The Performance of Low-Pressure Seawater as a CO₂ Solvent in Underwater Air-Independent Propulsion Systems

Abstract

Air-independent propulsion systems have improved the performance and decreased the vulnerability of underwater weapon systems. Reforming systems, however, generates large amounts of water and CO₂. The recovery or separation of CO₂, a residual gas component generated in vessels, entails considerable cost and energy consumption. It is necessary to understand the characteristics of the interaction between CO₂ and seawater under the conditions experienced by underwater weapon systems to design and optimize a CO₂ treatment process for dissolving CO₂ in seawater. In this study, numerical analysis was conducted using the derived experimental concentration and MATLAB. The diffusion coefficient was derived as a function of temperature according to the CO₂ dissolution time. Experiments on CO₂ dissolution in seawater were conducted. The concentration of CO₂ according to the reaction pressure and experimental temperature was obtained. The diffusion coefficient between CO₂ and seawater was found to be 6.3 × 10⁻⁵ cm²/s at 25 °C and 7.24 × 10⁻⁵ cm²/s at 32 °C. CO₂ concentration could be estimated accurately under vessel operating conditions using the derived CO₂ diffusion coefficients. Optimal design of the residual gas treatment process will be possible using the derived seawater–CO₂ diffusion coefficients under the actual operating conditions experienced by underwater weapon systems.

1. Introduction

Existing submarines are equipped with diesel propulsion systems, in which the energy for submerged operation is stored in lead-acid batteries. The capacity of these batteries limits the underwater range. The batteries are charged by a diesel generator during snorkeling, during which the submarine is exposed to a higher risk of detection [1]. Basically, the submarine is propelled by an electric motor and so the objective of the air-independent propulsion system is to silently generate electric energy when under the water. Electric energy can be produced with a diesel generator engine when the submarine is on the water surface or with a fuel cell with a reformer when the submarine is in military operation under the water. The steam reformer generates H₂ as fuel for the fuel cell and CO₂ vapor as a byproduct. However, CO₂ vapor cannot be discharged under the water during military operation because undissolved CO₂ will explode when rising up, which will be detected by others [2,3,4]. The current technology used still requires considerable cost and high energy consumption to recover or separate CO₂ discharged from vessels. Thus, technological innovation is required.

The aim of this research was to understand how CO₂ generated from a reformer fully dissolves in seawater in a short time period. Regarding studies on dissolution rate, Cavenati et al. [5] studied the adsorption of methane, CO₂, and N₂ by zeolite 13X under various pressures (0–5 MPa) and temperatures (298, 308, and 323 K). The CO₂ adsorption capacity of zeolite 13X was much higher than its adsorption capacity for other gases and the adsorption capacity increased with the pressure. Dash et al. [6] conducted research on the solubility of CO₂ according to the reaction temperature (303–328 K) and CO₂ partial pressure (0.2–1500 kPa) in an aqueous solution of 2-amino-2-methyl-1-propanol and piperazine. Increasing the concentration of 2-amino-2-methyl-1-propanol and adding piperazine affected the absorption capacity, where the CO₂ absorption capacity of the solvent increased under a high operation pressure and low operating temperature. Manic et al. [7] measured the solubility of CO₂ in seven ionic liquids in the 8–22 MPa pressure range and at temperatures of 313.2 and 323.2 K. They found that the solubility of CO₂ increased when the pressure increased and the temperature decreased.

With regard to dissolution velocity, Hirai et al. [8] measured the CO₂ dissolution velocity while the flow velocity, temperature, and pressure conditions were varied. It was found that the dissolution velocity increased when the temperature, pressure, and flow velocity increased. Dang and Rochelle [9] measured the solubility of CO₂ and its absorption rate in monoethanolamine (MEA)/piperazine/water at 40–60 °C. The absorption rate of MEA with 0.6–1.2 M piperazine added was 1.5–2.5-times higher than that when MEA was used alone. Faiz and Al-Marzouqi [10] developed a model for absorbing CO₂ from natural gas at high pressures of up to 5000 kPa. They showed that the CO₂ removal rate increased with pressure, whereas the CO₂ absorption rate increased when chemical solvents, such as MEA, were used.

To understand the dynamic characteristics of CO₂, Lawal et al. [11] investigated the effects of operating conditions in CO₂ capture facilities and performed dynamic modeling to solve possible issues proactively. With regard to the modelling, the analysis was conducted using equilibrium- and velocity-based approaches. The authors mentioned that the velocity-based model provided better predictions of the chemical absorption process than the equilibrium-based model with regard to understanding the dynamic behavior of the absorber and the failure of the stripper. Munusamy et al. [12] measured the volumes of CO₂, N₂, CH₄, and CO and conducted research on their dynamic adsorption characteristics. The equilibrium adsorption capacities of each composition in the powder and granules of MIL-101(Cr) were measured at 288, 303, and 313 K. The CO₂ and CH₄ absorption of MIL-101(Cr) increased with the adsorption temperature.

Breault and Huckaby [13] simulated adsorber performance using multiphase computational fluid dynamics (CFD) that included heat transfer. They investigated the behavior and performance of the riser adsorber for the solid circulation rate, gas flow rate, and heat removal. CO₂ adsorption increased with the solid flow and it decreased with the gas flow. Zhang et al. [14] performed CFD for CO₂ capture at a membrane using methyldiethaneolamine and 2-(1-piperazinyl)-ethylamine. They intensively studied the membrane gas absorption (MGA) method for CO₂ separation, developed a 2D mass transfer model, and examined the effect of membrane performance on adsorption performance. Giammanco et al. [15] investigated the dynamic characteristics of CO₂ gas for an optimal ionic liquid system. They suggested that a large amount of gas can be dissolved in imidazolium-based ionic liquids. Kim et al. [16] examined the fluid dynamics and CO₂ removal efficiency of amine absorbents on a pilot scale with structured packing using a gas–liquid multiphase Euler CFD model.

Many studies have been conducted that focus on CO₂ capture technologies from the perspective of power generation efficiency. Although research and development have been performed and continuous investments in such CO₂ capture technologies have been made, studies conducted under actual operating conditions of underwater weapon systems are insufficient and it remains difficult to conduct research on the development and application of technologies in underwater weapon systems to design and optimize CO₂ dissolution in seawater. Although processes with high-pressure and high-temperature absorbents exhibit high CO₂ recovery efficiencies, the absorbents are costly and the conditions are different from the actual operating conditions of underwater weapon systems. In this study, seawater was used as a solvent for CO₂ absorption. In addition, the actual operating conditions of underwater weapon systems were simulated by performing the absorption process under normal pressure instead of high pressure.

In this study, dissolution experiments were performed and dynamic characteristics were analyzed according to pressure and temperature. These experiments were carried out by applying dissolution technology using seawater as a solvent without an absorbent to improve the treatment of CO₂ after hydrocarbon reforming. The experiments were performed at equilibrium pressures of 2–5 bar and the results were compared to those of the MATLAB numerical analysis. In addition, the seawater–CO₂ diffusion coefficient was derived under experimental conditions.

The remainder of this paper is organized as follows: Section 2 presents the experimental setup and procedure used in the study, Section 3 explains the modeling equations used in this work as well as the sensitivity analysis, while Section 4 discusses the results of this study. Section 5 concludes this paper.

2. Experimental Setup and Procedure

2.1. Experimental Setup

CO₂ generated after hydrocarbon reformation was injected using an absorption and equilibrium system, which employed a batch-type reactor (Figure 1).

The flow rate of each gas was maintained at a constant level using a mass flow controller (Line Tech, Daejeon, Korea) (MFC) allowing for gas of the desired composition to be introduced into the buffer tank and the reactor. The buffer tank supplied gases of each composition to the reactor after maintaining it at a constant temperature and pressure. The volumes of the buffer tank and reactor were both 9 L. The temperature and pressure of the buffer tank were measured using a thermocouple (Sunil Instrument, Busan, Korea) (TT) and pressure transmitter (Wika, Germany) (PI, PT) with 99.5% accuracy. Thermocouples (TT) and pressure transmitter (PT) are used to measure pressure and temperature, which are variables used to calculate the gas phase moles of a reactor.

During the test, the temperature and pressure were measured respectively and the measured values were recorded in the data logger.

2.2. Experimental Procedure

In the experiments, the impurities retained in the buffer tank, reactor, and piping were removed using a vacuum pump. After the reactor temperature was increased to the operating temperatures of 25 and 32 °C, 99.8% pure CO₂ was injected into the buffer tank until the operating pressure was reached. When the reactor pressure was stabilized to a constant level, the gas in the buffer tank was supplied to the reactor. The experimental conditions used to focus on the effects of solvent type, temperature, and pressure on CO₂ concentration are summarized in

Table 1. Conditions of absorption experiments.

Gas Composition	Gas Concentration (%)	Absorbents	Temperature (°C)	Pressure (bar)
CO2	More than 99.8	Distilled water	25, 32	2, 3, 5
		Sea water

.

All the solutions were tested in 99.9% pure distilled water (6 L) and seawater. For seawater, artificial seawater was fabricated and used in accordance with ASTM-D1141-98.

Table 2. Chemical composition of synthetic seawater used in this study.

Compound	Concentration (g/L)
NaCl	24.53
MgCl2	5.20
Na2SO4	4.09
CaCl2	1.16
KCl	0.695
NaHCO3	0.201
KBr	0.101
H3BO3	0.027
SrCl2	0.025
NaF	0.003

lists the composition of the artificial seawater [17].

At the initial stage, the buffer tank and reactor were isolated from each other and the empty buffer tank was pressurized with CO₂ and the reactor filled with solution in vacuum state. After, the pressure and temperature were stabilized in both chambers. The gas in the buffer tank was fed into the reactor via an isolation valve that, when open, resulted in a pressure decrease in buffer tank and increase in the reactor. The pressure and temperature were data logged until both tank pressures were stabilized, which was assumed to be equilibrium state.

2.3. Amount of Gas Dissolved as a Function of Pressure and Temperature

The CO₂ pressure was estimated from the pressure change in the system. To obtain the removal rate of the injected gas, the actual gas state equation was used. The number of moles of gas dissolved in the solvent in the reactor was calculated using the pressure and temperature of the buffer tank and those of the reactor, as shown in Equations (1) and (2) [18,19,20].

The initial number of moles of injected CO₂ ($n_1$) was calculated by substituting the pressure ($P_1$) and volume ($V_1$) of the buffer tank into Equation (1):

$$n_{C{O}_2}=\frac{PV}{zRT},$$

(1)

where $z=V_{Actual}/V_{Ideal}$.

The compressibility factor (z) was adopted from HYSYS program, generally used in chemical process engineering, at a given pressure and temperature. The value varied from 0.975 to 0.99 in our research conditions.

The number of moles of CO₂ ($n_2$) at the equilibrium state between the buffer tank and the reactor could be calculated using the equilibrium pressure ($P_2$) and the sum of the volumes of the buffer tank and the reactor ($V_2$). The number of moles absorbed $(n_{C{O}_2,liq}$) was calculated as follows:

$$n_{C{O}_2,liq}=n_1-n_2.$$

(2)

Here, pressure $\left(P\right)$ is given in $\mathrm{bar}$, temperature $\left(T\right)$ is given in $\mathrm{K}$, volume $\left(V\right)$ is given in ${\mathrm{m}}^3$, z is the compressibility factor and $\left(n\right)$ is the number of moles of the gas. The gas constant $\left(\mathrm{R}\right)$ has the value 8.3144·10⁻⁵$\frac{\mathrm{bar}·{\mathrm{m}}^3}{\mathrm{mol}·\mathrm{K}}$.

3. Modelling Equations

Various models have been proposed for CO₂ absorption in amines, but few models use seawater or are implemented at normal pressure. The objective of this study was to develop a dynamic model of CO₂ absorption in seawater.

3.1. Governing Equation

A mathematical model of diffusion through a fluid was used to determine the amount of dissolution. The diffusion process is governed over time by the diffusion-advection equation. In this study, analysis was conducted in an unsteady state and the flow velocity of the fluid was ignored [21]. Fick’s law of diffusion and binary aqueous diffusion coefficients were used for the mass transfer calculations. This was appropriate because the highest concentration of solutes occurred in the chamber liquid. At such concentrations, it is safe to assume that the CO₂ mainly interacts with water. Equation (3) is the resulting instationary conservation equation for each of the solutes:

$$\frac{\partial C}{\partial t}=D\Delta C,$$

(3)

where, C mol/m³ is the concentration of the substance dissolved in the fluid and D m²/s is the diffusion coefficient of the solute in the solvent, i.e., the material property of the substance.

3.2. Liquid-Phase Equation

The continuity equation for the unsteady state for CO₂ transport in the liquid phase of the reactor was obtained using Fick’s diffusion law for the estimation of diffusion flux [22,23,24,25,26,27]:

$$N_A=k_{g}P\left(Y_A-Y_{Ai}\right)=k_l\left(C_{Ai}-C_A\right),$$

(4)

where:

• $N_A$ = molar flux of A, mol·cm⁻²·s⁻¹;
• $k_g$ = gas-phase mass transfer coefficient, (mol flue gas)·cm⁻²·s⁻¹·atm⁻¹;
• $k_l$ = liquid-phase mass transfer coefficient, cm·s⁻¹;
• $Y_A$= bulk gas-phase mole fraction of A, mol A/mol flue gas;
• $Y_{Ai}$ = interfacial gas-phase mole fraction of A, mol Ai/mol flue gas;
• $\mathrm{P}$ = Total pressure, atm;
• $C_A$ = bulk liquid-phase concentration of A, mol A·cm⁻³;
• $C_{Ai}$ = interfacial liquid-phase concentration of A, mol Ai·cm⁻³.

The gas-liquid equilibrium at the interface was calculated by the well-known Henry’s law. Here, the Henry solubility constant is defined as $\mathrm{H}=\frac{c_L}{p},$ where $c_L$ is the concentration of a species in the aqueous phase and p is the partial pressure of that species in the gas phase under equilibrium conditions [28].

Henry’s constant varies with the temperature of the system, as well as with the solvent and solute. Many researchers have derived Henry’s CO₂ constants from $3.1\times {10}^{-4}\mathrm{mol}/{\mathrm{m}}^3\mathrm{Pa}$ to $3.6\times {10}^{-4}\mathrm{mol}/{\mathrm{m}}^3\mathrm{Pa}$. A value of $3.4\times {10}^{-4}\mathrm{mol}/{\mathrm{m}}^3\mathrm{Pa}$ was used as Henry’s constant in this model. The temperature dependence of the equilibrium constant can generally be explained by the Van’t hoff equation, which also applies to the Henry law constant [28,29]:

$$H\left(T\right)=H^{\circ }\times exp\left[\frac{-{\Delta }_{sol}H}{R}\left(\frac{1}{T}-\frac{1}{T^{\diamond }}\right)\right],$$

(5)

where, $H^{\circ }$ at the reference temperature $T^{\circ }=298.15K$, CO₂ $\frac{-{\Delta }_{sol}H}{R}$ = 2400.

Using Equation (5), Henry’s constant at 32 degrees Celsius for CO₂ was $2.79\times {10}^{-4}\mathrm{mol}/{\mathrm{m}}^3\mathrm{Pa}$. The Henry’s constant for seawater at 25 and 32 degrees Celsius was obtained as $3.01\times {10}^{-4}\mathrm{mol}/{\mathrm{m}}^3\mathrm{Pa}$, $2.53\times {10}^{-4}\mathrm{mol}/{\mathrm{m}}^3\mathrm{Pa}$ using Equation (5) [30]. This was very similar to the Henry’s constant for 35% saline water previously reported by Weiss [31].

The concentration distributions in the liquid interface where Henry’s law was applied and in the liquid bulk were calculated by solving the diffusion equation using Fick’s diffusion law:

$$D_{liquid}\left[\frac{{\partial }^{2}C}{\partial x^2}\right]=\frac{\partial C}{\partial t}.$$

(6)

$$D_{C{O}_2-H_{2}O}=7.4\times {10}^{-8}{\left(\varnothing M_{H_{2}O}\right)}^{1/2}T/\left({\eta }_{H_{2}O}{V}^{0.6}{}_{C{O}_2}\right).$$

(7)

The Wilke–Chang equation (Equation (7)) is widely used for diffusion coefficients in liquid-phase diluted solutions. It is based on Eyring theory and the Stokes–Einstein equation. The effect of the solute is expressed by the molar volume and that of the solvent based on the molecular weight. Here, $\varnothing$ is a compounding factor that represents the effect of the combination of solvent molecules on the diffusion of the solute. This value is 2.6 when the solvent is water. $M_{H_{2}O}$ is the molecular weight of water, T is the temperature, ${\eta }_{H_{2}O}$ is the viscosity of water, and $V_{C{O}_2}$ is the molar volume of CO₂ at an abnormal boiling point [32].

Several experimental methods have been proposed for measuring gas diffusion in liquids. The existing methods are classified into direct and indirect methods. In the conventional direct methods, the composition of the liquid phase is analyzed by sampling at various times during the experiment. The direct methods include the Taylor–Aris dispersion method proposed by Frank et al. [33], the capillary cell method used by Witherspoon and Saraf [34], and gas adsorption in a jet presented by Tang and Himmelblau [35]. The main limitations of these direct analysis methods are high pressure and temperature conditions and difficulties with sampling [33,34,35,36]. The diffusion coefficient for the experimental conditions of this study is presented in the next section.

A mathematical model for explaining the phenomenon that occurs in the seawater–CO₂ system was developed. The basic assumptions for CO₂ capture are as follows:

• Heat transfer by conduction and radiation can be ignored in the axial direction;
• Henry’s law is applicable to the CO₂ solubility in the liquid phase;
• Absorption reactions occur only in liquids;
• Vaporization of liquids does not occur;
• The reactor is adiabatic.

The boundary condition equations of diffusion are as follows:

$$\mathrm{at}x=0,C_0=\frac{P}{H},$$

(8)

$$\mathrm{at}x=\mathrm{L},\frac{\partial C}{\partial x}=0(\mathrm{insulation}\mathrm{boundary}).$$

(9)

3.3. Sensitivity Analysis

To determine mesh size, a sensitivity study was performed by reducing the mesh size by 50%. Regarding the mesh size of the model, six cases were assumed and Reactor P was calculated. The results showed that the pressure was reduced below 2% when the mesh size was smaller than 0.00024 (m), as shown in

Table 3. Sensitivity scenarios.

Scenario	Mesh Size (m)	Reactor P (bar)	Sensitivity (%)
Case 1	0.00384	4.373	24.25
Case 2	0.00192	4.369	15.98
Case 3	0.00096	4.366	6.75
Case 4	0.00048	4.364	4.39
Case 5	0.00024	4.363	1.99
Case 6	0.00012	4.362	-

. The mesh size for analysis to determine the diffusion coefficient was determined to 0.00012 (m).

4. Results and Discussion

The results of the dissolution experiment and numerical analysis for distilled water and seawater at 25 and 32 °C, respectively, are presented in the following sections to verify the reliability and reproducibility of the fabricated experimental setup as well as to elucidate the long-term diffusion coefficient.

4.1. Long-Term Reaction Characteristics Using Distilled Water

Figure 2 shows the CO₂ concentration in distilled water over time according to the temperature at the equilibrium pressure of 5 bar. These experimental results were compared to the results of a simulation in which the diffusion coefficient values in

Table 4. CO₂ diffusion coefficients in water as per the literature.

Source	Method	Solution	Temperature (°C)	Diffusion Coefficient (10−5 cm2/s)
Tang and Himmelblau [35]	Jet	Water	25	1.92
Unver and Himmelblau [37]	Jet	Water	6.5–65	1.145–4.296
Thomas and Adams [38]	Jet	Water	18.5–75.1	1.65–5.40
Tamimi et al. [39]	-	Water	20–80	1.76–8.20

were used. The CO₂ concentration increased with the equilibrium pressure and the decrease in reactor temperature, but the dissolution velocity was dependent on the temperature according to Equation (7).

Hirai et al. [8] mentioned that the dissolution velocity increases with reaction temperature, but the difference is difficult to detect, as shown in Figure 2. The data obtained from the numerical analysis conducted using the diffusion coefficient values from the literature agree with the experimental data measured in this study at the beginning of the experiments. This agreement, however, decreased over time, which indicates that the conditions of the diffusion coefficient used for CO₂ diffusion and dissolution were different.

4.2. Short-Term Reaction Characteristics Using Distilled Water

Figure 3 shows the CO₂ concentration in distilled water over time according to the equilibrium pressure and temperature. Figure 3 shows that the diffusion and dissolution velocity of CO₂ were related to temperature. The observed concentration, using the diffusion coefficient values obtained from the literature (Table 3), was compared to the experimental results. The results of the experiments were in good agreement with those of the simulation in terms of the CO₂ concentration at the beginning of the experiments, but this agreement deviated over time.

We estimated that the CO₂ concentration would continue to increase over time according to Henry’s constant. This observation showed that the diffusion coefficients obtained from the literature were substantially lower than those from the experiments. Thus, the diffusion coefficients were obtained through numerical analysis.

4.3. Experimental Approach Considering Concentration in Distilled Water

For the diffusion coefficient values presented in Table 4, the jet method was used as the experimental method. In this case, a very short contact time and high liquid velocity were used [40]. The diffusion coefficient values of CO₂ and water used for numerical analysis are listed in Table 4. The average standard deviation of the reported experimental values was 0.1 × 10⁻⁵ cm²/s at 25 °C.

4.4. Mid-Term Reaction Characteristics Using Distilled Water

One important prerequisite for the accurate simulation of CO₂ diffusion is an appropriate CO₂–H₂O diffusion coefficient. The diffusion coefficient derived though numerical analysis was introduced and the results were compared to those obtained experimentally. The CO₂ diffusion coefficient in distilled water was 7.06 × 10⁻⁵ cm²/s at 25 °C and 8.56 × 10⁻⁵ cm²/s at 32 °C.

Figure 4 shows the simulation data obtained by applying the derived diffusion coefficient values and experimental data at changing equilibrium pressure and temperature. As the derived diffusion coefficient increased, the CO₂ concentration increased in the simulation results, which is in good agreement with the experimental results. According to this, the diffusion coefficient of CO₂ increases with the temperature and the diffusion coefficient increases as the contact time increases, unlike in previous studies that derived the diffusion coefficients for very short periods of time using the jet method.

4.5. Experimental Approach Considering Concentration in Seawater

This section describes the attempt to derive the concentration of CO₂ and the diffusion coefficient according at equilibrium pressure and experimental temperatures under seawater conditions by increasing the salinity.

Table 5. CO₂ diffusion coefficients in brine as found in the literature.

Source	Solution	Pressure (kPa)	Temperature (°C)	Diffusion Coefficient (10−5 cm2/s)
Renner [41]	Brine	2186–5861	25	9.07–9.86
Wang et al. [42]	Brine	1524–5178	38	2.93–4.83
Yang C and Gu [43]	Brine	2600–7500	27–58	170.7–269.8
Azin et al. [44]	Brine	5858–6898	40–45	3.52–6.16
Mojtaba et al. [45]	Brine	3450	38	1.75
Zhang et al. [46]	Brine	1170	25	1.5–1.91

summarizes the CO₂ diffusions coefficient in brine provided in the literature. As shown, most of the studies on the CO₂ diffusion coefficient in seawater were conducted under high-pressure, high-temperature, and supercritical conditions and the diffusion coefficient was derived under extreme conditions. As studies on CO₂ absorption capacity of seawater at normal temperature and pressure are not sufficient, estimating the seawater–CO₂ diffusion coefficient under ordinary conditions was attempted through experiments and simulations.

4.6. Short-Term Reaction Characteristics in Seawater

Figure 5 shows the CO₂ concentration in seawater over time based on the results of the six diffusion experiments performed under the equilibrium pressures of 2, 3, and 5 bar and the temperatures of 25 and 32 °C. The concentration of CO₂ increased with the increase in equilibrium pressure and the decrease in reaction temperature, while the dissolution velocity of CO₂ was determined using Equation (7). As shown in Table 5, previous studies derived the CO₂ diffusion coefficient under high-pressure and high-temperature conditions. In Figure 5, the seawater–CO₂ diffusion coefficient for the corresponding conditions is shown based on the simulation using numerical modeling.

The CO₂ concentration increased with the equilibrium pressure and it decreased or increased as the temperature increased. The CO₂ diffusion coefficient in seawater estimated through the simulation was 6.3 × 10⁻⁵ cm²/s at 25 °C and 7.24 × 10⁻⁵ cm²/s at 32 °C.

4.7. Mid-Term Reaction Characteristics in Seawater

Figure 6 shows the concentration of CO₂ in seawater over time, up to 600 s under equilibrium pressures of 2, 3, and 5 bar and temperatures of 25 and 32 °C. When the numerical analysis was conducted by applying the diffusion coefficient values selected from Figure 5, the concentration of CO₂ increased with the increase in equilibrium pressure, which is in good agreement with the experimental results. The diffusion coefficient in seawater was approximately 17% lower than that in distilled water. Many ions and types of organic matter exist in seawater and the CO₂ diffusion coefficient decreased as the total dissolved solids increased. Moreover, the concentration of CO₂ in seawater decreased with the increase in salinity and the diffusion coefficient in seawater was low because of limited CO₂ diffusion. When CO₂ is dissolved in water, it is divided into $D_{HC{O}_{3^{-}}}$ and $D_{C{O}_3{}^{2-}}$. These components have different diffusion coefficients whose effects become visible over time [46,47].

Table 6. Comparison of CO₂ diffusion coefficients by temperature.

	Diffusion Coefficient (10−5 cm2/s)
	Distilled Water		Seawater
	25 °C	32 °C	25 °C	32 °C
Reference	1.85–2.0	2.08–2.16	-	-
Experiment	7.06	8.56	6.3	7.24

lists shows the optimized CO₂ diffusion coefficient results obtained when distilled water and seawater were used as solvents at normal pressure and temperature. The diffusion coefficient values estimated experimentally were approximately three-times higher than the reference diffusion coefficient values in distilled water. Following previous studies [34,37,39], the CO₂ diffusion coefficient was presented using the jet method. As the contact time between the liquid and gas is very short and the liquid velocity is high in the jet method, differences from the D values estimated from the experiments are observable at long experimental times. The reference diffusion coefficient values in seawater were based on the high-pressure, high-temperature, and supercritical conditions (Table 5), which were not consistent with the experimental conditions. The CO₂ diffusion coefficient in seawater obtained through the numerical analysis under the experimental conditions was 6.3 × 10⁻⁵ cm²/s at 25 °C and 7.24 × 10⁻⁵ cm²/s at 32 °C. The CO₂ diffusion coefficient at 32 °C was approximately 13% higher than that at 25 °C.

5. Conclusions

This study was conducted to investigate the characteristics of the CO₂ diffusion coefficient, an essential element that affects the concentration of CO₂ over time, in the treatment of the residual gas generated in a vessel by dissolving it in seawater and discharging it to the outside of the vessel. The temperature and solvent, which affect the CO₂ diffusion coefficient, were examined by using a theoretical approach, conducting dissolution experiments, and analyzing the dynamic characteristics. The following conclusions were drawn:

(1)

For the treatment of the residual gas generated in the reformer, the concentration of CO₂, a residual gas component, was observed at different pressures and temperatures from the perspective of dissolution using seawater and the CO₂ diffusion coefficient was derived through numerical analysis using MATLAB;

(2)

It was confirmed that the experimental time, temperature, and pressure could be variables in selecting the CO₂ diffusion coefficient for each solvent;

(3)

The CO₂ concentration in seawater was approximately 55% higher when the equilibrium pressure was 5 bar and the reaction temperature was 25 °C than when these parameters were 2 bar and 32 °C;

(4)

Under the actual operating conditions of underwater weapon systems, the CO₂ diffusion coefficient in distilled water and seawater, according to the dissolution time, was derived by temperature. The CO₂ diffusion coefficient in seawater was 6.3 × 10⁻⁵ cm²/s at 25 °C and 7.24 × 10⁻⁵ cm²/s at 32 °C. The CO₂ diffusion coefficient was approximately 13% higher at 32 °C than at 25 °C;

(5)

It is possible to accurately estimate the concentration of CO₂, a residual gas component of the reformer, under the operating conditions of each vessel using the derived CO₂ diffusion coefficient as a function of temperature.

If a process for estimating the concentration of the residual gas generated in a reformer is implemented using the seawater–CO₂ diffusion coefficient based on the results from the actual operating conditions of underwater weapon systems, innovative developments will be possible.