Transcript Pipeline Network Design Presentation 2

PIPELINE NETWORK
DESIGN
Landon Carroll & Wes Hudkins
Overview




Goals
Background Information
Conventional Pipeline
Optimization Analysis
Mathematical Model Analysis
 Expansion
 Conventional
Comparison
 Application

Conclusion and Recommendations
Goal

Create a program that will design an optimal
pipeline network, which is faster and more
accurate than conventional design methods
Natural Gas Industry



The US consumes 1.5 to 2.5
million cubic feet (MMscf) per
month
97% of this gas is piped from
the well all the way to your
furnace
Large upside due to clean
Natural Gas power plants and
Compressed Natural Gas CNG
automobiles
Natural Gas Price Breakdown
*Standard Heating value Gas of 1000 Btu/scf. Thus, $12/Mscf = $12/MMBtu
Pipeline Optimization Basics
Pipeline Optimization Methods

Hydraulic Analysis
 Conventional
 Various
Equations
derived from The
General Flow Equation
 New
Method
 General
Equation
combines constants into
two parameters, A and B

Economic Analysis
 Conventional
 J-Curves
 New
Method
 Mathematical
Programming using a
General Algebraic
Modeling System
(GAMS) interface
NATURAL GAS HYDRAULICS
Landon Carroll
Wes Hudkins
Natural Gas Hydraulics 101

Steady State Mechanical Energy Balance on Pipe:
(PE) + (ΔP) + (KE) + (Friction Loss) = 0
g  dy 
dP

 v  dv  f
dx v
2
0
D 2
In most liquids, density is constant:
y1  g 
v
2
1
2

P1

 hL  y 2  g 
v
2
2
2
Natural Gas:
Therefore, Integration is slightly more difficult
Use average z, T, and P to simplify integration:

P2

Natural Gas Hydraulics 101

KE: Negligible
∆P:

PE:

Friction Loss:

Therefore,
,
Combine, solve for Q:
General Flow Equation

Conventional Hydraulic Equations are derived from
this equation; just insert different values for the
friction factor, f
Conventional Hydraulic Equations
1.
2.
3.
4.
5.
6.
7.
8.
9.
Colebrook-White
Modified Colebrook-White
AGA
Panhandle
Weymouth
IGT
Spitzglass
Mueller
Fritzsche
Equation Accuracy Analysis

Theoretical Pipe
 Set
the Temperature, Inlet
Pressure and Natural Gas
Flow Rate
 Solve ∆P with Equation for
various diameters and
elevation changes

Simulate Pipe: Pro/II
 Set

same conditions
Compare Results
Natural Gas Composition Used
Natural Gas Component
Mole Fraction
C1
0.949
C2
0.025
C3
0.002
N2
0.016
CO2
0.007
C4
0.0003
iC4
0.0003
C5
0.0001
iC5
0.0001
O2
0.0002
Equation Example

Modified-Colebrook




2

0 . 06843  d  H 2  H 1  Pavg
Q  Pst

2
P1   P2 


T avg z avg
 
2 . 825
2 .5

26 . 5972  D  log 10 


 3 . 7 D Re  f





2



 L  d  T avg  z avg













1/ 2
Modified-Colebrook Results
1800
50
NPS = 16; Pro-II
NPS =18
NPS =18; Pro-II
1400
40
NPS = 18; Analytical
NPS = 20; Pro-II
1200
NPS = 20; Analytical
NPS = 22; Pro-II
1000
NPS = 16
45
NPS = 16; Analytical
Percent Error
Pressure Drop (psia)
1600
NPS = 22; Analytical
800
NPS =20
NPS = 22
35
30
25
20
600
15
400
10
200
5
0
125
175
225
275
Flowrate (MMSCFD)
325
0
150
200
250
300
Flowrate (MMSCFD)
350
Costly Error!

One Pipeline
 Flowing
200 (MMscfd)
 Operating 350 days/year
 Averaging $8 per Mcf
 EIA States 3-5% of gas flow is used for
compressor fuel

1% of hydraulic error is $224
wasted Natural Gas per compressor
per year!
Range of Error
Cost of Error
($ of fuel cost/compressor/yr)
Equation Name
Range of Error
Panhandle
3.5 – 10%
784 – 2,240
Colebrook
2.4 – 10%
538 – 2,240
Modified-Colebrook
1.0 – 8.8%
224 – 1,971
AGA
0.2 – 15%
45 – 3,360
IGT
7.6 – 17%
1,702 – 3,808
Mueller
13 – 20%
2,912 – 4,480
Mathematical Model
General Flow Equation:
Where,
Rearrange:
Thus:
Equation becomes:
Where,
Mathematical Model Analysis
1800
100
NPS = 16; Pro-II
NPS = 16; Analytical
1600
90
NPS =18; Pro-II
Pressure Drop (psia)
1200
NPS = 18; Analytical
80
NPS = 16
NPS = 20; Pro-II
70
NPS =18
60
NPS =20
Percent Error
1400
NPS = 20; Analytical
NPS = 22; Pro-II
1000
NPS = 22; Analytical
800
600
NPS = 22
50
40
30
400
20
200
10
0
0
50
150
250
350
50
100
150
Flow Rate (MMSCFD)
Equation Name
Range of Error
Mathematical Model
0 – 0.9%
200
250
300
350
Flow Rate (MMSCFD)
Cost of Error
($ of fuel cost/compressor/yr)
0 –
200
400
THE MATHEMATICAL MODEL
VS. J-CURVE ANALYSIS
Landon Carroll
Wes Hudkins
J-Curve - Simulator Trials



Simulations are used to generate diameter/flowrate/pressure
drop correlations for the J-curves
Three pressure parameters (P3) were selected discretely– 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
J-Curve - Procedure




Simulations are run to generate pressure drop at a given
flowrate and diameter
Cost calculations are completed for these pressure drops which
relate to compressor and operating costs
Plot cost vs. flowrate
Repeat at various diameters and/or pressures
The lowest cost at the desired flowrate ‘wins’
$1.60
TAC per MCF

$1.20
NPS = 16
NPS = 18
NPS = 20
$0.80
$0.40
$0.00
100
200
300
Flow Rate (MMSCFD)
400
500
$1.60
$1.40
$1.20
$1.00
$0.80
$0.60
$0.40
$0.20
$0.00
$1.60
Segment 1
P = 750
NPS = 16
NPS = 18
NPS = 20
NPS = 22
TAC per MCF
TAC per MCF
J-Curve – Segment 1 Optimum
0.3287
100
200
300
400
500
Segment 1
P = 850
TAC per MCF
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)
NPS = 16
NPS = 18
NPS = 20
NPS = 22
$0.40
0.353
$0.00
200
300
400
500
Flow Rate (MMSCFD)

$1.20
$0.80
100
Flow Rate (MMSCFD)
$1.60
Segment 1
P = 800
$1.20
500
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
Why so many decimal places? At high
flowrates, these fractions of cents per
MCF can become millions of dollars.
J-Curve - Segment 2 Optimum
$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 is 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
Order of Optimization
Optimizing Segment 1 First; 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 First; 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
The optimum pressure is 850 psig, and the optimum pipe sizes are 18 inches in
both segments.
Shown: Optimization of Segment 1 at Segment 2’s optimum pressure.
Overall Optimum
P=850
$1.5
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
TAC per MCF
$1.3
$1.1
$0.9
$0.7
0.6174
0.6164
$0.5
100
200
300
Flow Rate (MMSCFD)
400
500
# J-Curves Required
For un-branched pipeline networks such as this one, the number of J-Curves
required for optimization is:
# pipes
# diameters
# orders
# discrete
pressures
As the number of pipes in a pipelines network increases, the number of
J-Curves required for optimization increases exponentially.
Two-Segment Network
Economic Optimums



Segment
Optimum
Pressure
Optimum
Diameters
TAC per
MCF
Total Annual
Cost (millions)
1
750
18 & 18
$ 0.631
$ 66
2
850
18 & 18
$ 0.616
$ 65
Both*
850
18 & 18
$ 0.616
$ 65
Optimizing Segment 1 first gave the incorrect solution.
All possible combinations must be analyzed to find an overall
optimum.
In order to analyze both segments at once, 48 J-curves must be
analyzed for even this simple two pipe network!
Mathematical Model Results
Nonlinear 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 mathematical model reached an optimum of $2,000 per
MCF less than the J-curve method. Why? The J-curve method
ignores volume buildup, time value of money, inflation, and
many cost variations over time.
Remember, this required 48 J-curves and 432 simulations with
the conventional method and the results are not even accurate!
THE MATHEMATICAL MODEL
Landon Carroll
Wes Hudkins
Model Expansion

Willbros, Inc.
 Friday,
February 20th,
2008
 Diameter
 Coating cost
 Transportation cost
 Quadruple random
length joints

Dr. Bagajewicz
 Installation
cost
 Pipe maintenance cost
 Compressor
maintenance cost
Model Logic

Linear Model
 Generates
discrete pressures
 Minimizes net present total annual cost
 Gives optimum diameters, compressor locations,
compressor installation time, and compressor size

Nonlinear model
 These
optimums are then input into the nonlinear
model
 Minimizes net present total annual cost
Model Logic - Input
Model
Economics
Diameter Options
Supplier Temperatures
Supplier Pressures
Consumer Demands (V/t)
Demand Increase (%/yr)
Min/Max Operating Pressure
Compressor Location Options
Elevations
Pipe Connections
Distances
Project Lifetime
Operating Cost ($/P*t)
Maintenance Cost ($/hp,%TAC)
Operating Hours (hr/yr)
Interest Rate
Consumer Price ($/V)
Steel Cost(d) ($/L)
Coating Cost(d) ($/L)
Transportation Cost(d) ($/L)
Installation Cost(d) ($/L)
Hydraulics
Gas Density
Compressor Efficiency
Compressibility Factor
Compressibility Ratio
Heat Capacity
Model Logic – Economic Calculations
Objective Function: Net Present Total Annual Cost
TAC(t)
Total Annual Cost
Operating Cost
Pipe Cost
Compressor Cost
Maintenance Cost
Compressor Cost
Pipe Cost
Maintenance Cost
Operating Cost
Capacities and Works come
from hydraulic calculations.
Model Logic – Linear Hydraulic Calculations
Capacities to Compressor Cost
and Maintenance Cost Equations
Capacity Limits
Compressor Work
Works To Operating
Cost Equation
Maximum Capacity
Total Demand
Total Demand
Pressure Works
Hydraulic Equation Part A
Pressure Work
Hydraulic Equation Part B
Pressures
DPDZ
Discrete Pressures
Discrete Pressures
Model Logic – Nonlinear Hydraulic Calculations
To Compressor Cost Equation
and Maintenance Equation
Works to Operating
Cost Equation
Capacity Limits
Compressor Work
Pressures
Hydraulic Equation
Model Logic - Output
Economics
Physical
Pipe Locations
Pipe Diameters
Demand at Each Period
Flowrates
Inlet and Outlet Pressures
Compressor Locations
Compressor Capacities
Net Present Value
Net Present Total Annual Cost
Total Annual Cost at Each Period
Fixed Capital Investment
Revenue
Operating Cost
Pipe Cost
Compressor Cost
Maintenance Cost
Penalties
CASE STUDY
Landon Carroll
Wes Hudkins
Case Study - Given
Fairfield
Supply P (kPa)
3548.7
Supply T (°R)
529.67
MinOP (kPa)
10050.5
MaxOP (kPa)
4200
Elevation (km)
0.185928
Initial Demand (Mcmd)
Price ($/m3)
Elevation (km)
• 10% Annual Demand Increase
• Season Demand Variation
• 8 Year Project Lifetime
Mavis
Mayberry
Split
Beaumont
Travis
283.17
566.34
0
2831.7
1699
0.32
0.33
0
0.3
0.3
0.56376
0.54864
0.2286
0.10668
0.12816
Case Study - J-Curves
# simulations
per curve
# diameters
# discrete
pressures
# pipes
# possible
compressor
location
configurations
# possible
orders of
optimization
Optimization of this case study using J-curves would require 293,932,800 simulations!
If a person were to run this many simulations 24/7 at 5 minutes per simulation, it would take
2796 years!
If this person only worked the standard 40 hours per week, it would take 11,776 years!
In order to accomplish the design in 6 months, it would require 23,552 employees!
At minimum wage, that’s $153,088,000!
Case Study - Results
8 Year Economics
Non-Graphical Results
100
$ million
80
Pipe 1 ID (in.)
22
Pipe 2 ID (in.)
22
Pipe 3 ID (in.)
22
Operating Cost
Pipe 4 ID (in.)
18
Compressor Cost
Pipe 5 ID (in.)
12
FCIinit=$303,036,750
TAC
60
FCI
40
20
0
0
5
10
Time Periods (6 Months)
NPV ($)
15
MMscmd
8 Year Consumer Demand
7
6
5
4
3
2
1
0
Consumer1 Demand
Consumer2 Demand
Consumer4 Demand
Consumer5 Demand
0
5
10
Time periods (6 months)
15
This took 1 person about 1 hour!
4,392,078,000
NPTAC ($)
243,706,100
Pipe Cost ($)
185,720,700
Supplier Compressor
Capacity (hp)
22,929.16
Consumer1 Compressor
Capacity (hp)
13,365.09
Consumer2 Compressor
Capacity (hp)
13,293.76
Consumer3 Compressor
Capacity (hp)
8,439.168
CONCLUSIONS
Landon Carroll
Wes Hudkins
Recommendations




Expand model to incorporate
more pipeline details (i.e.
thickness, friction due to
fittings, heat transfer)
Make more user friendly
GAMS coupled with GAMS
data exchanger (GDX) to
create user interface
Uncertainty added to model
Conclusion



Conventional hydraulic equations inaccurate
J-Curve analysis inaccurate and time consuming.
Does not allow for complex networks.
Mathematical model produces accurate results
and when coupled with GAMS saves time and
money
Special Thanks






Willbros, Inc. – industry feedback and input
Debora Faria – original program author
Chase Waite – last year’s group member
Vi Pham – teaching assistant
Mark Bothamley – industrial feedback and input
Miguel Bagajewicz - professor
Any Questions
Please see us at our poster with questions.