Fire model for sizing high consequence areas associated with natural gas pipelines

Model for Sizing High Consequence Areas Associated with Natural Gas Pipelines
Prepare by: Prakash Thapa “A Model for Natural Gas Pipelines Sizing High Consequence Analysis” Page 1
Introduction
The subject report is developing by Prakash Thapa Memorial University St. Johns,
Newfoundland, Canada for the Research unite in Oil Gas and Safety Engineering for
Memorial University St. John’s Newfoundland Canada. The report was dated November 20th
2015 and the report’s recommended equation for determining potential impact radius (PIR) of
a natural gas pipeline rupture is included in 49 CFR 192.903. This PIR equation is given as:
 
5.0
2
69.0 Pdr  (1)
Where:
r = PIR, ft.;
P = pipeline pressure, psig; and
d = pipeline diameter, in.
The above equation is also included in ASME B31.8S and is given for any gas
as follows:
5.0
2
8
920,115









I
pd
FHCFer
s
fcdd

 (2)
where:
μ = combustion efficiency factor;
e = emissivity factor;
Fd = release rate decay factor;
Cd = discharge coefficient;
Hc = heat of combustion;
Ff = flow factor;
ʋs = speed of sound in gas;
I = heat flux;

p = pipeline pressure, psi; and
d = pipe diameter, in.
 



















12
1
1
2 k
k
f
k
kF (3)
where:
k = ratio of specific heats.
The velocity of sound in the gas is given by C-FT as:
5.0







m
TRk
s (4)
Where:
R = gas constant,
T = gas temperature, and
m = gas mole weight.
Unfortunately, ASME B31.8S does include all the units in the equations, but it
appears that English units are used. The recommended values of Hc, Fd, Ff, e,
and μ are not given.
If the recommended values for the PIR equation in the C-FT report and English
units are used, the calculated PIR, r, using the ASME B31.8S equation for the
example of 24 inch pipe at 1000 psi:
.4.520
145050008
241000764.0500,2162.033.02.035.0920,115
5.0
2
ftr
xx
xxxxxxxx
r








The above calculation is close to the calculated PIR of 524 ft. determined from
equation (1), therefore, the B31.8S equation (2) requires the use of English
units.

Bases for PIR Equation
A radiation heat intensity of 5000 BTU/ft.2
-hr. was used as I for the C-FT PIR
equation, based on the following stated criteria:
1. One percent change of mortality for a person with 30 seconds of exposure
to find a shelter.
2. Requires 1162 seconds (about 20 minutes) of exposure for wood shelter
to ignite with piloted (spark) ignition.
The C-FT PIR model assumes that a person would take five (5) seconds after a
fire to analyze the situation and run for 25 seconds at 2.5 m/s and find shelter.
The PIR equation used a gas flow rate decay release factor (Fd) of 0.33 even
though the report indicates the Fd may be as high as 0.5. This indicates that the
PIR is not based on the initial flow rate when the pipeline ruptured, but a flow
rate at some extended time after the rupture. This time period is not included in
the calculations and will vary with different pipelines.
The discharge coefficient in the PIR equation is for an orifice meter type of
discharge to indicate the restricted flow pattern downstream of a restricted
opening. With a severed pipeline, you don’t have a restricted hole. The PIR
equation should not have used an orifice meter equation and a discharge
coefficient of 0.62.
The PIR equation also contains the flow factor, Ff, defined earlier as equation
(3). For a value of k = 1.306 for methane, as given in the report, the value of Ff
is:
612.0
306.2
306.2
2
306.1 





fF
764.05848.0306.1  xFf
The speed of sound, ʋs, is calculated for methane at 15°C (59°F), the
temperature used for PIR, with equation (4) as follows:
5.0
16
2888310306.1







xx
s

.sec.1450.sec440 perftpermeterss 
The Crane Technical Paper No. 410 (Crane 410) indicates that ʋs can also be
determined for methane at 15°C (59°F) and 1000 psig as follows:
5.0
1.68 







 a
s
pk
(5)
Where:
pa = gas pressure, psia and
ρ = gas density at given pressure, lbs. per ft.3
.sec.1355
35.3
7.1014306.1
1.68
5.0
perft
x
s 






At 90°F and 1000 psig, the speed of sound in methane is:
.sec.1402
125.3
7.1014306.1
1.68
5.0
perft
x
s 






For methane at 59°F and 14.7 psia, the density is 0.04228 pcf and the speed of
sound using equation (5) is:
.1450
04228.0
7.14306.1
1.68
5.0
fps
x
s
s










Equation (4) used in the PIR is for low pressure gas without the effect of
pressure. Equation (5) appears to be more appropriate for high pressure gas.
A temperature of 59°F is low for a gas transmission line, because significant
compression heat is added at each compression station. A temperature range of
80°F to 140°F is more appropriate for gas pipelines depending on the proximity
to compression facilities and geographic location.
Natural gas is not pure methane, but is usually a mixture of 95 to 99% methane
with ethane and heavier fluids. The effective k is often taken as 1.4 and the

effective molecular weight is higher than 16. The mole weight of methane is
16.043, of ethane is 30.07, of propane is 44.097, and of butane is 58.123.
If a gas was composed of 92% methane, 5% ethane, 2% propane, and 1%
butane, the molecular weight would be about:
0.92 x 16.043 = 14.76
0.05 x 30.07 = 1.50
0.02 x 44.097 = 0.88
0.01 x 58.12 = 0.58
17.72
The C-FT PIR equation is based on a combustion efficiency factor, μ, of 0.35
and an emissivity factor, e, of 0.2.
The heat of combustion, Hc, is taken as 50,000 kJ/kg for methane, which is
21,500 BTU/lb.
The heat intensity model used for the C-FT PIR equation is indicated as being
the model given in the 1990 edition of API 521 and is stated as equation 2.1 in
the C-FT report:
2
4 xn
HQe
I ce


 (6)
where:
Qe = effective gas flow rate, lbs. per hour;
n = number of fire sources;
x = distance from fire, ft.;
I = 5000 BTU/ft.2
-hr.;
μ = 0.35;
e = 0.2;
n = 1; and
Hc = 21,500 BTU/lb.

For the values given, equation (6) can be reduced to:
5.0
120







I
Q
x m
(7)
For a 24 inch pipeline at 1000 psi the calculated PIR, r and x, is calculated with
equation (1) as follows:
  .52424100069.0
5.0
2
ftxxorr 
The effective gas flow rate that corresponds to a PIR (r or x) of 524 ft. using
equation (6) is:
c
e
He
Ixn
Q

 2
4
 (8)
For the C-FT recommended values and a PIR of 524 ft., equation (8) is
calculated as follows:
.sec.3184
..228,464,11
500,212.035.0
500052414 2
perlbsQ
hrperlbsQ
xx
xxxx
Q
e
e
e




Equation 2-4 in C-FT report indicated that the effective flow rate, Qe, from a
ruptured pipe is to be determined as follows:
mde QFQ 2 (9)
where:
2 = number of pipe ends of ruptured pipe;
Fd = pipe release decay factor, 0.33; and
Qm = peak release rate from the pipeline after the rupture occurs.
Therefore, in our example of d = 24 inches, p = 1000 psi, and r = 524 ft., the
peak release flow rate from each end of the 24 inch pipeline using equations (8)
and (9) is:

.sec.4824
33.02
3184
2
perlbs
xF
Q
Q
d
e
m 
When the improper use of Cd = 0.62 is removed from the C-FT PIR equation,
Qm is:
.sec.7780
62.0
.sec.4824
perlbs
perlbs
Qm 
Crane Technical Paper No. 410
CF-T indicated that the PIR equation is based on the following equation for
sonic or choked flow that is stated in Report No. GRI 0189 as being from Crane
410 as follows:
s
f
dm
F
p
d
CQ


4
2
 (10)
where:
Qm = flow rate in unknown units and
Cd = 0.62.
However, the equation (10) is not found in Crane 410.
On pages 2-15 of the 2006 edition of Crane 410, it is stated that their equation
2-24 may be used for discharge of compressible fluids through a nozzle to a
downstream pressure lower than indicated by the critical pressure ratio, rc, by
using values of:
Y = minimum per page A-21,
C = from page A-20,
Δp = p(1 – rc) per page A-21, and
ρu = weight density at upstream conditions.
Equation 2-24 in Crane 410 is:

5.0
1442





 

u
pg
YCAq

(11)
where:
q = volumetric gas flow rate at flowing conditions, ft.3
per sec.;
Y = net expansion factor;
C = flow coefficient;
A = pipe or orifice cross sectional area, ft.2
;
g = 32.2 ft. per sec.2
;
Δp = differential pressure, psi; and
ρu = upstream gas density, lbs. per ft.3
1. Step 1. Although a rupture pipe does not have an orifice or nozzle
restriction, an artificial value must be selected for this equation. The
maximum pipe orifice or nozzle opening given on page A-21 of Crane
410 is 85% of the pipe diameter for the critical pressure determination
and 75% for the expansion factor.
2. For an 85% opening (β = .85) and k = 1.31, rc = .633. For pμ = 1014.7
psia and rc = .633, the downstream pressure is 642.3 psia and Δp is 372.4
psi. The pressure ratio, Δp ÷ pa, is 0.367 (372.4 psi ÷ 1014.7 psia). For k
= 1.3, Δp ÷ pa = .367, β = .75, and Y = .70.
3. On page A-20, the value of C where β = .75 at a high Reynolds number is
C = 1.20. A value of C = Cd only applies to square edge orifices with
small openings. For a large opening the product of C x Y appears to
approach 1.0.
Equation 2-24 in Crane 410 (equation 11) can now be solved for methane at
1014.7 psia and 59°F where ρu = 3.35 lbs. per ft.3
as follows:
.sec.2679
35.3
4.3726.9273
4
2
2.17.0
3
5.0
2
perftq
x
xxq










The mass flow rate, Qm, at ρ = 3.35 lb. per ft.3
is 8976 lbs. per sec.
Page 3-3 in Crane 410 includes the following information on fluid specific
volume or density to use in compressible flow calculations.
1. When pressure drop is greater than 10% of inlet pressure, use density or
specific volume at inlet or outlet conditions.
2. When pressure drop is greater than 10%, but less than 40% of inlet
pressure, use the average of density or specific volume at inlet and outlet
conditions.
3. When pressure drop is greater than 40% of inlet pressure, use equation 3-
20.
When flow is sonic, the limiting values of Δp/p1 and Y shown on page A-22 for
the given resistance coefficients, k, are to be used in equation 3-20. For k = 1.3,
the maximum value for Y is 0.718 and Δp/p1 is 0.920. For k = 1.4, the maximum
value for Y is 0.710 and Δp/p1 is 0.926.
Equation 3-20 from Crane 410 is as follows:
5.0
12
5.0
12
5253.0
3600
1891





 





 

K
p
dY
K
p
dYQm

(12)
d
l
fK
12
 (13)
where:
Qm = mass flow rate, lbs. per sec.;
Y = expansion factor for flow into larger area;
Δp = p1 – p2 = pressure drop in pipe, psi;
ρ1 = gas density in the pipeline;
f = friction factor;
l = pipeline length or distance from exit, ft.; and
d = pipe diameter, in.

For a very high Reynolds number above 107
, the friction factor for 24 inch pipe
remains constant at about 0.015. For pipe exit conditions, K = 1.0.
For pipe exit conditions where K = 1.0, equation (12) becomes:
   
5.0
1
2
5.0
1
2
5253.0
3600
1891
 pdYp
dY
Qm  (14)
For a 24 inch pipeline at 1000 psig and 59°F where gas density is 3.35 lbs. per
ft.3
, equation (14) is solved as follows:
 
.sec.053,12
35.37.1014926.02471.05253.0
5.0
2
perlbsQ
xxxxQ
m
m


If the exit K = 1.0 is neglected,
txl s and (15)







d
t
fK s12
(16)
where:
t = time after rupture, sec.
For ʋs = 1356 ft. per sec., 24 inch pipe and f = 0.015, K = 10.17 t.
Equation 1-1 in Crane 410 can be rearranged as follows to solve volumetric and
mass flow rate at any point in the pipeline including exit from a ruptured
pipeline:
 qQandAq m  (17)
where:
q = volumetric flow rate, ft.3
per sec.;
A = pipe cross sectional area, ft.2
;
ʋ = average fluid velocity in pipe, ft. per sec.; and

ρ = average density in pipe, lbs. per ft.3
.
Crane 410 also illustrates the analysis on page 4-13 in example 4-20 as follows
using equation 3-2 on page 3-2.

 2
2
005454.0
36000509.0
d
x
d
Q s
s
m  (18)
where:
Qm = flow rate, lbs. per sec.;
ʋ = ʋs = fluid velocity at exit conditions, ft. per sec.; and
ρ = fluid density at exit conditions, lbs. per ft.3
.
Derivation of the C-FT Equation for Qm
Equation 9 from the C-FT report can be derived from equations (5) and (17) as
follows:
1. AQm
 (Equation 17)
2.
5.0
1.68 








pk
s (Equation 5)
3. At the end of the pipe, ʋ = ʋs, A = 0.005454 d2
, p = pe, and ρ = ρe.
4. Equation 5 can be rearranged as follows:
2
1.68







s
ee pk


5. Equation 18 can be solved as follows:
2
2 1.68
005454.0 






s
esm pkdQ



s
e
m
pkd
Q

2
3.25
 (19)
6. C-FT added a Ff [see equation (3)]to the flow equation to apparently, but
wrongly, account for the reduced pressure at the ruptured pipe outlet and:
k
pF
p f
e
1
 (20)
where:
pe = gas pressure at exit conditions, psia and
p1 = gas pressure before rupture, psia.
7. A Cd was arbitrarily added to the flow equation by C-FT and the equation
for pipeline exit mass flow rate wrongfully became:
s
fd
m
pFdC
Q

1
2
3.25
 (21)
Where:
Qm = mass exit flow rate, lbs. per sec.;
Cd = discharge coefficient, 0.62;
d = pipe diameter, inches;
k = ratio of specific heats, 1.307 for methane,
Ff = flow factor, see equation (3);
p1 = pipeline pressure before rupture, psia; and
ʋs = gas sonic velocity at exit conditions, ft. per sec.
For a 24 inch pipeline at 1000 psig and 59°F where gas density is 3.35 lbs. per
ft.3
and the exit sonic gas velocity is estimated at 1400 fps, the mass gas rate
from equations (20) and (21) would be:

psia
x
pe 592
31.1
7.1014764.0

.sec.5003
1400
7.1014764.02462.03.25 2
perlbs
xxxx
Qm 
If the Cd is properly eliminated from equation (21) for an open ended exit area
for the pipeline, Qm becomes 8070 lbs. per sec.
AGA Pipeline Rupture Propagation Studies
Pipeline rupture studies at Battelle et al have assumed that the gas
decompression process is isentropic and the decompressed pressure in the pipe
is:
1
2
1
1
1
1
2 



















k
k
s
c
d
k
k
k
pp


(22)
where:
pd = decompressed pressure, psia;
p1 = initial pressure in pipe;
k = ratio of specific heats;
ʋc = rupture propagation velocity, ft. per sec.; and
ʋs = gas sonic velocity at initial conditions, ft. per sec.
For k = 1.31 for methane, the equation (22) becomes:
45.8
1 1
134.0866.0









s
cd
p
p


For ʋc = 750 ft. per sec. and 1s = 1355 ft. per sec., the equation (22) becomes:
594.0
1355
750
134.0866.0
45.8
1







p
pd
When the rupture is complete and ʋc = 0, the ratio of pd/p1 becomes:
















1
2
1
2
1 k
k
kp
pd
(23)
3.0)866.0( 45.8
1

p
pd
For a rupture length of 50 feet for 24 inch pipe, the estimated time for the
cracking would be 0.067 seconds (50 ft. ÷ 750 ft. per sec.) and the amount of
released gas from 24 inch pipe would be:
3
2
..35.3.50
4
2
ftperlbsxftxQm


.sec067.0526 inpoundsQm 
.sec7850 perpoundsQm 
For a 24 inch pipeline at 1000 psig, 1014.7 psia and 59°F with methane (k =
1.31), the exit mass flow rate using equation (18) is:
1. From equation (23), pd/p1 = 0.3 and pd = 0.3 x 1014.7 psi = 304.4 psia.
2. The density of methane when isentropically decompressed from 1014.7
psi and 59°F to 304.4 psia is 1.37 lbs. per ft.3
3. The velocity of sound in isentropically decompressed methane at 304.4
psia is:
.sec.1162
37.1
4.30431.1
1.68
5.0
perft
x
s 






4. The exit mass methane flow rate using equation (18) is:
.sec.500037.1241162005454.0 2
perlbsxxxQm 
The American Petroleum Institute “Guidance Manual for Modeling
Hypothetical Accidental Releases to the Atmosphere”, Publication No. 4628
dated November 1996 contains the following guidance for modeling gas
pipeline releases.

1. The second law of thermodynamics requires:
Δs > 0
where:
s = entropy.
2. With an isentropic process Δs = 0. This is an idealization which can
never be attained in practice, but is a useful concept for modeling gas
decompression.
3. An isenthalpic process is inappropriate for a situation in which a
substantial change in kinetic energy occurs to a releasing fluid, typical of
a gas or flashing liquid release from high pressure.
4. For an ideal gas,
TRnpV  (24)
where:
p = gas pressure, psia;
V = gas volume;
n = number of moles;
R = gas constant; and
T = gas temperature, °k.
5. For isentropic conditions,





 







k
k
p
p
T
T
1
1
2
1
2
(25)
where:
T1 = upstream gas temperature, °k;

T2 = downstream gas temperature, °k;
p1 = upstream gas pressure, psia;
p2 = downstream gas pressure, psia.
6. For isentropic conditions





















1
1
2
1
2 k
k
c
kp
p
r (26)
where:
rc = critical pressure ratio
7. The initial maximum flow rate during a pipeline failure is:
5.0
1
1
112
1
2




























k
k
dm
k
pkACQ  (27)
5.0
1
1
1
12
1
2

































k
k
dm
kTR
M
kpACQ (28)
where:
Qm = initial flow rate through an orifice opening in the pipe;
Cd = discharge coefficient;
A2 = area of discharge opening;
p1 = upstream pressure, psia; and
ρ1 = upstream density, lbs. per ft.3
The critical pressure ratio, rc, in equation (26) agrees with the equation for rc
given in equation (8.125) of Victor L. Streeter’s Handbook of Fluid Dynamics,
First Edition, 1961, McGraw-Hill.

API Publication No 4628 does not contain all the units and complete equations
for calculation purposes. However, the equation can be derived from other
equations in this report in the following steps.
1. Equation (17) is:
AQm 
2. With a ruptured pipe the mass flow rate is based on conditions at the end
of the pipe where:
eesm AQ  , (29)
where:
Qm = gas mass flow rate, lbs. per sec.;
A = pipe cross sectional area, ft.2
;
ʋs,e = gas velocity of sound at exit conditions, ft. per sec.; and
ρe = density of gas at exit conditions, lbs. per ft.3
.
3. The gas velocity of sound at pipeline exit conditions from equation (5) is:
5.0
, 1.68 






e
e
es
pk


4. The exit pressure is:
1prp ce  (30)
5. The critical pressure ratio according to API Publication 4628 is:















1
1 1
2 k
k
e
c
kp
p
r (31)
6. The exit density is:
k
ce r
1
1  (32)

7. Steps 2 – 6 can be combined as:
a.  
5.0
5.0
1.681.68 ee
e
e
em pkA
pk
AQ 

 






b.
5.0
11
11
5.0
1
1
1 1.681.68 











k
cc
k
cm rpkArprkAQ  (33)
c.




















1
1
111
1
2 k
k
k
k
c
k
c
k
rr
d.
5.0
1
1
11
1
2
1.68




























k
k
m
k
pkAQ  (34)
8. The pipe cross sectional area is:
2
2
005454.0
1444
d
x
d
A 

9. Equation (34) can be changed to:
5.0
1
1
11
2
1
2
3714.0




























k
k
m
k
pkdQ  (35)
Equation (35) is the full equation for calculation of mass exit flow rate from a
ruptured pipeline based on API Publication 4628.
For a 24 inch pipeline at 1000 psig and 59°F where methane gas density is 3.35
and k = 1.31, equation (35) based on API 4628 is solved as follows:
5.0
45.7
2
31.2
2
7.101435.331.1243714.0














 xxxQm
.sec.8288 perlbsQm 

Gas Flow within a Ruptured Pipeline
Calculation of gas flow within a ruptured pipeline using equation (12) is
illustrated with the following example:
1. d = 24 inch;
2. p1 = 1000 psig, 1014.7 psia;
3. T1 = 59°F;
4. ρ = 3.35 lbs. per ft.3
; and
5. Methane where k = 1.31.
The calculation steps are:
1. Use equation (5) to calculate ʋs at pipeline conditions before the rupture
as follows:
5.0
35.3
7.101431.1
1.68 






x
S
.sec.1356 perfts 
2. After 1 sec., l = 1356 ft.
3. Use equation (16) to determine flow resistance K as follows.
2.11
24
135612015.0
1 
xx
K
4. Use equation (31) to calculate the exit pressure conditions at critical
flow:
544.0
131.1
2 1
1








k
k
d
p
p
psiaxpd 5527.1014544.0 
5. The differential pressure Δp, in the ruptured pipe is:

psipp d 7.4625527.10141 
6. Equation (12) can be solved as follows:
5.0
2
2.11
35.37.462
3600
241891







xx
Qm
.sec.3559 perlbsQm 
Since Qm within the pipeline is less than the exit flow rate from the pipeline, the
density and pressure of the gas at the exit point will diminish with time. With
isentropic conditions:
k
k p
pV

 is constant and
k
k
s
s
p
p 2
1
1
2
2
1










. (36)
Comparison of Initial Ruptured Pipeline Exit Flow Equation
The initial ruptured pipeline exit flow rate equations without an orifice
discharge factor can be compared for the example of a 24 inch pipeline at 59°F
and 1000 psig where the initial gas density is 3.38 lbs. per ft.3
1. C-FT PIR equation, Qm = 7,780 lbs. per sec.
2. Equation 2-24 in Crane 410 = 8,976 lbs. per sec.
3. Equation 3-20 in Crane 410 = 12,053 lbs. per sec.
4. C-FER Technologies Equation = 8,070 lbs. per sec.
5. Equation (18) with rc = 0.3 = 5,000 lbs per sec.
6. API 4628 equation = 8,288 lbs. per sec.
The API 4628 equation (35) without the Cd is recommended for use in ruptured
gas pipeline modeling. For a 24 inch gas pipeline at 1000 psig and 59°F where
the methane gas density is 3.35 lbs. per ft.3
, Qm = 8,288 lbs. per sec.
A ruptured pipe release decay factor, Fd, similar to the one used by C-FT in
equation (9) can be used to calculate the effective release rate versus time.
Figure 2.3 in the C-FT report contains release decay factors for an 8-inch
pipeline at 580 psig and a 36-inch pipeline at 870 psig. As shown on Figure 2.3
of the C-FT report, a decay factor of 0.33 was used for the PIR equation.
The C-FT report states “it follows from Figure 2-3 that a rate decay factor of 0.2
to 0.5 will likely yield a representative steady state approximation to the release

rate for typical pipelines”. However, only a value of 0.33 is used for all
pipelines and all times after the rupture occurs.
For a 24 inch pipeline using C-FT report Figure 2.3, the following decay factors
appear to be appropriate.
Time, sec. Fd
0 1.00
1 0.80
2 0.65
3 0.55
4 0.50
5 0.45
10 0.35
20 0.28
30 0.24
60 0.20
API RP 521
The May 2008 edition of API Standard 521, “Guide for Pressure-Relieving and
Depressuring Systems”, in section 6.4.2.3.3 indicates that “The following
equation by Hajek and Ludwig may be used to determine the minimum distance
from a flare to an object whose exposure to thermal radiation must be limited.”
5.0
4 








I
HFF
x rt

(37)
where:
x = distance to object from center of fire, ft.;
Ft = fraction of heat intensity transmitted;
Fr = fraction of heat radiated;
H = heat release, BTU per hr.; and
I = allowable heat radiation, BTU per hr. ft.2

cm HQH  (38)
where:
Qm = mass flow rate, lbs. per hr. and
Hc = heating value of combusted material, BTU per lb.
16
1
16
1
100100
79.0 












xR
F
H
t (39)
where:
RH = relative humidity, percent.
If RH = 50% and x = 500 ft.,
75.0
500
100
50
100
79.0
16
1
16
1












dF
If RH = 50% and x = 1000 ft., Ft is 0.714.
The fraction of heat radiated in calculation examples for flares, Fr, is taken as
0.3 and Hc = 21,5000 BTU per lb. for methane. The C-FT model includes a
combustion efficiency of 0.35. The API Standard 521 model does not include
such a factor. For methane, equation (37) can be rewritten as:
5.0
4
500,213.075.0







I
Qmxxx
x

(40)
5.0
385







I
Q
x m
(41)
where:
Qm = sustained flow rate, lbs. per hr. and
I = heat radiation intensity, BTU per ft.2
hr.

Equation (41) calculates hazardous distances that are 1.78 times the value of the
C-FT equation (7). API RP 521 contains the following recommended limits on
allowable heat radiation, I:
1. 5000 BTU per hr.-ft.2
in areas where workers are not likely to be
performing duties and where shelter from radiant heat is available.
in areas where exposure is limited to a few seconds
for escape only.
in areas where emergency actions up to one minute
may be required without shielding, but with appropriate clothing.
in areas where emergency actions lasting several
minutes may be required by personnel without shielding, but with
appropriate clothing.
in areas where personnel with appropriate clothing
may be continuously exposed.
Solar radiation generally ranges from 250 to 330 BTU per hr.-ft.2
. Correction
for solar radiation is indicated as being proper. Corrections for solar radiation
are left to individual companies.
In industrial locations around flares, workers normally wear fire resistant safety
clothing with long sleeves and hard hats to provide protection for 90+% of the
body from heat radiation.
However, in non-industrial areas people are not likely to be wearing flame
retardant protective clothing and may only have about 60% of the body covered
with non fire retardant clothing. It appears at a maximum allowable heat
radiation intensity of 500 to 1500 BTU per hr.-ft.2
would be appropriate for
protection of the public in areas near a pipeline rupture. A heat radiation
intensity of 5000 BTU per hr-ft.2
, used in the C-FT report, is clearly too high for
public exposure to a fire.
Frank P. Lees’ Book on Loss Prevention
Loss Prevention in the Process Industries by Frank P. Lees contains
considerable information on the effects of fire exposure. Chapter 16 on fire is
318 pages in length. The effects of fire exposure depend on the radiant heat
intensity and the exposure time.

The effects of fire exposure depend on exposure time and heat radiation
intensity. A thermal load is used to define the effects of time and heat intensity.
Heat exposure considerations create a thermal load as follows:
000,10
333.1
It
L  (42)
where:
L = thermal load;
t = exposure time, sec; and
I = thermal radiation intensity, watts per meter2
.
The effects of various thermal loads from work by Hymes are given as follows:
L Effects
1,200 Second degree burns
1,060 1% mortality
2,300 50% mortality
2,600 Third degree burn
1,100- 4,000 Piloted ignition of clothing
3,000-10,000 Unpiloted ignition of clothing
The effects of various thermal loads from work by Lee are as follows:
L Effects
1,000 2.5% mortality
1,600 20% mortality
2,000 31% mortality
2,500 45% mortality
3,000 59% mortality
4,500 100% mortality
For an initial exposure time of 30 seconds before finding shelter, as assumed in
the C-FT report on the PIR, the corresponding values of I for the above effects
given by Lee are:
Thermal Intensity for 30 Second

Exposure Time
L W per m2
BTU per hr.-ft.2
1,000 14,230 4,500
1,600 20,263 6,415
2,000 23,965 7,585
2,500 28,344 8,970
3,000 32,509 10,290
4,500 44,098 13,960
Other heat intensity considerations are 10-12 kW per m2
(3,165 to 3,800 BTU
per hr.-ft.2
) is heat intensity for vegetation to ignite (from Mechlenburg). A heat
intensity of 6 kW per m2
(1900 BTU per hr. ft.2
) is the tolerable level for
escaping personnel in an industrial location.
Lee’s book on loss prevention refers to work by Hymes on the ignition of
clothing. Hymes found that clothing ignition can be predicted as follows:
ccc DIt 
2
(43)
where:
tc = clothing exposure time, sec.;
Ic = thermal radiation intensity, kW per m2
; and
Dc = clothing ignition load, (sec.-kW per m2
)2
.
The clothing ignition load, Dc, is normally 25,000 to 45,000 [sec. (kW per m2
)2
].
For a midpoint ignition load of Dc = 35,000, the thermal radiation intensity vs.
time is:
Ic
Time, sec. kW per m2
BTU per hr. ft.2
*
1 187 59,200
5 84 26,580
10 59 18,670
20 42 13,290
50 26.5 8,385
100 18.7 5,920
200 13.2 4,100
500 8.4 2,660

* 0.00316 BTU per ft.2
– hr. = kW per m2
Lee’s book on loss prevention indicates that ignition of clothing has the
following two effects.
1. Ignition of clothing distracts the wearer. He may stop running and try to
douse the flames, with effects not only on the speed of escape, but also on
the orientation of the body.
2. The other effect is the injury from burning clothing.
For mortality studies, the amount of skin exposed to heat radiation is typically
taken to be 20% or less. For 20% exposure area and burn area, the mortality
rates for various age groups are:
Age Mortality Rate, %
0-44 0 to <10% mortality
44-59 10% average mortality
85+ 90% average mortality
In an industrial environment, workers probably wear protective fire retardant
clothing with heavy boots, gloves and hard hat. The exposure area is probably
less than 5%. When running, the hard hat is probably lost and the body
exposure increases to 10%. Without gloves, the exposure would be 15%.
However, on a warm day, the public may have a body exposure of 40%. With
40% exposure area and burn area, the mortality rates become:
0-4 0 to <10% mortality

If the clothing ignites, the burn area and mortality rates increase. If clothing
ignites and the burn area increases from 40% to 60% burn area, the mortality
rates become:
Normally, persons are seldom admitted to a hospital for treatment for first
degree burns. Admittance for second degree burns depends on where the burns
occur and percent of body affected. The thermal load for a second degree burn
is 1200 s(W/m2
)1.333
÷ 10,000 and for 1% mortality is 1060 s(W/m2
)1.333
÷ 10,000
according to studies by Hymes.
The effects of age groups can also be evaluated by studying the effects of
percent burn area versus mortality rate. For a 20-49 age group that represents
workers at an industrial location, the mortality rates versus percent burn area
are:
Mortality Rate
% Burn Area 20 Years 49 Years Average
10 0 < 10 < 10
20 < 10 10 < 10
30 10 20 15
40 20 40 30
50 30 60 45
60 50 80 65
70 70 90 80
80 80 100 90
85 90 100 95
90 100 100 100
For a 60 -79 age group, the mortality rates versus percent burn area are:
Mortality Rate
% Burn Area 60 Years 79 Years Average

10 10 40 25
20 30 80 55
30 50 100 75
40 80 100 90
50 90 100 95
60 100 100 100
Although I have not seen studies on the mortality rates of older people with less
amounts of body coverage with clothing, it appears that the mortality rate for
60-79 years with 30% to 40% body exposure (60% to 70% body coverage)
would be expected to be over 50% mortality at the heat load that causes second
degree burns or L = 1200 sec (W/m2
)1.333
÷ 10,000. The heat radiation levels
versus exposure time that corresponds to a thermal load of L = 1200 sec
(W/m2
)1.333
÷ 10,000 are:
Heat Radiation Intensity, I
Time, sec. W per m2
BTU per hr.-ft.2
30 15,905 5,035
60 9,460 2,995
120 5,625 1,780
180 4,150 1,315
300 2,828 895
480 1,980 625
1,200 1,000 315
As shown above the mortality rate with 30 seconds of exposure at about 5,000
BTU per hr.-ft.2
, the heat radiation intensity used in the C-FT study for 1%
mortality in an industrial environment would be expected to be above a 50%
mortality for persons between 60 and 80 years of age.
Fireball Models
The PIR model does not include the effects of a fireball caused by a delayed
ignition of a ruptured pipeline. Prugh gives the following relationships for a
propane fireball in Lees’ loss prevention book.
1. x for 1% mortality is 5.0 W 0.46
(44)
(45)
(46)
4. x for second degree burns is 5.3 W 0.46
(47)

where:
x = distance from the fire, ft. and
W = amount of fuel in fireball, lbs.
Distances for the above mortality rates for a 50,000 pound fireball are:
.725)000,50(5%1
46.0
ftmortalityforx 
.523)000,50(6.3%50
46.0
.363)000,50(5.2%99
46.0
The models of A.F. Roberts developed in 1981/1982 predict the following
fireball parameters:
333.0
5.4 Mtd  (48)
where:
td = fireball duration, sec. and
M = mass of fuel (LPG), metric tonne.
Equation (48) can be modified as follows to calculate td in terms of lbs.
  333.0
347.0 Mtd  (49)
where:
M = mass of fuel, lbs.
For a 50,000 pound 22.7 tonne, fireball, the duration is:
.sec7.12)7.22(5.4
333.0
dt
The distances from the fire for 1% and 50% mortality from the Roberts model
are:
1. x for 1% mortality = 30 t0.366
M0.306
(50)

2. x for 50% mortality = 22 t0.366
M0.307
(51)
where:
x = distance from the fireball, meters;
t = exposure time, sec.;
M = mass of fuel (LPG), tonne.
For M = 50,000 lbs. (22.7 tonne) and t = td = 12.7 seconds, values of x are:
1. x for 1% mortality = 30 (12.7)0.366
(22.7)0.306
= 198 m = 650 ft.
2. x for 50% mortality = 22 (12.7)0.366
(22.7)0.306
= 145 m = 475 ft.
The above model of Roberts applies to 10<M<3000 tonne and 10<t<300
seconds.
Another model by Prugh for a propane fireball is:
x for 50% mortality = 38 M 0.46
(52)
where:
x = distance from fireball, m and
M = mass of fuel, tons.
For 25 tons of fuel, x for 50% mortality is:
x for 50% mortality = 38 (25)0.46
= 167 m (548 ft.)
Hardee and Lees developed the following model for a propane fireball as
follows:
D = 5.55 M 0.333
(53)
where:
D = fireball diameter, m.
M = propane mass, kg.

In English units, equation (53) becomes:
333.0
14 MD 
where:
D = fireball diameter, ft. and
M = propane mass, lbs.
Hardee, Lees and Benedick later in (1978) developed the following model for
LNG (methane) fireballs.
R = 3.12 M 0.333
(54)
D = 6.24 M 0.333
(55)
td = 1.11 M0.167
(56)
where:
R = radius of fireball, m;
D = fireball diameter, m;
M = fuel mass, kg; and
td = fireball duration, sec.
Roberts developed the following model for hydrocarbon fireballs:
D = 5.8 M 0.333
(57)
The models of Roberts [equations (48) and (51)] can be compared to the API
521 model indicated as equation (41) in this report in the following steps:
1. LPG fuel released for fireball = 50,000 lbs, 25 tons, 22.7 tonnes.
2. Distance criterion is for 50% mortality.
3. Fireball duration [equation (48)], td, is = 4.5 M 0.333
= 12.7 sec.

4. For td = 12.7 sec. and M = 50,000, the average fireball fuel consumption
rate, Qm, is 3937 lbs. per sec. = 14,170, 000 lbs per hr.
5. For 50% mortality, the required thermal load, L [equation (40)], is 2300
to 2600, according to Hymes and Lee.
6. For L = 2300, equation (42) can be used to calculate the required
radiation intensity, I, for t = td = 12.7 sec.
22
333.1
..700,15510,49
2300
000,10
7.12
fthrperBTUmperWI
I
L


7. For I = 15,700 BTU per hr.-ft.2
using equation (41), the hazardous
distance is:
.589
700,15
000,170,14385
5.0
ft
x
x 






8. For L = 2600 and t = 12.7 sec., equation (42) is used to calculate I as
54,280 W per m2
= 17,185 BTU per hr.-ft.2
.
9. For I = 17,185 BTU per hr.-ft.2
using equation (41), the hazardous
distance is:
.563
185,17
000,170,14385
5.0
ft
x
x 






10. Equation (45) can be used to calculate the distance from the fire where
the radiation intensity will cause a 50% mortality rate as follows:
  .522000,506.36.3
46.046.0
ftWx 
11. Equation (51) can also be used to calculate the distance from the fire
where the radiation intensity and duration time will cause a 50%
mortality rate as follows:
.475)7.22()7.12(22
306.0366.0
ftx 

12. Two fireball models and two thermal loads and the calculated hazardous
distances were within 24% of each other.
Recommended Models for Pipeline Ruptures
The potential hazards of a pipeline rupture should be based on the following
criteria:
1. Fireball from delayed ignition.
2. Heat intensity that would impede escape from the area of the fire.
3. Heat intensity that would cause clothing to ignite.
4. Heat intensity that causes buildings to ignite.
5. Heat intensity for 1% mortality.
6. Heat intensity for 50% chance of mortality.
7. Heat intensity for 100% chance of mortality.
8. Heat intensity for second degree burns.
The hazards of initial high heat intensity for short periods need to be compared
to lesser sustained heat for long periods.
The models should also cover the effects of age groups and clothing protection
of the public exposed to gas pipeline ruptures.
Use of Fireball Model for Ruptured Pipelines
The fireball model should consider the mass of gas lost during the initial rupture
and the amount of gas initially released from each end of the pipeline until the
gas is ignited. A reasonable estimate is needed for delayed ignition of the
escaping gas.
C-FT dismissed the hazard of a flash fire or fireball with the following rationale:
1. The possibility of a significant flash fire resulting from delayed remote
ignition is extremely low due to the buoyant nature of the vapor, which
generally precludes the formation of a persistent flammable vapor cloud.
2. In the event of line rupture, a mushroom-shaped gas cloud will form and
then grow in size and rise due to discharge momentum and buoyancy.
3. If ignition occurs before the initial fireball disperses, the flammable vapor
will burn as a rising and expanding fireball before it decays into a

sustained jet or trench fire.
4. If ignition is slightly delayed, only a jet or trench fire will develop.
5. The added effect on people and property of an initial transient fireball can
be accounted for by overestimating the intensity of the sustained jet or
trench fire that remains following the dissipation of the fireball.
6. A trench fire is essentially a jet fire in which the discharging gas jet
impinges upon an opposing jet and/or the side of the crater formed in the
ground.
7. Impingement dissipates some of the momentum in the escaping gas and
directs the jet upward, thereby producing a fire with a horizontal profile
that is generally wider, shorter and more vertical in orientation, than
would be the case for a directed and unobstructed jet.
8. The total ground area affected can, therefore, be greater for a trench fire
than an unobstructed jet fire, because more of the heat-radiating flame
surface will typically be concentrated near the ground.
9. An estimate of the ground area affected by a credible worst-case failure
event can, therefore, be obtained from a model that characterizes the heat
intensity associated with a rupture failure of the pipe, where the escaping
gas is assumed to feed a sustained trench fire that ignites very soon after
line failure.
10. Because the size of the fire will depend on the rate at which fuel is fed to
the fire, it follows that the fire intensity and the corresponding size of the
affected area will depend on the effective rate of the gas release.
11. The release rate can be shown to depend on the pressure differential and
the hole size.
12. For guillotine-type failures where the effective hole size is equal to the
line diameter, the governing parameters are, therefore, the line diameter
and the pressure at the time of failure.
13. Given the wide range of actual pipeline sizes and operating pressures, a
meaningful fire hazard model should explicitly acknowledge the impact of
these parameters on the area affected.
Analyses of the above comments in the C-FT report are:

1. The buoyant nature of the natural gas vapor should not be a factor unless
there is vertical momentum of the gas such as with a vertical flare.
However, with a trench fire and two opposing jets in a trench, there should
be little initial vertical momentum to the escaping gas. However, there will
be significant turbulence and mixing with the air near the ground level.
2. A cloud of some shape, not necessarily “mushroom-shaped” will form and
grow in size as indicated by the C-FT.
3. The C-FT report indicates that a fireball can ignite before the gas disperses,
and will rise and expand as a fireball.
4. It is assumed in the C-FT report that ignition will only be slightly delayed
after the rupture and only a trench or jet fire will develop.
5. The C-FT model did not over estimate the intensity of the fire to account for
an initial transient fireball.
6. Although a trench fire is discussed in the C-FT report, only an unlikely
vertical jet fire was modeled.
7. The C-FT model did not include the effect of a “horizontal profile”
of the fire in their PIR model.
8. The C-FT fire model did not include the effects of the total ground area
affected by a trench fire being greater than for an unobstructed jet fire. The
fire was model as an unobstructed jet fire.
Recommended Fireball Model
The recommended equations or models to be used for fireball analyses of
delayed ignitions of ruptured natural gas pipeline are:
Step 1 Initial pipeline release in ruptured area:
1lAM  (58)
1444
2
d
A

 (59)
dl 5.2 (60)

1
3
0136.0 dM  (61)
Where:
M = mass of gas initially released, lbs.;
A = cross sectional area of pie, ft.2
;
ρ1 = initial gas density, lbs. per ft.3
; and
d = pipe diameter, inches.
Step 2 Initial gas exit rate from each end of the rupture pipe based on on
API Publication 4628 [equation (35)] as follows:
5.0
1
1
11
2
1
2
3714.0




























k
k
m
k
pkdQ 
Step 3 Gas exit rate from each end of the ruptured pipe based on equation (35)
and exit rate reduction factors from Figure 2.3 in C-FT report.
Step 4 Calculate the gas exit rate for various time increments until the delayed
ignition time using the methods given in Step 3.
Step 5 Sum up the gas exit quantities determined in Steps 1 and 4 up to the
delayed ignition time.
Step 6 Calculate the fireball duration time using equation (49) as follows:
333.0
)(347.0 Mtd 
Where:
td = fireball duration time, sec. and
M = gas mass in fireball, lbs.
Step 7 Calculate the hazardous distances for 1%, 50% and 99% mortality using
equations (44), (45) and (46) respectively as follows:

a. x for 1% mortality = 5.0 W0.46
b. x for 50% mortality = 3.6 W 0.46
c. x for 99% mortality = 2.5 W 0.46
Step 8 Calculate the diameter of the fireball using equation (53) in
English units:
 
333.0
14 MD 
For a 24 inch pipeline at 1000 psi and 59°F and a delayed ignition of 30 to 120
seconds, the fireball analyses are as follows:
Step 1 .63135.3240136.0 3
lbsxxM 
Step 2 3424.0)866.0(
1
2 45.71
1

















k
k
k
and
 
.sec.8353
3424.07.101435.331.1243714.0
5.0
2
perlbsQ
xxxxQ
m
m


Step 3 For two ends, initial Qm = 16,706 lbs. per sec.
a. At t = 0 sec., Fd = 1.0 and Qm = 16,706 lbs. per sec.
b. At t = 1 sec., Fd = 0.8 and Qm = 13,365 lbs. per sec.
c. At t = 2 sec., Fd = 0.65 and Qm = 10,859 lbs. per sec.
d. At t = 3 sec., Fd = 0.55 and Qm = 9,188 lbs. per sec.
e. At t = 4 sec., Fd = 0.50 and Qm = 8,353 lbs. per sec.
f. At t = 5 sec., Fd = 0.45 and Qm = 7,518 lbs. per sec.
g. At t = 10 sec., Fd = 0.35 and Qm = 5,847 lbs. per sec.
h. At t = 20 sec., Fd = 0.28 and Qm = 4,678 lbs. per sec.
i. At t = 30 sec., Fd = 0.24 and Qm = 4,009 lbs. per sec.
j. At t = 60 sec., Fd = 0.20 and Qm = 3,341 lbs. per sec.
Steps 4 & 5.
Accumulated Time, sec. W, lbs. Σ W, lbs.
0 631 631
1 15,036 15,661
2 12,112 27,779
3 10,024 37,803
4 8,771 46,574
5 7,936 54,510

10 33,413 87,923
20 52,625 140,548
30 43,435 183,983
60 110,250 294,233
120 200,000 494,233
Step 6 For a 30 second delayed ignition,
  ondstd sec7.19983,183347.0
333.0

Step 7
a. For a 1% mortality, x = 5.0 (183,983)0.46
= 1,321 ft.
b. For a 50% mortality, x = 3.6 (183,983)0.46
= 951 ft.
c. For a 99% mortality, x = 2.5 (183,983)0.46
= 660 ft.
Step 8
.793)983,183(14
333.0
ftD 
For a 60 second delayed ignition W = 294,233 lbs. and steps 6, 7 and 8 are:
Step 6 For a 60 second delayed ignition,
  ondstd sec0.23233,294347.0
333.0

Step 7
= 1,638 ft.
= 1,180 ft.
= 819 ft.
Step 8
.927)233,294(14
333.0
ftD 
For a 120 second delayed ignition, W = 494,000 lbs. and steps 6, 7 and 8 are:
Step 6

  ondstd sec3.27000,494347.0
333.0

Step 7
= 2,080 ft.
= 1,498 ft.
= 1,040 ft.
Step 8
.102,1)000,494(14
333.0
ftD 

Fire model for sizing high consequence areas associated with natural gas pipelines

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Fire model for sizing high consequence areas associated with natural gas pipelines