Experimental and Theoretical Investigation of the Interaction between

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Experimental and Theoretical Investigation of the Interaction between Hydrate Formation and Wax Precipitation in Water-in-Oil Emulsions Yuchuan Chen, Bohui Shi,* Yang Liu, Shangfei Song, and Jing Gong*

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National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum-Beijing, Changping, Beijing 102249, China ABSTRACT: The study of the interaction between hydrate formation and wax precipitation in water-in-oil (W/O) emulsions is of great significance for the security of development in deep-water waxy oil and gas fields. Experiments of natural gas hydrate formation in W/O emulsions containing wax crystals were performed in a high-pressure autoclave. The macro-parametric data, including pressure, temperature, hydrate induction time, hydrate growth amount and rate, were compared and analyzed. Results indicated that the stage behavior of hydrate formation process was not affected by the precipitated wax crystals in W/O emulsions. The mass transfer resistance of hydrate nucleation was enhanced in waxy W/O emulsions. Hence, the hydrate induction time was prolonged and could be estimated by a semiempirical crystallization model developed based on the Freundlich adsorption isotherm theory. Meanwhile, the precipitated wax crystals in W/O emulsions affected the porosity of the hydrate shell, leading to a decrease in the average hydrate growth rate, but the total hydrate growth amount increased compared to the emulsified systems without wax crystals. The effect of hydrate formation and dissociation on the wax precipitation was studied, combined with the data analysis obtained from the polarizing microscopic observation. More wax crystals precipitated in the systems after hydrate dissociation compared to the systems without hydrate formation. The fractal box dimension of the precipitated wax crystals was relatively larger affected by hydrate formation and dissociation, implying that the structure of precipitated wax crystals was more intricate.

1. INTRODUCTION With the increasing depletion of the onshore fossil energy resources, oil and gas exploration and development move toward deep-water fields. Challenges encountered in deepwater fields include colder water, longer subsea tiebacks, higher water cuts, and higher hydrostatic pressure, thereby increasing risks of plugging pipelines because of hydrate formation, wax/ asphaltene precipitation, or scaling.1,2 Hydrate flow assurance is a major technical concern by the flow assurance engineers in deep-water fields. Thermodynamic hydrate inhibitors (THIs) injecting or heating have been widely applied in flowlines to shift the operation condition outside of the hydrate formation boundary, making it thermodynamically unfavorable for hydrate formation.3−5 These methods are effective, but a large amount of additives is required to be injected and huge energy is needed for heating, which make them financially unattractive.6 Alternatively, a risk management method is presented to control hydrate blockage issues. Low dosage hydrate inhibitors (LDHIs) including anti-agglomerants (AAs) and kinetic hydrate inhibitors (KHIs) are gaining more attention for advantages in low dosage and environmental protection. AAs can be adsorbed on the surface of hydrate particles to reduce hydrate aggregation, so that hydrate can be transported in pipelines safely as a slurry.7−9 KHIs mitigate plug formation risk by inhibiting hydrate nucleation and hindering hydrate growth,10−14 so that hydrate cannot form during the retention period of fluid in pipelines. Under the condition of low temperature in subsea pipelines, hydrate blockage and wax deposition may exist simultaneously in the transport system, which will pose a great threat to the © XXXX American Chemical Society

safety of pipelines and increase the plugging risk of the subsea production system. Therefore, it is significant to study the coupling characteristics of hydrate formation and wax precipitation in W/O emulsions. There are many independent studies on hydrate formation15−22 and wax precipitation23−33 in W/O emulsions. Limited studies have been reported about the interaction mechanism of hydrate formation and wax precipitation, and few recognized conclusions can be obtained. Studies by Ji34 and Song et al.35 indicated that the precipitated wax crystals would inhibit hydrate crystallization and subsequently prolong hydrate induction time. Raman et al.36 concluded that the precipitated wax promoted hydrate formation in W/O emulsions. However, Mahammadi et al.37 proposed that wax crystals could inhibit hydrate nucleation, though wax crystals could provide nucleation sites for hydrate nucleation. Zheng et al.38 proposed that hydrate induction time increased as the wax content increased. Shi et al.39 proposed a mechanism to describe the inhibiting effect of the wax on hydrate crystallization. In addition, reports about the influence of the wax on hydrate growth are scarce. According to experiments carried out by Mahammadi et al.,37 wax crystals would promote hydrate growth. Liu et al.40 noted that although the precipitated wax hindered the growth process of hydrate formation, once hydrate began to form, there was a catastrophic decrease of transportation ability for the pipeline. Besides, Gao41 concluded that the formed hydrate could Received: May 16, 2018 Revised: August 7, 2018 Published: August 9, 2018 A

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Figure 1. Diagrammatic sketch of the apparatus.

contribute to the precipitation and deposition of the wax crystals. Additionally, Raman et al.36 suggested that the wax appearance temperature (WAT) would increase significantly because of the reduction of the wax solubility in the oil phase after hydrate dissociation. Therefore, the solid precipitation problem caused by the coexistence of hydrate and wax is a complicated issue, rather than a simple fusion of independent hydrate formation and wax precipitation research results. In this work, a series of experiments were performed to study the interaction between hydrate formation and wax precipitation using a high-pressure autoclave. The effect of precipitated wax crystals on hydrate nucleation and growth in W/O emulsions was discussed. A semiempirical kinetics model for predicting hydrate induction time in W/O emulsions containing wax crystals was developed based on the Freundlich adsorption isotherm theory. A mechanism was raised to elaborate how precipitated wax crystals affected the hydrate growth in W/O emulsions. In addition, the influence of hydrate formation and dissociation on the structure of precipitated wax crystals was studied. These findings are of significance for solving the serious flow assurance issue caused by the coexistence of hydrate formation and wax precipitation in waxy W/O emulsions in deep-water fields.

Materials included mineral oil D80 (Yan-Chang Petrochemical Company, Beijing), deionized water, natural gas (Shan-Jing Natural Gas Pipeline), wax (Daqing Petrochemical Branch Company, Daqing), and sorbitan monolaurate (Span 20, Sigma-Aldrich). Compositions of the mineral oil D80 and the natural gas are listed in Table 1 and Table 2. The wax hydrocarbon range is from C26 to

2. EXPERIMENTAL METHODS

Table 3. Carbon Number Distribution of Wax

Table 1. Mineral Oil D80 Composition composition

mol %

composition

mol %

C11 C12 C13

12 32 31

C14 C15

21 4

Table 2. Natural Gas Composition

2.1. Apparatus and Materials. Experiments of gas hydrate formation in waxy W/O emulsions were performed using a highpressure autoclave (500 mL), as shown in Figure 1. This highpressure autoclave with the maximum tolerable pressure of 15 MPa was pressured by a high-pressure natural-gas cylinder and a gas booster. A stirring system with a pusher propeller and a flat blade stirring paddle is installed in this autoclave to ensure a good mixing of the liquid mixtures, and its stirring speed ranges from 0 to 2800 rpm. The temperature and pressure data are measured by a thermocouple (Wrink-191) and a pressure transducer (Huaqiang sensor-HQ1000) respectively. The maximum division scale of the temperature measurement is 0.1 K, and the uncertainty of the measured pressure is within 0.25% of the total pressure. A water bath is used to control the autoclave temperature, and its temperature range is from 253.15 to 373.15 K. The data of the temperature and pressure in the autoclave are logged by a data acquisition system. A polarizing microscope (OLYMPUS-BX51) is used to observe the morphology of the precipitated wax crystals.

composition

mol %

composition

mol %

N2 CO CO2 C1 C2

1.53 2.05 0.90 89.02 3.06

C3 iC4 iC5 nC6+

3.07 0.32 0.04 0.01 -

carbon number

wt %

carbon number

wt %

C26 C27 C28 C29 C30 C31 C32 C33

7.23 12.22 11.34 11.02 8.57 7.15 6.41 6.43

C34 C35 C36 C37 C38 C39 C40

5.42 4.92 4.68 4.39 3.88 3.40 2.94

C40 as given in Table 3. Dosages of Span 20 and wax were calculated according to the mass fraction of the mineral oil. The unchanged experimental conditions included dosage of the surfactant Span 20, stirring speed and water cut, which were 1 wt %, 1800 rpm, and 30% respectively. The system target temperature (276.15 K) was the temperature inside the high-pressure autoclave cooled by the water bath, which remained unchanged at different wax contents. The initial B

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Energy & Fuels pressure was 7 MPa and remained unchanged for different wax contents. According to the report from Mahabadian et al.,42 the influence of wax on the thermodynamic phase equilibrium of hydrate/ solution/gas was marginal. The phase equilibrium temperature of natural gas hydrate formation under 7 MPa was 290.15 K, which was calculated using the HYDOFF program.43 All experiments at different wax contents were carried out far within the natural gas hydrate stability zone (line A−B represents the pressure−temperature trace, as shown in Figure 2).

was cleaned repeatedly. The procedure was repeated at least three times at the same wax content. 2.3. WAT Measured by Differential Scanning Calorimetry (DSC). The wax appearance temperatures (WATs) for different wax contents were determined using the differential scanning calorimetry (DSC) experiments. The experimental temperature ranged from 353.15 to 253.15 K, and the cooling rate was set as 5 K/min. It is known that the WAT is defined as the temperature when the curve of the heat flow starts to deviate from the baseline44 (Figure 3). The

Figure 3. Heat flow curve of wax precipitated at 3 wt % wax content.

Figure 2. Natural gas hydrate formation within the stability zone.

measured WATs at different wax contents are given in Table 4. Because WATs of 1 wt % to 6 wt % wax contents were higher than the system target temperature, wax crystals precipitated out before hydrate formation in all tests.

2.2. Experimental Procedures. For the experiment under the condition of 1800 rpm stirring speed, 276.15 K system target temperature, 7 MPa initial pressure, 30% water cut, 1 wt % Span 20 and 1 wt % wax content, the specific experimental procedure is shown as follows: First, the autoclave was pressurized to 7 MPa with nitrogen for checking the tightness, and the tightness was acceptable once the temperature and pressure in the autoclave did not change for at least 120 min. Subsequently, nitrogen was removed by opening the decompression valves. Thereafter, the autoclave was sealed and evacuated. The water bath temperature was set at 333.15 K to obtain a uniform temperature distribution in the autoclave. Meanwhile, mineral oil (210 mL), wax (1 wt %), and Span 20 (1 wt %) were loaded into a beaker, and then the beaker was put into the air bath at the temperature of 333.15 K to dissolve wax into the mineral oil for at least 90 min. Next, the mixed liquid was injected into the autoclave, including mineral oil D80 mixed with deionized water and Span 20. Afterward, the stirring system was turned on for at least 60 min to obtain a stable W/O emulsion. The system was cooled down to the target temperature at 276.15 K using the water bath. During the process of cooling the autoclave, when the temperature decreased to the equilibrium temperature (calculated using the HYDOFF program43) corresponding to the initial pressure (7 MPa), the autoclave was pressurized up to 7 MPa quickly by charging the natural gas, and the experimental condition at this time was corresponding to point A as shown in Figure 2. The fluid in the autoclave was saturated with natural gas under stirring, and the pressure was maintained at 7 MPa during the process of saturation, and the saturation process was finished within 1 min. The pressure and temperature were monitored and recorded by the data acquisition system every 1/6 min. Typically, the experiment was completed until there was no obvious change in the pressure and temperature for at least 30 min in the autoclave. Then, the formed hydrate was decomposed by depressurization. Samples were taken from the autoclave and dropped on a microscope slide to observe the morphology of the precipitated wax crystals at the room temperature (291.15 ± 0.5 K). Finally, the experimental system

Table 4. WATs Measured by DSC for Waxy W/O Emulsions wax content/wt %

WAT/K

wax content/wt %

WAT/K

1 2 3

283.65 286.21 290.56

4 5 6

292.67 293.84 295.33

2.4. Determination of Hydrate Formation Volume Fraction. Figure 4 displays the pressure and temperature versus time trace during the hydrate formation process in W/O emulsions. As depicted in Figure 4, the sharp decrease in the pressure indicates that a large amount of the hydrate forming gas is consumed. Determination of hydrate formation volume fraction is a key point for analyzing the process of hydrate formation, which is reported by the previous work published by Shi et al.45 This method involves a classical thermodynamics calculation for the gas compressibility factor and Chen-Guo46 model for the determination of the real hydration number.

3. RESULTS AND DISCUSSION 3.1. Behavior of Hydrate Formation and Macroscopic Morphologies of Hydrate. Hydrate formation process in W/O emulsions cannot be observed directly, because the highpressure autoclave is nontransparent. It is possible to compare and analyze the behavior of hydrate formation that is affected by the precipitated wax crystals in W/O emulsions, through the stage behavior characterized by the data of temperature and pressure against time. Figure 4 displays the pressure and temperature versus time trace during hydrate formation in W/ O emulsions with and without wax crystals. The precipitated C

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Figure 4. Trace of the pressure and temperature versus time for hydrate formation process (a: without wax; b: at 2 wt % wax content).

Figure 5. Morphologies of hydrate/wax observed in the autoclave with wax contents of 0−5 wt % at 273.15 K (±0.5 K).

Stage (I): gas dissolution. This stage is not presented in Figure 4. Natural gas is continuously dissolved in the oil until the saturation finishes under stirring. Stage (II): cooling and pressuring stage. The temperature in the autoclave continues to decrease through the heat exchange with the water bath. The pressure gradually decreases in the cooling process. Wax crystals have already precipitated in the continuous oil phase during this stage. Under the synergistic

wax crystals in emulsified systems have no appreciable influence on the stage behavior of natural gas hydrate formation process. Five stages can be observed through the data of the temperature and pressure during hydrate formation process in W/O emulsions with and without precipitated wax crystals. Details of these five stages are listed as follows: D

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Energy & Fuels effect of surfactant, some wax crystals are adsorbed onto the water droplets.47 The formation amount of gas hydrate during this stage is negligible, but this period is crucial for subsequent hydrate growth process.1 Stage (III): rapid hydrate growth stage. The pressure drops catastrophically, and temperature rises rapidly at this stage, indicating that a substantial amount of hydrate has formed. The temperature gradually increases to the maximum value, due to the faster release of hydrate crystallization heat than the heat transfer through the wall of the autoclave. The drop in the pressure and increase in the temperature in this stage result in a smaller driving force for continuous hydrate growth. Stage (IV): slow hydrate growth stage. The pressure continues to decrease, and the temperature subsequently drops to the target temperature, because of the continuous heat exchange between the experimental system and the water bath. Stage (V): system equilibrium stage. The pressure and temperature in the autoclave gradually remain unchanged, indicating that the experimental system reaches equilibrium and hydrate formation is finished. Figure 5 shows macroscopic morphologies for a few portions of hydrate observed in the high-pressure autoclave with different wax contents. To slow down the melting of hydrate as much as possible, the autoclave is depressurized within 1 min while maintaining the temperature of the water bath unchanged. And, all the macroscopic visualization experiments are performed at 273.15 (±0.5 K) for avoiding ice formation, which is reached by controlling the pressure relief rate to be much slower when the temperature in the high-pressure autoclave approaches 273.15 K. Then photographs are taken within 0.5 min. As shown in Figure 5, the natural gas hydrate is clumpy-like rather than slurry-like48 in general, and the precipitated wax crystals cannot affect the macroscopic morphology of the formed hydrate. However, hydrate formed in W/O emulsions without wax crystals is fragile and “hard” in terms of the mechanical property, while hydrate formed in W/O emulsions with wax crystals is “soft”,49 gel-like,41 and viscous, and thus the aggregates of hydrate and wax can adhere to the inner wall of the autoclave. These results can support the finding proposed by Gao;41 i.e., hydrate plugging risk is higher when hydrate and wax are present in the flow system simultaneously. Hydrate agglomeration, viscosity, and plug characterization in hydrate forming waxy emulsions deserve further investigations for flow assurance of waxy emulsified systems. 3.2. Effect of Precipitated Wax Crystals on Hydrate Nucleation. In hydrate nucleation process, the crystallization and growth of hydrate nuclei are difficult to measure by the macroscopic methods. Hydrate induction time is widely used to quantify the time needed for hydrate nucleation. And it is defined from the microscopic and macroscopic perspective respectively in academia.1,50,51 Specifically, from the microscopic point of view, the induction time includes the time taken for first hydrate crystal nuclei to appear for subsequently continuous growth; from the macroscopic point of view, the induction time includes the time elapsed until the appearance of a detectable volume of hydrate phase or until the consumption of a detectable number of moles of hydrate forming gas.1 In this work, hydrate induction time is defined from the time point when the experimental system is at phase equilibrium, to the time point when the system temperature starts to increase quickly due to the massive hydrate formed.52

Figure 6 shows that hydrate induction time is gradually prolonged with the increasing wax content in W/O emulsions,

Figure 6. Hydrate induction time at different wax contents.

which is in accordance with the result published by Zheng et al.38 When the wax content increases to 6 wt %, however, no obvious decrease in the pressure or rise in the temperature can be observed within 720 min. This indicates that gas hydrate nucleation has been inhibited severely, which is analogous to the inhibitory influence of KHIs on hydrate nucleation.11 The stochasticity of hydrate nucleation in waxy W/O emulsions is also observed in Figure 6, based on the repeated experiments for each experimental condition. Hydrate induction time is relatively approached and less stochastic at wax contents of 0 and 1 wt % compared to higher wax contents. This implies that the presence of precipitated wax crystals in W/O emulsion lead to the obvious scattering of the hydrate induction time, by affecting the heat and mass transfer during the hydrate nucleation process. Similarly, as one kind of classical KHIs, PVCap could not only prolong the average hydrate induction time, but also could increase the stochasticity of hydrate nucleation.53 It is worth noting that although the effect of precipitated wax on induction time resembles KHIs, wax cannot be deemed to be one kind of KHI essentially, because the required dosage of KHIs is typically lower than 1 wt %.1 The results shown in Figure 6 can provide us the inference that gas hydrate nucleation is relatively difficult during the transportation of water-in-crude oil emulsions containing the asphaltene, resin, and wax with high content, where the asphaltene and resin can act as the natural surfactant, because the precipitated wax crystals can be adsorbed onto the water droplets, inhibiting the process of hydrate nucleation subsequently. Figure 7 gives the microscopic image of the emulsion after wax precipitation and before hydrate formation with 5 wt % wax content at 291.15 K (±0.5 K). In waxy W/O emulsion systems, there are two types of the precipitated wax crystals observed. A-type wax crystals are adsorbed onto the water droplets under the synergistic effect of surfactant,47 which are believed to affect hydrate nucleation and growth process significantly. B-type wax crystals suspended in the oil can affect the gas diffusion in the liquid to some extent especially around the surface of water droplets. As can be inferred from Figure 6 E

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temperature of the experimental system (K), Δve is the volume difference between a gas hydrate building unit and a water molecule (nm3), and φ is the fugacity coefficient which is determined using the Peng−Robinson equation of state. Wax crystals adsorbed on the hydrate nuclei affects the growth rate of hydrate nuclei, and the growth rate is supposed to be proportional to the surface area which is not covered by wax crystals, while the surface area covered by wax crystals is inactive for the continuous growth of hydrate nuclei. Considering that hydrate induction time is inversely proportional to the growth rate of nuclei, thus hydrate induction time is inversely proportional to the surface area of nuclei that is not covered yet. If a parameter θ is introduced to quantify the occupancy ratio of wax crystals on the surface of hydrate nuclei, then the area ratio of the active hydrate nuclei is 1 − θ. Therefore, the hydrate induction time in waxy W/O emulsions can be expressed in eq 3. ÄÅ É Å B ÑÑÑ 1 ÑÑ t ind_with wax = K [S(S − 1)3 ]−1/4 expÅÅÅÅ ÅÅÇ 4 ln 2 S ÑÑÑÖ 1−θ (3)

Figure 7. Microscopic image of the emulsion before hydrate formation with 5 wt % wax content at 291.15 K (±0.5 K) (A: wax adsorbed onto the water droplet, B: wax suspended in the oil).

and Figure 7, the increase of resistance for mass transfer caused by the precipitated wax crystals dominates in the hydrate nucleation process, although wax crystals can provide nucleation sites as one kind of impurity in emulsified systems. On the basis of the one-component gas hydrate induction time model (eq 1) developed by Kashchiev and Firoozabadi54,55 considering crystallization theory, a crystallization model is developed for modeling the hydrate nucleation in waxy W/O emulsions. The assumptions made in this model are as follows: (1) Gas is dissolved in W/O emulsions. (2) The surface area of hydrate nuclei is reduced due to the adsorption of A-type wax crystals onto the hydrate nuclei, the influence of B-type wax crystals on hydrate nucleation is not considered presently in this model. (3) The ability of the wax crystals to provide new nucleation sites is ignored.

where tind_with wax (min) is the hydrate induction time in the presence of wax crystals, and θ is the fractional occupancy by wax crystals. Further, the occupancy ratio of wax crystals can be calculated based on the Freundlich adsorption isotherm theory56 as shown in eq 4. θ=

1/ n KFCwax 1/ n 1 + KFCwax

(4)

where KF is the Freundlich constant for wax crystals, n is the site number occupied by a single wax crystal on the surface of hydrate nucleus, and Cwax is the initial content (wt %) of wax crystals. Combining eqs 3 and 4, the gas hydrate induction time model in waxy W/O emulsion systems is established as shown in eq 5. ÄÅ É Å B ÑÑÑ 1/ n ÑÑ t ind_with wax = (1 + KFCwax )K [S(S − 1)3 ]−1/4 expÅÅÅÅ ÅÅÇ 4 ln 2 S ÑÑÑÖ

t ind_without wax = K [S(S − 1)3m ]−1/(1 + 3m) ÄÅ ÉÑ ÅÅ ÑÑ B Å ÑÑ Å expÅÅ Ñ 2 ÅÅÇ (1 + 3m) ln S ÑÑÑÖ (1) ÄÅ ÉÑ É Ä Ñ Å ÅÅ φ(P , T )P ÑÑ ÑÑ expÅÅÅÅ Δve(P − Pe) ÑÑÑÑ S = ÅÅÅÅ ÑÑ ÑÑ Å ÅÅ ÅÅÇ φ(Pe , T )Pe ÑÑÖ kT ÑÑÖ (2) ÅÇ where tind_without wax (min) is the hydrate induction time without wax, B is the dimensionless thermodynamic parameter, K is a kinetic constant (min), k is the Boltzmann constant (J/ K), m is a number related to the growth type of nuclei, if the hydrate forming gas is assumed to form a stagnant layer around the surface of hydrate nuclei by the way of volume diffusion, then the number of growth type is equal to one,55 P is the initial pressure (MPa), Pe is the hydrate/solution/methane equilibrium pressure (MPa) determined using the program HYDOFF,43 S is the supersaturation ratio, T is the target

(5)

The parameters K and B can be obtained by fitting the induction time without wax crystals and supersaturation ratio as shown in Table 5, and the fitting result is shown as Figure 8. The fitting results of K and B are equal to 8.2458 min and 1.6204 respectively. The Freundlich constant for wax crystals (KF) and the site number occupied by a single wax crystal on the surface of hydrate nucleus (n) can be obtained by fitting the average induction time with wax crystals and wax content (from 2 wt % to 5 wt %) using eq 5, as shown in Figure 9. Thus, the fitting results of KF and n are 0.0713 and 0.6076 respectively. It is worth noting that the hydrate induction time for wax contents ranging from 2 wt % to 5 wt % is more

Table 5. Basic Data for the Calculation of Empirical Parameters K and B expt

tind_without wax (min)

supersaturation ratio S

experimental pressure Pexp (MPa)

equilibrium pressure Pe (MPa)a

experimental temperature Texp (K)

1 2 3 4

50.4 58.2 55.8 62.4

1.6475 1.6296 1.6316 1.6101

6.45 6.47 6.48 6.50

3.67 3.63 3.63 3.60

276.45 276.55 276.55 276.65

a

Pe is calculated using the HYDOFF program.43 F

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Figure 8. Calculation result of the parameters K and B in eq 1.

Figure 10. Comparison of experimental and predicted hydrate induction time.

heat/mass transfer and intrinsic kinetics. As elaborated in Section 3.1, the precipitated wax crystals in emulsified systems have no obvious influence on the stage behavior of natural gas hydrate formation process, which includes the rapid hydrate growth stage (stage III in Figure 4) and slow hydrate growth stage (stage IV in Figure 4). However, analysis should be made further to study the effect of wax crystals on hydrate growth rate and amount. Hydrate formation volume fraction is used to quantify the hydrate growth amount herein. The method for calculating hydrate formation volume fraction is illustrated in Section 2.4. The hydrate growth rate is quantitatively analyzed by the average increasing rate of the hydrate formation volume fraction. A new parameter (tan δ) is introduced to illustrate the hydrate growth rate, which is the average increasing hydrate formation volume fraction within the time from the onset of growth to the inflection point (see Figure 11); the inflection point represents the finish of hydrate growth. As shown in Figure 12, the hydrate formation volume fraction for 0 wt % wax content emulsion system reaches 20.92% volume/volume at 26.33 min, and remains unchanged subsequently. The overall changing tendencies of hydrate formation volume fraction versus time at 1−5 wt % wax contents are similar to that at 0 wt % wax content. However, the maximum hydrate formation volume fractions are different at different wax contents. The maximum value of hydrate formation volume fraction increases rapidly up to 22.99% volume/volume when the wax content is increased from 0 wt % to 1 wt %. This phenomenon resembles the unusual effect of KHIs on hydrate growth; the final hydrate growth amount would increase in the systems containing KHIs compared to the blank experiments.57−60 However, the maximum value of

Figure 9. Calculation result of the parameters KF and n in eq 5.

stochastic than that for low wax contents (0−1 wt %), and hence the average values of the hydrate induction time are chosen for optimizing, as given in Table 6. The hydrate induction time for 1 wt % wax content is not used for optimizing, because the average induction time of 1 wt % is nearly equal to that of 2 wt %. Figure 10 shows the comparison of the predicted induction time with experimental data at different wax contents, which suggests that the error range of the predicted induction time and experimental data is within ±30%. The largest and lowest deviation are 29.47% and 1.17% respectively, and thus the semiempirical model established in this paper can predict the ability of wax crystals to prolong the gas hydrate induction time in waxy W/O emulsions. The application scope of this model is limited, such as the gas composition, wax contents, and stirring rate. 3.3. Influence of Precipitated Wax Crystals on Hydrate Growth. Hydrate growth rate and amount are important time-dependent parameters, which are essential for both industry and academia. During the hydrate growth process, hydrate forming gas is densely packed in the hydrate cages, and the hydrate growth process is controlled by the

Table 6. Basic Data for the Calculation of Empirical Parameters KF and n expt.

wax content (wt %)

tind_with wax (min)a

supersaturation ratio S

experimental pressure Pexp (MPa)

equilibrium pressure Pe (MPa)b

experimental temperature Texp (K)

1 2 3 4

2 3 4 5

63.6 78.6 85.4 106.6

1.6423 1.6359 1.6521 1.6402

6.48 6.45 6.45 6.47

3.67 3.67 3.63 3.67

276.65 276.65 276.55 276.65

a

tind_with wax is the average induction time at different wax contents. bPe is calculated using the HYDOFF program.43 G

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Figure 13. Effect of wax content on the average increasing rate of the hydrate growth.

Figure 11. Illustration of the average increasing rate of hydrate growth at 5 wt % wax content.

wax content increases from 2 wt % to 5 wt %. And, the average value of the hydrate growth rate remains around 0.55 (% volume/volume)/min with wax contents ranging from 2 wt % to 5 wt %. Therefore, the precipitated wax crystals in W/O emulsion systems can make the hydrate growth rate slower and cause the evolution time for hydrate growth to be longer. The entire hydrate growth amount increases due to the influence of precipitated wax crystals, combining the changes in the average increasing rate of hydrate growth and the evolution time for hydrate growth. Figure 12 and Figure 13 show that there is a gradual change in hydrate growth with increasing wax contents. The following discussion can be used to explain this phenomenon. The system target temperature and initial pressure are constant for experiments with different wax contents, so the intrinsic kinetics for hydrate growth is similar, and thus the mass transfer dominates in the process of hydrate growth. It is reasonable to ignore the effect of change in hydrate shell affected by the wax crystals on the migration of the guest molecules because the mobility of the water molecules is better than the diffusion ability of the gas molecules in the hydrate shell,61 and water penetration through the hydrate shell acts as a pivotal part in the hydrate shell growth.62 Ma et al.47 proposed that wax could be adsorbed at the water−oil interface. Aman et al.63 speculated that surfactant could be adsorbed at the interface between hydrate and oil. Brown57 proposed that wax could change the hydrate shell structure. Therefore, it can be assumed that wax crystals (A-type, as shown in Figure 7) could also be adsorbed onto the hydrate surface with the help of the surfactant, and the structure of hydrate shell is affected by the wax crystals during the continuous hydrate shell growth process. The hydrate shell contains a high degree of porosity at the beginning of hydrate growth process. Water seeps outward in the pore spaces of the hydrate shell due to the hydrophilic property of hydrate particles.62 According to the experiments carried out by Brown57 and Sharifi et al.,58−60 KHIs could result in a dramatic increase in the hydrate growth rate, although it prolonged hydrate induction time, which was supposed to be affected by the change in the porosity of hydrate shell. Consequently, it can be further speculated that the pores of the hydrate shell

Figure 12. Trace of hydrate formation volume fraction versus time after hydrate nucleation at different wax contents.

hydrate formation volume fraction increases slowly when the wax content gradually increases. The maximum values of hydrate formation volume fractions are 23.42, 23.59, 24.02, 24.26% volume/volume for wax contents varying from 2 wt % to 5 wt % respectively. This indicates that further increase of wax content has a limited promoting effect on the increase in the hydrate growth amount. Additionally, water is not converted into hydrate completely in hydrate forming emulsions after hydrate formation, which implies that the mass transfer limitations still play a significant role in the hydrate growth process in the waxy or wax-free W/O emulsions. Figure 13 shows the influence of wax content on the average increasing rate of hydrate growth. The average increasing rate of hydrate growth decreases from 0.81 (% volume/volume)/ min to 0.67 (% volume/volume)/min when the wax content in W/O emulsions increases from 0 wt % to 1 wt %. The average increasing rate of hydrate growth decreases slowly when the H

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Figure 14. Illustration of the mechanism of the hydrate growth with and without wax crystals.

Figure 15. Microscopic images of the waxy emulsions with 3 wt % wax content at 291.15 K (±0.5 K). (a: without hydrate formation; b: after hydrate dissociation).

could also change under the effect of wax crystals, perhaps leading to the change in the porosity and hydrophilicity of hydrate shell. The change in the porosity and hydrophilicity causes the water molecules to transfer from the inner surface of the hydrate shell to the hydrate/oil interface at a lower rate. As shown in Figure 14, a conceptual diagram is presented to illustrate the mechanism of the hydrate growth pattern with and without wax crystals. The upper panel of Figure 14 shows the hydrate growth pattern in W/O emulsion stabilized with Span 20. Hydrate growth pattern in waxy W/O emulsion is depicted in the lower panel of Figure 14. As displayed in Figure 12, the whole time needed for the water molecules to penetrate through the thin waxy hydrate shell is relatively longer than that in W/O emulsion without wax crystals; i.e., the evolution time for hydrate growth is longer affected by the precipitated

wax crystals. With the wax content increasing from 1 wt % to 5 wt %, the decreasing range of the rate for water penetration is relatively smaller. In summary, in W/O emulsion systems containing wax crystals, the hydrate growth rate decreases, and hydrate growth evolution time is relatively prolonged. The entire hydrate growth amount increases due to the precipitated wax crystals. However, further increase in wax content (from 2 wt % to 5 wt %) cannot result in a significant variation in the hydrate growth rate and amount. As noted, the influence of wax crystals on the hydrate shell structure needs to be further investigated by the microscopic experiments, for determining the microcosmic mechanism of the changes in the hydrate shell structure that is affected by the combination function of the surfactant and wax. I

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and breakage caused by the shear action.19 As a result, apart from the encapsulated oil and water trapped in the hydrate aggregates,19 the precipitated wax crystals can also be wrapped in the hydrate aggregates. The role of encapsulation makes the trapped wax crystals prefer to connect to each other, causing the structure of wax crystals to be more intricate. Additionally, the release of the gas molecules can also make the structure of the precipitated wax crystals more intricate after hydrate dissociation. More efforts should be made to research how hydrate formation and dissociation affect the morphology or structure of the precipitated wax crystals, mainly including the following process such as hydrate shell growth, hydrate aggregation with wax crystals wrapped inside, and decomposition of hydrate into water and gas.

3.4. Effect of Hydrate Formation and Dissociation on the Morphology of the Precipitated Wax Crystals. The morphology of the precipitated wax crystals acts as a pivotal part in the flow behaviors of waxy W/O emulsions when the system temperature is below the WAT. There have been many studies demonstrating that oil component44 and shearing64,65 can affect the morphology of the precipitated wax crystals. Our interest is to explore the influence of hydrate formation and dissociation on the morphology of the precipitated wax crystals by analyzing the fractal box dimension of the precipitated wax crystals. Details about the method for calculation of the fractal box dimension can be found in the published work by Gao et al.66 Figure 15 gives the microscopic images of the waxy emulsions without hydrate formation and after hydrate formation and dissociation with 3 wt % wax content at 291.15 K (±0.5 K). The amount of precipitated wax crystals is slightly increased after hydrate dissociation, compared to that in the systems without hydrate formation. This is likely because the formed hydrate particles and aggregates provide large surface areas, and wax crystals deposit on the hydrate aggregates much more easily.41 The fractal box dimensions of the measured wax crystals are 1.5660 (±0.0165) and 1.6038 (±0.0128) (as shown in Figure 16), where 1.5660 (±0.0165) corresponds to the micrograph

4. CONCLUSIONS The interaction of hydrate formation and wax precipitation was investigated using a high-pressure autoclave. The following conclusions were obtained. (1) There was no appreciable influence of the precipitated wax crystals in W/O emulsions on the stage behavior of natural gas hydrate formation process. Stages of hydrate formation process in waxy or wax-free W/O emulsions included gas dissolution, cooling and pressuring, rapid hydrate growth, slow hydrate growth, and stability. (2) With the synergistic effect of the surfactant, wax crystals could be adsorbed onto the water droplets, which resulted in the enhancement of the mass transfer resistance for hydrate nucleation, and hence the hydrate induction time was prolonged. When the wax content increased to 6 wt %, gas hydrate could not form within 720 min. (3) A semiempirical kinetics model for predicting hydrate induction time in waxy W/O emulsions was developed combining the classical hydrate nucleation theory with the Freundlich adsorption isotherm theory. And this model can predict the ability of wax crystals to prolong the gas hydrate induction time in waxy W/O emulsions. (4) The precipitated wax crystals in W/O emulsions were deemed to affect the structure of the hydrate shell, which caused natural gas hydrate to grow at a lower rate and for a longer evolution time. The total hydrate growth amount in waxy W/O emulsions increased compared to the emulsified systems without wax crystals. (5) More wax crystals precipitated after the formation and dissociation of natural gas hydrate compared to that without hydrate formation. The fractal box dimension of the wax crystals was relatively larger due to hydrate formation and dissociation, implying that the structure of the precipitated wax crystals was more intricate. The influence of wax crystals on the hydrate shell structure and the effect of hydrate formation and dissociation on the wax crystal structure need to be further investigated by microscopic experiments, for determining the microcosmic mechanism of the changes in hydrate shell structure affected by the combination function of surfactant and wax, and for figuring out how hydrate formation and dissociation affect the morphology or structure of the precipitated wax crystals.

Figure 16. Fractal box dimensions of the different objects (A: straight line; B: snow flake; C: wax crystals precipitated without hydrate formation; D: Sierpinski gasket; E: wax crystals precipitated after hydrate formation and dissociation; F: Sierpinski carpet).

taken from the system without hydrate formation, and 1.6038 (±0.0128) corresponds to the micrograph taken from the experimental system experiencing the process of hydrate formation and dissociation. For comparison, the theoretical box dimension values of straight line, snow flake, Sierpinski gasket, and Sierpinski carpet are 1.0000, 1.2620, 1.5850, and 1.8930 (as shown in Figure 16) respectively.67 Therefore, hydrate formation and dissociation cause the structure of the precipitated wax crystals to become more intricate,66 which is deemed to be unfavorable for the flow of waxy W/O emulsions in deep-water fields. As shown in Figure 7, A-type wax crystals are supposed to exist in the hydrate shell during the hydrate growth process. B-type wax crystals are possible to be trapped inside hydrate aggregates due to the collision, agglomeration,

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Corresponding Authors

*(B.S.) Phone: +86-010-89733804. E-mail: [email protected]. cn. *(J.G.) Phone: +86-010-89732156. E-mail: [email protected]. ORCID

Yuchuan Chen: 0000-0001-9919-0067 J

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Bohui Shi: 0000-0003-2683-6984 Yang Liu: 0000-0002-8556-8775 Jing Gong: 0000-0002-3722-5778 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 51534007 and No. 51774303), the National Key Research and Development Plan (No. 2016YFC0303704), the National Science and Technology Major Project of China (No. 2016ZX05028004-001 and 2016ZX05066005-001), the Science Foundation of China University of Petroleum-Beijing (No. C201602), all of which are gratefully acknowledged.

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