Hydrate Induction Time with Temperature Steps: A Novel Method for

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Cite This: Energy Fuels 2019, 33, 6113−6118

Hydrate Induction Time with Temperature Steps: A Novel Method for the Determination of Kinetic Parameters Valentino Canale,† Antonella Fontana,† Gabriella Siani,† and Pietro Di Profio*,†,‡ †

Department of Pharmacy, University of Chieti−Pescara “G. d’Annunzio”, Via dei Vestini 31, I-66013 Chieti, Italy Center of Excellence on Innovative Nanostructured Materials (CEMIN), Department of Chemistry, University of Perugia, Via Elce di Sotto 8, I-06123 Perugia, Italy

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‡

ABSTRACT: Gas hydrate formation usually occurs with a certain delay after a system composed of water and a hydrateforming gas is put under suitable thermodynamic conditions of pressure and temperature. This delay period is called the “induction time”, and because of its large variability within a single experimental setting, hydrate formation is often referred to as a stochastic process. The evaluation of induction times, together with other measurements, is taken as an indication for the efficiency of hydrate inhibitors, and they are usually carried out by simply putting the experimental system under chosen P/T conditions and then waiting for the hydrate to form and measuring the time elapsed. In this paper, we present an improved procedure by which the variability of hydrate induction times can be remarkably reduced, while keeping a good correlation of measured induction times with the respective temperatures as obtained by a constant cooling method. In this procedure, temperatures are lowered by 0.5 °C after each time span of 3 h with no hydrate formation. Induction times obtained in this way show a remarkably lower coefficient of variation as compared to a standard induction time measurement.

1. INTRODUCTION Several gas species form the so-called gas (clathrate) hydrates when interacting with water under high-pressure and lowtemperature conditions.1 Natural gas hydrate formation causes plugs in oil and gas pipelines, representing a major problem in the gas and oil industry. To inhibit the formation of hydrates within pipes, choke valves, and wellheads, several kinds of additives are used: thermodynamic inhibitors such as alcohols and glycols2−4 and low-dosage hydrate inhibitors (LDHIs). The latter category may be divided into kinetic inhibitors (KHIs)5 and antiagglomerants (AAs).6−8 The efficiency of hydrate inhibitors is evaluated in the laboratory by means of several experimental approaches, which are based on the determination of such relevant parameters as the time elapsed for a particular experimental setup to start forming hydrates, the subcooling with respect to the thermodynamic pressure/ temperature formation curve, and so forth. In particular, the isothermal induction time (IT) method and the constant cooling (CC) method are used to characterize LDHIs. In the former (IT), the experimental system (usually, a pressurized reactor containing water and an inhibitor) is put under suitable pressure and temperature conditions within the hydrate formation region, then the time until hydrate formation starts is taken as a direct measure of inhibition ability. In the CC method, an inhibition test starts at a temperature slightly above the boundary of the hydrate formation region, and then the system is cooled down at a constant rate until hydrate starts to form, with a lower formation temperature indicating a more efficient inhibitor. Another way for evaluating the ability of LDHIs is the crystal growth inhibition (CGI) method.9 This method is reportedly repeatable and can be adapted to different experimental setups. Furthermore, the CGI allows us to distinguish among several inhibition regions as a function of subcooling, ranging from complete inhibition to rapid growth. © 2019 American Chemical Society

While being a smart process for evaluating LDHIs, this method starts forming a preformed hydrate, which is a condition known to reduce the intrinsic stochasticity of hydrate formation. Finally, some groups have studied temperature ramping, but the experimental setups were quite different from ours.10,11 A detailed overview of those and other methods for evaluating LDHIs can be found in the recent literature.12−15 However, it is a widely recognized problem that the time and temperature parameters measured with the abovementioned methods are heavily dependent on a number of experimental details, such as the geometry of the reactor, stirring speed, cooling rate, volume and exposed water surface of the reactor, and so on, thus rendering a comparison among different experimental setups hardly significant.12 Another wellknown problem is that, particularly for IT measurements, the variance within a single experimental setup is intrinsically high, thus leading to helplessly define hydrate nucleation as a “stochastic” phenomenon.16 The abovementioned problems especially the latterhave been recently addressed on the basis that a stochastic process essentially only needs more data to be fully characterized. For example, several works have been performed with a novel high-pressure automated lag time apparatus (HP-ALTA), by which a much larger number of hydrate formation events could be followed in a certain time span.17,18 This approach led to statistically significant measurements of formation probability distributions for gas hydrates, which could then be compared to nucleation theory predictions.19−21 Another recent work aimed at circumventing the abovementioned problems based on a novel multitest tube rocking cell, which allowed the authors to obtain large amounts Received: March 21, 2019 Revised: June 5, 2019 Published: June 11, 2019 6113

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Energy & Fuels of data within reasonable times, and conclude that the beginning of hydrate growth is logarithmically related to the subcooling value.12 Finally, some recent studies adopted “survival curves” of water droplets placed under hydrate formation conditions as an indication of the stochasticity of hydrate nucleation.22,23 In the present work, we propose a relatively simple method for the determination of the KHI performance, which consists of performing nonisothermal IT measurements within a given time span with a step gradient of temperatures. This step induction time (SIT) method gave less variable results in terms of measured ITs of several low-molecular weight hydrate inhibitors and promoters, and also showed a higher correlation with inhibitor performances as determined by CC than a usual IT method. To test our method under the worst conditions, pure (>99.5%) methane was used as a sI-forming gas, being this a hydrate former, which is usually characterized by larger variance/stochasticity compared to sII formers (e.g., natural gas).

Figure 1. Schematics of the HM1.

2. EXPERIMENTAL SECTION

time. If hydrate did not form during this first isothermal step, the temperature was lowered to a second temperature T2, with a mild cooling rate of 0.1 °C/min, and left for the reported time. This procedure was iterated for as many steps (T3, T4, etc.) until hydrate formation was observed. After each loop, the temperature was raised to 32 °C, as mentioned above for IT. The following Figure 2 shows a schematics of the three methods.

2.1. Materials. The following materials were purchased from Sigma-Aldrich, and used as received: PVP, polyvinylpyrrolidone, powder, average Mw ≈ 55 000; CTABr, hexadecyltrimethylammonium bromide ≥98%; DoTABr, dodecyltrimethylammonium bromide ≥98%; SDS, sodium dodecyl sulfate ≥98.0% (gas chromatography); L-serine, ReagentPlus, ≥99% [high-performance liquid chromatography (HPLC)]; PVA, poly(vinyl alcohol) Mw 85 000−124 000, 99+ %; L-aspartic acid, reagent grade, ≥98% (HPLC); L-phenylalanine, reagent grade, ≥98%. The surfactant p-dodecyloxybenzyl-N,Ndimethyl-N-ethanolammonium bromide (p-DoDEtOHABr) was synthesized as described in a previous paper,24 with the exception that an ether solution of N,N-dimethyl ethanolamine was used instead of trimethyl amine in the last step. A white solid precipitated, which was filtered out, and crystallized from acetone−methanol. NMR was consistent with the target structure. CH4 (2.5 grade, >99.5 methane) was purchased from SOL S.p.A. Ultrapure water was imported from a Direct-Q device (Millipore). 2.2. Apparatus. Hydrate formation tests were performed with HM1 (hydrate machine 1). For a detailed description, refer to previous works by Di Profio et al.25,26 A high-power thermoelectric Peltier module was used in this apparatus to achieve a temperature range from −20 to 80 °C. This system, together with dedicated electronics, allows for an accurate control of temperature. Because of a custom PID algorithm, the instrument is able to accurately follow temperature ramps with a wide range of heating/cooling rates starting from 4 °C/min. A schematics of the HM1 is shown in Figure 1. 2.3. Procedure. IT: the water-filled (150 mL) reactor was flushed with methane for 5 min, then charged at 6 MPa with methane at rt while stirring. It was then cooled down to 10.55 °C (2 °C above the hydrate curve) in 10 min, left for 30 min at that temperature, then rapidly cooled to setpoint temperature (4.55 °C; 4 °C of subcooling) with a cooling rate of 1 °C/min. Pressure was kept constant through the electro-pneumatic device (see 2.2, above). IT measurement started as soon as the setpoint temperature was reached, and ended with the combined occurrence of (i) a substantial temperature increase, and (ii) a measurable gas flow through the flow meter. After each loop (5 in total for each experiment), the temperature was raised to 32 °C over 1 h and kept there for 1 h for history removal. For CC, the procedure is the same as mentioned above up to the resting phase at 10.55 °C, and then the cooling ramp was started at the reported rate (0.25−1.50 °C/h). Formation temperature was taken as the value under which both temperature and gas flow showed hydrate formation (see above). For SIT, the procedure is the same as above up to the resting phase at 10.55 °C, then the reactor was cooled down to a first temperature T1 (8.05 °C; 0.5 °C of subcooling), and left there for the reported

3. RESULTS AND DISCUSSION 3.1. Optimization of Experimental Conditions. While a few novel, high-throughput approaches have been recently proposed for reducing the stochasticity of IT measurements,12,17,18 they all rely on specific, multireactor designs aimed at obtaining a large amount of experimental data, whose averaging can then be reasonably said statistically significant, even in the face of large variances. On the other hand, there is still lacking a method for intrinsically reducing the variability of ITs (or their proxies), which means obtaining a relatively reliable value of the inhibitor (or promoter) performance with few replicates in a single reactor. As an example of typical scattering of IT data, we carried out preliminary IT measurements of methane hydrates with our apparatus by running five replicates per experiment at three temperatures and 6 MPa of pressure, thus obtaining the results shown in Figure 3: It comes with no surprise that deviations from the average are huge, and worse than that, simple averaging of such a small number of replicates is not statistically correct in terms of confidence intervals/limits. In addition, IT averages are not correlated with the subcooling degree. Therefore, the basic idea behind this work is that the IT method can be improved by introducing a step-wise, suitably chosen temperature gradient, which corresponds to a step-wise increase of the “driving force”. This should lead to IT values having a lower variance with respect to replicated runs, and possibly correlated to the inhibition performances as obtained with CC methods. Time spans thus measured can then be regarded as “proxies” of ITs and, consequently, useful as a measure of inhibitor (or promoter) performances. The first issue was determining a suitable pair of temperature drop/step time values, which gave a lower deviation among replicate experiments. Starting with pure water, under methane hydrate formation conditions (6 MPa, 6114

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Figure 2. Schematics showing temperature ramps vs time for CC, IT, and SIT methods, respectively.

Figure 4. RSDs of measured ITs as a function of (i) temperature differences between two successive cooling steps, and (ii) step times.

Figure 3. Average ITs measured for methane hydrate formation in ultrapure water (no inhibitors/promoters added) at 6 MPa and the indicated temperatures. Bars represent standard deviations.

8.05 °C, i.e., 0.5 °C of subcooling with respect to the equilibrium curve, as calculated with the CSMHYD software),27 we explored three temperature drop values (0.5, 1.0, 1.5 °C), and three isothermal step times (3, 6, 9 h) by running five experiments for each temperature/time pair. As a result, Figure 4 shows the relative standard deviations (RSDs) for each experiment. We opted for a combination of 0.5 °C and 3 h because it gave a low RSD value combined with the lowest increase of the driving force for each step. Also, the shorter time span was preferable in terms of experimental output. Because another goal was to determine whether there was a correlation between inhibitor performances as measured with IT (SIT) and CC methods, we also performed a screening of the standard deviations among hydrate formation temperatures obtained with the CC routine under different cooling rates (0.25, 0.5, 1.0, 1.5 °C/h). Figure 5 shows that formation temperatures are consistently around 2.3−2.4 °C of subcooling (except for runs

Figure 5. Subcooling temperatures under different cooling rates. Values on the ordinate axis represent ΔT’s below the equilibrium temperature. Bars represent standard deviations.

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Energy & Fuels Table 1. Values of Modulator Performances CC

a

SIT

IT

sample

T (°C)

subcooling

st. dev.

min

st. dev.

% RSD

min

st. dev.

% RSD

Water PVP 3000 ppm CTABr 1 mM DoTABr 1 mM p-DoDEtOHABr 1 mM PVP 500 ppm SDS 300 ppm serine 400 ppm PVA 1000 ppm aspartic acid 300 ppm phenylalanine 300 ppm EtOH 5 wt %

6.86 3.54 6.22 6.33 5.97 4.76 6.50 7.36 6.99 5.53 6.42 3.61

1.69 5.01 2.33 2.22 2.58 3.79 2.05 1.19 1.56 3.03 2.13 4.94

0.49 1.02 0.47 0.19 0.33 0.31 0.28 0.17 0.36 0.23 0.19 0.42

531.75 1510.00 640.67 661.87 756.50 1001.25 561.75 254.20 220.00 781.00 515.00 1005.50

56.35 170.00 83.29 58.74 28.50 61.92 66.89 76.79 14.17 188.17 73.75 180.50

10.60 11.26 13.00 8.88 3.77 6.18 11.91 30.21 6.44 24.09 14.32 17.95

146.60 242 46.00 5.43

195.67 176.20 41.43 6.99

133.47 72.81 90.07 128.71

a

38.57 20.00 6.50 7

a

41.89 b

14.53

a

108.61 b

223.61

b

b

a

a

a

a

a

a

a

a

a

b

Not done. Standard deviation and % RSD could not be calculated because of a single experimental value obtained under the reported conditions (4 out of 5 experiments resulted in hydrate formation during the cooling ramp).

at 0.25 °C/h), whereas standard deviations are quite low for the second slowest rate (0.5 °C/h), and measurably higher for the two fastest. This led us to choose 0.5 °C/h as the cooling rate for performing CC cycles to be compared with IT (SIT) measurements. With this combination of operating parameters for SIT (0.5 °C/step; 3 h/step) and CC (0.5 °C/h), we performed hydrate formation experiments in the presence of chemical low-dosage inhibitors and promoters (modulators). 3.2. Testing of Modulators. Methane hydrate formation experiments were conducted according to each of the abovementioned methods (IT, SIT, CC) in the presence of several chemicals, some of which are known hydrate inhibitors (e.g., PVP as KHI, tetraalkyl ammonium surfactants as AAs or synergistics)28,29 or promoters (SDS).25 Other less known modulators are several amino acids, which are being studied both as promoters30 and inhibitors.31,32 Here, we also tested the amino acid serine, aspartic acid, and phenylalanine. Finally, 5 wt % ethanol was tested as a thermodynamic inhibitor. Table 1 reports the ITs (IT, SIT) and formation temperatures (CC) observed, together with the relevant deviations. Table 1 shows an intrinsic limitation of IT experiments, in that a particular subcooling value (4 °C in this case) chosen in order to avoid unfeasibly long lag times with strong inhibitors (e.g., PVP), was too much for some molecules, where hydrate formed during the cooling ramp. This fact, inherently limits the capability of this method in comparing differently performing modulators. Table 1 also clearly shows that “induction” times measured according to the SIT method have much lower variances (% RSD column) as compared to standard IT measurements. SIT times also show a much better correlation with CC values, as shown in Figures 6 and 7. Figure 6 shows that SIT and CC values are linearly correlated (R = 0.95), while no correlation exists for CC vs IT values (Figure 7). There is an intrinsic discrepancy between a purely kinetic approach (i.e., IT) and a mixed thermodynamic/ kinetic method (CC), as what the latter essentially does is continuously changing the thermodynamic conditions under which a hydrate-forming system is set. The kinetic part of CC methods is clearly dependent on the cooling rate, and a few papers investigate how changing those rates affects the outcome.33,34 In the SIT method, a thermodynamic “drive” (i.e., a small, stepwise decrease in T) is added, while keeping an

Figure 6. Plot of CC values vs SIT values. Bars represent standard deviations (R2 = 0.954).

Figure 7. Plot of CC values vs IT values. Bars represent standard deviations.

IT as the measured parameter. At each step, the driving force (subcooling) is increased by a small increment (0.5 °C in this work). The shift from T to (T0.5) occurred over 5 min with a relatively gentle slope of 0.1 °C/min, in order to prevent that an abrupt increase of driving force might prime a sudden 6116

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4. CONCLUSIONS We have proposed a variant of classical IT experiments, whereby the driving force is mildly increased (0.5 °C) in a step-wise manner among isothermal induction periods. It is shown that a limited number of IT-like experiments gives surprisingly low variances of measured times, which are much lower than those for standard ITs as measured according to a usual, purely isothermal procedure. Moreover, SIT times were highly linearly correlated with hydrate formation temperatures obtained from CC experiments, whereas those measured from IT experiments were not. Another difference between IT and SIT relates to the intrinsic difficulty of the former in comparing inhibitors having quite different inhibition performances. Indeed, in order for such a comparison to be strictly valid, IT experiments should be carried out under the same subcooling conditions (i.e., same ΔT from the equilibrium curve) for all tested inhibitors. This condition, however, often leads to either (i) hydrate formation during the cooling ramp while bringing the system to the target (subcooling) temperature when the compound under evaluation is a poor inhibitor; or (ii) almost indefinite (or at least very long) lag periods before hydrate occurrence in case of strong inhibitors. With the SIT method, it is possible to start from a very moderate subcooling value in order to avoid unwanted, early formation during the cooling process, with the working approximation that the following isothermal steps will give formation time values that can be considered as proxies or surrogates of ITs or, similarly, inhibition performances. Support to that approximation appears to stem from the very low variances observed with a limited number of replicates, which render this method ideally suitable for nonhigh throughput devices. Moreover, a very good correlation between SIT times and CC values also supports the potential applicability of this method. As mentioned in the Results and Discussion section above, no attempt has been made so far to integrate time values as obtained with a SIT method into an empirical/theoretical framework such as those developed by Firoozabadi, Chapoy, Maeda and other researchers. Success in this attempt could give rise to more refined time data sets, which should be comparable with even higher reliability.

crystallization. After each temperature decrease, the water + methane system is left under this new isobaric/isothermal condition, and observed for signs of detectable hydrate formation (temperature increase and gas inflow). If nothing happens within the set time (3 h in this work), a further decrease in T is operated, and the cycle is repeated until hydrate formation is observed. At this point, the elapsed time since the system reached 8.05 °C (i.e., the T value of the first isothermal step) is taken as a surrogate of the induction period. It should be noted that, while in most instances hydrate formation was observed within the same temperature step among replicates of a same experiment (i.e., same tested compound), in a few cases, hydrates formed at different temperatures. Also then, however, ITs showed a low variance, and correlated well with CC temperatures (Figure 6). As a first approximation, the correlation between formation temperatures measured with CC, and IT “proxies” as measured with the present SIT method should be regarded simply as a macroscopic index-supporting performance evaluation of a particular molecule (especially, an inhibitor). On a more fundamental level, the SIT method could be integrated within a quantitative frame of equations relating subcooling temperatures with ITs for a certain hydrate former in the absence and presence of inhibitors. For example, resort could be made to the theoretical framework developed by Kashchiev and Firoozabadi.35 With this integration in place, one should be able to enhance the “surrogate” time values as measured by a SIT method, to obtain “proper” ITs as they are cleaned up from the spurious increase of driving force as provided by the cooling steps. More recently, Mali et al.12 found that the subcooling value correlates logarithmically with the mean IT, but this relation does not fit our data, clearly owing to (i) the difference in the hydrate-forming gas (natural gas in Mali’s paper vs pure methane in the present work), and (ii) the difference between experimental setups (i.e., rocking cells vs stirred reactor), among other things. The recent, interesting papers by Maeda36,37 and Kwak38 are a vigorous attempt at finding a model-independent relation between ITs and subcooling values. One of the concerns in those works is that the choice of a suitable cooling rate should take into account the issue of undersaturation of methane in water if cooling is too fast. Reportedly,37 CC results approximately converge at rates of 3.6 and 7.2 °C/h. This should be compared with the 0.5 °C/h cooling rate in the present work, which should be sufficiently slow to reasonably assume that no undersaturation barrier is acting in our method, even if our experimental system (i.e., water volume) is much larger than the HP-ALTA. Another issue recognized by Maeda is that heat transfer limitations could potentially lead to cooling rate dependence of the nucleation rate. This problem is expected to be important in large-sized reactors, while Maeda’s HP-ALTA should be small enough to be relatively unaffected by thermal lag effects. Again, our system is much larger, but it is vigorously stirred (450 rpm ± 1%) to minimize heat transfer limitation and, also, methane undersaturation effects. Maeda also set out to derive empirical relations between subcooling temperatures and mean ITs, but his approach seems subject to the condition of having access to a statistically large number of experimental values, which is not the case for our system/procedure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: pietro.diprofi[email protected]. Phone: +39-0871-355 4791. ORCID

Antonella Fontana: 0000-0002-5391-7520 Gabriella Siani: 0000-0003-0380-367X Pietro Di Profio: 0000-0002-8038-7940 Notes

The authors declare no competing financial interest.

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ABBREVIATIONS IT = induction time SIT = step induction time CC = constant cooling

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REFERENCES

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on June 24, 2019, with an error in ref 1. The corrected version was reposted on June 26, 2019.

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