Pipeline discretization (BHR Multiphase 2009)

SDAG

Discretization Methods for Multiphase
Flow Simulation of Ultra-Long
Gas-Condensate Pipelines
Erich Zakarian & Henning Holm
Shtokman Development A.G.

www.bhrgroup.co.uk

14th International Conference Multiphase Production Technology
Cannes, France - 17th - 19th June 2009

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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


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Integrated Development of the Shtokman
Gas-Condensate Field – Phase 1


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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)
Shtokman
• Dry two-phase flow
Teriberka • CGR = from 2 to 16 Sm3/MSm3

Murmansk Paris

Cannes


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Shtokman pipeline profile
200

100
Elevation [m]

0

-100

-200

-300

-400
0 100 200 300 400 500
Distance [km]

• Detailed pipeline profile from seabed bathymetry survey (2007)
• Free span analysis and seabed intervention taken into account

108,785 points

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Pipeline profile discretization: objective
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

Target
 Simulation time ≥ 24 x CPU time


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The Shtokman case

Target ≈ 2500 pipes
for a total length of 554 km

• Average pipe length will be approximately 200 m

• Avoid small pipe sections to maximize numerical time steps

Δt < min (Δx/U)i


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Pipeline profile discretization: requirements
1. 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
3
2
4
Original profile


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Liquid5.3: liquid holdupvs. pipe inclination velocity
OLGAS
holdup vs. pipe  inclination and gas superficial
USL=0.003 m/s -  G=180 kg/m3 - o=775 kg/m3 - m G=0.02 cP - m O=2.5 cP
=0.0025 N/m - Wall roughness=30 mm - Inner diameter=0.9906 m
0.70

0.60
USG = 1.00 m/s
Liquid holdup [-]

USG = 1.50 m/s
0.50
USG = 2.00 m/s

0.40 USG = 2.50 m/s

USG = 3.00 m/s
0.30 USG = 3.50 m/s

USG = 4.00 m/s
0.20 USG = 4.50 m/s

0.10

0.00
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Pipe inclination [deg]


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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


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Method 1

Concept of pipeline profile indicator


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Definition: pipeline profile indicator
 Holdupi   Holdup0 Li
N

i 1
PI  N
 1000
 Li
i 1

Holdup i  
 Arctan1.9   i  1.66  0.25
0.49

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


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OLGAS 5.3: liquid holdup vs. pipe inclination and gas superficial velocity
Holdup function vs. OLGAS
USL=0.003 m/s -  G=180 kg/m3 - o=775 kg/m3 - m G=0.02 cP - m O=2.5 cP
=0.0025 N/m - Wall roughness=30 mm - Inner diameter=0.9906 m
0.70

0.60
Holdup function
USG = 1.00 m/s
Liquid holdup [-]

0.50
USG = 1.50 m/s
USG = 2.00 m/s
0.40
USG = 2.50 m/s
USG = 3.00 m/s
0.30
USG = 3.50 m/s
USG = 4.00 m/s
0.20
USG = 4.50 m/s

0.10

0.00
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Pipe inclination [deg]


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Pipeline profile indicator scale
From Total E&P experience in gas-condensate pipeline
design and operation
Pipeline profile is globally sloping downwards
PI < 0
No particular operating problem to be expected
Pipeline profile is nearly horizontal or over-simplified
0 < PI < 20
No particular operating problem to be expected
Pipeline profile is relatively flat or slightly hilly
20 < PI < 40
Possible troubles at very low flow rates or during restart
Pipeline crosses hilly terrain
40 < PI < 80
Design & Operation needs particular attention
Pipeline profile is very hilly or very steep
80 < PI Design & Operation needs very careful attention
Validity of simulation software to be checked

Shtokman pipeline profile indicator = 79.7

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Step 1: sub-profile selection
Pipe inclination Pipe inclination
10 10
8 8
Inclination [deg]

Inclination [deg]
6 6
4 4
2 2
0 0
-2 -2
-4 -4
-6 -6
-8 -8
-10 -10
230000 240000 250000 260000 270000 280000 410000 420000 430000 440000 450000 460000
Distance from offshore platform [m] Distance from offshore platform [m]

180
Pipeline indicattor [-]

160
140
120
100
80
60
40
20
0
0 100000 200000 300000 400000 500000
Distance from offshore platform [m]


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Step 2: simplification of the original profile
• 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


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Step 2: result
Pipeline geometry
200 5000
Pipe elevation (simplified profile) [m] 4500

Total climb [m]
100 Pipe elevation (original profile: 108,785 points) [m] 4000
Elevation [m]

0 Total climb (original profile: 108,785 points) [m] 3500
Total Climb (simplified profile) [m] 3000
-100 2500
2000
-200 1500
-300 1000
500
-400 0
0 100000 200000 300000 400000 500000
PI = 79.7
Pipe inclination 25.8
20
Pipe inclination (original profile: 108,785 points) [deg]
15
Inclination [deg]

Pipe inclination (simplified profile) [deg]
10
5
0
-5
-10
-15
0 100000 200000 300000 400000 500000


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Step 3: complexification
• Split the simplified profile into smaller pipes
5 smaller pipes per simplified pipe  pipe length ≈ 200 m
• Move new points up and down with a random process cum
Pipeline geometry Inverse of the standard normal
-305
4
Complexified profile
-310 3
Simplified profile
-315
For each sub-profile
2
Elevation [m]

-320
• Keep original pipeline
1

NormStd-1
-325 indicator within +/-1%
0

-330 • Keep original total climb
-1

within +/- 1%
-2
-335
-3
-340
-4
0 2000 4000 6000 8000 10000
0 0.1 0.2 0.3 0.4 0.5 0.6
Distance from offshore platform [m] Probability


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Step 3: result
Pipeline geometry
200 5000
Pipe elevation (complexified profile) [m] 4500

Total climb [m]
100 4000
Elevation [m]

Pipe elevation (original profile: 108,785 points) [m]
0 Total climb (complexified profile) [m] 3500
Total climb (original profile: 108,785 points) [m] 3000
-100 2500
2000
-200 1500
-300 1000
500
-400 0
0 100000 200000 300000 400000 500000

Pipe inclination
20
Pipe inclination (original profile: 108,785 points) [deg]
15
Inclination [deg]

Pipe inclination (complexified profile) [deg]
10
5
0
-5
-10
-15
0 100000 200000 300000 400000 500000


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Method 2

Concept of lumping elements with
similar inclination


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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.


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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)

25 1000
20 Elevation change of single pipe 900
15 Pipe length 800
Pipe elevation change (m)

Elevation change (m)
10 700

Pipe length (m)
5 600
Maximum elevation change
0 500
-5 400
-10 300
-15 200
-20 100
-25 0
Xmin Xmax -8 -6 -4 -2 0 2 4 6 8
Pipelength (m)
Pipe inclination (deg)


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Step 2)
Sort elements in the detailed profile by inclination in ascending order – divide into
0subsections if required

-200
Elevation (m)

-400

-600

-800

-1000

-1200
0 100000 200000 300000 400000 500000 600000
Distance (m)
-200 5
-300 4
-400 Original profile 3
Inclination (deg)

-500 2
Elevation (m)

-600
-700
Inclination
1
0
Step 3)
-800 -1 Lump together the sorted elements to
-900 -2
-1000 -3 longer pipes, starting with the element
-1100 Lumped, but not redistributed profile -4
-1200 -5
with the steepest downhill inclination.
0 50000 100000 The length of each pipe element is then
Distance (m)
limited by dominating criteria in 1).

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

600000 2000
grouping by inclination classes Original profile 20-70 km
Lumping by inclinations in 1800 'lumping by inclination in ascending order'
500000 ascending order
1600 'Sorted by inclination classes'

Condensate content [m3]
1400
Accumulated length (m)

400000
1200

300000 1000

800
200000
600

400
100000
200

0 0
-5 -4 -3 -2 -1 0 1 2 3 4 5 30 35 40 45 50 55 60 65 70
Inclination (deg)
Export flow rate [MSm3/d]


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Step 4)
Redistribution of elements by “Simulated Annealing” (Travelling salesman problem)
“minimize distance between detailed profile and simplified profile”
0

-200

Elevation (m)
-400

Cost function: -600

-800

F ( y)  i wi  ( yi  yi ) 2
-1000

-1200
0 100000 200000 300000 400000 500000 600000
Distance (m)

0

yi : values from the simplified profile -50
-100

Elevation (m)
-150
-200

ŷi : values from the detailed profile -250
-300
-350
-400
0 100000 200000 300000 400000 500000 600000

wi : weight factor Distance (m)

-230

where as “i” denotes: -240
Elevation (m)

-250
-260

1) Elevation -270
-280
-290

2) “Total Climb” -300
70000 75000 80000 85000 90000 95000 100000
Distance (m)
3) “Pipeline Indicator” *

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Comparison
Original Simplified Method 1 Method 2
profile profile profile profile
Number 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 4,187
Total length [m] 554,505 554,400 554,507 554,505
Pipeline geometry
-230
-240
Elevation [m]

-250
-260
-270
-280
-290
-300 Original profile
70000 75000 80000 85000 90000 Simplified profile
95000 100000
Discretized profile (method 1)
Distance from offshore platform [m] Discretized profile (method 2)


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Angle distributions
Pipe angle distribution
80000
Total pipe length per angle group [m]

Original profile
70000 Discretized profile (Method 2)
Discretized profile (Method 1)
60000
Simplified profile
50000

40000

30000

20000

10000

0
1)

5)
5)
)

)

)
(-3 0)

(-1 )

)

)

)
)

)
)

)

)
1)

20

90
0

,5

,7

,9
,2

,3
-5

25

.2

.4
.0

.2
.7
-6

-2

,-

,0

,0

(4

(6

(8
0,

0.

.5

.5

0,

0,
,0

,1
,0
(-2
0,

0,

(1

(2
,-

.1

.3

(1

(3
(0

(1
.5
(-9

(0

(0
.5

(0
(-0

Pipe angle group [deg]


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Steady-state simulation: original vs. discretization
Condensate content vs. export flow rate
42" ND pipeline - Fluid: 50%J0/50%J1 - OLGA steady-state pre-processor
2000
Original profile 20-70 km
1800
Discretized profile 20-70 km (Method 1)
Condensate content [m3]

1600
Discretized profile 20-70 km (Method 2)
1400

1200

1000

800

600

400

200

0
30 35 40 45 50 55 60 65 70

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Steady-state simulation: simplified vs. discretization
Total condensate content vs. export flow rate
10000 200
Total condensate content (simplified profile)
Total condensate content (method 1)
9000 Total condensate content (method 2)
Total condensate content [m3]

Inlet pressure (simplified profile) 180
8000 Inlet pressure (method 1)
Inlet pressure (method 2)

Inlet pressure [bara]
7000
160
6000

5000 140

4000
120
3000

2000
100
1000

0 80
20 25 30 35 40 45 50 55 60 65 70


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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

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Discretization Methods for Multiphase
Flow Simulation of Ultra-Long Gas-
Condensate Pipelines

Erich Zakarian, Henning Holm
Shtokman Development A.G., Russia
erich.zakarian@total.com, hthol@statoilhydro.com

Dominique Larrey
Total E&P, Process Department, France
dominique.larrey@total.com


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Back-up


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Why discretization is so important?
Total condensate content vs. export flow rate Poor discretization
10000  Incorrect design of
9000
Simplified profile
receiving facilities
Total condensate content [m3]

8000
 Wrong operating
7000

6000
envelope
5000  Reduced operating
4000 flexibility
3000

2000
 Higher risk of
1000
continuous flaring
0  Wrong model tuning
20 30 40 50 60 70
against field data


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Seabed profile
200

100
Elevation [m]

0

-100

-200

-300
3D Side Scan Sonar imagery

-400
0 100 200 300 400 500
Distance [km]

Ice scours & Pockmarks
depressions Elongated pockmarks Ridges & ice scours

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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


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Comparison of the discretization methods
Pipeline geometry
200 5000
Pipe elevation (discretized profile: first method) [m]
100

Total climb [m]
Pipe elevation (discretized profile: second method)[m] 4000
Elevation [m]

0 Total climb (discretized profile: first method) [m]
Total climb (discretized profile: second method) [m] 3000
-100
2000
-200
-300 1000

-400 0
0 100000 200000 300000 400000 500000

Pipe inclination (discretized profile: first method) [m]
Pipe inclination
10
8 Pipe inclination (discretized profile: second method) [m]
6
Inclination [deg]

4
2
0
-2
-4
-6
-8
-10
0 100000 200000 300000 400000 500000


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OLGA® Geometry Editor

• Ok for removing noise from as-built
Box filter pipeline survey
• Not recommended for hilly pipelines

Angle • Requires pre-definition of angle groups
• Several tries are necessary
distribution • Extremely difficult or even impossible to
preservation satisfy the four criteria


Pipeline discretization (BHR Multiphase 2009)

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