
2.3. Experimental procedure THF forms structure II hydrate in molar composition of THF.17H2O and at about 4.4 C under atmospheric pressure. 200 mL of the aqueous THF/H2O solution is prepared and then amino acid of 0.05e1.5 wt% is added. Experiments with the presence of acetone are conducted in acetone of 7.5 vol%. Final solution is placed on a shaker-heater system to get homogeny solution with initial temperature of 20 C. Afterward, the solution of THF/H2O/amino acid is injected into the reactor when the temperature of cooling bath is fixed so that the temperature of inside wall of the reactor is set at 0 C, which represents about 4.4 C subcooling. The stirrer is started and it is allowed to cool the solution. The temperature suddenly increases whilst hydrate forms because of heat generation, until to reach the equilibrium temperature of THF hydrate. Time and temperature of solution during process are recorded. 3. Kinetics modeling of THF hydrate formation In this study, a conceptual model has been served to study THF hydrate formation rate that defines a macroscopic driving force and uses only the initial conditions and final conditions (equilibrium conditions). The model is based on that there is only a unique path for each experiment which on this path decays the chemical affinity. The chemical reaction rate can correlate to the chemical affinity decay rate using the thermodynamic functions (Garfinkle, 1999). Considering the homogeneous stoichiometric chemical reaction proceeding in a closed system at constant volume V, the chemical affinity as a generalized force is defined as:
Table 1 The physicochemical properties of used amino acids (Sa et al., 2013). Glycine (Gly)
L-leucine (L-leu)
eH 2.41 88.3%
eCH2CH(CH3) 2.39 88.9%
10.32 100.0%
10.33 100.0%
0.4
3.8
Molecular structure
Side chain pKa1 (eCOOH) at 273.15 K Degree of ionization (eCOOH) at pH 3.29 pKa2 (eNH2) at 273.15 K Degree of ionization (eNH2) at pH 3.29 Hydrophobicity
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zQ ¼
nA ni nA nB
(3)
where ni is the mole of THF in the system at ith time. Karamoddin and Varaminian (2014b) suggested a relation to calculate the extent of reaction in constant pressure systems. They expressed that it is equivalent to temperature variation along time, as follows:
zQ ¼
X
ln zQi
(1)
where R is the universal gas constant, T is the temperature of system and zQ is a dimensionless measure of the extent of reaction on range of 0 zQ 1. Since the decay of the chemical affinity along a reaction path independently of reaction mechanism is described, natural path has been denoted by Garfinkle as follows (Garfinkle, 1999):
Ai ¼ Ar ln zti $exp 1 zti
(4)
where TA and TB indicate the initial and equilibrium temperature of hydrate formation, respectively, and Ti is the temperature of system at ith time. After the model parameters, Ar and tk, have been determined, the actual values of Ai and zQ are calculated by using of Eq. (2) and Eq. (1), respectively. Then Ti is obtained by Eq. (4) of the model and it is compared to experimental temperature.
Fig. 2. THF hydrate formation condition at constant pressure.
Ai ¼ RT
nA ni TA Ti ≡ nA nB TA TB
4. Results and discussion The experiments of THF hydrate inhibition have been carried out with amino acids and with or without acetone. The aqueous solutions of amino acids with concentration of 0.05e1.5 wt% and acetone with 7.5 vol% have been used. The model based on chemical affinity has been also used for modeling of THF hydrate formation rate in an isobaric system.
(2) 4.1. THF hydrate formation process
where Ar is the affinity rate constant and zti ¼ ðti =tk Þ on range of 0 zti 1 that tk is the expected time to attain equilibrium. By means of Eq. (2) can be calculated chemical affinity at every time. In order to determine the model parameters of Ar and tk, first chemical affinity from Eq. (1) is calculated, then Ai versus ln½zti $expð1 zti Þ is plotted. But first of all, extent of reaction should be indicated at specific system. As shown in Fig. 2, the experimental conditions for hydrate formation must be below the equilibrium temperature of THF hydrate. In constant pressure experiments, after the formation of hydrate crystals (point A), temperature increases suddenly because of heat generation, until to reach the equilibrium temperature of THF hydrate (point B). At this point, hydrate formation is stopped. The total amount of consumed THF during hydrate formation is equal to (nA nB) and the extent of reaction can be obtained from:
After the solution was enough cooled, the initial crystal nucleuses appeared on the inside wall of reactor and simultaneously the temperature of solution suddenly increased. The formed hydrate crystals grew and continued in the bulk solution when the temperature of solution remained on the equilibrium temperature. The un-hydrate solution remained in the middle of reactor. The stages of growth of THF hydrate are shown in Fig. 3. These images have been obtained during one of processes of THF formation in this study. 4.1.1. Delay time measurement for THF hydrate formation The THF/H2O hydrate equilibrium diagram for the systems that contained 8e50 wt% THF is shown in Fig. 4 (Zanota et al., 2005). According to this, if the temperature of solution (starting from
Fig. 3. The sequences of THF hydrate growth in this study.
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Table 2 Amino acids results on THF hydrate formation. Solution (wt%) THF THF THF THF THF THF THF THF THF
þ þ þ þ þ þ þ þ þ
pure water Gly 0.05% Gly 0.5% Gly 1% Gly 1.5% L-leu 0.05% L-leu 0.5% L-leu 1% L-leu 1.5%
Equilibrium temperature ( C)
Delay time (min)
4.4 4.3 4.3 4.1 3.7 4.3 4.2 4.1 4.1
4 4.5 7 4 10 4 7 5.5 4
(suddenly increase the temperature of system) has been indicated as delay time for hydrate formation. 4.2. Effect of amino acids on THF hydrate formation
Fig. 4. THF/H2O hydrate equilibrium diagram at atmospheric pressure (Zanota et al., 2005).
20 C) reaches to below the equilibrium temperature of THF hydrate (about 4.4 C), it would be exist enough driving force for hydrate formation. In this study, therefore, elapsed time from the solution temperature of 4.4 C up to hydrate formation moment
THF hydrate formation with and without amino acids at concentrations of 0.05e1.5 wt% is shown in Fig. 5 and also given in Table 2. As shown in Fig. 5, THF solution without any additive firstly formed hydrate at 1.9 C, while THF solution with amino acids turned to hydrate 0.4e2 C. According to Table 2, amino acids can inhibit THF hydrate formation for 10 min, which is the longest one among the solutions. The solution of Gly 1.5 wt% has higher subcooling and longer delay time than other solutions. It can be also said that by enhancing concentration of glycine in the solution,
Fig. 5. THF hydrate formation in the presence of amino acids (glycine and L-leucine) at different concentration.
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Fig. 6. THF hydrate formation in the presence of acetone (7.5 v/v%) and amino acids (glycine and L-leucine) at different concentration.
subcooling and delay time of hydrate formation is increased and equilibrium temperature is reduced. While, in the presence of Lleucine, the solution of L-leu 0.5 wt% has the highest delay time. It can be found that glycine has better inhibition performance on THF hydrate formation than L-leucine. Glycine, having a hydrogen substituent as its side chain with the formula NH2CH2COOH, is the smallest of the 20 amino acids commonly found in protein. Due to its minimal side chain of only one hydrogen atom, it can fit into hydrophilic or hydrophobic environments. While L-leucine is a branched chain a-amino acids with the chemical formula HO2CCH(NH2)CH2CH(CH3)2. It is classified as a hydrophobic amino acid due to its aliphatic isobutyl side chain (Plimmer and Hopkins, 2010). The physical and chemical
properties of amino acids are strongly dependent on the particular side chain. When investigating hydrophobic amino acids as KHIs, an important consideration is their perturbation of the local water structure. It has been demonstrated that the hydrogen bond network between water molecules around hydrophilic moieties of hydrophobic amino acids has been disrupted, while that around hydrophobic alkyl chains has been strengthened. The extent of
Table 3 Amino acids/acetone results on THF hydrate formation. Solution (wt%) THF THF THF THF THF THF THF THF THF THF
þ þ þ þ þ þ þ þ þ þ
pure water Acetone Acetone þ Gly 0.05% Acetone þ Gly 0.5% Acetone þ Gly 1% Acetone þ Gly 1.5% Acetone þ L-leu 0.05% Acetone þ L-leu 0.5% Acetone þ L-leu 1% Acetone þ L-leu 1.5%
Equilibrium temperature ( C)
Delay time (min)
4.4 2.1 2 2 1.8 1.6 1.8 1 1.4 1.1
4 9 11 8 13 7 11 20 23 13
Fig. 7. Affinity versus ln½zti $expð1 zti Þ for THF hydrate formation with the presence of amino acids.
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Table 4 The results of modeling (referred to Eq. (2)) for THF hydrate formation with the presence of amino acids and acetone. Solution (wt%)
Ar (kJ/mol)
tk (s)
Solution (wt%)
THF THF THF THF THF THF THF THF THF
1.76 1.77 1.99 1.66 1.73 1.68 2.42 2.19 0.98
204.78 207.68 162.79 227.51 111.63 182.53 77.69 98.43 319.52
THF THF THF THF THF THF THF THF THF
þ þ þ þ þ þ þ þ
Gly 0.05% Gly 0.5% Gly 1% Gly 1.5% L-leu 0.05% L-leu 0.5% L-leu 1% L-leu 1.5%
these perturbations is depended on the hydrophobicity of the amino acids (Hecht et al., 1993). It has been previously demonstrated that amino acids with lower hydrophobicity are better KHIs to delay nucleation and retard growth (Sa et al., 2013). The hydrophobicity of glycine is 0.4, while its value for L-leucine is 3.8. Therefore, according to above statements, glycine is more efficient KHIs than L-leucine and it has been observed in our work. 4.3. Effect of amino acids/acetone on THF hydrate formation THF hydrate formation with and without acetone of 7.5 vol% and amino acids at concentrations of 0.05e1.5 wt% is shown in Fig. 6 and also given in Table 3. In the presence of acetone, the solution formed hydrate at 0e1.1 C and prolonged about 23 min, which is the longest one among these solutions. In other words, acetone can enhance subcooling and delay time of the processes. Besides, the equilibrium temperatures of THF hydrate formation reduced significantly by about 1e2.1 C. It can be observed that the solutions of amino acids 1 wt% with the presence of acetone have the best performance. Although, on the contrary to previous section, the solutions included L-leucine have better inhibition performance on THF hydrate formation than glycine. Acetone is the simplest ketone with the formula (CH3)2CO. It is polar and miscible with water and serves as an important solvent in its own right (Sifniades and Levy, 2005). Acetone can form sII hydrate with water as a single guest. Also, promoting and inhibiting effect of acetone on hydrate formation/dissociation has been reported in the literature. Instances, it has been found that the presence of 0.0556 mole fraction acetone in aqueous solution reduces the hydrate dissociation pressure of the methane þ water system by approximately 11 MPa at given temperatures (KamranPirzaman et al., 2013). According to other work, acetone has an inhibiting effect on methane hydrate formation at high acetone concentrations of 0.75 and 0.90 mass fractions (Ng and Robinson, 1994). Some of researchers showed that acetone suppresses R22 hydrate formation for all the studied acetone concentrations of 0.02, 0.04 and 0.06 mole fractions (Javanmardi et al., 2004). Considering these results, the inhibiting or promoting effect of acetone on hydrate formation depends on its concentration in solution. In our work, it acts as an inhibitor on THF hydrate formation and reduces the water activity at concentration of 7.5 vol% with the presence of water and amino acids. Besides, acetone next to Lleucine has been known that it is better synergist than glycine. The reason for this performance might be that amino acids are almost soluble in water but insoluble in acetone and insolubility of Lleucine in acetone, because of its nonpolar side chain, and thereupon more dissolving in water overcomes low hydrophobicity effect of glycine on hydrate formation inhibition.
þ þ þ þ þ þ þ þ þ
Acetone Acetone Acetone Acetone Acetone Acetone Acetone Acetone Acetone
þ þ þ þ þ þ þ þ
Gly 0.05% Gly 0.5% Gly 1% Gly 1.5% L-leu 0.05% L-leu 0.5% L-leu 1% L-leu 1.5%
Ar (kJ/mol)
tk (s)
0.55 1.075 1.073 0.33 0.96 0.91 0.69 0.89 0.97
2096.22 413.74 735.10 3978.15 642.23 613.10 3673.71 2260.92 1299.42
the experiments, the temperature variations with time after the hydrate formation have been modeled. Fig. 7 shows chemical affinity versus ln½zti $expð1 zti Þ for this system. As seen, there is a linear relation between data and therefore the model parameters can be obtained in accord with Eq. (2). The variation of reactor temperature with time during hydrate formation has been calculated using averaged Ar and tk for each experiment. The results of modeling (the values of model parameters) are given in Table 4 and some of their plots are shown in Figs. 8 and 9. It can be seen that there is good agreement between calculated results and experimental data with average error of 0.9%. According to Table 4, Ar values in related to THF and glycine solutions are averagely lower than THF and L-leucine solutions. As previously said, Ar is the affinity rate constant and it can be considered as a kinetic parameter. Thus, the process of THF hydrate formation is slowed in the presence of glycine. Opposite of this statement is observed in the presence of acetone so that THF and L-leucine solutions have slower processes. Generally, when acetone is added to the solution, Ar decreases and tk considerably increases. In other words, acetone helps amino acids for inhibition of THF hydrate formation. 5. Conclusions In this study, inhibition performance of amino acids, glycine and on THF hydrate formation with and without the presence of acetone has been investigated. The thermodynamic natural path in chemical reaction kinetics has been also used to study the kinetics of THF hydrate formation. Although amino acids inhibition performance may be not better than that of chemical inhibitors such as poly(N-vinylpyrrolidone) and poly(N-vinylcaprolactam), but they are environmentally friendly and biodegradable. Glycine, with lower hydrophobicity, is better KHIs to delay nucleation and L-leucine,
4.4. Results of kinetics modeling of THF hydrate formation The thermodynamic natural path in chemical reaction kinetics has been used to study the kinetics of THF hydrate formation. In
Fig. 8. Experimental and calculated results for THF hydrate formation with the presence of amino acids.
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Fig. 9. Experimental and calculated results for THF hydrate formation with the presence of amino acids and acetone.
reduce growth. While, in the presence of acetone, L-leucine has better inhibition performance than glycine, because of its nonpolar side chain. Acetone as an inhibitor helps amino acids to increase their inhibitor capability and reduce the water activity. The results of modeling show that there is good agreement between model prediction and experimental data with average error of 0.9% and this model can well validate experimental data of THF hydrate formation in the presence of amino acids. Nomenclature A Ar n R t tk T V
chemical affinity constant of proportionality number of moles universal gas constant time time required to obtain equilibrium conditions temperature volume
Greek letters zQ extent of reaction based on mole zt extent of reaction based on time Subscripts A initial condition of hydrate formation B final condition of hydrate formation i index of time References Carroll, J., 2002. Natural Gas Hydrate. Elsevier Science & Technology Books.
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