Numerical simulation of small breathing loss in dome roof tanks under solar radiation

Cheng, Ligang; Zhang, Haijuan; Pang, Hao; Dong, Mei; Wang, Weiqiang

doi:10.1590/1517-7076-RMAT-2024-0687

ABSTRACT

In order to investigate the effect of periodic solar radiation on oil vapor diffusion and small breathing losses in dome roof tanks, a theoretical model of unsteady heat and mass transfer in dome tanks is established based on the ASHRAE clear-sky model and oil evaporation theory. The heat flux UDF is self-programmed, and CFD software is used to simulate the heat and mass transfer process in the gas space of the dome tank. Dynamic mesh technology is used to realize the overpressure relief of the breathing valve and calculate the small breathing losses. The results show that the gas space temperature decreases from top to bottom; it has a concave and convex distribution near the tank wall. The average temperature decreases with increasing liquid level. The vapor concentration in the gas space increases from top to bottom, and there is a clear concentration layer near the liquid level. The average vapor concentration increases with the liquid level. Gas space pressure increases gradually from top to bottom. The number of breathing valve exhausts decreases with the increase in liquid level. The small breathing losses increase with the liquid level and the seasonal warming, and the loss rate increases with the seasonal warming.

Keywords:
Dome roof tanks; Solar radiation; Heat and mass transfer; Small breathing losses; Numerical simulation

1. Introduction

China’s transition towards cleaner and low-carbon energy is accelerating under the “carbon peak, carbon neutral” dual-carbon goal [¹]. Consequently, the oil and gas storage and transportation industry is confronting challenges related to carbon emission control while exploring opportunities for low-carbon development [²]. China’s major petrochemical enterprises have numerous oil storage tanks in their storage systems. Among them, evaporation loss is the most common form of oil loss during the daily storage process of oil tanks. The volatile organic compounds (VOCs) generated through evaporation are released into the atmosphere, posing considerable risks to human health and the natural environment. To effectively control the emissions and recovery of VOCs in tank farms, domestic and foreign researchers have conducted extensive research. They have primarily focused on the evaporation characteristics of oil products, the impact of external environments, and the prediction and evaluation of tank oil loss.

Petroleum and petroleum products are multicomponent mixtures, and their evaporation losses vary depending on the oil components. MATSUMURA [³, ⁴] concluded that there is a correlation between the amount of evaporation losses of refined oil products and temperature and hydrocarbon concentration based on studying hydrocarbon substances evaporated from oil in refineries, petrol stations, and oil depots but did not provide a specific relationship between these factors. FINGAS [⁵, ⁶] studied the correlation between oil loss and time during evaporation for several crude oils and petroleum products. It was found that the evaporation rate of most oils and petroleum products was logarithmically related to time and that the fewer the components, the closer the evaporation rate with time was to the square root model. SHARMA et al. [⁷] monitored the temperature and saturated vapor pressure of 15 different grades of gasoline and found that in the initial stage of oil evaporation, components with low boiling points would evaporate faster due to temperature changes, and the evaporation loss was mainly due to the change of Reid vapor pressure. JIA [⁸] and XIAN [⁹] determined the evaporation rate of different oils and petroleum products by gas chromatography (GLC) and found that the distribution of hydrocarbons in different oils affects their evaporation loss, with more light components resulting in more evaporation loss. HUANG et al. [¹⁰] carried out chromatographic analysis of different monomer hydrocarbons and obtained the average carbon number of exhaled oil vapor by regression calculation, which provided accurate basic data for oil evaporation loss and its control technology. In summary, the evaporation loss of oil is closely related to the type of components and their physical properties, and the lighter the components, the more obvious the evaporation loss.

Based on the different oil types and physical properties of each component, researchers have proposed methods for evaluating breathing loss under different operating conditions. MONCALVO et al. [¹¹] investigated the breathing loss in low-pressure storage tanks resulting from atmospheric weather changes and developed an analytical model to predict the total inspiratory volume required for vapor condensation during prolonged rainfall. LIANG [¹²] examined the limitations of several small breathing loss calculation methods and employed programming techniques to derive average exhaled breath concentration, thereby establishing a new calculation model for small breathing losses that effectively reduces computational errors associated with previous models. FETISOV et al. [¹³] developed two estimation methods for the emission of VOCs from oil tanker tanks, employing both numerical and experimental approaches. The numerical assessment method accurately determined the dynamic growth of gas space pressure within the tank from both quantitative and qualitative perspectives. Meanwhile, the experimental method established an oil vapor recovery framework that predicts VOC emissions in Arctic regions by monitoring changes in terminal states. While these studies have assessed and quantified evaporation losses in oils, it is evident that progress in research concerning evaporation loss assessment methodologies remains relatively slow due to the diversity of tank types and complexity of loss mechanisms; thus, further improvements are necessary.

In the static storage process, the evaporation loss of oil inside the tank is constantly influenced by the external environment. SUN et al. [¹⁴] and WANG et al. [¹⁵] established a theoretical model for unsteady state heat transfer in floating roof tanks and simulated the heat transfer process of crude oil within the tank using CFD software. They found that solar radiation significantly influences temperature fluctuations, while atmospheric temperature has a more pronounced effect on the rate of temperature decline. LI et al. [¹⁶] conducted large eddy simulations (LES) to investigate the temperature field of crude oil within large floating roof tanks. Their findings indicate that when the oil temperature exceeds the ambient temperature, heat transfer within the tank is predominantly governed by natural convection; conversely, when the oil temperature is lower than that of the surrounding atmosphere, conductive heat transfer becomes predominant. Furthermore, this study quantitatively demonstrated the necessity of considering solar radiation in environments exposed to sunlight. YANG et al. [¹⁷] continuously measured the temperature change of oil in a fixed-roof metal oil tank for 24 h. It was found that only the temperature of the upper part of the oil changed slightly with the ambient temperature in 24 h, while the temperature of the oil from about 10 cm below the oil surface to the bottom of the tank basically unchanged in 24 h, and the overall temperature of the oil changed only with the ambient temperature. The overall temperature of the oil varied only with the ambient temperature. ZHANG et al. [¹⁸] utilized MATLAB software to obtain the variation rule of liquid phase evaporation with time in the dome roof tank on the vernal equinox and found that under the influence of solar radiation, the cumulative amount of liquid phase evaporation gradually increases during the day, but its increase rate is larger in the morning and afternoon and smaller at noon. In the above researches, the effects of transient solar radiation and ambient temperature variations on the temperature of oil and evaporative loss of oil in the tanks were analyzed, especially solar radiation is an important factor affecting the accurate simulation of the temperature field. However, the temperature and pressure variations in the gas space of dome roof tanks have a significant effect on the evaporation loss of oil under solar radiation as compared to floating roof tanks.

Currently, there is limited research on the heat and mass transfer in the gas space of dome roof tanks and the overpressure relief of the breathing valve under the working condition of the tanks. Additionally, the rotation and the revolution of the earth always affect the evaporation of oil in tanks; however, previous studies have not examined oil evaporation losses from the perspective of seasonal variations in solar radiation and ambient temperature. Therefore, this paper adopts the ASHRAE clear-sky model and oil evaporation theory to establish an unsteady heat and mass transfer model for dome roof tanks [¹⁹], compiles the heat flux User Defined Function (UDF), and simulates the effects of periodic solar radiation and ambient temperature on the gas space of the dome roof tank under different liquid level heights using CFD software. Furthermore, dynamic mesh technology is used to simulate the overpressure relief of the breathing valve. N-hexane is used as the gasoline representative to calculate the small breathing loss, and a new breathing loss evaluation method is proposed to provide a theoretical basis for the work of reducing the breathing loss of dome roof tanks and preventing the emission of VOCs.

2. Model establishment

2.1. Theoretical model

The unsteady state heat and mass transfer model for the dome roof tank was established based on the ASHRAE Clear-Sky Model and oil evaporation theory, as shown in Figure 1.

Figure 1
Theoretical modeling of unsteady state heat and mass transfer in dome roof tanks.

(1)
Solar radiation

Direct solar radiation (G_D) absorbed by a plane at an angle is calculated by equation (1, 2):

(1) $G_{D} = α G_{N D} \cos θ$

(2) $G_{N D} = \frac{A}{\exp (B / \sin β)} C_{N}$

Scattered radiation absorbed by the horizontal plane (G_dθ1) is expressed in equation (3):

(3) $G_{d θ 1} = α C G_{N D}$

Scattered radiation absorbed in a vertical plane (G_dθ2) is described in equation (4):

(4) $G_{d θ 2} = α C G_{N D} Y$

Ground scattered radiation (G_R)is described in equation (5):

(5) $G_{R} = α G_{t H} ρ_{g} \frac{1 - \cos θ}{2}$

In the equation: G_ND is the direct radiation intensity (W/m²); α is the absorption coefficient of the tank wall; θ is The inclination angle between the surface and the horizontal plane; ρ_g is the reflectivity of the ground; G_tH is the total radiation level (W/m²) that falls on the horizontal plane or ground in front of the wall; The values of coefficients A, B, C, C_N, Y and can be found in the references [²⁰].

The relationship between solar radiation flux q and time t was determined based on equations (1) to (5):

(6) $q = p_{1} t^{4} + p_{2} t^{3} + p_{3} t^{2} + p_{4} t + p_{5}$

In the equation: p₁~ p₅ is the fitting parameter.
(2)
Convective heat transfer(G_h)

(7) $G_{h} = h_{e} (T_{e} - T_{a})$

(8) $T_{a} = T_{d} - \frac{Δ T_{d}}{2} \cos ω_{0} (t - 2)$

In the equation: h_c is the convective heat transfer coefficient [W/(m²·K)]; T_c is the temperature of the outer surface of the storage tank (K); T_a is the ambient temperature (K); ∆T_d is the mean temperature of the atmosphere during day and night (K); ω₀ is the circular frequency (rad/h).
(3)
Radiation heat transfer (G_c)

(9) $G_{c} = \frac{ε \times C_{0} \times (T^{4}_{a} - T^{4}_{c})}{T_{c} - T_{a}} \times (T_{c} - T_{a})$

In the equation: ε is the blackness of the tank wall; The C₀ radiation coefficient of a blackbody C₀ = 5.67 W/(m²·K⁴)
(4)
Total heat flux

Under solar radiation, the tank shell is divided into the sunny side and the shady side. The types of solar radiation received at different locations of the dome roof tank are listed in Table 1.

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Table 1
Types of solar radiation received at different locations in a dome roof tank.

The total heat flux absorbed by different locations of the storage tank is calculated using equations (10) to (12).

(10) $G_{S u n n y w a l l} = G_{D} + G_{d θ 2} + G_{R} - G_{c} - G_{h}$

(11) $G_{S h a d e d w a l l} = G_{d θ 1} + G_{R} - G_{c} - G_{h}$

(12) $G_{r o o f} = G_{D} + G_{d θ 1} - G_{c} - G_{h}$
(5)
Oil surface temperature and mass fraction

After the oil has been stored in the tank for a certain period, the mean temperature of the oil, both day and night, approximately aligns with the daily mean atmospheric temperature at the location of the oil tank. Additionally, it is observed that the mean temperature of the oil surface during both day and night is slightly higher than that of the bulk oil product over a 24-hour cycle. This relationship can be calculated using Equation (13) [²¹]:

(13) $t_{l i q u i d} = 1 .05 t_{d}$

Due to the complexity of gasoline composition, gasoline vapors can be approximated as a single component substance [²²]. N-hexane, the main component of oil vapors, is chosen as a representative of gasoline [²³].

At the liquid surface, gasoline vapor is nearly in a saturated state. The mass fraction of gasoline vapor at various temperatures can be determined using Dalton’s law of partial pressures.

2.2. Mathematical model

(1)
Continuity equation.

(14) $\frac{\partial ρ}{\partial τ} + \frac{\partial}{\partial x_{j}} (ρ u_{j}) = 0$

In the equation: ρ is density (kg/m³); u_j is the velocity in the x and y directions (m/s).
(2)
Momentum conservation equation

(15) $\frac{\partial ρ}{\partial τ} (ρ u_{j}) + \frac{\partial}{\partial x_{j}} (ρ u_{i} u_{j}) = - \frac{\partial ρ}{\partial x_{j}} + \frac{\partial}{\partial x_{j}} (μ_{t} \frac{\partial u_{i}}{\partial x_{j}}) + ρ g_{i}$

In the equation: ρ is the absolute pressure (Pa); µ_t is the dynamic viscosity of the fluid (Pa·s); g_i is the gravitational acceleration in the i direction (m/s²).
(3)
Energy conservation equation.

(16) $\frac{\partial (ρ T)}{\partial τ} + \frac{\partial}{\partial x_{j}} (ρ u_{i} T) = \frac{\partial}{\partial x_{j}} (\frac{λ}{c_{p}} \frac{\partial T}{\partial x_{j}}) + S_{T}$

In the equation: T is the fluid temperature (K); λ is the thermal conductivity of the fluid [W/(m²·K)^–1]; c_p is the specific heat capacity [J/(kg·K)^–1]; S_T is the viscous dissipation term.
(4)
Component transport equation.

(17) $\frac{\partial (ρ ω)}{\partial τ} + \frac{\partial}{\partial x_{j}} (ρ u_{i} ω) = \frac{\partial}{\partial x_{j}} ( ρ D_{i} \frac{\partial ω}{\partial x_{j}})$

In the equation: D₁ is the turbulent diffusion coefficient (m²·s^–1); ω is the component mass fraction.
(5)
Turbulence model.

Choose the Realizable k – ε model [²⁴] to calculate turbulent kinetic energy and turbulence dissipation rate:

(18) $\frac{\partial}{\partial τ} (ρ k) + \frac{\partial}{\partial x_{j}} (ρ k u_{j}) = \frac{\partial}{\partial x_{j}} ( μ + \frac{μ_{t}}{σ_{k}} \frac{\partial k}{\partial x_{j}}) + G_{k} + G_{b} - ρ ε - γ_{M} + S_{k}$

(19) $\frac{\partial}{\partial τ} (ρ ε) + \frac{\partial}{\partial x_{j}} (ρ ε u_{j}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ε}}) \frac{\partial ε}{\partial x_{j}}] + C_{1 ε} \frac{ε}{k} (G_{k} + C_{3 ε} G_{b}) - C_{2 ε} ρ \frac{ε^{2}}{k} + S_{ε}$

(20) $μ_{t} = ρ C_{μ} \frac{k^{2}}{ε}$

In the equation: µ_t is the turbulent viscosity coefficient; G_k is the turbulent kinetic energy generated by velocity gradient; G_b is the buoyancy turbulence kinetic energy; S_k and S_ε custom source items; σ_k, σ_ε, C_1ε, C_2ε, C_3ε, C_µ is the empirical coefficients.

3. Numerical simulation and validation

3.1. Grid division

According to the design specifications for dome roof tanks [²⁵], a 1000 m³ dome roof tank is selected as the research object. This tank has a diameter of 11,500 mm, a wall height of 10,650 mm, and a dome roof height of 1,241 mm. The accessories on the dome roof tank include only the breathing valve; both the valve stem and retaining valve block are excluded from consideration. Given that the dome roof tank is symmetric, this three-dimensional problem can be simplified into a two-dimensional analysis. To more accurately capture temperature variations, mesh refinement is applied at both the gas space wall and the valve block wall during meshing in anticipation of improved computational results [²⁶]. A combination of structured and unstructured meshing techniques is employed; Figure 2 illustrates the mesh division for both the gas space and breathing valve located on top of the tank.

Figure 2
Gridding of gas space in dome roof tanks (level height: 2880 mm).

3.2. Boundary conditions and solving algorithm

The summer solstice, autumnal equinox, and winter solstice are selected to simulate the solar radiation received by the dome roof tank. The study is conducted in Shenyang, Liaoning, with a longitude of 123.36° and a latitude of 41.59°. The fitting parameters for solar radiation across different seasons are presented in Table 2. For the heat exchange between the tank and its external environment, a second type of boundary condition is employed. The heat flux is calculated using Equations (10) to (12) and compiled as a UDF, which serves as the thermal boundary condition for the tank. The wall surface is set to the enhanced wall function. Given that the heat transfer area of the breathing valve is significantly smaller than that of the storage tank, the wall of the breathing valve is treated as an adiabatic boundary condition. The inlet and outlet of the breathing valve adopt pressure boundary conditions and are connected with the atmosphere. The oil surface temperature is determined using equation (13). During the overpressure relief process of the storage tank, dynamic grid technology is employed to simulate the movement of the valve block, with a rated opening pressure for the breather valve set at 2000 Pa.

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Table 2
Solar radiation flux coefficient.

In this study, transient simulations are performed based on a pressure-based solver and coupled algorithm. The volume force algorithm is used for pressure interpolation schemes, and the discretization is in second-order windward format [²⁷].

3.3. Grid-independent verification

The temperature at the centerline of the storage tank is chosen as the standard for analysis. To validate this selection, five sets of grids with varying numbers are simulated to compare the temperatures along the centerline of the tank at different heights at 9:00 and 15:00. The results are presented in Figure 3.

Figure 3
Temperature distribution on the centreline of the tank at a) 9:00 and b) 15:00.

When the number of grids exceeds 238,844, the temperature variations along the centerline of the gas space are largely consistent. This indicates that the requirement for grid-independent solutions has been satisfied.

3.4. Model Validation

The gas space temperature inside a small dome roof tank with a liquid level height of 300 mm, a diameter of 800 mm, a wall height of 1000 mm, and a roof height of 200 mm is simulated and compared with data from the literature [²⁸], as shown in Figure 4.

Figure 4
Temperature distribution on the centerline of the gas space.

The temperature distribution along the centerline of the gas space within the storage tank generally aligns with data from existing literature [²⁸], thereby affirming the validity of the model.

4. RESULTS AND DISCUSSION

4.1. Temperature changes in gas space

Taking the summer solstice as an illustration, the temperature distribution within the gas space at different moments is analyzed, and the results are presented in Figure 5. In the longitudinal direction, due to direct solar radiation and variations in specific heat capacity between gas and liquid phases, the temperature within the gas space exhibits a gradient distribution: higher temperatures are observed in the upper region while lower temperatures prevail near the bottom. Notably, there exists a distinct low-temperature layer adjacent to the liquid surface. In the transverse direction, the solar radiation received by the sunny side of the tank wall exceeds that received by the shaded side. Consequently, the gas adjacent to the sunny side absorbs more heat compared to that near the shaded side. This leads to a convex temperature distribution on the sunny side and a concave distribution on the shaded side of the tank walls. Furthermore, as the disparity in solar radiation between these two sides increases, so does the prominence of both convex and concave temperature distributions.

Figure 5
Temperature maps of gas space at different moments of the summer solstice (liquid level height: 2880 mm. a) 08:00. b) 12:00. c) 16:00).

At the sunny tank wall near the liquid surface, more heat is absorbed, resulting in easier evaporation of the oil there, which leads to complex collisions and mixing of the hydrocarbon molecules overflowing from the liquid surface there with gases in other directions in the gas space. Eventually, a local high temperature zone is formed in the vicinity of the sunny tank wall near the liquid surface, and the greater the solar radiation received by the sunny tank wall, the more obvious the local high temperature zone.

The temporal variation of the mean temperature within the gas space is illustrated in Figure 6. From the summer solstice through the autumnal equinox to the winter solstice, as Earth transitions from perihelion to aphelion, there is a gradual decrease in solar radiation received by dome roof tanks, which corresponds with a decline in the temperature of the gas space. Throughout the day, the mean temperature of the gas space exhibits a pattern of initially increasing and then decreasing over time, reaching its peak around 14:00 hours. Furthermore, it is observed that as the liquid level rises, there is a corresponding decrease in the mean temperature of the gas space.

Figure 6
Trends of gas space means temperature over time for different seasons and liquid level heights.

4.2. Gasoline Vapor diffusion

Taking the summer solstice as an example, the oil vapor concentration distribution in the gas space at different moments is shown in Figure 7. From Figures 7 and 8, it can be seen that there exists a large oil vapor concentration layer near the liquid surface, and the oil vapor concentration in the upper part of the layer is lower but more uniformly distributed; in the large concentration layer, the variation of the oil vapor concentration along the height direction is unusually significant. The oil vapor concentrations at points of the same height on the liquid surface are very close to each other, and in the vicinity of the sunny tank wall near the liquid surface, the evaporation effect of the liquid surface is obvious due to the direct radiation from the sun, resulting in a larger oil vapor concentration than that in the vicinity of the shaded tank wall. From Figures 8 and 9, it is concluded that from the summer solstice to the autumn equinox to the winter solstice, the oil vapor concentration decreases as the season turns cold.

Figure 7
Cloud map of gas spatial concentration on the summer solstice (level height: 2880 mm. a) 08:00. b) 12:00. c) 16:00).

Figure 8
Trends of oil vapor concentration on the centerline of the gas space with height in different seasons and at different moments (liquid level: 2880 mm).

Figure 9
Trends of oil vapor concentration with height on the centerline of gas space in different seasons and at different liquid level heights.

The concentration distribution of the gas space under three liquid level conditions—high, medium, and low—in the tank is illustrated in Figure 9. When static storage occurs at medium and low liquid levels, the longitudinal oil vapor concentration distribution curve exhibits a distinct inflection point, that is to say, there exists a higher concentration layer near the oil surface. In contrast, this phenomenon is absent during high-liquid-level static storage, where the longitudinal oil vapor concentration gradient decreases gently and progressively from top to bottom.

4.3. Change in gas space pressure

Taking the noon hour of the summer solstice as an example, the gas space pressure distribution is analyzed as shown in Figure 10. In the longitudinal direction, the gas space pressure exhibits a uniform gradient distribution that gradually increases from top to bottom, with a pressure difference of approximately 100 Pa. Conversely, in the horizontal direction, the pressure distribution remains nearly uniform. The variation of the average pressure in the tank with time in different seasons and at different liquid level heights is shown in Figure 11. From sunrise to 14:00, the average pressure inside the tank gradually increases, and when the pressure inside the tank reaches 2000 Pa, the tank starts to release pressure. From 14:00 to sunset, the average pressure inside the tank gradually decreased. In addition, as the oil storage level increases, the exhaust frequency of the breathing valve decreases, and the initial opening time of the breathing valve is delayed. The reason for this phenomenon is that as the liquid level rises, the solar radiation received by the gas space tank wall decreases. As a result, less heat is absorbed by the gas, and the temperature decreases accordingly, ultimately leading to a lower pressure in the gas space. Simultaneously, the higher the liquid level, the easier the heat from the top of the tank is transferred to the liquid surface, accelerating the evaporation of the oil and further lowering the temperature in the gas space due to the evaporation and heat absorption at the liquid surface, leading to a consequent decrease in pressure.

Figure 10
Gas space pressure cloud on the summer solstice (level height: 2880 mm, time: 12:00).

Figure 11
Trends in gas space mean pressure over time.

From the summer solstice to the autumnal equinox to the winter solstice, solar radiation and ambient temperature gradually decrease, and the number of overpressure releases from storage tanks also decreases accordingly. The time range of overpressure release also narrows down to the vicinity of the highest temperature moment in the gas space.

4.4. Small breathing losses of storage tanks throughout the day

The small breathing losses of the storage tank only occur during the relief process of the breathing valve during the daytime, and the dynamic grid technology is used to simulate the overpressure relief of the storage tank. The small breathing loss quantity is obtained by monitoring the mass fraction and mass flow rate of the exhaled oil vapor during the relief process of the breathing valve. The daily small breathing losses of the storage tank are calculated by equation (21):

(21)

Δ M = \sum_{i = 1}^{n} \int M_{i} • ω_{i} d t

In the equation: ∆M is the small breathing losses of the storage tank (kg); M_t is the mass flow rate (kg/m³) for the i-th breathing valve exhaust process; ω_i is the mass fraction of the substance during the i-th breathing valve relief process.

The breathing loss rate (η) is used to evaluate the small breathing losses of storage tanks in different seasons and liquid levels. The breathing loss rate is calculated using equations (22) to (23):

(22)

η_{C 6} ​ = \frac{Δ M}{M_{l i q u i d}}

(23)

η_{g a s o i l} ​ = \frac{P_{v}}{P_{v, ​ C 6}} η_{C 6}

In the equation: η_C6 and η_gasoil are the daily losses rates of n-hexane and gasoline (g/t); P_vand P_v,C6 are the saturated vapor pressure of n-hexane and gasoline (Pa); M_liquid is to store the quality of the liquid (t).

The calculation results of the breathing losses and loss rate for a day in the dome roof tanks are shown in Table 3. The daily mean loss rates of gasoline in storage tanks on the summer solstice, autumn equinox, and winter solstice are 23.649 g/t, 15.193 g/t, and 10.187 g/t, respectively. Additionally, the daily mean loss rates of gasoline in storage tanks with liquid level heights of 2880 mm, 5190 mm, and 8370 mm are recorded as 14.786 g/t, 13.088 g/t, and 22.706 g/t, respectively. Consequently, the annual mean daily loss rate and the total annual loss rate for a 1000 m³ dome tank in Shenyang, Liaoning Province, are approximately 17.431 g/t and 6.36 kg/t, respectively. In comparison to national standards [²⁹], the annual mean daily loss rate and total annual loss rate for the Liaoning region are reported as 19.35 g/t and 7.063 kg/t, respectively. Thus, the calculated values presented in Table 3 are generally consistent with the recommended values of national standards.

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Table 3
Static breathing losses and losses rates.

At the same liquid height, the magnitude and rate of breathing losses during the summer solstice are greater than those observed during the autumnal equinox and winter solstice. The breathing losses from the storage tank increase with rising liquid level height; however, the rate of these breathing losses does not exhibit a straightforward linear relationship with liquid level height. Instead, it varies due to the synergistic effects of both the volume of breathing losses and liquid level height.

5. CONCLUSIONS

By developing an unsteady state heat and mass transfer model for the dome roof tank, implementing a self-programming heat UDF, and utilizing CFD software, this study investigates the variations in temperature, oil vapor concentration, and pressure within the gas space of the dome roof tank across different seasons and liquid level heights. Additionally, it calculates small breathing losses. The following conclusions were drawn from this analysis:

(1)
The temperature within the gas space displays a clear longitudinal gradient, with temperatures gradually decreasing from the top to the bottom. In the horizontal direction, the temperature of the tank wall on the sunny side is higher than that on the shaded side, resulting in a “convex-concave” temperature distribution near the tank wall. Throughout the day, from sunrise to sunset, the average temperature of the gas space initially rises and subsequently declines, reaching its peak around 14:00. Additionally, it is observed that as liquid levels increase and during colder seasons, there is a corresponding decrease in the average temperature of the gas space.
(2)
The gas space exhibits a large oil vapor concentration layer near the oil surface, and the oil vapor concentration in the upper part of the layer is lower but more uniformly distributed. Within this large concentration layer, variations in oil vapor concentration along the vertical axis are particularly pronounced. Notably, the average oil vapor concentration increases with both rising liquid levels and seasonal warming.
(3)
The distribution of gas space pressure within the tank exhibits a gradual increase from the top to the bottom. The average pressure in the tank rises from sunrise until approximately 14:00, followed by a decrease from 14:00 until sunset. Additionally, it is observed that the pressure within the tank correlates negatively with the liquid level. The average pressure in the tank decreases as the level rises. The number of breather valve releases decreases as the season turns colder, and the time frame for overpressure releases narrows as the season turns colder to the vicinity of the moment of maximum gas space temperature.
(4)
In the Liaoning region, the mean daily loss rates and total annual loss rates are approximately 19.35 g/t and 7.063 kg/t, respectively. The small breathing losses of the dome roof tank increase with the increase of liquid level height and seasonal heat transfer. The rate of these breathing losses increases as the season turns hotter.

The research findings provide a theoretical basis for understanding the heat and mass transfer of periodic solar radiation on dome roof tanks, as well as for reducing static breathing losses and improving equipment management levels. Furthermore, it is recommended to enhance the surface of storage tanks by applying efficient reflective coatings or installing reflective insulation panels. This approach aims to increase the tank’s ability to reflect solar radiation, thereby lowering both the gas space temperature and its fluctuations, ultimately contributing to a reduction in VOCs emissions from the storage tank. At the same time, it is recommended that in the operation and management of dome roof tanks, efforts should be made to fill the oil products to the specified safe capacity of the dome tank. This approach can effectively reduce the gas space volume within the tank and subsequently lower VOCs emissions from the dome tank.

6. BIBLIOGRAPHY

^[1] Zhou, S.H., Gao, X., Wang, J., et al, “Influencing factors of carbon emissions in China’s oil and gas exploitation industry under dual carbon goals”, Oil & Gas Storage and Transportation, v. 42, n. 7, pp. 743–753, 2023. doi: http://doi.org/10.6047/j.issn.1000-8241.2023.07.003.
» https://doi.org/10.6047/j.issn.1000-8241.2023.07.003
^[2] Huang, W.Q., Xu, X., Lou, J.J., et al, “Research progress of oil evaporation and vapor diffusion for traceability of carbon emissions from storage tanks”, Oil & Gas Storage and Transportation, v. 41, n. 2, pp. 135–145, 2022. doi: http://doi.org/10.6047/i.issn.1000-8241.2022.02.002.
» https://doi.org/10.6047/i.issn.1000-8241.2022.02.002
^[3] Matsumura, I., “Evaporation loss of hydrocarbon in handling petroleum”, Bulletin of The Japan Petroleum Institute, v. 16, n. 2, pp. 132–139, 2008. doi: http://doi.org/10.1627/jpi1959.16.132.
» https://doi.org/10.1627/jpi1959.16.132
^[4] Matsumura, I., “Hydrocarbon emission and its preventive measure in petroleum industry”, Journal of the Japan Institute of Energy, v. 57, n. 10, pp. 849–859, 1978. doi: http://doi.org/10.3775/jie.57.10_849.
» https://doi.org/10.3775/jie.57.10_849
^[5] Fingas, M.F., “Studies on the evaporation of crude oil and petroleum products I. the relationship between evaporation rate and time”, Journal of Hazardous Materials, v. 56, n. 3, pp. 227–236, 1997. doi: http://doi.org/10.1016/S0304-3894(97)00050-2.
» https://doi.org/10.1016/S0304-3894(97)00050-2
^[6] Fingas, M.F., “Studies on the evaporation of crude oil and petroleum products II. boundary layer regulation”, Journal of Hazardous Materials, v. 57, n. 1–3, pp. 41–58, 1998. doi: http://doi.org/10.1016/S0304-3894(97)00051-4.
» https://doi.org/10.1016/S0304-3894(97)00051-4
^[7] Sharma, Y.K., Majhi, A., Kukreti, V.S., et al, “Stock loss studies on breathing loss of gasoline”, Fuel, v. 89, n. 7, pp. 1695–1699, 2010. doi: http://doi.org/10.1016/j.fuel.2009.08.006.
» https://doi.org/10.1016/j.fuel.2009.08.006
^[8] Jia, Z.H., “Study on risk analysis of tank farm and estimation of Tank’s Evaporation Loss in Petroleum Storage and Transportation”, Master’s thesis, publisher, Xuzhou, 2014.
^[9] Xian, J., “Research and application of oil storage tank loss reduction technology in Xin Jiang Northern Oilfield”, Master’s thesis, publisher, Qingdao, 2014.
^[10] Huang, W.Q., Lu, J.G., Zhao, S.H., “Study on the method for calibration of petroleum vapor concentration”, Oil & Gas Storage and Transportation, v. 27, n. 11, pp. 31–35, 2008. doi: http://doi.org/10.6047/j.issn.1000-8241.2008.11.009.
» https://doi.org/10.6047/j.issn.1000-8241.2008.11.009
^[11] Moncalvo, D., Davies, M., Weber, R., et al, “Breathing losses from low-pressure storage tanks due to atmospheric weather change”, Journal of Loss Prevention in the Process Industries, v. 43, pp. 702–705, 2016. doi: http://doi.org/10.1016/j.jlp.2016.06.006.
» https://doi.org/10.1016/j.jlp.2016.06.006
^[12] Liang, Y., “A study on regula pattern of evaporation loss in the fixed-roof tank”, Master’s thesis, Xi’an Petroleum University, Xi’an, China, 2013.
^[13] Fetisov, V., Pshenin, V., Nagornov, D., et al, “Evaluation of pollutant emissions into the atmosphere during the loading of hydrocarbons in marine oil tankers in the Arctic region”, Journal of Marine Science and Engineering, v. 8, n. 11, pp. 917, 2020. doi: http://doi.org/10.3390/jmse8110917.
» https://doi.org/10.3390/jmse8110917
^[14] Sun, W., Cheng, Q., Zheng, A., et al, “Research on coupled characteristics of heat transfer and flow in the oil static storage process under periodic boundary conditions”, International Journal of Heat and Mass Transfer, v. 122, pp. 719–731, 2018. doi: http://doi.org/10.1016/j.ijheatmasstransfer.2018.02.010.
» https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.010
^[15] Wang, M., Yu, B., Zhang, X., et al, “Experimental and numerical study on the heat transfer characteristics of waxy crude oil in a 100,000 m³ double-plate floating roof oil tank”, Applied Thermal Engineering, v. 136, pp. 335–348, 2018. http://doi.org/10.1016/j.applthermaleng.2018.03.018.
» https://doi.org/10.1016/j.applthermaleng.2018.03.018
^[16] Li, W., Shao, Q.Q., Liang, J., “Numerical study on oil temperature field during long storage in large floating roof tank”, International Journal of Heat and Mass Transfer, v. 130, pp. 175–186, 2019. doi: http://doi.org/10.1016/j.ijheatmasstransfer.2018.10.024.
» https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.024
^[17] Yang, H.W., Yang, S.L., Fei, Y.W., et al, “Temperature gradient of hydrocarbon space in fixed roof tank and measures of reducing consumption by breathing loss”, Oil & Gas Storage and Transportation, v. 30, n. 4, pp. 314–315, 2011. doi: http://doi.org/10.3969/j.issn.1001-9677.2013.01.051.
» https://doi.org/10.3969/j.issn.1001-9677.2013.01.051
^[18] Zhang, P.Y., Huang, W.Q., Jing, H.B., et al, “Numerical simulation and experiment study of oil evaporation loss in dome-roof tanks”, Safety and Environmental Engineering, v. 27, n. 4, pp. 143–151, 2020. doi: http://doi.org/10.13578/j.cnki.issn.1671-1556.2020.04.019.
» https://doi.org/10.13578/j.cnki.issn.1671-1556.2020.04.019
^[19] Chen, Z.H., Liu, H.B., Yan, X.Y., et al, “Research on the temperature field of suspendome with stacked arch in Chipin Gymnasium”, Spatial Structures, v. 16, n. 1, pp. 76–81, 2010. doi: http://doi.org/10.13849/j.issn.1006-6578.2010.01.014.
» https://doi.org/10.13849/j.issn.1006-6578.2010.01.014
^[20] Abouhashish, M., “Applicability of ASHRAE clear-sky model based on solar-radiation measurements in Saudi Arabia”, AIP Conference Proceedings, v. 1850, n. 1, pp. 140001, 2017. doi: https://doi.org/10.1063/1.4984509.
» https://doi.org/10.1063/1.4984509
^[21] Guo, G.C., Dong, W.L., Zhang, Z.L., Design and management of oil depot, Dong Ying, China University of Petroleum Press, 2006.
^[22] Sun, W.W., Li, Z.L., Sun, F.F., “Study on the evaporation loss of light oil”, Journal of Petrochemical Universities, v. 30, n. 3, pp. 90–96, 2017. doi: http://doi.org/10.3969/j.issn.1006-396X.2017.04.017.
» https://doi.org/10.3969/j.issn.1006-396X.2017.04.017
^[23] Fang, J., Huang, W., Huang, F., et al, “Investigation of the superposition effect of oil vapor leakage and diffusion from external floating-roof tanks using CFD numerical simulations and wind-tunnel experiments”, Processes (Basel, Switzerland), v. 8, n. 3, pp. 299, 2020. doi: http://doi.org/10.3390/pr8030299.
» https://doi.org/10.3390/pr8030299
^[24] Lateb, M., Masson, C., Stathopoulos, T., et al, “Comparison of various types of k–e models for pollutant emissions around a two-building configuration”, Journal of Wind Engineering and Industrial Aerodynamics, v. 115, pp. 9-21, 2013. doi: http://doi.org/10.1016/j.jweia.2013.01.001.
» https://doi.org/10.1016/j.jweia.2013.01.001
^[25] CHINESE HG STANDARDS, HG 21502.1-1992 Steel Vertical Cylindrical Fixed Roof Storage Tank Series, 1992, accessed in January 2025, https://www.bzxz.net/bzxz/5237.html
» https://www.bzxz.net/bzxz/5237.html
^[26] Du, M.J., Zhang, Z.G., Xu, X.F., et al, “Study of unsteady heat transfer numerical of large crude oil storage tank based on CFD”, Journal of Liaoning Shihua University, v. 36, n. 4, pp. 24–28, 2016. doi: http://doi.org/10.3969/j.issn.1672-6952.2016.04.006.
» https://doi.org/10.3969/j.issn.1672-6952.2016.04.006
^[27] Li, C.X., Ji, B., Wei, G.Q., “Numerical calculation of the temperature drop of the waxy crude oil pipeline”, Journal of Petrochemical Universities, v. 32, n. 3, pp. 95–102, 2019. doi: http://doi.org/10.3969/j.issn.1006-396X.2019.03.016.
» https://doi.org/10.3969/j.issn.1006-396X.2019.03.016
^[28] Huang, W.Q., Wang, S., Jing, H.B., et al, “A calculation method for simulation and evaluation of oil vapor diffusion and breathing loss in a dome roof tank subjected to the solar radiation”, Journal of Petroleum Science Engineering, v. 195, pp. 107568, 2020. doi: http://doi.org/10.1016/j.petrol.2020.107568.
» https://doi.org/10.1016/j.petrol.2020.107568
^[29] CHINESE GB STANDARDS, GB/T 11085-1989 Loss of Bulk Petroleum Liquid Products, 1989, accessed in January 2025, https://webstore.ansi.org/standards/spc/gb110851989-1680213
» https://webstore.ansi.org/standards/spc/gb110851989-1680213

Publication Dates

Publication in this collection
07 Feb 2025
Date of issue
2025

History

Received
13 Oct 2024
Accepted
18 Dec 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] ^[1] Zhou, S.H., Gao, X., Wang, J., et al, “Influencing factors of carbon emissions in China’s oil and gas exploitation industry under dual carbon goals”, Oil & Gas Storage and Transportation, v. 42, n. 7, pp. 743–753, 2023. doi: http://doi.org/10.6047/j.issn.1000-8241.2023.07.003.
» https://doi.org/10.6047/j.issn.1000-8241.2023.07.003

[2] ^[2] Huang, W.Q., Xu, X., Lou, J.J., et al, “Research progress of oil evaporation and vapor diffusion for traceability of carbon emissions from storage tanks”, Oil & Gas Storage and Transportation, v. 41, n. 2, pp. 135–145, 2022. doi: http://doi.org/10.6047/i.issn.1000-8241.2022.02.002.
» https://doi.org/10.6047/i.issn.1000-8241.2022.02.002

[3] ^[3] Matsumura, I., “Evaporation loss of hydrocarbon in handling petroleum”, Bulletin of The Japan Petroleum Institute, v. 16, n. 2, pp. 132–139, 2008. doi: http://doi.org/10.1627/jpi1959.16.132.
» https://doi.org/10.1627/jpi1959.16.132

[4] ^[4] Matsumura, I., “Hydrocarbon emission and its preventive measure in petroleum industry”, Journal of the Japan Institute of Energy, v. 57, n. 10, pp. 849–859, 1978. doi: http://doi.org/10.3775/jie.57.10_849.
» https://doi.org/10.3775/jie.57.10_849

[5] ^[5] Fingas, M.F., “Studies on the evaporation of crude oil and petroleum products I. the relationship between evaporation rate and time”, Journal of Hazardous Materials, v. 56, n. 3, pp. 227–236, 1997. doi: http://doi.org/10.1016/S0304-3894(97)00050-2.
» https://doi.org/10.1016/S0304-3894(97)00050-2

[6] ^[6] Fingas, M.F., “Studies on the evaporation of crude oil and petroleum products II. boundary layer regulation”, Journal of Hazardous Materials, v. 57, n. 1–3, pp. 41–58, 1998. doi: http://doi.org/10.1016/S0304-3894(97)00051-4.
» https://doi.org/10.1016/S0304-3894(97)00051-4

[7] ^[7] Sharma, Y.K., Majhi, A., Kukreti, V.S., et al, “Stock loss studies on breathing loss of gasoline”, Fuel, v. 89, n. 7, pp. 1695–1699, 2010. doi: http://doi.org/10.1016/j.fuel.2009.08.006.
» https://doi.org/10.1016/j.fuel.2009.08.006

[8] ^[8] Jia, Z.H., “Study on risk analysis of tank farm and estimation of Tank’s Evaporation Loss in Petroleum Storage and Transportation”, Master’s thesis, publisher, Xuzhou, 2014.

[9] ^[9] Xian, J., “Research and application of oil storage tank loss reduction technology in Xin Jiang Northern Oilfield”, Master’s thesis, publisher, Qingdao, 2014.

[10] ^[10] Huang, W.Q., Lu, J.G., Zhao, S.H., “Study on the method for calibration of petroleum vapor concentration”, Oil & Gas Storage and Transportation, v. 27, n. 11, pp. 31–35, 2008. doi: http://doi.org/10.6047/j.issn.1000-8241.2008.11.009.
» https://doi.org/10.6047/j.issn.1000-8241.2008.11.009

[11] ^[11] Moncalvo, D., Davies, M., Weber, R., et al, “Breathing losses from low-pressure storage tanks due to atmospheric weather change”, Journal of Loss Prevention in the Process Industries, v. 43, pp. 702–705, 2016. doi: http://doi.org/10.1016/j.jlp.2016.06.006.
» https://doi.org/10.1016/j.jlp.2016.06.006

[12] ^[12] Liang, Y., “A study on regula pattern of evaporation loss in the fixed-roof tank”, Master’s thesis, Xi’an Petroleum University, Xi’an, China, 2013.

[13] ^[13] Fetisov, V., Pshenin, V., Nagornov, D., et al, “Evaluation of pollutant emissions into the atmosphere during the loading of hydrocarbons in marine oil tankers in the Arctic region”, Journal of Marine Science and Engineering, v. 8, n. 11, pp. 917, 2020. doi: http://doi.org/10.3390/jmse8110917.
» https://doi.org/10.3390/jmse8110917

[14] ^[14] Sun, W., Cheng, Q., Zheng, A., et al, “Research on coupled characteristics of heat transfer and flow in the oil static storage process under periodic boundary conditions”, International Journal of Heat and Mass Transfer, v. 122, pp. 719–731, 2018. doi: http://doi.org/10.1016/j.ijheatmasstransfer.2018.02.010.
» https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.010

[15] ^[15] Wang, M., Yu, B., Zhang, X., et al, “Experimental and numerical study on the heat transfer characteristics of waxy crude oil in a 100,000 m³ double-plate floating roof oil tank”, Applied Thermal Engineering, v. 136, pp. 335–348, 2018. http://doi.org/10.1016/j.applthermaleng.2018.03.018.
» https://doi.org/10.1016/j.applthermaleng.2018.03.018

[16] ^[16] Li, W., Shao, Q.Q., Liang, J., “Numerical study on oil temperature field during long storage in large floating roof tank”, International Journal of Heat and Mass Transfer, v. 130, pp. 175–186, 2019. doi: http://doi.org/10.1016/j.ijheatmasstransfer.2018.10.024.
» https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.024

[17] ^[17] Yang, H.W., Yang, S.L., Fei, Y.W., et al, “Temperature gradient of hydrocarbon space in fixed roof tank and measures of reducing consumption by breathing loss”, Oil & Gas Storage and Transportation, v. 30, n. 4, pp. 314–315, 2011. doi: http://doi.org/10.3969/j.issn.1001-9677.2013.01.051.
» https://doi.org/10.3969/j.issn.1001-9677.2013.01.051

[18] ^[18] Zhang, P.Y., Huang, W.Q., Jing, H.B., et al, “Numerical simulation and experiment study of oil evaporation loss in dome-roof tanks”, Safety and Environmental Engineering, v. 27, n. 4, pp. 143–151, 2020. doi: http://doi.org/10.13578/j.cnki.issn.1671-1556.2020.04.019.
» https://doi.org/10.13578/j.cnki.issn.1671-1556.2020.04.019

[19] ^[19] Chen, Z.H., Liu, H.B., Yan, X.Y., et al, “Research on the temperature field of suspendome with stacked arch in Chipin Gymnasium”, Spatial Structures, v. 16, n. 1, pp. 76–81, 2010. doi: http://doi.org/10.13849/j.issn.1006-6578.2010.01.014.
» https://doi.org/10.13849/j.issn.1006-6578.2010.01.014

[20] ^[20] Abouhashish, M., “Applicability of ASHRAE clear-sky model based on solar-radiation measurements in Saudi Arabia”, AIP Conference Proceedings, v. 1850, n. 1, pp. 140001, 2017. doi: https://doi.org/10.1063/1.4984509.
» https://doi.org/10.1063/1.4984509

[21] ^[21] Guo, G.C., Dong, W.L., Zhang, Z.L., Design and management of oil depot, Dong Ying, China University of Petroleum Press, 2006.

[22] ^[22] Sun, W.W., Li, Z.L., Sun, F.F., “Study on the evaporation loss of light oil”, Journal of Petrochemical Universities, v. 30, n. 3, pp. 90–96, 2017. doi: http://doi.org/10.3969/j.issn.1006-396X.2017.04.017.
» https://doi.org/10.3969/j.issn.1006-396X.2017.04.017

[23] ^[23] Fang, J., Huang, W., Huang, F., et al, “Investigation of the superposition effect of oil vapor leakage and diffusion from external floating-roof tanks using CFD numerical simulations and wind-tunnel experiments”, Processes (Basel, Switzerland), v. 8, n. 3, pp. 299, 2020. doi: http://doi.org/10.3390/pr8030299.
» https://doi.org/10.3390/pr8030299

[24] ^[24] Lateb, M., Masson, C., Stathopoulos, T., et al, “Comparison of various types of k–e models for pollutant emissions around a two-building configuration”, Journal of Wind Engineering and Industrial Aerodynamics, v. 115, pp. 9-21, 2013. doi: http://doi.org/10.1016/j.jweia.2013.01.001.
» https://doi.org/10.1016/j.jweia.2013.01.001

[25] ^[25] CHINESE HG STANDARDS, HG 21502.1-1992 Steel Vertical Cylindrical Fixed Roof Storage Tank Series, 1992, accessed in January 2025, https://www.bzxz.net/bzxz/5237.html
» https://www.bzxz.net/bzxz/5237.html

[26] ^[26] Du, M.J., Zhang, Z.G., Xu, X.F., et al, “Study of unsteady heat transfer numerical of large crude oil storage tank based on CFD”, Journal of Liaoning Shihua University, v. 36, n. 4, pp. 24–28, 2016. doi: http://doi.org/10.3969/j.issn.1672-6952.2016.04.006.
» https://doi.org/10.3969/j.issn.1672-6952.2016.04.006

[27] ^[27] Li, C.X., Ji, B., Wei, G.Q., “Numerical calculation of the temperature drop of the waxy crude oil pipeline”, Journal of Petrochemical Universities, v. 32, n. 3, pp. 95–102, 2019. doi: http://doi.org/10.3969/j.issn.1006-396X.2019.03.016.
» https://doi.org/10.3969/j.issn.1006-396X.2019.03.016

[28] ^[28] Huang, W.Q., Wang, S., Jing, H.B., et al, “A calculation method for simulation and evaluation of oil vapor diffusion and breathing loss in a dome roof tank subjected to the solar radiation”, Journal of Petroleum Science Engineering, v. 195, pp. 107568, 2020. doi: http://doi.org/10.1016/j.petrol.2020.107568.
» https://doi.org/10.1016/j.petrol.2020.107568

[29] ^[29] CHINESE GB STANDARDS, GB/T 11085-1989 Loss of Bulk Petroleum Liquid Products, 1989, accessed in January 2025, https://webstore.ansi.org/standards/spc/gb110851989-1680213
» https://webstore.ansi.org/standards/spc/gb110851989-1680213

LOCATION	TYPES OF SOLAR RADIATION
Tank roof	Direct and scattered solar radiation
Sunny wall	Direct solar radiation, scattered radiation, and ground reflection radiation
Shaded wall	Scattered radiation, ground reflection radiation

SEASON	LOCATION	ρ ₁	ρ ₂	ρ ₃	ρ ₄	ρ ₅
Summer Solstice	Tank roof	4.547e–16	–3.929e–11	1.153e–07	0.03168	118.9
	Right tank wall	–3.056e–15	2.64e–10	–7.032e–06	0.05741	331.2
	Left tank wall	–2.75e–16	2.376e–11	–7.38e–07	0.00971	61.71
Autumn Equinox	Tank roof	1.148e–15	–1.001e–10	1.571e–06	0.02656	–5.57
	Right tank wall	–5.3e–15	4.571e–10	–1.314e–05	0.1426	–7.062
	Left tank wall	–3.627e–16	3.133e–11	–1.065e–06	0.01679	–9.859
Winter Solstice	Tank roof	9.69e–16	–6.977e–11	5.544e–07	0.02525	–82.84
	Right tank wall	–8.93e–15	6.43e–10	–1.737e–05	0.2087	–414.7
	Left tank wall	–5.077e–16	3.656e–11	–1.118e–06	0.01657	–35.97

LIQUID LEVEL HEIGHT/mm	SUMMER SOLSTICE		AUTUMN EQUINOX		WINTER SOLSTICE		MEAN VALUE
LIQUID LEVEL HEIGHT/mm	∆M/kg	η_C6/(g/t)	∆M/kg	η_C6/(g/t)	∆M/kg	η_C6/(g/t)	η_C6/(g/t)	η_gasoil/(g/t)
2880 mm	3.154	14.652	1.984	9.216	1.0596	4.922	8.645	14.786
5190 mm	4.914	12.667	2.522	6.502	1.352	3.484	7.366	13.088
8370 mm	14.213	22.717	6.898	11.025	2.485	3.972	12.571	22.706
Mean value η_C6	—	16.679	—	8.914	—	4.126	9.717	—
Mean value η_gasoil	—	23.649	—	15.193	—	10.187	—	17.431