Question

In receiving terminals of petrochemical plants, some of the liquid natural gas (LNG) storage Tanks are designed to be in ground, to avoid receiving radiation from the sun and also being protected from direct hit. Even though, they are buried in the ground the top ceiling is exposed to the environment and can absorb radiation of the sun, sky and surroundings. The absorbed energy by the ceiling can increase the internal energy of the stored liquid methane and at some the liquid methane will evaporate. Evaporated methane will increase the pressure of the tank can cause catastrophe. To avoid any accident a boil-off gas compressor with 0.2% volume full tank capacity per day discharge is installed in a plant. The detail design of the storage tank is as below: Tank Diameter = 15 m Tank Height = 15 m Ceiling (Roof) = black body at TRoof Liquid CH4 surface = black body at TSat Side wall = gray, diffuse (?3=0.6) at T=( TRoof+ TSat )/2 Max. Liquid depth Lmax=10 m TRoof=55°C A designer suggests modeling the tank as a three surfaces enclosure as below: a) For this assembly, find the net radiative transfer to the liquid in kW, for different values of Liquid height (5, 6, 7, ..., 10 m). b) Find if the capacity of boil-off gas compressor is sufficient to condense the flow rate of evaporated Methane? c) Repeat your calculations in part a and b, for the case which a radiation shield with diameter 15[m] is installed exactly at the top of cylindrical wall. The (?Shield=0.4) HINT: YOU NEED TO APPLY THERMAL CIRCUIT FOR RADIATION AND CALCULATED THE q2 ENTERING SURFACE 2. Thermophysical properties of Methane Critical Temperature, Tc=190.5 K, Pc=4.6 MPa Tsat= 113.15 K, Psat=1 atm. | | Liquid at 1atm, Tsat. | Gas at 1atm, Tsat. | | :--- | :---: | :---: | | Cp [kJ/kg. K] | 3.349 | 2.260 | | ? [kg/m³] | 422.63 | 1.75 | | ? [N. s /m²] | 1.17 X 10?? | 4.20 X 10?? | | K [W/m. K] | 0.1862 | 0.0132 | | Pr (Prandtl number) | 2.098 | 0.789 | | hfg [kJ/kg] (latent heat of vaporization) = 511 | | |

          In receiving terminals of petrochemical plants, some of the liquid natural gas (LNG) storage Tanks are designed to be in ground, to avoid receiving radiation from the sun and also being protected from direct hit. Even though, they are buried in the ground the top ceiling is exposed to the environment and can absorb radiation of the sun, sky and surroundings. The absorbed energy by the ceiling can increase the internal energy of the stored liquid methane and at some the liquid methane will evaporate. Evaporated methane will increase the pressure of the tank can cause catastrophe. To avoid any accident a boil-off gas compressor with 0.2% volume full tank capacity per day discharge is installed in a plant. The detail design of the storage tank is as below:

Tank Diameter = 15 m
Tank Height = 15 m
Ceiling (Roof) = black body at TRoof
Liquid CH4 surface = black body at TSat
Side wall = gray, diffuse (?3=0.6) at T=( TRoof+ TSat )/2
Max. Liquid depth Lmax=10 m
TRoof=55°C

A designer suggests modeling the tank as a three surfaces enclosure as below:

a) For this assembly, find the net radiative transfer to the liquid in kW, for different values of Liquid height (5, 6, 7, ..., 10 m).
b) Find if the capacity of boil-off gas compressor is sufficient to condense the flow rate of evaporated Methane?
c) Repeat your calculations in part a and b, for the case which a radiation shield with diameter 15[m] is installed exactly at the top of cylindrical wall. The (?Shield=0.4)

HINT: YOU NEED TO APPLY THERMAL CIRCUIT FOR RADIATION AND CALCULATED THE q2 ENTERING SURFACE 2.

Thermophysical properties of Methane
Critical Temperature, Tc=190.5 K, Pc=4.6 MPa
Tsat= 113.15 K, Psat=1 atm.

| | Liquid at 1atm, Tsat. | Gas at 1atm, Tsat. |
| :--- | :---: | :---: |
| Cp [kJ/kg. K] | 3.349 | 2.260 |
| ? [kg/m³] | 422.63 | 1.75 |
| ? [N. s /m²] | 1.17 X 10?? | 4.20 X 10?? |
| K [W/m. K] | 0.1862 | 0.0132 |
| Pr (Prandtl number) | 2.098 | 0.789 |
| hfg [kJ/kg] (latent heat of vaporization) = 511 | | |

In receiving terminals of petrochemical plants, some of the liquid natural gas (LNG) storage Tanks are designed to be in ground, to avoid receiving radiation from the sun and also being protected from direct hit. Even though, they are buried in the ground the top ceiling is exposed to the environment and can absorb radiation of the sun, sky and surroundings. The absorbed energy by the ceiling can increase the internal energy of the stored liquid methane and at some the liquid methane will evaporate. Evaporated methane will increase the pressure of the tank can cause catastrophe. To avoid any accident a boil-off gas compressor with 0.2% volume full tank capacity per day discharge is installed in a plant. The detail design of the storage tank is as below:

Tank Diameter = 15 m
Tank Height = 15 m
Ceiling (Roof) = black body at TRoof
Liquid CH4 surface = black body at TSat
Side wall = gray, diffuse (?3=0.6) at T=( TRoof+ TSat )/2
Max. Liquid depth Lmax=10 m
TRoof=55°C

A designer suggests modeling the tank as a three surfaces enclosure as below:

a) For this assembly, find the net radiative transfer to the liquid in kW, for different values of Liquid height (5, 6, 7, ..., 10 m).
b) Find if the capacity of boil-off gas compressor is sufficient to condense the flow rate of evaporated Methane?
c) Repeat your calculations in part a and b, for the case which a radiation shield with diameter 15[m] is installed exactly at the top of cylindrical wall. The (?Shield=0.4)

HINT: YOU NEED TO APPLY THERMAL CIRCUIT FOR RADIATION AND CALCULATED THE q2 ENTERING SURFACE 2.

Thermophysical properties of Methane
Critical Temperature, Tc=190.5 K, Pc=4.6 MPa
Tsat= 113.15 K, Psat=1 atm.

| | Liquid at 1atm, Tsat. | Gas at 1atm, Tsat. |
| :— | :—: | :—: |
| Cp [kJ/kg. K] | 3.349 | 2.260 |
| ? [kg/m³] | 422.63 | 1.75 |
| ? [N. s /m²] | 1.17 X 10?? | 4.20 X 10?? |
| K [W/m. K] | 0.1862 | 0.0132 |
| Pr (Prandtl number) | 2.098 | 0.789 |
| hfg [kJ/kg] (latent heat of vaporization) = 511 | | |

Added by Workemail T.

Question

Please give Ace some feedback