Tank Thermal Breathing - Proposed Equation Correlate API Std 2000 Data

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Earlier post "Tank Normal Venting Rate Estimation Using Siddhartha Equation", Siddhartha equation has been presented. The proposed equations are rather simple and easy to use.

Following post will discuss the comparison between prediction Siddhartha equation and API Std 2000 data. New equations with better accuracy are proposed.

Thermal Inbreathing
From earlier post, thermal inbreathing flow cause by ambient cooling can be determined based on following equations :

If V_tank less than or equal to 3500 m3,

Q_{thermal in,air} = 0.178 x V_tank......[1]

If V_tank more than 3500 m3,

Q_{thermal in,air} = 3.2 x V_tank^0.651......[2]

where
Q_{thermal in,air} = Thermal inbreathing in Sm3/h (Air)
V_tank = Tank capacity in m3

To convert Sm3/h to Nm3/h, divide inbreathing / outbreathing flow with a factor of 1.055. Refer "Relate NORMAL to STANDARD Volumetric Flow"

The error difference for thermal inbreathing between above equations and API Std 2000 data is about :

• 0.17% for tank volume less than or equal to 3500 m3
• 3.75% for tank volume more than 3500 m

Above error is rather small and should be acceptable from engineering aspect. Nevertheless, further investigations found the following equations giving slightly lower error :

If V_tank more than 3500 m3, a polynomial equation is proposed.

Q_{thermal in,air} = a.V_tank⁶ + b.V_tank⁵+ c.V_tank⁴
+ d.V_tank³ + e.V_tank² + f.V_tank + g ......[3]

with

a = -4.333E-23
b = + 4.974E-18
c = - 2.281E-13
d = + 5.328E-09
e = - 6.681E-05
f = + 0.494
g = - 549.435

where
Q_{thermal in,air} = Thermal inbreathing in Nm3/h (Air)
V_tank = Tank capacity in m3

The error difference for thermal inbreathing between above proposed equation and API Std 2000 data is about 1.25% for tank volume more than 3500 m

Thermal Outbreathing
From earlier post, thermal outbreathing flow cause by ambient heating can be determined based on following equations :

Liquids with a flash point (FP) greater than 37.8°C or Normal Boiling Point (NBP) above 149°C

If V_tank less than or equal to 3500 m3,

Q_{thermal out,air} = 0.107 x V_tank ......[4]

If V_tank more than 3500 m3,

Q_{thermal out,air} = 1.92 x V_tank^0.651 ......[5]

where
Q_{thermal out,air} = Thermal inbreathing in Sm3/h (Air)
V_tank = Tank capacity in m3

The error difference for thermal inbreathing between above equations and API Std 2000 data is in the range of 0.09% - 16.88%

Above error diefference is rather big. However, it may be still acceptable in practical application. Care shall be taken when these equqation are used.

Further investigations found the following equations giving better estimation :

a) Liquids with a flash point (FP) greater than 37.8°C or Normal Boiling Point (NBP) above 149°C

If V_tank less than or equal to 3000 m3,

Q_{thermal out,air} = 0.1012 x V_tank ......[6]

If V_tank more than 3000m3 and less than or equal to 8000 m3,

Q_{thermal out,air} =+ a.V_tank⁴ + b.V_tank³
+ c.V_tank² + d.V_tank + e ......[7]

with
a = -2.659E-12
b = + 6.206E-08
c = - 5.35E-03
d = + 2.073
e = - 2541.692

If V_tank more than 8000 m3,

Q_{thermal out,air} = a.V_tank⁵ + b.V_tank⁴+ c.V_tank³

+ d.V_tank² + e.V_tank + f ......[8]

with

a = 1.0318E-18
b = - 8.775E-14
c = + 2.742E-09
d = - 3.925E-05
e = + 0.302
f = - 282.206

The error difference for thermal inbreathing between above equations and API Std 2000 data is in the range of 0.1 - 3.95%.

b) Liquids with a flash point less than 37.8°C or Normal Boiling Point (NBP) below 149°C

Similar equation [3] may be used.

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