Transcript NEW METHODS FOR PIPELINE DESIGN Chase Waite Kristy Booth Debora Faria Miguel Bagajewicz Introduction     Goals Background Conventional Pipeline Network Design Mathematical Models Goals  Design a pipeline network with economically optimized configurations under growing and.

NEW METHODS FOR
PIPELINE DESIGN
Chase Waite
Kristy Booth
Debora Faria
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
Linear
Parallel
Ramified
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 fuels
 Economic
 Weather
growth
Average Heating Season Price (dollars per MCF)
Natural Gas Price Breakdown
$18
Transmission and Distribution Costs
$16
Commodity (the gas itself)
$14
$12
$10
$8
$6
$4
$2
$0
2002-2003
2003-2004
2004-2005
2005-2006
2006-2007
2007-2008
CONVENTIONAL METHOD
Chase 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
$5.00
J-Curve
Total Annual Cost per MCF
$4.00
NPS = 18
NPS = 16
NPS = 20
NPS = 22
$3.00
$2.00
$1.00
$0.59
$0.58
$0.00
50
100
150
200
250
300
350
Flow Rate (MMSCFD)
400
450
500
Conventional Method

Problems:
 Analytical methods predict inaccurate
pressure drops
 J-curves are too time-consuming for
large-scale application

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.


J-curves become exponentially more time
consuming
Correlations
1.0788
 Tb 
Q  435.87E  
 Pb 

 P12  e s P22  2.6182

D
 G 0.8539T L Z 
f e


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
 1


    Z1  Z 2  1  P2  
QT1 
HP  0.0857
    1
   1   2  a   P1 


ηa = compressor adiabatic efficiency
γ = ratio of specific heats of gas, dimensionless
T1=suction temperature of gas
P1 = suction pressure of gas
P2=discharge pressure of gas
Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC
Simulation Highlights

Pro-II was used first for a single pipe
Natural Gas Component
Mole Fraction
C1
0.949
Simulations were run for increasing flow rates
C2
0.025
at four different pipe diameters
C3
.002
N2
0.016
CO2
0.007
C4
0.0003
iC4
0.0003
C5
0.0001
iC5
0.0001
O2
0.0002
segment with compressor


Pro-II was used to find the compressor work
and outlet pressure

Natural Gas Composition Used
Overall heat transfer coefficient calculated
to be 0.3 Btu/hr-ft2˚F
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
Q = 50 – 500
Pcomp
P2 = 800 psig
MMSCFD
P1 = 800 psig
L = 120 mi
Panhandle Versus Simulation
Error with respect to
literature value for the
pipeline efficiency of
0.921,2,3
35
Percent Error
simulations using the
Pressure Drop Error with Pipeline
Efficiency = 0.92
40
NPS = 16
30
NPS =18
25
NPS =20
20
NPS = 22
15
10
5
0
150
200
250
300
350
400
Flowrate MMSCFD
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
After minimizing error with
changing the pipeline
efficiency (E) in the
Panhandle equation
35
Percent Error
respect to simulations by
Pressure Drop Error with Pipeline
Efficiency = 0.97
40
NPS = 16
30
NPS =18
25
NPS =20
20
NPS = 22
15
10
5
0
150
200
250
300
350
400
Flowrate MMSCFD
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
COSTS
Chase 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
($3.00 per MCF)
The miscellaneous costs were estimated to be
40% of the equipment costs
Omega Steel Company http://www.omegasteel.com/
Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC
Total Pipe Costs

Pipe Installation Costs vary by pipe size:
Typical Pipeline Installation Costs

NPS
Cost, k$/km
16
206
18
261
20
393
24
527
Total Pipe Costs = PMC + Installation + Wrapping & Coating
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:

CompressorCost  0.79 1799.7 HP  3106

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
RESULTS
Chase Waite
Kristy Booth
Total Annual Cost per MCF
Selecting the Optimum
J-Curve
$5.00
NPS = 18
NPS = 16
NPS = 20
NPS = 22
$4.00
4,530 HP
14,130 HP
$3.00
$2.00
$1.00
$0.00
50
100
150
200
250
300
350
400
450
500
Flow Rate (MMSCFD)


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.
Modified J-Curves
One compressor for the whole range - instead of one compressor for each point.
Total Annual Cost per 100 km per MCF

Total Cost per MCF
NPS = 16
$2.20
Range of flow rates and
costs for a compressor
designed at Q = 200
$1.70
Q = 300
$1.20
Q = 400
$0.70
Original J-curve
$0.20
50
100
150
200
250
300
350
400
450
500
Flow Rate (MMSCFD)


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
Including Compressor Efficiency
Total Annual Cost per MCF
1.8
Total Cost per MCF For NPS = 16
1.6
Considering Efficiency
as a function of flow
rate at Q = 400
1.4
1.2
Fixed Efficiency of 80%
at Q = 400
(solid line)
1
0.8
0.6
0.4
100
150
200
250
300
350
400
Flow Rate (MMSCFD)

This examines the difference between using a
constant compressor efficiency of 0.8 versus
using a variable compressor efficiency
450
500
550
TWO-SEGMENT NETWORK
Chase 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 twosegment 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
Q = 100 – 500
MMSCFD
P1 = 800 psig
P2
P3
P4
L = 60 mi
P5 = 800 psig
L = 60 mi
Q = 50 MMSCFD
$1.60
Segment 1
P = 850
TAC per MCF
$1.20
NPS = 16
NPS = 18
NPS = 20
NPS = 22
$0.80
$0.34
$0.40
0.356
$0.00
100
200
300
400
Flow Rate (MMSCFD)
Segment 1
P = 800
TAC per MCF
$1.60
500
Comparing costs of
Segment 1 at Q = 300 for
three different pressures,
P = 800 is least optimal
NPS = 16
$1.20
NPS = 18
NPS = 20
$0.80
NPS = 22
$0.40
0.353
$0.00
100
150
200
250
300
350
Flow Rate (MMSCFD)
400
450
500
Optimizing Segment 1
$1.60
Segment 1
P = 750
$1.40
NPS = 16
NPS = 18
TAC per MCF
$1.20
NPS = 20
$1.00
NPS = 22
$0.80
$0.60
$0.40
0.3287
$0.20
$0.00
100
150
200
250
300
350
400
450
500
Flow Rate (MMSCFD)


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
Optimizing Segment 1
$3.00
Segment 2
P = 750
TAC per MCF
$2.50
NPS = 16
NPS = 18
$2.00
NPS = 20
NPS = 22
$1.50
$1.00
$0.50
0.3026
$0.00
0.3063
100
200
300
400
500
Flow Rate (MMSCFD)

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
TAC per MCF
Optimizing Segment 1 first, Compared
to Optimizing Segment 2 first
Optimizing Segment 1; P = 750
$1.4
$1.21.299
NPS = 18 Segment 1 &
NPS = 18 Segment 2
$1.0
$0.8
0.908
0.740
$0.6
0.663
0.631
0.626
0.635
0.654
0.679
250
300
350
400
450
500
$0.4
100
150
200
Flow Rate (MMSCFD)
Optimizing segment 2
first results in the
optimum design
Optimizing Segment 2; P=850
TAC per MCF
$1.20
$1.00
NPS = 18 Segment 1 &
NPS = 18 Segment 2
0.907
$0.80
0.734
$0.60
0.652
0.616
0.607
0.613
0.629
0.652
250
300
350
400
450
500
$0.40
100
150
200
Flow Rate (MMSCFD)
Overall Optimum & Relevance of Optimum
Overall Optimum
P=850
$1.5
TAC per MCF
$1.1
$0.9
$0.7
1.2
NPS = 18 Segment 1 &
NPS = 18 Segment 2
1
0.8
0.6
0.63
0.4
50
150
250
350
450
550
Flow Rate (MMSCFD)
NPS = 18 Segment 1 &
NPS = 16 Segment 2
NPS = 18 Segment 1 &
NPS = 18 Segment 2
NPS = 18 Segment 1 &
NPS = 20 Segment 2
NPS = 18 Segment 1 &
NPS = 22 Segment 2
$1.3
P = 750 Optimizing Segment 1
1.4
TAC per MCF
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
Difference in Difference in
TAC per MCF TAC per year
$ 0.001
$ 105,000
$ 0.015
$ 1,600,000
0.6174
0.6164
$0.5
100
200
300
Flow Rate (MMSCFD)
400
500
Two-Segment Network
Economic Optimums



Segment
Optimum
Pressure
Optimum
Diameters
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
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 MODELS
Chase 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
Mathematical Model
NPV   DFt * ( Revenuet  FCIt )
WS s ,t k  1   3.0127 10
t
FCI t  Pipet  Comprt
Pipet   XDSCs ,c,d(33)
,t * PCd   XDCCc ,c*,d ,t * PCd
s
c
d
c
c*
d
3
W  3.0127 10
Comprss,t  (VCC * Capss,t  XCSs,t * FCC)
WC c ,t k  1  3.0127 10
c*
c*
QCc,t  Demandc,t
c, t
K Q  P P
n
b
2
1
2
2


 XDCC
 XDSC
c ,c*,d ,t
d
s ,c , d ,t
 XPCCc,c*,t
 XPSCs,c,t
d
QCCc,c*,t  UBt * XPCCc,c*,t
QSCs,c,t  UBt * XPSCs,c,t
 XCS
s ,t
 PXCSs
s
t
 XCCs,t  PXCCc
t
c
c ,c*,t

 1

 
kT
s, t
amb



 Poutc
 Pin
c

 k 1 
z

 k 



 k 1 
z

 k 

 1


s, t

 1


c, t
t t *
c, t
Poutc,t  Pinc,t
c, t
Poutc,t  Pinc,t  M *  XCCs,t*
Capss,t  M * XCSs,t
t *t
DPs,t  SPs *  XCSs,t*
Q2L
2
 A * Pin2  Pout
 B * Z
5
D
 QCC

k 
c*
WS s ,t   Capss ,t*
c


Opert   WS s,t  WC c,t  *OPC * OPH
c
 s

QSCs,c,t  QCCc*,c  QCCc,c*  QCc,t
s

z
P  
k
Q
T1  2 
k  1  P1 

3
Comprt   Comprss ,t   Comprcc,t
s

 DP
c QSCs,c,t k STs  SPs
 s
k

1


3
c, t
s, t
s, t
t *t
Ve 
c, c*,t
s, c, t
c, c*,t
s, c, t
C
 0.5
QCCc2,c*,t LCCc ,c* 
  IDd5 * XDCCc ,c*,d ,t *  A  Poutc2  Pinc2*   B  ZCc*  ZSc*   ; c, c*, t
d
 
 


Penalt     Agreeds,t -  QSCs,c,t  * SPenals     Demandc,t - QCc,t * CPenalc 
c


 s 
  c
QSCs2,c,t LSCs,c   IDd5 * XDSCs,c,d ,t *  A  DPs2  Pinc2   B  ZCc  ZSs   ; s, c, t
d
Revenuet   QCc,t * CPricec   QSCs,c,t * SPrices  Opert  Penalt
c
s
c
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
USE LOGIC CONSTRAINTS (BINARIES)
 Compressors capacities
 Pressures relations

Mathematical Model

Energy Balances (pressure drop through the pipe
sections)
g c . R Z b .Tb
Qb  
1,856 Pb

2
58G H Pave
P P 
R Tave Z ave
Tave Z ave G L
2
out
2
in
 
2
Qb  A * Pin2  Pout
2
1 2.5
D
f

Required (re)compression work

k  Pout

W  0.0857 Qb T1

k  1  Pin




 k 1 
Z

 k 

 1



D5
 B * Z
L
Relaxed variables
A linear model was developed which relaxes the pressure parameters and estimates the
upper and lower bounds of the operating conditions
Parameters of pressure drop equation

Linear regression of simulation data used
to find A = 67.826 and B = -2 x 107 / -∆Z
NPS 28 Segment 2
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
Millions

Q2L
D5
3000
2500
2000
1500
y = 67.826x - 2E+07
R² = 0.9999
1000
500
0
0
10
20
30
Pin2-Pout2
40
50
Millions
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
Pressure Drop from Pro-II, and from the
Empirical Equation
20000
Pressure Drop (kPa)
18000
16000
16; Pro-II
16; Analytical
18; Pro-II
18; Analytical
12000
20; Pro-II
20; Analytical
10000
22; Pro-II
22; Analytical
14000
8000
6000
4000
2000
0
0
50
100
150
200
250
300
350
400
Flow Rate (MMSCFD)
The correlation analyzed above was found to be accurate, and was therefore used in
the mathematical models
Model – Single Pipe Segment
Mathematical model optimized a single pipe segment for three flow rates
∆Z=0 with the following results:
Mathematical Model Pressure Drop Error
Q
dP Model
dP Pro-II
MMSCFD
(kPa)
(kPa)
200
4975
5055
1.62
300
7425
7326
1.34
400
9950
9845
1.05
NPS 18
% Error
Mathematical Model Results
Non Linear Model – 2 Pipe Network
Pipe 1
Pipe 2
22
22
Compressor Work (hp)
10,740
0
Pressure Drop (psi)
1,830
1,490
Pipe Diameter (in)


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
MMm3/day
Variation in Demand as a Function
of Time for Segment 3
50
45
40
35
30
25
0
5
10
15
Year
20
25
Model for Nine-Pipe Segment
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


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!
Ramified Pipeline Network
102 km
23,000
HP
80 km
C2
30 km
C3
18.24 Mm3/day
2.3%
2148.2 Mm3/day
3%
C1
C4
134.4 Mm3/day
57 km
27,000
HP
81 km
25 km
38 km
C5
200 km
3617.1 Mm3/day
2.6%
C6
C7
384.2 Mm3/day
3.7%
Model Cost Analysis (Ramified)
Non Linear Model – Ramified Network
Pipe S1-C1 Pipe C1-C2 Pipe C2-C3 Pipe S2-S4 Pipe S2-S5 Pipe C5-C6 Pipe C5-C7
Pipe
Pipe Diameter (in)
Compressor Work (hp)
Pressure Drop (psi)

24
24
24
24
28
28
24
5,010
0
0
8,350
8,350
0
0
65
4,190
4,255
180
30
100
10
The linear model predicted that the range for the
Total Annual Cost would be between 95 million and
130 million for the TAC
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