Pipeline discretization (BHR Multiphase 2009)

www.bhrgroup.co.uk

14th International Conference Multiphase Production Technology

Cannes, France - 17th - 19th June 2009

SDAG

Discretization Methods for Multiphase

Flow Simulation of Ultra-Long

Gas-Condensate Pipelines

Erich Zakarian & Henning HolmShtokman Development A.G.



SDAG

Contents

• The Shtokman field development

• Profile discretization of gas-condensate pipelines

• Objective and requirements

• Method 1 – concept of pipeline profile indicator

• Method 2 – concept of lumping and redistribution

• Comparison and simulation

• Conclusions



SDAG

Integrated Development of the Shtokman

Gas-Condensate Field – Phase 1



SDAG

Cannes

ParisMurmansk

Teriberka

Shtokman

Gas export to shore • 70 MSm3/d (2.5 BCFD) – Phase 1

• 2 x 36” ND trunklines (0.86 m ID)

• Length 558 km (347 miles)

• Dry two-phase flow

• CGR = from 2 to 16 Sm3/MSm3



SDAG

-400

-300

-200

-100

0

100

200

0 100 200 300 400 500

Distance [km]

Ele

vati

on

[m

]

Shtokman pipeline profile

• Detailed pipeline profile from seabed bathymetry survey (2007)

• Free span analysis and seabed intervention taken into account

108,785 points



SDAG

Given either as-built profile or detailed terrain survey

• In transient multiphase flow simulation, the actual or

expected pipeline geometry must be simplified to achieve

reasonable CPU time

• For long pipelines (> 100 km) laid on rough terrain,

compression of a large set of data points is required

typically from 104-105 points to few 103 points

Pipeline profile discretization: objective

Target

Simulation time ≥ 24 x CPU time



SDAG

The Shtokman case

• Average pipe length will be approximately 200 m

• Avoid small pipe sections to maximize numerical time steps

Δt < min (Δx/U)i

Target ≈ 2500 pipesfor a total length of 554 km



SDAG

Pipeline profile discretization: requirements1. The total pipe length must be conserved

2. The simplified geometry must have the same overall shape (large and small scale undulations)

3. The pipe angle distribution of the discretized profile must be as close as possible to the original distribution

4. The total climb (cumulative length of uphill pipes) must be conserved to predict the same overall liquid content in steady-state flow conditions

1

2

4

3

Original profile



SDAG

Liquid holdup vs. pipe inclinationOLGAS 5.3: liquid holdup vs. pipe inclination and gas superficial velocity

USL=0.003 m/s - G=180 kg/m3 - o=775 kg/m3 - mG=0.02 cP - mO=2.5 cP

=0.0025 N/m - Wall roughness=30 mm - Inner diameter=0.9906 m

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Pipe inclination [deg]

Liq

uid

ho

ldu

p [

-]

USG = 1.00 m/s

USG = 1.50 m/s

USG = 2.00 m/s

USG = 2.50 m/s

USG = 3.00 m/s

USG = 3.50 m/s

USG = 4.00 m/s

USG = 4.50 m/s



SDAG

Two methods for a single objective

Method 1: concept of pipeline profile indicator

• Select, simplify and complexify relevant sub-profiles

• Use the pipeline profile indicator and the total climb to

match the original angle distribution

Method 2: concept of lumping elements with similar

inclination

• Redistribution to match the original large & small

scale topographies



SDAG

Method 1

Concept of pipeline profile indicator



SDAG

Definition: pipeline profile indicator

θi = inclination of pipe i with respect to horizontal [%]

Li = length of pipe i [m]

N = number of pipes

B. Barrau, “Profile indicator helps predict pipeline holdup, slugging”, Oil & Gas Journal

Vol. 98, Issue 8, p. 58-62, Feb 21, 2000

1000

0

1

1

N

ii

N

iii

L

LHoldupHoldup

PI

25066191490

...tanArc.

Holdup ii



SDAG

Holdup function vs. OLGAS OLGAS 5.3: liquid holdup vs. pipe inclination and gas superficial velocity

USL=0.003 m/s - G=180 kg/m3 - o=775 kg/m3 - mG=0.02 cP - mO=2.5 cP

=0.0025 N/m - Wall roughness=30 mm - Inner diameter=0.9906 m

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Pipe inclination [deg]

Liq

uid

ho

ldu

p [

-]

Holdup function

USG = 1.00 m/s

USG = 1.50 m/s

USG = 2.00 m/s

USG = 2.50 m/s

USG = 3.00 m/s

USG = 3.50 m/s

USG = 4.00 m/s

USG = 4.50 m/s



SDAG

Pipeline profile indicator scale

PI < 0Pipeline profile is globally sloping downwards

No particular operating problem to be expected

0 < PI < 20Pipeline profile is nearly horizontal or over-simplified

No particular operating problem to be expected

20 < PI < 40Pipeline profile is relatively flat or slightly hilly

Possible troubles at very low flow rates or during restart

40 < PI < 80Pipeline crosses hilly terrain

Design & Operation needs particular attention

80 < PI

Pipeline profile is very hilly or very steep

Design & Operation needs very careful attention

Validity of simulation software to be checked

From Total E&P experience in gas-condensate pipeline

design and operation

Shtokman pipeline profile indicator = 79.7



SDAG

Step 1: sub-profile selection

020406080

100120140160180

0 100000 200000 300000 400000 500000

Pip

eli

ne in

dic

att

or

[-]

Distance from offshore platform [m]

-10-8-6-4-202468

10

230000 240000 250000 260000 270000 280000

Incli

nati

on

[d

eg

]


Pipe inclination

-10-8-6-4-202468

10

410000 420000 430000 440000 450000 460000

Incli

nati

on

[d

eg

]


Pipe inclination



SDAG

• Final average pipe length should be about 200 m

(target ≈ 2500 pipes)

• For example, use the Box Filter from OLGA®

Geometry Editor

• Or simply select one point every 1 km

Step 2: simplification of the original profile



SDAG

0500100015002000250030003500400045005000

-400

-300

-200

-100

0

100

200

0 100000 200000 300000 400000 500000

To

tal c

limb

[m]E

levati

on

[m

]


Pipeline geometry

Pipe elevation (simplified profile) [m]

Pipe elevation (original profile: 108,785 points) [m]

Total climb (original profile: 108,785 points) [m]

Total Climb (simplified profile) [m]

-15

-10

-5

0

5

10

15

20

0 100000 200000 300000 400000 500000

Incli

nati

on

[d

eg

]


Pipe inclination

Pipe inclination (original profile: 108,785 points) [deg]

Pipe inclination (simplified profile) [deg]

PI = 79.7

25.8

Step 2: result



SDAG

Step 3: complexification

Pipeline geometry

-340

-335

-330

-325

-320

-315

-310

-305

0 2000 4000 6000 8000 10000


Ele

vati

on

[m

]

Complexified profile

Simplified profile

Inverse of the standard normal cumulative distribution

-4

-3

-2

-1

0

1

2

3

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ProbabilityN

orm

Std

-1

For each sub-profile

• Keep original pipeline

indicator within +/-1%

• Keep original total climb

within +/- 1%

• Split the simplified profile into smaller pipes5 smaller pipes per simplified pipe pipe length ≈ 200 m

• Move new points up and down with a random process



SDAG

0500100015002000250030003500400045005000

-400

-300

-200

-100

0

100

200

0 100000 200000 300000 400000 500000

To

tal c

limb

[m]E

levati

on

[m

]


Pipeline geometry

Pipe elevation (complexified profile) [m]

Pipe elevation (original profile: 108,785 points) [m]

Total climb (complexified profile) [m]

Total climb (original profile: 108,785 points) [m]

-15

-10

-5

0

5

10

15

20

0 100000 200000 300000 400000 500000

Incli

nati

on

[d

eg

]


Pipe inclination

Pipe inclination (original profile: 108,785 points) [deg]

Pipe inclination (complexified profile) [deg]

Step 3: result



SDAG

Method 2

Concept of lumping elements with similar inclination



SDAG

Method 2 – “Lumping and redistributing”

1. Define the criteria (in priority) to determine the pipe length to be used for

the simplified profile :

1. minimum pipe length

2. maximum elevation change for a pipe element

3. maximum pipe length

2. Sort all elements in the detailed profile by inclination in ascending order

3. Lump together the sorted elements to longer pipes, starting with the

element with the steepest downhill inclination. The length of each pipe

element is then limited by dominating criteria in 1).

4. Distribute the pipe elements in the simplified profile to match the large

scale and small scale topography of the detailed profile.



SDAG

Pipelength (m)

Pip

e e

lev

ati

on

ch

an

ge

(m

)

Xmin Xmax

Maximum elevation change

-25

-20

-15

-10

-5

0

5

10

15

20

25

-8 -6 -4 -2 0 2 4 6 8

Pipe inclination (deg)

Ele

va

tio

n c

ha

ng

e (

m)

0

100

200

300

400

500

600

700

800

900

1000

Pip

e l

en

gth

(m

)

Elevation change of single pipe

Pipe length

Step 1)

Define the criteria (in priority) to determine the pipe

length to be used for the simplified profile :

1. minimum pipe length (200 m)

2. maximum elevation change for a pipe element (5 m)

3. maximum pipe length (1000 m)



SDAG

Step 3)Lump together the sorted elements to

longer pipes, starting with the element

with the steepest downhill inclination.

The length of each pipe element is then

limited by dominating criteria in 1).

-1200

-1000

-800

-600

-400

-200

0

0 100000 200000 300000 400000 500000 600000

Distance (m)

Ele

vati

on

(m

)

-1200

-1100

-1000

-900

-800

-700

-600

-500

-400

-300

-200

0 50000 100000

Distance (m)

Ele

vati

on

(m

)

-5

-4

-3

-2

-1

0

1

2

3

4

5

Incli

nati

on

(d

eg

)Original profile

Inclination

Lumped, but not redistributed profile

Step 2) Sort elements in the detailed profile by inclination in ascending order – divide into

subsections if required



SDAG

”Inclination classes” versus ”lumping by inclination in ascending order ”

0

100000

200000

300000

400000

500000

600000

-5 -4 -3 -2 -1 0 1 2 3 4 5

Inclination (deg)

Accu

mu

late

d l

en

gth

(m

)

grouping by inclination classes

Lumping by inclinations in

ascending order

0

200

400

600

800

1000

1200

1400

1600

1800

2000

30 35 40 45 50 55 60 65 70

Export flow rate [MSm3/d]

Co

nd

en

sa

te c

on

ten

t [m

3]

Original profile 20-70 km

'lumping by inclination in ascending order'

'Sorted by inclination classes'



SDAG

Step 4)Redistribution of elements by “Simulated Annealing” (Travelling salesman problem)

“minimize distance between detailed profile and simplified profile”

yi : values from the simplified profile

ŷi : values from the detailed profile

wi : weight factor

where as “i” denotes:

1) Elevation

2) “Total Climb”

3) “Pipeline Indicator” *

2)()( ii ii yywyF

Cost function:

-1200

-1000

-800

-600

-400

-200

0

0 100000 200000 300000 400000 500000 600000

Distance (m)

Ele

vati

on

(m

)

-400

-350

-300

-250

-200

-150

-100

-50

0

0 100000 200000 300000 400000 500000 600000

Distance (m)

Ele

vati

on

(m

)

-300

-290

-280

-270

-260

-250

-240

-230

70000 75000 80000 85000 90000 95000 100000

Distance (m)

Ele

vati

on

(m

)



SDAG

Original

profile

Simplified

profile

Method 1

profile

Method 2

profileNumber of pipes 108,784 554 2,766 2,550

Pipeline profile indicator 79.7 25.8 80.3 80.3

Total climb [m] 4,187 1,235 4,180 4,187Total length [m] 554,505 554,400 554,507 554,505

Comparison

Pipeline geometry

-300

-290

-280

-270

-260

-250

-240

-230

70000 75000 80000 85000 90000 95000 100000


Ele

vati

on

[m

]

Original profile

Simplified profile

Discretized profile (method 1)

Discretized profile (method 2)



SDAG

Angle distributionsPipe angle distribution

0

10000

20000

30000

40000

50000

60000

70000

80000

(-90,

-60)

(-30,

-20)

(-10,

-5)

(-2, -

1)

(-0.5

, -0.

25)

(0, 0

.01)

(0.1

, 0.2

)

(0.3

, 0.4

)

(0.5

, 0.7

5)

(1, 1

.25)

(1.5

, 2)

(2.5

, 3)

(4, 5

)

(6, 7

)

(8, 9

)

(10,

20)

(30,

90)

Pipe angle group [deg]

To

tal

pip

e l

en

gth

per

an

gle

gro

up

[m

]

Original profile

Discretized profile (Method 2)


Simplified profile



SDAG

Steady-state simulation: original vs. discretizationCondensate content vs. export flow rate

42" ND pipeline - Fluid: 50%J0/50%J1 - OLGA steady-state pre-processor

0

200

400

600

800

1000

1200

1400

1600

1800

2000

30 35 40 45 50 55 60 65 70


Co

nd

en

sate

co

nte

nt

[m3]

Original profile 20-70 km

Discretized profile 20-70 km (Method 1)

Discretized profile 20-70 km (Method 2)



SDAG

Steady-state simulation: simplified vs. discretizationTotal condensate content vs. export flow rate

42" ND pipeline - Fluid: 50%J0/50%J1 - OLGA steady-state pre-processor

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

20 25 30 35 40 45 50 55 60 65 70


To

tal

co

nd

en

sa

te c

on

ten

t [m

3]

80

100

120

140

160

180

200

Inle

t pre

ss

ure

[ba

ra]

Total condensate content (simplified profile)Total condensate content (method 1)Total condensate content (method 2)Inlet pressure (simplified profile)Inlet pressure (method 1)Inlet pressure (method 2)



SDAG

Conclusions

• Simplification of long and rough gas-condensate

pipeline profiles is a key issue for correct design

• Two methods were introduced for the development

of the Shtokman field – Phase 1

• Essential characteristics of the original detailed

pipeline profile are conserved:

Length + Topography + Angle distribution + Total climb

• The hydrodynamic behavior of the original profile is

conserved through both methods despite significant

data compression



SDAG

Discretization Methods for Multiphase

Flow Simulation of Ultra-Long Gas-

Condensate Pipelines

Erich Zakarian, Henning HolmShtokman Development A.G., Russia

[email protected], [email protected]

Dominique LarreyTotal E&P, Process Department, France

[email protected]



SDAG

Back-up



SDAG

Why discretization is so important?

Poor discretization

Incorrect design of

receiving facilities

Wrong operating

envelope

Reduced operating

flexibility

Higher risk of

continuous flaring

Wrong model tuning

against field data

Total condensate content vs. export flow rate42" ND pipeline - Fluid: 50%J0/50%J1 - OLGA steady-state pre-processor

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

20 30 40 50 60 70


To

tal

co

nd

en

sate

co

nte

nt

[m3]

Simplified profile





SDAG

Seabed profile

-400

-300

-200

-100

0

100

200

0 100 200 300 400 500

Distance [km]

Ele

vati

on

[m

]

Ice scours &

depressions Elongated pockmarksPockmarks

Ridges & ice scours3D

Sid

e S

can S

onar

imagery



SDAG

Total climb

• Total climb = cumulative length of uphill pipes

• Helpful indicator as a first check

• Relevant indicator in addition to the pipeline profile

indicator to match the original angle distribution

Shtokman original pipeline profile (2007 survey)

Total climb = 4187 m



SDAG

Comparison of the discretization methodsPipeline geometry

-400

-300

-200

-100

0

100

200

0 100000 200000 300000 400000 500000


Ele

vati

on

[m

]

0

1000

2000

3000

4000

5000

To

tal c

limb

[m]

Pipe elevation (discretized profile: first method) [m]

Pipe elevation (discretized profile: second method)[m]

Total climb (discretized profile: first method) [m]

Total climb (discretized profile: second method) [m]

Pipe inclination

-10-8-6-4-202468

10

0 100000 200000 300000 400000 500000


Incli

nati

on

[d

eg

]

Pipe inclination (discretized profile: first method) [m]

Pipe inclination (discretized profile: second method) [m]



SDAG

OLGA® Geometry Editor

Box filter

Angle

distribution

preservation

• Ok for removing noise from as-built

pipeline survey

• Not recommended for hilly pipelines

• Requires pre-definition of angle groups

• Several tries are necessary

• Extremely difficult or even impossible to

satisfy the four criteria

Pipeline discretization (BHR Multiphase 2009)

Documents

multiphase flow simulation

total pipe length

sdag contents

sdag discretization

sdag liquid holdup

discretized profile

sdag integrated development

pipe inclinationolgas