Prediction of boil-off gas and boil-off rate in cargo tank of NGH carrier

2.1 Verification of thermal analysis and reliability using GTT’s data

Table 1 reviews a report on the heat ingress of LNG cargo tanks for preliminary calculations based on GTT’s thermal data for membrane-type LNG carriers. First, we reviewed the data to determine the type and volume of cargo tank to be analyzed and derived the values by calculating the total heat flow rate flowing into the cargo tank. Because shipyards normally select a reliability of less than 3% tolerance for estimating the BOG of an LNG carrier, the same level of reliability was applied.

Table 1:

Review of heat ingress to LNG cargo tanks for preliminary calculations based on GTT’s data

• (1) Environmental conditions and properties of LNG carrier
• ▪ Environmental conditions:
  • - Air temperature:        45 °C
  • - Seawater temperature:       32 °C
• ▪ LNG properties:
  • - Tank filling ratio:        98%
  • - Composition:     Pure methane CH₄
  • - Temperature:        -161.5 °C
  • - Specific density:      425 kg/m³
  • - Latent heat of vaporization:      511 kJ/kg
• (2) BOG calculation

• $\[ \mathit{BOR}=\frac{\varnothing }{{\rho }_m\bullet V\bullet L}\bullet 3600\bullet 24 \]$

  (1)

Here,

• ϕ : sum of all local heat transfers
• ρ_m : density of methane
• L : vaporization latent heat of methane
• V : cargo capacity (corresponding to 98.0% of total tank capacity)

2.2 Analysis model and boundary conditions

The analysis model for the LNG cargo tank was based on real ship data from the GTT. Because the heat transfer characteristics in the width and longitudinal directions are equal, only one-fourth of the cargo tank volume was modeled in order to reduce the calculation time for grid nodes. The membrane tank was adopted as the thermal analysis model, and the primary/secondary invar and wood for wall insulation were not considered at the wall of the membrane tank. This was so thin because the primary and secondary insulations were made of 0.7 mm invar. The inner wall as modeled using only two-layer insulation because standards organizations have interpreted in rule that it does not have a significant effect on heat ingress from outside the hull. The hull reinforcement of the outer cargo tank was simplified; all external heat effects of the various reinforcements attached to the hull plate were ignored except for some hull structures that can pass well into the cargo tank.

Figure 1 shows the concept for thermal analysis of the hull of an LNG carrier. The process of heat ingress from the air and seawater flows into the inner cargo tank through conduction and convection. The conduction coefficients at each hull part should be determined from the material properties, so the coefficients for conduction in the hull parts and the coefficients of insulation in the insulating materials were formulated according to the properties.

Figure 1:

Concept model for thermal analysis of LNG carrier

The commercial software ANSYS Fluent ver.14.0 [16] was used for the numerical analysis. The initial temperature conditions were set according to the IGC code (IGC 83/ 90 Amend/ Annex/ Chapter 7/ 7.1.2, Design Temperature) [17] to estimate the BOG of the cargo tank in the LNG carrier. Boundary conditions for all edge parts except the cofferdam were set up under the symmetry condition. Table 2 and Figure 2 present the boundary conditions for thermal analysis of the LNG tank, side/inner void, ballast tank, and insulation according to IGC 83/90.

Table 2: Boundary conditions for thermal analysis

Figure 2:

Boundary conditions for cargo hold in LNG carrier

2.3 Definition of insulation

Because the physical properties of a heat-insulating material used to suppress thermal effects are generally private information, it is difficult to know the characteristics of the insulation installed in the cargo tank on each vessel. In general, insulating materials such as polyurethane foam, perlite, and superlite are applied to the cargo tanks of LNG carriers. In this analysis, the heat-insulating material was given the heat transfer characteristics of perlite of S-shipbuilding.

Each insulation has different heat transfer characteristics depending on the temperature variation, like the coefficient of conduction. Therefore, the coefficient of conductivity for this temperature change was considered in the CFD code, and the thermal conductivity was defined as shown in Figure 3.

Figure 3:

Conductivity of insulation with changing temperature

2.4 Analysis method and results

Figure 4 shows the heat transfer rate over time based on transient analysis of the LNG cargo tank. The quantity of the heat flow changed over time. In GTT’s thermal analysis conditions, the BOR was not considered for the loading of LNG or cooling of the cargo tank. Thus, the BOR in our estimation was calculated under thermal equilibrium considering only the operating conditions of the ship. In this study, the thermal equilibrium state was considered to be the average heat flux (25 - 48h) after 24 hours and was used as a factor needed to calculate the BOR (see section A in Figure 4).

Figure 4:

Heat transfer rate by time evolution in LNG cargo tank

Through a comparison with GTT’s BOR method (see Table 3), the accuracy of the derived prediction model was verified; the maximum relative difference was less than 2% compared with our estimation. Figure 5 (a) and Figure 5 (b) show the temperature distribution of the inner hull structure and the section temperature contours over time. The loading/unloading volumes of the third tank for the LNG ship were calculated as 48,641 (m³) × 0.98. Then, the total ingress calories (φ) for a day was estimated as 152,906(W) × 3,600 (s) × 24 (h).

Table 3:

BOG validation between CFD estimation and GTT’s data

Figure 5:

Temperature profile of cargo tank and section over time

3.1 Analysis of heat transfer

NGHs are known to contain large amounts of natural gas (about 160-180 times their volume) and they are easy to store and safe to transport at about -20 °C under atmospheric pressure because of the “self-preservation effect” with the help of insulation. Heat ingress from the outside through the heat-insulating material should be blocked as much as possible, but heat flowing inside the cargo tank from an external heat source is inevitable. We estimated the heat ingress to a cargo tank through heat transfer analysis using the commercial code CFD program Fluent. By calculating the BOG volume based on the CFD analysis, we determined the presence/absence of insulation and its thickness and selected equipment specifications for BOG treatment.

Figure 7 describes the heat transfer mechanism between an external heat source (sea and atmosphere) and the cargo tank of an NGH carrier. The BOG/BOR due to dissociation generated in the cargo tank can be estimated by calculating (a) the heat of the atmosphere and sea flowing into the cargo tank by conduction and convection; (b) the heat ingress inside the cargo tank by the convection of the external heat source, the heat flux of the hull, and the thermal insulating capacity of the insulation; (c) and the amount of heat ingress.

Figure 7:

Concept model for thermal analysis of NGH carrier

3.2 Definition of analysis model and grid generation

Figure 8 shows the general arrangement and definitions of the model for a 115K NGH carrier. Because the thermal boundary conditions of the longitudinal and transverse direction in the cargo hold are symmetrical, only a quarter of the cargo hold was modeled in this analysis to reduce the computational load. The effects of various reinforcements attached to the hull plate were not considered. Also, the insulating layer, which has complicated geometry in the cargo tank, was ignored because the flow characteristics within the cargo tank were not analyzed.

Although the hull and cargo tank vary slightly in thickness by location, the modeling was carried out using the mean values of the inner and outer hulls for convenience. The thickness of the insulation was set to 100 mm.

Figure 8:

General arrangement and definitions of model

3.3 Boundary conditions

The heat sources affecting the BOG in an NGH carrier can be classified as internal heat sources in the cargo tank and external heat sources from the air/sea. Heat transfer takes place by convection in the cargo hold and at the atmosphere/seawater interface and by conduction through the hull and insulating materials. The internal void tank is transferred by convection through the air. Figure 9 and Table 4 present the boundary conditions for each part.

Table 4:

Boundary conditions for thermal analysis of 115K NGH carrier

Figure 9:

Boundary conditions for cargo hold in NGH carrier

Table 5 presents the thermal conductivity, specific heat, and density for the insulating materials in the cargo tank of NGH carrier based on the temperature variation. Polyurethane foam was used for its material properties; its heat transfer characteristics vary according to the temperature. Thus, in order to consider the coefficient of heat transfer depending on the temperature of the heat-insulating material, the insulation characteristics were considered in the analysis model.

Table 5:

Properties of material by temperature change in NGH carrier

3.4 Results and discussion

As shown in Figure 10, the heat transfer rate confirmed that the amount of heat flow inside the cargo tank of an NGH carrier varies with time. In order to estimate the total heat flow in the cargo tank, the evaluation method for heat transfer in an LNG carrier was also applied to the NGH cargo tank. We assumed thermal equilibrium conditions and calculated the total heat flow for 24 –48 h (period A) based on the heat flow rate for 24 h. As indicated in Table 6, the BOG and BOR values were estimated using the necessary calories to convert ice in the hydrates and the total amount of gas shipped.

Figure 10:

Variation in heat transfer rate with time

Table 6:

BOG and BOR with necessary calories and total shipped gases for conversion from hydrate to ice

The total heat ingress into the NGH cargo tank over 24 – 48 h was about 2,744,389kJ, and the BOG and BOR based on the amount of heat inflow to the cargo hold were about 1.57 × 10⁵ mol/day and 0.17%/day, respectively. If the BOR is calculated according to the heat flow entering into the cargo tanks under the conditions of atmospheric pressure and ocean temperature using the IGC code of IMO, approximately 0.17% of the total cargo volume would dissociate.

In general, 1.6% of the BOR in hydrates is generated by the self-preservation effect under the environmental conditions at 1 barg and –20 °C. Then the BOR that may occur during ship operation under actual sea conditions was estimated to be 1.77% by summing the dissociation that occurs naturally and caused by an external heat source. Figure 11 and 12 present the temperature distribution in the outer hull and the temperature profile by section in the fourth cargo tank. Heat flowed into the cargo tank over time.

Figure 11:

Temperature distribution in out hull

Figure 12:

Temperature profile at section with time in fourth cargo hold