New insights into the effect of polyvinylpyrrolidone (PVP) concentration on methane hydrate growth. 1. Growth rate

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New insights into the effect of polyvinylpyrrolidone (PVP) concentration on methane Hydrate growth. 1. growth rate Dany Posteraro, Jonathan Verrett, Milan Maric, Phillip Servio

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S0009-2509(14)00723-4 http://dx.doi.org/10.1016/j.ces.2014.12.009 CES12033

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Chemical Engineering Science

Received date: 9 October 2014 Revised date: 17 November 2014 Accepted date: 1 December 2014 Cite this article as: Dany Posteraro, Jonathan Verrett, Milan Maric, Phillip Servio, New insights into the effect of polyvinylpyrrolidone (PVP) concentration on methane Hydrate growth. 1. growth rate, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2014.12.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Title

New insights into the effect of polyvinylpyrrolidone (PVP) concentration on methane hydrate growth. 1. Growth rate

Authors

Dany Posteraro, Jonathan Verrett, Milan Maric, Phillip Servio*

Department of Chemical Engineering, McGill University, 3610 University Street, Wong Building, Montreal, Canada, H3A 0C5

*Corresponding author: Tel: +1 514 398 1026; fax: +1 514 398 6678. Email address: [email protected]

Abstract

To further understand the effects of polyvinylpyrrolidone (PVP) on methane hydrate growth, the current study evaluates initial hydrate growth rate over a wide range of PVP concentrations from 0.7 to 20 000 ppmw (2 wt%) in a stirred tank crystallizer. Tests were undertaken at temperatures ranging from 275.1 to 279.1 K, pressures from 4645 to 7183 kPa and PVP molecular weights of 10 000, 40 000 and 360 000 g/mol. Throughout all these conditions, a common sigmoidal trend between growth rate and PVP concentration was observed. Initial growth rates were the same as that of pure water at PVP concentrations under 10 ppmw but decreased rapidly to near zero growth at concentrations above 1000 ppmw. PVP reduced the initial growth rate by roughly 50% over the concentration range of 10 to 100 ppmw. Such low concentrations have not previously been investigated and provide insight into the PVP inhibition mechanism. PVP was shown to be less effective at inhibiting hydrate growth as reactor pressure increased. The various molecular weights investigated showed similar effects on growth rate at the same mass concentrations, showing no improvement in inhibition by varying polymer chain length over the range tested.

1.0 Introduction

Gas hydrates are nonstoichiometric crystalline compounds formed by a cage network of water molecules containing small non-polar guest molecules. The water cage is held together by hydrogen bonding and is stabilized by van der Waals interactions with the guest substances. There are three principal hydrate structures: structure I (sI), incorporating small gas molecules such as methane; structure II (sII), incorporating molecules larger than ethane but smaller than pentane; and structure H (sH), enclathrating large guests with a diameter up to 0.9 nm (Sloan, 1998). Interest in gas hydrates was initially academic, however industrial research began once hydrate structures were found to cause blockages in oil and gas pipelines (Hammerschmidt, 1934). Inhibitory compounds were sought as additives to assure flow in these pipelines. Two main categories of inhibitors emerged: thermodynamic inhibitors, which affect equilibrium, and kinetic inhibitors, which affect hydrate growth kinetics.

A variety of polymers have been shown to be effective kinetic hydrate inhibitors (KHIs) (Kelland, 2006). Used to prevent nucleation or to slow the growth of hydrates following formation, KHIs can be preferable to thermodynamic inhibitors due to their effectiveness at lower weight fraction, resulting in potential process, environmental and economic savings (Kashchiev and Firoozabadi, 2003; Perrin et al., 2013). The most effective KHIs to date are water-soluble polymers containing a lactam ring structure that binds to the hydrate crystals. The lactam ring has been found to adsorb in open cages at the surface of the hydrate crystal where guest molecules would normally interact, thus disrupting

hydrate formation (Carver et al., 1995; Ohno et al., 2012). The interaction of groups, such as the lactam with the hydrate crystal surface, is thought to be the main parameter affecting hydrate inhibition, and much work has been done to model surface interactions (Anderson et al., 2005; Zeng et al., 2007).

The

most

commonly

researched

KHIs

are

polyvinylpyrrolidone

(PVP)

and

polyvinylcaprolactam (PVCap), both of which contain lactam ring structures (Al-Adel et al., 2008; Pic et al., 2001; Sloan et al., 1998). Many experiments report the effectiveness of these compounds at increasing the driving force necessary to achieve an equivalent hydrate growth rate to pure water systems (Larsen et al., 1998; O'Reilly et al., 2011). Both theoretical and experimental studies have been performed looking into the mechanism of hydrate growth inhibition at either the nucleation or hydrate growth stage (Anderson et al., 2005; Freer and Sloan, 2000). At the nucleation stage, lactam polymers affect hydrate formation by either disrupting hydrate nuclei before they reach a critical size or affecting structural arrangements of water molecules to prevent nucleation (Yang and Tohidi, 2011). Once stable hydrate nuclei have formed and the system is at the growth stage, lactam polymers inhibit growth by a very rapid adsorption of polymer onto the crystal surface (Larsen et al., 1998). Studies have shown PVP to adsorb in a monolayer on the tetrahydrofuran (THF) hydrate crystal (sII) surface and follow a Langmuir type isotherm (Zhang et al., 2009). To demonstrate the strength of the adsorption, Larsen et al. undertook a study whereby hydrate crystals (of sI and sII) were grown and then exposed to inhibitors (including PVP and PVCap) in a quiescent solution for a minimum of five minutes. These were then placed in an uninhibited solution under a

sufficient driving force for hydrate growth; however, growth was not found to resume for at least three hours and did not continue from previous crystal surfaces, appearing instead to have nucleated new crystals (Larsen et al., 1998). This demonstrated both the speed and strength of interaction between PVP and the crystal. In another study by Pic et al., up to 1 wt% PVP, which is generally more than sufficient to have an effect on growth, was injected immediately following methane hydrate (sI) nucleation in a stirred reactor (Pic et al., 2001). Despite these injections, growth continued at the same rate as that initially observed for up to 9000 seconds following the injection, after which time the experiment was stopped. However solutions tested with PVP injected before nucleation showed slower crystal growth and methane consumption rates, indicating that PVP had an effect only if it was present before nucleation. These apparently contradictory results demonstrate the need for further studies to explain the inhibitor mechanism, most notably during the growth phase.

Investigation of growth kinetics of hydrates while exposed to KHIs have been previously performed (Daraboina et al., 2011; Jensen et al., 2011). Pic et. al. evaluated the effect of PVP concentration on gas consumption and turbidity (Pic et al., 2001). Such studies have notably evaluated the effect of PVP concentration on hydrate growth kinetics over a limited concentration range, generally higher than 0.05 wt%. The small number of PVP concentrations previously studied makes it difficult to quantify the relationship between PVP concentration and hydrate growth inhibition.

The effect of an inhibitor polymer’s molecular weight on hydrate inhibition has been a topic of interest in previous studies. Higher molecular weight polymers contain longer polymer chains and thus more binding sites per molecule, which is thought to lead to a stronger attachment to the crystal surface. Some studies have found that larger molecules are more effective at completely inhibiting hydrate growth (O'Reilly et al., 2011), whereas lower molecular weights have been shown to be more effective at perturbing water structure and limiting hydrate nucleation (Long et al., 1994). Others still have found that there are optimal sizes for growth inhibition, or perhaps a mixture of molecular weights may be most effective (Kelland, 2006; Sloan et al., 1998). Monte Carlo simulations of PVP attachment to methane have shown that ring groups in the polymer may compete for adsorption sites and adsorption at multiple sites does not significantly increase the energy of adsorption (Carver et al., 1995). This indicates that there may be little relation between polymer molecular weight and the polymer’s growth inhibition effects following nucleation.

To elucidate further information on the effects of PVP concentration and molecular weight, the current study assesses the effect of temperature, pressure, PVP concentration and PVP polymer molecular weight on methane hydrate growth kinetics by measuring the initial hydrate growth rate in a stirred crystallizer at a variety of growth conditions. A detailed analysis of the effect of PVP concentration from 0.7 ppmw to 20 000 ppmw shows a clear trend and provides insight into the kinetic inhibition mechanism.

2.0 Materials and Methods

2.1 Experimental Setup

Details of the experimental setup can be found in previous reports (Bergeron and Servio, 2008a, b). Briefly, hydrates are formed in a 316 stainless steel crystallizer with a 12 MPa pressure rating and an internal volume of 600 cm3. The crystallizer has two polycarbonate windows for visual inspection and is equipped with a top-mounted PPI DYNA/MAG MM-006 mixer (0-2500 rpm). Gas is supplied to the crystallizer from a 1000-cm3 reservoir using a Baumann 51000 Series control valve. The valve is set to maintain a constant pressure during hydrate formation. Reservoir and reactor biases are used to increase the accuracy of the pressure readings. The crystallizer is placed in a 20% ethylene glycol/water bath that is temperature controlled by a NESLAB RTE Series chiller. Temperature within the reactor and reservoir is monitored using Omega platinum resistance temperature device probes with an accuracy of ± 0.15 K. Pressure is monitored using Rosemount pressure transducers configured to a span of 0-14 MPa and differential (bias) pressure transducers configured to a span of 0-2 MPa, each with an accuracy of ±0.065% of the given span. A National Instruments NI-DAQ 7 data acquisition system coupled with LabVIEW software is used to record all readings. The LabVIEW interface is set up to record the gas reservoir pressure and temperature, and uses the Treble-Bishnoi equation of state to calculate the number of moles consumed at any given time (Trebble and Bishnoi, 1987).

2.2 Materials

Polyvinylpyrrolidone (PVP) was obtained from Sigma Aldrich in powder form at average molecular weights of 10 000 g/mol (PVP10), 40 000 g/mol (PVP40) and 360 000 g/mol (PVP360). The methane gas used was ultra-high purity in excess of 99.99% obtained from MEGS Inc. Deionized water was produced on-site by reverse osmosis using a 0.22-µm filter with a final conductivity of 10 µS and total organic content under 10 ppb.

2.3 Procedure for kinetic experiments

The procedure used is similar to that of previous studies performed (Verrett et al., 2012; Verrett and Servio, 2012). To clean the reactor of any previous solution, the reactor is washed and purged three times with 300 mL of the desired solution. Following this, a 300-mL sample of the desired solution is injected into the reactor. To purge the gas phase and remove air, the reactor is pressurized to 1000 kPa, allowed to mix for 5 minutes, and then depressurized to 200 kPa (all pressures noted are in absolute units). This gas purging is repeated three times. The system is then left to cool and reach a stabilized temperature. When the desired temperature is reached, the reactor is then pressurized to roughly 1500 or 2500 kPa above the hydrate-liquid-vapour equilibrium value (Frost and Deaton, 1946). Experimental temperatures, pressures and driving forces can be found in Table 1. Experimental conditions were chosen based on the experimental equipment available. Temperatures lower than 273.1 K could have led to ice formation in the reactor, whereas

temperatures above 279.1 K would have required pressures difficult to manage with the control valve. The reservoirs and biases were set to pressures 400 kPa higher than the reactor. Once the pressure and temperature of the gas are stabilized, the computer is set to record pressure and temperature data and the control valve is set to maintain the reactor pressure at the desired value. The stirrer is then turned on and set at 750 rpm in order to stir vigorously but avoid entraining gas in the liquid. Following formation, the hydrates are allowed to grow for 900 seconds. The data is then saved, the control valve is turned off, and the reactor is brought to 400 kPa to dissociate the hydrates. The reactor is then left for a sufficient time with mixing to ensure hydrate deformation (generally 4 hours). Following this, another experimental run may then be performed with the same liquid sample by repeating the above procedure, or a new sample solution may be introduced.

3.0 Results and Discussion

3.1 Inhibitor effects on hydrate growth

Typical gas consumption curves obtained at a selection of PVP10 concentrations can be seen in Fig. 1. These curves were obtained at 275.1 K and 4645 kPa but are similar to those observed at other conditions. The general shape of the curves shows initial methane consumption leading to saturation and eventual supersaturation of the liquid phase. Following supersaturation, a hydrate phase is formed with the time for this process being stochastic. Hydrate crystal growth is generally indicated by a sharp change in gas consumption. A temperature change in solution is also observed due to the exothermic nature of hydrate crystallization (not shown). Methane gas is then consumed after hydrate formation as methane is integrated into the solid hydrates. Initial growth rates observed under the various conditions were calculated using the total gas consumption data over the first 900 seconds after nucleation. Without inhibitors present in the system, gas consumption during initial growth is approximately linear due to a quasi-steady state within the reactor as described in previous literature (Bergeron et al., 2009; Bergeron and Servio, 2009). Note that these results are consistent within the given hydrodynamic system; effects such as reactor size, shape, and stirring rate can affect hydrate growth. To ensure that the results observed were accurate, replicates were performed at each of these conditions and 95% confidence intervals were calculated.

The various steps of hydrate formation can be seen in any of the curves in Fig. 1. The curve for pure water shows saturation followed by a sudden shift to a linear gas consumption profile following hydrate formation. Upon introducing some inhibitor, in this case 70 ppmw of PVP10, the system appears to take longer to nucleate and the initial gas consumption rate following crystal formation is significantly lower. Nucleation time, also known as induction time, was not a focus of this study because of the large number of replicates required to study such a stochastic process; however, studies with a significant number of replicates have shown that PVP leads to increased induction times (May et al., 2014). At higher inhibitor concentrations, shown by the 700-ppmw curve, the initial growth is no longer linear following nucleation, but appears as a curve, consistent with the results of other studies (Hong et al., 2012; Pic et al., 2001). It has been suggested that this curved growth profile is due to a surface area limitation during hydrate growth with inhibitors (Al-Adel et al., 2008). At very high inhibitor concentrations it is difficult to determine when hydrates nucleate due to the extremely slow growth and the small temperature change of nucleation. Within this study the inflection point in the curve is used to indicate nucleation and as a basis for calculating the initial growth rate. Growth rates calculated at such high PVP concentrations are near zero, and no significant differences in growth rate due to the choice of the nucleation point were found.

3.2 PVP10 experiments

Initial growth rates over a range of PVP10 concentrations can be found in Fig. 2. Growth rates for PVP concentrations above 1 000 ppmw were not included in the figure because of near zero growth and for graphical clarity (to avoid skew). Tests were performed over the range of temperature and pressure conditions denoted in Table 1. Exact growth rate values and confidence intervals can be found in the Appendix. Initial hydrate growth rates are seen to decrease as PVP concentration increases, with a notably sharp decrease at PVP concentrations below 100 ppmw. A reduction in growth rate of over 50% between 0 and 70 ppmw is observed for nearly all samples. This is followed by a smaller decrease in growth rate as concentration is increased further. This trend is present for all conditions tested, with varying rates of growth decrease. Growth rates for experiments performed with low-pressure driving forces display a much faster reduction than those at higher driving forces. These two distinct groups are clearly visible on the graph and reinforce that driving force has an appreciable effect on inhibitor function, with higher driving forces making inhibitors less effective.

These overall trends in growth are believed to be linked to the adsorption process of PVP onto the gas hydrate structure. A previous study by Zhang et al. quantified the adsorption of PVP onto cyclopentane hydrates (sII) (Zhang et al., 2009). sI and sII hydrates have similar cage structures so it is not unreasonable to believe that PVP interactions will also be similar with the sI crystal (Sloan, 1998). The study did not investigate concentrations below 0.1 wt%, but a sharp increase in adsorption appears to occur between the lowest investigated concentration (~0.1 wt%) and the origin (having zero concentration and zero adsorption). This sharp increase is followed by a more

gradual increase in adsorbed amount of PVP as PVP concentration increases. A similar trend of a large reduction in growth rate with small changes in PVP concentration initially, followed by a more gradual decline at larger concentrations, is also observed in this study.

To visualize growth inhibition at higher PVP concentrations, a logarithmic scale for concentration was used. Figure 3 shows growth rates for PVP solutions tested at 275.1 K. The large concentration range tested and the number of data points allow unprecedented visualization of the shift from a growth rate similar to that of water (shown at a concentration of 0.1 ppmw) to near zero growth. The sigmoidal trend observed is common for all temperature conditions tested. Interpreting this trend, we find that at low PVP concentration (<10 ppmw), the growth rate is nearly identical to that of water. One imagines that at these conditions there is insufficient inhibitor in the system to significantly affect growth rate. Although all PVP molecules may be adsorbed onto hydrate crystal surfaces, there are not enough PVP molecules to affect the growth rates because there are far more growth sites than inhibitors available to block them. At higher PVP concentrations there begins to be enough inhibitor to significantly reduce growth. This shift is mostly seen from 10 to 1000 ppmw. Within this concentration range PVP binds to a sufficient number of growth sites on crystal surfaces to affect growth rates. As PVP concentration increases above 1000 ppmw, it reaches a level that saturates all the growth sites and near zero growth is then observed. At such high PVP concentrations slight growth is still found because hydrate nuclei continue to form in solution, even if subsequent growth following nucleation is completely inhibited by PVP adsorption.

Eventually all PVP molecules will be adsorbed to hydrate nuclei, leaving newly created nuclei uninhibited and allowing growth to proceed. The highly irreversible nature of PVP adsorption has been shown in previous reports, and thus it is unlikely that PVP desorbs, especially in the growth timescale in this study (Larsen et al., 1998). Should PVP not bind irreversibly, a similar result would be observed, whereby uninhibited sites for hydrate growth will continue to increase as time goes on due to hydrate nucleation and growth. Previous literature studies generally tested concentration ranges above 0.05 wt% (500 ppmw) in order to find inhibitor concentrations that completely stop growth. There are few, if any, studies that investigate inhibitor effects in concentration ranges below 500 ppmw. Given the significant effect on growth within this concentration range, characterization of PVP effects such as adsorption at low concentrations could provide insight into growth inhibition mechanisms. To characterize and compare the relationship between initial growth rate and PVP concentration at the various temperatures and pressure conditions tested, a sigmoidal equation of the form in Eq. (1) has been fitted to the data. G (c ) = A +

B− A (1 + 1/ c D ) E

(1)

Within this equation, “G” represents the growth rate in µmol/s and “c” is the PVP concentration in ppmw. “A” represents the maximum growth rate, which the equation approaches at low PVP concentration. “B” represents the minimum growth rate, which the equation approaches at high PVP concentration. “D” represents the sensitivity of growth rate to PVP concentration - the higher the value of “D”, the steeper the curve. “E” represents the skew of the sigmoid curve - the higher the value of “E”, the more sensitive the growth rate to lower PVP concentrations. If “E” is unity, the sigmoid curve would be

symmetrical. Figure 4 shows the fit of the equation to the data at 277.1 K. The equation was also fitted to the data at 275.1 K; data at 279.1 K was not fitted due to a smaller number of PVP concentrations tested. Values for the equation at the various operating conditions can be found in Table 2. As expected, the maximum growth rate (A) values increase when the pressure driving force is increased at the same temperature. Between different temperatures at roughly the same pressure driving force, the temperature driving force does not have a proportional relationship to growth rate. This is most notably seen with the 1500-kPa driving forces at 275.1 K and 277.1 K. Both these conditions have similar maximum growth rates; however at 275.1 K the temperature driving force is 3.6 K, and at 277.1 K the driving force is 2.8 K. Previous studies have also shown temperature to have a more complex effect on hydrate growth than pressure (Bergeron et al., 2009). Minimum growth (B) is found to be near zero for all conditions tested indicating that at high PVP concentrations, hydrate growth can be substantially suppressed at early growth stages. Non-zero values are found for both low-pressure driving force conditions. These values are most likely due to experimental variance in growth rates at high concentrations caused by difficulty in evaluating initial growth rates at these conditions. At these high PVP concentrations, the confidence intervals of growth rates nevertheless overlap zero growth. The slope (D) and skew (E) both show a trend of decreasing as pressure driving force increases for both temperature conditions studied. The decrease in slope indicates that the growth rate diminishes over a broader concentration range, while the decrease in skew means that growth rate does not change as drastically at low PVP concentrations and the curve is more symmetric. Both these trends indicate that at higher driving forces, hydrate growth

is not as sensitive to PVP concentration and growth rates vary over a larger concentration range. At higher pressures, PVP requires higher concentrations before reaching near zero growth. This agrees with previous studies showing that with higher driving forces, PVP and other kinetic hydrate inhibitors become less effective at the same concentration (Koh et al., 2002). Using the equation, the PVP concentration necessary to reduce growth rate by half has been calculated and can be found as C50. Concentrations were all found to be under 0.025 wt%, further highlighting the need for studies at low concentrations.

3.3 Effect of PVP molecular weight on hydrate growth

Plots of initial growth rates at various PVP concentrations and molecular weights at 277.1 K and 6282 kPa can be found in Fig. 5. Hydrate growth inhibition was found to be comparable for all molecular weights tested (PVP10, PVP40 and PVP360) at the same PVP concentration by mass. Sigmoidal curve parameters were similar for all molecular weights tested and can be found in Table 3. C50 concentrations were again very small, with all of them being under 0.05 wt%. Previous tests using PVP at molecular weights of 8 000, 60 000, 300 000 and 1 300 000 g/mol showed significant differences in inhibition between the three smallest molecular weights at the same concentration by mass (O'Reilly et al., 2011). The most notable difference in the study was between the lowest molecular weight (8 000 g/mol) and 60 000 g/mol. Differences between this study and the one performed by O’Reilly et al. may be attributed to the latter being performed in quiescent systems with evaluation based on no observable hydrate growth. Nevertheless, the results of both studies show that beyond a certain molecular weight, there is little

observable difference in growth inhibition by varying molecular weight. Molecular modeling studies with methane hydrate have shown that when multiple units in a polymer chain bind to sites on the clathrate crystal, they may bind competitively and will not significantly enhance adsorption (Carver et al., 1995). Results from this study indicate that following nucleation there is no significant difference in PVP inhibition within the molecular weight range of 10 000 to 360 000 g/mol in well-mixed systems. Since previous modeling and experimental results indicate that a lower weight polymer may be advantageous for preventing nucleation, choosing the lowest molecular weight polymer with equivalent effects on growth inhibition may be advantageous for hydrate inhibition (Long et al., 1994).

4.0 Conclusions

A detailed study of the effect of polyvinylpyrrolidone (PVP) on hydrate growth was undertaken over a broad concentration range from 0.7 to 20 000 ppmw (2 wt%). The number of data points taken allowed unprecedented visualization of the effects of PVP on hydrate growth, most notably at low PVP concentrations. A sigmoidal relationship between growth rate and concentration was found, with growth remaining similar to that of water at low PVP concentrations and progressing to near zero growth over the concentration range of 10 to 1000 ppmw, with a very notable decrease of over 50% growth in the region of 10 to 100 ppmw. Effects of pressure, temperature and molecular weight were also analyzed. Increases in pressure (holding temperature constant) decreased the effectiveness of PVP at inhibiting hydrate growth, requiring higher amounts of PVP to achieve a similar hydrate growth rate. Temperature driving force was found to have a complex effect on growth rate. The PVP molecular weights tested, 10 000, 40 000 and 360 000 g/mol, revealed nearly identical trends in hydrate inhibition, showing no advantages of higher molecular weight polymers in this range for inhibiting growth following nucleation. Further kinetic and adsorption studies at low concentrations may help elucidate further understanding of the PVP inhibition mechanism.

5.0 Acknowledgements

The authors are grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC), Imperial Oil, McGill University and specifically the McGill Engineering Doctoral Award (MEDA) and Vadasz fellowship, le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) and the Canada Research Chair Program (CRC) for financial funding and support.

6.0 References

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Tables Legends

Table 1: Experimental conditions with corresponding temperature (dT) and pressure (dP) driving forces

Table 2: Sigmoidal growth equation parameters for PVP10 at various temperature and pressure conditions

Table 3: Sigmoidal growth equation parameters at 277.1 K and 6282 kPa at various PVP molecular weights

Figure Legends

Fig. 1: Typical gas consumption curves observed at 275.1 K and 4645 kPa with various PVP concentrations.

Fig. 2: Growth rates observed at various PVP10 concentrations and conditions. Temperature conditions are 275.1 K (blue triangles), 277.1 K (red squares) and 279.1 K (black circles). Higher pressure driving forces at each temperature condition are denoted by dashed lines and white data markers. Lines are included for ease of viewing data sets and do not model the data.

Fig. 3: Growth rates observed at various PVP10 concentrations at 275.1 K and pressures of 4645 kPa (black circles) and 5645 kPa (white squares) with 95% confidence intervals. Pure water values are found at 0.1 ppmw (due to log scale).

Fig. 4: Growth rates observed at 277.1 K and 5282 kPa at various PVP10 concentrations (white triangles) with 95% confidence intervals. The sigmoidal equation (dashed line) is fitted to the observed growth rates.

Fig. 5: Growth rates at 277.1 K and 6282 kPa for various PVP molecular weights at different concentrations by mass including 95% confidence intervals.

Appendix

This section includes growth rate data calculated at all conditions tested. Initial growth rates calculated at a given temperature and pressure condition for a variety of PVP10 concentrations can be found in Tables S.1-S.6. Initial growth rates for tests with PVP40 and PVP360 at 277.1 K and 6282 kPa can be found in Tables S.7 and S.8 respectively.

Confidence intervals (C.I.s) were calculated using the values obtained from the various sample bombs. The standard formula for confidence intervals was used and can be found as Eq. (A.1) (Montgomery and Runger, 2006)

C.I . = µ − x = ±

tα /2,n −1 * s

(A.1)

n

where µ is the expected value, x is the sample mean, n is the number of samples, s is the standard deviation and t is obtained based on the selected confidence level α (in this case 0.05) from the t-distribution.

Percent (%) inhibition is calculated using the Eq. (A.2) where G is the initial growth rate.

% inhibition =

Gwater − Gsample Gwater

(A.2)

Appendix References

Montgomery, D.C., Runger, G.C., 2006. Applied statistics and probability for engineers, 4th edition. John Wiley & Sons, Inc. Hoboken, NJ. p. 769.

Appendix Table Legends Table A.1 Calculated initial growth rates at various PVP10 concentrations at 275.1 K and 4645 kPa

Table A.2 Calculated initial growth rates at various PVP10 concentrations at 275.1 K and 5645 kPa

Table A.3 Calculated initial growth rates at various PVP10 concentrations at 277.1 K and 5282 kPa

Table A.4 Calculated initial growth rates at various PVP10 concentrations at 277.1 K and 6282 kPa

Table A.5 Calculated initial growth rates at various PVP10 concentrations at 279.1 K and 6183 kPa

Table A.6 Calculated initial growth rates at various PVP10 concentrations at 279.1 K and 7183 kPa

Table A.7 Calculated initial growth rates at various PVP40 concentrations at 277.1 K and 6282 kPa

Table A.8 Calculated initial growth rates at various PVP360 concentrations at 277.1 K and 6282 kPa

Table 1: Experimental conditions with corresponding temperature (dT) and pressure (dP) driving forces T (K)

P (kPa)

dT (K)

dP (kPa)

275.1

4645

3.6

1497

275.1

5645

5.5

2497

277.1

5282

2.8

1414

277.1

6282

4.6

2414

279.1

6183

2.4

1429

279.1

7183

3.9

2429

Table 2: Sigmoidal growth equation parameters for PVP10 at various temperature and pressure conditions T (K)

P (kPa)

A

B

(µmol/s)

(µmol/s)

D

E

C50 (ppmw)

275.1

4645

9.28

0.118

0.742

15.91

69.67

275.1

5645

14.47

0

0.326

2.74

45.70

277.1

5282

8.87

0.442

1.557

250.20

48.48

277.1

6282

10.93

0

0.361

5.16

217.04

Table 3: Sigmoidal growth equation parameters at 277.1 K and 6282 kPa at various PVP molecular weights MW (g/mol) A (µmol/s)

B (µmol/s)

D

E

C50 (ppmw)

10 000

10.93

0

0.3605

5.16

217.04

40 000

9.42

0

0.4687

12.28

433.72

360 000

9.792

0

0.4808

11.55

326.48

Table A.1 Calculated initial growth rates at various PVP10 concentrations at 275.1 K and 4645 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

9.47

0.7

% inhibition

# replicates

0.74

0.0

3

8.76

0.57

7.5

2

7

9.36

0.63

1.1

2

35

5.85

1.19

38.2

3

70

5.02

1.32

47.0

2

350

2.27

1.14

76.0

2

700

0.54

0.38

94.3

2

7000

0.11

0.80

98.9

2

20000

0.40

0.88

95.7

3

Table A.2 Calculated initial growth rates at various PVP10 concentrations at 275.1 K and 5645 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

14.60

0.7

% inhibition

# replicates

1.58

0.0

4

12.19

1.34

16.5

3

7

10.35

2.05

29.1

2

35

7.71

1.30

47.2

2

70

6.36

0.08

56.4

2

350

5.25

0.06

64.0

3

700

3.77

1.65

74.2

2

7000

0.71

0.46

95.1

2

20000

1.48

1.15

89.8

2

Table A.3 Calculated initial growth rates at various PVP10 concentrations at 277.1 K and 5282 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

9.23

0.7

% inhibition

# replicates

1.33

0.0

2

8.80

0.41

4.6

2

7

8.45

1.37

8.5

2

35

5.68

0.45

38.5

3

70

2.93

0.21

68.3

3

350

0.59

0.54

93.6

3

700

0.17

0.12

98.2

3

7000

0.29

1.68

96.8

2

20000

1.16

1.75

87.5

2

Table A.4 Calculated initial growth rates at various PVP10 concentrations at 277.1 K and 6282 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

10.81

0.7

% inhibition

# replicates

0.39

0.0

2

11.07

1.53

-2.4

2

7

9.46

0.04

12.5

2

35

7.27

0.25

32.7

2

70

6.60

1.19

39.0

2

350

6.06

0.05

44.0

2

700

4.68

0.45

56.7

2

7000

0.98

1.20

90.9

2

20000

0.65

1.20

94.0

2

Table A.5 Calculated initial growth rates at various PVP10 concentrations at 279.1 K and 6183 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

8.55

70 700

% inhibition

# replicates

4.93

0.0

2

2.10

0.21

28.3

2

0.21

0.70

97.5

2

Table A.6 Calculated initial growth rates at various PVP10 concentrations at 279.1 K and 7183 kPa Concentration

Initial growth

95% C.I.

% inhibition

# replicates

(ppmw)

rate (µmol/s)

(µmol/s)

0

10.14

0.62

0.0

2

70

6.13

1.11

39.5

2

700

4.86

0.77

52.0

2

Table A.7 Calculated initial growth rates at various PVP40 concentrations at 277.1 K and 6282 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

10.81

0.7

% inhibition

# replicates

0.39

0.0

2

9.29

0.22

14.0

3

7

8.76

0.17

19.0

3

35

8.21

0.14

24.0

4

70

7.25

0.61

32.9

4

350

4.87

0.50

55.0

3

700

5.19

0.00

52.0

3

7000

0.97

0.29

91.0

3

20000

0.07

0.19

99.3

2

Table A.8 Calculated initial growth rates at various PVP360 concentrations at 277.1 K and 6282 kPa Concentration

Initial growth

95% C.I.

(ppmw)

rate (µmol/s)

(µmol/s)

0

10.81

0.7

% inhibition

# replicates

0.39

0.0

2

9.63

0.58

10.9

2

7

8.98

0.47

17.0

3

35

8.82

0.64

18.4

4

70

6.66

0.55

38.4

4

350

5.14

0.29

52.5

4

700

4.52

0.00

58.2

3

7000

0.59

0.33

94.5

3

20000

0.22

0.46

98.0

2

0

2

4

6

8

10

0.1

10

100

1000

10000

100000

sigmoidal equation

growth rate

PVP10 concentration (ppmw) [log]

1

Graphical Abstract (for review) 12 growth rate (µmol/s)

Figure1-1column

Figure2-1column

Figure3-1column

Figure4-1column

Figure5-1column

Highlights -

Effect of PVP on hydrate growth over concentration range of 0.7 to 20 000 ppmw

-

Over 50% decrease in hydrate growth rate versus water baseline with 70 ppmw PVP

-

Investigate the effect of pressure and temperature changes on PVP inhibition

-

PVP chain length does not affect growth over the range of 10 000 to 360 000 g/mol !