Geological storage of carbon dioxide (CO₂) is considered a major measure for reducing carbon content in the earth’s atmosphere. Depleted oil and gas reservoirs are widely used as geological structures for CO₂ storage [1] . A major advantage of using depleted oil and gas reservoirs as CO₂ storage is the elimination of the cost for drilling new wells. Another advantage of oil and gas reservoirs is their high injectivity and high-volumetric efficiency due to their high permeability and porosity. A disadvantage of using these wells is the risk of CO₂ leak through wellbores due to the high corrosivity and mobility of CO₂ in gaseous and supercritical state [2] [3] . Studies have shown that the risk of CO₂ leak is lower from subsea geological structures than from onshore oil and gas reservoirs due to the low mobility of CO₂ in liquid state in the former environment [4] . The pioneer process of CO₂ storage in subsea water zone is the Sleipnir project in the Norwegian Sea [5] . Another example process is the Hokkaido project [6] - [8] . However, storing CO₂ in liquid form in subsea structures is not an optimum solution because the stored CO₂ is still at risk of leaking.

CO₂ can exist in the form of gas hydrates which have no mobility and corrosivity. Gas hydrates are solids where small molecule gases are trapped inside the cages of water molecules at high-pressure and low-temperature conditions [9] . Numerous researchers have studied the formation of gas hydrates in static conditions in the past both experimentally and theoretically. The kinetics of formation of gas hydrates was formulated by Englezos et al. [10] . The gas hydrate formation rate was found directly proportional to the hydrate crystal particle area, and the difference in gas fugacity was found at the in-situ condition and the gas fugacity at the three-phase equilibrium conditions. Englezos et al.’s formula was modified by Skovborg and Rasmussen [11] by replacing the particle area with crystal film during hydrate formation. Chemical potential difference was used as the driving force for hydrate formation by Mohebbi [12] and Kashchiev [13] . The driving force was defined as the temperature difference between the equilibrium and testing conditions by Vysniauskas and Bishnoi [14] , while it was defined as the pressure difference between the equilibrium and testing conditions by Natarajian [15] . Based on the knowledge accumulated in the past decades, the conditions (pressure and temperature) for CO₂ hydrate formation are accurately predictable. The pressure and temperature of CO₂ hydrate formation under static conditions are given by Sloan and Koh [9] .

Previous studies proposed storing CO₂ in hydrate (solid) forms in subsea formations, including natural gas hydrate reservoirs, where the geological temperatures are below the hydrate-forming temperature of CO₂ [16] [17] . This can greatly reduce the leak probability because CO₂ is locked inside its hydrates, eliminating the problems of its high corrosivity and high mobility. However, efficient placement of CO₂ in the formation is a big issue. The low injectivity of CO₂ into the formations is due to the low permeability of the formations (normal silt-sand) [18] . The use of radial-lateral wells for placing CO2 in marine gas hydrate reservoirs may partially solve the injectivity problem, but it will induce additional costs for well drilling [19] . In this case, CO₂ can form hydrates in the formations during injection, which reduces injectivity [20] . Although using geothermal energy to enhance natural gas production from gas hydrate reservoirs by CO₂ swapping can be a long-term solution to the injectivity problem [21] , a significant amount of initial investment is required.

This study proposes an innovative process to permanently store CO₂ in solid form on the sea floor to solve the problems of injectivity and leak risk. Site selection criteria and required technologies are discussed. It should be considered the ultimate process for safely and economically storing CO₂ for carbon reduction in the atmosphere of the Earth.

This section describes required pressures and temperatures for stable CO₂ hydrates, seawater temperature, and densities of seawater, CO₂ liquid and CO₂ hydrates. The favorable seawater depths for disposals of CO₂ will be identified accordingly.

Deposition of CO₂ in hydrae status on seafloor below the critical depth requires that CO₂ hydrates are generated instantly in seawater unless the water depth is greater than the depth for stable CO₂ liquid where hydrates can form slowly without concern of hydrate-floating up. To generate CO₂ hydrates instantly, a super-cooling technique is proposed using the Joule-Thomson cooling effect. Figure 7 presents a schematic diagram of a CO₂ hydrate generation process using a jet-cooling method. Ship 1 is loaded with liquid CO₂ from carrier connector 2 or pipeline hose to CO₂ tank 3. The liquid CO₂ is cooled by cooler 4 to increase density. The cooled CO₂ is pumped by pump 5 into hose 6, leading to the injection head 7 where the CO₂ is expanded through the jetting nozzles 8. Due to the Joule-Thomson cooling effect the jetted CO₂ stream should be further cooled below the seawater temperature, causing the formation of CO₂ hydrates immediately. The remaining CO₂, if there is any, will form hydrates in buffer chamber 9. Depth control room 10 receives seawater depth data from the sonar depth surveyor 11 and adjusts the location of the injection head 7 to keep it close to the seafloor. CO₂ monitoring room 12 receives data from CO₂ detector 13 and sends a signal to the CO₂ pump control to reduce the CO₂ injection rate if free CO₂ is detected. The CO₂ hydrates generated should remain on the seafloor due to their density being higher than seawater. The ship moves forward slowly as needed.

The total cross-sectional area of the nozzles should be designed to cause a significant pressure drop at the nozzles to generate adequate Joule-Thomson cooling effect. The temperature at the downstream of the nozzles can be estimated based on choke flow theory [26] :

$T_{\text{dn}}=T_{\text{up}}\frac{z_{\text{up}}}{z_{\text{outlet}}}{\left(\frac{p_{\text{outlet}}}{p_{\text{up}}}\right)}^{\frac{k-1}{k}}$(2)

where p_outlet is the pressure at nozzles’ outlet, p_up is the upstream pressure, and k is the specific heat ratio of CO₂. The outlet pressure is equal to the sea water pressure in subsonic (subcritical) flow conditions. Sonic (critical) flow conditions can be used to achieve the maximum temperature drop. The critical pressure ratio through nozzles is expressed as [26] :

${\left(\frac{p_{\text{outlet}}}{p_{\text{up}}}\right)}_c={\left(\frac{2}{k+1}\right)}^{\frac{k}{k-1}},$(3)

where the value of k for CO₂ is about 1.28, the critical pressure ratio is about 0.55 for CO₂. This suggests that the upstream pressure should be more than double the downstream pressure which is the in-situ seawater pressure. For example, if the in-situ seawater temperature is 276˚ K (3˚C), the in-situ seawater pressure should be selected to be at least 16.6 bar for hydrate formation. The nozzle size should be designed to create upstream pressure of at least 13.2 bars for instant hydrate formation. The relation between the upstream pressure, CO₂ flow rate, and total nozzle area can be found in literature [26] .

The study proposes a jet-cooling process that exploits Joule-Thomson expansion

to form CO₂ hydrates immediately above the seabed, thereby immobilizing the gas and lowering leakage risk. Pressure-temperature envelopes, seawater density data and hydrate stability charts are combined to define two operational depth windows (>4000 m for liquid CO₂; 700 - 4000 m for hydrate formation). A schematic system layout with CO₂ cooler, pump, hoses, sonic nozzles, buffer chamber, floor survey and depth control, and CO₂ monitoring is outlined. A guideline for designing sonic nozzles is provided. The technique could offer a virtually unlimited, leakage-free offshore storage capacity for captured CO₂. This document provides an early technical assessment of the process only. More research work needs to be conducted to support the engineering design of the system and assess the potential impact of the process on the environment of seafloors. The following work is specially recommended for future focus:

1) Conducting experimental investigations of the proposed jet-cooling process to validate the concept. This is being designed and prepared using a high-pressure-low-temperature windowed cell to observe the settling of CO₂ hydrates and CO₂ liquid due to gravitational segregation.

2) Performing a quantitative hydrate formation kinetics analysis to determine the minimum required residence time of the jet plume for full solidification under the seawater condition of the proposed process. This information will be used to design the geometry (diameter and length) of the buffer chamber to ensure 100% conversion of CO₂ to hydrates before the CO₂ plume exits the buffer chamber.

3) Carrying out research work to analyze the long-term stability of the deposited hydrate layer, including potential resuspension by sea bottom currents, sediment interaction, warming scenarios, and aviation of artificial objects.

4) It is understood that Equation (1) was established based on the data in Figure 3 . Under other seawater conditions, either the actual temperature data from local survey or Equation (1) validated using the actual data should be used to determine the critical water depth for CO₂ hydrate formation.

An efficient process called jetting-cooling and a technology suite to realize the process for safely depositing CO₂ on the sea floor are presented in this study. The advantages of CO₂ storage on the sea floor in hydrate form include no limitation to storage capacity and stability. There is no concern about the size of geological traps and CO₂ leakage to the atmosphere. The following conclusions are drawn regarding the favorable water depth and necessary equipment design.

CO₂ can be injected and stored on the sea floor in its liquid-then-hydrate form if the sea water is deep enough. In typical seawater environments, if the water depth is greater than 4000 m, CO₂ can be deposited directly to the sea floor in liquid form. The liquid CO₂ will then form hydrates and stay on the sea floor.

CO₂ can be stored on the sea floor in its hydrate form if the sea water is deep enough. In typical sea water environments, if the water depth is greater than 700 m, CO₂ can be injected through nozzles to reduce its temperature and generate hydrates. The generated hydrates will then be deposited on the sea floor due to gravity.

The nozzles for reducing CO₂ temperature to generate hydrate are the key component of the proposed technology suite. The nozzles should be sized based on the required pressure differential and CO₂ flow rate. Sonic (critical) flow condition is preferred to maximize the cooling efficiency.

The authors are grateful to BIRD for funding the project “Safe, sustainable, and resilient development of offshore reservoirs and natural gas upgrading through innovative science and technology: Gulf of Mexico—Mediterranean”, through grant No. EC-19 Fossil Energy.

*Corresponding author.