The purity of 99.99% CO₂ was provided by Guangzhou Spectrum Source Gas Co., Ltd. The deionized water (resistivity of 18.25 MΩ cm) prepared by the laboratory water purification mechanism was used as pure water for CO₂ hydrate formation. Potassium thiocyanate (KSCN) was made in Beijing Merida Technology Co., Ltd. to detect metal cations produced on the anode during electrolysis.

The schematic diagram of the experimental apparatus is shown in Figure 1A. The crystallizer with the inner volume of 380 ml (with inner length and width of 6.9 cm and inner height of 11 cm) and pressure tolerance of 10 MPa was applied for the kinetic experiments of CO₂ hydrate formation. It was made of 316 stainless steel. The front and back of the crystallizer were equipped with visual windows for observing the formation and decomposition of CO₂ hydrate. The inside of the crystallizer was coated with a polytetrafluoroethylene film to make it insulating. A mechanical stirring was set at the top of the reactor to thoroughly mix the gas and liquid phase. The crystallizer was immersed in a constant temperature water bath filled with 25 wt% ethylene glycol solution to maintain a constant temperature. The vacuum pump was used to free the reactor before feeding CO₂. The cathode and anode electrodes (length, 49 mm; width, 34 mm) with a thickness of 1.2 mm were inserted in the liquid phase, as shown in Figure 1B. The spacing between the two electrodes was 3 cm. The electrodes were linked to a DC power supply, an ammeter, and a voltmeter. The cathode was coated with a 24-μm Parylene-C dielectric layer by vapor deposition technique. Then, only the dielectric layer on either side of the cathode electrode was removed to guarantee a small amount of current flowing. There will be sensible current flow through the liquid phase without the dielectric layer, leading to a great deal of Joule heating and water electrolysis. Two PT100 thermocouples with an accuracy of 0.1 K and a pressure sensor with an accuracy of 0.01 MPa were respectively arranged inside the crystallizer to monitor the temperature and pressure change. All the data during experiments were collected by Agilent 34970A.

Before the hydrate formation experiment, the solubility of CO₂ in the effect of CF and the chemical reaction between cathode and anode were studied. The crystallizer was firstly cleaned three times with deionized water and then dried by a dryer. After then, 180 ml of deionized water was injected into the crystallizer. Then, the crystallizer was placed in the water bath to maintain the temperature of 283.15 K. After the temperature of liquid reached the set temperature and kept stable, the vacuum pump started to make the reactor air free. Subsequently, CO₂ was pressurized into the reactor to the desired pressure of 3.5 MPa. Then, both the stirring at the speed of 450 rpm and DC power supply started at one time (this time was set to 0). Furthermore, to detect the chemical reaction on the bipolar plate during power-on, a few prepared KSCN solutions were dropped into the liquid phase at normal temperature and pressure to observe the changes in the liquid phase.

The experiment process of the kinetics of CO₂ hydrate formation is as follows. The preparatory work in the early stage was the same as above. The temperature of the water bath was set at 274.15 K. After gas injection, the pressure, temperature, and current experimental data were recorded every 10 s. It was considered the completion of CO₂ hydrate formation when the pressure drop was not sensible for at least 2 h, and the temperature remained constant at the set temperate. Each experimental result in this study was the average of at least two independent tests.

The amount of CO₂ gas consumption could be calculated by the following equation: Δ n CO 2 = P 0 V 0 Z 0 RT 0 − P t V t Z t RT t   (1) where P 0 , V 0 , and T 0 are the pressure, temperature, and volume of gas phase at time 0, respectively. P t , V t , and T t are the pressure, temperature, and volume of gas phase at any time t, respectively. R is the ideal gas constant, 8.3145 J ⋅ mol − 1 ⋅ k − 1 . Z 0 and Z t are the gas compressibility calculated by Peng–Robinson equation (Smith and Ness, 2000).

The CO₂ gas consumption consists of the moles of CO₂ dissolved in water and the moles of CO₂ trapped into the hydrate phase. The relationship between the three is shown in the following equation: Δ n CO 2 H = Δ n CO 2 − Δ n CO 2 S (2) where Δ n CO 2 H is the mole of CO₂ trapped into the hydrate phase, and Δ n CO 2 S is the moles of CO₂ dissolved in water.

The solubility of CO₂ gas, x C O 2 (mol%), in the presence of hydrates can be calculated as follows, according to the research of Diamond et al. (Diamond and Akinfiev, 2003): x CO 2 = 1.570415 + 7.887505 × 10 − 2 T + 4.734722 × 10 − 3 T 2 + 4.56477 × 10 − 4 T 3 − 3.796084 × 10 − 5 T 4 (3) where T (°C) is the temperature at which the hydrate is stable, ranging from −1.48°C to 9.93°C.

The moles of CO₂ dissolved in water can be calculated by the following equation: Δ n CO 2 S = ( n w − Δ n CO 2 H ⋅ H n ) ⋅ x CO 2 (4) where n w is the mole of water in the reactor. H n is hydration number, which is the number of water molecules per CO₂ molecule. The hydration number for structure I of CO₂ hydrates is calculated as follows (Mohammadi et al., 2014): H n = 46 6 θ L + 2 θ S (5) where θ L and θ S are the fractional filling of large and small cavities, respectively. On the basis of Langmuir adsorption theory, the fractional filling of cavities ( θ i ) can be obtained as follows: θ i = C i f CO 2 1 + C i f CO 2 (6) where C_i is the Langmuir constant of CO₂ in the type i cavity; f_CO2 represents the fugacity of CO₂ in the gas phase, which is calculated by the Peng–Robinson equation of state. The Langmuir constant of CO₂ C_i is formulated as follows: C i = A i T exp ( B i T ) (7) where T is the temperature; A_i and B_i are constants.

According to Eqs 2–4, the mole of CO₂ trapped into the hydrate phase can be attained by the following equation: Δ n CO 2 H = Δ n CO 2 − n w x CO 2 1 − H n x CO 2 (8)

Water to hydrate conversion, C W H (%), is computed as follows: C WH = Δ n CO 2 H n w × H n   × 100 (9)

CO₂ to hydrate conversion, C C H (%), is computed as follows: C CH = Δ n CO 2 H n 0 − n eq × 100 (10) where n 0 is the initial mole of CO₂ fed into the reactor at time 0. n eq is the mole of CO₂ at phase equilibrium condition. The data of CO₂ phase equilibrium can be predicted by CSMGem (Sloan et al., 2007) at given experimental conditions.

The average rate of hydrate formation is computed as follows: ( d Δ n CO 2 dt ) t = Δ n CO 2 , t + Δ t − Δ n CO 2 , t Δ t , Δ t = 10 s (11)

The average value (R_av) of these rates is calculated every 30 min as follows: R av = ∑ t = 1 m ( d Δ n CO 2 dt ) t m , m = 180 (12)

The ability of the supersaturation system to maintain a metastable state can be evaluated by the induction period, which is a key parameter in the process of CO₂ hydrate nucleation. In this study, the induction time (t_in) is defined as the period from time 0 (the opening of stirring and DC supply) to a detected significant temperature increase and sudden pressure drop. Semi-completion time (t_90%) is defined as the time between time 0 and the time required to capture 90% of the general entrapped CO₂ gas (Pahlavanzadeh et al., 2020b). The hydrate formation time is a critical parameter for hydrate application. After the hydrate conversion rate gets 90% of the total, the gas consumption rate becomes very slow, and the hydrate formation time is relatively long. Hence, t_90% can be approximately taken as the completion time of hydrate formation.

Figure 5 shows the curves of the pressure of the system, the temperature of the liquid phase, and current during the hydrate formation process of CO₂ hydrate at 3.5 MPa and 274.15 K in the application of 15 V at the first 3 h. The pressure of the system decreased as the dissolution of CO₂ in the initial period, and the temperature of the liquid phase was maintained stable. Subsequently, an amount of CO₂ gas molecules entrapped into hydrate cages formed water molecules, resulting in an abrupt rise in temperature and sensible decrease in pressure. Then, the temperature of the liquid phase returned to the set temperature. Nevertheless, the pressure still continually decreased because CO₂ hydrates continued to generate, and hydrate grew and crept along the agitator arm toward the gas phase, as shown in Figure 5. This phenomenon of wall-creeping hydrate growth also was reported by the previous research (Huang, 2005). The current increased with the dissolution of CO₂ and tended to be stable until the CO₂ dissolve to saturation. The conductivity in the solution depends on ion concentration and ion mobility, which is proportional to temperature (Zatsepina and Buffett, 2001). Therefore, much heat generates instantly due to the nucleation of CO₂ hydrate, which accelerates the ion mobility to increase the current in the solution. The resistance of the system increases because of the hydrate formation, and the current gradually decreases with the growth of the hydrate. However, the feed water in this experiment is excessive. Hence, when CO₂ hydrates ultimately form, there is still a certain amount of free water in the system, and the current of the system cannot decrease to zero. According to Faraday’s electrolysis law, the calculation shows that less than 0.1% of water is electrolyzed. Thus, electrolysis would not affect the composition of components.

Figure 6 shows the induction time and semi-completion time of CO₂ hydrate formation by applying different voltages ranging from 0 to 60 V at experimental conditions of 274.15 K and 3.5 MPa. Interestingly, the induction time was totally reduced under the action of CF. The shortest induction time was obtained by applying voltage of 10 V, and it was reduced by 54% compared with that in without voltage. At the same time, we found that the induction time was prolonged with the increase of voltage. Significantly, the induction time in the application of 60 V became nearly consistent with that in without voltage. Hence, higher voltage may have a little positive effect on the nucleation of CO₂ hydrate. The current flow in the solution resulted in electrolysis at the electrodes in the application of voltages. The electrolytic corrosion of the electrode plate occurred at the anode accompanying by the production of metal ions (Fe³⁺), and hydrogen bubbles busted out at the cathode. The growth and rupture of bubbles could disturb the system and increase the probability of CO₂ hydrate nucleation. Meanwhile, the production of metal cations at anode also promoted the nucleation of crystals (Kumano et al., 2012). The empty hybrid orbitals of Fe³⁺ form coordination bonds with water molecules to promote the ordered arrangement of water molecules. The enhancement of the local hydrogen-bonding network can promote CO₂ hydrate nucleation to reduce the induction time of CO₂ hydrate. However, the faster rate of ions migrating to the electrode promotes the formation of Fe(OH)₃ and shortens the residence time of Fe³⁺ in liquid phase with the increase of voltage. Furthermore, the more Joule heat is not conducive to the process of CO₂ hydrate nucleation. Hence, the induction time was prolonged with the increase of voltage. As can be seen in Figure 6, the semi-completion time was prolonged except for voltage of 15 V compared with 0 V. The semi-completion time of CO₂ hydrate formation was decreased by 27.8% in the application of 15 V. The semi-completion time represents the hydrate formation rate that can be controlled by kinetics or heat and mass transfer. Iron ions produced by electrolysis are more easily diffused to the gas–liquid interface area under the action of stirring in the application of 10 V under the weak electric field force. This leads to more hydrate growth at the interface, hindering the further diffusion of CO₂. Thus, the semi-completion time was increased in the application of 10 V. More CO₂ hydrates are formed in the whole liquid phase under the action of electrolytic product Fe³⁺ in the application of 15 V, which greatly shortens the semi-completion time. However, more Joule heat can inhibit the growth of hydrate with the increase of voltage.

The curve of the CO₂ gas consumption per mole of water (gas uptake) in the application of different DC voltages is illustrated in Figure 7. The gas consumption increased gradually during the process of hydrate formation until the completion of hydrate formation. The gas consumption in the first 0.7 h was almost the same due to the dissolution of CO₂, but the differences subsequently arose under the action of the CF. It is observed that different DC voltages may have adverse effects on the gas consumption rate and the final amount of gas consumption. When 10- and 15-V DC voltage were applied to the system, the gas consumption rate was accelerated, with 15 V more pronounced. The amount of Joule heat is meager at low voltage, and it has little effect on the temperature of the system. On the contrary, the rate and final amount of CO₂ gas consumption during the hydrate formation process were lower in applying voltage of 30 and 60 V compared with that in the absence of CF. This means that the CO₂ gas molecules entrapped into hydrate cages become more difficult at higher DC voltage.

In Figure 8, the rates of CO₂ hydrate formation in the application of different voltages were compared. In all experiments, the beginning of the hydrate reaction had the highest rate of hydrate formation due to the CO₂ gas dissolved rapidly in the aqueous phase and then the hydrate formation rates fell as a series of fluctuations to zero. It can be clearly seen in Figure 8 that the application of voltage slightly reduced the initial dissolution rate of CO₂ in water, and the hydrate formation rate was obviously increased with the process of the hydrate formation under the action of CF. In the first 2 h, the rate of hydrate formation in the application of voltages was higher than that without voltage. We have known that the induction time could be shortened in the effect of CF based on the above discussion. More CO₂ gas molecules were captured by the hydrate cage during this period. However, the rate of hydrate formation in the pure water system suddenly increased after 2 h. The relatively long induction time prolonged the time for many CO₂ gas molecules entering the hydrate phase in the pure water system. The rate of hydrate growth depends on heat and mass transfer (Sloan et al., 2007). In the application of low voltages, anions and cations produced by electrolysis reaction and ions (CO₃ ^2-/HCO₃ ⁻) existing in the solution will migrate under the action of electric field force, which promotes the diffusion of CO₂ and strengthens the formation of hydrate. However, when a high voltage (60 V) was applied to the system, the hydrate formation rate was significantly lower than that in other conditions. It may be due to the rising temperature of the system for more Joule heat generating at the higher voltage. Furthermore, the more production of metal cations may enhance the gas–liquid surface tension. Hence, these cause the decrease of gas consumption and hydrate formation rate after the induction period.

The microscopic schematic diagram of CO₂ hydrate formation under the action of CF is shown in Figure 9A. The CO₂ gas molecules were mainly distributed on the gas phase region at time 0. Under the action of stirring and CF, CO₂ molecules gradually dissolved into the liquid phase and reacted with water to generate carbonic acid. Carbonic acid ionized H⁺, HCO₃ ⁻, and CO₃ ^2- ions. The anode electrolysis produced Fe³⁺, and the cathode produced H₂ bubbles and OH⁻ ions. Cations and anions migrated in opposite directions under the action of the electric field. The empty hybrid orbitals of Fe³⁺ formed coordination bonds with water molecules, promoting the ordered arrangement of water molecules. The generation of H₂ bubbles could provide more locations for the nucleation CO₂ hydrate. These all greatly increase the probability of CO₂ hydrate nucleation. Meanwhile, the action of the electric field promotes heat and mass transfer to strengthen the growth of hydrates. However, part of electrical energy will be converted into thermal energy due to the resistors of the system in the application of high voltage. It will have a specific inhibition effect on the growth of hydrate.

The process of CO₂ hydrate formation is shown in Figure 9B. The CO₂ hydrate film firstly formed at the gas–liquid interface, and a small amount of hydrate was adsorbed on the stirring rod under the action of disturbance. Subsequently, the free CO₂ gas in the vapor region and dissolved in water diffused to the hydrate layer, making the hydrate film thicker and thicker. In addition, the cavity in the hydrate film was gradually filled with CO₂ gas, whereas many hydrates formed in the liquid phase region. Last, the CO₂ hydrate distributed in the whole liquid phase zone. In addition to the hydrate formation in the liquid phase zone, the hydrate would form in the gas phase zone along the stirring rod until the whole rod was covered, which was called wall-creeping hydrate growth. The morphology characteristics of CO₂ hydrate could be changed under the effect of CF. Gel-like CO₂ hydrate crystals formed in the liquid phase when a low voltage (0–30 V) was applied. Differently, whisker-like CO₂ hydrate crystals appeared in the liquid phase when the voltage of 60 V was applied. Tiny bubbles suspended in water under the action of mixing and low voltage, and the CO₂ hydrate films gradually formed on the surfaces of these bubbles. During the process of stirring and bubble collision, bubbles could continuously generate and break. The hydrate film shells left by broken bubbles increased continuously, making the liquid phase of the system present milky gel-like shape. However, more Joule heat was produced because of the electrolysis in the application of 60 V voltage, which changes the supercooling degree of the system. At the same time, the generation of a certain amount of iron ions and hydrogen bubbles combining into iron hydroxide precipitation produce strong capillary action in the liquid phase and make the vapor pressure above the water pressure, which provides suitable conditions for the growth of whisker hydrate. However, the adsorption capillary channel is tiny; hence, the formation rate of whisker hydrate is low, which further verifies the previous results.