NEW METHODS FOR PIPELINE DESIGNChase Waite Debora Faria

Kristy Booth Miguel Bagajewicz

Introduction

Goals Background Conventional

Pipeline

Network Design Mathematical

Models

Goals

Design a pipeline network with economically optimized configurations under growing and uncertain gas demands at multiple locations

RamifiedLinear Parallel

The Importance of Natural Gas

Natural gas is an attractive fuel because it is clean burning and efficient

97% of the natural gas consumed in

the U.S. is produced either in the U.S.

or in Canada

The U.S. could soon become part of a larger global market by increasing the imports of LNG

Natural Gas Demand Variability

Natural gas demand in North America is driven by:Relative prices of other fuelsEconomic growthWeather

Natural Gas Price Breakdown

2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 2007-2008$0

$2

$4

$6

$8

$10

$12

$14

$16

$18Transmission and Distribution Costs

Avera

ge H

eati

ng

Season

Pri

ce (

do

l-la

rs p

er

MC

F)

CONVENTIONAL METHODChase Waite

Kristy Booth

Conventional Method

Procedure:

1) Use analytical correlations or simulations to calculate pressure drop and compressor work

Over a range of flow rates for each pipe size and pressure parameter

2) Estimate costs for each pipe size and compressor

3) Create “J-curves” for each combination of pipe sizes

4) Choose an optimum pipe diameter and pressure for each segment as well as compressor sizes

One Segment Network

50 100 150 200 250 300 350 400 450 500$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

J-CurveNPS = 18NPS = 16NPS = 20NPS = 22

Flow Rate (MMSCFD)

Tota

l A

nn

ual

Cost

per

MC

F

Conventional Method

Problems: Analytical methods predict inaccurate

pressure drops J-curves are too time-consuming for

large-scale application J-curves become exponentially more time

consuming J-curves do not efficiently allow for future demand

variability Our Goals:

Show error in analytical method Using simulator (Pro-II) data, show error in J-curves Highlight results from an alternative method.

Correlations

Where Q = gas volumetric flow rate, MMSCFD

E = pipeline efficiency

Le = equivalent length of pipe segment, mi.

With a known gas flow rate and P2 we can find the required compressor outlet pressure

ηa = compressor adiabatic efficiencyγ = ratio of specific heats of gas, dimensionless

T1=suction temperature of gas

P1 = suction pressure of gas

P2=discharge pressure of gas

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Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

Simulation Highlights

Pro-II was used first for a single

pipe segment with compressor

Simulations were run for increasing

flow rates at four different pipe

diameters

Pro-II was used to find the

compressor work and outlet

pressure

Overall heat transfer coefficient

calculated to be 0.3 Btu/hr-ft2˚F

Natural Gas Composition Used

Natural Gas Component

Mole Fraction

C1 0.949

C2 0.025

C3 .002

N2 0.016

CO2 0.007

C4 0.0003

iC4 0.0003

C5 0.0001

iC5 0.0001

O2 0.0002

Union Gas http://www.uniongas.com/aboutus/aboutng/composition.asp

Simulation set up

In the Pro-II simulations, the compressor outlet pressure, Pcomp, was varied to give a downstream pressure of P2 = 800 psi.

The compressor inlet pressure P1 was set to equal P2

P1 = 800 psig

Pcomp P2 = 800 psig

L = 120 mi

Q = 50 – 500

MMSCFD

Panhandle Versus Simulation

150 200 250 300 350 4000

5

10

15

20

25

30

35

40 Pressure Drop Error with Pipe-line

Efficiency = 0.92NPS = 16

NPS =18

NPS =20

NPS = 22

Flowrate MMSCFD

Perc

en

t E

rror

Error with respect

to simulations

using the literature

value for the

pipeline efficiency

of 0.921,2,3

1 Lyons, Plisga. Standard Handbook of Petroleum & Natural Gas Engineering (2nd Edition). 2005 by Elsevier

2 McAllister.  Pipeline Rules of Thumb Handbook - A Manual of Quick, Accurate Solutions to Everyday Pipeline Engineering Problems (6th Edition). 2005 by Elsevier

3 Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

Panhandle Versus Simulation

150 200 250 300 350 4000

5

10

15

20

25

30

35

40 Pressure Drop Error with Pipe-line

Efficiency = 0.97NPS = 16

NPS =18

NPS =20

NPS = 22

Flowrate MMSCFD

Perc

en

t E

rror

After minimizing

error with respect to

simulations by

changing the

pipeline efficiency (E)

in the Panhandle

equation

Still requires use of simulations in order to accurately

predict the pipeline efficiency and use the Panhandle

equations.

It is pointless to use the equation at this point if a simulator is

available

COSTSChase Waite

Kristy Booth

Cost Assumptions

The cost for steel per ton was assumed to be $800 per ton based on values from Omega Steel Company

The fuel cost was assumed to be $3.72 per MCF based on an adjusted 2005 value ($3.00 per MCF)

The miscellaneous costs were estimated to be 40% of the equipment costs

Omega Steel Company http://www.omegasteel.com/Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

Total Pipe Costs

Pipe Installation Costs vary by pipe size:

Total Pipe Costs = PMC + Installation + Wrapping & Coating

Typical Pipeline Installation CostsNPS Cost, k$/km

16 206

18 261

20 393

24 527

Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

Compressor Station Costs

Compressor station costs depend on the required power of installed compressors

The following cost includes the labor and materials costs for compressor stations:

61037.179979.0 HPCostCompressor

Total Annual Costs

Total Annual Costs include:• Annualized Capital Costs

• Annual Fuel Costs

• Operating & Maintenance Costs

Where Q is flow rate, MMSCFD

Based on 350 operating days per year

Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

RESULTSChase Waite

Kristy Booth

50 100 150 200 250 300 350 400 450 500$0.00

$1.00

$2.00

$3.00

$4.00

$5.00 J-CurveNPS = 18NPS = 16NPS = 20

Flow Rate (MMSCFD)

Tota

l A

nn

ual

Cost

per

M

CF

Selecting the Optimum

To select the optimum, select the lowest Total Annual Cost per MCF at the flow rate of interest

However, this will only represent the TAC at that flow rate, and does not consider the more realistic case with change in demand through time.

4,530 HP 14,130 HP

Modified J-Curves

This case accounts for a range of flow rates a compressor can actually achieve

However, it does not account for the changes in compressor efficiency as the flow rate deviates from the design point

One compressor for the whole range - instead of one compressor for each point.

50 100 150 200 250 300 350 400 450 500$0.20

$0.70

$1.20

$1.70

$2.20Total Cost per MCF

NPS = 16

Flow Rate (MMSCFD)

Tota

l A

nn

ual

Cost

per

10

0 k

m

per

MC

F

Range of flow rates and costs for a com-pressor designed at Q = 200 Q = 400Q =

300

Original J-curve

Including Compressor Efficiency

This examines the difference between using a constant compressor efficiency of 0.8 versus using a variable compressor efficiency

100 150 200 250 300 350 400 450 500 5500.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Total Cost per MCF For NPS = 16

Flow Rate (MMSCFD)

Tota

l A

nn

ual

Cost

per

M

CF

Considering Effi-ciency as a function of flow rate at Q = 400

Fixed Efficiency of 80% at Q = 400(solid line)

TWO-SEGMENT NETWORKChase Waite

Kristy Booth

Two-Segment Network Goals

We want to show that:

Even using Pro-II simulations becomes extremely complicated and time consuming for a simple two-segment pipeline

Optimizing the segments in the wrong order may not lead to the economic optimum

Simulator Trials

In the Pro-II simulations, P1 and P5 are always 800

psig

Three pressure parameters (P3) were selected –

750, 800, and 850 psig Both segments will have distinct optimums

P1 = 800 psig

P2 P5 = 800 psig

L = 60 mi

Q = 100 – 500 MMSCFD

L = 60 mi

P3 P4

Q = 50 MMSCFD

100 150 200 250 300 350 400 450 500$0.00

$0.20

$0.40

$0.60

$0.80

$1.00

$1.20

$1.40

$1.60

$0.34

0.356

Segment 1P = 850

NPS = 16NPS = 18NPS = 20NPS = 22

Flow Rate (MMSCFD)

TA

C p

er

MC

F

100 150 200 250 300 350 400 450 500$0.00

$0.20

$0.40

$0.60

$0.80

$1.00

$1.20

$1.40

$1.60

0.353

Segment 1P = 800

NPS = 16

NPS = 18

NPS = 20

NPS = 22

Flow Rate (MMSCFD)

TA

C p

er

MC

F

Comparing costs of Segment 1 at Q = 300 for three different pressures,

P = 800 is least optimal

Optimizing Segment 1

The lowest TAC at Q=300 is achieved with NPS = 18 for all three pressures

P = 750 gives the lowest overall TAC for NPS = 18

100 150 200 250 300 350 400 450 500$0.00

$0.20

$0.40

$0.60

$0.80

$1.00

$1.20

$1.40

$1.60

0.3287

Segment 1P = 750 NPS =

16

NPS = 18

Flow Rate (MMSCFD)

TA

C p

er

MC

F

Optimizing Segment 1

Since P = 750 was the optimum pressure parameter for Segment 1, we then determine the optimum diameter for Segment 2 at P = 750

The optimum diameter is then NPS = 18 Then, optimize the system starting with segment 2

100 150 200 250 300 350 400 450 500$0.00

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

0.3026

0.3063

Segment 2P = 750 NPS = 16

NPS = 18NPS = 20NPS = 22

Flow Rate (MMSCFD)

TA

C p

er M

CF

100 150 200 250 300 350 400 450 500$0.40$0.50$0.60$0.70$0.80$0.90$1.00$1.10$1.20

0.907

0.7340.652 0.616 0.607 0.613 0.629 0.652

Optimizing Segment 2; P=850

NPS = 18 Segment 1 & NPS = 18 Seg...

Flow Rate (MMSCFD)

TA

C p

er M

CF

Optimizing Segment 1 first, Compared to Optimizing Segment 2 first

100 150 200 250 300 350 400 450 500$0.4

$0.6

$0.8

$1.0

$1.2

$1.4

1.299

0.908

0.7400.663 0.631 0.626 0.635 0.654 0.679

Optimizing Segment 1; P = 750 NPS = 18 Seg-ment 1 & NPS = 18 Segment 2

Flow Rate (MMSCFD)

TA

C p

er M

CF

Optimizing segment 2 first results in the optimum design

100 200 300 400 500$0.5

$0.6

$0.7

$0.8

$0.9

$1.0

$1.1

$1.2

$1.3

$1.4

$1.5

0.6164

0.6174

Overall OptimumP=850

NPS = 18 Seg-ment 1 & NPS = 16 Segment 2

NPS = 18 Seg-ment 1 & NPS = 18 Segment 2

Flow Rate (MMSCFD)

TA

C p

er

MC

FOverall Optimum & Relevance of Optimum

50 100 150 200 250 300 350 400 450 500 5500.4

0.6

0.8

1

1.2

1.4

0.63

P = 750 Optimizing Segment 1

NPS = 18 Segment 1 & NPS = 18 Segment 2

Flow Rate (MMSCFD)

TA

C p

er

MC

F

Difference in TAC per MCF

Difference in TAC per year

$ 0.001 $ 105,000

$ 0.015 $ 1,600,000

By analyzing all 48 J-curves, or getting lucky and picking the correct order to optimize the network, the optimum pressure is 850 psig, and the optimum pipe sizes are 18 inches in both segments

Economic Optimums

Segment

Optimum Pressure

Optimum Diameter

s

TAC per MCF

Total Annual Cost

(millions)

1 P = 750 18 & 18 $ 0.631 $ 66

2 P = 850 18 & 18 $ 0.616 $ 65

Both* P = 850 18 & 18 $ 0.616 $ 65

Two-Segment Network

Optimizing Segment 1 first gave the incorrect solution

It is unlikely to predict the order segments should be optimized in that will produce the overall optimum

All possible combinations must be analyzed to find overall optimum

*In order to analyze both segments at once, 48 J-curves must be analyzed for even this simple two pipe network!

Conclusions

For a two pipe network, there are two sequences to optimize the network For four pipes; 24 different sequences or a 1 in

24 chance of getting lucky It becomes exponentially unlikely the pipes

will be optimized in the correct order J-curves require exponentially more time

gathering and analyzing simulator data

Drawback of J-Curve Method based on Simulation

For a two-pipe segment: 9 flow rates, 4 pipe diameters, 3 pressures Requires 432 simulations, or 3 hours! 48 possible diameter and pressure combinations

A four-pipe segment requires 62,208 simulations, or 150 hours!

The soon to be discussed ramified section would take over 1 billion simulations and 10 years!

This is only for fixed flow rates, and does not take into consideration changes in demand or price!

MATHEMATICAL MODELSChase Waite

Kristy Booth

Mathematical Models

Goals: Show that the non-linear mathematical

model is more accurate than using J-curves

Show that mathematical models are much quicker than J-curves

Show that the mathematical models allow for analysis of designs too complicated for J-curves

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Mathematical Model

Mathematical Model Constraints

Constraints: Flow rate balance in each node Consumers demand Pressure drop equations Required (re)compression work Maximum allowed velocities inside the pipes Diameter choice Compressors timing installation Compressors capacities Pressures relations

USE LOGIC CONSTRAINTS (BINARIES)

Mathematical Model

Energy Balances (pressure drop through the pipe sections)

Required (re)compression work

A linear model was developed which relaxes the pressure parameters and estimates the upper and lower bounds of the operating conditions

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Relaxed variables

Linear regression of simulation data

used to find A = 67.826 and B = -2 x

107 / -∆Z

688 simulations to find 108 different

correlations for the pipeline networks

analyzed in this project

Single Pipe Network

2-Pipe Network

9-Pipe Network with elevation and

demand variations, and without

Ramified Network

Parameters of pressure drop equation

0 20000000 40000000 600000000

500000000

1000000000

1500000000

2000000000

2500000000

3000000000

f(x) = 67.8256997 x − 15686518R² = 0.999921489519673

NPS 28 Segment 2

Pin2-Pout2

5

2

D

LQ

Mathematical Model

Instead of performing countless simulations for a network, a relatively few simple simulations can find the constants A and B. Then, the mathematical model can find the economic optimum for the network

Since there is some error in the simplification of the pressure drop analysis, check the optimum solution with a simulator to determine the most accurate pressure drop and corresponding compressor power

Error in resulting correlation

0 50 100 150 200 250 300 350 4000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000Pressure Drop from Pro-II, and from

the Empirical Equation

16; Pro-II16; Analytical18; Pro-II18; Analytical20; Pro-II

Flow Rate (MMSCFD)

Pre

ssu

re D

rop

(k

Pa)

The correlation analyzed above was found to be accurate, and was therefore used in the mathematical models

Model – Single Pipe Segment

Mathematical Model Pressure Drop Error

QMMSCFD

dP Model (kPa)

dP Pro-II (kPa)

% Error

200 4975 5055 1.62

300 7425 7326 1.34

400 9950 9845 1.05

Mathematical model optimized a single pipe segment for three flow rates

∆Z=0 with the following results:

NPS 18

Mathematical Model Results

Non Linear Model – 2 Pipe Network

Pipe 1 Pipe 2

Pipe Diameter (in) 22 22

Compressor Work (hp)

10,740 0

Pressure Drop (psi)

1,830 1,490

TAC Model $ 0.596

TAC J-Curves $ 0.616 The linear model predicted that the range for the Total Annual Cost would be between $ 0.68 and 0.84 million for the TAC

Remember, this required 48 J-curves and 432 simulations with the conventional method!

Nine-Pipe Segment

0 5 10 15 20 2525

30

35

40

45

50

Variation in Demand as a Function of Time for

Segment 3

Year

MM

m3

/day

Model for Nine-Pipe Segment

The linear model predicted that the range for the Total Annual Cost would be between 375 million and 482 million for the TAC

This would take 15.5 billion simulations!

Non Linear Model – 9 Pipe Network

Pipe 1 2 3 4 5 7 6 8 9

Pipe Diameter (in)

36 36 36 32 32 24 24 24 24

Compressor Work (hp)

16,700 730 0 0 0 0 0 0 0

Ramified Pipeline Network

C2

23,000HP

C3

C4

C6

C7

18.24 Mm3/day 2.3%30 km

80 km102 km

57 km

27,000 HP

2148.2 Mm3/day3%

134.4 Mm3/day

81 km

25 km 200 km

38 km

3617.1 Mm3/day 2.6%

384.2 Mm3/day 3.7%

C5

C1

Model Cost Analysis (Ramified)

The linear model predicted that the range for the Total Annual Cost would be between 95 million and 130 million for the TAC

Non Linear Model – Ramified NetworkPipe Pipe S1-C1

Pipe C1-C2

Pipe C2-C3

Pipe S2-S4

Pipe S2-S5

Pipe C5-C6

Pipe C5-C7

Pipe Diameter (in) 24 24 24 24 28 28 24

Compressor Work (hp)

5,010 0 0 8,350 8,350 0 0

Pressure Drop (psi) 65 4,190 4,255 180 30 100 10

Ramified Pipeline Network

For the example ramified network: 8 pipe sections 4 pipe diameters 3 pressures

This would take 1.1 billion simulations

Working non-stop, this would take 10 years!

Conclusions

J-curves are too time consuming to use in the design of a pipeline network. Even the slightest complexity makes the task unrealistic

The use of a mathematical model saves time. We successfully developed one that picks the pipe diameters and compressor locations taking into account future variations in demand and addressing expansions rigorously. This task is close to impossible with a combinatorial use of J-Curves

References

1. Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

2. Energy Information Administration www.eia.doe.gov

3. Understanding Natural Gas Markets Lexecon

4. Fundamentals of Momentum, Heat and Mass Transfer, Welty, et. al., © 1969 John Wiley & Sons, Inc.

5. Natural Gas Compressor Stations on the Interstate Pipeline Network: Developments Since 1996

6. U.S. Department of Labor Bureau of Statistics

7. Internal Report – Pipeline Cost Estimation, Sarah Scribner, Debora Faria and Miguel Bagajewicz, University of Oklahoma August 2007

8. National Post www.nationalpost.com/rss/Story.html?id=145263

9. www.rolfkenneth.no/NWO_review_Sutton_Soviet.html

10. GE Energy http://www.geoilandgas.com

11. Union Gas http://www.uniongas.com/aboutus/aboutng/composition.asp

12. Omega Steel Company http://www.omegasteel.com/

QUESTIONS?

Thanks to Dr. Miguel Bagajewicz and Debora Faria