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Insights into kinetic inhibition effects of MEG, PVP, and L-tyrosine aqueous solutions on natural gas hydrate formation

Insights into kinetic inhibition effects of MEG, PVP, and L-tyrosine aqueous solutions on natural... It is necessary to understand all the prerequisites, which result in gas hydrate formation for safe design and control of a variety of processes in petroleum industry. Thermodynamic hydrate inhibitors (THIs) are normally used to preclude gas hydrate formation by shifting hydrate stability region to lower temperatures and higher pressures. Sometimes, it is difficult to avoid hydrate formation and hydrates will form anyway. In this situation, kinetic hydrate inhibitors (KHIs) can be used to postpone formation of gas hydrates by retarding hydrate nucleation and growth rate. In this study, two kinetic parameters including natural gas hydrate formation induction time and the rate of gas consumption were experimentally investigated in the presence of monoethylene glycol (MEG), L-tyrosine, and polyvinylpyrrolidone (PVP) at various concentrations in aqueous solutions. Since hydrate formation is a stochastic phenomenon, the repeatability of each kinetic parameter was evaluated several times and the average values for the hydrate formation induction times and the rates of gas consumption are reported. The results indicate that from the view point of hydrate formation induction time, 2 wt% PVP and 20 wt% MEG aqueous solutions have the highest values and are the best choices. It is also interpreted from the results that from the view point of the rate of gas consumption, 20 wt% MEG aqueous solution yields the lowest value and is the best choice. Finally, it is concluded that the combination of PVP and MEG in an aqueous solution has a simultaneous synergistic impact on natural gas hydrate formation induction time and the rate of gas consumption. Furthermore, a semi-empirical model based on chemical kinetic theory is applied to evaluate the hydrate formation induction time data. A good agreement between the experimental and calculated hydrate formation induction time data is observed. Keywords Gas hydrate · Clathrate hydrate · Natural gas · Kinetic hydrate inhibitor (KHI) · Induction time · Kinetics List of symbolsPVP Polyvinylpyrrolidone MEG Monoethylene glycol rpm Round per minute K Kelvin SNG Synthetic natural gas KHI Kinetic hydrate inhibitor THI Thermodynamic hydrate inhibitor PEO Polyethylene oxide A –A Optimized parameter 1 5 PVCap Polyvinylcaprolactam AAE Average absolute error AARE Average absolute relative error B Nucleation rate Edited by Yan-Hua Sun b Arbitrary fitting constant * Amir H. Mohammadi C Arbitrary constant amir_h_mohammadi@yahoo.com k Arbitrary fitting constant m Fitting parameter Department of Natural Gas Engineering, School of Chemical m.f Mass fraction of PVP in aqueous solution and Petroleum Engineering, Shiraz University, Shiraz 71345, PVP Iran m.f Mass fraction of MEG in aqueous solution MEG N Avogadro number Department of Process Engineering, National Iranian Gas Company (NIGC), South Pars Gas Complex (SPGC) Phases N N umber of data points 4&5, Bushehr 75391/311, Iran n Arbitrary fitting constant t=0 Discipline of Chemical Engineering, School of Engineering, n Initial mole of gas in the cell cell University of KwaZulu-Natal, Howard College Campus, t n Mole of gas at time t cell King George V Avenue, Durban 4041, South Africa Vol.:(0123456789) 1 3 496 Petroleum Science (2021) 18:495–508 P System’s initial pressure in MPa Among all the aforementioned methods, injecting hydrate P Critical pressure inhibitors is more possible and easy to use way (Sloan and P Cell pressure Koh 2008). In traditional form, two types of hydrate inhibi- cell R Universal gas constant tors are utilized for industrial applications: Thermodynamic r Arbitrary fitting constant hydrate inhibitors (THIs) tend to decrease water activity and S Supersaturation ratio shift hydrate phase equilibrium curve to lower temperatures T Critical temperature and higher pressures. Examples of this type of inhibitors T Cell temperature are methanol, ethanol, monoethylene glycol (MEG), sodium cell T Gas hydrate phase equilibrium temperature chloride (NaCl), etc. (Sloan and Koh 2008; Ghaedi et al. T Cell temperature, which is kept constant for 2018; Masoudi et al. 2005; Najibi et al. 2013; Haghighi et al. target hydrate to form 2009; Lee and Kang 2011; Hemmingsen et al. 2011; Moeini t Induction time et  al. 2018). On the other hand, there are kinetic hydrate ∆T Degree of subcooling inhibitors (KHIs) that act differently. They increase hydrate ∆t Time interval between two experiments formation induction time and decrease hydrate nucleation V Cell volume and crystal growth rates. The well-known KHIs are polyvi- cell V Cr ystal molar volume nylpyrrolidone (PVP) and polyvinylcaprolactam (PVCap) Z Com pressibility factor of gas (Sloan and Koh 2008; Daraboina et al. 2011, 2013; Kelland cell δ Arbitrary fitting constant 2006; Salamat et al. 2013; Villano et al. 2009; Rasoolzadeh σ Average surface tension on the liquid–solid et al. 2016; Cha et al. 2013; Kakati et al. 2016). THIs are interface normally used in large quantities even up to 50 wt% but in λ Arbitrary fitting constant some specific cases, injecting THIs in large quantities has ω Acentric factor an insufficient impact on gas hydrate formation because the Number of ions per dissolved molecule conditions are very convenient for gas hydrates to form. In these cases, KHIs can be used to delay formation of gas hydrates, as mentioned earlier (Sloan and Koh 2008). One 1 Introduction can define the induction time as an interval between reaching hydrate formation conditions and occurring hydrate forma- Natural gas is the cleanest fossil fuel that has been widely tion (Sloan and Koh 2008; Daraboina et al. 2011; Daraboina used in various applications. The irregular, uncontrolled, et al. 2013; Kelland 2006; Salamat et al. 2013; Villano et al. and vast consumption of natural gas will make this type of 2009; Rasoolzadeh et al. 2016; Cha et al. 2013; Kakati et al. energy resource coming to end in future. Therefore, it neces- 2016). In the past decade, the focus of scientific investiga - sitates employing safe and efficient methods in exploitation, tions was on the new group of inhibitors like some kinds of processing, transportation, storage, and delivery of natural ionic liquids (ILs) that not only shift hydrate phase equilib- gas. One of the major obstacles that is likely to threaten nat- rium curve to lower temperature/higher pressure regions but ural gas flow assurance is gas hydrates, or clathrate hydrates, also increase hydrate formation induction time. These com- which can form inside pipelines, valves, cold boxes, and pounds are called dual function inhibitors (DFIs) (Rasoolza- other production and processing facilities (Villicaña-García deh et al. 2016). A large number of studies of DFIs are avail- and Ponce-Ortega 2019; Rimos et al. 2014). For gas hydrates able in the literature. Xiao et al. investigated the inhibition to form, several conditions have to be prepared such as high performances of imidazolium-based ILs on methane and pressures, existence of sufficient amounts of water in the natural gas hydrates formation. They concluded that the form of water vapor, liquid water, or ice called the host used ILs (due to strong electrostatic charges and hydrogen molecules and existence of some small and light molecules bonds) not only shift the hydrate equilibrium curve/hydrate of gases and volatile liquids, which play roles of the guest dissociation conditions to lower temperatures and higher molecules (Sloan and Koh 2008). Gas hydrates crystal- pressures but also slow down the hydrate nucleation and line lattices formed by water molecules can be stabilized growth rate (Xiao and Adidharma 2009; Xiao et al. 2010). by occupation of cavities with guest molecules (Sloan and Kim et al. synthesized pyrrolidinium cation-based ILs and Koh 2008). studied their thermodynamic and kinetic impacts on meth- Gas hydrate formation in pipelines can cause blockage ane hydrate formation. They also observed the dual-function and sudden pressure drops and huge economic losses are the inhibition impacts of the pyrrolidinium cation-based ILs on results of this phenomenon (Sloan and Koh 2008; Hammer- methane hydrate (Kim et al. 2011). Tariq et al. reviewed the schmidt 1934). Heating, pressure reduction, water removal, roles of ILs on gas hydrate formation. They reviewed all and injecting some kinds of inhibitors to pipelines are some of the available kinetic and thermodynamic hydrate inhibi- recommended methods to avoid gas hydrate formation. tion data in the attendance of ILs to evaluate the strength of 1 3 Petroleum Science (2021) 18:495–508 497 each IL on gas hydrate inhibition (Tariq et al. 2014). Lim leads to a synergistic effect on hydrate inhibition (Kakati et al. used morpholine as a DFI for gas hydrate formation. et  al. 2016). Kim et al. conducted an experimental study They applied the powder X-ray diffraction, Raman spectros- on hydrate formation of SNG in the presence of MEG and copy, and nuclear magnetic resonance (NMR) analyses to PVCap. They suggested that mixing small amounts of investigate molecular behavior and the crystal structure of PVCap with MEG leads to a synergistic effect on hydrate hydrate in the presence of morpholine (Lim et al. 2014). inhibition and the amounts of MEG can be reduced substan- Qureshi et al. studied kinetic and thermodynamic effects of tially (Kim et al. 2014). polyethylene oxide (PEO) and vinyl caprolactam (VCap) This contribution is intended to experimentally evaluate with two ILs on synthetic natural gas hydrate formation. the performances of KHIs, THIs, and their mixtures on natu- They took into account that the addition of the synergents ral gas hydrate formation kinetic parameters like induction to the ILs could effectively improve the gas hydrate inhi - time and the rate of gas consumption. Several mixtures at bition strength of the ILs (Qureshi et al. 2016). Lee et al. various experimental conditions were applied for this pur- evaluated dual-function inhibition performances of ILs in pose. MEG was used as THI, PVP and L-tyrosine were used the presence/absence of polyvinyl caprolactam (PVCap) on as KHIs in this work. Moreover, for the case of MEG and methane hydrate formation. They observed that the utiliza- PVP, a partly empirical model based on the chemical kinet- tion of IL and PVCap mixture results in the enhanced kinetic ics theory was handled to correlate the natural gas hydrate inhibition effect on methane hydrate formation (Lee et al. formation induction time data. 2016). Haji Nasrollahebrahim et al. investigated thermo/ kinetic inhibition effects of six ILs on methane hydrate for - mation by molecular dynamics simulation. They concluded 2 Experimental that among the investigated ILs, 1-(2-hydroxyethyl)-3-meth- ylimidazolium bis(fluorosulfonyl)imide ([C OHmim][f N]) 2.1 Materials 2 2 and 1-(2,3-dihydroxypropyl)-3 methylimidazoliumbis(fluoro sulfonyl)imide ([C (OH) mim][f N]) have stronger thermo- Monoethylene glycol (MEG) (99.5% purity) and L-tyrosine 3 2 2 dynamic/kinetic inhibition effects (Haji Nasrollahebrahim (99.0 wt% purity) were purchased from Merck. Polyvi- et al. 2013). Yaqub et al. reviewed the roles of DFIs on gas nylpyrrolidone (PVP) (99.0 wt% purity) was purchased from hydrate inhibition. They calculated the average temperature Sigma-Aldrich, with a molecular mass of 40,000 g/mol. depression and relative inhibition power for various ILs for The natural gas mixture was purchased from Fara Fan Gas selection of the best IL for academic and industrial applica- and its composition is shown in Table 1. Deionized water tions (Yaqub et al. 2018). Khan et al. experimentally stud- was used in the experiments. ied inhibition strength of tetramethyl ammonium chloride MEG in mass fractions of 0.10 and 0.20, PVP and (TMACl) on the formation of methane and carbon dioxide L-tyrosine in mass fractions of 0.01 and 0.02 were used in hydrates. They used 1, 5, and 10 wt% TMACl aqueous solu- this work. The aqueous solutions were prepared by the gravi- tion and concluded that TMACl can be used as potential metric method using the electronic A&D balance (EK-300) DFI for both methane and CO hydrates (Khan et al. 2019). with ± 0.01 g readability. Although the investigations into THIs and KHIs are abun- dant, there is limited information on the mixed solutions 2.2 Apparatus of THIs and KHIs. Daraboina et al. experimentally stud- ied the impacts of polyethylene oxide (PEO) and NaCl on A 250 cm stainless steel (SS-316) cell is an important part the performance of Luvicap to inhibit natural gas hydrate of the experimental equipment, which can tolerate pres- formation. They concluded that the addition of PEO and sures up to 35 MPa. Circulation of water and ethylene glycol NaCl on Luvicap decreases the nucleation of hydrate, which means the enhancement of inhibition strength of Luvicap Table 1 Composition of natural gas mixture used in this study (Daraboina et al. 2013). Cha et al. experimentally investi- gated the inhibition effects of MEG and PVP on synthetic Component Mole fraction natural gas (SNG) hydrate formation. They stated that the CH 0.8040 kinetic inhibition effect of MEG is an important factor in C H 0.1030 2 6 decreasing MEG injection for offshore petroleum pipelines C H 0.0500 3 8 (Cha et al. 2013). Kakati et al. performed an experimental n-C 0.0072 study of the addition of L-tyrosine and NaCl to PVP as a i-C 0.0165 widely-used gas hydrate inhibitor to study its performance N 0.0011 on (methane-ethane-propane) gas mixture hydrates. They CO 0.0182 observed that the addition of L-tyrosine and NaCl on PVP 1 3 498 Petroleum Science (2021) 18:495–508 aqueous solution in the constant-temperature bath controls 3 Induction time and gas consumption rate the cell temperature. A high-precision temperature sensor modeling with ± 0.1 K readability was used to measure the cell tem- perature. A piezoresistive pressure transducer (Keller, 23S) The rate of gas consumption can be determined using the was applied to measure the cell pressure, with a standard following procedure: uncertainty of ± 0.015% of total pressure. A magnetic stirrer Step 1 The initial mole of gas in the cell is calculated as fol- was used to agitate the fluid and solid hydrate phases in the low (Rasoolzadeh et al. 2016): vessel at a speed of 500 rpm. The setup also consists of a t=0 t=0 P V data acquisition program to log several parameters like pres- cell cell t=0 n = (1) cell t=0 t=0 sure, temperature, and stirrer speed at every few seconds. R T Z cell cell Figure 1 demonstrates a schematic view of the setup. where P is the cell pressure, V stands for the cell vol- cell cell ume (250 cm ), R represents the universal gas constant, T cell 2.3 Procedure designates the cell temperature and Z indicates the com- cell pressibility factor of the gas mixture, which is calculated After washing and drying the experimental cell, a leakage using the Peng–Robinson equation of state and the van der test was performed by injecting nitrogen at 1 MPa. After- Waals (vdW) mixing rules (Peng and Robinson 1976). ward, all the remained gases in the cell were removed using Step 2 After completion of hydrate formation, the mole a two-stage rotary vacuum pump (Adixen Pascal Series of gas is calculated thusly (Rasoolzadeh et al. 2016, 2019; 2005SD) for about half an hour. Then, 50 cm of an aqueous Aliabadi et al. 2015): solution as a feed was injected into the cell. The pressure of t t (P )(V ) cell cell the vessel was adjusted to the desired pressure through the t n = (2) cell t t gas injection. To avoid gas hydrate memory effect, the tem- R(T )(Z ) cell cell perature of the cell was elevated to 313 K and kept constant Step 3 The rate of gas consumption at time t can be cal- (313 K) for 30 min while the stirrer rotated at the constant culated as follow (Rasoolzadeh et al. 2016): rate of 500 rpm. The bath temperature was set to two dis- tinct targets temperatures of 277.15 and 280.15 K for each t=0 t n − n cell cell (3) v = experiment. The cell temperature decreased from 313 K to Δt −1 the target temperatures with the cooling rate of 0.3 K min and gave enough time to ensure gas hydrate formation com- where v is the rate of gas consumption. pletion. Finally, the system temperature increased to 313 K After completion of hydrate formation, the gas phase com- and the next test was performed. position changes, and to calculate the number of moles, the Gas pressure Isolation Inlet gas filter Vacuum pump Torque meter regulator valves Inlet gas Pressure sensor Bath temperature Thermocouple Cooling bath Fig. 1 The simplified arrangement of the experimental setup 1 3 Petroleum Science (2021) 18:495–508 499 gas phase composition should be included. We had no equip- where t represents the induction time; r and  are arbitrary ment to measure the gas phase composition. It requires a gas constants. Rearranging Eqs. (5) and (6) leads to the follow- chromatography (GC) analyzer connected to the cell to exactly ing relation (Rasoolzadeh et al. 2016): measure the gas phase composition. Because of the lack of equipment, it was assumed that the composition of the gas t = = × i n r nr k (7) exp(− ) mixture is constant. Table 2 presents the critical properties and kexp − the acentric factors of the gas mixture components required to calculate the compressibility factor of the gas mixture. The nucleation rate has the inverse relationship with (8) supersaturation (Rasoolzadeh et  al. 2016; McCabe and Stevens 1951; Mullin 1993): m = nr 16 V N M A B = Cexp − (9) (4) 2 2 3 (RT) S −m t = exp − (10) where B stands for the nucleation rate, N is Avogadro number, R represents the universal gas constant, as men- We considered the dimensionless subcooling as the super- tioned earlier, V and σ represent the crystal molar volume saturation driving force and hydrate nucleation. Therefore, and the average surface tension on the liquid–solid inter- Eq. (10) is converted to the following form (Rasoolzadeh face, respectively. C is an arbitrary constant, S denotes the et al. 2016): supersaturation ratio and  is the number of ions per dis- −m bT solved molecule. Equation (4) can be re-written as follows t = exp (11) (Rasoolzadeh et al. 2016): ΔT where  is a function of the aqueous solution molecular B = kexp − (5) weight, MEG mass fraction, PVP mass fraction, and the sys- tem initial pressure; m and b are the fitting parameters that where k , b , and n are arbitrary fitting constants. are optimized using the gas hydrate formation induction time It is obvious that there is an inverse relation between the data; T is the gas hydrate phase equilibrium temperature induction time and the nucleation rate (Rasoolzadeh et al. that can be calculated using the van der Waals-Platteeuw 2016; Natarajan 1993): (vdW-P)-based model (Sloan and Koh 2008) presented in our previous work (Saberi et al. 2018); ΔT is the difference t = i r (6) (B ) between the hydrate phase equilibrium temperatures.  is defined as follows: MW solution = A + A exp + A exp m.f + A exp m.f − A ln(P) (12) 1 2 3 PVP 4 MEG 5 MW pure water where m.f is the mass fraction of PVP in the aqueous PVP solution, m.f represents the mass fraction of MEG in MEG the aqueous solution, and P is the system’s initial pressure in MPa. It is worth mentioning that the role of guest mol- Table 2 The critical properties and acentric factors of the gas mixture components (Perry et al. 2015) ecule is important in induction time calculation but as we have investigated only one type of gas sample, no parameter Component Critical temper- Critical pres- Acentric factor ɷ ature T , K sure P , MPa for representing the guest molecule is needed to add to the c c induction time model. CH 190.56 4.59 0.0115 C H 305.32 4.87 0.0995 2 6 C H 369.83 4.24 0.1523 3 8 4 Results and discussion n-C 425.12 3.79 0.2002 i-C 407.80 3.64 0.1835 Two kinetic parameters were experimentally investigated in N 126.20 3.40 0.0377 this work: the induction time and the gas consumption rate. CO 304.21 7.38 0.2236 The definition of the induction time is presented in Fig.  2. 1 3 500 Petroleum Science (2021) 18:495–508 8.5 formation. Figure 4 exhibits the variations of gas consump- Cooling curve tion with pressure and temperature in the specified time Hydrate equilibrium curve 8.0 interval for pure water. Table 3 presents the natural gas hydrate phase equilib- 7.5 rium temperatures, target temperatures, and subcooling for various aqueous solutions. In the previous studies (Kang 7.0 et al. 2014; Ke et al. 2016), it was stated that low amounts 6.5 of LDHIs do not affect hydrate phase equilibrium curves in general. However, some LDHIs may affect hydrate phase 6.0 equilibrium curves. Since we have no experimental hydrate phase equilibrium data in the presence of the LDHIs at exact 5.5 pressures and aqueous solution concentrations, therefore, we 5.0 assumed that the hydrate phase equilibrium conditions in the 275280 285 290 295 300 presence/absence of the LDHIs are the same. Temperature T, K The experiments were conducted at the initial system pressures of 8 and 6 MPa. Since hydrate formation is a sto- Fig. 2 Representation of induction time in a pressure-temperature chastic phenomenon, for some of the solutions, the experi- diagram ments were repeated to check the repeatability of the hydrate formation. Tables  4 and 5 indicate the hydrate formation 300 8.0 induction times and the gas consumption rates for vari- Temperature Induction time ous cases of water, PVP, MEG, and MEG + PVP mixture Pressure 296 7.5 solutions. For each aqueous solution, the experiment was repeated more than three times. For several cases, no hydrate 292 7.0 was formed and we did not include those obtained results in Tables 4 and 5. 288 6.5 It is interpreted from Tables 3 and 4 that as the subcooling increases, the induction time decreases. The reason is that as 284 6.0 the hydrate formation driving force increases by increasing 280 5.5 the subcooling, the induction time decreases consequently. It is obvious from Table 4 that the 1 wt% PVP and 20 276 5.0 wt% MEG aqueous mixture has the maximum induction 050 100 150 time with the value of 187.5 min at the target temperature Time, min of 277.15 K. By increasing the PVP concentration from 1 wt% to 2 wt% in this aqueous mixture, the induction time Fig. 3 Temperature and pressure profiles for 1.00 wt% of PVP in decreases. This fact indicates that the aqueous mixture of 1 aqueous solution wt% PVP and 20 wt% MEG is the best choice for hydrate inhibition at the initial pressure of 8 MPa. It is noteworthy The hydrate formation in the cell is represented by: (1) that the kinetic parameters like the gas hydrate formation A sudden pressure drop in the system because considerable induction times are not deterministic phenomena and for amounts of gas are trapped in hydrate cavities. (2) A sudden the other cases or at different conditions, they would have peak in temperature profile since hydrate formation is an some variations. The induction time is dependent on sev- exothermic reaction that leads to a sudden peak in tempera- eral factors like: cooling rate, subcooling, gas composition, ture profile. Figure  3 demonstrates the pressure and tem- aqueous phase concentration, type of additive, pressure, perature profiles for one of our experiments, which are for temperature, existence of additive in the system, etc. Even hydrate formation in the presence of 1.00 wt% of PVP in at the same experimental condition for the same solution, aqueous solution. Induction time is also determined in this different values of induction time are obtained. No deter - figure. It is worth mentioning that for several experimental ministic model is available to predict the induction time and tests in our investigations, no hydrate was formed, therefore, in all induction time modeling studies, a semi-empirical or no induction time could be reported. an empirical approach is used and some parameters are fit- It is clear from Fig.  3 that, a low-pressure drop has ted using experimental induction time data. It is interpreted occurred at the beginning of the experiment, which is due from Table 4 that the minimum induction time belongs to the to the solubility of gases in the aqueous phase and cooling pure water with the value of 35.7 min at the target tempera- of the solution. The next pressure drop is due to hydrate ture of 277.15 K. This shows that MEG, together with PVP, 1 3 Induction time Temperature T, K Pressure P, MPa Sudden pressure drop Pressure drop due to gas solubility and cooling Pressure drop due to hydrate formation Pressure P, MPa Petroleum Science (2021) 18:495–508 501 (a) (b) 0.35 8.5 0.35 293 0.30 8.0 0.30 0.25 7.5 0.25 Pressure Temperature Gas consumed Gas consumed 0.20 7.0 0.20 0.15 6.5 0.15 0.10 6.0 0.10 0.05 5.5 0.05 0 5.0 0 273 050100 150200 250300 050100 150200 250300 Time, min Time, min Fig. 4 Variations of gas consumption with pressure and temperature in the specified time interval for pure water increases the hydrate formation induction time with respect the rate of gas consumption is that the aqueous mixture of 2 to the pure water and acts as the kinetic hydrate inhibitor. wt% PVP and 20 wt% MEG causes a low gas consumption The values of induction time for various concentrations of rate. This means that this aqueous mixture simultaneously PVP and MEG are higher than 35.7 min. For instance, at the increases the induction time (control and slow down the target temperature of 277.15 K, 2 wt% PVP has the induction nucleation) and decreases the gas consumption rate (con- time value of 87.5 min, for 10 wt% and 20 wt% MEG the trol and slow down the hydrate growth rate). This confirms induction time values are 46.3, and 65.3 min, respectively. that PVP plays an important role in hydrate nucleation while For the two solutions (1 wt% PVP + 10 wt% MEG and 2 wt% MEG has a strong effect on hydrate growth rate. This also PVP + 20 wt% MEG) in Table 4, no hydrate formation was confirms the fact that the combination of MEG and PVP is observed and it may be as a result of the probabilistic nature a good choice for gas hydrate inhibition from the view point of hydrate formation. Finally, it is clear from Table 4 that of nucleation and hydrate growth rate control. for most of the aqueous solutions, MEG by itself has a low In this study, a partly empirical model (Rasoolzadeh et al. to moderate effect on the natural gas hydrate inhibition but 2016; McCabe and Stevens 1951) based on chemical kinet- acts as a synergist when added to the PVP aqueous solutions. ics theory was applied to correlate the natural gas hydrate Table 5 indicates that in a similar manner to the initial formation induction time data. Seven parameters in Eqs. pressure of 8 MPa, in the initial pressure of 6 MPa, PVP and (11) and (12) were optimized using the induction time data. MEG increase the hydrate formation induction time values Table 6 presents the optimized parameters. with respect to the pure water. In Table  5, the maximum It is concluded from the optimized parameters that time is 195 min for 2 wt% PVP + 20 wt% MEG at the tar- increasing the mass fractions of PVP and MEG brings about get temperature of 280.15 K and the minimum induction an increase in the induction time and increasing the initial time is 51.8 min for pure water at the target temperature pressure leads to a decrease in the induction time. One of of 277.15 K, respectively. For some aqueous solutions, no the advantages of the proposed model is its generalized hydrate formation was observed at the initial pressure of form from the view points of aqueous solution concentra- 6 MPa. The other results are the same as those obtained tion and pressure. Unlike the previous studies (Rasoolzadeh from Table 4. et  al. 2016; Aliabadi et al. 2015), the parameters are not From the view point of the rate of gas consumption in optimized for each solution specifically and the parameters Tables 4 and 5, the results reveal that although PVP aque- are optimized for all types of aqueous solutions. This may ous solutions have a great effect on hydrate inhibition, they increase the error of the model but makes it more gener- increase the average rate of gas consumption, which means alized. Table 7 compares the experimental and correlated PVP aqueous solutions control and slow down the nucleation induction time data for all the solutions. in hydrate formation but they accelerate the hydrate growth Figure 5 compares the experimental and correlated induc- rate. Unlike PVP aqueous solutions, MEG aqueous solutions tion time data for all the solutions. have great effects on the rate of gas consumption and control The model outputs elucidate that although the hydrate for- the hydrate growth rate well. The important conclusion from mation induction time is a probabilistic phenomenon, except 1 3 Gas consumption, mol Pressure P, MPa Gas consumption, mol Temperature T, K 502 Petroleum Science (2021) 18:495–508 Table 3 Natural gas hydrate phase equilibrium temperatures, target temperatures and subcooling values for different aqueous solutions ΔT Solution P , MPa T , K T , K ΔT , K exp s target Pure water 8.00 293.97 280.15 13.82 0.0470 Pure water 8.00 293.97 277.15 16.82 0.0572 1 wt% PVP 8.00 293.97 280.15 13.82 0.0470 2 wt% PVP 8.00 293.97 280.15 13.82 0.0470 2 wt% PVP 8.00 293.97 277.15 16.82 0.0572 1 wt% L-tyrosine 8.00 293.97 280.15 13.82 0.0470 2 wt% L-tyrosine 8.00 293.97 280.15 13.82 0.0470 10 wt% MEG 8.00 291.70 280.15 11.55 0.0396 10 wt% MEG 8.00 291.70 277.15 14.55 0.0499 20 wt% MEG 8.00 288.99 277.15 11.84 0.0410 Pure water 6.00 292.35 280.15 12.20 0.0417 Pure water 6.00 292.35 277.15 15.20 0.0520 1 wt% PVP 6.00 292.35 280.15 12.20 0.0417 1 wt% PVP 6.00 292.35 277.15 15.20 0.0520 2 wt% PVP 6.00 292.35 280.15 12.20 0.0417 2 wt% PVP 6.00 292.35 277.15 15.20 0.0520 1 wt% L-tyrosine 6.00 292.35 280.15 12.20 0.0417 2 wt% L-tyrosine 6.00 292.35 280.15 12.20 0.0417 10 wt% MEG 6.00 290.12 280.15 9.97 0.0344 10 wt% MEG 6.00 290.12 277.15 12.97 0.0447 20 wt% MEG 6.00 287.46 280.15 7.31 0.0254 20 wt% MEG 6.00 287.46 277.15 10.31 0.0359 1 wt% PVP + 10 wt% MEG 8.00 291.70 280.15 11.55 0.0396 1 wt% PVP + 10 wt% MEG 8.00 291.70 277.15 14.55 0.0499 1 wt% PVP + 20 wt% MEG 8.00 288.99 277.15 11.84 0.0410 1 wt% PVP + 20 wt% MEG 8.00 288.99 280.15 8.84 0.0306 2 wt% PVP + 10 wt% MEG 8.00 291.70 280.15 11.55 0.0396 2 wt% PVP + 10 wt% MEG 8.00 291.70 277.15 14.55 0.0499 2 wt% PVP + 20 wt% MEG 8.00 288.99 280.15 8.84 0.0306 1 wt% PVP + 10 wt% MEG 6.00 290.12 277.15 12.97 0.0447 1 wt% PVP + 10 wt% MEG 6.00 290.12 280.15 9.97 0.0344 1 wt% PVP + 20 wt% MEG 6.00 287.46 280.15 7.31 0.0254 1 wt% PVP + 20 wt% MEG 6.00 287.46 277.15 10.31 0.0359 2 wt% PVP + 10 wt% MEG 6.00 290.12 280.15 9.97 0.0344 2 wt% PVP + 10 wt% MEG 6.00 290.12 277.15 12.97 0.0447 2 wt% PVP + 20 wt% MEG 6.00 287.46 280.15 7.31 0.0254 2 wt% PVP + 20 wt% MEG 6.00 287.46 277.15 10.31 0.0359 for a few solutions, the model can correlate the induction � exp � N model ⎛ p ⎞ � t − t � i i � � time data with acceptable accuracy. This shows the capa- ⎜ ⎟ AARE = × 100% (14) exp ⎜ N ⎟ bility of the proposed generalized model in the correlation p i=1 ⎝ ⎠ of hydrate formation induction time data. The errors of the model are calculated as follows (Rasoolzadeh et al. 2016): where N represents number of data points and t is the p  induction time. The AAE (average absolute error) and exp  AARE (average absolute relative error) of the model are model AAE = t − t  (13) i i N 16.16 min and 13.82%, respectively. i=1 1 3 Petroleum Science (2021) 18:495–508 503 Table 4 Hydrate formation induction time and the rate of gas consumption for different aqueous solutions at 8 MPa Solution N ∆T, K Average induction Induction time range, min Average rate of gas time, min consumption, mole/ min Pure water 4 13.82 47.0 28.0–65.0 0.0187 Pure water 4 16.82 35.7 30.0–53.0 0.0210 1 wt% PVP 2 13.82 106.5 88.0–125.0 0.0162 2 wt% PVP 2 13.82 126.5 106.0–147.0 0.0233 2 wt% PVP 2 16.82 87.5 80.0–95.0 0.0183 10 wt% MEG 2 11.55 57.0 26.0–88.0 0.0102 10 wt% MEG 3 14.55 46.3 35.0–53.0 0.0124 20 wt% MEG 3 11.84 65.3 53.0–80.0 0.0053 1 wt% PVP + 10 wt% MEG 1 11.55 No hydrate No hydrate formed – 1 wt% PVP + 10 wt% MEG 1 11.55 Mixer failed – – 1 wt% PVP + 10 wt% MEG 2 14.55 89.5 77.0–102.0  0.0185 1 wt% PVP + 20 wt% MEG 2 11.84 187.5 187.0–188.0 0.0124 2 wt% PVP + 10 wt% MEG 2 11.55 82.5 77.0–88.0 0.0165 2 wt% PVP + 20 wt% MEG 1 8.84 170.0 170.0 0.0063 2 wt% PVP + 20 wt% MEG 1 8.84 Mixer failed – – 2 wt% PVP + 20 wt% MEG 3 11.84 No hydrate No hydrate formed – Table 5 Hydrate formation induction time and the rate of gas consumption for different aqueous solutions at 6 MPa Solution N ∆T, K Average induction time, min Induction time range, min Average rate of gas consumption, mole/ min Pure water 2 12.20 64.0 35.0–93.0 0.0157 Pure water 3 15.20 51.8 32.0–125.0 0.0129 1 wt% PVP 1 12.20 110.0 110.0 0.0177 1 wt% PVP 2 12.20 No hydrate No hydrate formed – 1 wt% PVP 1 15.20 70.0 70.0 0.0211 2 wt% PVP 1 12.20 130.0 130.0 0.0234 2 wt% PVP 1 12.20 Data was missed due to power failure 2 wt% PVP 1 15.20 100.0 100.0 0.0180 2 wt% PVP 1 15.20 Leakage from venting connection 10 wt% MEG 1 9.97 115 115.0 0.0099 10 wt% MEG 1 9.97 Leakage from venting connection 20 wt% MEG 1 7.31 123.0 123.0 0.0038 20 wt% MEG 1 10.31 80.0 75.0–85.0 0.0058 1 wt% PVP + 10 wt% MEG 1 9.97 85.0 85.0 0.0160 1 wt% PVP + 10 wt% MEG 1 9.97 No hydrate formed 1 wt% PVP + 10 wt% MEG 3 12.97 94.0 77.0–103.0 0.0197 1 wt% PVP + 20 wt% MEG 3 7.31 No hydrate No hydrate formed – 1 wt% PVP + 20 wt% MEG 3 10.31 No hydrate No hydrate formed – 2 wt% PVP + 10 wt% MEG 2 9.97 136.5 133.0–140.0 0.0082 2 wt% PVP + 10 wt% MEG 2 12.97 174.0 168.0–180.0 0.0191 2 wt% PVP + 20 wt% MEG 2 7.31 195.0 150.0–240.0 0.0055 1 3 504 Petroleum Science (2021) 18:495–508 It is worth mentioning that this semi-empirical correla- Table 6 The parameters optimized in this work tion can only be used for the aforementioned aqueous solu- Parameter Value tions within the studied pressure and temperature ranges. b 18.297 By comparing the values of AAE and AARE of this work and the errors of several induction time models reported m − 0.208 A − 84.034 in the literature (Talaghat and Khodaverdiloo 2019), it can be concluded that considering the generalization of the A 0.966 A 85.438 model, the errors are acceptable. Figures 6 and 7 illustrate the average induction time data, the range of experimental A 0.014 A 1.279 data, and the correlated induction time data for various solutions. It is interpreted from Figs. 6 and 7 that for most of the aqueous solutions, the errors are acceptable. However, for a few solutions, the errors are approximately high, which are due to the weakness of the model in considering the Table 7 The experimental and correlated induction time data for all the aqueous solutions Solution N ∆T, K Average induction time Induction time range, min Correlated (experimental), min induction time, min Pure water 4 13.82 47.0 28.0–65.0 43.97 Pure water 4 16.82 35.7 30.0–53.0 38.28 1 wt% PVP 2 13.82 106.5 88.0–125.0 72.08 2 wt% PVP 2 13.82 126.5 106.0–147.0 100.49 2 wt% PVP 2 16.82 87.5 80.0–95.0 87.50 10 wt% MEG 2 11.55 57.0 26.0–88.0 57.42 10 wt% MEG 3 14.55 46.3 35.0–53.0 48.53 20 wt% MEG 3 11.84 65.3 53.0–80.0 65.30 1 wt% PVP + 10 wt% MEG 1 11.55 No hydrate No hydrate formed – 1 wt% PVP + 10 wt% MEG 2 14.55 89.5 77.0–102.0 75.69 1 wt% PVP + 20 wt% MEG 2 11.84 187.5 187.0–188.0 96.95 2 wt% PVP + 10 wt% MEG 2 11.55 82.5 77.0–88.0 122.01 2 wt% PVP + 20 wt% MEG 1 8.84 170.0 170.0 104.42 2 wt% PVP + 20 wt% MEG 3 11.84 No hydrate No hydrate formed – Pure water 2 12.20 64.0 35.0–93.0 60.70 Pure water 3 15.20 51.8 32.0–125.0 51.80 1 wt% PVP 1 12.20 110.0 110.0 91.36 1 wt% PVP 2 12.20 No hydrate No hydrate formed – 1 wt% PVP 1 15.20 70.0 70.0 77.97 2 wt% PVP 1 12.20 130.0 130.0 122.35 2 wt% PVP 1 15.20 100.0 100.0 104.42 10 wt% MEG 1 9.97 115 115.0 78.66 20 wt% MEG 1 7.31 123.0 123.0 113.37 20 wt% MEG 2 10.31 80.0 75.0–85.0 86.43 1 wt% PVP + 10 wt% MEG 1 9.97 85.0 85.0 114.42 1 wt% PVP + 10 wt% MEG 3 12.97 94.0 77.0–103.0 94.00 1 wt% PVP + 20 wt% MEG 3 7.31 No hydrate No hydrate formed – 1 wt% PVP + 20 wt% MEG 3 10.31 No hydrate No hydrate formed – 2 wt% PVP + 10 wt% MEG 2 9.97 136.5 133.0–140.0 150.57 2 wt% PVP + 10 wt% MEG 2 12.97 174.0 168.0–180.0 123.70 2 wt% PVP + 20 wt% MEG 2 7.31 195.0 150.0–240.0 205.64 1 3 Petroleum Science (2021) 18:495–508 505 PVP-MEG interactions or inherent errors in the experi- mental induction time data measured in this work. The last inhibitor studied in this work is the L-tyrosine. Table  8 indicates the results for L-tyrosine and L-tyros- ine + MEG aqueous solutions. For the case of L-tyrosine aqueous solutions, it is con- cluded that L-tyrosine aqueous solutions have very weak effects on gas hydrate formation induction time and even decrease in  the induction time compared to pure water. These results are in good agreement with the data obtained by Salamat et al. (2013). This shows that from the point of 15 hydrate formation induction time, L-tyrosine is not a good 0 choice. Also, the results show that L-tyrosine + MEG aque- 0 15 30 45 60 75 90 105 120 135 150 165 180 195 ous solution has more inhibition effect on gas hydrate for - Experimental induction time mation induction time. The reason is that the L-tyrosine is a kind of amino-acid and as the pH of the solution is low- Fig. 5 Resemblance between experimental and calculated induction ered (in the presence of MEG aqueous solution), the amino times for all the aqueous solutions acid solubility increases because of the stabilization of the cation species (Carta and Tola 1996). This may increase P = 8 MPa, T = 277.15 K P = 8 MPa, T = 280.15 K (a) target (b) target 200 200 Experimental Experimental Model Model 150 150 100 100 50 50 0 0 Pure 2 wt% 10 wt% 20 wt% 1 wt% 1 wt% Pure 1 wt% 2 wt% 10 wt% 2 wt% 2 wt% water PVP MEG MEG PVP+ PVP+ water PVP PVP MEG PVP+ PVP+ 10 wt% 20 wt% 10 wt% 20 wt% MEG MEG MEG MEG Fig. 6 Experimental and correlated induction time data at the pressure of 8 MPa P = 6 MPa, T = 277.15 K P = 6 MPa, T = 280.15 K (a) target (b) target 200 250 Experimental Experimental Model Model 0 0 Pure 1 wt% 2 wt% 20 wt% 1 wt% 2 wt% Pure 1 wt% 2 wt% 10 wt% 20 wt% 1 wt% 2 wt% 2 wt% water PVP PVP MEG PVP+ PVP+ water PVP PVP MEG MEG PVP+ PVP+ PVP+ 10 wt% 10 wt% 10 wt% 10 wt% 20 wt% MEG MEG MEG MEG MEG Fig. 7 Experimental and correlated induction time data at the pressure of 6 MPa 1 3 Calculated induction time Induction time, min Induction time, min Induction time, min Induction time, min 506 Petroleum Science (2021) 18:495–508 Table 8 Hydrate formation induction time, and the rate of gas consumption for L-tyrosine aqueous solutions Solution P , MPa T , K T , K Number of experi- Subcooling, K Induction time, Average gas con- exp eq target ments min sumption rate, mole/min Fresh Used Fresh Used Fresh Used Fresh Used 1 wt% L-tyrosine 9.0 294.55 280.15 1 5 14.4 4.8–7 35 < 25 0.013 0.024 2 wt% 8.64 294.15 280.15 1 5 14.0 5.5–7.3 45 < 30 0.013 0.016 L-tyrosine 2 wt% 8.83 292.15 280.15 1 4 12.0 7.5–10.5 53 < 28 0.010 0.012 L-tyrosine + 10 wt% MEG 2 wt% 8.73 289.45 280.15 1 5 9.3 6.7–8.7 65 < 32 0.008 0.012 L-tyrosine + 20 wt% MEG the interactions between water and L-tyrosine and results in average rate of gas consumption were investigated. The an increase in the hydrate formation induction time. results elucidate that both MEG and PVP increase the induc- Unlike MEG and PVP, fresh and re-used L-tyrosine aque- tion times with respect to pure water and PVP is stronger ous solutions even by removing the memory effect, show dif- in decreasing the induction times. Adding MEG to PVP, ferent results. Although it was expected by lowering the sub- for several cases leads to the synergistic inhibition effect, cooling, the induction time increases, the re-used L-tyrosine and for some cases, it deteriorates the inhibition effect. For aqueous solutions yield lower induction times with respect the case of gas consumption rate, MEG is the better choice to fresh L-tyrosine aqueous solutions. compared to PVP. From the point of hydrate formation It is concluded that L-tyrosine loses its ability to inhibit induction time, L-tyrosine is not a good choice. Also, the hydrate formation after removing its memory effect. It may results show that L-tyrosine + MEG leads to more inhibition be due to its structural transition and the polymer property effect on gas hydrate formation induction time. The reason changes. Although the method to remove the memory effect is is that L-tyrosine is a kind of amino-acid and as the pH of the same for all the aqueous solutions but the results indicate the solution is lowered (in the presence of MEG), the amino that L-tyrosine aqueous solutions behave in a different man- acid solubility increases because of the stabilization of the ner in comparison with PVP aqueous solution and pure water. cation species. This may increase the interactions between This may be the result of the existence of the alkyl side chain water and L-tyrosine and result in an increase in the hydrate of L-tyrosine. Also, it may be due to the variation of the ion formation induction time. For the hydrate growth inhibition, distribution of L-tyrosine, and consequently showing differ - L-tyrosine acts well. The reason is that L-tyrosine shows ent behavior (Sa et al. 2013). Therefore, L-tyrosine is not a different growth inhibition mechanisms compared to PVP. good candidate for natural gas nucleation inhibition. Finally, In L-tyrosine, the balance between the effects of the hydro- the results show that although the performance of L-tyrosine philic terminal groups and the hydrophobic side chains on is not good in the nucleation step it plays a crucial role in the the local water structure determines their effectiveness in hydrate crystal growth rate step and decreases the average gas terms of growth inhibition. Furthermore, a partly empirical consumption rate significantly. The reason is that L-tyrosine model was used to estimate the induction time for MEG and shows die ff rent growth inhibition mechanisms compared to PVP aqueous solutions. It was concluded that the model can PVP. In L-tyrosine, the balance between the effects of the correlate the induction time data with acceptable accuracy. hydrophilic terminal groups and the hydrophobic side chains Open Access This article is licensed under a Creative Commons Attri- on the local water structure determines their effectiveness bution 4.0 International License, which permits use, sharing, adapta- in terms of growth inhibition (Sa et al. 2013). Therefore, tion, distribution and reproduction in any medium or format, as long L-tyrosine performs successfully in hydrate growth inhibition. as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated 5 Conclusions otherwise in a credit line to the material. 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Insights into kinetic inhibition effects of MEG, PVP, and L-tyrosine aqueous solutions on natural gas hydrate formation

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Abstract

It is necessary to understand all the prerequisites, which result in gas hydrate formation for safe design and control of a variety of processes in petroleum industry. Thermodynamic hydrate inhibitors (THIs) are normally used to preclude gas hydrate formation by shifting hydrate stability region to lower temperatures and higher pressures. Sometimes, it is difficult to avoid hydrate formation and hydrates will form anyway. In this situation, kinetic hydrate inhibitors (KHIs) can be used to postpone formation of gas hydrates by retarding hydrate nucleation and growth rate. In this study, two kinetic parameters including natural gas hydrate formation induction time and the rate of gas consumption were experimentally investigated in the presence of monoethylene glycol (MEG), L-tyrosine, and polyvinylpyrrolidone (PVP) at various concentrations in aqueous solutions. Since hydrate formation is a stochastic phenomenon, the repeatability of each kinetic parameter was evaluated several times and the average values for the hydrate formation induction times and the rates of gas consumption are reported. The results indicate that from the view point of hydrate formation induction time, 2 wt% PVP and 20 wt% MEG aqueous solutions have the highest values and are the best choices. It is also interpreted from the results that from the view point of the rate of gas consumption, 20 wt% MEG aqueous solution yields the lowest value and is the best choice. Finally, it is concluded that the combination of PVP and MEG in an aqueous solution has a simultaneous synergistic impact on natural gas hydrate formation induction time and the rate of gas consumption. Furthermore, a semi-empirical model based on chemical kinetic theory is applied to evaluate the hydrate formation induction time data. A good agreement between the experimental and calculated hydrate formation induction time data is observed. Keywords Gas hydrate · Clathrate hydrate · Natural gas · Kinetic hydrate inhibitor (KHI) · Induction time · Kinetics List of symbolsPVP Polyvinylpyrrolidone MEG Monoethylene glycol rpm Round per minute K Kelvin SNG Synthetic natural gas KHI Kinetic hydrate inhibitor THI Thermodynamic hydrate inhibitor PEO Polyethylene oxide A –A Optimized parameter 1 5 PVCap Polyvinylcaprolactam AAE Average absolute error AARE Average absolute relative error B Nucleation rate Edited by Yan-Hua Sun b Arbitrary fitting constant * Amir H. Mohammadi C Arbitrary constant amir_h_mohammadi@yahoo.com k Arbitrary fitting constant m Fitting parameter Department of Natural Gas Engineering, School of Chemical m.f Mass fraction of PVP in aqueous solution and Petroleum Engineering, Shiraz University, Shiraz 71345, PVP Iran m.f Mass fraction of MEG in aqueous solution MEG N Avogadro number Department of Process Engineering, National Iranian Gas Company (NIGC), South Pars Gas Complex (SPGC) Phases N N umber of data points 4&5, Bushehr 75391/311, Iran n Arbitrary fitting constant t=0 Discipline of Chemical Engineering, School of Engineering, n Initial mole of gas in the cell cell University of KwaZulu-Natal, Howard College Campus, t n Mole of gas at time t cell King George V Avenue, Durban 4041, South Africa Vol.:(0123456789) 1 3 496 Petroleum Science (2021) 18:495–508 P System’s initial pressure in MPa Among all the aforementioned methods, injecting hydrate P Critical pressure inhibitors is more possible and easy to use way (Sloan and P Cell pressure Koh 2008). In traditional form, two types of hydrate inhibi- cell R Universal gas constant tors are utilized for industrial applications: Thermodynamic r Arbitrary fitting constant hydrate inhibitors (THIs) tend to decrease water activity and S Supersaturation ratio shift hydrate phase equilibrium curve to lower temperatures T Critical temperature and higher pressures. Examples of this type of inhibitors T Cell temperature are methanol, ethanol, monoethylene glycol (MEG), sodium cell T Gas hydrate phase equilibrium temperature chloride (NaCl), etc. (Sloan and Koh 2008; Ghaedi et al. T Cell temperature, which is kept constant for 2018; Masoudi et al. 2005; Najibi et al. 2013; Haghighi et al. target hydrate to form 2009; Lee and Kang 2011; Hemmingsen et al. 2011; Moeini t Induction time et  al. 2018). On the other hand, there are kinetic hydrate ∆T Degree of subcooling inhibitors (KHIs) that act differently. They increase hydrate ∆t Time interval between two experiments formation induction time and decrease hydrate nucleation V Cell volume and crystal growth rates. The well-known KHIs are polyvi- cell V Cr ystal molar volume nylpyrrolidone (PVP) and polyvinylcaprolactam (PVCap) Z Com pressibility factor of gas (Sloan and Koh 2008; Daraboina et al. 2011, 2013; Kelland cell δ Arbitrary fitting constant 2006; Salamat et al. 2013; Villano et al. 2009; Rasoolzadeh σ Average surface tension on the liquid–solid et al. 2016; Cha et al. 2013; Kakati et al. 2016). THIs are interface normally used in large quantities even up to 50 wt% but in λ Arbitrary fitting constant some specific cases, injecting THIs in large quantities has ω Acentric factor an insufficient impact on gas hydrate formation because the Number of ions per dissolved molecule conditions are very convenient for gas hydrates to form. In these cases, KHIs can be used to delay formation of gas hydrates, as mentioned earlier (Sloan and Koh 2008). One 1 Introduction can define the induction time as an interval between reaching hydrate formation conditions and occurring hydrate forma- Natural gas is the cleanest fossil fuel that has been widely tion (Sloan and Koh 2008; Daraboina et al. 2011; Daraboina used in various applications. The irregular, uncontrolled, et al. 2013; Kelland 2006; Salamat et al. 2013; Villano et al. and vast consumption of natural gas will make this type of 2009; Rasoolzadeh et al. 2016; Cha et al. 2013; Kakati et al. energy resource coming to end in future. Therefore, it neces- 2016). In the past decade, the focus of scientific investiga - sitates employing safe and efficient methods in exploitation, tions was on the new group of inhibitors like some kinds of processing, transportation, storage, and delivery of natural ionic liquids (ILs) that not only shift hydrate phase equilib- gas. One of the major obstacles that is likely to threaten nat- rium curve to lower temperature/higher pressure regions but ural gas flow assurance is gas hydrates, or clathrate hydrates, also increase hydrate formation induction time. These com- which can form inside pipelines, valves, cold boxes, and pounds are called dual function inhibitors (DFIs) (Rasoolza- other production and processing facilities (Villicaña-García deh et al. 2016). A large number of studies of DFIs are avail- and Ponce-Ortega 2019; Rimos et al. 2014). For gas hydrates able in the literature. Xiao et al. investigated the inhibition to form, several conditions have to be prepared such as high performances of imidazolium-based ILs on methane and pressures, existence of sufficient amounts of water in the natural gas hydrates formation. They concluded that the form of water vapor, liquid water, or ice called the host used ILs (due to strong electrostatic charges and hydrogen molecules and existence of some small and light molecules bonds) not only shift the hydrate equilibrium curve/hydrate of gases and volatile liquids, which play roles of the guest dissociation conditions to lower temperatures and higher molecules (Sloan and Koh 2008). Gas hydrates crystal- pressures but also slow down the hydrate nucleation and line lattices formed by water molecules can be stabilized growth rate (Xiao and Adidharma 2009; Xiao et al. 2010). by occupation of cavities with guest molecules (Sloan and Kim et al. synthesized pyrrolidinium cation-based ILs and Koh 2008). studied their thermodynamic and kinetic impacts on meth- Gas hydrate formation in pipelines can cause blockage ane hydrate formation. They also observed the dual-function and sudden pressure drops and huge economic losses are the inhibition impacts of the pyrrolidinium cation-based ILs on results of this phenomenon (Sloan and Koh 2008; Hammer- methane hydrate (Kim et al. 2011). Tariq et al. reviewed the schmidt 1934). Heating, pressure reduction, water removal, roles of ILs on gas hydrate formation. They reviewed all and injecting some kinds of inhibitors to pipelines are some of the available kinetic and thermodynamic hydrate inhibi- recommended methods to avoid gas hydrate formation. tion data in the attendance of ILs to evaluate the strength of 1 3 Petroleum Science (2021) 18:495–508 497 each IL on gas hydrate inhibition (Tariq et al. 2014). Lim leads to a synergistic effect on hydrate inhibition (Kakati et al. used morpholine as a DFI for gas hydrate formation. et  al. 2016). Kim et al. conducted an experimental study They applied the powder X-ray diffraction, Raman spectros- on hydrate formation of SNG in the presence of MEG and copy, and nuclear magnetic resonance (NMR) analyses to PVCap. They suggested that mixing small amounts of investigate molecular behavior and the crystal structure of PVCap with MEG leads to a synergistic effect on hydrate hydrate in the presence of morpholine (Lim et al. 2014). inhibition and the amounts of MEG can be reduced substan- Qureshi et al. studied kinetic and thermodynamic effects of tially (Kim et al. 2014). polyethylene oxide (PEO) and vinyl caprolactam (VCap) This contribution is intended to experimentally evaluate with two ILs on synthetic natural gas hydrate formation. the performances of KHIs, THIs, and their mixtures on natu- They took into account that the addition of the synergents ral gas hydrate formation kinetic parameters like induction to the ILs could effectively improve the gas hydrate inhi - time and the rate of gas consumption. Several mixtures at bition strength of the ILs (Qureshi et al. 2016). Lee et al. various experimental conditions were applied for this pur- evaluated dual-function inhibition performances of ILs in pose. MEG was used as THI, PVP and L-tyrosine were used the presence/absence of polyvinyl caprolactam (PVCap) on as KHIs in this work. Moreover, for the case of MEG and methane hydrate formation. They observed that the utiliza- PVP, a partly empirical model based on the chemical kinet- tion of IL and PVCap mixture results in the enhanced kinetic ics theory was handled to correlate the natural gas hydrate inhibition effect on methane hydrate formation (Lee et al. formation induction time data. 2016). Haji Nasrollahebrahim et al. investigated thermo/ kinetic inhibition effects of six ILs on methane hydrate for - mation by molecular dynamics simulation. They concluded 2 Experimental that among the investigated ILs, 1-(2-hydroxyethyl)-3-meth- ylimidazolium bis(fluorosulfonyl)imide ([C OHmim][f N]) 2.1 Materials 2 2 and 1-(2,3-dihydroxypropyl)-3 methylimidazoliumbis(fluoro sulfonyl)imide ([C (OH) mim][f N]) have stronger thermo- Monoethylene glycol (MEG) (99.5% purity) and L-tyrosine 3 2 2 dynamic/kinetic inhibition effects (Haji Nasrollahebrahim (99.0 wt% purity) were purchased from Merck. Polyvi- et al. 2013). Yaqub et al. reviewed the roles of DFIs on gas nylpyrrolidone (PVP) (99.0 wt% purity) was purchased from hydrate inhibition. They calculated the average temperature Sigma-Aldrich, with a molecular mass of 40,000 g/mol. depression and relative inhibition power for various ILs for The natural gas mixture was purchased from Fara Fan Gas selection of the best IL for academic and industrial applica- and its composition is shown in Table 1. Deionized water tions (Yaqub et al. 2018). Khan et al. experimentally stud- was used in the experiments. ied inhibition strength of tetramethyl ammonium chloride MEG in mass fractions of 0.10 and 0.20, PVP and (TMACl) on the formation of methane and carbon dioxide L-tyrosine in mass fractions of 0.01 and 0.02 were used in hydrates. They used 1, 5, and 10 wt% TMACl aqueous solu- this work. The aqueous solutions were prepared by the gravi- tion and concluded that TMACl can be used as potential metric method using the electronic A&D balance (EK-300) DFI for both methane and CO hydrates (Khan et al. 2019). with ± 0.01 g readability. Although the investigations into THIs and KHIs are abun- dant, there is limited information on the mixed solutions 2.2 Apparatus of THIs and KHIs. Daraboina et al. experimentally stud- ied the impacts of polyethylene oxide (PEO) and NaCl on A 250 cm stainless steel (SS-316) cell is an important part the performance of Luvicap to inhibit natural gas hydrate of the experimental equipment, which can tolerate pres- formation. They concluded that the addition of PEO and sures up to 35 MPa. Circulation of water and ethylene glycol NaCl on Luvicap decreases the nucleation of hydrate, which means the enhancement of inhibition strength of Luvicap Table 1 Composition of natural gas mixture used in this study (Daraboina et al. 2013). Cha et al. experimentally investi- gated the inhibition effects of MEG and PVP on synthetic Component Mole fraction natural gas (SNG) hydrate formation. They stated that the CH 0.8040 kinetic inhibition effect of MEG is an important factor in C H 0.1030 2 6 decreasing MEG injection for offshore petroleum pipelines C H 0.0500 3 8 (Cha et al. 2013). Kakati et al. performed an experimental n-C 0.0072 study of the addition of L-tyrosine and NaCl to PVP as a i-C 0.0165 widely-used gas hydrate inhibitor to study its performance N 0.0011 on (methane-ethane-propane) gas mixture hydrates. They CO 0.0182 observed that the addition of L-tyrosine and NaCl on PVP 1 3 498 Petroleum Science (2021) 18:495–508 aqueous solution in the constant-temperature bath controls 3 Induction time and gas consumption rate the cell temperature. A high-precision temperature sensor modeling with ± 0.1 K readability was used to measure the cell tem- perature. A piezoresistive pressure transducer (Keller, 23S) The rate of gas consumption can be determined using the was applied to measure the cell pressure, with a standard following procedure: uncertainty of ± 0.015% of total pressure. A magnetic stirrer Step 1 The initial mole of gas in the cell is calculated as fol- was used to agitate the fluid and solid hydrate phases in the low (Rasoolzadeh et al. 2016): vessel at a speed of 500 rpm. The setup also consists of a t=0 t=0 P V data acquisition program to log several parameters like pres- cell cell t=0 n = (1) cell t=0 t=0 sure, temperature, and stirrer speed at every few seconds. R T Z cell cell Figure 1 demonstrates a schematic view of the setup. where P is the cell pressure, V stands for the cell vol- cell cell ume (250 cm ), R represents the universal gas constant, T cell 2.3 Procedure designates the cell temperature and Z indicates the com- cell pressibility factor of the gas mixture, which is calculated After washing and drying the experimental cell, a leakage using the Peng–Robinson equation of state and the van der test was performed by injecting nitrogen at 1 MPa. After- Waals (vdW) mixing rules (Peng and Robinson 1976). ward, all the remained gases in the cell were removed using Step 2 After completion of hydrate formation, the mole a two-stage rotary vacuum pump (Adixen Pascal Series of gas is calculated thusly (Rasoolzadeh et al. 2016, 2019; 2005SD) for about half an hour. Then, 50 cm of an aqueous Aliabadi et al. 2015): solution as a feed was injected into the cell. The pressure of t t (P )(V ) cell cell the vessel was adjusted to the desired pressure through the t n = (2) cell t t gas injection. To avoid gas hydrate memory effect, the tem- R(T )(Z ) cell cell perature of the cell was elevated to 313 K and kept constant Step 3 The rate of gas consumption at time t can be cal- (313 K) for 30 min while the stirrer rotated at the constant culated as follow (Rasoolzadeh et al. 2016): rate of 500 rpm. The bath temperature was set to two dis- tinct targets temperatures of 277.15 and 280.15 K for each t=0 t n − n cell cell (3) v = experiment. The cell temperature decreased from 313 K to Δt −1 the target temperatures with the cooling rate of 0.3 K min and gave enough time to ensure gas hydrate formation com- where v is the rate of gas consumption. pletion. Finally, the system temperature increased to 313 K After completion of hydrate formation, the gas phase com- and the next test was performed. position changes, and to calculate the number of moles, the Gas pressure Isolation Inlet gas filter Vacuum pump Torque meter regulator valves Inlet gas Pressure sensor Bath temperature Thermocouple Cooling bath Fig. 1 The simplified arrangement of the experimental setup 1 3 Petroleum Science (2021) 18:495–508 499 gas phase composition should be included. We had no equip- where t represents the induction time; r and  are arbitrary ment to measure the gas phase composition. It requires a gas constants. Rearranging Eqs. (5) and (6) leads to the follow- chromatography (GC) analyzer connected to the cell to exactly ing relation (Rasoolzadeh et al. 2016): measure the gas phase composition. Because of the lack of equipment, it was assumed that the composition of the gas t = = × i n r nr k (7) exp(− ) mixture is constant. Table 2 presents the critical properties and kexp − the acentric factors of the gas mixture components required to calculate the compressibility factor of the gas mixture. The nucleation rate has the inverse relationship with (8) supersaturation (Rasoolzadeh et  al. 2016; McCabe and Stevens 1951; Mullin 1993): m = nr 16 V N M A B = Cexp − (9) (4) 2 2 3 (RT) S −m t = exp − (10) where B stands for the nucleation rate, N is Avogadro number, R represents the universal gas constant, as men- We considered the dimensionless subcooling as the super- tioned earlier, V and σ represent the crystal molar volume saturation driving force and hydrate nucleation. Therefore, and the average surface tension on the liquid–solid inter- Eq. (10) is converted to the following form (Rasoolzadeh face, respectively. C is an arbitrary constant, S denotes the et al. 2016): supersaturation ratio and  is the number of ions per dis- −m bT solved molecule. Equation (4) can be re-written as follows t = exp (11) (Rasoolzadeh et al. 2016): ΔT where  is a function of the aqueous solution molecular B = kexp − (5) weight, MEG mass fraction, PVP mass fraction, and the sys- tem initial pressure; m and b are the fitting parameters that where k , b , and n are arbitrary fitting constants. are optimized using the gas hydrate formation induction time It is obvious that there is an inverse relation between the data; T is the gas hydrate phase equilibrium temperature induction time and the nucleation rate (Rasoolzadeh et al. that can be calculated using the van der Waals-Platteeuw 2016; Natarajan 1993): (vdW-P)-based model (Sloan and Koh 2008) presented in our previous work (Saberi et al. 2018); ΔT is the difference t = i r (6) (B ) between the hydrate phase equilibrium temperatures.  is defined as follows: MW solution = A + A exp + A exp m.f + A exp m.f − A ln(P) (12) 1 2 3 PVP 4 MEG 5 MW pure water where m.f is the mass fraction of PVP in the aqueous PVP solution, m.f represents the mass fraction of MEG in MEG the aqueous solution, and P is the system’s initial pressure in MPa. It is worth mentioning that the role of guest mol- Table 2 The critical properties and acentric factors of the gas mixture components (Perry et al. 2015) ecule is important in induction time calculation but as we have investigated only one type of gas sample, no parameter Component Critical temper- Critical pres- Acentric factor ɷ ature T , K sure P , MPa for representing the guest molecule is needed to add to the c c induction time model. CH 190.56 4.59 0.0115 C H 305.32 4.87 0.0995 2 6 C H 369.83 4.24 0.1523 3 8 4 Results and discussion n-C 425.12 3.79 0.2002 i-C 407.80 3.64 0.1835 Two kinetic parameters were experimentally investigated in N 126.20 3.40 0.0377 this work: the induction time and the gas consumption rate. CO 304.21 7.38 0.2236 The definition of the induction time is presented in Fig.  2. 1 3 500 Petroleum Science (2021) 18:495–508 8.5 formation. Figure 4 exhibits the variations of gas consump- Cooling curve tion with pressure and temperature in the specified time Hydrate equilibrium curve 8.0 interval for pure water. Table 3 presents the natural gas hydrate phase equilib- 7.5 rium temperatures, target temperatures, and subcooling for various aqueous solutions. In the previous studies (Kang 7.0 et al. 2014; Ke et al. 2016), it was stated that low amounts 6.5 of LDHIs do not affect hydrate phase equilibrium curves in general. However, some LDHIs may affect hydrate phase 6.0 equilibrium curves. Since we have no experimental hydrate phase equilibrium data in the presence of the LDHIs at exact 5.5 pressures and aqueous solution concentrations, therefore, we 5.0 assumed that the hydrate phase equilibrium conditions in the 275280 285 290 295 300 presence/absence of the LDHIs are the same. Temperature T, K The experiments were conducted at the initial system pressures of 8 and 6 MPa. Since hydrate formation is a sto- Fig. 2 Representation of induction time in a pressure-temperature chastic phenomenon, for some of the solutions, the experi- diagram ments were repeated to check the repeatability of the hydrate formation. Tables  4 and 5 indicate the hydrate formation 300 8.0 induction times and the gas consumption rates for vari- Temperature Induction time ous cases of water, PVP, MEG, and MEG + PVP mixture Pressure 296 7.5 solutions. For each aqueous solution, the experiment was repeated more than three times. For several cases, no hydrate 292 7.0 was formed and we did not include those obtained results in Tables 4 and 5. 288 6.5 It is interpreted from Tables 3 and 4 that as the subcooling increases, the induction time decreases. The reason is that as 284 6.0 the hydrate formation driving force increases by increasing 280 5.5 the subcooling, the induction time decreases consequently. It is obvious from Table 4 that the 1 wt% PVP and 20 276 5.0 wt% MEG aqueous mixture has the maximum induction 050 100 150 time with the value of 187.5 min at the target temperature Time, min of 277.15 K. By increasing the PVP concentration from 1 wt% to 2 wt% in this aqueous mixture, the induction time Fig. 3 Temperature and pressure profiles for 1.00 wt% of PVP in decreases. This fact indicates that the aqueous mixture of 1 aqueous solution wt% PVP and 20 wt% MEG is the best choice for hydrate inhibition at the initial pressure of 8 MPa. It is noteworthy The hydrate formation in the cell is represented by: (1) that the kinetic parameters like the gas hydrate formation A sudden pressure drop in the system because considerable induction times are not deterministic phenomena and for amounts of gas are trapped in hydrate cavities. (2) A sudden the other cases or at different conditions, they would have peak in temperature profile since hydrate formation is an some variations. The induction time is dependent on sev- exothermic reaction that leads to a sudden peak in tempera- eral factors like: cooling rate, subcooling, gas composition, ture profile. Figure  3 demonstrates the pressure and tem- aqueous phase concentration, type of additive, pressure, perature profiles for one of our experiments, which are for temperature, existence of additive in the system, etc. Even hydrate formation in the presence of 1.00 wt% of PVP in at the same experimental condition for the same solution, aqueous solution. Induction time is also determined in this different values of induction time are obtained. No deter - figure. It is worth mentioning that for several experimental ministic model is available to predict the induction time and tests in our investigations, no hydrate was formed, therefore, in all induction time modeling studies, a semi-empirical or no induction time could be reported. an empirical approach is used and some parameters are fit- It is clear from Fig.  3 that, a low-pressure drop has ted using experimental induction time data. It is interpreted occurred at the beginning of the experiment, which is due from Table 4 that the minimum induction time belongs to the to the solubility of gases in the aqueous phase and cooling pure water with the value of 35.7 min at the target tempera- of the solution. The next pressure drop is due to hydrate ture of 277.15 K. This shows that MEG, together with PVP, 1 3 Induction time Temperature T, K Pressure P, MPa Sudden pressure drop Pressure drop due to gas solubility and cooling Pressure drop due to hydrate formation Pressure P, MPa Petroleum Science (2021) 18:495–508 501 (a) (b) 0.35 8.5 0.35 293 0.30 8.0 0.30 0.25 7.5 0.25 Pressure Temperature Gas consumed Gas consumed 0.20 7.0 0.20 0.15 6.5 0.15 0.10 6.0 0.10 0.05 5.5 0.05 0 5.0 0 273 050100 150200 250300 050100 150200 250300 Time, min Time, min Fig. 4 Variations of gas consumption with pressure and temperature in the specified time interval for pure water increases the hydrate formation induction time with respect the rate of gas consumption is that the aqueous mixture of 2 to the pure water and acts as the kinetic hydrate inhibitor. wt% PVP and 20 wt% MEG causes a low gas consumption The values of induction time for various concentrations of rate. This means that this aqueous mixture simultaneously PVP and MEG are higher than 35.7 min. For instance, at the increases the induction time (control and slow down the target temperature of 277.15 K, 2 wt% PVP has the induction nucleation) and decreases the gas consumption rate (con- time value of 87.5 min, for 10 wt% and 20 wt% MEG the trol and slow down the hydrate growth rate). This confirms induction time values are 46.3, and 65.3 min, respectively. that PVP plays an important role in hydrate nucleation while For the two solutions (1 wt% PVP + 10 wt% MEG and 2 wt% MEG has a strong effect on hydrate growth rate. This also PVP + 20 wt% MEG) in Table 4, no hydrate formation was confirms the fact that the combination of MEG and PVP is observed and it may be as a result of the probabilistic nature a good choice for gas hydrate inhibition from the view point of hydrate formation. Finally, it is clear from Table 4 that of nucleation and hydrate growth rate control. for most of the aqueous solutions, MEG by itself has a low In this study, a partly empirical model (Rasoolzadeh et al. to moderate effect on the natural gas hydrate inhibition but 2016; McCabe and Stevens 1951) based on chemical kinet- acts as a synergist when added to the PVP aqueous solutions. ics theory was applied to correlate the natural gas hydrate Table 5 indicates that in a similar manner to the initial formation induction time data. Seven parameters in Eqs. pressure of 8 MPa, in the initial pressure of 6 MPa, PVP and (11) and (12) were optimized using the induction time data. MEG increase the hydrate formation induction time values Table 6 presents the optimized parameters. with respect to the pure water. In Table  5, the maximum It is concluded from the optimized parameters that time is 195 min for 2 wt% PVP + 20 wt% MEG at the tar- increasing the mass fractions of PVP and MEG brings about get temperature of 280.15 K and the minimum induction an increase in the induction time and increasing the initial time is 51.8 min for pure water at the target temperature pressure leads to a decrease in the induction time. One of of 277.15 K, respectively. For some aqueous solutions, no the advantages of the proposed model is its generalized hydrate formation was observed at the initial pressure of form from the view points of aqueous solution concentra- 6 MPa. The other results are the same as those obtained tion and pressure. Unlike the previous studies (Rasoolzadeh from Table 4. et  al. 2016; Aliabadi et al. 2015), the parameters are not From the view point of the rate of gas consumption in optimized for each solution specifically and the parameters Tables 4 and 5, the results reveal that although PVP aque- are optimized for all types of aqueous solutions. This may ous solutions have a great effect on hydrate inhibition, they increase the error of the model but makes it more gener- increase the average rate of gas consumption, which means alized. Table 7 compares the experimental and correlated PVP aqueous solutions control and slow down the nucleation induction time data for all the solutions. in hydrate formation but they accelerate the hydrate growth Figure 5 compares the experimental and correlated induc- rate. Unlike PVP aqueous solutions, MEG aqueous solutions tion time data for all the solutions. have great effects on the rate of gas consumption and control The model outputs elucidate that although the hydrate for- the hydrate growth rate well. The important conclusion from mation induction time is a probabilistic phenomenon, except 1 3 Gas consumption, mol Pressure P, MPa Gas consumption, mol Temperature T, K 502 Petroleum Science (2021) 18:495–508 Table 3 Natural gas hydrate phase equilibrium temperatures, target temperatures and subcooling values for different aqueous solutions ΔT Solution P , MPa T , K T , K ΔT , K exp s target Pure water 8.00 293.97 280.15 13.82 0.0470 Pure water 8.00 293.97 277.15 16.82 0.0572 1 wt% PVP 8.00 293.97 280.15 13.82 0.0470 2 wt% PVP 8.00 293.97 280.15 13.82 0.0470 2 wt% PVP 8.00 293.97 277.15 16.82 0.0572 1 wt% L-tyrosine 8.00 293.97 280.15 13.82 0.0470 2 wt% L-tyrosine 8.00 293.97 280.15 13.82 0.0470 10 wt% MEG 8.00 291.70 280.15 11.55 0.0396 10 wt% MEG 8.00 291.70 277.15 14.55 0.0499 20 wt% MEG 8.00 288.99 277.15 11.84 0.0410 Pure water 6.00 292.35 280.15 12.20 0.0417 Pure water 6.00 292.35 277.15 15.20 0.0520 1 wt% PVP 6.00 292.35 280.15 12.20 0.0417 1 wt% PVP 6.00 292.35 277.15 15.20 0.0520 2 wt% PVP 6.00 292.35 280.15 12.20 0.0417 2 wt% PVP 6.00 292.35 277.15 15.20 0.0520 1 wt% L-tyrosine 6.00 292.35 280.15 12.20 0.0417 2 wt% L-tyrosine 6.00 292.35 280.15 12.20 0.0417 10 wt% MEG 6.00 290.12 280.15 9.97 0.0344 10 wt% MEG 6.00 290.12 277.15 12.97 0.0447 20 wt% MEG 6.00 287.46 280.15 7.31 0.0254 20 wt% MEG 6.00 287.46 277.15 10.31 0.0359 1 wt% PVP + 10 wt% MEG 8.00 291.70 280.15 11.55 0.0396 1 wt% PVP + 10 wt% MEG 8.00 291.70 277.15 14.55 0.0499 1 wt% PVP + 20 wt% MEG 8.00 288.99 277.15 11.84 0.0410 1 wt% PVP + 20 wt% MEG 8.00 288.99 280.15 8.84 0.0306 2 wt% PVP + 10 wt% MEG 8.00 291.70 280.15 11.55 0.0396 2 wt% PVP + 10 wt% MEG 8.00 291.70 277.15 14.55 0.0499 2 wt% PVP + 20 wt% MEG 8.00 288.99 280.15 8.84 0.0306 1 wt% PVP + 10 wt% MEG 6.00 290.12 277.15 12.97 0.0447 1 wt% PVP + 10 wt% MEG 6.00 290.12 280.15 9.97 0.0344 1 wt% PVP + 20 wt% MEG 6.00 287.46 280.15 7.31 0.0254 1 wt% PVP + 20 wt% MEG 6.00 287.46 277.15 10.31 0.0359 2 wt% PVP + 10 wt% MEG 6.00 290.12 280.15 9.97 0.0344 2 wt% PVP + 10 wt% MEG 6.00 290.12 277.15 12.97 0.0447 2 wt% PVP + 20 wt% MEG 6.00 287.46 280.15 7.31 0.0254 2 wt% PVP + 20 wt% MEG 6.00 287.46 277.15 10.31 0.0359 for a few solutions, the model can correlate the induction � exp � N model ⎛ p ⎞ � t − t � i i � � time data with acceptable accuracy. This shows the capa- ⎜ ⎟ AARE = × 100% (14) exp ⎜ N ⎟ bility of the proposed generalized model in the correlation p i=1 ⎝ ⎠ of hydrate formation induction time data. The errors of the model are calculated as follows (Rasoolzadeh et al. 2016): where N represents number of data points and t is the p  induction time. The AAE (average absolute error) and exp  AARE (average absolute relative error) of the model are model AAE = t − t  (13) i i N 16.16 min and 13.82%, respectively. i=1 1 3 Petroleum Science (2021) 18:495–508 503 Table 4 Hydrate formation induction time and the rate of gas consumption for different aqueous solutions at 8 MPa Solution N ∆T, K Average induction Induction time range, min Average rate of gas time, min consumption, mole/ min Pure water 4 13.82 47.0 28.0–65.0 0.0187 Pure water 4 16.82 35.7 30.0–53.0 0.0210 1 wt% PVP 2 13.82 106.5 88.0–125.0 0.0162 2 wt% PVP 2 13.82 126.5 106.0–147.0 0.0233 2 wt% PVP 2 16.82 87.5 80.0–95.0 0.0183 10 wt% MEG 2 11.55 57.0 26.0–88.0 0.0102 10 wt% MEG 3 14.55 46.3 35.0–53.0 0.0124 20 wt% MEG 3 11.84 65.3 53.0–80.0 0.0053 1 wt% PVP + 10 wt% MEG 1 11.55 No hydrate No hydrate formed – 1 wt% PVP + 10 wt% MEG 1 11.55 Mixer failed – – 1 wt% PVP + 10 wt% MEG 2 14.55 89.5 77.0–102.0  0.0185 1 wt% PVP + 20 wt% MEG 2 11.84 187.5 187.0–188.0 0.0124 2 wt% PVP + 10 wt% MEG 2 11.55 82.5 77.0–88.0 0.0165 2 wt% PVP + 20 wt% MEG 1 8.84 170.0 170.0 0.0063 2 wt% PVP + 20 wt% MEG 1 8.84 Mixer failed – – 2 wt% PVP + 20 wt% MEG 3 11.84 No hydrate No hydrate formed – Table 5 Hydrate formation induction time and the rate of gas consumption for different aqueous solutions at 6 MPa Solution N ∆T, K Average induction time, min Induction time range, min Average rate of gas consumption, mole/ min Pure water 2 12.20 64.0 35.0–93.0 0.0157 Pure water 3 15.20 51.8 32.0–125.0 0.0129 1 wt% PVP 1 12.20 110.0 110.0 0.0177 1 wt% PVP 2 12.20 No hydrate No hydrate formed – 1 wt% PVP 1 15.20 70.0 70.0 0.0211 2 wt% PVP 1 12.20 130.0 130.0 0.0234 2 wt% PVP 1 12.20 Data was missed due to power failure 2 wt% PVP 1 15.20 100.0 100.0 0.0180 2 wt% PVP 1 15.20 Leakage from venting connection 10 wt% MEG 1 9.97 115 115.0 0.0099 10 wt% MEG 1 9.97 Leakage from venting connection 20 wt% MEG 1 7.31 123.0 123.0 0.0038 20 wt% MEG 1 10.31 80.0 75.0–85.0 0.0058 1 wt% PVP + 10 wt% MEG 1 9.97 85.0 85.0 0.0160 1 wt% PVP + 10 wt% MEG 1 9.97 No hydrate formed 1 wt% PVP + 10 wt% MEG 3 12.97 94.0 77.0–103.0 0.0197 1 wt% PVP + 20 wt% MEG 3 7.31 No hydrate No hydrate formed – 1 wt% PVP + 20 wt% MEG 3 10.31 No hydrate No hydrate formed – 2 wt% PVP + 10 wt% MEG 2 9.97 136.5 133.0–140.0 0.0082 2 wt% PVP + 10 wt% MEG 2 12.97 174.0 168.0–180.0 0.0191 2 wt% PVP + 20 wt% MEG 2 7.31 195.0 150.0–240.0 0.0055 1 3 504 Petroleum Science (2021) 18:495–508 It is worth mentioning that this semi-empirical correla- Table 6 The parameters optimized in this work tion can only be used for the aforementioned aqueous solu- Parameter Value tions within the studied pressure and temperature ranges. b 18.297 By comparing the values of AAE and AARE of this work and the errors of several induction time models reported m − 0.208 A − 84.034 in the literature (Talaghat and Khodaverdiloo 2019), it can be concluded that considering the generalization of the A 0.966 A 85.438 model, the errors are acceptable. Figures 6 and 7 illustrate the average induction time data, the range of experimental A 0.014 A 1.279 data, and the correlated induction time data for various solutions. It is interpreted from Figs. 6 and 7 that for most of the aqueous solutions, the errors are acceptable. However, for a few solutions, the errors are approximately high, which are due to the weakness of the model in considering the Table 7 The experimental and correlated induction time data for all the aqueous solutions Solution N ∆T, K Average induction time Induction time range, min Correlated (experimental), min induction time, min Pure water 4 13.82 47.0 28.0–65.0 43.97 Pure water 4 16.82 35.7 30.0–53.0 38.28 1 wt% PVP 2 13.82 106.5 88.0–125.0 72.08 2 wt% PVP 2 13.82 126.5 106.0–147.0 100.49 2 wt% PVP 2 16.82 87.5 80.0–95.0 87.50 10 wt% MEG 2 11.55 57.0 26.0–88.0 57.42 10 wt% MEG 3 14.55 46.3 35.0–53.0 48.53 20 wt% MEG 3 11.84 65.3 53.0–80.0 65.30 1 wt% PVP + 10 wt% MEG 1 11.55 No hydrate No hydrate formed – 1 wt% PVP + 10 wt% MEG 2 14.55 89.5 77.0–102.0 75.69 1 wt% PVP + 20 wt% MEG 2 11.84 187.5 187.0–188.0 96.95 2 wt% PVP + 10 wt% MEG 2 11.55 82.5 77.0–88.0 122.01 2 wt% PVP + 20 wt% MEG 1 8.84 170.0 170.0 104.42 2 wt% PVP + 20 wt% MEG 3 11.84 No hydrate No hydrate formed – Pure water 2 12.20 64.0 35.0–93.0 60.70 Pure water 3 15.20 51.8 32.0–125.0 51.80 1 wt% PVP 1 12.20 110.0 110.0 91.36 1 wt% PVP 2 12.20 No hydrate No hydrate formed – 1 wt% PVP 1 15.20 70.0 70.0 77.97 2 wt% PVP 1 12.20 130.0 130.0 122.35 2 wt% PVP 1 15.20 100.0 100.0 104.42 10 wt% MEG 1 9.97 115 115.0 78.66 20 wt% MEG 1 7.31 123.0 123.0 113.37 20 wt% MEG 2 10.31 80.0 75.0–85.0 86.43 1 wt% PVP + 10 wt% MEG 1 9.97 85.0 85.0 114.42 1 wt% PVP + 10 wt% MEG 3 12.97 94.0 77.0–103.0 94.00 1 wt% PVP + 20 wt% MEG 3 7.31 No hydrate No hydrate formed – 1 wt% PVP + 20 wt% MEG 3 10.31 No hydrate No hydrate formed – 2 wt% PVP + 10 wt% MEG 2 9.97 136.5 133.0–140.0 150.57 2 wt% PVP + 10 wt% MEG 2 12.97 174.0 168.0–180.0 123.70 2 wt% PVP + 20 wt% MEG 2 7.31 195.0 150.0–240.0 205.64 1 3 Petroleum Science (2021) 18:495–508 505 PVP-MEG interactions or inherent errors in the experi- mental induction time data measured in this work. The last inhibitor studied in this work is the L-tyrosine. Table  8 indicates the results for L-tyrosine and L-tyros- ine + MEG aqueous solutions. For the case of L-tyrosine aqueous solutions, it is con- cluded that L-tyrosine aqueous solutions have very weak effects on gas hydrate formation induction time and even decrease in  the induction time compared to pure water. These results are in good agreement with the data obtained by Salamat et al. (2013). This shows that from the point of 15 hydrate formation induction time, L-tyrosine is not a good 0 choice. Also, the results show that L-tyrosine + MEG aque- 0 15 30 45 60 75 90 105 120 135 150 165 180 195 ous solution has more inhibition effect on gas hydrate for - Experimental induction time mation induction time. The reason is that the L-tyrosine is a kind of amino-acid and as the pH of the solution is low- Fig. 5 Resemblance between experimental and calculated induction ered (in the presence of MEG aqueous solution), the amino times for all the aqueous solutions acid solubility increases because of the stabilization of the cation species (Carta and Tola 1996). This may increase P = 8 MPa, T = 277.15 K P = 8 MPa, T = 280.15 K (a) target (b) target 200 200 Experimental Experimental Model Model 150 150 100 100 50 50 0 0 Pure 2 wt% 10 wt% 20 wt% 1 wt% 1 wt% Pure 1 wt% 2 wt% 10 wt% 2 wt% 2 wt% water PVP MEG MEG PVP+ PVP+ water PVP PVP MEG PVP+ PVP+ 10 wt% 20 wt% 10 wt% 20 wt% MEG MEG MEG MEG Fig. 6 Experimental and correlated induction time data at the pressure of 8 MPa P = 6 MPa, T = 277.15 K P = 6 MPa, T = 280.15 K (a) target (b) target 200 250 Experimental Experimental Model Model 0 0 Pure 1 wt% 2 wt% 20 wt% 1 wt% 2 wt% Pure 1 wt% 2 wt% 10 wt% 20 wt% 1 wt% 2 wt% 2 wt% water PVP PVP MEG PVP+ PVP+ water PVP PVP MEG MEG PVP+ PVP+ PVP+ 10 wt% 10 wt% 10 wt% 10 wt% 20 wt% MEG MEG MEG MEG MEG Fig. 7 Experimental and correlated induction time data at the pressure of 6 MPa 1 3 Calculated induction time Induction time, min Induction time, min Induction time, min Induction time, min 506 Petroleum Science (2021) 18:495–508 Table 8 Hydrate formation induction time, and the rate of gas consumption for L-tyrosine aqueous solutions Solution P , MPa T , K T , K Number of experi- Subcooling, K Induction time, Average gas con- exp eq target ments min sumption rate, mole/min Fresh Used Fresh Used Fresh Used Fresh Used 1 wt% L-tyrosine 9.0 294.55 280.15 1 5 14.4 4.8–7 35 < 25 0.013 0.024 2 wt% 8.64 294.15 280.15 1 5 14.0 5.5–7.3 45 < 30 0.013 0.016 L-tyrosine 2 wt% 8.83 292.15 280.15 1 4 12.0 7.5–10.5 53 < 28 0.010 0.012 L-tyrosine + 10 wt% MEG 2 wt% 8.73 289.45 280.15 1 5 9.3 6.7–8.7 65 < 32 0.008 0.012 L-tyrosine + 20 wt% MEG the interactions between water and L-tyrosine and results in average rate of gas consumption were investigated. The an increase in the hydrate formation induction time. results elucidate that both MEG and PVP increase the induc- Unlike MEG and PVP, fresh and re-used L-tyrosine aque- tion times with respect to pure water and PVP is stronger ous solutions even by removing the memory effect, show dif- in decreasing the induction times. Adding MEG to PVP, ferent results. Although it was expected by lowering the sub- for several cases leads to the synergistic inhibition effect, cooling, the induction time increases, the re-used L-tyrosine and for some cases, it deteriorates the inhibition effect. For aqueous solutions yield lower induction times with respect the case of gas consumption rate, MEG is the better choice to fresh L-tyrosine aqueous solutions. compared to PVP. From the point of hydrate formation It is concluded that L-tyrosine loses its ability to inhibit induction time, L-tyrosine is not a good choice. Also, the hydrate formation after removing its memory effect. It may results show that L-tyrosine + MEG leads to more inhibition be due to its structural transition and the polymer property effect on gas hydrate formation induction time. The reason changes. Although the method to remove the memory effect is is that L-tyrosine is a kind of amino-acid and as the pH of the same for all the aqueous solutions but the results indicate the solution is lowered (in the presence of MEG), the amino that L-tyrosine aqueous solutions behave in a different man- acid solubility increases because of the stabilization of the ner in comparison with PVP aqueous solution and pure water. cation species. This may increase the interactions between This may be the result of the existence of the alkyl side chain water and L-tyrosine and result in an increase in the hydrate of L-tyrosine. Also, it may be due to the variation of the ion formation induction time. For the hydrate growth inhibition, distribution of L-tyrosine, and consequently showing differ - L-tyrosine acts well. The reason is that L-tyrosine shows ent behavior (Sa et al. 2013). Therefore, L-tyrosine is not a different growth inhibition mechanisms compared to PVP. good candidate for natural gas nucleation inhibition. Finally, In L-tyrosine, the balance between the effects of the hydro- the results show that although the performance of L-tyrosine philic terminal groups and the hydrophobic side chains on is not good in the nucleation step it plays a crucial role in the the local water structure determines their effectiveness in hydrate crystal growth rate step and decreases the average gas terms of growth inhibition. Furthermore, a partly empirical consumption rate significantly. The reason is that L-tyrosine model was used to estimate the induction time for MEG and shows die ff rent growth inhibition mechanisms compared to PVP aqueous solutions. It was concluded that the model can PVP. In L-tyrosine, the balance between the effects of the correlate the induction time data with acceptable accuracy. hydrophilic terminal groups and the hydrophobic side chains Open Access This article is licensed under a Creative Commons Attri- on the local water structure determines their effectiveness bution 4.0 International License, which permits use, sharing, adapta- in terms of growth inhibition (Sa et al. 2013). Therefore, tion, distribution and reproduction in any medium or format, as long L-tyrosine performs successfully in hydrate growth inhibition. as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated 5 Conclusions otherwise in a credit line to the material. 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