An in situ method on kinetics of gas hydrates

Clathrate hydrates or gas hydrates are solid compounds that are formed when water and gas come together at high pressure and low temperature. These hydrates are composed of approximately 85 mol. % of water, and many of their properties are similar to ice (e.g., physical appearance, refractive index, and density), whereas other properties are in contrast to those of ice (e.g., mechanical strength and thermal properties).^1–10 In gas hydrates, water molecules (host lattice) are linked through hydrogen bonding and create cavities that can enclose a large variety of molecules (guests). There is no chemical bonding between the host water molecules and the enclosed guest molecule. Some of the cages in the structure can be vacant; however, guest molecules must occupy a sufficient number of cages for the hydrate to be stable. These hydrates may exist at a temperature below as well as above the normal ice formation temperature.^11,12

Deepwater offshore oil fields provide both high pressure and low temperature environments; therefore, the risk of gas hydrate formation and blockages in pipelines and offshore facilities is extreme. In addition, gas hydrate formation is a critical issue in deepwater oil/gas production in terms of safety.^13,14 As witnessed in 2010, gas hydrates were a major problem in the containment of the oil leak (100-ton containment) following the deepwater oil/gas well blowout of the Macondo well in the Gulf of Mexico.¹ Despite their negative impact in oil/gas pipelines, gas hydrates are a potential asset when present in large natural deposits in arctic regions or in oceanic sediments along the continental margins.^15–38 The global estimate of the amount of energy (methane gas) in natural gas hydrate deposits is approximately twice that of all fossil fuel reserves available worldwide. In addition, gas hydrates have shown promise as a storage medium for natural gas^39–41 and hydrogen (H₂).^42–51 

As gas hydrates form quickly, they are the most serious and common flow assurance challenge in subsea systems.⁵² Sometimes, thermodynamic inhibition of gas hydrate formation becomes unfeasible (economically and/or technically) requiring large amounts of methanol (∼40-60 vol. %) injection.^1,53,54 The modern strategies for hydrate mitigation have shifted from thermodynamic inhibition to risk management.^52,55–57 In these new mitigation strategies, hydrate formation is allowed as long as they do not cause plugging of pipelines. The role of the pipe surface on reduction in adhesion of the hydrate phase is becoming an important field of study.^58–65 That is, an understanding of growth kinetics and time-dependent properties of gas hydrates is critical in risk management strategies. Although the thermodynamics of gas hydrate formation is well studied^66–75 and the accuracy of the prediction software versus the measured data is satisfactory, the kinetics of gas hydrate formation remains an unresolved problem.

In the growth regime of hydrates, heat transfer from the interface and mass transfer to the interface govern kinetics of growth. Seminal studies of Vysniauskas and Bishnoi,⁷⁶ Englezos et al.,⁷⁷ and Skovborg and Rasmussen,⁷⁸ and Kumar et al.⁷⁹ elucidated mass transfer to the interface in hydrate formation and the study explored role of heat transfer on the kinetics of growth.⁸⁰ However, accurate measurement of hydrate growth kinetics through non-optical approaches remains a challenge. Specially, in some embodiments, optical access is either not feasible or in highly chaotic fluid mixtures, optical approaches are unable to provide reliable information on growth kinetics.

Here, we report an in situ method to probe kinetics of hydrate growth both under mixing and flow conditions. As thermal properties of gas hydrate and its initial constituents (water/hydrocarbon) are different, by probing the transient thermal properties, we determined motion of gas hydrate growth front. This approach provides an accurate tool to determine kinetics of gas hydrate formation in applications where there is no optical access.

Cyclopentane (CyC5) 98% was purchased from Sigma-Aldrich. Annealed platinum wire 99.99% with a diameter of 250 µm was purchased from Goodfellow, Inc.

The schematic of the experimental setup is shown in Fig. 1 (Multimedia view). We used a source meter (Keithley 2602B) to provide current to both ends of the platinum wire and to measure the voltage along the mid-section. We also used a refrigerated circulating bath (VWR, 7L) to control temperature inside the insulated aluminum chamber. We implemented a VWR advanced vortex mixer to provide necessary mixing condition for hydrate formation.

The schematic of the experimental setup is shown in Fig. 2. We used a closed hydraulic loop with a peristaltic pump to circulate a well stirred mixture of water and CyC5 with a volumetric ratio of 3 to 1. Furthermore, we used a refrigerated circulating bath to control the temperature of copper tube walls at 2 ± 0.5 °C. Thermal properties of medium surrounding the hot-wire were probed at various time steps.

We incorporated the hot wire approach for thermal diffusivity measurement^81–85 in gas hydrate studies. Comparing properties of the gas hydrate and water shows that the thermal diffusivity of gas hydrate is two times higher than that of the water phase. Thus, this property can serve as an appropriate tool to distinguish the existence of water and hydrate phases. In the developed experimental platform, we probe temperature change and heat flux of a thin hot wire in a medium through the four-probe method. We consider CyC5 as the hydrate structure former since this hydrate can be formed at ambient pressure in the laboratory. This fluid is immiscible with water and has a hydrate equilibrium temperature of 7.7 °C at atmospheric pressure, which is above the freezing temperature of water.

As shown in Fig. 1 (Multimedia view), we used a vortex mixer to provide the necessary mixing condition for hydrate formation. It is reported in the literature that since the melting ice acts as a template for the hydrogen bonds in the hydrate structure, hydrate formation from agitated (melting) ice is much faster than formation from bulk water.^86,87 Therefore, initially, we put water and CyC5 inside the aluminum chamber with a volumetric ratio of 3 to 1 and then reduced the cold plate temperature to −10 °C to completely freeze the water. Subsequently, we set the temperature at 1 °C to initiate ice melting. Once the ice melted down, we started the mixing process. At different time intervals, we stopped the mixing for 2-3 s and conducted the measurements. We measured the separation time which is ∼11 s (Multimedia View of Fig. 1). Thus, we note that the separation does not occur while we are conducting the measurements.

Formation of the hydrate phase affects thermal properties of the medium surrounding the hot wire. That is, for an input heat flux to the wire, transient temperature of the hot wire depends on the thermal conductivity of the surrounding medium,⁸⁸ 

where r denotes the radial coordinate, t is the time, q is the heat flux, k is the thermal conductivity, α is the thermal diffusivity, and C is a constant equal to 1.781. By differentiating Eq. (1) with respect to ln(t), one finds

We denote the diameter of hot wire as a. Substituting Eq. (2) in Eq. (1), thermal diffusivity is written as

Note that once a heat flux is applied to the hot wire, the penetration depth grows as a function of time. For a given penetration depth, the correlation between ΔT(a) and ln(t) should be linear. This linear function provides information on thermal properties of the surrounding medium.

Initially, we calibrated the new in situ device with only water inside the chamber. The transient temperature of the hot wire as a function of time is shown in Fig. 3, which suggests a value of 1.35 × 10⁻⁷ m² s⁻¹ for thermal diffusivity of water. These measured values are in good agreement with the reported thermal properties of water.¹ This calibration suggests that the developed experimental setup provides an accurate method to examine thermal properties of the medium surrounding the hot wire. We should add that the estimated error in thermal property measurement in the hot wire method in mixing and flow experiments are 4% and 2%, respectively (supplementary material I).

Following the procedure discussed above, we studied transient temperature of the hot wire while the hydrate grows around the wire. At various time steps, the hot wire method was used to probe thermal properties of the surrounding medium and the results are presented in Fig. 4. During the experiments, we ensured that the hot wire temperature is below the solid-liquid phase change temperature (7.7 °C) by a margin of ∼2 °C. Therefore, heating does not cause any hydrate dissociation or affect the growth rate.

As time goes by, the hydrate phase forms around the wire and propagates. We should mention that hydrate does not form a uniform phase around the hot wire. That is, the thickness of the formed hydrate phase varies along the length of the hot wire. Thus, the measurements provide an average value for kinetics of growth along the hot-wire length. For a linear functionality between ΔT(r, t) and ln(t), Eq. (1) is rewritten as

where A denotes the slope of the linear function and B is the intercept.

The information on the linear curve could be used to extract information on thermal properties of the medium surrounding the hot wire. We should mention that the time scale for transient hot wire measurement is in order of seconds. Since the maximum measured growth rate (dr/dt) is in order of ∼10⁻⁵ mm s⁻¹, change in the hydrate structure is negligible. As discussed, formation of the hydrate phase on the hot wire is not uniform. Thus, we define an effective thermal diffusivity for the medium surrounding the hot wire. The thermal conductivity of water (0.58 W m⁻¹ K⁻¹) and hydrate (0.51 W m⁻¹ K⁻¹)¹ is similar and may not act as a distinguishable property. According to Eq. (2), only the slope of the ΔT − ln(t) graph is needed to determine thermal conductivity. However, in thermal diffusivity calculations, Eq. (3), the accurate value of intercept is also required. Thus, we increased time resolution of the measurements to accurately determine intercept of the ΔT − ln(t) graph. By interpreting the data from t = 0 to t = 1 s, we consider a cylindrical volume surrounding the hot-wire with a radius equal to the penetration depth after 1 s, corresponding to ln(t) = 0. This choice of ln(t) satisfies the linearity condition as shown in all the measurements; see Fig. 4. That is, all the measurements show linear characteristics from start of the experiment until ln(t) = 0. Thus, based on Eqs. (3) and (4), effective thermal diffusivity of this cylindrical volume is written as

Time evolution of effective thermal diffusivity is shown in Fig. 5. As shown, effective thermal diffusivity increases until it reaches a plateau. Interestingly, this plateau corresponds to thermal diffusivity of the gas hydrate phase. That is, once this plateau is reached, the cylindrical volume (corresponding to penetration depth radius) surrounding the hot wire is filled with the hydrate phase. No further change in thermal properties occurs with growth of the hydrate phase.

As discussed, medium surrounding the wire is a combination of the formed hydrate phase and water/CyC5 mixture. The thermal diffusivity of water and CyC5 being identical,⁸⁹ we can consider this combination to be consisting of two-phases: Hydrate and water/CyC5 mixture. For this composite, effective thermal diffusivity, α_e, is written as⁹⁰ (supplementary material II)

where φ denotes the hydrate volume fraction in the cylindrical volume (φ = $VHydrateVPenetration$⁠) and subscripts e, m, and h are effective, mixture, and hydrate phases, respectively. Given the effective thermal diffusivity, thermal diffusivity of hydrate (plateau value, 2.5 × 10⁻⁷ m² s⁻¹, which is in good agreement with the reported value for structure II gas hydrates)¹ and thermal diffusivity of water/CyC5 mixture, we could calculate fraction of the hydrate phase in the considered cylindrical volume as a function of time, φ = φ(t), which is written as

and

And consequently, through Eqs. (7) and (8), the growth rate of the hydrate phase is written as

where τ denotes the duration of each measurement used to calculate the penetration depth. The results are shown in Fig. 6. This graph suggests that the average hydrate growth rate (ρdr/dt) is equal to ∼1.9 × 10⁻⁵–3.9 × 10⁻⁵ kg m⁻² s⁻¹. Even after 3 h after reaching a plateau, thermal diffusivity of the medium surrounding the hot wire as shown in Fig. S1 (supplementary material III) is close to thermal diffusivity of structure II hydrate which confirms the complete hydrate formation in the thermal penetrated depth. Hydrate formation is a nucleation/growth process. Therefore, due to a lower Gibbs energy barrier, heterogeneous nucleation starts on the wire (solid boundaries) and growth continues on top of the initially formed layer. It is also observed by Taylor et al.⁹¹ and Aman et al.⁹² that the hydrate phase grows radially. For CH₄ hydrates, Ohmura et al.⁹³ measured a growth rate of 2.1 × 10⁻⁴ kg m⁻² s⁻¹ at a temperature of 0.15 °C and a pressure of 10 MPa and Freer et al.⁸⁰ reported a growth rate of 1.86 × 10⁻² kg m⁻² s⁻¹ at a temperature of 3 °C and a pressure of 9.7 MPa. Note that in approximately similar experimental conditions, the reported growth rates vary by two orders of magnitude. Both approaches use optical methods for these measurements. Thus, an accurate measurement method to measure growth kinetics is a highly beneficial tool in this field.

In this section, we implemented the developed in situ approach under flow condition to measure hydrate growth rate. As depicted in Fig. 2, the hydrate phase forms around the wire as well as the tube walls. As mentioned before, hydrate does not form a uniform phase around the hot wire. Thus, similar to mixing condition, the measurements provide an average value for kinetics of growth along the hot-wire length. The in situ measurements for some time intervals are shown in Fig. 7. We conducted these measurements at 9 time steps. For each time step, we stopped the mixture flow for a few seconds to measure the thermal properties. The fluid flow condition leads to large variation in the measurements of hot-wire temperature, and reliable data could not be collected. The graphs show a linear characteristic and may deviate from this linearity after a time period. We did not continue the experiment to observe this deviation as it leads to a hot wire temperature higher than the hydrate melting temperature (i.e., 7.7 °C). This deviation is caused by natural convection effects.⁸⁸ 

As shown in Fig. 8, effective thermal diffusivity increases until it reaches a plateau which corresponds to thermal diffusivity of the gas hydrate phase. As mentioned earlier, once the plateau is reached, the cylindrical volume (corresponding to thermal penetration depth radius) is filled with the hydrate phase (see Fig. 9). Based on measured effective thermal diffusivities and by implementing Eq. (6), we could calculate the hydrate volume fraction inside the cylindrical tubes and the corresponding average hydrate radius. Results are plotted in Fig. 9 which suggests that the average growth rate of hydrate under the flow condition is 4.51 × 10⁻⁶ kg m⁻² s⁻¹. This growth rate is much smaller than what is seen in mixing experiments. There are two reasons behind this slower rate: (1) as reported before, hydrate formation from water is much slower than its formation from agitated (melting) ice;⁸⁶ (2) the advection in the flow affects nucleation and growth of hydrate crystals. In the dynamic condition, we tried to minimize the flow rate to suppress the role of advection in these experiments. However, in no flow condition, the contrast between density of CyC5 and water leads to buoyancy separation of these two fluids. The CyC5 concentrates at the top portion of the experimental tube, while water settles at the bottom portion of the tube. In this condition, no meaningful measurements on the growth kinetics of the hydrate phase can be conducted. To further validate the measured growth rate of hydrate, we continued the flow experiments for 12 days. We noticed that after 12 days, the flow is stopped and the tube is completely blocked by the hydrate formation. If we consider growth of hydrate from the tube wall to the center and simultaneously from the hot wire toward the wall, for complete blocking of the tube with a radius of 8.71 mm, dr/dt is 4.6 × 10⁻⁹ m/s. That is, the growth rate of hydrate (i.e., ρdr/dt) is approximately 4.1 × 10⁻⁶ kg m⁻² s⁻¹ which is within 10% of the measured growth rate by the hot-wire method. This agreement justifies accuracy of the hot-wire method to examine the growth rate of gas hydrates in an in situ approach. In the mixing condition, due to complexity of the geometry and growth of hydrate from the walls in all directions, we could not use time for complete formation of hydrate to re-evaluate measured growth rate by the hot-wire method.

We present an accurate and in situ approach to determine the gas hydrate growth rate in both mixing and flow conditions. The hydrate phase forms in a medium surrounding the hot-wire, and probing thermal properties of the surrounding medium provide information on the kinetics of hydrate formation. We used the developed approach for measurement of cyclopentane hydrate growth. We find that the growth rate of hydrate, at ambient pressure and a temperature of 1-2 °C, in mixing condition is 1.9 × 10⁻⁵–3.9 × 10⁻⁵ kg m⁻² s⁻¹, while in dynamic condition, this growth rate drops to 4.5 × 10⁻⁶ kg m⁻² s⁻¹. Compared with other approaches, this new approach provides high accuracy and feasibility of hydrate growth studies in complex embodiments where there is no-optical access. Information on kinetics of hydrate growth is crucial for risk-management strategies in oil/gas infrastructure. Furthermore, this new approach does not have any restriction on temperature/pressure of the system and could be used in harsh environments of subsea systems. We envision this new tool to provide a route to elucidate underpinnings of hydrate growth in other hydrate systems.

See supplementary material for error estimation for thermal properties measurement in the hot wire method, calculation of hydrate volume fraction in heat penetrated volume, static experiments of hydrate formation (PDF).

The authors gratefully acknowledge funding support from the Air Force Office of Scientific Research (AFOSR) for Grant No. FA9550-16-1-0248 with Dr. Ali Sayir as the program manager, the Office of Naval Research for Grant No. N00014-17-1-2978, the National Science Foundation (Grant No. NSF- 1804204) with Dr. Susan Muller as the program manager, and the ACS Petroleum Research Fund (Grant No. 59590) with Burtrand Lee as the program manager.

The authors declare no competing financial interest.