Hydrate Management in Deadlegs: Effect of Wall Temperature on

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Hydrate Management in Deadlegs: Effect of Wall Temperature on Hydrate Deposition Xianwei Zhang, Bo Ram Lee, Jeong-Hoon Sa, Keijo Kinnari, Kjell Magne Askvik, Xiaoyun Li, and Amadeu K. Sum Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03962 • Publication Date (Web): 09 Feb 2018 Downloaded from http://pubs.acs.org on February 14, 2018

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Hydrate Management in Deadlegs: Effect of Wall Temperature on Hydrate Deposition

Xianwei Zhang1, Bo Ram Lee1&, Jeong-Hoon Sa1, Keijo J. Kinnari2, Kjell M. Askvik3*, Xiaoyun Li4, and Amadeu K. Sum1*

1

Hydrates Energy Innovation Laboratory, Chemical & Biological Engineering Department, Colorado School of Mines, Golden, CO 80401 – USA 2

Statoil ASA, N-4035 Stavanger – NORWAY 3

4

Statoil ASA, N-5020 Bergen – NORWAY

Statoil ASA, N-7005 Trondheim – NORWAY

* Corresponding authors: [email protected] (KA), [email protected] (AKS)

&

Currently at the Department of Chemical Engineering, Pohang University of Science & Technology, Cheongam-Ro, Nam-

Gu, Pohang, Gyeongbuk, 37673–KOREA

ACS Paragon Plus Environment

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Abstract Deadlegs in oil and gas production systems are pipe sections with no through flow. They are often connected to a hot header but exposed to a cold environment. Deadlegs face hydrate challenges, as water condensation on the cold pipe wall can lead to continuous hydrate deposition. The water condensation and hydrate deposition are strongly influenced by temperature. The temperature boundary conditions of a deadleg consist of the header and the wall temperature, and both affect the temperature field and the hydrate deposition process. This study focuses on the effects of the wall temperature on hydrate deposition in a 2-inch-ID gas-filled vertical deadleg at constant header temperature. The wall temperatures considered are 4, 10, and 15 °C, with header temperatures at 30 °C and 80 °C. All the experiments are conducted with a methane/ethane (75/25 mol%) gas mixture (sII hydrate) at a constant pressure of 100 bar. The hydrate equilibrium temperature is 18.9 °C from the prediction tool (CSMGem). The results show that a high wall temperature leads to a warm environment which subsequently reduces the hydrate deposit growth rate and delays the eventual plugging of the deadleg. However, the results also suggest that a high wall temperature may not eliminate the possibility of forming a plug as long as the conditions in the deadleg are lower than the hydrate equilibrium temperature. Moreover, the wall temperature seems to have a small impact on the potential hydrate plug location. The results of this study provide further understanding of the wall temperature in the hydrate deposition mechanism in deadlegs.

Keywords: hydrate deposition; wall temperature; vertical deadleg; flow assurance.


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Introduction Gas hydrates form from water and small guest molecules at appropriate temperature and pressure conditions 1. The small guest molecules in nature are usually hydrocarbons, which makes hydrates in nature a potential energy resource 2, 3. The requirement of certain temperature and pressure, on the other hand, makes hydrate formation a potential tool for gas separation 4, sea water desalination 5, sewage treatment

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and etc. However, in the oil and gas production systems where all the hydrate forming

conditions are met, hydrate occurrence is strongly undesirable. Hydrates can exist as a deposit, and the unmanaged hydrate deposition in flowlines can have severe consequences, as the deposit constricts flow and could eventually plug the flowline

1, 7

. The growth rate of hydrates is often determined by the

limitations in the intrinsic kinetics, mass transfer, and heat transfer. One of the mechanism for hydrate accumulation in flowing systems is hydrate deposition which has been studied in a bench-scale rocking cell and a flowloop for a range of flowing conditions 8-10. One major mechanism of hydrate deposition is considered to be the liquid water buildup on the cold wall surfaces, resulting from direct wetting, droplet attachment, capillary wetting, and condensation. Condensation can contribute significantly to the liquid water buildup when little or no free water phase exists. Under appropriate conditions (subcooling and availability of gas), the liquid water can readily convert into hydrate deposit.

Deadlegs are pipe sections with no (or negligible) through flow such as branches of a main flowline 11. They are a common structure in the oil and gas production systems and are used only intermittently. Examples include chemical lines, instrument lines, pressure safety valve lines, production lines, and etc. Because of the lack of flow through deadlegs, the temperature inside deadlegs are usually much colder than the main flowline, which increases the risk for hydrate deposition, especially in gas-filled deadlegs. The consequences of hydrate deposition can be detrimental. For example, a hydrate plug in a pressure


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safety valve system may lead a failure of emergency depressurization, result in over-pressurization and finally potential rupture in some parts of the production system. Based on a comprehensive survey of the literature, despite the severity and importance for hydrate deposition in deadlegs, only a very small number of studies have been published addressing this topic. In practice, the current management strategies for hydrate deposition in deadlegs are based on rules-of-thumb and are rarely reported. Most relevant studies up to date focus on deadlegs without hydrates or hydrate deposition in a main flowline.

Of the few available studies on deadlegs without hydrates, the focus has been on liquid-filled deadlegs. Bloom studied the velocity field in vertical deadlegs with water 12. Habib et al. reported similar studies but with oil/water flows and the separation is stressed 13. Asteriadou et al. reported studies on deadlegs with non-isothermal water flow

14

. The center temperature in the deadleg is found to decrease

exponentially after a threshold depth. These studies provide basic understanding of the velocity and temperature field inside liquid-filled deadlegs, but hydrate risks in such systems are not investigated. Based on field experience, gas-filled deadlegs are more prone to hydrate issues than liquid-filled deadlegs

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, which indicates the velocity and temperature fields in gas dominated deadlegs can have

different patterns from liquid dominated ones.

Operational issues for gas-filled deadlegs are well known in the oil and gas industry. Anderson simulated the velocity and temperature field under natural convections using CFD and evaluated the hydrate risks

16

. However, the simulations did not have any experimental data for validation, thus the

validity of the conclusions are unknown. Nazeri et al. experimentally studied the hydrate formation in a deadleg with a vertical pipe 17. The major conclusion was that hydrate deposition occurs in the gas-filled


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part of the pipe above the liquid, and kinetic inhibitors can prevent hydrate in the liquid. The study did not evaluate any environment variable or any hydrate deposition mechanism.

There is much value and need in studying hydrate deposition in deadlegs, as better understanding of hydrate formation rates and plugging conditions can help in the formulation of design guidelines and operational procedures to prevent/minimize the risk of hydrate problems in deadlegs. To reach this goal, our group has undertaken a substantial effort to systematically study hydrate deposition in gas-filled deadlegs by constructing an experimental system to mimic vertical deadlegs connected to a header supplying the water and gas

11, 18-20

. In the field, while the header temperature is strongly influenced by

the wellbore conditions, the wall temperature is mainly determined by the environment and the thermal resistance though the pipe wall. If the pipe is uninsulated, the wall temperature will be very close to the environment temperature. The typical header temperature ranges from 20 °C to 100 °C and the typical environment temperature ranges from -10 °C to 30 °C, which in most cases of interests fall within conditions susceptible to hydrate formation.

Our previous reported study investigated the effect of the header temperature (Tr) in a 3-inch pipe system while maintaining the wall temperature (Tw) at constant 4 °C

18

. In that study, Tr ranged from

30 °C to 80 °C, causing the temperature field in the pipe to significantly change, and consequently affecting the hydrate deposition in the pipe. A high Tr generates a warm environment deep into the deadleg and limits the hydrate deposition near the header. Hydrate deposition was observed to vary along the pipe and most hydrate forms where the deposition was the fastest in the pipe. The results showed that most hydrate is formed where the temperature in the pipe is slightly below the hydrate equilibrium temperature after the initial temperature increase. It was also determined that the distance


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between such location and the header is positively correlated to the Tr in the tested conditions. Furthermore, hydrate deposition is also studied in a 1-inch pipe system with a permittivity sensor and varying Tr

19, 20

. The general observations are similar to that in the 3-inch pipe system, but the

permittivity measurement further confirms that the different condensation rates and different growth rates at different Tr.

In this study, the focus is on the effects of Tw in a 2-inch pipe system. The Tw considered are 4 °C, 10 °C, and 15 °C while maintaining Tr at either 30 °C or 80 °C. Tw and Tr together determine the thermal boundary conditions of the system. Possibly because the range of Tr is larger than Tw, varying Tw shows a smaller effect in the deposit distribution. On the other hand, varying Tw does show a significant effect on the deposit growth rate. The results to be reported include the temperature profile, the hydrate deposition rate and distribution, and hydrate plugging conditions.

Experimental Apparatus Figure 1 shows the illustration of the experimental apparatus–the deadleg system for hydrate deposition. Some details of the apparatus are introduced in our previous study

18

. The apparatus in this study

includes a 2-inch (5.0-cm) inner diameter vertical pipe to mimic an uninsulated deadleg. The pipe is divided into five sections, which are labeled sections 1 to 5 from top to bottom. Each section is 20 cm long and the gap between two adjacent sections is 3 cm. Each section has its own cooling jacket, which is connected to a chiller controlling the wall temperature (Tw). The part of the pipe above section 1 is 6 cm. It is not directly cooled by a cooling jacket but insulated with foam. The total length of the pipe (Lpipe) is considered to be 121 cm. The pipe has a polycarbonate window at the top which allows direct visual observation and a camera to monitor the inner pipe. The pipe also has at least one window in each


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section which provides possibilities of direct observation and light into the pipe. Different colors of light are used to help identify the section.

The bottom of the pipe is connected to a water reservoir, so called a header. The adapter connecting the pipe to the header is 30 cm and uninsulated. The header is used for water supply. The header is 6.38 L in volume and is equipped with a ceramic heater to control the temperature (Tr), an impeller for mixing, and a water level gauge to monitor water consumption. The water level in the gauge is continuously monitored via a camera. The accuracy is ±0.13 mol, which corresponds to the change of one pixel on the image. A 1000 ml syringe pump (Teledyne, USA) is connected to the top of the header to maintain a constant system pressure during the experiments. The entire system was custom-built, with the major components manufactured by SejinYoungTech (Korea).

The system has multiple temperature and pressure sensors. All temperature sensors in the system are RTDs (resistance temperature detectors, Omega PT100 PR-17 series, ± 0.1 °C). There is one RTD in each cooling jacket and at least one RTD in each section, which is at the center (radially and axially) of the section (2.5 cm from the inner wall). There are two RTDs in the header, one in the gas phase at the top close to the entrance of the pipe and one in the water at the bottom of the header. There is one RTD at the top of the syringe pump, which is thermally insulated but not temperature controlled. The pressure transducer (Wikai, A-10, ±0.5% of pressure span) is positioned at the top of the header.


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Figure 1. Apparatus illustration. The scale marks the distance to the inner diameter (x/ID) of a given location to the bottom of section 5.

Experimental Procedure Each experiment consisted of two steps: hydrate formation and hydrate dissociation. The details of the procedure are introduced in our previous study 18. Hydrate formation is at constant pressure (100 bar) using a methane/ethane (75/25 mol%, ± 2% accuracy based on GC FTIR) gas mixture (General Air, USA). The set pressure corresponds to a typical pressure value in an oil/gas flowline. The gas mixture is chosen to form sII hydrate that is commonly encountered in the field. For this particular gas mixture, the hydrate equilibrium temperature (HET) at 100 bar is 18.9 °C (from CSMGem). The header is typically filled with 3.00 L of deionized water and the water is kept at a uniform temperature by setting the impeller speed to 1000 RPM. The system is first left for equilibrium for 24 hours after water injection and gas pressurization. The experiment is then initiated by setting Tw and Tr to the desired values. At the same time, the syringe pump is started to maintain the pressure and the data acquisition system is


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initiated to collect data (temperature, pressure, images). When Tr is set at 30 °C, the Tr and Tw reaches the desired temperature within 0.5 hour. When Tr is set at 80 °C, the Tr and Tw reaches the desired temperature within 2 hours. The hydrate formation step proceeds for a predetermined period, approximately 168 hours (7 days) for these studies, such that a large amount of hydrate deposition occurs in the pipe.

At the conclusion of the formation step, the hydrate dissociation is performed under pressure. The Tr is first decreased to 30 °C, if needed, and the header impeller speed reduced to 100 RPM. The reduction in Tr minimizes further hydrate deposition during the dissociation process of the undissociated sections. The reduction of the impeller speed minimizes water level fluctuations and allow for more accurate results. After the system cools down, hydrates are dissociated by increasing Tw section by section, starting from section 5 (bottom) to section 1 (top), to 25 °C, which is above the HET. The hydrate dissociation of each section is completed when no deposit can be visually observed and the temperature and pressure are stable. The water recovery from each section is monitored to calculate the amount of hydrate and related properties.

The conditions of the experiments considered in the study are listed in Table 1. Experiments 1 to 3 and Experiments 4 to 6 are for different Tw at Tr = 30 °C (temperature is slightly higher than the room temperature and is the lowest temperature the heater can be stably maintained) and Tr = 80 °C, respectively. In experiment 1-1, no RTD is used in order to evaluate the interference of the intrusive probes. The results show that the effects should be negligible with respect to the water consumption, gas consumption, and hydrate distribution (Supporting Information). In the result section, the data of experiment 1-2 will be used to represent the experiment at Tr = 30 °C and Tw = 4 °C.


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Table 1. List of the experiments and experimental conditions. All experiments performed at 100 bar with methane/ethane (75/25 mol%) gas mixture.

a

Exp

Tr (°C)

Tw (°C)

Subcooling on the wall (°C)

Duration (hour)

1-1a

30

4

14.9

165

1-2

30

4

14.9

167

2

30

10

8.9

167

3

30

15

3.9

166

4

80

4

14.9

169

5

80

10

8.9

161

6

80

15

3.9

168

No RTDs used.

Results and Discussion

Hydrate Formation Temperature Profiles Figure 2 shows the center temperature (Tcenter) profiles of the 2-inch pipe for experiments at Tr = 30 °C for the three Tw of 4 °C, 10 °C, and 15 °C. At Tr = 30 °C, all temperature readings are lower than or close to the HET. As can be seen, the Tcenter of all sections increases with increasing Tw, which is expected, as the wall is the only cooled section of the pipe. It is also observed that the temperature gradient along the axial direction (bottom to top) decreases with increasing Tw. Last, because of the low Tr (30 °C), the pipe is sufficiently cooled in all the three experiments that the Tcenter of the top sections is close to the Tw.


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Figure 2. Center temperature profiles of 2-inch pipe experiments at Tr = 30 °C and (a) Tw = 4 °C, (b) Tw = 10 °C, and (c) Tw = 15 °C. Temperature profile for sections 1 to 5 are black, red, blue, orange, and green, respectively. Shaded region represents where the temperature is above HET.

During the hydrate formation period, the temperature profiles of the Tw = 4 °C case start to decline after about 24 hours. An indication of some fluctuation is observed after 144 hours in section 5 close to the entrance of the deadleg. Such variation in the temperature should be related to hydrate deposition on the pipe wall, as similarly observed in the 3-inch system 18. As the hydrate deposit grows and gradually fills the pipe, certain sections experience narrowing cross sectional area, resulting in changes in the convection of gas in the pipe. The hydrate deposit also increases the thermal resistance to heat transfer toward the environment. The changed heat transfer due to the hydrate deposit and convection then change the temperature field. On the other hand, these factors are coupled. The changed temperature can in turn change the deposit growth as well as the convection.

Hydrates have a similar thermal conductivity to water

21, 22

, which is much higher than that of the gas.

As such, when the hydrate deposit grows and covers the RTD sensor, the temperature reading for that sensor will decrease due to the better heat transfer with the cold wall. Because the deposit grows from the wall, the temperature readings of the RTDs close to the wall firstly decreases (Supporting


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Information). For experiments at Tr = 30 °C, a significant amount of hydrate is formed between sections 4 and 5. The fluctuations for the temperature in section 5 are possibly caused by hydrate dissociation and reformation as a result of the temperature change.

The temperature profiles at higher Tw (10 °C and 15 °C) are much smoother, indicating a slower growth rate and a thinner hydrate deposit. Only the Tcenter of section 5 show an obvious increase, which results from the hydrate insulation effect

7, 18

. The Tcenter of sections 1 to 3 have a slight increase at the hydrate

onset (beginning of the experiment) and remain almost unchanged afterwards.

Figure 3 shows the Tcenter profiles of the 2-inch pipe for the experiments at Tr = 80 °C and the three Tw. Comparing to the experiments with Tr = 30 °C, the higher Tr has a significant impact in temperature profiles. The Tcenter in the bottom sections becomes much higher than the HET, indicating that hydrate deposition in those sections is strongly limited. Some visual evidence for the limited hydrate deposition is shown in the Supporting Information. Interestingly, the temperature profiles also show a different pattern from the experiments with Tr = 30 °C. The Tcenter of sections 4 and 5 are nearly the same regardless of the Tw, while the temperature profiles of sections 3 and above shift to higher temperatures with increasing Tw. In all cases, the temperature in sections 1 and 2 approach the Tw, and the difference between sections 1 and 2 is only 1-2 °C.


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Figure 3. Center temperature profiles of 2-inch pipe experiments at Tr = 80 °C with (a) Tw = 4 °C, (b) Tw = 10 °C, and (c) Tw = 15 °C. Temperature profile for sections 1 to 5 are black, red, blue, orange, and green, respectively. Shaded region represents where the temperature is above HET.

Most hydrate forms in section 3 at Tr = 80 °C and all three Tw. The Tcenter of section 3 changes significantly at Tw = 4 °C (Figure 3a). The temperature rises fast in the first 24 h due to the insulation and drops afterwards due to the plug formation. The deposit embeds the temperature probes, prevents the convective heat transfer from the gas, promotes the heat transfer to the wall, and thus causes the temperature to decrease significantly. In the sections below where most hydrate forms, the Tcenter are higher than the HET (within shaded region in the plots). The Tcenter have similar values, which is not seen in the cases without hydrate (see Supporting Information for comparison). In these sections, hydrate growth is limited and deposition only occurs close to the wall, forming a thin deposit that has its surface temperature approaching the HET. The measurement from the radial temperature also supports the statement. For example, the readings of the RTD 0.5 cm from the wall in section 5 is higher than the HET at Tr = 80 °C in all three experiments. Especially in section 5, all temperature profiles are stable after the initial increase, suggesting that the deposit has approached an equilibrium state. The hydrate deposit thermally insulates the wall and changes the equivalent gas-solid interface temperature to the HET.


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The hydrate deposit has different thickness at different conditions, but as long as the gas temperature is high enough, the thickness is relatively thin compared to the pipe diameter. For example, by the end of the formation in experiment 3, the average deposit thickness in section 4 is only approximately 3 mm from the recovered water amount assuming 50 % porosity and 100 % conversion. The average thickness of section 5 in experiment 3 should be even thinner due to higher Tcenter. Because such insulation by the hydrate deposit results in similar environments (similar hydraulic pipe diameter and interface temperature), the Tcenter becomes almost the same regardless of the actual Tw in the bottom sections. Another consequence of the insulation is that because the temperature at the bottom is very similar, the Tcenter in the experiments at different Tw only becomes different from where Tcenter is close to the HET and the deposit is considerably thick. In other words, Tw is not effective to change the distribution of the hydrate stable region. When the Tcenter is lower than the HET, which is common above where most hydrate forms, hydrate growth is significantly slowed because of a small temperature gradient (center to wall) and limited water mass transfer. Because the deadleg is long enough, the gas at such locations can be sufficiently cooled in all cases to be close to Tw and the Tcenter therefore changes with the Tw.

Water Consumption and Recovery The header water level is monitored during the experiments to evaluate the water consumption for hydrate deposition. Figure 4 shows the water level changes from the beginning of the experiments. For all experiments, the hydrate onset occurs at approximately 1.0-2.0 h. All curves show an initial rapid increase in the water consumption before 24 h, and then a more gradual consumption until the end of the formation period.


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Figure 4. Water level change in experiments with different Tw with (a) Tr = 30 °C and (b) Tr = 80 °C. Lines are for trends. The data for Tw = 4, 10, and 15 °C are colored black, red, and blue, respectively.

Table 2 shows the average rates of the early and late periods at different conditions, which are obtained from the data in Figure 4. Because there are no obvious inflection points in the water consumption plots, the two periods for comparison are chosen as 0–24 h and 48–168 h. The average growth rates of the two periods clearly show a decline. Moreover, the total water consumption as well as the rate of consumption decreases with increasing Tw. The trends at the two Tr are very similar, with the higher Tr having a larger total amount of water consumed to form hydrates. The water consumption rate is the result of the water mass transfer in the system, which includes the saturation of the gas, condensation of water on the cold pipe wall surface, hydrate formation, water that may be trapped inside the porous hydrate formed, and water that may fall back into the header. Because only the total water consumption and the total water recovered are measured, only the net amount of water contained in the deadleg is known.


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Table 2. Water consumption rates of experiments with different Tw. 0–24 h

48–168 h

0–24 h

48–168 h

(mol/h)

(mol/h)

(mol/h)

(mol/h)

1-2

0.112

0.046

4

0.297

0.033

2

0.081

0.032

5

0.108

0.039

3

0.052

0.027

6

0.108

0.020

Exp #

Exp #

The results show that in the 0–24 h when the hydrate amount is relatively small, the consumption rate is higher at lower Tw and higher Tr. The faster consumption may result from a faster condensation and a faster hydrate formation. The consumption rates seem to reduce to a relatively constant value in all experiments after 48 h. Interestingly, the rates in the 48–168 h differ much less at different Tw than those in the 0-24 h, suggesting the effects of Tw to become weaker over time. The reason can be that after the initial deposit growth, the environments for further condensation and deposition become similar, such as similar deposit surface temperature (at the HET).

Tw affects the water mass transfer by changing the temperature gradient and the natural convection. The axial temperature gradient in the system, from the header to the top of the pipe, induces natural convection in the system, which in turn causes the water to be transported into the pipe. Any changes that enlarges the temperature gradient, such as the increase of Tr or the decrease of Tw, can enhance both heat and mass convection in the system. The changes can be observed from the images.


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Tw affects the condensation on the surface, too. The water condensation from the saturated vapor occurs on the cold pipe wall or the hydrate deposit surface. Assuming the gas phase is saturated, the water condensation on the pipe wall or hydrate surface is mostly dependent on the temperature difference between the gas phase and the Tw. However, the correlation between Tw and condensation is complicated. A detailed discussion is beyond the scope of this study. A high Tw reduces the temperature gradient between the gas and the wall as observed. On the other hand, a high Tw increases the gas temperature. The solubility of water in the gas phase increases exponentially with temperature. The warmer gas can carry a larger quantity of water, which may offset the decreased condensation driving force.

Figure 5 shows the images from the top window at different conditions. The images are another tool to exam the temperature gradient. Figure 5a is taken before starting the experiment when Tr = Tw = 23 °C. The image is clear within the entire range. Figure 5b is taken from experiment 3 at 2 h, when Tr = 30 °C and Tw = 15 °C. Condensation can be observed and no deposit has formed yet (not until 3.3 h). The image shows slight blurriness for the bottom sections (3 and 4). For example, some details of the RTD bundle in section 3 is lost. The blurriness is caused by the gas density gradient, which results from the temperature gradient. The blurriness becomes more obvious in Figure 5c, which is taken from experiment 6 at 2 h, Tr = 80 °C and Tw = 15 °C. The increased blurriness indicates the increasing temperature gradient. In Figure 5c, the details of sections 3 and 4 are almost lost entirely. For example, each RTD of the RTD bundle in section 3 becomes difficult to distinguish. Such loss is not due to the deposit growth. The deposit just starts to grow and is very thin at the time (less than 0.1 mm from visual estimation). The blurriness in Figure 5d becomes more significant as the Tw becomes lower. Even the details of section 2 cannot be seen, suggesting that the temperature gradient becomes more significant in the entire pipe.


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Figure 5. Images showing the effect of Tw on temperature gradient. The blue light is in section 4 in all these images. (a) Experiment 4, Tr = Tw = 23 °C, before starting the experiment. (b) Experiment 3, Tr = 30 °C, Tw = 15 °C, 2 h. (c) Experiment 6, Tr = 80 °C, Tw = 15 °C, 2 h. (d) Experiment 4, Tr = 80 °C, Tw = 4 °C, 2 h.

There are two competing effects that increasing Tr affects the system: increasing the condensation rate and increasing the temperature in the pipe. The condensation rate increase is a consequence of the temperature increase, but they have opposite effects to the hydrate formation. While the increasing condensation rate increases the supply of water for the hydrate formation, the temperature increase can reduce the driving force for hydrate formation. Their relative significance can also be different at different locations in the pipe and at different stages during an experiment. In the 0–24 h of the experiment when there is no or little hydrates, the former effect may be more significant. The water consumption rates at Tr = 80 °C nearly doubles from the rate at Tr = 30 °C at the same Tw. In the 48–168 h, the slowed water consumption rate is much less dependent on Tr. In this period, a certain amount of hydrate deposit has formed and even though a higher Tr can bring more water to the hydrate surface, the corresponding higher gas temperature can offset the condensation by allowing more water trickle back to the header.


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Figure 6 shows the water recovery of all experiments considered in this study. Figure 7 shows illustrations of deposit distributions based on the recovery and the visual observation. As noted before, the amount of water recovered is the water from the hydrate deposit combined with any water trapped within the porous deposit, which may be relatively small; as such, the amount corresponds to the “volume” of hydrate deposit in each section (to obtain an actual volume of the hydrate deposit, the porosity of the hydrate deposit is required).

For the experiments at Tr = 30 °C (Figure 6a), most of the water is recovered at the bottom of the pipe, which agrees with the observation (Figure 7a to Figure 7c). The deposits at the top is scarce and the amount decreases with increasing Tw. The amount of water recovered decreases towards the upper sections. The amount of water recovered in sections 1 and 2 sometimes is too small to be measured by the water level gauge, which causes some error in the recovery results. When the Tw increases from 4 to 10 and 15 °C, the overall amount of water recovered reduces by 19% and 38%, respectively. Most of the reduction is attributed to the change in section 5, and a larger proportion of water is recovered from sections 1–4. In the experiments at Tr = 80 °C (Figure 6b), most of the water recovered is from the middle sections of the pipe. In all three experiments, the distribution of water (hydrate deposits) are similar. As the Tw increases, the overall amount of water recovered decreases and a smaller portion of water is recovered from sections 3 and 4 and more from section 2.


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Figure 6. Water recovery of experiments with different Tw. (a) Recovery per section at Tr = 30 °C. (b) Recovery per section at Tr = 80 °C. The bars for sections 1 to 5 are colored black, red, blue, orange, and green, respectively. The symbol “*” in place of the bar means negligible amount recovered. (c) Total recovery. The data for Tr = 30 °C and 80 °C are colored black and red, respectively.

Figure 7. Illustration and images of hydrate deposit at the end of formation. White areas represent hydrate deposit. Images are taken at the end of the formation. Images (a)–(f) are for Experiments 1–6, respectively. (a) Tr = 30 °C, Tw = 4 °C, (b) Tr = 30 °C, Tw = 10 °C, (c) Tr = 30 °C, Tw = 15 °C, (d) Tr = 80 °C, Tw = 4 °C (plug formed at the bottom of section 3). (e) Tr = 80 °C, Tw = 10 °C, (f) Tr = 80 °C, Tw =


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15 °C. In images (b), (c), (d), and (f), the blue light is in section 4. In images (a) and (e), the blue light is in section 5 and the red light is in section 3.

The amount of water recovery does not equal to the water amount converted to hydrates, but based on visual observations, there is a strong correlation for the amount recovered and the amount of hydrates in a section. The water recovered also gives the maximum possible amount of hydrates formed in a section (by assuming no free water is trapped within the hydrate deposit). For both the experiments at Tr = 30 and 80 °C, the total water recovery decreases by approximately 40 % from Tw = 4 °C to 15 °C. The plot of total recovery against the Tw suggests a possible simply correlation between them (Figure 6c). Moreover, the section with most hydrate remains the same at a given Tr.


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Figure 8. Correlation of the center temperature of at different distance (x/ID) at 24 h (left) and the deposit distribution (right) at 168 h. The data of Tr = 30 °C and 80 °C are drawn with dashed and solid lines, respectively. The temperature obtained with Tw = 4, 10, and 15 °C are colored in black, red, and blue, respectively. Shaded region in the plot represents temperatures above HET. The white areas in the right figure represent hydrate deposit in the deadleg.

A plot between the temperature profiles at 24 h and the hydrate distributions can be plotted (Figure 8), as in the previous study 18, to better understand the hydrate deposition in a deadleg. The location where most hydrate forms is of special interest because at such location the deposit is likely to fill completely the pipe cross sectional area given enough time. Because hydrate growth depends on supply of both gas and water, as well as subcooling from the HET, most hydrate forms where the Tcenter is close to the HET and the combination of these factors gives the maximum growth. Tcenter can be the representative temperature at a certain height. When Tcenter is significantly above the HET, hydrates formation is limited as some subcooling is required for hydrate growth. When Tcenter is significantly below the HET, the temperature at the height usually approaches Tw and both the axial and the radial temperature gradients greatly reduce. The reduced temperature depletes water from the gas. The reduced temperature gradient weakens the natural convection and the water mass transfer. The reduced radial temperature gradient diminishes the driving force of water condensation. Consequently, water condensation is significantly reduced. Because of these reasons, as Figure 8 shows, at Tw = 4 °C, the hydrate plug would appear first within the hydrate stable region where the Tcenter is close to the HET, and then possibly gradually extend to the boundary of the region where the temperature equals the HET.


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As has been discussed, the Tw is not effective in changing the hydrate stable region, the plug locations therefore should not change much at different Tw. The water recovery results also support such statement. Therefore, Figure 8 shows that the major effect of the Tw is to determine the driving force of hydrate formation and affect the kinetics. At approximately the same location (x/ID), the subcooling decreases sharply with increasing Tw.

Besides the potential plugging location, the relative amount of hydrate formed in each section changes. As Tw increases, the percentage of the water recovered from the bottom sections decreases, whereas that from the upper sections increases. Below where most hydrate forms, the hydrate amount as well as the water recovery decrease as Tw increases, due to the thermodynamic limit. In these areas, Tcenter is high, inducing a steady water condensation and limited hydrate formation only close to the wall. Hydrate deposit may initially grow fast, but the high Tw increases the temperature close to the wall, which decreases the maximum hydrate deposit thickness. For example, the 1 mm RTD readings in section 5 for the experiments with Tr = 80 °C indicate stabilized temperatures at 17, 20, and 23 °C at Tw = 4, 10, and 15 °C, respectively. The changes show that the potential hydrate deposit thickness changes from more than 1 mm to less than 1 mm.

Above where most hydrate forms, the hydrate amount as well as the water recovery increase with increasing Tw. In these areas, hydrate deposition is limited by the mass transfer of water at all tested Tw. The low temperature and the small temperature gradients (axial and radial) lead to reduced water content in the vapor, and a slow condensation rate. However, because of the slow hydrate growth rate of the entire pipe at high Tw, there is more time for the water to be transported to the top of the pipe. For long


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periods of time, a high Tw may increase the amount of hydrate deposit above the plugging location, however, based on the water recovery data, such increase may only be significant beyond 168 h.

Conclusions

The visual observation and the water recovery results directly show that, in 168-hour experiments, high Tw (within the experiment range, 4-15 °C) slows the deposit thickness growth and reduces the total amount of water recovery. It only slightly affects the water recovery distribution. With increasing Tw, the temperature profiles fluctuate much less and change more slowly and smoothly, supporting that the deposition rate is reduced. Because of its effects on the growth rate, a smaller portion of deposit forms below the potential plugging location and a larger portion of deposit accumulates above it.

Tw is one of the boundary conditions of the system. Without hydrate, when Tw increases, all temperature readings will have a corresponding increase. However, when hydrate exists, the temperature increase is mainly observed in the top sections above the potential plugging location. The Tcenter of the bottom sections below the potential plugging location stabilizes at similar values independent of the Tw due to the hydrate insulation. The insulation thus leads to similar plugging locations at tested Tw.

Tw affects the deposition rate by changing the subcooling and the condensation. The combined effects on the subcooling and the condensation are reflected on the water consumption rate and the water recovery. When Tw increases, the water consumption becomes slower and the amount of water recovery reduces. The consumption rates also decline over time.


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For the 2-inch system in this study, the pipe is long enough for the center temperature to be cooled below HET, which suggests that the plug is ultimately unavoidable. The hydrate risks in terms of plugging still exist at high Tw, but only after a long-time period. Given the relationship among the temperature, the convection, and the deposition, CFD modeling may be a very promising tool to simulate the process and get further insight into the dynamics in the deadleg. The knowledge obtained in this study about the effects of wall temperature can help to predict the plugging position and the time of formation, and design deadlegs to prevent hydrate plugs, which is part of our future work direction.


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ASSOCIATED CONTENT

Supporting Information include additional details for: radial temperature profiles of each experiment, center temperature profiles with nitrogen, summary of water recovery, list of light color, comparison between experiments 1-1 and 1-2, and limited deposition in section 5 at Tr = 80 °C.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (KMA), [email protected] (AKS) ORCID Jeong-Hoon Sa: 0000-0002-8579-1643 Amadeu K. Sum: 0000-0003-1903-4537 Notes The authors declare no competing financial interest.

Acknowledgements The authors wish to express their appreciation to Statoil for funding this project and granting permission to publish this paper.

References 1.

Sloan, E. D., Jr; Carolyn, K., Clathrate Hydrates of Natural Gases. 3rd ed.; CRC Press: 2007.


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Page 27 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2.

Energy & Fuels

Sloan, E. D., Fundamental principles and applications of natural gas hydrates. Nature 2003, 426, (6964), 353-363.

3.

Kerr, R. A., Gas Hydrate Resource: Smaller But Sooner. Science 2004, 303, (5660), 946-947.

4.

Xu, C.-G.; Li, X.-S., Research progress of hydrate-based CO2 separation and capture from gas mixtures. RSC Adv. 2014, 4, 18301-18316.

5.

Kang, K. C.; Linga, P.; Park, K.-n.; Choi, S.-J.; Lee, J. D., Seawater desalination by gas hydrate process and removal characteristics of dissolved ions (Na+, K+, Mg2+, Ca2+, B3+, Cl-, SO42-). Desalination 2014, 353, (17), 84-90.

6.

Song, Y.; Dong, H.; Yang, L.; Yang, M.; Li, Y.; Ling, Z.; Zhao, J., Hydrate-based heavy metal separation from aqueous solution. Scientific Reports 2016, 6.

7.

Lingelem, M. N.; Majeed, A. I.; Stange, E., Industrial Experience in Evaluation of Hydrate Formation, Inhibition, and Dissociation in Pipeline Design and Operation. Annals of the New York Academy of Sciences 1994, 715, 75-93.

8.

Grasso, G. A.; Sloan, E. D.; Koh, C. A.; Sum, A. K.; Creek, J. L.; Kusinski, G., Hydrate Deposition Mechanisms on Pipe Walls. In Offshore Technology Conference, Houston, Texas, USA, 2014.

9.

Rao, I.; Koh, C. A.; Sloan, E. D.; Sum, A. K., Gas Hydrate Deposition on a Cold Surface in WaterSaturated Gas Systems. Ind. Eng. Chem. Res. 2013, 52, (18), 6262-6269.

10. Lorenzo, M. D.; Aman, Z. M.; Soto, G. S.; Johns, M.; Kozielski, K. A.; May, E. F., Hydrate Formation in Gas-Dominant Systems Using a Single-Pass Flowloop. Energy & Fuels 2014, 28, 3043-3052. 11. Kinnari, K. J.; Askvik, K. M.; Li, X.; Austvik, T.; Zhang, X.; Sa, J.-H.; Lee, B. R.; Sum, A. K., Hydrate Management of Deadlegs in Oil and Gas Production Systems - Background and Development of Experimental Systems. Energy & Fuels 2017, 31, (11), 11783-11792.


27

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 29

12. Bloom, G. R. Turbulent hydraulic penetration from turbulent pipe flow into stagnant columns. Washington State Univ., Pullman, Pullman, Washington, USA, 1978. 13. Habib, M. A.; Badr, H. M.; Said, S. A. M.; Hussaini, I.; Al-Bagawi, J. J., On the Development of Deadleg Criterion. Journal of Fluids Engineering 2005, 127, (1), 124-135. 14. Asteriadou, K.; Hasting, A. P. M.; Bird, M. R.; Melrose, J., Computational Fluid Dynamics for the Prediction of Temperature Profiles and Hygienic Design in the Food Industry. Food and Bioproducts Processing 2006, 84, (2), 157-163. 15. Lunde, K.; Kinnari, K.; Labes-Carrier, C. Deadleg. US Patent 9,297,237, 2016. 16. Anderson, H. Computational Study of Heat Transfer in Subsea Deadlegs for Evaluation of Possible Hydrate Formation. MS Thesis, Telemark University College, Porsgrunn, Norway, 2007. 17. Nazeri, M.; Tohidi, B.; Chapoy, A., An Evaluation of Risk of Hydrate Formation at the Top of a Pipeline. Oil and Gas Facilities 2014, 3, (2), 67-72. 18. Zhang, X.; Lee, B. R.; Sa, J.-H.; Kinnari, K. J.; Askvik, K. M.; Li, X.; Sum, A. K., Hydrate Management in Deadlegs: Effects of Header Temperature on Hydrate Deposition. Energy & Fuels 2017, 31, (11), 11802-11810. 19. Sa, J.-H.; Lee, B. R.; Zhang, X.; Kinnari, K. J.; Li, X.; Askvik, K.; Sum, A. K., Hydrate Management in Deadlegs: Hydrate Deposition Characterization in a 1-in. Vertical Pipe System. Energy & Fuels 2017, 31, (12), 13536-13544. 20. Sa, J.-H.; Lee, B. R.; Zhang, X.; Folgerø, K.; Haukalid, K.; Kocbach, J.; Kinnari, K.; Li, X.; Askvik, K.; Sum, A., Hydrate Management in Deadlegs: Detection of Hydrate Deposition using Permittivity Probe. Energy & Fuels 2018, Article ASAP. 21. Yang, L.; Zhao, J.; Wang, B.; Liu, W.; Yang, M.; Song, Y., Effective thermal conductivity of methane hydrate-bearing sediments: Experiments and correlations. Fuel 2016, 179, (1), 87-96.


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22. Krivchikov, A. I.; Gorodilov, B. Y.; Korolyuk, O. A.; Manzhelii, V. G.; Conrad, H.; Press, W., Thermal Conductivity of Methane-Hydrate. Journal of Low Temperature Physics 2005, 139, (5), 693-702.


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Hydrate Management in Deadlegs: Effect of Wall Temperature on

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