# Rollover Prevention Model for Stratified Liquefied Natural Gas in Storage Tanks

^{*}

## Abstract

**:**

^{3}, the approximate time of the rollover occurrence was determined for two cases. In the first case, for heavier LNG, the rollover phenomenon will occur 193.25 h after the start of the calculations from the assumed initial conditions. In the second case, for light LNG with a higher initial liquid level in the tank, the rollover will occur after 150.25 h.

## 1. Introduction

^{3}(min. 0.5–1%) may disturb the stability of the storage process. Incorrect management of the storage process may lead to the stratification of the cryogenic liquid in the tank. The consequences of undetected liquid stratification in the tank may cause severe damage of a storage tank which is not properly secured. When liquid stratification occurs, free evaporation from the bottom layer of LNG is not possible, as a consequence of its increase of temperature and decrease of density. When the density of the bottom layer equalizes to that of the top layer, the LNG in the tank will mix rapidly with the evaporation of significant amounts of overheated LNG from the bottom layer. This phenomena is called rollover.

^{3}) tank in Nantes [9]. The first several parameter models were successively developed by Chatterjee and Geist [10] and Germeles [11] to predict rollover occurrence during storage process. These research was developed on the same fundamental concepts by Heedstand and Shipman [12], Bates and Morrison [13], and Deshpande et al. [14]. These mentioned models are focused on the heat and mass transfers between bottom and top layers which are determined by empirical formulas and correlations primarily applied for pure or binary liquids. In these models impact of the hydrodynamics during rollover phenomenon is not fully appreciated. Hydrodynamic effect at the beginning of rollover is the source of the heat and mass transfers between top and bottom liquid layers, also the complexity of this multicomponent liquid has an additional influence on the course of the phenomenon. Despite some imperfections, these models are used widely in the LNG industry [5].

## 2. LNG Properties and Stratification Causes

## 3. LNG Stratification and Rollover

## 4. Analytical Prevention Model—Stable Stratification Model (SSM)

#### 4.1. Physical Description

_{i}—Poynting correction factor:

_{sat}is the saturation pressure, whereas T denotes temperature of the liquid and vapor subsystems in the film interface under saturation pressure.

_{L}) evaporates to the gas phase, the top layer has a new temperature at the end of the time step. The heat balance equation for the top layer is as follows:

_{T}, h

_{T}are overall enthalpy and molar enthalpy for the liquid phase in the top layer, B

_{L}is the amount of vaporized gas, Q

_{VL}—the amount of heat transferred from the gas phase, h

_{Vo}—unit enthalpy of LNG vapor in the state of equilibrium, Q

_{INL}—the amount of heat exchanged with the bottom layer.

_{B}, h

_{B}are overall enthalpy and molar enthalpy for the liquid phase in the bottom layer, Q

_{F}—the amount of heat penetrating through the bottom of the tank, Q

_{INL}—the amount of heat exchanged with the top layer.

_{i}to t = t

_{i}

_{+1}is defined as follows:

_{V}was divided into a given number of integration intervals.

_{VL}:

_{pV}is the specific heat of the gas phase, T

_{Vi}is the temperature of the gas phase at the beginning of the time step, T

_{Vav}is the temperature of the gas phase at the end of the time step.

#### 4.2. Model Algorithm

_{i}

_{,}and the end of the time step t

_{i}

_{+1}, the computational procedure is completed when the iteration counter of the time steps reaches the value k and the end time is indicated as t

_{k}. The presented model is based on an algorithm in which input data (storage tank data, operational data, layer composition) are determined for time t

_{i}. Then, equilibrium calculations are performed for the initial state (calculation of the boiling point of the top liquid layer and the initial temperature of the vapor phase). In the next steps, subsequent calculations are performed in parallel for both layers of the liquid phase and the vapor phase, with the equilibrium calculations covering the top liquid layer and the vapor phase. The new mass balance of each layer of the liquid phase and gas phase and energy balance of these layers is checked in next steps. If the energy balance of the liquid layers, i.e., the supplied heat, is equal to the enthalpy increase, the condition of equal density of both layers of the liquid phase is checked. In the stable stratification model, the final criterion, in addition to the assumed number of time steps, is the equalization of the density of both layers of the liquid phase as a necessary condition for the rollover phenomenon. The result of calculations made using the SSM model in this case is the time of the rollover occurrence and results describing the parameters of the liquid layers (including compositions) and the gas phase in time t

_{k}.

## 5. Assumptions

^{3}, and in the second variant, it was about 435 kg/m

^{3}. Differences in the density between top and bottom layers for both variants are approx. 1.5 kg/m

^{3}. The presented calculations assume a stably stratified liquid in the storage tank, the composition and physical properties of individual layers are described in Table 3.

## 6. Results and Discussion

- (1)
- densities of top and bottom layers;
- (2)
- temperatures of the bottom layer and the top layer of LNG;
- (3)
- vapor phase temperature;
- (4)
- boil off rate (BOR);
- (5)
- thicknesses of bottom and top layers;
- (6)
- heat transferred into storage tank and between phases and layers in tank.

_{B}—density of bottom layer, ρ

_{T}—density of top layer, ν—kinematic viscosity.

## 7. Conclusions

^{3}.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | area of heat transfer, m^{2} |

B_{L} | liquid vaporized (boil off gas), moles |

B | vapor vented from tank, moles |

C_{p} | isobaric heat capacity, J/mole |

f | fugacity, Pa |

H | enthalpy, J |

h | molar enthalpy, J/mole |

k | thermal conductivity, W/(m·K) |

N | total moles, moles |

Q | heat transferred, J |

T | temperature, K |

U | heat transfer coefficient, W/(m^{2}·K) |

z | height, m |

Greek symbols | |

α | thermal diffusivity, m^{2}/s |

ν | kinematic viscosity, m^{2}/s |

ρ | density, kg/m^{3} |

φ | fugacity coefficient |

Subscripts | |

amb | ambient |

av | average |

B | liquid bottom layer |

F | y tank bottom slab (foundation) |

i | initial, beginning of time step |

i + 1 | end of time step, initial of next step |

in | inleak |

INL | interlayer |

R | by tank roof |

T | liquid top layer |

V | vapor phase (vapor layer) |

VL | vapor to liquid |

VZ | vapor phase at z height |

W | by tank side wall |

Acronyms | |

LNG | Liquefied natural gas |

BOR | Boil off rate |

SSM | Stable stratification model |

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**Figure 2.**Illustrative diagram of the LNG storage tank, including the stable stratification of the cryogenic liquid in the non-equilibrium model.

**Figure 4.**Algorithm of Stable Stratification Model (SSM) for prediction the time of rollover occurrence.

**Table 1.**LNG compositions from various export sources, based on [44].

Composition | Methane | Ethane | Propane | C4+ | Nitrogen |
---|---|---|---|---|---|

Source | %mole | %mole | %mole | %mole | %mole |

Australia NWS | 87.33 | 8.33 | 3.33 | 0.97 | 0.04 |

Australia Darwin | 87.64 | 9.97 | 1.96 | 0.33 | 0.10 |

Algieria–Skikda | 91.40 | 7.35 | 0.57 | 0.05 | 0.63 |

Brunei | 90.12 | 5.34 | 3.02 | 1.48 | 0.04 |

Egypt–Idku | 95.31 | 3.58 | 0.74 | 0.35 | 0.02 |

Egypt–Damietta | 97.25 | 2.49 | 0.12 | 0.12 | 0.02 |

Indonesia–Badak | 90.14 | 5.46 | 2.98 | 1.41 | 0.01 |

Libya | 81.39 | 12.44 | 3.51 | 0.64 | 2.02 |

Malaysia–Bintulu | 91.69 | 4.64 | 2.60 | 0.93 | 0.14 |

Nigeria | 91.70 | 5.52 | 2.17 | 0.58 | 0.03 |

Norway | 92.03 | 5.75 | 1.31 | 0.45 | 0.46 |

Oman | 90.68 | 5.75 | 2.12 | 1.25 | 0.20 |

Peru | 89.06 | 10.26 | 0.10 | 0.01 | 0.57 |

Qatar | 90.91 | 6.43 | 1.66 | 0.73 | 0.27 |

Russia–Sakhalin | 92.54 | 4.47 | 1.97 | 0.95 | 0.07 |

Trynidad | 96.78 | 2.78 | 0.37 | 0.06 | 0.01 |

USA–Alaska | 99.70 | 0.09 | 0.03 | 0.01 | 0.17 |

Yemen | 93.17 | 5.92 | 0.77 | 0.12 | 0.02 |

Parameter | Value | Unit |
---|---|---|

Inner tank diameter | 50 | m |

Inner tank wall thickness | 40 | mm |

Primary thermal insulation thickness | 800 | mm |

Secondary thermal insulation thickness | 400 | mm |

Outer concrete wall thickness | 500 | mm |

Foundation plate thickness | 1200 | mm |

Foundation thermal insulation thickness | 1000 | mm |

Thickness of suspended roof | 40 | mm |

Thickness of roof insulation | 500 | mm |

Thermal conductivity of inner tank wall | 90 | W/(m·K) |

Thermal conductivity of primary insulation | 0.05 | W/(m·K) |

Thermal conductivity of secondary insulation | 0.1 | W/(m·K) |

Thermal conductivity of concrete wall and foundation plate | 1.8 | W/(m·K) |

Thermal conductivity of foundation plate insulation | 0.1 | W/(m·K) |

Tank height | 43 | m |

First Variant (1) | Second Variant (2) | |
---|---|---|

Ambient air temperature | 293 K | 293 K |

Ground temperature | 285 K | 285 K |

Initial temperature in bottom layer | 116.12 K | 115 K |

Tank operational pressure | 1.5 bar(a) | 1.3 bar(a) |

Initial density of top layer | 451.19 kg/m^{3} | 434.01 kg/m^{3} |

Initial density of bottom layer | 452.68 kg/m^{3} | 435.52 kg/m^{3} |

Initial level of LNG in tank | 24 m | 26 m |

Initial thickness of top layer | 9 m | 9 m |

Composition of top layer | ||

methane | 90.0% | 95.5% |

ethane | 6.7% | 3.2% |

propane | 2.3% | 0.9% |

n-butane | 0.5% | 0.0% |

iso-butane | 0.5% | 0.3% |

nitrogen | 0.0% | 0.1% |

Composition of bottom layer | ||

methane | 90.1% | 94.8% |

ethane | 6.4% | 3.3% |

propane | 2.1% | 1.0% |

n-butane | 0.4% | 0.2% |

iso-butane | 0.5% | 0.1% |

nitrogen | 0.5% | 0.6% |

Time Step | t = 0 h | t =30 h | t = 60 h | t = 90 h | t = 120 h | t = 150 h | t = 180 h |
---|---|---|---|---|---|---|---|

Temperature of bottom layer, K | 116.124 | 116.3609 | 116.5512 | 116.79 | 117.0298 | 117.2703 | 117.5601 |

Temperature of top layer, K | 117.9392 | 117.9403 | 117.9413 | 117.9425 | 117.9438 | 117.945 | 117.9464 |

Temperature of gas phase, K | 126.5542 | 162.533 | 180.7731 | 193.6171 | 200.0772 | 202.9652 | 203.3263 |

Density of top layer, kg/m^{3} | 451.2055 | 451.2373 | 451.2655 | 451.3007 | 451.336 | 451.3713 | 451.4137 |

Density of bottom layer, kg/m^{3} | 453.6301 | 453.2938 | 453.0234 | 452.6838 | 452.3425 | 451.9996 | 451.5862 |

Density difference, kg/m^{3} | 2.424581 | 2.056484 | 1.75796 | 1.383114 | 1.006509 | 0.628253 | 0.172478 |

Composition of top layer: | |||||||

Methane | 0.900 | 0.899904 | 0.899822 | 0.899719 | 0.899617 | 0.899514 | 0.899390 |

Ethane | 0.067 | 0.067069 | 0.067124 | 0.067192 | 0.067261 | 0.06733 | 0.067413 |

Propane | 0.023 | 0.023019 | 0.023038 | 0.023061 | 0.023085 | 0.023109 | 0.023137 |

n-Butane | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

iso-Butane | 0.010 | 0.010008 | 0.010016 | 0.010027 | 0.010037 | 0.010047 | 0.01006 |

Nitrogen | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Time Step | t = 0 h | t =30 h | t = 60 h | t = 90 h | t = 120 h | t = 150 h |
---|---|---|---|---|---|---|

Temperature of bottom layer, K | 115.5 | 115.697 | 115.8942 | 116.0915 | 116.2888 | 116.4857 |

Temperature of top layer, K | 115.0313 | 115.0415 | 115.054 | 115.067 | 115.08 | 115.0926 |

Temperature of gas phase, K | 123.0159 | 154.2574 | 170.4496 | 177.5019 | 181.4353 | 181.9967 |

Density of top layer, kg/m^{3} | 434.0142 | 434.01 | 434.0081 | 434.0074 | 434.0078 | 434.0093 |

Density of bottom layer, kg/m^{3} | 435.4609 | 435.1719 | 434.8822 | 434.592 | 434.3017 | 434.0117 |

Density difference, kg/m^{3} | 1.446645 | 1.161924 | 0.874034 | 0.584666 | 0.293898 | 0.002427 |

Composition of top layer: | ||||||

Methane | 0.955 | 0.954976 | 0.954948 | 0.954909 | 0.954858 | 0.954813 |

Ethane | 0.032 | 0.032041 | 0.032083 | 0.032138 | 0.032208 | 0.032267 |

Propane | 0.009 | 0.009009 | 0.009021 | 0.009036 | 0.009056 | 0.009073 |

n-Butane | 0 | 0 | 0 | 0 | 0 | 0 |

iso-Butane | 0.003 | 0.003003 | 0.003007 | 0.003012 | 0.003019 | 0.003024 |

Nitrogen | 0.001 | 0.00097 | 0.000941 | 0.000904 | 0.000859 | 0.000823 |

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**MDPI and ACS Style**

Włodek, T.; Łaciak, M.
Rollover Prevention Model for Stratified Liquefied Natural Gas in Storage Tanks. *Energies* **2023**, *16*, 7666.
https://doi.org/10.3390/en16227666

**AMA Style**

Włodek T, Łaciak M.
Rollover Prevention Model for Stratified Liquefied Natural Gas in Storage Tanks. *Energies*. 2023; 16(22):7666.
https://doi.org/10.3390/en16227666

**Chicago/Turabian Style**

Włodek, Tomasz, and Mariusz Łaciak.
2023. "Rollover Prevention Model for Stratified Liquefied Natural Gas in Storage Tanks" *Energies* 16, no. 22: 7666.
https://doi.org/10.3390/en16227666