Effect of Wax Crystals on Nucleation during Gas Hydrate Formation

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Effect of Wax Crystals on Nucleation during Gas Hydrate Formation Dongxu Zhang, Qiyu Huang, Haimin Zheng, Wei Wang, Xianwen Cheng, Rongbin Li, and Weidong Li Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 22 May 2019 Downloaded from http://pubs.acs.org on May 23, 2019

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Effect of Wax Crystals on Nucleation during Gas Hydrate Formation Dongxu Zhang,† Qiyu Huang,*,† Haimin Zheng,†,‡ Wei Wang,† Xianwen Cheng,† Rongbin Li,† and Weidong Li†

†Beijing

Key Laboratory of Urban Oil and Gas Distribution Technology, China University

of Petroleum, Beijing 102249, P. R. China

‡CNOOC

Research Institute Co., Ltd., Beijing 100027, P. R. China

KEYWORDS: Wax crystals, Hydrate nucleation, Water-in-waxy oil emulsion, Molecular dynamics simulations

ABSTRACT

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Hydrate formation and wax deposition pose great flow assurance challenges to subsea oil pipes, especially when the two phenomena co-occur. Wax crystals can have significant impact on hydrate nucleation and growth kinetics, but this phenomenon has not been studied in great detail. Here, the effect of wax crystals on hydrate nucleation was investigated using both molecular dynamics simulation methods, and experiments conducted using a custom-designed high pressure autoclave equipped with an on-line viscometer. Both the simulation and the experimental results demonstrated that the presence of wax crystals inhibits hydrate nucleation. The simulations showed that water droplets tend to approach and adsorb on wax crystals prior to nucleation, thus inhibiting the formation of hydrate cages. The experiments demonstrated that water cut and stirring rate play a significant role in determining hydrate nucleation rate. In addition, adding more wax increased the viscosity of the emulsion, which limits mass transfer of gas to the oil-water interface.

1. INTRODUCTION


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Gas hydrates are solid crystalline compounds wherein water molecules form cage-like structures around guest gas molecules at low temperatures and high pressures1,2. Gas hydrates have been extensively studied in the oil and gas industry as their formation in transmission lines may result in oil pipeline blockage and economic hazards3–6. Another concern in the oil and gas industry is a phenomenon known as wax deposition7, wherein wax molecules dissolved in crude oil can crystallize out and deposit on the inner pipe wall below the wax appearance temperature (WAT). With the exploration and development of oil fields moving into ever deeper waters, multiphase pipelines containing water, oil, and gas are widely used to deliver petroleum fluids from offshore to onshore processing facilities. The fluids are usually present in the form of water-in-oil emulsions in the multiphase pipelines due to the presence of natural surfactants and low water cut (i.e., the volume fraction of water in the liquid). However, deep water multiphase pipelines at high pressures and low temperatures can provide favorable conditions for gas hydrate formation and wax deposition. The mechanisms of hydrate formation and wax deposition in water-in-oil emulsions have been widely studied, which has greatly improved our scientific understanding of


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these phenomena. One of the methods commonly used to study hydrate formation includes the use of differential scanning calorimetry (DSC), autoclaves, and high pressure flow loops8–12. A series of studies on the rheology of hydrate slurries formed from emulsions have been also reported in the literature13–17. In addition, several notable studies have focused on hydrate particle formation kinetics and mechanisms18– 20.

Li et al.18 found that the rate of hydrate formation increased with increasing total

water droplets surface area, and established a mathematical model of hydrate formation kinetics in water-in-oil emulsions based on crystal growth theory and gas mass transfer. Sloan et al.19 monitored the process of water droplets converting to hydrates in water-inoil emulsions and found that every water droplet acted as an individual reactor and supported a hydrate shell formation model. A number of studies have been performed to understand the characteristics of wax deposition in water-oil two-phase flows using either flow loop or cold finger apparatus21– 27.

Effects of the droplet size and distribution of dispersed phase and water cut on wax

deposition in water-in-oil emulsions have been studied by Zhang et al.21 Zheng et al.24 characterized the droplet size in the deposited and bulk phases using NMR techniques,


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and found the incorporation of droplets led to slough-off of the deposit in pipe flow. Bruno28 proposed that dispersion of water droplets in the emulsion reduced the wax diffusion coefficient and made diffusion path more tortuous due to the incompatibility of the two phases. Couto and Bruno also proposed oil-water wax deposition models22,23. In most of the studies in the field till date, hydrate formation and wax deposition have been investigated independently, effectively being treated as unrelated problems. Only a select few studies investigating the effects of wax formation on the hydrate phase boundary have presented thermodynamic models combing wax precipitation with hydrate formation29,30. In particular, Mahabadian’s30 work analyzed the component effects of wax precipitation on hydrate formation, and found the amount of heavy alkanes in the liquid decreased after the wax separated out, promoting hydrate formation by leaving more light hydrate forming components in the mixture. However, the effect of wax crystals on hydrate formation from a kinetic standpoint is still short of investigation. Gao31 investigated the interactions between gas hydrates and wax precipitation using a hydrate rocking cell apparatus, and concluded that hydrate particle formation could assist in the precipitation, and subsequent deposition of wax out of the


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solution. However, in most real-world scenarios in deep water multiphase pipelines, the WAT is above the hydrate formation temperature. Therefore, it is of key importance to study the effect of wax crystals on hydrate formation and investigate the kinetics of the process. Molecular dynamics (MD) simulations are a helpful and efficient tool for obtaining a deep understanding of hydrate formation processes and mechanisms at molecular level32,33. Information on the kinetic and structural properties of hydrate systems may be more easily accessible through simulations rather than experimental techniques as the required conditions of high pressure and low temperature are challenging to recreate in a laboratory setting. Jacobson et al.34,35,along with Vatamanu and Kusalik36 proposed a two-step nucleation mechanism based on MD simulations, where amorphous hydratelike solids are formed first as intermediates, and later grow or transform into crystalline hydrates. Bai et al.37 successfully employed MD simulations of kinetic pathways in the process of CO2 hydrate formation on the silica surface and proposed a three-step nucleation process. Recently, Liang et al.32 conducted MD studies of hydrate nucleation near the silica surface with the results indicating that nucleation can initiate from the


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surfaces of model hydroxylated silica. Zhang et al.38 found that the guest’s hydration shell was more ordered, and that the system entropy was lowered with increasing guest concentration, causing the system structure to tend towards the solid phase. However, in simulations, the nucleation of CH4 or CO2 hydrates can take quite long even under strong driving forces39,40. It has been shown that H2S can nucleate more easily than other natural gas components,41 and in addition, CH4 and H2S have similar molecular diameters (4.36 and 4.58 Å, respectively) and are both thought to form structure I hydrates42. As a result of this, the present study used H2S hydrates to investigate the effect of wax on gas hydrate nucleation in the MD simulations. In the present study, the effect of precipitated wax crystals on the nucleation process during hydrate formation in water-in-oil emulsions was investigated by means of MD simulations and experiments. In the simulation work, three systems was considered, wherein the initial distance between the water droplet and the wax crystal was varied. In the experimental work, hydrate formation was carried out in water-in-oil emulsions with different wax contents. A high pressure autoclave with an on-line viscometer was


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employed for this purpose. Furthermore, the hydrate nucleation rates in water-in-waxy oil emulsions with various water cuts and various stirring rates were also investigated.

2. SIMULATION METHODOLOGY

In the present study, the TIP4P/2005 model43 was employed for calculating the intermolecular potential of water. This model has been widely used in molecular simulations of hydrate formation, and is suitable over the temperature range from 123 to 573 K44,45. For H2S molecules, a four-site potential model put forward by Forester et al.46 was chosen, which has been demonstrated to describe the properties of H2S well in both the solid and the bulk liquid phases. The solid phase wax crystal composed of Lennard-Jones interaction sites was added at the boundary of the system. A schematic of the initial configuration setup is shown in Figure 1. The Lennard-Jones sites were arranged in an FCC [111] structure and placed at specific locations away from the spherical water droplet. Five-layer wax molecules are distributed symmetrically on the intermediate layer, as shown in pink in Figure 1. As the figure shows, three simulation


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systems of water droplets were established, considering of droplets (1) far away from, (2) near, and (3) on the wax crystal surface; these are referred to in the text as system-1, system-2, and system-3, respectively. It can be seen that the spherical water droplet in system-1 is in the middle of the box in the initial state, and the lengths a and b are equal, but in system-3, a >> b, such that b is effectively zero. In addition, a system without wax was built as a contrast, and the initial structure of which is shown in Figure 2. Parameters of these systems, the potential equation and the values of the water and H2S models are presented in the simulation details section of the supporting information included with this work. The molecular dynamics package Gromacs47 was used for MD simulations, with Lorentz-Berthelot mixing rules48 used for the interactions between different molecules. A cut off of 1.0 nm was utilized for van der Waals forces whereas the long-ranged coulomb forces were calculated using Particle-Mesh Ewald (PME)49. The truncation radius of adjacent atomic search was set as 1.0 nm. MD simulations were performed at NPT ensemble50,51, wherein constant pressure and temperature were maintained using the Parrinello-Rahman and Nose-Hoover algorithms, respectively. The hydrate


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formation process simulations runs and the simulations of water droplet trajectory before nucleation were performed at 220 K and 250 K, respectively, with all runs performed at a pressure of 50 MPa. The segment times used in this work were 50 ns in the simulation runs of the trajectory of the spherical water droplet and 600 ns for the hydrate formation process, with a time step of 2 fs. The initial systems were equilibrated for 10000 ps, following which five independent simulation runs (denoted as A to E) were performed that were extracted from the last 200 ps of the equilibrium trajectory.

Figure 1. Initial simulation structure of the systems with wax. The yellow points represent H2S molecules, blue and white balls represent oxygen and hydrogen atoms, and pink balls represent wax molecules, respectively.


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Figure 2. Initial simulation structure of the system without wax. The yellow points represent H2S molecules, and pink and white balls represent oxygen and hydrogen atoms, respectively.

3. EXPERIMENTAL SECTION

3.1.Apparatus A schematic diagram of the experimental apparatus employed in this work is shown in Figure 3. The apparatus mainly consisted of an autoclave, a pressure control system, two temperature control systems, a gas flowmeter, a stirring device, an on-line viscometer, and a data logger. The autoclave was constructed from 316 stainless steel with an effective volume of 4.5 L, and is rated for pressures up to 15 MPa. It was connected to a CO2 gas tank via a pressure-regulated valve. A gas flowmeter (with a


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range of 0 to 1000 mL/min) was installed at the autoclave inlet to measure gas consumption. Two temperature control systems (thermostatic baths) were used to control the autoclave temperature: one on the outside, and one on the cold finger in the middle of the autoclave. The temperature range of both thermostatic baths was −20 to 100 °C. During the experimental process, the pressure and temperature in the autoclave were displayed and recorded using a pressure transducer and a thermal resistance detector, respectively. The contents of the autoclave were stirred by a magnetically driven anchor agitator on the lid of the autoclave with a range of 0 to 800 rpm. An on-line viscometer (VSICOpro 2000, Cambridge, USA) was used in the autoclave, with a range of 0.1 to 1000 cP, and a pressure rating up to 12 MPa. The operating principles of the viscometer are introduced in the supporting information. More details of the apparatus can be found elsewhere52.


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Figure 3. Schematic drawing of the high pressure autoclave apparatus.

3.2. Materials The continuous oil phase used throughout the experiments was -10# diesel, provided by SINOPEC filling station (China). All water used in the experiments was de-ionized using a water purification machine, and the CO2 gas used was 99.99% pure (Shaanxi Hongwei Gas Technology Co., Ltd., China). Wax (Fushun Petrochemical Company, China) employed in the experiments was a paraffin mixture from C17 to C35. The carbon number distribution of the wax is listed in Table S2 of the supporting information.


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3.3. Wax dissolution and emulsion preparation The first step in the experiments was dissolving the wax in diesel, with the resulting mixture referred to as waxy oil. A certain mass of wax was weighed and added into diesel, then agitated at 500 rpm in a 60 °C temperature-controlled water bath for 15 min to ensure that the wax was completely dissolved. Once mixing was complete, the WAT of the waxy oil was measured using DSC53. Following this, the water-in-oil emulsion was prepared by agitating a mixture of waxy oil and de-ionized water at 60 °C using an IKARW 20 Digital stirrer at 800 rpm for 30 min. The sample container was thoroughly sealed to prevent evaporation of volatile hydrocarbons during the stirring process.

3.4. Hydrate formation Prior to the experiments, the autoclave was cleaned using petroleum ether and deionized water, and the cleaning procedure was repeated twice54. The temperature of the autoclave was set to the predetermined value and, once stabilized, the prepared emulsion was poured into the autoclave. Following this, the autoclave was sealed and any air remaining inside was removed by displacement with the experimental gas (CO2).


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Gas was injected while stirring the tank until the target pressure was reached. The autoclave was kept under pressure for a specified time period55 and then allowed to cool. The start of the cooling process was defined as the time-zero for the hydrate formation experiment. During the cooling process, gas was added to the autoclave at regular intervals to maintain the pressure at the desired value until the target temperature was reached. The nucleation point was identified as the moment that the temperature spiked suddenly, since hydrate formation is exothermic reaction55,56.

4. RESULTS AND DISCUSSION

4.1. Effect of wax on nucleation of H2S hydrate To deconvolute the effect of wax crystals on gas hydrate nucleation, simulations of the hydrate cage formation rate and the trajectory of the water droplet before nucleation in the presence of wax were performed using Gromacs. The degree of liquid water into hydrate conversion obtained from the simulations was reflected by the evolution of the total number of different cages57, on account of temperature invariability in the NPT


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ensemble. The various hydrate cage types (i.e., 512, 51262, 51263, 51264, 4151062, 51268, 435663) were identified by the topological structure of hydrogen bonds between water molecules58. Water molecules were considered to be hydrogen-bonded when the distance between the corresponding oxygen atoms was less than 0.35 nm (i.e., Roo < 0.35 nm) and the angle between the two oxygen atoms and the hydrogen atom was less than 30º (i.e., ∠OOH < 30º)59. Figure 4 shows typical curves for the evolution of cage types over one simulation run in the system without wax (Figure 4a) and in system-1 (Figure 4b). As the Figure 4a shows, 512 cages have the highest number of cages, followed by the 51262 cages, which in accordance with the results of Lauricella et al.60. As we know, H2S is observed mainly to form sI hydrates under moderate pressures, where the guests occupy both the 512 and 51262 cages1. Recently, it has been demonstrated that H2S hydrate can form variety types including cages of crystalline sI, structure II (sII), and HS-I hydrates, as well as other irregular cages in NPT simulations6,41, wherein sI and sII are the two dominants. Both sI and sII crystals have 512 cages. In addition, previous have found that typically mall 512 cages dominate the system in the initial stages6,71. Therefore, 512 cages are first in abundance. The next


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in abundance, large 51262 cages, reflect the thermodynamic preference for sI. Similar to the evolution of various cage types without wax, the 512 cages and 51262 cages are observed to dominate in the system-1 (Figure 4b), which indicates that wax has little effect on cage types and distribution proportion in hydrate formation.

Figure 4. Evolution of seven cage types in one simulation run: (a) run D in the system without wax; (b) run A in the system with the water droplet far away from the wax crystal surface.

4.1.1 Effect of wax crystal on the time evolution of the total number of cages Figure 5 shows the time evolution of the total number of cages. It should be noted that the evolution in each simulation run appeared somewhat different as the molecular


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motion is a stochastic process within certain limits. In order to confirm the reproducibility and to achieve estimates of average value, five independent simulation runs were conducted at the same scenarios for investigation, which were widely used in MD simulations6,41. The time evolution of the total number of cages indicates that the wax crystal has a significant hindering effect on hydrate cage formation. For the systems with wax, shown in Figure 5a to 5c, the hydrate cage formation is fastest in system-1 and slowest in system-3. This is quantified in Figure 5e, which shows that the average times over five simulation runs for the 10 cages are 276 ns, 287 ns and 387 ns in systems-1, -2, and -3, respectively. Hence, with the distance between the droplet and wax crystal decreasing, the rate of cage formation decreased. On the other hand, the average time requirement for 10 cages is 74 ns in the system without wax (Figure 5d), which is 202 ns less than that of system-1. Moreover, Figure 5d shows that the maximum time requirement for 50 cages is less than 150 ns in the system without wax, which is far less than that for the systems with wax.


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Figure 5. Evolution of the total number of cages over the five runs in: (a) the system with the water droplet far away from the wax crystal surface; (b) the system with the droplet near wax crystal surface; (c) the system with the droplet on the wax crystal surface; (d) the system without wax. (e) Average time requirement for different total numbers of cages over the five runs in the three systems with wax. All the runs were performed at 220 K, 50 MPa.

In the wax-free system, no sticking of the water droplet with the surface of wax, and the whole surface acts as a hydrate nucleation space; hence, the hydrate cages formed faster. In the presence of wax, however, the wax crystal may impact the trajectory of the


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water droplet and adsorb on the droplet surface, hence decreasing the cage formation rate and hindering the nucleation process. Furthermore, the time needed for cage formation appeared to be positively correlated to the distance between the water droplet and the wax. In actual deep water pipelines, the consequence of this is that in water-inoil emulsions with higher wax content, droplets are closer to wax crystal surfaces as more crystals are precipitated, and the chances of contact and adsorption increase accordingly; hence, the rate of hydrate nucleation may be much slower than that of waxfree condition. 4.1.2 Trajectory of water droplet To gain a deeper understanding of the effects of wax on hydrate nucleation, simulations of the droplet movement trajectory before nucleation in the three systems with wax were performed. The probability distribution of the water droplet in the z-direction at different times was then calculated according to the values over the five independent simulation runs, with the location of the droplet represented by its center of mass. The origin of the coordinate system was chosen as the center of mass of the spherical water droplet in system-1. As shown in Figure 6, the probability distribution of the water droplet


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approaching both wax layers in system-1 is relatively uniform, without an obvious tendency to either side. On the other hand, in system-2, the probability of positive abscissa is significantly higher, which means, that the water droplet tends to move towards the wax crystal layer which it is closer to initially. In system-3 however, the spherical water droplet almost always stayed at the initial position, rarely moving along the z-direction. As stated earlier, the probability distribution results showed that the water droplet tends to approach the wax crystal surface that it is closest. In addition, the droplet would quickly adsorbs on the wax crystal surface and rarely separates out. This causes the cage formation rate of water droplets to decrease, and as shown in Figure 5e, as there is less space available due to wax occupation. In real-life deep water multiphase pipelines, a mass of wax crystals is dispersed around the water droplets at temperatures below the WAT. In such case, water droplets and wax crystal particles can easily adsorb on each other in water-in-waxy oil emulsions and move together in the bulk, especially in the high wax content conditions. As a result, the wax crystals can


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impact the trajectory of water droplets and adsorb on the water surface, thus thus inhibiting hydrate nucleation.

Figure 6. Probability distribution of the water droplet in the z-direction from 10–50 ns (with temporal resolution of 0.001 ns), at 250 K and 50 MPa. The center of the droplet in system-1 was taken as z = 0.

4.2. Effect of wax on nucleation of CO2 hydrates To obtain more concrete evidence of the impact of wax crystals on hydrate nucleation, gas hydrate formation experiments in water-in-waxy oil emulsions with various wax


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contents were conducted using the high pressure autoclave apparatus described in section 3.1. CO2 was selected as the gas phase for use in the experiments due to operational safety considerations and considering its increasing application in enhanced oil recovery in the oil and gas industry61. In addition, CO2 is a common component in natural gas62, with CH4 and CO2 both being known to form structure I hydrates. WAT of the samples was measured using DSC (Auto Q20, TA Instruments, USA). During testing, the reference and sample were heated to 60 °C63 and then cooled to −20 °C at a rate of 5 °C/min. The relationship between heat flow and temperature was recorded to determine the WAT (Figure 7a).64,65 The measured WATs in these experiment were all above 10 °C, which is higher than the hydrate formation temperature (< 7 °C); hence, the solid wax crystals appeared prior to hydrate formation. The details of the measured WATs and the amount of precipitated wax at 3.5 °C are presented in Table S5 of the supporting information. An example of the typical temperature variation during the hydrate formation process is presented in Figure 7b. Here, the sudden increase in temperature at 409 min indicates the moment at which hydrate nucleation occurred.


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Figure 7. (a) Heat flow curve of waxy oil with 8 wt % wax content, and (b) variation of temperature with time during the process of hydrate formation at a pressure of 2.3 MPa, stirring rate of 300 rpm, 5 wt % wax content, and 20 vol % water cut.

4.2.1 Hydrate nucleation with varying wax content Figure 8 shows the temperature variation tendency in emulsions with different wax content (defined as the wax mass fraction of the diesel and wax mixture). As the figure shows, the wax crystals impeded hydrate nucleation, which was consistent with MD simulations. Hydrate nucleation was most rapid in the emulsion without wax, and the rate of nucleation decreased successively for the emulsions with 3 wt %, 5 wt %, and 8


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wt % wax, respectively. For the emulsion with 10 wt % wax content, no hydrate was formed over the experimental period of 1000 min.

Figure 8. Temperature evolution of the hydrate formation process in samples with different wax content at the target conditions of 3.5 °C, 2.3 MPa, 300 rpm stirring rate and 20 vol % water cut52.

In water-in-oil emulsions, hydrates form at the water-oil interface as not enough water molecules are available in the bulk oil phase. In experiments, emulsions were prepared with the same water cut (20 vol %), while the wax content was varied. This means that the proportion of available water molecules was the same for each sample; however, it


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was found that hydrate nucleation was delayed with increasing wax content, which indicates that wax crystals may inhibit the formation of hydrates through adsorption on the water-oil interface or encasement of water droplets, as was seen earlier in the MD simulations. The adsorption or encasement at the water-oil interface not only decreases the available area for nucleation sites but also reduces the chances of cross nucleation, i.e., the collision of a hydrate particle with another water droplet which can seed hydrate growth in the droplet19. Figure 9 illustrates some of the mechanisms by which wax content inhibits nucleation. In Figure 9b, the surfaces of water droplets are partially encased by wax crystals, which causes the number of available sites for hydrate nucleation to decrease. On another hand, the probability of cross nucleation is also reduced, as represented by the red arrows. In water-in-oil emulsions with higher wax content, droplets and wax crystals were more likely to contact and adsorb on each other due to shorter distances between them as demonstrated in the MD simulations. In addition, higher wax content results in more wax crystals appearing in the bulk phase. Hence, as depicted in Figure 9c, when wax content is high enough, the abundant wax solid crystals fully encase the water


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droplets, essentially preventing hydrate nucleation, as was seen in the emulsion with 10 wt % wax content the experiments.

Figure 9. Schematic drawing of different wax content effects on nucleation: (a) water droplets; (b) partilly encased water droplets; (c) encased water droplets. The green and red arrows represent successful and unsuccessful cross nucleation, respectively.

4.2.2 Viscosity of emulsions during the process of hydrate nucleation The viscosity of the water-in-waxy oil emulsions during the process of hydrate nucleation was measured using the on-line viscometer described in section 3.1. A typical viscosity profile from this series of experiments is shown in Figure 10a, from


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which it may be observed that the viscosity can be divided into four regions (denoted as I–IV). In regions I and II, the temperature drops continuously from 35 °C to the target value and, once this value is reached, it remains constant in regions III and IV. In region II, the viscosity increases rapidly as the wax crystals continuously precipitate out of the bulk phase when the temperature is below the WAT66,67. In regions III, the viscosity gradually lowers due to continuous stirring. Hydrate nucleation (as indicated by the green circles in Figure 10a and 10b) occurs when nuclei reach the critical hydrate radius,68 resulting in a spike in the viscosity, which corresponds very well to the nucleation point of the temperature curve. Region IV is the hydrate growth stage, during which the viscosity is higher in the presence of larger hydrate particles. Figure 10b shows the viscosity profiles of emulsions with varying wax content as a function of time. It can be seen in Figure 10b that prior to nucleation the viscosity is positively correlated with wax content. The viscosities of the emulsions with no wax and 3% wax content were very low, which are less than 1.5 mPa·s before nucleation; however, the viscosities increased appreciably as the wax content increased to 5 wt %,


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8 wt %, and 10 wt %, respectively. The viscosity of the emulsion with 10 wt % wax can up to 9 mPa·s in the late region II.

Figure 10. (a) Viscosity and temperature of the emulsion with 8 wt % wax. (b) Viscosity variation of emulsions in the process of hydrate nucleation with varying wax content at the target conditions of 3.5 °C,2.3 MPa, 300 rpm stirring rate, and 20 vol % water cut.

The Einstein-Smoluchowski equation69 is shown as follows:

D=

kT



  6 a

(1)

(2)


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where D is diffusion coefficient (m2/s),  is the friction coefficient (kg/s),  is the viscosity of the solvent (Pa·s), and a is the radius of the sphere (m). As Equations (1) and (2) show, the diffusion coefficient decreases with higher viscosity; hence, the diffusion coefficient is smaller in emulsions with higher wax content. This is likely due to the gas bubbles or molecules facing a higher resistance in going from the bulk solution to the water-oil interface in higher wax content emulsions, thus leading to lower mass transfer rates. In addition, the existence of wax crystals can distort the diffusion path of dissolved gas molecules, thus increasing the diffusion distance in bulk solution. This distorting effect is greater in emulsions with higher wax content as more wax precipitates out. 4.2.3 Gas diffusivity around water droplets A number of studies have proposed that high local gas concentrations can promote hydrate nucleation41,70 and have suggested a critical threshold for gas concentration71,72. As illustrated in Figure 11a, there are two diffusive boundary layers in water-in-oil emulsions, the gas/oil layer and the oil/water layer. The gas concentration profiles in each layer before hydrate nucleation are shown in Figure 11a. Gas concentration


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decreases in the diffusion process from the gas-oil interface to the bulk oil, and further decreases in the oil/water layer. However, the subsequent appearance of wax solid crystals may disturb gas diffusion from the oil to the water surface, as shown in Figure 11b. The wax crystals are adsorbed or encased on the surface of the water droplet, which adds a second diffusive boundary layer between the oil and water. This acts as a barrier preventing gas concentration from reaching the critical threshold and minimizes gas diffusion from oil into the water droplets, as solid diffusivities are usually on the order of 105 times smaller than liquid diffusivities43,73. Consequently, hydrate nucleation becomes mass-transfer limited due to the low gas concentration.


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Figure 11. Schematic diagram of gas concentration profiles in: (a) emulsion without wax crystals; (b) emulsion with wax crystals.

4.3. Water cut effect on hydrate nucleation in the presence of wax To determine the effect of water cut on the hydrate formation process, experiments were conducted varying the water cut in the emulsions both without wax and with 7 wt % wax content. The resulting temperature-time curves are shown in Figures 12 and 13, respectively. It can be seen in Figure 12 that while the hydrate nucleated more rapidly with increasing water cut, the increase in hydrate nucleation rate was not large. Hydrates were formed at 362 min, 378 min, 392 min, and 408 min in emulsions with 40


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vol %, 30 vol %, 20 vol %, and 10 vol % water cut, respectively. Therefore, a four-fold increase in water cut only decreased the nucleation onset time by around 11%. In water-in-oil emulsions without wax, the entire water-oil interfacial area is available for hydrate nucleation, as described in Equation (3): Seff  S water oil

(3)

where Seff refers to the available water-oil interfacial area for hydrate nucleation and

S water oil refers to the total water-oil interfacial area. The total water-oil interfacial area increases with water cut as follows: S water oil ,40%  S water oil ,30%  S water oil ,20%  S water oil ,10%

(4)

where the number in the subscript refers to the water cut. All of the emulsions were prepared with the same stirring rate and total stirring time. Thus, the energy provided by the stirring process to disperse water droplets was equal for all of the emulsions. Hence, the size of water droplets increased somewhat with higher water cut, as less energy was available per water droplet. The average water droplets diameters were 30.4 μm, 37.7 μm, 48.8 μm and 58.7 μm in emulsions with 10 vol %, 20 vol %, 30 vol %, and 40


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vol % water cut, respectively. As a result, the increase in the available water-oil interfacial area, which determines the hydration rate, was relatively small compared to the increase in water cut.

Figure 12. Temperature variation during the hydrate formation process for emulsions with different water cuts in the absence of wax at the target conditions of 4 °C, 2.7 MPa, and 300 rpm stirring rate.


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Figure 13. Temperature variation during the hydrate formation process for emulsions with different water cuts and 7% wax content at the target conditions of 3.5 °C, 2.1 MPa, and 300 rpm stirring rate.

In water-in-waxy oil emulsions, the effect of water cut on the hydrate nucleation rate was larger than that in emulsions without wax, as Figure 13 shows. Here, hydrates were formed at 380 min, 636 min, and 1072 min in emulsions with 40 vol %, 30 vol %, and 20 vol % water cut, respectively. For the emulsion with 10% water cut, hydrates did not form in the period of 1500 min. The discrepancy between the two sets of experiments (without and with wax) is due to the wax crystals being adsorbed or encased on the water-oil surface, thus reducing the available water-oil interfacial area for nucleation.


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Here, the relationship between the effective and real water-oil interfacial area is given by

Equation (5): Seff  S water oil  S wax

(5)

where S wax refers to the surface encased or occupied by wax crystals. For waxy emulsions with 10% water cut, hydrates did not form in the experimental time of 1500 min, which indicated that the effective water-oil interfacial area was almost zero in this case. In these experiments, it was shown that in the presence of wax, the minimum water cut required for hydrate formation is larger than that for emulsions without wax. In addition, the effect of water cut on hydrate nucleation is much more pronounced than that for wax-free emulsions.

4.4. Stirring rate effect on hydrate nucleation in the presence of wax Temperature-time curves during the hydrate formation process at different stirring rates in the presence of wax are shown in Figure 14a. As the figure shows, the hydrate


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nucleation rate increased with an increase in stirring rate. One reason for this is that the higher stirring rate increases the degree of dispersion of the water in the emulsion, providing more nucleation sites. Moreover, at higher stirring rates, the larger water-oil interfacial area and higher shear force also promote cross nucleation, and the increased gas dissolution and dispersion can enhance the mass transfer rate and further promote hydrate nucleation. In addition, in water-in-waxy oil emulsions, stirring intensity can impact the distribution of wax crystals in the bulk, as these have a tendency to distribute on the water surface after precipitation and move together with droplets, as illustrated in Figure 14b. When the stirring rate is low, the shear force is not large enough to separate wax crystals from the water droplets, and may even strengthen the motion and collision of the two. However, higher stirring rates may cause the crystals to separate from the water-oil interface, thus increasing Seff and promoting hydrate nucleation.


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Figure 14. (a) Temperature variation during the hydrate formation process at different stirring rates for an emulsion with 20 vol % water cut and 7 wt % wax at the target conditions of 4 °C and 2.3 MPa; (b) schematic drawing of the effect of stirring rate on wax particles in the emulsion.

5. CONCLUSIONS

MD simulations and experiments were performed to investigate the effect of wax crystals on hydrate nucleation in water-in-waxy oil emulsions. The simulation results showed that wax crystals limit the number of hydrate cages in nucleation of H2S. In addition, the experimental results indicated that the hydrate nucleation rate of CO2


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decreases with increasing wax content. Thus, the inhibition hydrate nucleation by wax crystals was observed in both simulations and experiments. As shown in the simulations, water droplets tended to approach and adsorb on wax crystals before nucleation, which is thought to be the primary mechanism behind the inhibition effect, as this decreases the available surface area for hydrate nucleation and lowers the probability of cross nucleation. Moreover, wax crystals encased at the water-oil interface from a diffusive boundary layer, thereby limiting the mass transfer of gas molecules to the water droplet surface. It was also observed that increasing the amount of wax in the emulsion increased its viscosity, thus further lowering the mass transfer rate. The experimental results from this study also showed that in emulsions both with and without wax the hydrate nucleation rate increased with increasing water cut; however, this effect was more pronounced in the emulsions with wax. In addition, a threshold water cut was identified below which hydrates cannot form due to the limited interfacial surface area for wax crystal adsorption and encasement. Finally, it was also found that increasing the stirring rate enhanced hydrate nucleation. Future studies will include


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experiments with field wax deposits and crude oil, and will further investigate the effect of wax on the hydrate growth stage and formation rate.

ASSOCIATED CONTENT

Supporting Information The supporting information is available free of charge via the ACS publication website, and includes:

specific details of the simulation systems (Table S1), schematics and parameters of TIP/2005 water model (Table S2 and Figure S1) and H2S model (Table S3 and Figure S2) carbon number distribution of wax (Table S4), the measured WAT with various wax contents in waxy oils (Table S5) and the operation principles of the on-line viscometer.

AUTHOR INFORMATION

Corresponding Author *E-mail:

[email protected]


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ORCID

Dongxu Zhang: 0000-0003-4240-636X

Haimin Zheng: 0000-0003-1358-3762

Wei Wang: 0000-0001-9885-3092

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT

This work was supported by grants from the National Natural Science Foundation of China (No. 51534007 and No. 51374224), which are gratefully acknowledged.

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Effect of Wax Crystals on Nucleation during Gas Hydrate Formation

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