**4. Discussion: Simple Analysis on the Sealing Capacity of CO2 Hydrate-Bearing Sediments**

There are two major sealing mechanisms for CO2 structural trapping. One is the capillary seal, which occurs by capillary pressure between CO2 and water in pores. The other sealing mechanism is the permeability seal, which is related to the laminar flow velocity of CO2 in pores due to a pressure gradient. In view of the two sealing mechanisms, a simple analysis on the sealing capacity of the CO2 hydrate-bearing sediment was performed using the experimental results.

#### *4.1. Capillary Sealing Capacity*

Capillary pressure is the difference in pressure across the interface between two fluids. In petroleum reservoirs, capillary pressure between oil and water in rock pores is responsible for trapping oil [32,33]. In the same manner, capillary pressure between water and CO2 can trap CO2. For a given pore structure, the CO2 breakthrough pressure (*PC\** ) induced by capillarity can be described using the Young–Laplace equation:

$$P\_{\mathbb{C}}{}^{\*} = \frac{4\chi\cos\theta}{d^{\*}},\tag{1}$$

where γ is interfacial tension between water and CO2, θ is wetting angle, and *d\** is the critical pore throat diameter. Several researchers have measured various temperatures and pressures for the interfacial tension between water and CO2 [34–36].

In this study, the CO2 hydrate-bearing sediment layer could maintain about 0.71 MPa of pressure difference between the upper and lower part of the cell (Figure 12). Thus, the minimum breakthrough pressure (*PC\* min*) can be assumed as the average pressure difference between the upper and lower parts of the cell (Δ*Paverage*), which is described in Figure <sup>12</sup> (i.e., *PC\** ≥ *PC\* min* = Δ*Paverage*). Then, the maximum critical pore throat diameter of CO2-hydrate bearing sediments (*d\*max*) was calculated as 132 nm using Equation (1). The values used in this calculation are summarized in Table 1.

**Figure 12.** Pressure differences between upper (layer A1, A2, and A3) and lower (layer A4 and A5) parts of the cell (Δ*P*). When the CO2 hydrates formed and stabilized, the average Δ*P* (Δ*Paverage*) was about 0.71 MPa.

**Table 1.** Assumed values for the calculation of *dmax*.


If the pressure difference between the fluid interface exceeds *PC\** , then CO2 breaks through the interface, and laminar flow occurs [35,37,38]. Thus, in order for the capillary sealing mechanism to work, the breakthrough pressure (*PC\** ) must be larger than the buoyancy pressure of the CO2 plume. The buoyancy pressure (*PB*) that is induced by the density difference between water and CO2 can be described as

$$P\_B = \lg(\rho\_{water} - \rho\_{CO\_2})\_\prime \tag{2}$$

where *g* is the acceleration of gravity, *h* is the thickness of the CO2-stored layer, and ρ*water* and ρ*CO2* are the density of water and CO2, respectively. In a similar manner to the calculation of *d\*max*, the minimum buoyancy pressure (*PBmin*) which could be maintained by the CO2 hydrate-bearing sediment can be assumed as Δ*Paverage* (i.e., *PB* ≥ *PBmin* = Δ*Paverage*). At a similar thermodynamic condition of the experiment in this study (i.e., pressure of 6 MPa and temperature of 15 ◦C), ρ*CO2* was 784 kg/m3 [39]. Then, the minimum thickness of the CO2-stored layer (*hmin*) was calculated as 335 m according to Equation (2). Thus, we can presume that the capillary trapping capacity of the CO2 hydrate-bearing sediment is high enough.

The wettability (i.e., wetting angle) could be altered by the increase of the gas hydrate saturation because the solid materials contacting pore fluids are changed from sand particles to CO2 hydrates. For simplicity, this wettability alteration was not considered in this study. Further studies are required to evaluate the effect of wettability iteration on CO2 capillary sealing capacity.

#### *4.2. Permeability Sealing Capacity*

When the buoyancy pressure (*PB*) is higher than breakthrough pressure (*PC\** ), CO2 flow occurs. Fluid flow through soils finer than coarse gravel is laminar [40]. For laminar flow in CO2-saturated sediments the flow velocity, *v*, can be expressed by Darcy's law as follows:

$$\nu = K \frac{\rho\_{\rm CO\_2} \mathcal{g}}{\mu\_{\rm CO\_2}} i\_\prime \tag{3}$$

where *K* is absolute or intrinsic permeability of the sediments, ρ*CO2* is the density of CO2 fluids, *g* is the gravity constant, μ*CO2* is the viscosity of CO2 fluids, and *i* is the hydraulic gradient which is expressed by the difference between two hydraulic heads over the flow length. Note that the hydraulic gradient (*i*) is 1 for a vertical flow. Meanwhile, the average flow velocity for flow through a round capillary tube (*v0*) can be described by Poiseuille's law as follows:

$$\nu\_0 = \frac{\rho\_{CO\_2} \mathcal{g} d^2}{32 \mu\_{CO\_2}} i\_\prime \tag{4}$$

where *d* is the diameter of the capillary tube. The flow velocity determined by Poiseuille's law (*v*0) is the upper limit of the flow velocity (i.e., *v* ≤ *v*0) in porous media because flow velocity in sediments decreases by the tortuosity of the flow channel. Therefore, the upper limit of the absolute permeability of sediments can be defined using Equations (3) and (4) as

$$
\mathcal{K} \le \frac{d^2}{32}.\tag{5}
$$

The maximum absolute permeability of CO2 hydrate-bearing sediment (*Kmax*) can, therefore, be calculated using the *d\* max*, which was obtained before. *Kmax* is about 5.55 <sup>×</sup> <sup>10</sup>−<sup>4</sup> darcy. This value is similar to the permeability of fine-grained sediments (i.e., 10<sup>−</sup>3–10−<sup>7</sup> darcys [20]), and can be considered as "very low" permeability [41].

#### *4.3. Comparison with Other Materials*

Estimated maximum absolute permeability (*Kmax*) and minimum breakthrough pressure (*PC\* min*) are compared with measured absolute permeability (*K*) and breakthrough pressure (*PC\** ) of various sediment samples, as shown in Figure 13. We presumed that the breakthrough pressure of F110 sand increases by more than 102 times with CO2 hydrate formation. The minimum breakthrough pressure (*PC\* min*) of the CO2 hydrate-bearing sediments estimated in this study is comparable with that of unconsolidated clays and the shale sample. Meanwhile, the actual *PC\** of CO2 hydrate-bearing sediments in this experimental simulation may be higher than the estimated *PC\* min* because the latter was estimated conservatively using the pressure difference between upper and lower parts of the cell, instead of being measured directly. In the same manner, actual *K* of CO2 hydrate-bearing sediments in this experimental simulation may be lower than estimated *Kmax*. This might be attributed to the *Kmax* being calculated conservatively using the assumption of fluid flow in a round capillary tube without any tortuosity. To determine the range of absolute permeability and breakthrough pressure of CO2 hydrate-bearing sediments, further experimental studies are required.

**Figure 13.** Absolute permeability and breakthrough pressure of various consolidated and unconsolidated sediments and estimated values in this study. Filled circle represents estimated values of minimum breakthrough pressure and maximum permeability of CO2 hydrate-bearing sediments. Hollow circles represent F110 sand, kaolinite clay, and montmorillonite clay [42], hollow diamonds represent low-permeability sandstone cores [43], and hollow triangle represents shale [44]. The vertical and horizontal bars indicate the range of the measured values.

#### **5. Conclusions**

We performed an experimental simulation of CO2 geological storage in marine unconsolidated sediments in this study. CO2 hydrates were formed during the CO2 liquid injection process, and we observed the self-trapping effect of CO2 hydrates. In addition, simple analyses were conducted using the experimental results. The feasibility of CO2 geological storage in marine unconsolidated sediments was experimentally verified using 1-m-height high-pressure cell. CO2 hydrates instantly formed in the unconsolidated sediments with CO2 introduction, and prevented any upward leakage of CO2. The main findings are summarized as follows:


Permeability and breakthrough pressure of CO2 hydrate-bearing sediments depend on the saturation of CO2 hydrates in the pore system. However, CO2 hydrate saturation was not analyzed in detail in the present study, as sufficient information regarding maximum CO2 hydrate saturation via experimental simulation was lacking. We expect that a geophysical analysis using experimental data from a denser sensor array could overcome this limitation. Meanwhile, the electrical and geochemical behavior of the CO2-containing sediments in this study was different from that in real marine sediments because distilled water was used as pore water instead of saline water. To overcome this limitation, an experiment using saline water will be performed for further study.

**Author Contributions:** Conceptualization, G.-C.C. and H.-S.K.; Methodology, G.-C.C. and H.-S.K.; Writing—Original Draft Preparation, H.-S.K.; Writing—Review & Editing, G.-C.C.; Visualization, H.-S.K.; Supervision, G.-C.C.

**Funding:** This research was supported by the Korea government (Ministry of Trade, Industry, and Energy) through the Project "Gas Hydrate Exploration and Production Study (19-1143)" under the management of the Gas Hydrate Research and Development Organization (GHDO) of Korea, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) (No. 2017R1A5A1014883).

**Conflicts of Interest:** The authors declare no conflict of interest.
