1

_____________•

OCS Study

MMS 2002 - 033

Pipeline Oil Spill Volume

Estimator

P

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c

k

e

t

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POCKET GUIDE 2

DISCLAIMER

This Pipeline Oil Spill Volume Estimator known as the "Pocket

Guide" was prepared under contract between the Minerals

Management Service (MMS) and SINTEF Applied Chemistry.

Publication of this Pocket Guide does not necessarily imply

that the contents reflect the views and policies of MMS. The

discharge volumes derived from this Pocket Guide reflect an

estimate and the MMS is not responsible for the accuracy of

those estimates. This is merely a tool to be used for

estimating oil spill releases from pipeline ruptures. Further,

this Pocket Guide does not constitute rulemaking and it must

not be used for regulatory compliance.

TABLE OF CONTENTS

Introduction............................................................................. 3

1. Initial estimate of oil release............................................... 5

2. Advanced Method ............................................................ 15

Variable Description and Unit Conversion............................ 27

LIST OF TABLES

TABLE 1.1: VOLUME ESTIMATE OF PIPELINE ....................... 7

TABLE 1.2: AMBIENT PRESSURE, PAMB.............................. 10

TABLE 1.3: MAXIMUM RELEASED VOLUME FRACTION, FREL . 11

TABLE 1.4: GOR REDUCTION FACTORS, FGOR .................. 11
POCKET GUIDE 3

INTRODUCTION

The Pipeline Oil Spill Volume Estimator includes two methods

that can be used to calculate the amount of oil that will

escape from a leaking pipeline. The Pocket Guide and an

associated computer model were developed by SINTEF and

Well Flow Dynamics under a contract funded by the Minerals

Management Service. 

The “Initial” volume calculation method is intended to be a first

best guess on the amount of oil that has been released so

that spill responders can mobilize adequate equipment to the

spill site. It is to be used when data on the event are limited

and quick decisions on response strategy are mandatory to

minimize spill impacts.

The “Advanced” method allows for the refinement of the spill

volume estimate as the spill response proceeds. More

variables are required, but the refined estimate will provide a

more realistic volume for assisting in developing response

strategies and revising incident action plans.

Both the “Initial” and “Advanced” methods assume:

• A single horizontal pipeline segment;

• A full pipeline break or rupture.

These methods are therefore not applicable to pinhole leaks

or other small pipeline fractures.

The computer model removes the limitations found in the

“Initial” and “Advanced” methods by allowing the user to input

pipeline leak hole size, fluid properties, and variable water

depths. The users can also create a pipeline network that

may contain many pipeline segments. Model output includes

reports that show pipeline leakage rates versus time and

cumulative leak rates with reports being in both tabular and

graphic formats. 
POCKET GUIDE 4

Additionally, the model includes a near field module that

produces an estimate of the partitioning of released oil

between the water and the surface, as well as an estimate of

the distribution of oil thickness in the surface slick.

The computer model can be downloaded from the MMS

website at http://www.mms.gov. The website also contains a

User’s Manual on model operations.

The figure below defines the simplified problem graphically. 

Lpipe

pipe

Original flow direction

PpipeTpipe

PambTamb

Lpipe

IDpipe Ppipe, Tpipe
POCKET GUIDE 5

1. INITIAL ESTIMATE OF OIL RELEASE

1.1 Introduction

This initial approach will give a quick estimate of the total oil

released if a pipeline rupture occurs. 

1.2 Required data

This calculation procedure requires the following data:

• Pipeline internal diameter, IDpipe [in] 

• Pipeline length, Lpipe [ft]

• Pipeline pressure, Ppipe [psi]

• Gas-oil-ratio, GOR [scf/stb]

• Water depth at rupture location, d [ft]

• Pipeline flow rate, Q [stb/d]

• Time before shut-in, t [min]

For unit conversion, please refer to Page 27.

1.3 Calculation procedure

1.3.1 Simple equation

The total released volume of oil, Vrel, is found from

Equation 1.1

Vrel = 0.1781 • Vpipe • frel • fGOR + Vpre-shut Eq. 1.1

where,

Vrel - Total volume released [bbls ] 

Vpipe - Volume of pipeline [ft3], see section 1.3.3, Page 6

frel - Maximum release volume fraction [-] 

Dimensionless, see section 1.3.4 , Page 8

fGOR - GOR reduction factor [-], see section 1.3.5, Page 11

Vpre-shut - Volume of oil released prior to pipe shut-in, [bbls]
POCKET GUIDE 6

1.3.2 Volume of oil released prior to pipe shut-in, Vpre-shut

The oil volume released before shut-in can be calculated by

using Equation 1.2. 

Vpre-shut = 1440

Q ⋅ t [bbls] Eq. 1.2

where,

Q - Pipeline flow rate [stb/d]

t - Time before shut-in [min]

1.3.3 Pipeline volume

The pipeline volume can be calculated by using Equation 1.3.

Alternatively Table 1.1 can be used. Table 1.1 is meant to be

used when a calculator is not available.

Length 3.14

24

Internal Diameter of pipe Volume of pipe

2

⋅ ⋅ 





 





 =

Vpipe = ⋅ ⋅π 















pipe

pipe L

ID 2

24 Eq. 1.3

where, 

Vpipe - volume of pipeline [ft3]

IDpipe - internal diameter of pipeline [in]

Lpipe - pipeline length [ft]
POCKET GUIDE 7

Table 1.1: Volume estimate of pipeline

Internal

Diameter 

Volume per

1000 ft 

IDpipe [in] [ft3]

2 21.8

4 87.3

6 196

8 349

10 545

12 785

14 1069

16 1396

20 2180

22 2640

24 3142

28 3403

Example:

A 10,000 ft 12" ID pipeline has ruptured.

Find the volume of the pipeline.

Solution alternative 1:

A calculator is not available ⇒ Table 1.1 is used.

Look in Table 1.1 and find

the internal diameter of your

pipe, 12". Find the volume

per 1000 ft. 785ft3.

You have now found the

volume of 1000 ft pipe. Your

pipe is 10,000 ft.

Result: 10,000ft 785ft2 10ft 7850ft3 1000ft

785ft3 ⋅ = ⋅ =

Internal 

Diameter 

Volume per 

 1000 ft 

 Dpipe [in] [ft3] 

8 349 

10 545 

12 785 

15 1230 

17 1580 

IDpipe
POCKET GUIDE 8

Solution alternative 2:

A calculator is available ⇒ Equation 1.3 is used.

Inserting pipe data: 10,000 3.14

24

12 V

2

pipe ⋅ ⋅ 





 





 = = 7850ft3

1.3.4 Release volume fraction, frel

The maximum release fraction, frel,, represents the maximum

ratio of oil released relative to the volume of the pipeline.

To find the release volume fraction, the relative pressure

difference over the leak point has to be known. The relative

pressure ratio, Prel, is found from Equation 1.4. 

amb

pipe

rel P

P

∆P = Eq. 1.4

The ambient pressure Pamb can be found from Equation 1.5 or

from Table 1.2.

Pamb = d 0.446533 ⋅ Eq. 1.5

where

Pamb - pressure outside leakage [psi]

d - water depth at leak point [ft]

Use Table 1.3 to find the maximum release fraction, frel, and

the Gmax. Gmax is used in section 1.3.5 to find the GOR

reduction factor (fGOR).
POCKET GUIDE 9

Example:

The pipeline pressure is 950 psi. The gas-oil-ratio (GOR) of

the fluid in the pipeline is 450 scf/stb. A rupture occurs at a

water depth of 100 ft. Find the maximum release volume

fraction, frel.

Solution 

Step 1

Find ambient pressure at leak point, 100 ft water depth.

There are to alternative methods to find the ambient pressure.

A calculator is not available ⇒ use Table 1.2.

For 100 ft water depth, the corresponding ambient pressure is

44.65 psi.

A calculator is available ⇒ use equation 1.5

The ambient pressure at 100 ft water depth is:

Pamb = 00 0.446533 ⋅1 = 44.65 psi

Step 2

Find the relative pressure ratio.

Use Equation 1.4:

amb

pipe

rel P

P

∆P = = 44.65

950 = 21

Step 3

Find the maximum release volume fraction and the Gmax

Use Table 1.3. The value of ∆Prel has been found to be 21.

Look in Table 1.3 and pick the frel and Gmax corresponding to

this value. Result: frel = 0.71 and Gmax= 168 scf/stb.
POCKET GUIDE 10

Table 1.2: Ambient pressure, Pamb

Sea depth Pressure

[ft] [psi]

0 0.00

25 11.16

50 22.33

75 33.49

100 44.65

150 66.98

200 89.31

250 111.6

300 134.0

400 178.6

500 223.3

600 267.9

700 312.6

800 357.2

900 401.9

1000 446.5

1100 491.2

1300 580.5

1500 669.8

1700 759.1

1900 848.4

2100 937.7

2300 1027

2500 1116

2700 1206

2900 1295

3100 1384

3300 1474

3500 1563

3700 1652

3900 1741

4100 1831

4300 1920

4500 2009
POCKET GUIDE 11

Table 1.3: Maximum released volume fraction, frel

Relative pressure

ratio ∆Prel [-]

Maximum

release fraction

frel [-]

Maximum Release

occurs for a GOR of

Gmax [scf/stb]

1 0.0 not applicable (no leakage)

1.1 - 1.2 0.08 140

1.2 - 1-5 0.17 225

1.5 - 2 0.30 337

2 - 3 0.40 449

3 - 4 0.47 505

4 - 5 0.50 560

5 - 10 0.55 505

10 - 20 0.64 337

20 - 30 0.71 168

30-50 0.74 140

50 - 200 0.76 112

>200 0.77 112

1.3.5 GOR reduction factor, fGOR

The total released volume of oil is strongly connected to the

the gas-oil-ratio of the oil. The table below gives the volume

reduction factor to be used in Equation 1.1 as function of the

GOR. 

In Table 1.4 columns two and three give reduction factors.

Column two is used if GOR of the pipeline fluid is less than

the Gmax. The maximum Gmax that can be found from Table 1.3

is 561 scf/stb. If the GOR of the fluid is higher than this value,

the GOR will always be higher than Gmax. Column three is

used for GOR higher than Gmax. Gmax is found in Table 1.3.

Table 1.4: GOR reduction factors, fGOR

GOR GOR reduction factors, fGOR [-]

[scf/stb] GOR<Gmax GOR>Gmax

0-225 1

225-280 0.98

280-340 0.97

340-420 0.95

420-560

max

GOR G

GOR f =

0.9

560-1100 0.85

1100-1700 0.82

1700-2800 0.63

2800-5600 0.43

5600-11300

Will not

occur

0.26
POCKET GUIDE 12

Example Fluid 1:

The Gas-oil ratio (GOR) of the fluid in the pipeline is

450 scf/stb. Find the GOR reduction factor, fGOR. All the

other data are the same as in the examples above. 

Solution:

The release volume fraction, frel and Gmax has been found to

be: frel = 0.71 and Gmax= 168 scf/stb.

GOR GOR reduction factors, fGOR [-] 

[scf/stb] GOR<GORmax GOR>GORmax

55-225 1 

225-280 0.98 

280-340 0.97 

340-420 0.95 

420-560 

max

GOR GOR

GOR f =

0.9 

560-1100 0.85 

1100-1700 0.82 

1700-2800 0.63 

2800-5600 0.43 

5600-11300 

Will not 

occur 

0.26 

max

GOR G

GOR f =

GOR > Gmax

⇓ Table 1.3

fGOR= 0.9

0

Example Fluid 2:

The Gas-oil ratio (GOR) of the fluid in the pipeline is

150 scf/stb. Find the GOR reduction factor, fGOR. All the

other data are the same as in the examples above.

Solution:

The release volume fraction, frel and Gmax has been found to

be: frel = 0.71 and Gmax= 168 scf/stb.
POCKET GUIDE 13

GOR GOR reduction factors, fGOR [-] 

[scf/stb] GOR<GORmax GOR>GORmax

55-225 1 

225-280 0.98 

280-340 0.97 

340-420 0.95 

420-560 

max

GOR GOR

GOR f =

0.9 

560-1100 0.85 

1100-1700 0.82 

1700-2800 0.63 

2800-5600 0.43 

5600-11300 

Will not 

occur 

0.26 

max

GOR G

GOR f =

GOR < Gmax

⇓Table 1.3

max

GOR G

GOR f = 0.89

168

150 = =

0

Example Fluid 3:

The Gas-oil ratio (GOR) of the fluid in the pipeline is

700 scf/stb. Find the GOR reduction factor, fGOR. All the

other data are the same as in the examples above.

Solution:

The release volume fraction, frel and Gmax has been found to

be: frel = 0.71 and Gmax= 168 scf/stb.
POCKET GUIDE 14

1.3.6 General Trends Regarding the Reduction Factors

(Tables 2.3 and 2.4)

• An increase in the pressure difference between the pipe

pressure, Ppipe, and the ambient pressure at the leak

point, Pamb, will result in an increased oil release.

• An increase in the fluid Gas-Oil-Ratio, GOR, will result in

reduced oil release as long as GOR>Gmax. If GOR<Gmax,

the oil release will increase.

• Higher pipe volume Vpipe will result in a higher amount of

oil released.

Example:

A 10,000 ft 12" ID pipeline is shut-in with a pressure of 

950 psi. The Gas-oil ratio (GOR) of the fluid in the pipeline is

450 scf/stb. A rupture occurs at a water depth of 100 ft.

Calculate the total oil release. The pipeline is shut-in 2

minutes after the leakage occurred. The oil is transported at

a rate of 18000 stb/d.

Solution:

1. Volume released prior to shut-in

 Vpre-shut = 1440

Q ⋅ t = 25 bbls

1440

18000 2 = ⋅

2. Total pipeline volume is 7850 ft3 (from Table 1.1)

3. Ambient pressure at leak point is 44.65 psi (from

Table 1.2). 

4. Relative pressure difference is

950 psi / 44.65 psi = 21

5. From Table 1.3 frel is 0.71 and

Gmax is 168 scf/stb. 

6. From Table 1.4 fGOR is 0.9 since GOR > Gmax

Total release of oil from Equation 1.1: 

Vrel = 0.1781 ⋅ 7850 [ft3] ⋅ 0.71 ⋅ 0.9 + 25 = 918 bbls
POCKET GUIDE 15

2. ADVANCED METHOD

2.1 Introduction

The calculation approach presented in this Chapter is a more

advanced method than the "Initial" approach presented in

Chapter 1. To be able to follow this advanced method, a

calculator is needed. This method is based on the principle of

conservation of mass and the equilibrium of the oil fluid. 

The fluid calculation equations presented in section 2.4 are

based on experience and observations from a limited quantity

of representative data and should be used with proper

caution.

• These fluid calculation equations should not be used for

very light crude oil or gas condensates.

The method presented in this Chapter assumes:

• A single horizontal pipeline segment.

• A full pipeline break or rupture (not applicable to pinhole

leaks or other small pipeline fractures).

2.2 Required data

Following data are required to perform the calculations:

• Pipeline internal Diameter, IDpipe [in]

• Pipeline length, Lpipe [ft]

• Pipeline Pressure, Ppipe [psi]

• Pipeline Temperature, Tpipe [°F]

• Ambient pressure, Pamb [psi]

• Ambient temperature, Tamb [°F]

• Gas-oil ratio at standard conditions, GOR [scf/stb]

• Oil density at standard conditions, γAPI [-] (API gravity,

dimensionless), ρl

stc [lb/ft3] and γo [-] (specific gravity,

dimensionless)

• Gas density at standard conditions, ρg

stc [lb/ft3],

γg [-] (Specific gravity, dimensionless)

• Pipeline flow rate, Q [stb/d]

• Time before shut-in, t [min]

For unit conversion, please refer to Page 27.
POCKET GUIDE 16

2.3 Step by step procedure

1. Calculate total volume of pipe, Vpipe:

pipe

2

Pipe

pipe L

24

ID

V ⋅ π ⋅ 













 = [ft3]

2. Calculate the oil and gas densities at initial operational

conditions, initial

g

initial ρo and ρ (Use procedure given in

Section 2.4). Units: [lb/ft3]

3. Calculate oil volume fraction at initial operational

conditions (Ppipe, Tpipe), initial

ovf X (Use procedure given in

Section 2.4). Dimensionless.

4. Calculate the initial mass in the pipeline:

( ) ( ( )) initial

pipe ovf

initial

g

initial

pipe ovf

initial

o

initial mtot = ρ ⋅ V ⋅ X + ρ ⋅ V ⋅ 1− X [lb]

5. Calculate the oil and gas densities at ambient pressure

and temperature, amb

g

amb ρo and ρ (Use procedure given in

Section 2.4). Units: [lb/ft3]

6. Calculate oil volume fraction at ambient pressure and

temperature (Pamb, Tamb), amb

ovf X (Use procedure given in

section 2.4). Dimensionless.
POCKET GUIDE 17

7. Calculate the total mass in the pipeline when pressure in

pipeline has reached ambient pressure:

( ) ( ( )) amb

pipe ovf

amb

g

amb

pipe ovf

amb

o

amb mtot = ρ ⋅ V ⋅ X + ρ ⋅ V ⋅ 1− X [lb]

8. Calculate the total mass released

amb

tot

initial mtot _ rel = mtot − m [lb]

9. Calculate the gas mass fraction at standard

conditions. Dimensionless.

(GOR )

5.614583

1+

1 X

stc

g

stc

L

stc

gmf

⋅ ρ

ρ ⋅ = [-]

10. Calculate the volume of oil releases prior to shut-in.

Vpre-shut = 1440

Q ⋅ t [bbls]

11. Calculate the volume of oil released, standard

conditions. ( ) stc

o

stc

gmf rel stc

rel

m 1 X

V 0.1781

ρ

− = ⋅ + Vpre-shut [bbls]
POCKET GUIDE 18

2.4 Fluid Calculations

This section gives a procedure to calculate fluid properties at

a given pressure and temperature (P, T). The gas and oil

densities at standard conditions (60°F, 14.7psi) and the GOR

of the fluid have to be known.

Find constants needed to calculate gas solubility:

Coefficient γAPI30 γAPI>30

C1

C2

C3

0.0362

1.09

25.7

0.0178

1.19

23.9

Calculate gas gravity at 100 psi

( ) API

3 γg100 = γg 1.0 − 3.1126 ⋅10 γ −

Calculate gas solubility





 





+

γ = γ ⋅ T 460

R C p exp C API

3

C2 S 1 g100

Find coefficients needed to calculate bubble point pressure

Coefficient γAPI30 γAPI>30

K1

K2

K3

27.62

0.9143

11.13

56.18

0.8424

10.39
POCKET GUIDE 19

Calculate coefficient needed to calculate bubble point

pressure

T 460

K a 3 API

+

− γ =

Calculate bubble point pressure

K2

a

g100

1

b 10 K GOR P 































γ =

Find coefficients needed to calculate formation volume factor

Coefficient γAPI30 γAPI>30

X1

X2

X3

4.677 ·10-4

1.751 ·10-5

-1.811 ·10-8

4.670 ·10-4

1.100 ·10-5

1.337 ·10-9

Calculate the formation volume factor, Bo

If pressure is below bubble point pressure, Pb, then

( ) ( ) 2 3 s

g100

API Bo 1.0 X1Rs T 60 ⋅ X + X R 















γ

γ = + + − ⋅

If pressure is above bubble point pressure, Pb, then

Calculate the isothermal compressibility of oil

0.0355

g100

0.36 0.77

API

0.5

s

6

o R T

P

6.83 10 c −

−

⋅ ⋅ γ ⋅ ⋅ γ ⋅ =
POCKET GUIDE 20

Calculate the BO factor 

B 1.0 X GOR ( ) T 60 ( ) X2 X3GOR

g100

API

1

'

o + 















γ

γ = + + −

[ ] ( ) o b

' Bo = Bo exp − c P −P

If Bo < 1 then Bo = 1

Calculate specific gravity of dissolved gas in the oil phase

( 3.57 10 2.86 10 ) Rs 0.02 API 0.25 9

API

6 γgd = − ⋅ ⋅ γ − ⋅ ⋅ + γ + − −

If γgd < 0.56 Then γgd = 0.56

If γgd < γg Then γgd = γg

Calculate specific gravity of free gas

s

g s gd

gf GOR R

GOR R

−

⋅ γ − γ

γ =

If γgf < 0.56 Then γgf = 0.56

If γgf > γg Then γgf = γg

Calculate the oil density

If pressure below bubble point pressure

o

o s gd

o B

62.4γ + 0.0136R γ

ρ = [lb/ft3]

If pressure above bubble point pressure

co ( ) P Pb

o

o gd

o e B

62.4 0.0136GOR − ⋅















 γ + γ

ρ = [lb/ft3]
POCKET GUIDE 21

Calculate pseudocritical temperature [°R]

2

pc g 5 g T = 187 + 330γ − 71. γ

Calculate reduced temperature, Tpr

pc

pr T

T 460 T + =

Calculate pseudocritical pressure [psi]

2

pc g 1 g P = 706 − 51.7γ −11. γ

Calculate reduced pressure, Ppr

pc

pr P

P P =

Pick gas compressibility factor Z from the chart below
POCKET GUIDE 22

Calculate the gas density

Z( ) T 460

2.7 gf P

g +

⋅ γ ⋅ ρ = [lb/ft3]

Calculate the gas mass fraction of free gas.

Rsfree = GOR − Rs

Calculate the gas mass fraction

(R )

5.615

1+

1 X

stc

sfree g

stc

L

gmf

⋅ ρ

ρ ⋅ = if 0 Xgmf < 0 ⇒ Xgmf =

Calculate the volume fraction of oil

( )

( ) gmf o gmf g

gmf g

ovf X 1 X

1 X

X ⋅ ρ + − ⋅ ρ

− ⋅ρ =
POCKET GUIDE 23

Example:

A 10 000 ft 12" ID pipeline is shut-in with a pressure of 3000

psi and a operational temperature of 80°F. The Gas-oil ratio

(GOR) of the fluid in the pipeline is 450 scf/stb. The oil and

gas densities at standard conditions are 65 lb/ft3 and 0.05

lb/ft3 respectively. A rupture occurs at a water depth of 100

ft. The seabed temperature is 65°F. Calculate the total oil

release. The pipeline is shut-in 2 minutes after the leakage

occurs. The oil is transported at a rate of 18000stb/d.

Solution:

Unit Conversion

Gas density

0.05 lb/ft3, In the fluid calculation equations, the gas density

has to be known in gas gravity. To convert from lb/ft3 to gas

gravity, multiply by 12.98408. Result: γg = 0.649 (gas

gravity)

Oil density

50 lb/ft3, In the fluid calculation equations the gas density

has to be known in specific gravity and in API gravity. From

lb/ft3 to specific gravity multiply by 0.016018. Result: γo =

0.8009 (specific gravity)

From specific gravity to API gravity, the following formula

must be used: 131.5

141.5 −

specific gravity

= 0.8009

141.5 -131.5

= 45.18 API gravity

1. Calculate total volume of pipe, Vtot:

pipe

2

Pipe

pipe L

24

ID

V ⋅ π ⋅ 













 = = 3.14 10000

24

12 2

 ⋅ ⋅ 

 



 = 7850
POCKET GUIDE 24

2. Calculate the oil and gas densities at initial operational

conditions (Use procedure given in section 2.4).

γg100 0.5579 

Rs 251.7 

a -0.87 

Pb 1548 

Bo 1.14 

γgd 1.11 

γgf 0.56 

ρo 47.4 

Tpc 371 

Tpr 1.45 

Ppc 668 

Ppr 1.42 

Z 0.81 

ρg 3.28 

Oil density, initial ρo : 47.4 lb/ft3

Gas density, initial ρg : 3.28 lb/ft3

3. Calculate oil volume fraction at initial operational

conditions (Use procedure given in section 2.4).

Rsfree 198.3 

Xgmf 0.03411 

Xovf 0.6628 

Volume fraction of oil, initial X = 0.729 (Dimensionless) ovf

4. Calculate the initial mass in the pipeline:

( ) ( ( )) initial

pipe ovf

initial

g

initial

pipe ovf

initial

o

initial mtot = ρ ⋅ V ⋅ X + ρ ⋅ V ⋅ 1− X

m ( ) () 47.4 lb/ft3 7850 ft3 0.6628 ( ) 3.28 lb/ft3 7850 ft3 1 0.6628 initial

tot = ⋅ ⋅ + ⋅ ⋅ −

initial mtot = 2.55  105

 lb
POCKET GUIDE 25

5. Calculate the oil and gas densities at ambient pressure

and temperature (Use procedure given in section 2.4).

γg100 0.5579 

Rs 7.1 

a -0.90 

Pb 1475 

Bo 1.008 

γgd 1.15 

γgf 0.64 

ρo 49.7 

Tpc 371.1 

Tpr 1.14 

Ppc 668 

Ppr 0.067 

Z 0.99 

ρg 0.149 

Oil density, end ρo : 49.7 lb/ft3

Gas density, end ρg : 0.149 lb/ft3

6. Calculate oil volume fraction at ambient pressure and

temperature (Use procedure given in section 2.4).

Rsfree 442.9 

Xgmf 0.073 

Xovf 0.037 

Volume fraction of oil, end X : 0.037 (Dimensionless) ovf

7. Calculate the total mass in the pipeline when pressure

in pipeline has reached ambient pressure:

( ) ( ( )) end

pipe ovf

end

g

end

pipe ovf

end

o

end mtot = ρ ⋅ V ⋅ X + ρ ⋅ V ⋅ 1− X

m ( ) () 49.7 lb/ft3 7850 ft3 0.037 ( ) 0.149 lb/ft3 7850 ft3 1 0.037 end

tot = ⋅ ⋅ + ⋅ ⋅ −

end mtot = 15561 lb

8. Calculate the total mass released

end

tot

initial

tot

released mtot _ rel = m − m

m 2.55 10 lb 15561lb released 5

tot _ rel = ⋅ − = 239439 lb
POCKET GUIDE 26

9. Calculate the gas mass fraction at standard

conditions. Dimensionless.

(GOR )

5.614583

1+

1 X

stc

g

stc

L

stc

gmf

⋅ ρ

ρ ⋅ = 0.0742

(450 0.05)

50 5.614583 1+

1 =

⋅

⋅ =

10. Calculate the volume of oil releases prior to shut-in.

Vpre-shut = 1440

Q ⋅ t = 144018000 ⋅ 2 = 25 [bbls]

11. Calculate the total volume released, standard

conditions

( ) pre_shut stc

o

stc

gmf

released

tot _rel stc

rel V m 1 X

V 0.1781 + ρ

−

= ⋅

( ) 25

50 lb / ft3

239439lb 1 0.0742 V 0.1781 stc

rel + ⋅ − =

= stc Vrel 815 bbls
POCKET GUIDE 27

APPENDIX A 

VARIABLE DESCRIPTION AND UNIT CONVERSION

Pipeline Length, Lpipe

This is the length of the pipeline including risers.

Units

The unit of the length has to be in ft when used in the further

studies.

The conversion factors to use are listed below:

To convert from To Multiply by

M Ft 3.2808

Pipeline Internal Diameter, IDpipe

This is the inside diameter of the pipeline.

Units

The unit of the diameter has to be in in when used in the

further studies.

The conversion factors to use are listed below:

To convert from To Multiply by

M In 39.37

Ft In 12
POCKET GUIDE 28

Pipeline Pressure, Ppipe

The operational pressure of the pipeline has to be known to

get an estimate of the total amount of oil released.

Units

The unit of the operational pressure has to be in Psi when

used in the further studies.

The conversion factors to use are listed below:

To convert from To Multiply by

Bar Psi 14.503774

Pipeline Temperature, Tpipe

This is an average temperature inside the pipe during

transportation. 

Units

The unit of the operational temperature has to be in °F when

used in the further studies.

The conversion factors to use are listed below:

To convert from To Conversion formula

°C °F T 32

5

9 T f = C +
POCKET GUIDE 29

Water Depth at Rupture Location, d

The water depth at rupture location is used to calculate the

ambient pressure. 

Units

The unit of the water depth has to be in ft when used in the

further studies.

The conversion factors to use are listed below:

To convert from To Multiply by

m Ft 3.2808

Ambient Pressure, Pamb

This is the pressure outside the pipe at the location of the

rupture. 

This pressure is a function of the sea depth:

P = Water depth [ft] * 0.446686 [psi]

Units

The unit of the ambient pressure has to be in Psi when used

in the further studies.

The conversion factors to use are listed below:

To convert from To Multiply by

Bar Psi 14.503774
POCKET GUIDE 30

Ambient Temperature, Tamb

This is the temperature outside the pipe at the location of the

rupture. 

A typical value for the sea bottom temperature is 35°F

Units

The unit of the ambient temperature has to be in °F when

used in the further studies.

The conversion factors to use are listed below:

To convert from To Conversion formula

°C °F T 32

5

9 T f = C +

 Gas-oil ratio, GOR

This is the Gas-oil ratio of the pipeline fluid at standard

conditions.

Units

The unit of the GOR has to be in scf/stb when used in the

further studies.

The conversion factors to use are listed below:

To convert from To Multiply by

Sm3/ Sm3 Scf/stb 5.6146
POCKET GUIDE 31

Oil Density, γAPI, ρl

stc

This is the density of the oil phase at standard conditions.

Units

For further calculation, the unit of the oil density has to be

known in API gravity, γAPI, and lb/ft3,ρl

stc.

The conversion factors to use are listed below:

To convert from To Multiply by

lb/ft3 Specific gravity [-] 0.016018

kg/m3 lb/ft3 0.062428

kg/m3 Specific gravity [-] 0.001

Specific gravity [-] API gravity [-] 131.5

141.5

−

specific gravity

Gas Density, γg, ρg

stc

This is the density of the gas phase at standard conditions.

Units

For further calculation, the unit of the gas density has to be

known in gas gravity, γg, and lb/ft3, ρg

stc.

The conversion factors to use are listed below:

To convert from To Multiply by

lb/ft Gas gravity [-] 12.984

kg/m3 lb/ft 0.06243

kg/m3 Gas gravity [-] 1.2337

1
POCKET GUIDE 32

List of conversion factors

To convert from To Multiply by

Length

M Ft 3.2808

M In 39.37

Ft In 12

Volume

ft3 Bbls 0.1781

Bbls Ft3 5.615

Pressure

Bar Psi 14.503774

Water depth(h), m Psi 0.446533

Temperature

°C °F T 32

5

9 T f = C +

°F °R Tr = Tf + 460

Gas-oil ratio, GOR

Sm3/ Sm3 Scf/stb 5.6146

Density

lb/ft Gas gravity [-] 12.984

kg/m3 Lb/ft 0.06243

kg/m3 Gas gravity [-] 1.2337

1

lb/ft3 Specific gravity [-] 0.016018

kg/m3 Specific gravity [-] 0.001

Specific gravity [-] API gravity [-] 131.5

141.5

−

specific gravity