Discretization Methods for Multiphase Flow Simulation...

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.

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

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 500Distance [km]

Elev

atio

n [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

24

3

Original profile


SDAG

Liquid holdup vs. pipe inclination

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 10Pipe inclination [deg]

Liqu

id h

oldu

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 objectiveMethod 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

( ) ( )[ ] 25066091490 ...tan.+−×= ii ArcHoldup θ

πθ

( ) ( )[ ]1000

0

1

1 ××−

=

∑

∑

=

=N

ii

N

iii

L

LHoldupHoldupPI

θ


SDAG

Holdup function vs. OLGAS

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 10Pipe inclination [deg]

Liqu

id h

oldu

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 < 0 Pipeline profile is globally sloping downwardsNo particular operating problem to be expected

0 < PI < 20 Pipeline profile is nearly horizontal or over-simplifiedNo particular operating problem to be expected

20 < PI < 40 Pipeline profile is relatively flat or slightly hillyPossible troubles at very low flow rates or during restart

40 < PI < 80 Pipeline crosses hilly terrainDesign & Operation needs particular attention

80 < PIPipeline profile is very hilly or very steepDesign & Operation needs very careful attentionValidity of simulation software to be checked

From Total E&P experience in gas-condensate pipelinedesign and operation

Shtokman pipeline profile indicator = 79.7


SDAG

Step 1: sub-profile selection

020406080

100120140160180

0 100000 200000 300000 400000 500000

Pipe

line

indi

catto

r [-]

Distance from offshore platform [m]

-10-8-6-4-202468

10

230000 240000 250000 260000 270000 280000

Incl

inat

ion

[deg

]


Pipe inclination

-10-8-6-4-202468

10

410000 420000 430000 440000 450000 460000

Incl

inat

ion

[deg

]


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

Total climb [m

]Elev

atio

n [m

]


Pipeline geometryPipe 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

-505

101520

0 100000 200000 300000 400000 500000

Incl

inat

ion

[deg

]


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

PI = 79.7 25.8

Step 2: result


SDAG

Step 3: complexification

-340

-335

-330

-325

-320

-315

-310

-305

0 2000 4000 6000 8000 10000


Elev

atio

n [m

]

Complexified profile

Simplified profile

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

Total climb [m

]Elev

atio

n [m

]


Pipeline geometryPipe 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

-505

101520

0 100000 200000 300000 400000 500000

Incl

inat

ion

[deg

]


Pipe inclinationPipe 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 length2. maximum elevation change for a pipe element3. 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)

Pipe

ele

vatio

n ch

ange

(m)

Xmin Xmax

Maximum elevation change

-25-20-15-10

-505

10152025

-8 -6 -4 -2 0 2 4 6 8Pipe inclination (deg)

Elev

atio

n ch

ange

(m)

01002003004005006007008009001000

Pipe

leng

th (m

)

Elevation change of single pipePipe 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

vatio

n (m

)

-1200-1100-1000-900-800-700-600-500-400-300-200

0 50000 100000

Distance (m)

Elev

atio

n (m

)

-5-4-3-2-1012345

Incl

inat

ion

(deg

)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)

Acc

umul

ated

leng

th (m

)

grouping by inclination classes

Lumping by inclinations inascending 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]

Con

dens

ate

cont

ent [

m3]

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)

Elev

atio

n (m

)

-400-350-300-250-200-150-100-50

0

0 100000 200000 300000 400000 500000 600000

Distance (m)

Ele

vatio

n (m

)

-300-290-280-270-260-250-240-230

70000 75000 80000 85000 90000 95000 100000

Distance (m)

Elev

atio

n (m

)


SDAG

Original profile

Simplifiedprofile

Method 1profile

Method 2profile

Number of pipes 108,784 554 2,766 2,550Pipeline profile indicator 79.7 25.8 80.3 80.3Total 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


Elev

atio

n [m

]

Original profileSimplified profileDiscretized profile (method 1)Discretized profile (method 2)


SDAG

Angle distributionsPipe angle distribution

0

10000

20000

30000

40000

50000

60000

70000

80000

(-90,

-60)(-3

0, -20)

(-10,

-5)(-2

, -1)

(-0.5,

-0.25

)(0,

0.01

)(0.

1, 0.2)

(0.3, 0

.4)(0.

5, 0.75

)(1,

1.25

)(1.

5, 2)

(2.5, 3

)(4,

5)(6,

7)(8,

9)(10

, 20)

(30, 9

0)

Pipe angle group [deg]

Tota

l pip

e le

ngth

per

ang

le g

roup

[m]

Original profileDiscretized profile (Method 2)Discretized profile (Method 1)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 70Export flow rate [MSm3/d]

Con

dens

ate

cont

ent [

m3]

Original profile 20-70 km

Discretized profile 20-70 km (Method 1)



SDAG

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


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

20 25 30 35 40 45 50 55 60 65 70


Tota

l con

dens

ate

cont

ent [

m3]

80

100

120

140

160

180

200

Inlet pressure [bara]

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 facilitiesWrong operating envelopeReduced operating flexibilityHigher risk of continuous flaringWrong model tuning against field data

Poor discretizationIncorrect design of receiving facilitiesWrong operating envelopeReduced operating flexibilityHigher risk of continuous flaringWrong 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 70Export flow rate [MSm3/d]

Tota

l con

dens

ate

cont

ent [

m3]

Simplified profile

Discretized profile (Method 1)

Discretized profile (Method 2)


SDAG

Seabed profile

-400

-300

-200

-100

0

100

200

0 100 200 300 400 500Distance [km]

Elev

atio

n [m

]

Ice scours & depressions Elongated pockmarks

PockmarksRidges & ice scours3D

Sid

e S

can

Son

ar im

ager

y


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


Elev

atio

n [m

]

0

1000

2000

3000

4000

5000

Total climb [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


Incl

inat

ion

[deg

]

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


SDAG

OLGA® Geometry Editor

Box filterBox filter

Angle distribution

preservation

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


SDAG

Next?• Improve the simplification step (method 1) to keep as many original high & low points as possible

• Sensitivity analysis to pipe sectioning (meshing) in dynamic simulation

• Seabed topography characterization with pipeline profile indicator

Build realistic profile when no detailed survey is available


SDAG

Hydraulic/level gradients at low flow rate

Keep as many original high & low points as possible to match hydraulic gradients

• Level gradients included in OLGA 6 (steady-state pre-processor)

• Implicitly included in dynamic mode but fine mesh is required


SDAG

Pipeline route

-400

-300

-200

-100

0

100

200

0 100 200 300 400 500Distance [km]

Elev

atio

n [m

]


SDAG

The devil is in the details…

‐360‐340‐320‐300‐280‐260‐240‐220

0 10 20 30 40 50 60 70 80 90 100

Elevation [m

]

Distance from offshore platform [km]

‐285

‐280

‐275

‐270

‐265

50 51 52 53 54 55 56 57 58 59 60


SDAG

050010001500200025003000350040004500

-400

-300

-200

-100

0

100

200

0 100000 200000 300000 400000 500000

Total climb [m

]Elev

atio

n [m

]


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

Pipe elevation & total climb vs. seabed topologyBe

nign Ice

scou

rs

& de

pres

sions

Pock

mar

ksEl

onga

ted

pock

mar

ks

Beni

gn

Elon

gate

d po

ckm

arks

Beni

gn

Beni

gnPo

ckm

arks

Ice

scou

rs

& po

ckm

arks

Beni

gn

Pock

mar

ksLa

ndfa

ll - S

hore

Ridg

es

& Ic

e sc

ours


PockmarksRidges & ice scours3D

Sid

e S

can

Son

ar im

ager

y


SDAG

Pipeline profile indicator vs. seabed topology

020406080

100120140160180

0 100000 200000 300000 400000 500000

Pipe

line

indi

catto

r [-]


Pock

mar

ks


PockmarksRidges & ice scours

Beni

gn Ice sc

ours

& de

pres

sions

Elon

gate

d po

ckm

arks

Beni

gn

Elon

gate

d po

ckm

arks

Beni

gn

Beni

gnPo

ckm

arks

Ice

scou

rs

& po

ckm

arks

Beni

gn

Pock

mar

ksLa

ndfa

ll - S

hore

Ridg

es

& Ic

e sc

ours

3D S

ide

Sca

n S

onar

imag

ery


SDAG

Method 1: sub-profile indicator and total climb

Length range [km] 0-10 10-20 20-70 70-140 140-180 180-200Pipeline indicator [-] 58.48 89.24 104.83 82.48 61.97 80.77Total climb [m] 55.04 75.12 483.90 612.43 199.31 131.14Length range [km] 200-220 220-230 230-280 280-320 320-360 360-410Pipeline indicator [-] 97.95 63.40 45.57 77.01 100.03 67.64Total climb [m] 189.26 58.97 171.22 273.30 386.93 254.57Length range [km] 410-460 460-500 500-510 510-540 540-554

Pipeline indicator [-] 106.54 38.09 64.23 85.74 151.63Total climb [m] 599.81 144.93 49.85 195.13 306.09


SDAG

‐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

Probability

NormStd‐

1

Inverse of the standard normal cumulative distribution

Cx = complexification coefficient

Rnd = random value between 0 and 1

( )RndNormStdCyy xoldi

newi

1−×+=

( ) ∫∞−

−

=x z

dzexNormStd 2

2

21π

Method 1: profile complexification


SDAG

Steady-state simulation: original vs. discretizationInlet pressure vs. export flow rate


110

120

130

140

150

160

170

180

190

10 20 30 40 50 60 70Export flow rate [MSm3/d]

Inle

t pre

ssur

e at

KP

20 [b

ara]

Original profile 20-70 kmDiscretized profile 20-70 km (Method 1)Discretized profile 20-70 km (Method 2)Back-pressure - Kilometer Point 70


SDAG

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


0

2000

4000

6000

8000

10000

12000

10 20 30 40 50 60 70Export flow rate [MSm3/d]

Con

dens

ate

cont

ent [

m3]

Original profile 20-70 km




SDAG

Dynamic simulationTotal condensate content vs. export flow rate

42" ND pipeline - Fluid: 50%J0/50%J1

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

30 35 40 45 50 55 60 65 70


Tota

l con

dens

ate

cont

ent [

m3]

First discretization method - OLGA SS pre-processorSecond discretization method - OLGA SS pre-processorFirst discretization method - OLGA dynamicSecond discretization method - OLGA dynamic


SDAG

CPU time

30 days

20 days

7 days5 days

28 35 49 70


Required simulation time to reach steady‐state flow conditions

Simulation time

21 h 20 h

10 h

5 h

33 h

21 h

10 h6 h

28 35 49 70


Required computation time to reach steady‐state flow conditions

First discretization method

Second discretization method

DELL OptiPlex 755 - Intel® Core TM 2 Duo Processor E6750 (2.66 GHz) and 3.25 GB of DDR2 RAM.


SDAG

Dynamic simulationTotal condensate content and inlet pressure vs. time

Winter conditions - Fluid 50%J0 / 50%J1 - Flowrate = 49MSm3/d

1,038

1,040

1,042

1,044

1,046

1,048

1,050

1,052

1,054

0 1 2 3 4 5 6 7 8 9 10

Time [d]

Tota

l con

dens

ate

cont

ent [

m3]

139.3

139.4

139.5

139.6

139.7

139.8

139.9

140.0

140.1


Total condensate content [m3]



SDAG

Ramp-up from unpacked conditions

Transient


SDAG

3D Side Scan Sonar imagery

Objective: to detect potentially dangerous objects and seabed features


SDAG

Characterization

• Iceberg scours 46% - typically 250m across x 8m deep

• Pockmarks 20% - mostly ’elongated’ - 150m long x 5m deep

• Benign 34% - posing no problem for pipeline

Water depths

• Maximum 346m - mostly 200-250m

• Minimum 123m - except for final 3km shore approach

Seabed

• Generally soft clay

Shtokman pipeline route


SDAG

Pockmarks• Local craters/depressions of conical form• Related to fluid expulsion from seabed,

either liquid (water) or gas from natural or biogenic origin

• Apart from iceberg scours, the most prominent features found on the seabed

• Diameters from 5 to 120 m• Depths from 0.5 m to 8 m• Wall inclinations from 1.5° to 25°• Densities from 16 to 350 per km²• Can form chain-like features• Approximately 13,500 along trunkline

corridor


SDAG

Elongated pockmarks• Local elongated craters/depressions

• Lengths 60 – 400m,

• Widths 25 – 120m

• Depths 0.5 – 10m

• Wall inclinations in the main direction from 0.5° to 3.5°

• Opposite wall inclination from 2° to 7°


SDAG

Iceberg scours• Crisscrossing scours

• Depths 0.8 – 16 m

• Widths 37 – 300 m

• Lengths 3.5 – 6 km

• V-shaped or U-shaped cross-sections

• Wall inclinations 2.5° – 37.5°


SDAG

Gas export system


SDAG

Pipe wall thickness – 2x36” trunkline (X65)


SDAG

Pipe stability – 2x36” trunkline (X65)

Discretization Methods for Multiphase Flow Simulation...

Documents

Transcript of Discretization Methods for Multiphase Flow Simulation...