A Combined Experimental and Computational Study on the Effect of the Reactor Configuration and Operational Procedures on the Formation, Growth and Dissociation of Carbon Dioxide Hydrate

Abstract

Clathrate hydrate-based technologies are considered promising and sustainable alternatives for the effective management of the climate change risks related to emissions of carbon dioxide produced by human activities. This work presents a combined experimental and computational investigation of the effects of the operational procedures and characteristics of the experimental configuration, on the phase diagrams of CO₂-H₂O systems and CO₂ hydrates’ formation, growth and dissociation conditions. The operational modes involved (i) the incremental (step-wise) temperature cycling and (ii) the continuous temperature cycling processes, in the framework of an isochoric pressure search method. Also, two different high-pressure PVT configurations were used, of which one encompassed a stirred tank reactor and the other incorporated an autoclave of constant volume with magnetic agitation. The experimental results implied a dependence of the subcooling degree, (P, T) conditions for hydrate formation and dissociation, and thermal stability of the hydrate phase on the applied temperature cycling mode and the technical features of the utilized PVT configuration. The experimental findings were complemented by a thermodynamic simulation model and other calculation approaches, with the aim to resolve the phase diagrams including the CO₂ dissolution over the entire range of the applied (P, T) conditions.

1. Introduction

Clathrate hydrates (also called gas hydrates) are nonstoichiometric crystalline ice-like substances, consisting of a hydrogen-bonded lattice formed by water molecules (host) and entrapped gas molecules (guest gas), which are not bonded with the lattice. One of the advantages of gas hydrates is the drastic reduction in the volume of the enclathrated gas compared with that in the gaseous phase. Under standard temperature and pressure, the volume of gas stored in 1 m³ of CO₂ hydrate is about 120–160 m³ [1]. The large uptake of CO₂ in clathrate hydrates renders them a promising option for either storing, transportation or even disposing and sequestration.

CO₂ hydrates have been investigated with regard to their formation conditions and potential applications in all large-scale fields of the Carbon Capture and Storage (CCS) system, including (i) the flow assurance and safe CO₂ pipeline transportations [2,3,4,5], (ii) CO₂ storage and separations [6,7,8], including Post-Combustion Capture [9,10], and Pre-Combustion Capture [11,12,13] applications, and (iii) CO₂ sequestration [14,15,16] in deep sea sediments and other subsurface storage sites to mitigate the global warming, as well as in natural gas hydrate reservoirs to facilitate CH₄ extraction and recovery, and to prevent the release of the greenhouse gas to the atmosphere [17,18,19]. Another application of gas hydrate technologies pertains to CO₂-rich natural gas upgrade [20], and biogas upgrade via CO₂-CH₄ separation, which leads to biomethane production [21,22].

Gas hydrate crystals are formed when a gas hydrate former and water are mixed and the temperature and pressure conditions of the system reach the hydrate–water-rich liquid–gas (H-L_w-G) equilibrium curve, where the three phases co-exist. Conversely, gas hydrates decompose when the (P, T) conditions diverge from the (H-L_w-G) phase equilibrium [23]. Hydrate dissociation is an endothermic process in which the hydrogen bonds between the water molecules of the hydrate lattice and the van der Waals interaction between the guest and water molecules of the lattice break to release water and gas. Several experimental methodologies have been used to study the phase behavior and equilibrium of the CO₂-H₂O system, including the formation and dissociation conditions of CO₂ hydrates [23,24,25,26,27]. These conditions are determined either by visual observation using high-pressure optical cells or by monitoring the total pressure of the system as a function of temperature that allows for constructing the (P-T) phase diagrams.

Three static methods were applied to study the gas–liquid–hydrate phase equilibrium and gas hydrate formation kinetics, in particular, the Isothermal Pressure-Search, the Isobaric Temperature-Search, and the Isochoric Pressure-Search methods. The Isochoric Pressure-Search method [27,28,29] allows us to determine the (P-T) phase diagram (phase envelope) of the system, and it is based on conducting a cooling/heating cycle at a constant volume. In this method, the cell volume is kept constant and the temperature undergoes a cyclic alteration procedure consisting of a cooling step, an isothermal step, and a slow incremental heating step, whereas the pressure is monitored constantly. Hydrate formation is initiated under sufficient subcooling, ΔT_sub, which is defined as the difference between the experimental temperature where gas hydrate nucleation takes place, T_exp, and the equilibrium temperature, T_eq, which corresponds to the theoretical (H-L_w-G) equilibrium conditions (T_eq, P_eq), i.e., ΔT_sub, = T_eq − T_exp, where T_exp < T_eq [30,31,32,33,34]. Hydrate crystals’ growth is detected from a sharp pressure drop at a constant temperature. After the completion of hydrates’ formation, the hydrate crystals decompose through step-wise heating. At each isothermal step of the heating process, enough time is provided to the system to establish (H-L_w-G) equilibrium and, thus, to derive a (P_eq, T_eq) curve that passes through consecutive equilibrium points. In the corresponding (P-T) phase diagram, the point where the heating curve joins the cooling curve and the slope of the heating curve changes abruptly is considered the point of complete hydrate dissociation [28]. The dissociation point is often confirmed by visual observation.

An interesting issue related to the experimental techniques that were applied to study the (P, T) formation conditions and kinetics of growth and dissociation of CO₂ hydrates pertains to the effects of the design and technical characteristics of the gas hydrate autoclave and experimental configuration [35,36,37]. The design, geometrical and technical features of the experimental setup utilized, as well as the operational modes, can affect the characteristics of mass and heat transfer. It has been reported that the application of batch stirring can improve the mass transfer and heat transfer performances of the methane hydrate formation process [36]. The use of a stirrer can enhance the mass transfer driving force, which—unless excessive agitation is applied—can promote gas hydrate nucleation and growth, thereby increasing hydrate growth rate. Englezos et al. [38] developed a kinetic model of hydrate formation by assuming that the hydrate formation process is similar to the crystallization process composed of two successive steps with different mass transfer resistances. In the first step, the dissolved guest molecules diffuse from the bulk of the liquid into the liquid water–hydrate interface through the laminar diffusion layer around a particle. The second step consists of adsorption of the guest molecules at the liquid water–hydrate interface, followed by their incorporation and the stabilization of the structured framework of the water/guest gas cages. When the agitation is conducted at a high stirring rate, the mass transfer resistance and heat-transfer resistance around the crystal seed become negligible [38]. Experimental formation data obtained in a semi-batch stirred tank reactor implied that, at a stirring rate of 400 rpm, the mass transfer resistance around the crystal seeds is eliminated, and it is no longer affected by a further increase in the rpm [38]. A stirring rate of 400 rpm was chosen as the most suitable one to avoid extensive rippling on the gas–liquid interface. This stirring rate was also able for continuous removal of the hydrate seeds from the gas–liquid interface to the bulk liquid.

On the other hand, during the growth of gas hydrate crystals, an amount of latent heat of formation is released, which has to be effectively transferred to the cooling bath in order to control the temperature. The heat transfer rate between the hydrate former–liquid system and the cooling medium is affected by the design and technical features of the employed PVT setup, the stirring mode (mechanical agitation or magnetic stirring), the design of the autoclave, the geometry and dimensions of the stirrer, the stirring rate, the contact between the autoclave and the coolant (i.e., direct contact by immersion of the autoclave into a cooling bath or cooling of the cell via coolant circulation through a coil), the coolant circulation rate, and the applied cooling/heating rate determine the heat transfer rate. The mass and heat transfer can affect the phase transitions (and, thus, the obtained phase envelopes) in the hydrate former–liquid system, gas dissolution rate, supersaturation of the aqueous solution, and the hydrate nucleation process, which, in turn, determines the induction period for nucleation. Insufficient heat transfer rates can reduce subcooling, which is a driving force for hydrate formation [36].

The gas hydrate dissociation process essentially involves multiphase heat and mass transfer coupled with intrinsic decomposition kinetics [28]. The hydrate dissociation rate depends on the intrinsic dissociation rate, heat transfer rate, and mass transfer rate [39]. A number of theoretical models have been developed to predict the intrinsic decomposition rate of gas hydrates [40,41,42,43]. On the basis of comparisons with experimental data on gas hydrate dissociation, Hong et al. [44] and Davis et al. [45] developed theoretical models for heat transfer-limited hydrate dissociation, showing that heat transfer plays the dominant role in dissociation rather than intrinsic kinetics.

Therefore, elucidation of the effects of the technical characteristics of the hydrate formation autoclave and PVT configuration on the phase behavior of CO₂-H₂O systems and (P, T) conditions for CO₂ hydrate growth can enable (i) CO₂ hydrates’ growth at a higher temperature (i.e., shorter metastability region/lower subcooling) and (ii) less experimental time due to the shortening of the induction period. Suitable process modes and conditions can enhance the hydrate nucleation kinetics and facilitate the two aforementioned effects. As a result, less energy- and time-consuming processes can be developed without any usage of kinetic promoters. Also, the potential to form CO₂ hydrate slurries with thermal stability up to 4–5 °C in a reproducible manner, by applying processes that are based on efficient operational modes and suitable PVT configurations, is of practical importance.

The data derived from gas hydrate formation experiments can be compared with a suitable Equation of States that calculates the incipient (P, T) conditions for CO₂ hydrate formation (i.e., the conditions at which the first hydrate crystals emerge in the aqueous phase), which coincide with the (P, T) conditions of complete thermal hydrate dissociation. On the other hand, it is interesting to investigate the potential of simple calculation approaches to predict the solubility of CO₂ hydrate even under hydrate formation conditions by elaborating experimental equilibrium data and evaluate their prediction accuracy with accurate yet complex thermodynamic models or gas-hydrate-related calculation models incorporated in commercial simulation software [46,47,48,49,50]. By calculating the CO₂ solubility and CO₂ fugacity in the gas phase at each equilibrium temperature (using an accurate EoS), the CO₂ mole fractions and partitioning of CO₂ among the gas, hydrate, and aqueous phase can be approximated.

The objective of this work was to investigate the effect of (i) the applied experimental procedures, and (ii) the characteristics of two different PVT configurations on the (P, T) conditions of formation and dissociation of CO₂ hydrates, and on the respective phase envelopes. The experimental procedures involved (i) the continuous temperature cycling mode, and (ii) the incremental (step-wise) temperature cycling mode in the framework of the Isochoric Pressure Search method. Both experimental modes proceeded through consecutive stages of initial equilibration, cooling, isothermal cooling, and heating of the studied CO₂-H₂O systems. In addition, two different high-pressure PVT configurations were used, of which one encompassed a stirred tank reactor and the other incorporated an autoclave of constant volume with magnetic agitation. A qualitative interpretation of the observations has been provided with the aim of gaining an insight into the effect of the design and technical features of the two experimental setups on the consecutive steps of hydrates nucleation, crystal growth and thermal decomposition, as well as the form and stability of the hydrate phase. The experimental findings were complemented by two calculation approaches, one of which was a thermodynamic simulation model and the other was a developed semi-empirical calculation method, with the aim of resolving the obtained phase envelopes including CO₂ dissolution and solubility evolution over the entire range of the applied (P, T) conditions.

2. Materials and Methods

2.1. Chemicals

CO₂ gas with a minimum listed purity of 99.998% (SOL) was used in this work. Deionized water was used after being subjected to a thorough degassing procedure.

2.2. Experimental Setups

The phase behavior and gas hydrate formation conditions of the CO₂-H₂O system were studied using two different experimental setups. The first high-pressure PVT apparatus consists of two basic parts, namely, a reactor cell (autoclave) inside an air-bath-thermostated cabinet, and a gas preparation manifold. A detailed description of the PVT apparatus was provided in the work of Kastanidis et al. [51]. The second PVT configuration includes a high-pressure stirred tank reactor immersed in a thermostated bath. The reactor shares the same gas preparation manifold with the first PVT apparatus, the description of which is given below.

2.3. Gas Preparation Manifold

The gas preparation manifold is the system in which CO₂ or any other hydrate former can be stored and delivered to the PVT cell under high pressures. It includes (i) a reservoir vessel with a volume of 24 L and maximum operating pressure of 12 bar, four toggle valves, and one pressure transducer (WICA D-10) for pressures up to 20 bar (with a measurement precision of ±0.02 bar); and (ii) a pneumatic gas booster (JULY GB25) bearing a pilot air valve (Swagelok, Solon, OH, USA), which is used to receive gas from the reservoir vessel, and deliver it to the PVT cell at several target pressures. The gas booster has a pressure multiplying ratio of 20 in relation to the pressure of the pilot air. Evacuation of the reservoir vessel down to a pressure of 10⁻⁸ bar can be attained by means of a turbomolecular pump (Leybold, Cologne, Germany, Turbovac 361 C), assisted by a rotary pump (Leybold, D16B), that is connected to one of the toggle valves. The three additional toggle valves are used for supplying single pure gases into the reservoir vessel and are connected to gas cylinders equipped with pressure regulators.

2.4. Description of the First PVT Apparatus

2.4.1. High-Pressure PVT Cell

The high-pressure PVT cell, which has an internal volume of ~ 325 mL, is constructed from a special alloy (Alloy 20, Mikrotechniki, Athens, Greece). The PVT cell consists of a cup and a container that can be easily separated from each other. The cup is firmly mounted in an air-bath cabinet. Two feed-through connectors, each one bearing a K-type thermocouple with a measurement precision of ±0.1 °C, are mounted on top of the cup. The thermocouples monitor the temperature of the gas and liquid phases inside the container. On top of the cup are also two additional feed-through connectors which allow small quantities to be removed from the gas and liquid phase inside the cell via the respective gas and liquid sampling valves and loops. Also, the top of the cup bears an optical window where an external camera (Supereyes™) is mounted. The camera video-monitors the gas/liquid interface during the experiments, allowing us to optically supervise the entire gas hydrate formation and dissociation processes. The bottom of the PVT cell is in contact with a magnetic agitator with controllable rotation speed, which causes the rotation of a magnetic bar to facilitate the mixing of the components of the liquid phase.

2.4.2. Thermostated Air Cabinet

The PVT cell is housed in an insulated cabinet with air circulation. The temperature in the cabinet is precisely controlled by a PID temperature controller (Jumo dTRON 316) and can be kept constant with an accuracy of ±0.1 °C. The insulated cabinet interior also accommodates a high-pressure transducer (WICA D-10) for pressures in the range of 0–200 bar with a measuring accuracy of ±0.2 bar, and a pressure transducer for the low-pressure range 0–10 bar (WICA D-10) with a measuring accuracy of ±0.01 bar. In addition, the cabinet contains the sampling loops for the gas and liquid phase with precisely defined volumes, and a pressure relief cell for the liquid sampling. All high-pressure (24 MPa) diaphragm valves (Swagelok) are accessible from the front panel of the cabinet. An overview picture of all the equipment located inside the insulated cabinet can be found in the work of Kastanidis et al. [51].

The temperature of the air-bath cabinet interior, as well as of the gas and liquid phases inside the reactor cell, is displayed by three digital indicators/controllers (Jumo) located on the front panel. The panel also contains digital readouts of the three pressure transducers attached to the reactor cell, the pressure relief cell for the liquid phase, and the primary vessel in the gas preparation manifold. A thermal bath with a water/ethylene-glycol mixture as coolant and controlled by an automatic temperature controller (type ECO Silver RE 630S, Lauda) was used to thermostatize the PVT cell with a maximum deviation of ±0.02 °C over the temperature range of our measurements. The coolant from the bath circulates through a thermally insulated cooling coil, which passes though the cabinet interior and is firmly mounted around the PVT cell. Both the coil and the cell are firmly enclosed by an insulating jacket. The coil can be easily removed from the PVT cell whenever its container needs to be removed for cleaning.

2.4.3. Monitoring and Data Acquisition

The readings of the two thermocouples for the gas and liquid phases inside the reactor cell, as well as those of the pressure transducers mounted on the reactor and relief cells, are monitored, saved and acquired in a data acquisition unit using a virtual instrument application (VI) developed in a Labview environment. The communication is performed via an RS232 interface.

2.5. Description of the PVT Configuration Incorporating a Stirred Reactor

2.5.1. Stirred Reactor

A high-pressure stirred tank reactor was used for the experimental investigation of CO₂ hydrates’ formation and (H-L_w-G) equilibrium (Figure 1). The configuration includes a Parr 4561 bench top high-pressure stirred reactor made of T316 stainless steel, equipped with a magnetic drive for internal stirring with controllable speed of the stirrer motor (A1120HC drive model), a Parr stirring control unit (model 4565M), a refrigeration unit, a single-piston sampling cylinder, and a high-pressure automated water pump. The stirred reactor encompasses a bomb cylinder (cell) with an inner free volume of 100 mL and I.D. 2.1 inches, a gas inlet valve, a liquid sampling valve, a gas release valve, a mounted J-type thermocouple (with precision of ±0.3 °C over the range 0–+200 °C), a part of which reaches to the cell interior, a pressure gauge and a burst disc. In all experimental runs, the incoming gas was introduced through the gas inlet valve, which is connected to a tube that reaches below the surface of the liquid and near the bottom of the cell.

The pressure of the gas phase inside the cell is monitored by using an electronic pressure transducer (type PXM4202-6KGI, Omega Engineering Inc., Norwalk, CT, USA) with a measurement precision of 0.1 bar, operation range of 0–6000 psig, and an analog signal output of 4–20 mA, which is mounted on the outlet of the gas release valve. The same automated thermal bath that is connected to the first large PVT apparatus is also used for thermostating the stirred reactor of the second PVT setup. In this case, the small reactor cell is immersed in the bath in direct contact with the coolant.

2.5.2. Data Monitoring and Acquisition System

The temperatures of the refrigeration bath and the reactor cell interior are monitored by using a digital thermometer (type P655 instrument, Dostmann electronic, Wertheim, Germany) encompassing an A/D converter that receives the analog signals from the two J-type thermocouples, one mounted inside the reactor cell (as mentioned in Section 2.5.1), and one partially immersed into the coolant in the refrigeration bath. The signals from the P655 thermometer’s digital output are transmitted to an RS232 interface in a PC. The analog readings from the pressure transducer are transmitted to a BNC-2110 A/D card with 15 BNC connectors for analog and digital I/O signal connections that transmits the digitalized signals to the PC through a PCI card. A VI application in the employed NI Labview (32-bit) software (version 6.1) is used for data logging, storage, and acquisition.

2.6. Water Supply Configuration

A high-pressure continuous-flow, pulse-free pump (VP-6K Ambient pump model, Vindum Engineering Inc., Sandpoint, ID, USA) was used to deliver water into the reactor cell of both PVT setups, with a precisely controllable flow rate and pressure, and accurately monitor the gas phase pressure over the entire course of the experiments via internal pressure transmitters with an accuracy +/−0.1% of full scale. The water amounts were introduced to the reactor cell through the high-pressure single-piston sampling cylinder mentioned in Section 2.5.1 (type ProLight Ti-690 64 MB, Proserv), with inlet and outlet valves, which is connected to the water pump. The cylinder has a total internal volume of 629 mL and a maximum pressure limit of 690 bar. The side of the cylinder that is fixed to the liquid sampling valve of the reactor cell is filled with deionized that was degassed for 5 h under vacuum using a rotary pump and intense magnetic stirring. The pump has a maximum pressure rating of 6500 psi, minimum flow rate of 0.00002 mL/min, pressure resolution 0.1 psi, and flow rate and volume accuracy +/− 0.1% of set point. The pump allows for logging and acquisition of water flow rate and pressure data and, thus, it can be used complementary to the readings from the pressure transducers mounted on the two PVT setups, which are monitored using the employed NI Labview (32-bit) data recording software (version 6.1).

2.7. Experimental Procedure

The Isochoric Pressure-Search method was applied in both PVT configurations to determine the (P, T) conditions for the formation and complete thermal dissociation of gas hydrates, and construct the phase diagrams of the studied CO₂-H₂O systems. At first, the gas primary vessel and PVT apparatus were thoroughly evacuated using a turbomolecular pump (Leybold, Turbovac 361 C) assisted by a rotary pump (Leybold, D16B). CO₂ gas was then loaded into the gas primary vessel up to a pressure of 5 bar. The reactor cell was cleaned with methanol and then repeatedly with deionized water, followed by drying using compressed air. The cell was then tightly sealed and thoroughly evacuated along with the gas feed line to remove the atmospheric gases while pressure and temperature data were recorded. After the evacuation step, the temperature of the thermal bath was set to 23–25 °C and the empty reactor cell of the small PVT setup was immersed in the bath, whereas in the large PVT apparatus, the temperature of the reactor cell was regulated by the coolant circulating through the cooling coil in firm contact with the cell. Subsequently, pure CO₂ was fed into the reactor cell and pressurized to a selected target pressure, at bath temperature, by using the gas booster described in Section 2.3. The (P, T) data were recorded every 30 s, and after remaining stable for 3 h, their average values were considered the feed (P, T) conditions.

Subsequently, a certain volume of deionized and degassed water was loaded into the autoclave through the single-piston cylinder, which was connected to the high-pressure water pump. Upon completion of water addition to the cell, the contained liquid was stirred either by using a magnetic agitator in the large PVT configuration or via the magnetic drive bearing a four-blade impeller when the small PVT setup was used. After charging the required amount of water to the autoclave and setting the stirring rate, the pressure began to decrease (at constant temperature), as a result of gas dissolution in water, until absorption equilibrium was reached, as indicated by the stabilization of the pressure. This way of supplying the gas and water components makes it possible to calculate the exact amount of gas inside the cell by determining the compressibility factor, Z, at the steady feed conditions (P, T) of the hydrate former (whose volume is known), using the Peng–Robinson (P-R) or another Equation of State. In addition, this method allows us to correctly determine the H₂O:CO₂ mole ratio in the cell based on the supplied amounts of CO₂ and water.

Accordingly, each CO₂-H₂O binary system was slowly cooled down to 13.7–13.8 °C and kept under isothermal conditions to establish absorption equilibrium. Then, the system was further cooled to ~0 °C or −1 °C to study CO₂ dissolution and form gas hydrates by applying either an incremental (step-wise, SW) mode (~1 °C temperature drop per reduction step) or a continuous cooling (CC) mode. The system was kept at the lower temperature limit for 24 or 48 h to study hydration and (H-L_w-G) equilibrium. Subsequently, a step-wise or continuous heating stage was conducted to thermally decompose the formed hydrate phase and close the phase envelope. The duration of the individual isothermal steps in the SW cycling mode was not predetermined but varied depending on the time required for the system to reach absorption (at the cooling stage) or desorption equilibrium (on heating) or gas–liquid–hydrate equilibrium.

The applied H₂O:CO₂ mole ratios (denoted hereafter as MR) ranged between 20.48 and 21.91. The loading conditions of the two components, experimental parameters, and employed PVT configuration for all experimental runs are listed in

Table 1. Feed conditions, water amounts, MRs, temperature cycling modes, temperature and duration of the first and second isothermal steps, stirring rates, and employed PVT configuration.

Experiment No.	Feed Pressure (bar)	Water Amount (mL)	H2O:CO2 Mole Ratio (MR) (−)	Stirring Rate (rpm)	Temperature/Duration of First Isothermal Step (°C)/(hours)	Temperature/Duration of Second Isothermal Step (°C)/(hours)	Temperature Alteration Mode/Heating Stage (1)	Inner Total Volume of the PVT Cell (mL)
1	32.09	60	20.48	400	13.90/12	0.25/24	SW/−	100
2	31.40	60	21.37	400	13.96/12	−0.25/24	SW/+	100
3	31.40 (2)	60	21.37 (2)	400	13.65/12	−0.90/24	SW/+	100
4	31.04	195	21.66	400	16.80/12	−0.32/24	SW/+	325
5	31.39	60	21.67	900	14.01/12	0.17/24	SW/+	100
6	31.36	195	21.91	400	13.82/12	2.17/24	SW/+	325
7	33.14	60	20.09	400	12/2	0.1/24	CM/+	100
8	32.99 (3)	60	20.21 (3)	400	12/2	0.1/24	CM/+	100
9	32.75	60	20.28	400	12/2	0.1/48	CM/+	100
10	32.99 (4)	60	20.21 (4)	400	12/2	0.1/24	CM/+	100

⁽¹⁾ SW: step-wise cooling–heating mode; CM: continuous cooling–heating mode; (+): heating stage included, (−): without heating stage. ⁽²⁾ Experiment No. 3 was a repetition of the experiment No. 2, which commenced once the system’s temperature at the heating stage reached 13.65 °C, without removal of the CO₂ and H₂O components from the cell. ⁽³⁾ In the experiments No. 8 and 9, perforated plates and spacers were fixed along the rotation axis of the magnetic drive. ⁽⁴⁾ Experiment No. 10 was a repetition of the experiment No. 8, which commenced once the system’s temperature at the heating stage reached room temperature, without removal of the CO₂ and H₂O components from the cell. An equilibration step of the system at room temperature for 48 h was performed prior to the commencement of the cooling stage.

.

3. Results

3.1. Experimental Pressure vs. Temperature Phase Diagrams

3.1.1. Experimental Runs Performed in Continuous Temperature Cycling Mode

The (P, T) phase diagrams derived from the experiments conducted in the continuous temperature cycling mode are presented in Figure 2. The steep and drastic pressure drop steps during the cooling stage, which imply the extensive formation of CO₂ hydrates, were affected by the cooling rate and the presence of perforated plates on the rotation axis of the magnetic drive, as regards (i) the onset temperature of each abrupt pressure reduction step, and (ii) the pressure reduction profile that led to the final (P_eq, T_eq) conditions of the (H-L_w-G) equilibrium. The pressure reduction reached the same equilibrium pressure (12.07, 12.13, and 12.58 bar) at the lowest applied temperature limit of 0.02, 0.07, and 0.24 °C, (i.e., the same (P_eq, T_eq) equilibrium point, as is also shown in Figure S1). The equilibrium pressures were close to the P_eq values at similar temperatures as those referred to in the literature (P_eq = 12.7 bar at 0.35 °C [52]; P_eq = 13.8 bar at 0.7 °C [23]).

It is worth mentioning that the faster applied cooling rate (1 °C/2 h) significantly reduced the subcooling and induction periods of the CO₂ hydrate nucleation phase, thereby accelerating the initiation of the subsequent stage of hydrate crystals’ growth. The latter stage is related to the extensive absorption and transfer of CO₂ from the gas phase to the hydrate crystals, which accounted for the observed drastic pressure reduction.

In addition, a similar (P-T) phase diagram was obtained from a repetition experiment, when upon completion of the experiment with MR_20.21, the same CO₂-H₂O system was initially equilibrated at room temperature for 48 h and was then subjected to the same continuous temperature cycling process with the same cooling–heating rate of 1 °C/2 h. The (P-T) phase diagrams of the two experiments are compared in Figure S2. The small difference in the initial pressure between these two runs is due to CO₂ absorption during the initial equilibration step in the repetition experiment. As can be observed, the usage of perforated plates facilitated the formation and growth of hydrate crystals since the surface area of these plates provided an additional large number of nucleation sites and, thus, it served as a kinetic promoter by reducing the induction time of the nucleation phase, which leads to hydrate crystals’ growth.

Regarding the heating curves, in all experiments, the pressure increased as soon as the heating stage commenced and kept increasing smoothly up to the point where the heating curves joined the respective cooling curves. The evolution of pressure with raising temperature was common for the three runs. The observed pressure evolution might be indicative of a heat-sensitive hydrate phase, which consists of isolated hydrate crystals dispersed within the bulk aqueous liquid, the external layers of which are gradually decomposed with increasing temperature. This dissociation releases CO₂ molecules into the aqueous liquid in a continuous but not abrupt manner, which are subsequently desorbed into the gas phase. Furthermore, the temperature at which the heating curves (showing hydrate thermal dissociation) and cooling curves joined ranged between 8.15 and 8.45 °C.

3.1.2. Experimental Runs Performed in Incremental Temperature Cycling Mode

The pressure and temperature data acquired during the cooling, isothermal and heating stages from the runs performed with the studied CO₂-H₂O systems via the SW-mode were used to identify the (P, T) conditions to reach (H-L_w-G) equilibrium and construct the phase envelope of the respective systems. The (P, T) phase diagrams are presented in Figure 3, whereas Figure 4 depicts the experimental (P, T) points at equilibrium conditions (either (L_w-G) or (H-L_w-G) equilibrium). In Figure 4, the respective phase envelopes were formed from the equilibrium data acquired at the cooling and heating stage of each run. The SW-mode experiments were conducted using feed H₂O:CO₂ mole ratios within the range of 20.48–21.91.

Regarding the stirred tank reactor, with the exception of one experiment performed with MR_21.37, in the other three runs, no hydrate formation took place at all during the entire cooling period, as observed in Figure 3a and Figure 4a. In these three runs, the CO₂-H₂O system at the cooling stage did not undergo any transition from a two-phase (L_w-G) to a three-phase (H-L_w-G) system, even though (P, T) conditions were applied at which this phase transition should have taken place. On the contrary, regarding the runs performed in the large PVT apparatus, the application of similar H₂O:CO₂ feed mole ratios allowed for CO₂ hydrate formation, as observed in Figure 4b. The formation and growth of gas hydrates was deduced by the steep and drastic pressure reduction at the cooling stage. CO₂ hydrate crystals exhibit substantially higher capacity for CO₂ absorption compared to liquid water.

It is known that the formation of CO₂ hydrates is a two-phase process that includes (i) the formation of fine nuclei consisting of CO₂ molecules enclathrated within ice-like crystalline lattices (crystal seeds), which grow in size via clustering; and (ii) the growth of bulky hydrate crystals [53]. The duration of the hydrate nuclei formation phase (nucleation phase) is defined as the induction period. During this period, the aqueous phase becomes increasingly supersaturated with CO₂. The nucleation phase is ended by the formation of stable hydrate nuclei clusters of critical size. As soon as the growing nuclei exceed the critical size, they begin to grow spontaneously (in size and number) as bulky hydrate crystals, and, in this way, the crystal growth phase commences. The greater the subcooling and supersaturation, the greater the driving force for hydrate nucleation and the rate of hydrate crystal growth.

The situation where only the gas and aqueous phase coexist under hydrate formation conditions corresponds to a metastable equilibrium between the gas phase and a super-saturated aqueous liquid, which contains a large population of dispersed hydrate nuclei. According to microsecond molecular dynamics simulations performed by He et al. [54], nucleation is closely related to the CO₂ hydration shells (HS) in water, in particular, to the transformation of a CO₂ HS into an incipient hydrate 4¹5¹⁰6² cage, which is rather amorphous due to its metastable structure. It was also found that high CO₂ concentrations in the aqueous solution are required for adsorption of sufficient numbers of CO₂ molecules onto the hydration shells to effectively stabilize the developed hydrogen bonds and facilitate the transformation of the hydration shells into incipient gas hydrate cages with a size similar to that of the CO₂ hydration shell.

In contrast to the solubility, which has a saturation limit, the metastability is not thermodynamically stable and depends on process parameters such as impurities, cooling rate, agitation characteristics, and time. Gets et al. [55] conducted a molecular dynamics study on the process of hydrate formation in supersaturated solutions, and showed that a steady growth occurs at CO₂ concentrations of 4.94–12.20 mol%. At lower concentrations, there are no significant changes in the structure of the solution over the considered time interval. At higher concentrations of CO₂, the hydrate growth is accelerated up to a critical value, after which separation into the gas phase and saturated solution is observed. Metastability is associated with a supercooled liquid where the hydrate nuclei aggregation/clustering process, which normally leads to hydrate clusters of critical size necessary for crystal growth, is prohibited. This may lead to a relatively long induction period and increased supersaturation of the aqueous phase. As a result of excessive obstruction, supersaturation may be inadequate to rapture metastability and enable the gas–liquid system to undergo the phase transition related to the commencement of growth of stable hydrate crystals, even if a large concentration of hydrate nuclei is contained in the supersaturated solution. This phenomenon seems to be a reasonable assumption to explain the absence of any macroscopically observed hydrate formation throughout the entire cooling stage for the experiments with H₂O:CO₂ mole ratios of 20.48, 21.37 (repeat run), and 21.67. Hence, it is important to elucidate the impact of the applied experimental procedures and the technical characteristics of the two experimental setups, on the (P, T) phase diagrams and phase transitions related to gas hydrate formation in the studied CO₂-H₂O systems.

Both temperature cycling processes (by SW or continuous temperature cycling) enable the monitoring of hydrate formation temperatures. The application of the SW-mode that proceeds though consecutive isothermal equilibrium steps of gas dissolution, hydrate formation, and hydrate dissociation/gas desorption results in prolonged processes, which can assist the stabilization of the hydrate phase depending on the agitation conditions.

Application of intense agitation during the cooling stage will increase the gas dissolution rate along with the rate of CO₂ hydrate nuclei formation within the bulk liquid and on the gas/liquid interface, and renew the gas–liquid interface more efficiently. However, the application of large mass fluxes, as in the case of a tank reactor bearing an impeller for stirring, can deteriorate hydrate phase stability, as the intense shear does not favor aggregation of the hydrate nuclei. Excessive agitation and shear, especially for quite long periods, would destabilize and decompose the hydrate nuclei clusters, thereby hindering their aggregation and formation of stable clusters of critical size, capable of initiation of crystal growth. As a consequence, the subcooling degree and the nucleation induction time will increase and the gas/liquid system may even become unable to undergo the phase transformation needed to establish (H-L_w-G) equilibrium. The hindrance of the hydrate nuclei clustering is possibly the reason for the lack of a CO₂ hydrate phase for the experiments with MR_20.48, MR_21.37 (repetition experiment), and MR_21.67. For the run with MR_21.37, the conditions at which (H-L_w-G) equilibrium was established were identified at (i) T = 0.46 °C and P = 12.83 bar, (ii) T = −0.25 °C and P = 12.4 bar.

Heat transfer plays a critical role, as the heat released during crystal growth should be swiftly removed from both the bulk liquid and the interface between dissolved guest molecules and individual crystal lattices. Presumably, application of the continuous temperature cycling mode allowed for better heat removal efficiency, even when applying a slow temperature ramp of 1 °C/4 h. This enabled stabilization of the hydrate clustering process, under the same agitation method (including the stirring rate) as those in the SW cycling mode. Stabilization of the hydrate nuclei clustering process was further facilitated when a larger cooling rate was applied, i.e., 2 °C/2 h, as indicated by the shortening of the metastable zone width (see Figure 2).

For the runs with a H₂O:CO₂ mole ratio of 21.66 and 21.91, the pressure drop became rapid and prominent below ~3 °C. As observed in the phase envelopes of the experiments with MR_21.37, MR_21.66 and MR_21.91 (Figure 3a,b), the temperature difference between the point of complete hydrate decomposition and the onset of hydrate crystal growth (i.e., the degree of subcooling) is either moderate, as in the two latter runs (ΔΤ_sub = 2.74 °C and 4.18 °C, respectively), or high, as in the experiment with MR_21.37 (ΔΤ_sub = 6.74 °C). The onset temperature of hydrate crystals’ growth (i.e., rapture of metastability) was taken as the temperature of the sudden heat release (temperature jump).

Further evidence for gas hydrate formation is provided by the first derivative of pressure with respect to temperature (dP/dT) vs. temperature curves at the SW cooling stage, as shown in Figure S3. In the case of the experiments with MR_21.37 and MR_21.91, an intense maximum is observed at 0.46 and 2.17 °C, respectively, which starts to emerge at 1.34 and 4.29 °C. Another important finding is the different profiles of the heating curves obtained from the two PVT configurations. This dissimilarity could arise from the different internal design and liquid agitation mode of the crystallization autoclaves, which affect the mass and heat transfer rates (lower temperature reduction rate in the large PVT autoclave compared to the cell of the stirred reactor, for the same cooling rate), as will be discussed later. It can be deduced that the milder agitation and less shear applied in the large PVT autoclave for the same stirring rate, compared to the stirred tank reactor, enables formation and growth of a thermally stable hydrate phase, even when the SW temperature cycling is applied, and despite the slower heat removal from the studied systems during the cooling stage. The profiles of the heating curve in both phase envelopes in Figure 4b, reveal the thermal stability of the formed hydrate phase in contrast to that of the CO₂ hydrates produced in the stirred tank reactor by applying both SW and continuous temperature cycling. This difference in the heating curve profiles may reflect differences in the mechanism of hydrate crystal growth. It can be suggested that the thermal stability of the hydrate phase depends on the capability for growth of a stable thick hydrate layer on the interface, which in turn is largely affected by the mass transfer and shear. This means that the thermal stability of the hydrate phase is determined by the type and geometry of the stirrer and the agitation intensity and not that much by the cycling mode. The two applied temperature cycling modes tended to exhibit different CO₂ hydrate stability and formation capability when intense agitation was applied.

3.2. Correlation of the Pressure Evolution during the Cooling Stage with Crystallization Effects

Several kinetic models have employed a driving force as key component for both of the two crystallization steps. Since the fugacity of a hydrate former such as CO₂, at (H-L_w-G) equilibrium conditions represents the minimum fugacity at which hydrates of this particular gas can exist, Englezos et al. [38,56] proposed in their hydrate growth model, that the difference between the fugacity of the gas, f_g, and the three-phase equilibrium fugacity, f_eq, at the same temperature (overpressurizing level), namely Δf = f_g − f_eq, can be regarded as the overall driving force for the hydrate growth process. On the other hand, several optical microscopy studies have revealed that the growth rate of the hydrate film depended on the system subcooling ΔT_sub [30,31,32,33]. The greater the subcooling, the greater the driving force for spontaneous hydrate crystals formation, and the larger the hydrate growth rate and related pressure reduction rate.

The effect of the subcooling degree on the extent and rate of CO₂ hydrate growth and associated pressure drop, can be assessed by the phase envelopes of the runs with MR_21.37, MR_21.66, and MR_21.91. Since the three experiments were performed using the same stirring rate (400 rpm) and at nearly the same initial pressure (31.04–31.40 bar, see Table 1), the sharper pressure reduction that occurred in the first run can be associated with the greater subcooling and induction time. Similar findings regarding the effect of subcooling on the hydrate growth rate have been reported in the literature, although cases with large variability in induction times within a single experimental setup have also been reported [57,58].

On the other hand, the larger induction time and subcooling can be attributed to the intense shear or turbulence imposed in the aqueous liquid by the rotation of the impeller, that could mechanically extort CO₂ molecules for the hydrate nuclei dispersed in the liquid phase, especially when prolonged cooling stages are applied. This would prevent the formation of stable hydrate nuclei clusters of critical size, until the driving force for this clustering at a sufficiently low temperature, eventually overcomes the mass transfer limitation. It is noted that for all runs performed in the stirred tank reactor by applying the SW mode, the experiment with MR_21.37 was the only case where a CO₂ hydrate phase was formed. This is indicative of the hindering effect of the excessive shear/turbulence, and prolonged process time, in the capability of CO₂-H₂O systems to undergo the phase transition that will lead to the formation of a gas hydrate phase, despite the higher heat flux.

In the two latter runs that were performed in the large PVT setup, the pressure reduction became sharp below ~3 °C (for MR_21.91) or ~4 °C (for MR_21.66). It is likely that the moderate mass transfer imposed by magnetic stirring did not hinder aggregation of hydrate nuclei dispersed in the aqueous liquid—this aggregation is an essential process for hydrate crystal growth—since no excessive shear and turbulence conditions were applied in the liquid to destabilize clustering of hydrate nuclei. This would result in the observed lowering of the subcooling degree compared to the high ΔT_sub that was observed when the stirred tank reactor was used (experiment with MR_21.37).

Besides the abrupt pressure reduction in the experiments with MR_21.66 and MR_21.91, a rapid switching in the appearance of the aqueous phase was observed, from a lucid solution to an opaque one. The surface of the stirred liquid became essentially opaque to optical observation by the mounted camera (rather suddenly) once the autoclave was cooled below nearly 3 °C, indicating the formation of a non-transparent hydrate layer. Several optical microscopy studies have revealed that during the hydrate crystals’ growth phase, a CO₂ hydrate film can be formed and expand laterally along the gas/liquid interface [59]. The lateral growth rate of this hydrate film also depends on the system’s subcooling ΔT_sub.

Prior to the sharp pressure reduction that occurred at the cooling stage for the runs with MR_21.37, MR_21.66, and MR_21.91, an instantaneous increase (jump) of the liquid’s temperature was observed, which coincided with the onset of the drastic pressure drop. Natarajan et al. [60] reported a slight but detectable rise in the aqueous solution’s temperature at the turbidity point because of the heat released by the sudden formation of stable hydrate nuclei. The sudden increase in temperature [61] can be attributed to the rapid initiation of growth of stable hydrate crystals, which is an exothermic process. In fact, the temperature jump was more pronounced when it took place at a lower temperature and, thus, at a greater subcooling degree, possibly due to the larger population of critical hydrate nuclei clusters in the supersaturated aqueous phase, which would cause rapid hydrate crystals’ growth and an abrupt release of larger amounts of hydration heat during the growth phase. Although the excessive agitation in the stirred tank reactor and the direct contact of the reactor with the coolant resulted in enhanced heat transfer rates that maintain constant temperature, the release of substantial amounts of hydration heat can impose a temporary increase in both temperature and pressure inside the reactor, thereby introducing a negative effect, as can be observed in Figure 3a.

3.3. Thermal Dissociation of the Hydrate Phase

The thermal dissociation stage of the hydrate phase was studied with regard to the evolution of the gas pressure with increasing temperature. In the experiments where the system established (H-L_w-G) equilibrium (i.e., those with MR_21.37, MR_21.66 and MR_21.91), the pressure exhibited two different behaviors. In the run with MR_21.37, the pressure did not change up to 0.8 °C, whereas in the other two experiments it remained either constant or even further decreased as the system was heated from the lower temperature limit up to ~4 °C, thereby demonstrating the thermal stability of the CO₂ hydrate phase up to this threshold. However, it is likely that the stability of the pressure over this temperature range is due to the growth of a thick dense hydrate layer on the gas/liquid interface rather than to a slow heat transfer and dissociation rate of large CO₂ hydrate crystals dispersed in the bulk liquid. This hydrate layer acted as a practically impermeable cap separating the gaseous from the aqueous phase, thus preventing the desorption of released CO₂ molecules from decomposed hydrate crystals below the solid layer/liquid interface towards the gas phase. Once the temperature exceeded 4 °C, the gradual decomposition and pore opening of the hydrate barrier layer enabled the release of considerable amounts of CO₂ into the gas phase and this decomposition–desorption process continued up to 8 °C.

The prominent first derivative dP/dT peak at 4.58 °C for the experiment with MR_21.91 (7.09 bar/°C), which implies the considerable release of CO₂ amounts into the gas phase (which started between 3.76 and 4.36 °C), is indicative of the dense hydrate cap assumption. At the temperature of ~8 °C, the phase envelopes closed, similar to what was observed in the experiment with MR_21.37. For all three experiments, the “hydrate decomposition point” at which the thermal decomposition curve joins the cooling curve was reproducible to within 0.37 °C (8.08 °C for the MR_21.37, 8.41 °C for the MR_21.66, and 8.04 °C for the MR_21.91).

3.4. Phase Transformations and Equilibrium at CO₂ Hydrate Formation Conditions

As mentioned previously, during the crystal growth phase, a rapid decline in pressure occurs owing to the extensive CO₂ absorption by the hydrate phase. The spontaneous growth of hydrate crystals leads to the formation of a thin hydrate film that propagates along the gas/liquid interface. Eventually the hydrate film covers the entire interface, and then it grows in thickness into the aqueous phase-side. It has been reported that the size of the hydrate crystals decreases and the lateral film growth rate increases with greater supercooling [57,58]. An explanation for the effect of supercooling on the lateral growth rate of the hydrate films along gas/water interfaces has been provided in the literature by a film growth model involving convective transfer of the heat of hydrate formation from the edge of the film to the surrounding phases [62].

There are two sources of CO₂ molecules that contribute to the lateral growth and thickness of a gas hydrate film; these are the gas phase and the bulk aqueous phase. Mori et al. [63] and Sugaya et al. [64] considered the hydrate film to be a thin water-permeable hydrophilic crystalline plate with numerous microperforations which are much larger than the molecular dimensions of the hydrate formers and water. In each microperforation, liquid water diffuses continuously by capillary forces toward the gas phase-side surface of the hydrate layer, resulting in successive formation of hydrate crystals on this surface and, therefore, in the thickening of the hydrate film [65]. At the same time, the opposite surface of the hydrate film is eroded as a result of the dissociation of the hydrate crystals exposed to the bulk aqueous phase. Dissociation is enhanced with increasing rate of diffusive or convective removal of the gas molecules from the aqueous phase-side of the hydrate layer, which is inherently dependent on the flow of water relative to the film. The film thickness is inversely proportional to the mass transfer coefficient on the aqueous phase-side of the film [66].

In contrast, at low subcooling and low supersaturation levels, the population of hydrate nuclei is lower, and the lateral growth rate of the hydrate layer is controlled by the growth rate of a single crystal. As a result, the hydrate film surface becomes rougher and the lateral growth proceeds at a lower rate [67,68]. The lower lateral growth rate of the hydrate layer provides the crystals in the film front with sufficient time to grow to 3D dimensions, which leads to the formation of a thicker and coarser hydrate film. The wider inter-crystalline gaps (film capillaries), in conjunction with the coarser internal texture (which provides larger hydrophilic surface area), favor the transfer of water and CO₂ molecules from the gas phase, which come into contact on the pore mouths. Eventually, if the temperature becomes quite low, the width of pores may substantially decrease, and then the hydrate film will become practically impermeable to gas permeation. In this case, the hydrate film will separate the two fluid phases from each other and as a result, the pressure decrease will cease and the system will reach a steady state, which, however, is not identical to the actual (H-L_w-G) equilibrium.

Indeed, if the phase diagrams of the experiments with MR_21.37, MR_20.09 (stirred tank reactor, Figure 3a and Figure 4) and MR_21.66, MR_21.91 (large PVT setup, Figure 3b) are compared, it can be deduced that the larger mass transfer and shear, established in the mechanically agitated tank reactor, prevented the formation of a mechanically and thermally stable hydrate layer. Since a dense hydrate layer could hardly appear on the gas/liquid interface under such conditions, the bulk liquid was accessible to CO₂ dissolution from the gas phase until (H-L_w-G) equilibrium was eventually established and the pressure drop ceased, as observed in Figure 4a. This was also the reason for the larger reduction in the normalized pressure, as seen in Figure S3a. The structural instability of the CO₂ hydrate layer could account for the fact that it started decomposing gradually almost as soon as the temperature of the system was raised (MR_21.37).

On the other hand, in the case of the large autoclave, the moderate magnetic stirring resulted in slower mass transfer between the hydrate crystals and the surrounding fluid liquid. Thus, destabilization of the hydrate nuclei clusters was prevented, and enough time was provided to the individual clusters to continue enclathrating CO₂ molecules and grow in dimensions up to a critical size. Such operational conditions tended to induce a shortening of induction period and produce a thicker hydrate layer with low porosity on the gas/liquid interface, which acted like an impermeable cap, separating the gas phase from the bulk liquid phase [66,67,68]. As a result, the system reached a steady state that was far from the theoretical (H-L_w-G) equilibrium. This case is different from what was observed in the run with MR_21.37, during which, once the rapid consumption of CO₂ was completed and the pressure reached a constant limiting value, the system reached the (P, T) conditions for (H-L_w-G) equilibrium.

3.5. Comparison between Experimental and Computational Results on the Phase Behavior of the Studied CO₂-H₂O Systems

3.5.1. Computational Results on the Incipient Conditions for CO₂ Hydrate Formation

In addition to the experimental investigation of the phase behavior and hydrate formation conditions, a commercial thermodynamic software (Multiflash v.6.1) was used to computationally determine the incipient pressure for CO₂ hydrate formation, P_inc, and CO₂ solubility in the aqueous phase, at each equilibrium temperature, T_eq, for all experiments. The simulation model used for these calculations was the CPA Infochem Equation of State, which is available in the simulation software. Figure 5 depicts a collocation of the experimental (P_eq, T_eq) equilibrium curves for the cooling stage with the (P_inc, T_eq) curves that were calculated by applying the CPA Infochem model and for the same equilibrium temperatures.

According to the simulation results presented in Figure 5, there is a temperature threshold at which the experimental equilibrium (P_eq, T_eq) curve for each run intersects with the respective calculated (P_inc, T_eq) curve, below which the experimental pressures exceed the predicted incipient pressure at any equilibrium temperature, T_eq. This intersection point is detected at a different temperature depending on the applied H₂O:CO₂ mole ratio. For all experiments, the intersection point ranges between ~7.9 and 8.38 °C and, thus, it coincides to the “hydrate decomposition point” of the respective phase envelopes. The computational results in the case of the run with MR_21.37 also showed two more intersection points at the experimental conditions where (H-L_w-G) was established (see Section 3.1.2).

At the experimental pressures above the calculated incipient ones (at the same temperatures), the studied CO₂-H₂O systems are two-phase gas hydrate–water-rich liquid (H-L_w) systems, and, thus, the gas phase should have been completely depleted and CO₂ would only be distributed between the hydrate phase and the aqueous liquid. The conditions for (H-L_w-G) equilibrium in CO₂-H₂O systems with H₂O:CO₂ mole ratios of 20:1, 30:1, and 40:1 were determined by applying the CPA Infochem model, and the calculation results are shown in Figure S4. The temperature range in which (H-L_w-G) equilibrium can be attained varies from 271.81 to 283.31 K for the MR_20:1 and MR_30:1, and from 271.81 to 280.37 K for the MR_40:1. Figures S5–S7 in the Supplementary Materials present the density and volume values of the aqueous phase, as well as the change in volume (%) of the aqueous phase, at the (P_eq, T_eq) equilibrium conditions of the experiments, which were calculated using the CPA Infochem model.

3.5.2. CO₂ Solubility Calculations

CO₂ solubility in the aqueous phase at the applied (P_eq, T_eq) equilibrium conditions was calculated using three approaches: (i) calculation of the Henry coefficient for all equilibrium temperatures by a fitting equation, which was derived from an extended database of experimental measurements of CO₂ solubility in water, combined with the calculation of CO₂ fugacity at absorption equilibrium using the Peng–Robinson EoS, (ii) the CPA Infochem model of the Multiflash v.6.1 software, and (iii) the simple subtraction of the CO₂ amount in the gas phase—at each phase equilibrium point (P_eq, T_eq)—from the initial CO₂ amount supplied in the autoclave at the feed conditions, using the Peng–Robinson EoS. The CO₂ solubility values calculated by the three aforementioned approaches were compared regarding their mutual deviations and with respect to their temperature dependence over the entire cooling stage (including superaturation conditions), and at the (H-L_w-G) equilibrium stage. The evolution of CO₂ solubility in the aqueous phase with decreasing temperature in the presence of hydrates was resolved, and the results of the three calculation approaches will be discussed.

Henry Coefficients at the Equilibrium Temperatures

Carroll et al. [69] performed a thorough review of the research literature on CO₂ dissolution in water and found approximately 80 experimental studies that reported dissolution equilibrium data for pressures lower than 10 bar. The authors developed a model based on Henry’s law and the experimental solubility data derived from the literature to calculate Henry’s coefficient values, and allowed for the data to be compared and correlated. The developed model related the calculated Henry’s coefficients (expressed in terms of mole fraction) as a function of absolute temperature, as follows:

$$ln{H}_{21}=-6.8346+1.2817\times {10}^4/T-3.7668\times {10}^6/T^2+2.997\times {10}^8/T^3,$$

(1)

where H₂₁ is the Henry coefficient of the system H₂O (solvent, component 1)–CO₂ (solute, component 2), in MPa/(mole fraction) and T is the absolute temperature. This correlation was found to be valid for the temperature range between 0 and 160 °C. The Henry coefficients at any experimental temperature can be calculated by applying the fitting equation.

The maximum total pressure where the experimental data from the literature were taken into account to produce the above fitting equation was limited to about 10 bar because this model ignores the deviation from the ideal behavior of the liquid phase, which starts to become significant at pressures greater than 10 bar. At higher pressures, the solubility of CO₂ increases to the point where the activity coefficients can no longer be ignored. Also, at pressures above 10 bar, the Poynting correction (the effect of pressure on the reference volatility) becomes significant. The error resulting from neglecting the Poynting factor at a pressure of 10 bar was estimated to be about 1%. For a gas–liquid solvent system and a given temperature, the Henry coefficient expresses the solubility of the gas and is defined by the following relationship:

$$H_{21}=\underset{x_i\to 0}{\lim }{\displaystyle \frac{y_i{f}_i}{x_i}}=\underset{x_i\to 0}{\lim }{\displaystyle \frac{y_i{\widehat{\phi }}_{i}P}{x_i}},$$

(2)

where x_i is the mole fraction of gas component i in the liquid phase, y_i is the mole fraction of gaseous component i in the gas phase, f_i is the fugacity of component i in the gas phase, φ_i is the fugacity coefficient of component i in the gas phase, and P is the total pressure. The product y_i·P is the partial pressure (p_i) of component i (in this case, CO₂) in the gas phase, x_i = x_CO2,aq, and y_i·f_i = φ_i·p_i. It is mentioned that in order for the calculated Henry constants to be valid, the mole fraction of the dissolved gas must be quite small (normally x_CO2,aq → 0 and φ → 1).

Subsequently, the CO₂ solubility curves, which are calculated by applying the fitting Equation (1) coupled with the Peng–Robinson EoS for CO₂, and the Henry coefficient equation, that is H₂₁ = φ_CO2·p_CO2/x_CO2,aq, can be compared with the simulation results for CO₂ solubility in water at various (P, T) conditions. In particular, the equilibrium (P, T) conditions of the experimental runs will be the selected parameters for comparison purposes.

Figure 6a depicts the effect of temperature on CO₂ solubility. The CO₂ mole fractions in the liquid were calculated using the fitting Equation (1) to determine the Henry constant for each temperature and the Peng–Robinson EoS to calculate the fugacity at the respective experimental equilibrium pressures. Since the fitting Equation (1) was produced by collecting a large number of CO₂ solubility data published in the literature, the two calculation models (CPA Infochem and P-R EoS) can be indirectly validated with regard to their agreement with the experimental results for CO₂ absorption in water reported in the literature.

Calculation of CO₂ Dissolution in Water Using the Simulation Model and Comparison with the Calculation Results Derived from the Fitting Equation-Based Approach

Figure 6b presents the CO₂ solubility, calculated by applying the CPA Infochem model, as a function of temperature, for all applied MRs. The simulation model calculates the amount (in moles) and the mole fraction of CO₂ in any phase in equilibrium. Figure S8 presents the deviations in the calculated values of CO₂ solubility in water as a function of temperature between the CPA Infochem EoS and the H₂₁ vs. T fitting Equation (1). The deviations are given as a mean absolute percentage deviation (MAPD). A reasonable agreement between the fitting Equation (1) and the thermodynamic model, especially at the higher equilibrium temperatures, can be deduced. A small deviation of the calculated results between the two approaches emerges at the lower temperature regime. Therefore, the simple calculation approach that is based on the fitting Equation (1) can be useful for simple and rough predictions of the CO₂ solubility in CO₂-H₂O systems (and mass balances as well), even under gas hydrate formation conditions. The usage of a more complex EoS will add complexity to this approach without significantly enhancing the accuracy.

Furthermore, in the experiment with MR_21.37, the CO₂ amount (moles) that remained in the gas phase at 0.46 °C, calculated by using the CPA Infochem EoS, reached 16.1% of its initial amount at the feed. At the lowest temperature of −0.25 °C, the respective CO₂ amount was slightly reduced to 15.65%. It is worth mentioning that these two equilibrium temperatures correspond to (H-L_w-G) equilibrium conditions, as mentioned in Section 3.1.2. In the experiment with MR_21.66, the remaining CO₂ amount in the gas phase at −0.32 °C reached 27.41% of its initial amount at the feed, even though the initial gas pressures in these two runs were almost equal (31.4 and 31.04 bara, respectively; see Table 1). The difference in the remaining CO₂ amount in the gas phase between these two experiments can be attributed to the assumption of the growth of an impermeable hydrate layer on the gas–liquid interface and the subsequent establishment of a steady-state condition in the experiment with MR_21.66, which prevented the CO₂-H₂O system from reaching the actual (H-L_w-G) phase equilibrium.

Calculation of CO₂ Dissolution in Water Using the Peng–Robinson EoS

The CO₂ solubility values that were calculated using the approaches described above (i.e., H₂₁ vs. T fitting equation, CPA Infochem model, and P-R EoS), as a function of temperature, are presented in Figure 7. The calculation results presented refer to both PVT configurations. In almost all cases, the CO₂ solubilities calculated by using the P-R EoS clearly diverge from the results obtained from the other two calculation approaches, especially under the conditions at which the formation of hydrates occurred.

Furthermore, the results reveal a decline in CO₂ solubility in the presence of the hydrate phase as the temperature decreased. This reduction was more pronounced in the experiment with MR_21.37 that exhibited the greater supercooling degree (minimum x_CO2,aq~0.015) and the sharpest and most pronounced pressure drop. The decline in the CO₂ mole fraction in the aqueous phase is a result of the enclathration of large amounts of gas at the expense of the gas dissolved in the super-saturated aqueous liquid. The decrease in CO₂ solubility with decreasing temperature over the hydrate formation region has been previously reported by other research groups [24,70].

4. Conclusions

In this work, the phase behavior, and gas hydrates’ formation and dissociation conditions of CO₂-H₂O systems were experimentally investigated with respect to (i) the applied temperature cycling procedures and (iii) the characteristics of the experimental PVT configuration. The operational procedures involved (i) the incremental temperature cycling mode and (ii) the continuous temperature cycling process, in the framework of the Isochoric Pressure-Search method. The (P, T) conditions required to reach the (H-L_w-G) equilibrium depend on the temperature cycling mode applied, as well as on the design and technical characteristics of the reactor cell. The incremental temperature cycling mode imposes longer induction times and higher subcooling when the experiments are performed using the agitated tank reactor compared to the magnetically stirred autoclave.

Qualitative considerations on the subcooling, induction time, and thermal stability of the developed hydrate phases allowed us to gain an insight into the effect of the technical parameters of the two PVT setups (i.e., agitation method, internal design, mass and heat transfer coefficients, shear, perforated plates), on the growth rate thickness, and the porosity of the hydrate layer on the gas–liquid interface. A thin permeable hydrate layer will allow the system to reach actual (H-L_w-G) equilibrium, whereas a thick dense layer with low porosity may act as an impermeable barrier separating the two fluid phases from each other. As a result, the system may eventually reach a steady state where the gas phase is isolated from the aqueous/hydrate phase, which is different from the actual (H-L_w-G) equilibrium.

As regards the continuous temperature cycling mode, the faster applied cooling rate significantly promoted the CO₂ hydrates growth. Also, the usage of perforated plates reduced the induction time of the nucleation phase and facilitated the formation and growth of hydrate crystals by providing an additional large number of nucleation sites on their surface. Moreover, the obtained heating curves joined the cooling curves at temperatures that ranged between 8.15 and 8.45 °C, similar to the cases of all runs performed by applying the SW operational mode which exhibited CO₂ hydrate formation, regardless of the PVT configuration employed. On the other hand, the profile of the heating curves in the CC operational mode was also similar to the heating curve of the run with M_21.37 that was performed in the same autoclave, i.e., the stirred tank reactor, indicating that usage of this type of hydrate formation setup can only result in the formation of a thin hydrate layer which is not thermally and mechanically stable, in opposition to the dense hydrate layer that is grown when the magnetically agitated PVT autoclave with moderate mass transfer is used.

The simulation results corroborated the experimental findings as regards the hydrate decomposition point, the metastability of the studied systems, and their ability to undergo the phase transformation that leads to CO₂ hydrates’ formation. CO₂ solubility at the equilibrium (P, T) conditions was resolved using two calculation approaches: (i) calculation of the Henry coefficient for the experimental temperatures by combining a fitting equation, which was derived from an extended database of experimental measurements of CO₂ solubility in water, with the Peng–Robinson EoS-based calculation of the CO₂ fugacity at the equilibrium (P, T) conditions; and (ii) the CPA Infochem model of a commercial simulation software. The results revealed a continuous decline in CO₂ solubility with decreasing temperature in the presence of CO₂ hydrates, while the opposite trend was found in the two-phase (L_w-G) regime. Thus, the contribution of each one of the CO₂ sources (i.e., the aqueous phase and the gas phase) to CO₂ hydrates’ formation was assessed.