Study on the Diffusion Mechanisms of Methanol Leakage in Confined Spaces

Abstract

With the rapid expansion of methanol-powered shipping, the emphasis within the industry has increasingly been placed on ensuring the operational safety of these alternative fuel vessels. In this study, the mixture and realizable k-ε models are adopted to simulate the liquid methanol leakage model, and the predictive accuracy of the model is verified through a comparative analysis with experimental results. Given the complexity of ship cabins, a comprehensive exploration of the leakage and diffusion behaviors of methanol under different ambient temperatures, main engine surface temperatures, and leakage port sizes is conducted. The research findings show that an increase in ambient temperature significantly accelerates vapor diffusion by enhancing evaporation and strengthening the wall-accumulation effect. In contrast, an increase in the main engine surface temperature mainly causes local vapor stagnation and has a relatively limited impact on the overall diffusion pattern. An increase in the leakage orifice diameter directly increases the leakage volume, shortens the diffusion period, and promotes nonlinear growth of the vapor height. The research results can not only provide a theoretical basis for the design of cabin structures and ventilation systems of methanol fuel ships but also be applied to the risk prevention and control of methanol leakage scenarios on ships.

1. Introduction

As the predominant facilitator of international commerce, maritime transportation underpins more than 90% of global trade volume. However, this critical sector faces escalating environmental challenges, currently contributing 3% of anthropogenic CO₂ emissions worldwide, a proportion projected to surge to 18% by 2050 in the absence of effective mitigation strategies [1]. In response to tightening emission standards under MARPOL Annex VI, which mandates sulfur content limits in marine fuels (≤0.5% mass/mass) and NOx emission thresholds (Tier III requirements), the maritime industry is compelled to transition toward sustainable energy solutions [2]. Current data show over 90,000 commercial ships globally, with only 2% using cleaner fuels. Methanol is the preferred alternative owing to its renewable potential and environmental benefits. It can reduce sulfur emissions and decrease greenhouse gas emissions compared to conventional fuels. The carbon reduction potential of conventional methanol is relatively limited; however, significant improvements can be achieved through the adoption of green methanol. Green methanol [3] is produced by the electrolysis of water using green electricity to produce hydrogen, which is then combined with carbon dioxide captured from the air through a catalytic reaction [4,5]. Consequently, the implementation of methanol/diesel dual-fuel engines in heavy-duty transportation applications presents a viable pathway for attaining carbon-emission reduction objectives [6].

However, methanol is a toxic and volatile liquid. When its concentration in the air reaches 39.3–65.5 g/m³, acute poisoning may occur. Inhalation of methanol vapor can cause direct damage to the respiratory mucosa and the optic nerve. Short-term exposure to high-concentration methanol vapors can induce severe respiratory tract irritation. In severe cases, it may lead to rapid breathing, retinal lesions, and even blindness. The leakage of methanol in enclosed ship compartments exposes crew members to life-threatening hazards. Therefore, it is necessary to simulate methanol leakage under different conditions in confined spaces and analyze leakage and diffusion patterns. This study aims to provide a theoretical foundation for the safe application of methanol fuel in the maritime sector.

Numerous scholars have conducted comprehensive investigations into the leakage, evaporation, and vapor diffusion mechanisms of hazardous chemicals. Notable experimental benchmarks in this field include the six-year Burro experiment by the U.S. Department of Energy, Thorney Island trials supervised by the UK’s Health and Safety Executive (HSE), and Shell’s pioneering release experiments [7,8]. Building upon the Burro experiment framework, researchers, including Hansen and Sun, have systematically advanced our understanding of hazardous chemical dispersion dynamics [9]. Hu et al. [10] developed an innovative monitoring system for chemical leaks in Louisiana’s industrial facilities, revealing persistent daily emissions of toxic substances through both operational processes and equipment fatigue failures in high-pressure systems. Zimmerman et al. [11] demonstrated significant seasonal variations in leak characteristics, showing temporal fluctuations in both leakage magnitude and dispersion patterns. Advanced modeling approaches have significantly enhanced these predictive capabilities. Pontiggia et al. [12] employed detailed 3D urban modeling to simulate (LPG) dispersion, successfully mapping the temporal evolution of hazard zones and ground deposition rates. Dahikar et al. [13] conducted comparative simulations of liquid ammonia jet releases, establishing the superior accuracy of Large Eddy Simulation (LES) models over traditional k-ε models in replicating real-world dispersion patterns. Their work included detailed analyses of the cross-sectional concentration gradients and thermal temporal profiles. Hydrogen safety research has particularly benefited from computational fluid dynamics (CFD) advancements. Heitsch et al. [14] differentiated between instantaneous and continuous hydrogen release behaviors in high-pressure systems through validated simulations, while Liu et al. [15] quantified parametric relationships between wind speed, pipeline diameter, and H₂ dispersion distances. Ichard et al. [16] revealed dual-phase liquid hydrogen behavior involving initial groundward droplet sedimentation followed by buoyant uplift, complemented by comprehensive temperature-distance-time mappings.

Hassanvand et al. [17] developed evaporation models for gasoline-water interactions, demonstrating temperature-dependent mass transfer kinetics through time-resolved vaporization curves. Transportation infrastructure studies have provided critical safety insights. Hussein et al. [18] identified optimal 0.5 mm Thermally-activated Pressure Relief Device (TPRD) configurations and escape route determinants for fuel cell vehicle leaks in underground parking facilities. Choi et al. [19] contrasted ventilated versus non-ventilated scenarios, revealing nonlinear combustible volume growth patterns and ventilation efficacy thresholds. Malakhard et al. [20] validated CFD models against mining tunnel experiments, differentiating among the dispersion patterns of high-pressure with low-flow and low-pressure with high-flow. Bie et al. [21] demonstrated ventilation-induced hydrogen concentration gradients in underwater tunnels and established upstream positions as safe zones during leak events. Stationary infrastructure analyses by Qian et al. [22,23] revealed minimal combustible cloud sensitivity to initial leak parameters but significant obstacle proximity and wind direction effects. Han et al. [24] optimized safety barrier designs through parametric studies on leak diameters and pressure dependency. Vehicle compartment studies by Salva et al. [25] and Yu et al. [26] identified rear vent concentration hotspots and quantified wind-mediated risk reduction strategies, while Xie et al. [27] developed blower-based dispersion protocols demonstrating outlet size-wind speed optimization principles. Industrial applications research by Houf et al. [28] validated passive ventilation effectiveness in forklift deflagration mitigation, whereas Klebanoff et al. [29,30] established maritime fuel cell compartment requirements through cryogenic fuel comparative analyses. These collective advancements underscore the critical importance of scenario-specific modeling in developing robust chemical safety protocols.

Current research has established comprehensive predictive capabilities for leakage and dispersion through multi-scale modeling and multi-method validation, providing theoretical foundations for scenario-specific safety protocols. However, a critical knowledge gap remains regarding the dispersion of liquid methanol in confined spaces. In this study, a 3D dispersion model is developed by integrating the mixture and realizable k-ε models. The computational framework is dedicated to exploring the release dynamics of liquid methanol and the diffusion patterns of its vapor within the engine compartments of methanol-powered ships. Given the complexity of ship cabins, a comprehensive exploration of the leakage and diffusion behaviors of methanol under different ambient temperatures, main engine surface temperatures, and leakage port sizes is conducted.

2. Numerical Methods and Details

The Mixture model demonstrates computational efficiency, while the Realizable k-ε model exhibits enhanced reliability over the Standard k-ε formulation in complex flow regimes and remains more economical than the Reynolds Stress Models (RSM) or Large Eddy Simulation (LES). Through collaborative model optimization, this approach addresses the technical limitations of conventional methods in resolving coupled multiphase flow-turbulence interactions, establishing a robust framework for analyzing multiphase turbulence phenomena in cutting-edge fields such as renewable energy and sustainable development. This methodology has emerged as a leading-edge practice in industrial CFD simulations.

2.1. Governing Equations

A mixture model is adopted to simulate the two-phase flow process of the liquid methanol spill. The primary phase is the gas phase, which consists of methanol and air, and the secondary phase is the liquid methanol. In the mixture model, the gas and liquid phases are assumed to be incompressible and in thermodynamic equilibrium. The two-phase flow of liquid methanol spill is predicted by solving the three-dimensional transient conservation equations for mass, momentum, and energy, as shown below [31]:

$${\displaystyle \frac{\partial {\rho }_m}{\partial t}}+\nabla \cdot ({\rho }_m\overrightarrow{{\nu }_m})=0$$

(1)

$$\begin{array}{r}{\displaystyle \frac{\partial }{\partial t}}\left({\rho }_m\overrightarrow{{\nu }_m}\right)+\nabla \cdot \left({\rho }_m\overrightarrow{{\nu }_m}\overrightarrow{{\nu }_m}\right)=-\nabla p+\nabla \cdot \left[{\mu }_m\left(\nabla \overrightarrow{{\nu }_m}+\nabla {\overrightarrow{{\nu }_m}}^T\right)\right]\\ +{\rho }_m{g}_i+\overrightarrow{F}-\nabla \cdot \left({\displaystyle \sum _{i=1}^n{\alpha }_i{\rho }_i\overrightarrow{{\nu }_{dr,i}}\overrightarrow{{\nu }_{dr,i}}}\right)\end{array}$$

(2)

$${\displaystyle \frac{\partial }{\partial t}}{\displaystyle \sum _{i=1}^n\left({\alpha }_i{\rho }_i{E}_i\right)}+\nabla \cdot {\displaystyle \sum _{i=1}^n\left({\alpha }_i\overrightarrow{{\nu }_i}\left({\rho }_i{E}_i+p\right)\right)}=\nabla \cdot \left(k_{eff}\nabla T\right)$$

(3)

The density, velocity, and kinetic viscosity of the mixture are denoted as ${\rho }_m={\alpha }_l{\rho }_l+{\alpha }_g{\rho }_g$ $\overrightarrow{v_m}=\left({\alpha }_l{\rho }_l\overrightarrow{{\nu }_l}+{\alpha }_g{\rho }_g\overrightarrow{{\nu }_g}\right)/{\rho }_m$ and ${\mu }_m={\alpha }_l{\mu }_l+{\alpha }_g{\mu }_g$, respectively. The subscripts l, g, and m represent the liquid phase, gas phase, and mixture phase, respectively. α is the volume fraction of each phase, $\overrightarrow{F}$ is the volume force, $\overrightarrow{v_{dr,i}}$ is the drift velocity, k_eff is the effective thermal conductivity, and E_k is the sensible enthalpy of the phase k.

2.2. Slip Model

In the mixture model, there is a slip velocity between the gas and liquid phases due to the large density difference. The slip velocity ($\overrightarrow{v_{pq}}$) is expressed as follows:

$$\overrightarrow{v_{pq}}={\displaystyle \frac{{\tau }_p}{f_{drag}}}{\displaystyle \frac{{\rho }_p-{\rho }_m}{{\rho }_p}}\overrightarrow{\alpha }$$

(4)

where the drag force (f_drag) is expressed as follows:

$$f_{drag}=\left\{\begin{array}{l}1+0.15{\mathrm{Re}}^{0.687},\mathrm{Re}\le 1000\\ 0.0183\mathrm{Re},\mathrm{Re}>1000\end{array}\right.$$

(5)

2.3. Mass Transport Model

The mass transfer process between the liquid and gas phases is predicted using the following equations [32]:

$${\displaystyle \frac{\partial }{\partial t}}\left({\alpha }_g{\rho }_g\right)+\nabla \cdot \left({\alpha }_g{\rho }_g\overrightarrow{v_g}\right)={\stackrel{·}{m}}_{\lg }-{\stackrel{·}{m}}_{gl}$$

(6)

where ${\stackrel{·}{m}}_{\lg }$ and ${\stackrel{·}{m}}_{gl}$ represent the mass transfer from the liquid phase to the gas phase and from the gas phase to the liquid phase, respectively, which can be calculated by the Lee model:

for the evaporation process:

$${\dot{m}}_{\lg }=coef{f}_{ev}\cdot {\alpha }_l{\rho }_l\left(T_l-T_{sat}\right),if{T}_l>T_{sat}$$

(7)

for the condensation process:

$${\dot{m}}_{\lg }=coef{f}_{con}\cdot {\alpha }_g{\rho }_g\left(T_{sat}-T_g\right),if{T}_g<T_{sat}$$

(8)

where $\dot{m}$ is the mass transfer rate during evaporation or condensation, T_l, T_g and T_sat are the liquid phase, gas phase, and saturation temperatures, respectively. coeff_ev and coeff_con are the evaporation and condensation coefficients, which are similar to the relaxation time. Their values must be finely tuned to ensure that the simulation results are consistent with the experimental results.

In addition, the local mass fraction of each species in the gas phase is calculated using the convective-diffusion equation:

$$\begin{array}{l}{\displaystyle \frac{\partial }{\partial t}}\left({\rho }_g{\alpha }_g{Y}_{g,i}\right)+\nabla \cdot \left({\rho }_g{\alpha }_g{Y}_{g,i}\right)=\\ -\nabla \cdot {\alpha }_g\left[-\left(\rho D_{g,i}+{\displaystyle \frac{{\mu }_t}{S{c}_t}}\right)\nabla Y_{g,i}\right]+\stackrel{·}{m_{\lg }^i}-\stackrel{·}{m_{gl}^i}\end{array}$$

(9)

where Y_g,i is the mass fraction of the component i in the gas phase, D_g,i is the molecular diffusion coefficient of the component i in the gas phase, μ_t is the turbulent viscosity, and Sc_t is the turbulent Schmidt number.

2.4. Turbulence Model

The Realizable k-ε model and enhanced wall treatment are chosen for turbulence closure, which has been validated to be suitable for turbulence simulation for dense gas diffusion in the presence of obstacles [33]:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho k{u}_j\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(u+{\displaystyle \frac{u_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon$$

(10)

$$\begin{array}{c}{\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho \epsilon u_j\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right)\cdot {\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+\rho C_{1\epsilon }E\epsilon \\ -\rho C_2{\displaystyle \frac{{\epsilon }^2}{k+\sqrt{\nu \epsilon }}}+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{C}_{3\epsilon }{G}_b\end{array}$$

(11)

where $C_1=\max \left[0.43,{\displaystyle \frac{\eta }{\eta +5}}\right]$, $\eta =\sqrt{2S_{ij}\cdot S_{ji}}\cdot {\displaystyle \frac{k}{\epsilon }}$, $S_{ij}={\displaystyle \frac{1}{2}}\left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)$, ${\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}$. G_k is the turbulent kinetic energy generated by the mean velocity gradient, and G_b is the turbulent kinetic energy generated by buoyancy.

2.5. Physical Model and Model Validation

This study is based on a ship with an overall length of 249.8 m and a beam of 44 m. The main engine compartment of the ship serves as the research focus. The structure and various internal components of the compartment were simplified to construct a geometric model. A schematic illustration of the 3D model is presented in Figure 1.

The numerical simulation domain is established with dimensional parameters of L × W × H = 35 m × 25 m × 4 m. The methanol release source is positioned 1.0 m above the deck level at the portside longitudinal frame. Ventilation apertures (1 m² cross-section each) were symmetrically distributed on both the port and starboard bulkheads.

In the simulation, the initial operating environment must be configured. The simulation in this paper focuses on methanol leakage and diffusion. During the simulation, the gravity term was enabled, with its direction along the y-axis and a value set to −9.81 m/s². The reference ambient pressure is set to atmospheric pressure, which is 1 atm, and the ambient temperature is set at 308 K. The methanol inlet is defined as a velocity inlet, with the methanol temperature set to 308 K. Ensure to define the component characteristics by mole fraction and input a methanol value of 1. The positions of the windows on both sides of the calculation domain are set as pressure outlets, with their parameters remaining at the default values. It is assumed that the leakage hole has a circular shape, the leakage state is a constant leakage, and the fluid is in an ideal state.

The comparative analysis presented in Figure 2 demonstrates excellent consistency between the numerical simulations and experimental measurements. The simulated results closely align with the experimental data within acceptable deviations, particularly when accounting for environmental perturbations (e.g., atmospheric instability) and instrumentation uncertainties inherent in field experiments. This quantitative agreement substantiates the validity of the proposed leakage and diffusion model for replicating real-world physical processes under complex operational conditions.

2.6. Grid Independence Verification

The general configuration of the refinement regions near the leakage port is shown in Figure 3.

To ensure the correctness of the grid division, grid independence verification was performed on the established geometric model. Based on the model and governing equations, three grid configurations—332,789, 430,005, and 545,996 elements—were tested to analyze the influence of grid density on the simulation results. As shown in Figure 4, the results obtained with 332,789 grids exhibit significant errors, whereas those with the other two grid counts show minimal discrepancies. The analysis reveals that increasing the grid count to 430,005 has a negligible impact on the accuracy of the results, while further refinement only prolongs computational time and reduces efficiency. Therefore, a grid size of 430,005 elements was selected for this study to balance the accuracy and computational performance.

3. Results and Discussion

3.1. The Impact of Ambient Temperature

The variation in the ambient temperature within the ship cabin can induce diverse changes in the leakage and diffusion of methanol. The core research focus of this section is the influence of ambient temperature alterations inside the cabin on methanol leakage and diffusion. Given that the temperature within the engine room of a ship typically fluctuates within the range of 298 K to 328 K, four parameter sets, namely 298 K, 308 K, 318 K, and 328 K, are selected for comparison in this section.

As shown in Figure 5, when the leakage occurrs for 3 s, a nearly circular methanol gas cloud forms beneath the leakage orifice. In the absence of obstacles, the shape of the methanal vapor is relatively regular. However, upon encountering an obstacle, gas cloud accumulation will occur at the position of the obstacle wall, resulting in a higher gas cloud concentration in this part. When the leakage reaches 6 s and 9 s, the gas cloud reaches the wall of the right-hand main engine. Compared with the left-hand side, the space on the right-hand side is more open; therefore, the concentration of the gas cloud on the right-hand side is lower than that on the left-hand side. At 12 s of leakage, the left-hand part of the gas cloud has diffused to the left-most wall of the compartment. At 15 s of leakage, both the left-hand and right-hand sides of the methanol vapor have diffused to the walls of the compartment.

As depicted in Figure 6, both the height and length of the methanol gas cloud increase as the leakage time progresses. Given that the density of methanol is greater than that of air, the methanol gas cloud assembles in a region near the ground. The height of the center of the methanol gas cloud is slightly higher than that of its two sides. Notably, at the outermost end of the gas cloud, a curled-up shape forms where the height of the gas cloud reaches its maximum value.

As shown in Figure 7 and Figure 8, an increase in the ambient temperature results in an increase in the distance between the gas cloud and the leakage port along the leakage direction. This phenomenon occurs because an increase in the ambient temperature hastens the evaporation rate of methanol. Consequently, a greater amount of liquid methanol vaporizes into gaseous methanol, allowing the methanol gas cloud to disperse to more remote areas. When the leakage time is 15 s, and the ambient temperature is 298 K, the gas cloud is in the closest proximity to the leakage port at a distance of 24.57 m.

At an ambient temperature of 308 K, the distance between the outermost end of the gas cloud and the leak port measures 24.82 m. At an ambient temperature of 318 K, this distance is 24.98 m. When the ambient temperature is 328 K, the gas cloud is at its maximum distance from the leak port, with a value of 25.00 m, having extended all the way to the wall opposite the leakage port.

As is clearly shown in Figure 9, as the ambient temperature increases, the distance between the methanol vapor on both sides of the leakage hole and the leakage port increases. On the right side of the leakage port, the methanol vapor gas cloud reaches the cabin wall 13 s after the leakage begins. On the left-hand side of the leakage port, the methanol vapor gas cloud reaches the cabin wall only 11 s after the leakage starts.

As is observable from Figure 10, in the main view, the methanol gas cloud exhibits a higher central height, with the height of the methanol vapor gradually diminishing from the middle toward both sides. However, the outermost end of the gas cloud attains the greatest height among all parts of the methanol vapor gas cloud. The height of the methanol gas cloud increases in tandem with the rise in ambient temperature.

Table 1. Gas cloud height (m) at different times and ambient temperatures.

Time/s	Ambient Temperature/K
	298	308	318	328
3	0.978	0.98	0.98	0.988
6	1.345	1.35	1.368	1.37
9	1.55	1.539	1.545	1.55
12	1.62	1.615	1.63	1.635
15	1.632	1.632	1.642	1.695

shows the heights of the gas clouds at different times and ambient temperatures. The influence of ambient temperature changes on the height of the gas clouds is plotted according to Table 1, as shown in Figure 11.

As is observable from Figure 11, When the leakage duration is 15 s, at an ambient temperature of 298 K, the height of the methanol vapor is the lowest, measuring 1.6 m. When the ambient temperature is 308 K, the gas cloud height reaches 1.632 m. At an ambient temperature of 318 K, the height of the methanol vapor is 1.642 m. When the ambient temperature is 328 K, the gas cloud reaches a maximum height of 1.695 m. In the scenario of an ambient temperature of 328 K, the height of the methanol vapor after 15 s of leakage increases notably. This is because the methanol gas cloud has reached the wall opposite the leakage port, causing the gas cloud to accumulate near the wall, which in turn leads to a significant increase in the height of the methanol vapor.

3.2. The Impact of Main/Auxiliary Engine Surface Temperature

The structure of a ship cabin is intricate. When the main engine and auxiliary engine are operational, the temperature of the surfaces can be extremely high, which may induce diverse alterations in the leakage and diffusion of methanol. The core research focus of this section is the impact of the variation in the wall temperature of the main and auxiliary engines on methanol leakage and diffusion. Since the wall temperature typically ranges from 308 K to 338 K, three parameter sets, namely 308 K, 323 K, and 338 K, are chosen in this section for comparison.

As shown in Figure 12, when the leakage occurs for 3 s, the gas cloud has not yet encountered any obstacles, its shape remains relatively regular, and the methanol gas cloud diffuses up to 6.45 m. When the leakage reaches 6 s and 9 s, upon encountering an obstacle, the methanol gas cloud accumulates on the obstacle’s wall. This leads to a higher gas cloud concentration in this area, and the gas cloud reaches the wall of the right-hand main engine. However, compared with the left-hand side, the space on the right-hand side is more expansive; therefore, the gas cloud concentration on the right-hand side is lower than that on the left-hand side.

The methanol gas cloud can diffuse to 11.58 m at 6 s leakage, and when the leakage time is 9 s, it can diffuse to 16.30 m. At 12 s leakage, the left-hand part of the gas cloud has spread to the left-most wall of the cabin, and the methanol gas cloud has spread to 20.63 m. At 15 s leakage, both sides of the gas cloud have spread to the cabin walls. The methanol gas cloud has spread to 24.78 m. Due to the increasing surface temperature of the main engine and auxiliary engine, the gas cloud concentration near the main engine and auxiliary engine is higher. This is a consequence of both gas cloud accumulation and accelerated evaporation triggered by the rise in surface temperature. An increase in the surface temperature can increase the local methanol concentration but has little effect on the overall methanol gas cloud diffusion.

As shown in Figure 13, with an increase in the ambient temperature, the distance between the methanol vapor and the leakage port in the direction of the leakage port increased. When the leakage time is 15 s, at a surface temperature of 308 K, the gas cloud is closest to the leakage port at a distance of 24.71 m. When the surface temperature is 323 K, the distance between the farthest end of the gas cloud and the leak port is 24.75 m. When the surface temperature is 338 K, the gas cloud is farthest from the leak port, and the distance is 24.77 m.

As shown in Figure 14, as the surface temperature increases, the distance between the gas clouds on both the left and right sides of the leak port and the leak port increases. On the right side of the leak port, the methanol vapor gas cloud reaches the cabin wall 13 s after the leakage starts. On the left side of the leak port, the methanol vapor gas cloud reaches the cabin wall only 11 s after the leakage begins.

Table 1 shows the heights of the gas clouds at different times for different surface temperatures. The influence of surface temperature changes on the height of the gas clouds is plotted according to

Table 2. Gas cloud height (m) at different surface temperatures at different times.

Time/s	Surface Temperature/K
	308	323	338
3	0.945	0.99	1.01
6	1.34	1.37	1.38
9	1.501	1.55	1.56
12	1.585	1.642	1.65
15	1.632	1.63	1.65

, as shown in Figure 15.

As shown in Figure 15, the methanol gas cloud features a relatively higher central height. The height of the methanol vapor gradually decreases from the middle toward both sides. However, the outermost end of the gas cloud attains the maximum height among all parts of the methanol vapor. As the temperature of the main and auxiliary engines increases, the height of the methanol gas cloud generally increases. Nevertheless, there are brief intervals during which the height of the methanol gas cloud experiences certain fluctuations. When the leakage duration reaches 15 s, the height of the methanol vapor is the lowest at a surface temperature of 323 K, measuring 1.63 m. When the surface temperature is 308 K, the height of the methanol vapor is 1.63 m. At a surface temperature of 338 K, the methanol vapor reaches its highest height of 1.65 m.

3.3. The Impact of Leakage Orifice Size

The variation in the size of the leakage port may give rise to diverse changes in the leakage and diffusion of methanol. The primary research focus of this section is the impact of the alteration of the leakage port size on the leakage and diffusion of methanol. In this section, four sets of parameters are chosen for comparison, with the diameters of the leakage ports being 6 cm, 8 cm, 10 cm, and 12 cm.

As shown in Figure 16, when the leakage persisted for 3 s, a nearly circular methanol gas cloud formed beneath the leakage port. The gas cloud extended to a distance of 3.21 m along the orientation of the leakage orifice and reached distances of 1.988 and 2.01 m on either side of the leakage port. When the leakage duration reached 6 s, the gas cloud propagated to 12.819 m along the orientation of the leakage orifice and to 10.425 m and 11.71 m on both sides of the leakage port. At 9 s after the leakage, the gas cloud advanced to 17.98 m along the orientation of the leakage orifice and to 14.715 m and 17.04 m on the two sides of the leakage port. At this juncture, as the gas cloud spread into an area with a relatively confined space, the concentration of methanol vapor was notably higher than that in other areas. When the leakage time reached 12 s, the gas cloud spread to 22.87 m along the orientation of the leakage orifice and had already reached the walls of both sides of the cabin. At 15 s, the gas cloud reached the wall opposite the leakage port in the direction of the leakage port.

As shown in Figure 17 and Figure 18, as the size of the leakage port increases, the distance between the methanol vapor and the leakage port along the orientation of the leakage orifice also increases, which has a significant impact on the length of the methanol gas cloud.

When the leakage time is 15 s, and the leakage port size is 6 cm, the gas cloud is closest to the leakage port, with a distance of 18.676 m. When the leakage port size is 8 cm, the distance between the farthest end of the gas cloud and the leakage port is 21.989 m. When the leakage port size is 10 cm, the distance between the farthest end of the gas cloud and the leakage port is 24.867 m. When the diameter of the leakage port is 12 cm, the gas cloud is the furthest from the leakage port, at a distance of 25 m.

With an increase in the diameter of the leakage port, the gas cloud diffuses further at the same time. On both sides of the leakage port, when the diameter of the leakage port is 6 cm, the gas cloud will not diffuse to the cabin wall. The larger the diameter of the leakage port, the shorter the time required for the methanol vapor gas cloud to reach the cabin wall. This is because a larger leakage port leads to an increase in the amount of methanol leakage, which, in turn, results in an increase in the evaporation of methanol.

Table 3. Gas cloud height (m) at different times for different leakage sizes.

Time/s	Leakage Size/cm
	6	8	10	12
3	0.86	0.95	0.997	1.07
6	1.12	1.261	1.367	1.455
9	1.35	1.45	1.55	1.596
12	1.435	1.588	1.64	1.66
15	1.585	1.607	1.63	2.95

shows the height of the gas clouds at different times for different leakage sizes. The influence of leakage size changes on the height of gas clouds is plotted according to Table 3, as shown in Figure 18.

As is evident from Figure 19 and Figure 20, in the main view, the methanol gas cloud exhibits a relatively higher central height. The height of the gas cloud gradually decreases from the middle toward both sides. However, the outermost end of the gas cloud is where the methanol vapor gas cloud attains its maximum height.

As the diameter of the leakage port increases, the overall height of the gas cloud will experience a slight increase. The height of the methanol gas cloud tends to stabilize and does not show a significant upward trend.

When the leakage duration is 15 s, with a leakage port diameter of 6 cm, the height of the gas cloud is at its lowest, measuring 1.585 m. When the leakage port diameter is 8 cm, the height of the methanol vapor is 1.63 m. When the leakage port diameter is 10 cm, the height of the methanol vapor is 1.607 m. When the leakage port diameter is 12 cm, the height of the methanol vapor reaches its maximum, which is 2.95 m. Therefore, continuous monitoring of methanol fuel pipelines is essential, and immediate emergency protocols—including forced ventilation—must be implemented upon detection of large-scale leakage to mitigate hazards.

4. Conclusions

This study systematically investigated the effects of ambient temperature, main/auxiliary engine surface temperature, and leakage orifice size on the methanol dispersion characteristics in ship compartments. The key findings are summarized as follows:

(1)

A significant increase in the ambient temperature notably augmented the evaporation rate of methanol and expedited the diffusion of its vapor. At 328 K, methanol vapor reached the opposite wall (25 m away) within 15 s. The diffusion distance of the methanol gas cloud increased by 6.7% compared to that at 298 K. The height of the methanol vapor was found to be temperature—dependent. The maximum height of the vapor increased from 1.6 m to 1.695 m, which is attributable to the wall-induced accumulation effect.

(2)

An increase in the surface temperature of the main engine/auxiliary engine promoted local steam accumulation near the heated surface. However, its impact on the overall diffusion pattern was not as pronounced as that of ambient temperature. The diffusion distance of the methanol gas cloud did not change substantially with increasing surface temperature.

(3)

The correlation between methanol leakage and diffusion was most strongly associated with the diameter of the holes. A larger hole increased the mass flux and reduced the contact time with the wall. For instance, with a 12-cm hole, full-chamber diffusion was achieved in 15 s. The vertical height of the vapor increased nonlinearly. The accumulation peak of 2.95 m in the 12-cm hole at 15 s was 86% higher than that in the 6-cm leak hole.

These findings highlight the necessity of incorporating thermal management strategies and leakage source monitoring in marine engine room design. Enhanced ventilation systems and thermal insulation of high-temperature surfaces could mitigate the risk of accumulation. For emergency response, evacuation protocols should prioritize the early detection of leaks in warmer zones and near large-diameter pipelines.