Assessment of safety and economic impact of boil-off-gas in LPG storage tanks

This study was carried out to assess effect of boil-off gas (BOG) on the safety and economic effectiveness of LPG storage tank. It


Introduction
Liquefied Petroleum Gas (LPG) is propane, butane, iso-butane, or mixtures of these gases, which are extracted from natural gas production fields or produced during the refining of petroleum (crude oil).LPG is stored and transported in steel cylindrical tanks as liquid under sufficiently high pressure [1].To allow for thermal expansion, these tanks are typically filled to between 80% and 85% of their capacity [2], [3].The LPG stored in a tank exists in equilibrium between a thermodynamic liquid and vapor.The storage tank is surrounded by ambient air that causes heat leakage into the storage tank due to the temperature between the LPG and ambient air [4], [5].The heat leakage into the tank causes portion of LPG to continue to evaporate, and generating a boil off gas (BOG) that causes changes in the thermodynamic properties of the LPG, and losses in the LPG supply chain over time [6], [7].
Different sources exist for the generation of BOG, these sources include heat leaks from ambient air around the storage tank, heat ingress due to the dissipation of pumping power inside the tanks, heat

A R T I C L E I N F O A B S T R A C T
This study was carried out to assess effect of boil-off gas (BOG) on the safety and economic effectiveness of LPG storage tank.It includes analysis of the thermodynamic properties of LPG; heat absorbed from ambient air by the storage tank that leaks into the LPG, and consequently generates boil-off gas in the supply chain, by utilizing appropriate thermodynamic and heat transfer equations.Analyzing the heat leakage required the estimations of the convective heat transfer coefficient of the ambient air in the supply location and the LPG supply chain, which amounted to 3335.9W/m2K and 21.058W/m2K, respectively, in the system under study.Analyzing the thermodynamic properties such as specific volume, entropy and enthalpy of the LPG, show that the entropy of LPG in the storage tank is negative, which suggested an endothermic process, validating that heat is added to the system from the surroundings.The heat absorbed in the LPG from the ambient air by the storage tank amounted to 1.785kW.The boil-off generation rate due to the storage tank heat leakage was 0.0049kg/s, which translates to a cost equivalent loss of 0.0069$/s at LPG selling price of 1.42$/kg.It was recommended that maintenance of insulation and other external factors such as wind speed, solar radiation, ambient temperature and thermal conductivity of the storage tank material are key factors in minimizing the heat leaks into LPG; hence BOG generation, which is of utmost importance in ensuring safety and economic loss in the LPG supply chain.leaks from pipelines, flash vapor generated by liquid rundown and displaced vapor from the tank due to liquid filling which is called the piston effect.The boil off of LPG causes excessive temperature and pressure build up in the tank, and as LPG is very sensitive to changes in temperature, an increase in its temperature leads to rapid evaporation and sudden increase of pressure in the storage tank [8], [9].It is imperative to ascertain methods to reduce the temperature changes in the tank to prevent generation of the boil off in order to maintain the tank pressure within economic and safety ranges.LPG safety required that its storage tanks and other equipment are made of suitable materials with the proper design engineering.
LPG is used as fuel gas in heating appliances, cooking equipment, and vehicles.It also powers many business and agricultural processes.LPG is increasingly used as an aerosol propellant and a refrigerant, replacing chlorofluorocarbons in an effort to reduce damage to the ozone layer [10].In Nigeria, LPG is becoming even more useful, especially now that the government is positioning LPG as an alternative for the eventual replacement of firewood and kerosene as domestic cooking fuel, and also canvassing the use of LPG as vehicle fuel (auto gas) for transportation [11].These have resulted in the emergence of a lot of LPG skid plants, without proper boil-off gas (BOG) recovery system nationwide.Thus, raises safety and profitability concern [12], [13].
Even though, government is encouraging technology development and safety enhancement to support sustainable LPG business growth [14].The generation of boil-off gas in the storage tank causes losses in the LPG supply chain over time [6].BOG is the continuously evaporated or boiled LPG vapor that causes the pressure inside the tank to rise due to heat entering the tank during storage and transportation, which may change the quality of LPG over time.This BOG is generated primarily due to heat leakage, resulting from the temperature difference between the ambient air and LPG.BOG generation rate is one of the most important factors for safety and economic assessment of in LPG storage tank.This study took place at GMPP LPG storage tanks located in Okigwe and manufactured by Hubei Chusheng Ltd. as a case study to use the thermodynamic and heat transfer methods to analyze the temperature that may contribute to boil-off gas generation in the plant, and evaluate the economic implication of the boil-off of gas generation during the LPG storage process.

Method
The materials for this study include the LPG storage tank catalogue, Data of thermo-physical properties of LPG (Butane) and ambient air, data of ambient climate condition of the storage tank location (Okigwe, Imo State, Nigeria), and GMPP LPG storage tank facility inventory record.The data analysis method was used in the study.The processes are as outlined: Collection of Data; Thermodynamic Properties of LPG; Description of LPG Storage Tank; Description of the Boil off Gas Generation; Analysis of Heat Leakage through Storage Tank; Analysis of the Boil Off Gas Generation Rate.The schematic display is presented in equation.
The inventory record of the GMPP LPG storage tank facility offered vital perspectives on its operational history and trends, leading to a more nuanced comprehension of the system's dynamics.Employing this comprehensive methodology, we were able to evaluate not just the rate of boil off gas generation but also pinpoint potential areas for optimizing and improving the efficiency of LPG storage and utilization.The research flow is shown in the Fig. 1.

Collection of Data
The data used in this study include the LPG skid plant technical parameters obtained from the LPG storage catalogue [15], thermo physical properties for the LPG (Butane) obtained from Beaton and Hewitt [16], thermo physical properties for the ambient air obtained from Cengel and Cimbala [17], ambient climate condition and other physical properties of the plant obtained from the various measuring and monitoring instruments fitted to the plant and recorded in facility inventory record.The operational environment of the LPG storage used in this study is Okigwe, Nigeria, which has a tropical climate, with an average annual temperature of 26°C [18].The annual average speed of air experienced in Okigwe is 2.32m/s [19].

Thermodynamic Properties of LPG
The heat leakage from the surroundings of the storage tank causes changes of temperature of the LPG, and consequently its composition vapor-liquid equilibrium which have a significant effect on its thermodynamic properties.The thermodynamic properties of the LPG include Pressure, Temperature, Specific Volume, Density, Enthalpy, Entropy and Heat Capacity [20], [21].Equations of state which relate Pressure-Volume-Temperature (P-V-T) are commonly used to described the behavior of real pure substances and mixtures, and can be used for the Analysis of the Specific Volume, Density, Enthalpy and Entropy as functions of Temperature and Pressure [22].

• Specific volume of the LPG
The changes in the temperature and pressure of the LPG in the storage tank also results in change in the volume and of the LPG.The volume of the LPG in the tank can be determined from the equation of state.There are different types of equations of states which are viral, cubic and complex, the greatest distribution was gained by the cubic equations of state for the simplicity of expression, ability with some degree of accuracy to describe thermodynamic properties of gases, the Van Der Waals equation of state that is useful for calculating the volume of gases below critical temperatures is used [23].The Van der Waals equation of state is given in equation 1.Where v = Specific volume (m3/mol), R = Specific gas constant (J/molK), T = Temperature (K), P = Pressure (N/m2).The value of the constants a and b for the Van der Waals equation of state for the gaseous elements and compounds contained in the LPG could be obtained from Cooper and Gold frank (1967).The specific volume can be expressed in cubic meter per kilogram (m3/kg) by the formula.
Where M = molecular weight of the gas (kg/Kmol).

• Entropy of LPG
Entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system.The change in entropy of a process can be expressed using Van der Waal equation of state as follows [24].
where Cv = Specific Heat at Constant Volume(kJ/kgK), To = Ambient Temperature (K), vo = volume of gas at ambient condition (m3/kmol).At standard temperature and pressure, volume of all gases is 22.4m3/kmol.

• Enthalpy of LPG
Enthalpy is a measure of the total energy of a thermodynamic system.It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy change accounts for energy transferred to the environment at constant pressure through expansion or heating.The change in enthalpy of the gas can be calculated using the equation 4.

∆𝐻 = 𝑇(𝑆 − 𝑆 𝑜 ) + 𝑉(𝑃 − 𝑃 𝑜 )
() • Energy Content of the LPG The energy content is the measure of equivalent energy released through combustion.The energy content of LPG is the central quantity upon which its economic value is determined and its value depends on the source of natural gas and the process used to liquefy the gas.The energy content (E) is expressed in Joule (J) and approximately given as.
Where Elpg= Energy transferred in LPG (kJ), Ebog = Energy transferred in BOG (kJ).According Elengy [25], the energy transferred in BOG is approximately 0.1% of the energy transferred in the LPG.The energy transferred in LPG is given as.
Where V = Volume of LNG in the Tank (m3), H= Heating value of the LNG loaded in the tank (J/kg).

Description of LPG Storage Tank
LPG storage tanks are made from welded steel and are designed for the required pressures and heat expansion of the stored hydrocarbon gases, including propane and butane.LPG storage tank integrates components such as pump, valves, pipelines and dispensing unit, all self-contained on a frame.The storage tank is a double containment, a steel-in-steel cylindrical tank with hemispherical covers at both ends.The annulus is a vacuum with per lite insulation, as shown in Fig. 2. • Vent: this an opening that allows air, gas or liquid to pass out of or into a confined space.
• Manhole: is an opening to a confined space such as a shaft, utility or large vessel.Manholes are often used as access point for an underground public utility, maintenance and system upgrades.
• Feed: This is a opening for supplying material to the LPG container.
• Pump: a pump is a device which moves fluids by mechanical action, from one place to another.
• Dispenser: This is where the desire amount of liquid, gas comes out from.
• Valve: A device for controlling the passage of liquid, gas, air through a pipe.
• Pressure gauges: they are devices that measure the internal pressure of media within a system.
• Temperature gauges: temperature gauges measure the thermal state of a homogenous substance.

Description of the Boil off Gas Generation
Boil off gas in the LPG storage tank is generated under the conditions that heat is absorbed from ambient air by the storage tank and leak into the LPG.A difference in temperature between the LPG and ambient air provides the driving force for heat transfer, and any temperature above the boiling point, LPG would immediately boil off into vapor [1].

Heat Leakage through Storage Tank
Heat is leak into the storage tank through the cylindrical shell and the hemispherical cover at both end of the cylinder as show in Fig. 3. Using Fig. 4, the heat leakage through the cylindrical shell and the hemispherical cover at both end of the storage tank, respectively, are given as [26].
where Qc = heat leakage through tank cylindrical shell (W), l = length of tank cylindrical \hemispherical end cover (W).

Convective Heat Transfer Coefficient through Storage Tank
The convective heat transfer coefficient for the airflow and LPG can be estimated using the Nusselt-Reynolds-Prandtl relation given as [27].where Re = Reynolds number, Pr = Prandtl number, k = thermal conductivity (W/mK), d = tank diameter (m).The Reynolds numbers for the airflow and the LPG would be, respectively, calculated by [28].

Total Heat Leakage into the Storage Tank
From Fig. 2 and Fig. 3, the total heat leakage into the storage tank is given as [20].
2.2.5.Boil off gas generated due to storage tank heat leakage The rate of BOG generated based on the heat leakage into the storage tank (mTank) is expressed in kilogram per second (kg/s) and is given as [22].

Cost Equivalent of LPG Loss
BOG generation resulted in losses of the LPG.The cost equivalent of loss LPG (CLoss) is expressed in the units of currency per second ($/s) and would be calculated using the formula.

Results and Discussion
Table 1 summarizes the collected data for the LPG parameters and the ambient air.The thermodynamic properties of the LPG in the storage tank were analyzed using the temperature and pressure obtained for the LPG storage in Table 1.
The analysis showed that the entropy of LPG in the storage tank is negative, which suggested an endothermic process.That is, heat is added to the system from the surroundings.

Analysis of Enthalpy of LPG in the Storage Tank
Applying Equation 4, the enthalpy of LPG in the storage tank is determined as follows: T = 291K, S -So = 0.1325kJ/kgK, V = 0.2m3/kg,Po= 101.3kPa,P = 200kPa, .
The analysis showed that the enthalpy of LPG in the storage tank is greater than zero, which suggested that heat is added to the system from the surroundings.

Analysis of Energy Content of the LPG
Applying Equation 3.6, the enthalpy of LPG in the storage tank is determined as follows: T = 291K, S -So = 0.1325kJ/kgK, V = 0.2m3/kg, Po = 101.3kPa,P = 200kPa.

Analysis of the Heat Leakages
The heat leak into the LPG through the storage tank, pump and pipeline are determined as follow.
3.6.1.Analysis of the BOG generation rate due to storage tank heat leakage Applying Equation 11, where QTank= 1.785kW, hfg = 367kJ/kg (from Table 1), the BOG generation rate due to storage tank heat leakage is calculated as mtank = 0.0049kg/s.
From the analysis, The BOG generation rate of 0.0049kg/s, has a cost equivalent loss of 0.0069$/s at LPG selling price of 1.42$/kg.

Conclusion
This study was carried out to analyze the thermodynamic properties of LPG; heat absorbed from ambient air by the storage tank that leaks into the LPG, and consequently generates boil-off gas in the supply chain, by utilizing appropriate thermodynamic and heat transfer equations.Analyzing the thermodynamic properties of the LPG, shows that the entropy of LPG in the storage tank was negative, which suggested an endothermic process, validating that heat is added to the system from the surroundings.Considering the heat leakage into the skid plant, gave the convective heat transfer coefficient of the ambient air in the supply location and the LPG in the supply chain, as 3335.9W/m2Kand 21.058W/m2K, respectively.Heat absorbed from the ambient air by the storage tank amounted to 1.785kW.Thus, the boil-off generation rate due to the storage tank heat leakage, was 0.0049kg/s, which translates to a cost equivalent loss of 0.0069$/s at LPG selling price of 1.42$/kg.Therefore, boil-off gas generation results from the heat leakages into the LPG through the tank wall.Thus, it is recommended for storage tank designers to provide perfect insulation to limit the admission of heat leakage that cause boil-off gas.In addition, a BOG Removing mechanism from the tanks would help storage of LPG at a

Vol. 2 ,Fig. 1 .
Fig. 1.Methodological process flow Collection of Data • Thermodynamic Properties of LPG Description of LPG Storage Tank Description of the Boil off Gas Generation Analysis of Heat Leakage through Storage Tank Analysis of the Boil Off Gas Generation Rate

Fig. 3 .
Fig.3.Schematic diagram of axial and radial direction heat leakage into the storage tank[1]

Fig. 4 .
Fig.4.Schematic diagram of the temperature distribution for the storage tank[26]

Table 2
summarizes the technical parameters of the LPG storage.

Table 2 .
Summary of LPG Storage Tank Technical Parameters