API RP 581 - 3rd Ed.2016 - Add.2-2020 - Risk-Based Inspection Methodology
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API RP 581 - 3rd Ed.2016 - Add.2-2020 - Risk-Based Inspection Methodology

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RISK-BASED INSPECTION METHODOLOGY, PART 3—CONSEQUENCE OF FAILURE METHODOLOGY 3-87Aburnpf , npoolWn= (3.131)m bFor instantaneous releases of the flammable liquid inventory to the ground, a practical limit to the amount ofpool spread should be used in the consequence calculations. The maximum size of the pool can be determinedbased on assuming a circle with depth of 5 mm (0.0164 ft), in accordance with The Netherlands Organizationfor Applied Scientific Research (TNO Yellow Book), 1997 [18] , recommendations.Amaxpf , nmassavail,n=C ⋅ frac ⋅ρ18rol(3.132)The pool fire area to be used in the consequence area calculation is then:A = min ⎡⎣Aburn , Amax ⎤⎦ (3.133)pf , n pf , n pf , nThe consequence of a pool release is directly dependent on the pool area, which is driven by assumptionsmade of the pool depth. In practice, areas have slopes for drainage, curbing, trenches, drains, and other groundcontours that collect or remove fluids. Applying conservative pool depth values (e.g. 5 mm depth [18] , 1 cm. [19] )provides unrealistically large pool areas. Site condition should be considered when estimating pool size. Adefault limit of 10,000 ft 2 may be appropriate for all but the largest releases. From this area, the radius of thepool fire can be determined:Rpf , nApf , n= (3.134)π5.8.2.4 Flame Length and Flame TiltThe SFPE Fire Protection Handbook [20] provides a correlation from Thomas that can be used for calculatingthe flame length of a pool fire, L .pf0.67⎡ m⎤L = 110⋅R ⎢⎥ u⎢⎣ρatm2⋅g⋅Rpf , n ⎥⎦b−0.21pf , n pf , n s(3.135)The non-dimensional wind velocity, us, cannot be less than 1.0 and is dependent on the wind speed as follows:usn ,⎡ ⎛ ρ ⎞v= max ⎢1.0 , uw⋅⎜ ⎢ ⎜2g mbR ⎟⎝ ⋅ ⋅ ⋅pf , n⎣⎠0.333⎤⎥⎥⎦(3.136)The American Gas Association provides the following correlation for estimating the flame tilt:1θ = (3.137)ucos pf , nsn ,5.8.2.5 Pool Fire Radiated Energy

3-88 API RECOMMENDED PRACTICE 581The amount of energy radiated by the pool fire (often referred to as surface emitted heat flux) is a fraction ofthe total combustion power of the flame [18] . The fraction of the total combustion power that is radiated, β , isoften quoted in the range of 0.15 to 0.35. A conservative value of 0.35 can be chosen. Therefore:QradpoolnC ⋅β⋅m⋅HC ⋅π⋅R=2 ⋅ ⋅ ⋅ + ⋅214 b l pf , n2π Rpf , nLpf , nπ Rpf , n(3.138)The amount of the radiated energy that actually reaches a target at some location away from the pool fire is afunction of the atmospheric conditions as well as the radiation view factor between the pool and the target. Thereceived thermal flux can be calculated as follows:Ith = τ ⋅Qrad ⋅ Fcyl(3.139)poolpooln atm,n n nThe atmospheric transmissivity is an important factor since it determines how much of the thermal radiation isabsorbed and scattered by the atmosphere. The atmospheric transmissivity can be approximated using thefollowing formula recommended by Pietersen and Huerta [21] :τ−( ) 0.09= C ⋅ P ⋅ xs(3.140)atm, n 19 w nThe water partial pressure expressed as a function of ambient temperature and relative humidity (RH) is givenby Mudan and Croce [22] as follows:w20( )⎡ ⎛ C⎢14.4114−⎜⎢⎣⎝T21⎟⎥atm ⎠⎥⎦= (3.141)P C RH e⎞⎤The radiation view factor can be calculated modeling the flame as a vertical cylinder and accounting for flametilt using the method provided by Mudan [23] as follows:Fcyl = Fv + Fh(3.142)2 2n n nThe vertical view factor can be calculated as follows:Fvn2( 1) 2 ( 1 sinθ, ) ⎞pf n A′ ( Y − )⎛2⎛ X cosθ⎞ ⎛ X + Y + − Y +pf , n⎡11 ⎤ ⎞⎜−⋅⎜⎟⋅ tan ⎢ ⎥+⎟⎜⎜Y X sinθ⎟⎝ −pf , n ⎠⎜ π AB ′ ′ ⎟ ⎣B′( Y + 1)⎦ ⎟⎜⎝ ⎠⎟⎜2 2cosθ⎛ ⎡XY −, 1( Y −1)sinθ⎤ ⎡pf npf , n sinθ1 pf , nY 1⎤⎞⎟⎛ ⎞ −−−= ⎜ ⋅ ⎜ tan ⎢⎥+ tan ⎢⎥ ⎟ − ⎟⎜⎜ ⎟2⎝ π C ′ ⎠ ⎜ ⎢ Y −1C′⎥ ⎢ C ′ ⎥ ⎟ ⎟⎜ ⎝ ⎣ ⎦ ⎣ ⎦⎠⎟⎜⎛ X cosθ⎞⎟⎜pf , n⎡−1 Y −1⎤⎟⋅ tan⎟⎢ ⎥⎜⎜π( Y − X sinθpf , n ) ⎟ Y + 1⎝⎠ ⎣ ⎦⎟⎝⎠(3.143)The horizontal view factor can be calculated as follows:

3-88 API RECOMMENDED PRACTICE 581

The amount of energy radiated by the pool fire (often referred to as surface emitted heat flux) is a fraction of

the total combustion power of the flame [18] . The fraction of the total combustion power that is radiated, β , is

often quoted in the range of 0.15 to 0.35. A conservative value of 0.35 can be chosen. Therefore:

Qrad

pool

n

C ⋅β⋅m

⋅HC ⋅π

⋅R

=

2 ⋅ ⋅ ⋅ + ⋅

2

14 b l pf , n

2

π Rpf , n

Lpf , n

π Rpf , n

(3.138)

The amount of the radiated energy that actually reaches a target at some location away from the pool fire is a

function of the atmospheric conditions as well as the radiation view factor between the pool and the target. The

received thermal flux can be calculated as follows:

Ith = τ ⋅Qrad ⋅ Fcyl

(3.139)

pool

pool

n atm,

n n n

The atmospheric transmissivity is an important factor since it determines how much of the thermal radiation is

absorbed and scattered by the atmosphere. The atmospheric transmissivity can be approximated using the

following formula recommended by Pietersen and Huerta [21] :

τ

−

( ) 0.09

= C ⋅ P ⋅ xs

(3.140)

atm, n 19 w n

The water partial pressure expressed as a function of ambient temperature and relative humidity (RH) is given

by Mudan and Croce [22] as follows:

w

20

( )

⎡ ⎛ C

⎢14.4114−⎜

⎢⎣

⎝T

21

⎟⎥

atm ⎠⎥⎦

= (3.141)

P C RH e

⎞⎤

The radiation view factor can be calculated modeling the flame as a vertical cylinder and accounting for flame

tilt using the method provided by Mudan [23] as follows:

Fcyl = Fv + Fh

(3.142)

2 2

n n n

The vertical view factor can be calculated as follows:

Fv

n

2

( 1) 2 ( 1 sinθ

, ) ⎞

pf n A′ ( Y − )

⎛

2

⎛ X cosθ

⎞ ⎛ X + Y + − Y +

pf , n

⎡

1

1 ⎤ ⎞

⎜

−

⋅⎜

⎟⋅ tan ⎢ ⎥+

⎟

⎜⎜Y X sinθ

⎟

⎝ −

pf , n ⎠

⎜ π AB ′ ′ ⎟ ⎣B′

( Y + 1)

⎦ ⎟

⎜

⎝ ⎠

⎟

⎜

2 2

cosθ

⎛ ⎡XY −

, 1

( Y −1)

sinθ

⎤ ⎡

pf n

pf , n sinθ

1 pf , n

Y 1⎤⎞

⎟

⎛ ⎞ −

−

−

= ⎜ ⋅ ⎜ tan ⎢

⎥+ tan ⎢

⎥ ⎟ − ⎟

⎜⎜ ⎟

2

⎝ π C ′ ⎠ ⎜ ⎢ Y −1

C′

⎥ ⎢ C ′ ⎥ ⎟ ⎟

⎜ ⎝ ⎣ ⎦ ⎣ ⎦⎠

⎟

⎜

⎛ X cosθ

⎞

⎟

⎜

pf , n

⎡

−1 Y −1⎤

⎟⋅ tan

⎟

⎢ ⎥

⎜⎜π

( Y − X sinθpf , n ) ⎟ Y + 1

⎝

⎠ ⎣ ⎦

⎟

⎝

⎠

(3.143)

The horizontal view factor can be calculated as follows:

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