Constant Density To Obtain Relieving Condition

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A pressure vessel or system expose to external fire, entire system may be isolated automatically by a plant wide emergency shutdown system (ESD) and emergency depressuring system will be initiated to depressure system to safe level and evacuate the inventory from high risk area (expose to external fire) to disposal system. Depressuring system is known as one of the most effective measures against external fire risk. Besides, there are others measures as discussed in "Protective Measures against FIRE...".

Pressure relief device (PRD) may not protect pressure vessel or system from external fire. Having said that PRD may serve in some circumtances to "buy time" for operator action. Besides, design code and/or local regulation demand a PRD in pressure vessel or system as ultimate protection.

One may have process simulation for normal production system. The stream for vessel or system expose to fire is at normal operating pressure and temperature. How shall one can adjust the process simulation to bring it up the relieving pressure ? One may consider a constant density method.

Constant density method
Pressure vessel expose to fire will be isolated and settled-out. Read more in "Adjusted Method For Compressor Settle Out (with Vapor & Liquid) Using HYSYS". Assuming no credit for automatic depressuring system and operator intervention, the inventory trapped in the pressure vessel will remain as trapped vapor mass (M_V0) with vapor volume (V_V0) and liquid mass (M_L0) with liquid volume (V_L0) at normal pressure (P₀) and temperature (T₀) when ESD is just initiated. Total trapped mass (M_T0) will be M_V0 + M_L0 and total trapped volume (V_T0) will be V_V0 + V_L0. Mix denstiy will be M_T0/V_T0.

Trapped inventory will be heated up with external fire. Heat added into the trapped system will cause temperature rise, more liquid vaporise and pressure rise upto relieving pressure, before pressure relief device is popped open. At relieving condition (relieving pressure and temperature), trapped vapor mass (M_Vr) with vapor volume (V_Vr) and liquid mass (M_Lr) with liquid volume (V_Lr). Total trapped mass (M_Tr) will be M_Vr + M_Lr and total trapped volume (V_Tr) will be V_Vr + V_Lr. Mix denstiy will be M_Tr/V_Tr. As there is no inventory evacuated from the system, total trapped mass (M_T0) and volume (V_T0) at normal condition will be same as trapped mass (M_Tr) and volume (V_Tr) at relieving condition.

M_T0 = M_Tr
V_T0 = V_Tr

Similar mix density (M_T0/V_T0) will remain same.

M_T0/V_T0 = M_Tr/V_Tr

This is commonly known as constant density method.

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Quick Estimation of Noise Level Across Pressure Reducing Device

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Pressure reducing device such as control valve, pressure relief valve, restriction orifice, etc, there will be pressure drop and mass passing through these device, internal acoustic energy is generated and transmitted to downstream piping and potentially lead to severe piping excitation, vibration and stresses on downstream piping and potentially lead to fatigue failure. Internal acoustic energy transmitted along the pipe may also transmitted to through the pipe and emitted as Noise.

One of the common safety requirement is limit the noise level to 85 dBA (Noise level with A-weighted) in continuous exposure and 115 dBA during intermittent exposure. In earlier conceptual or Front End Engineering Design (FEED) stage, the noise level across pressure reducing device may be estimated to determine overall noise control philosophy. The following will present a simple method to estimate noise level generated at 1 meter from a pressure reducing device.

Noise Level Estimation
Noise level at 1 meter from a pressure reducing device can be estimated from Sound Power Level (PWL) as discussed in "Sound Power Level (PWL) Prediction from AIV Aspect". The Sound Power Level will be transmitted across the pipe wall and emitted to atmosphere. There will be noise correction when Sound power is transmitted across pipe wall (metal). The noise correction is subject to wall thickness. Thicker wall will result higher noise correction. Following are typical noise correction for pipe size and wall thickness.

Noise Correction
Nominal Dia. (Inch)	Wall thickness (mm)	Noise Correction (dB)
25	3.38	54
50	3.91	50
100	6.02	50
150	7.12	49
200	8.18	48
250	9.3	47
300	9.53	47
350	9.53	46
450	9.53	46
600	9.53	45
750	9.53	43
900	9.53	43
1050	9.53	42

Noise level at 1 meter from a pressure reducing device,

L_1m = PWL - L_A

where
PWL = Sound Power Level (from Sound Power Level (PWL) Prediction)
L_A = Noise correction from above table

Example

A pressure control valve (PV) passing 100,000 kg/h of gas with molecular weight (MW) of 22. The inlet condition is 87 barg and 50 degC and downstream pressure is about 7 barg. The pipe diameter is 18 inch with wall thickness of 9.53mm, estimate noise level at 1 m from PV.

PWL = 10 x Log [((87-7) / (87+1.01325))^3.6
x (100,000 / 3600)^2
x ((50+273.15)/22)^1.2]
+ 126.1

PWL = 167.5 dB

Noise level at 1m,
L_1m = PWL - L_A
L_1m = 167.5 - 46
L_1m = 121.5 dBA

As the noise level at 1m (normal trim) is 121.5 dBA, this is far too big from normal requirement. A low noise trim control valve may be considered and/or acoustic insulation to be provided.


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API Std 521 - Errata and Addendum Released by API

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This post is intended to provide supplementary information for earlier post "API Std 521 ADDENDUM, MAY 2008 - Check Out Revised Section".

Addendum May 2008
API has released the Addendum details to API Std 521. It describes in detail the modified sections compare to earlier release in 2007. You may download Addendum May 2008 from here.

Errata June 2007
For those who don't not aware the Errata in June 2007 for API Std 521 released in 2007, you may read "ERRATA - API Std 521, Pressure Relieving and Depressuring Systems" and download Errata June 2007 from here.

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Quick Estimate Ground Level Unburnt Flammable Gas For Vent Pipe or Flame-out Flare Stack

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Flare is commonly installed in oil and gas process plant to burn hydrocarbon and/or toxic gas to avoid formation of combustible mixture, to minimize green house effect (GHE), to minimize health hazards to personnel on site, etc. Although there are many benefits in using flare for proper disposal of hydrocarbon gases, combustion efficiency is still a common concern about flare. It is commonly accepted a flare combustion efficiency can reach approximately 98% (refer API Std 521). This would still results some remaining unburnt hydrocarbon gases release into atmosphere. Thus, there are operators especially in high environment concern area, zero emission and flaring principle is implemented.

Flare is normally lit and a highly reliable pilot system is maintaining the flame at the flare tip. In an extreme condition i.e. storm, heavy rain, strong wind, long serviced pilot, etc, flare may lose the flame. This situation commonly called as flame-out condition. Any release during this period would lead to flammable gas (heavier than air) release and settle to ground level in process area. Wind blowing may disperse the flammable gas and reduce concentration of flammable gas at ground level. However, there is still possibility of flammable gas settled and form combustible mixture. Thus, it is very important to estimate maximum concentration of flammable gas at ground level.

Nowadays with sophisticated software development, software such as PHAST may be used to estimate concentration of flammable gas at ground level at specific location. However, quick estimation method may be important during conceptual phase. Following will present a simple estimation method to calculate maximum concentration of flammable gas at ground level.

Maximum Ground Level Concentration of flammable gas,

C = 0.23 x Q / (U x H'²)

where
C = Flammable gas concentration (g/m³)
Q = Mass flow of flammable gas (g/s)
U = Wind speed (m/s)
H' = Effective height (m)

Effective flare height can be determined with

H' = H_s + 3 d_s V_ex / U

where
H_s = Flare stack height (m)
d_s = Flare tip diameter (m)
V_ex = Exit velocity (m/s)
U = Wind velocity (m/s)

Concentration conversion g/m³ to ppm,

[C in ppm] = [C in mg/m³] x 24.45 / MW

where
[C in ppm] = Concentration in ppm
[C in g/m³] = Concentration in mg/m³
MW = Gas molecular weight

Example
Estimate the maximum ground-level concentration, C, if a flammable gas is accidentally released unburned from a flare, if the release rate to the atmosphere, Q, is 25,200 g/s, the exit
velocity is 83.8 m/s, and flare tip diameter is 0.46 m. The flare stack height is 61 m. Assume that the wind speed 3.1 m/s. The molecular weight of the gas is 54.

H' = H_s + 3 d_s V_ex / U
H' = 61 + 3 (0.46) (83.8 / 3.1)
H' = 98.3 m

C = 0.23 x Q / (U x H'²)
C = 0.23 x 25200 / (3.1 x 98.3²)
C = 0.193 g/m³

[C in ppm] = [C in mg/m³] x 24.45 / MW
[C in ppm] = 0.193 x 1000 x 24.45 / 54
[C in ppm] = 87.6 ppm

Ref : Section 15.11, Handbook of Chemical Engineering Calculations, 3rd Edition, Nicholas P. Chopey

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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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Tank Normal Venting Rate Estimation Using Siddhartha Equation

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Liquid product like Chemical, condensate, etc is commonly stored in fixed roof vertical cylindrical tank. Inert gas blanketing system is provided to avoid air and moisture contact and contaminate liquid product. Liquid movement by content filling (pump-in) or emptying (pump out) and weather changes (ambient heating or cooling) will results internal pressure increase (overpressure) or decrease (vacuum) in the tank. Thus, a protecting system providing inbreathing or outbreathing gas is provided to maintain a constant pressure in the tank.

Inbreathing
Emptying (pump-out) and ambient cooling will lead to normal inbreathing. Siddhartha (2006) proposed a general equation to determine inbreathing flow :

If V_tank less than or equal to 3500 m3,

Q_in,air = Q_outflow + 0.178 x V_tank

If V_tank more than 3500 m3,

Q_in,air = Q_outflow + 3.2 x V_tank^0.651

where
Q_in,air = Total inbreathing in Sm3/h (Air)
Q_outflow = Pump-out or emptying in m3/h
V_tank = Tank capacity in m3

Outbreathing
Filling (pump-out) and ambient heating will lead to normal outbreathing. Siddhartha (2006) proposed a general equation to determine outbreathing flow :

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_out,air = 1.069 x Q_inflow + 0.107 x V_tank

If V_tank more than 3500 m3,

Q_Out,air = 1.069 x Q_inflow + 1.92 x V_tank^0.651

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

If V_tank less than or equal to 3500 m3,

Q_out,air = 2.138 x Q_inflow + 0.178x V_tank

If V_tank more than 3500 m3,

Q_out,air = 2.138 x Q_inflow + 3.2 x V_tank^0.651

where
Q_out,air = Total outbreathing in Sm3/h (Air)
Q_inflow = Pump-in or filling in m3/h
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"

Note:
Sm3/h indicates volume flow at standard conditions of 101.325 kPa(a) and 15 degC
Nm3/h indicates volume flow at standard conditions of 101.325 kPa(a) and 0 degC


Ref : "Understanding Atmospheric Storage Tanks" by Siddhartha Mukherjee, Chemical Engineering, April 2006

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Above equations have been programmed by Ankur, a experience Chemical Engineer, share with readers of Chemical and Process Technology. You may download here.

Thanks to Ankur
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*If you have any useful program and would like to share within our community, please send to me.

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