NEW METHODS FOR PIPELINE DESIGN Chase Waite Kristy

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 growth Weather

Natural Gas Price Breakdown Average Heating Season Price (dollars per MCF) $18 $16 Transmission and Distribution Costs Commodity (the gas itself) $14 $12 $10 $8 $6 $4 $2 $0 2002 -2003 -2004 -2005 -2006 -2007 -2008

CONVENTIONAL METHOD Chase Waite Kristy Booth

Conventional Method Procedure: 1) Use analytical correlations or simulations to calculate pressure drop and compressor work Ø 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 $4. 00 Total Annual Cost per MCF 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 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 P 2 we can find the required compressor outlet pressure ηa = compressor adiabatic efficiency γ = ratio of specific heats of gas, dimensionless T 1=suction temperature of gas P 1 = suction pressure of gas P 2=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 C 1 0. 949 C 2 0. 025 C 3 . 002 N 2 0. 016 work and outlet pressure CO 2 0. 007 C 4 0. 0003 Overall heat transfer coefficient i. C 4 0. 0003 calculated to be 0. 3 Btu/hr-ft 2˚F C 5 0. 0001 i. C 5 0. 0001 O 2 0. 0002 segment with compressor Simulations were run for increasing flow rates at four different pipe diameters Natural Gas Composition Used Pro-II was used to find the compressor 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 P 2 = 800 psi. The compressor inlet pressure P 1 was set to equal P 2 Q = 50 – 500 MMSCFD Pcomp P 2 = 800 psig P 1 = 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 40 Pressure Drop Error with Pipeline Efficiency = 0. 92 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 (2 nd Edition). 2005 by Elsevier 2 Mc. Allister. Pipeline Rules of Thumb Handbook - A Manual of Quick, Accurate Solutions to Everyday Pipeline Engineering Problems (6 th Edition). 2005 by Elsevier 3 Gas Pipeline Hydraulics, E. Shashi Menon, © 2005 Taylor & Francis Group, LLC

Panhandle Versus Simulation 40 After minimizing error simulations by changing the pipeline efficiency (E) in the Panhandle equation Percent Error with respect to 35 Pressure Drop Error with Pipeline Efficiency = 0. 97 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:

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 $4. 00 4, 530 HP NPS = 18 NPS = 16 NPS = 20 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 50 150 250 350 450 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 Fixed Efficiency of 80% at Q = 400 (solid line) 1. 4 1. 2 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 two -segment pipeline � Optimizing the segments in the wrong order may not lead to the economic optimum

Simulator Trials In the Pro-II simulations, P 1 and P 5 are always 800 psig Three pressure parameters (P 3) were selected – 750, 800, and 850 psig Both segments will have distinct optimums Q = 100 – 500 MMSCFD P 1 = 800 psig P 2 P 3 P 4 L = 60 mi P 5 = 800 psig L = 60 mi Q = 50 MMSCFD

TAC per MCF $1. 60 Segment 1 P = 850 $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. 00 150 200 250 300 350 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 = 22 $1. 00 $0. 80 $0. 60 $0. 40 0. 3287 $0. 20 $0. 00 150 200 250 300 350 400 450 500 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 = 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 NPS = 18 Segment 1 & NPS = 18 Segment 2 $1. 299 $1. 0 $0. 8 0. 908 0. 740 $0. 6 $0. 4 100 150 200 0. 663 0. 631 0. 626 0. 635 0. 654 0. 679 250 300 350 400 450 500 Flow Rate (MMSCFD) Optimizing segment 2 first results in the optimum design Optimizing Segment 2; P=850 TAC per MCF $1. 201. 309 $1. 00 $0. 80 NPS = 18 Segment 1 & NPS = 18 Segment 2 0. 907 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. 3 NPS = 18 Segment 1 & NPS = 18 Segment 2 1 0. 8 0. 63 50 250 450 Flow Rate (MMSCFD) NPS = 18 Segment 1 & NPS = 18 Segment 2 $0. 9 $0. 7 1. 2 0. 4 NPS = 18 Segment 1 & NPS = 16 Segment 2 $1. 1 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 0. 6174 Difference in TAC per MCF Difference in TAC per year $ 0. 001 $ 105, 000 $ 0. 015 $ 1, 600, 000 0. 6164 $0. 5 100 200 300 Flow Rate (MMSCFD) 400 500

Two-Segment Network Economic Optimums Optimum Pressure 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 Segment 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 (33)

Mathematical Model 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 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 Millions 3000 2500 Single Pipe Network 2000 2 -Pipe Network 1500 9 -Pipe Network with elevation and 1000 demand variations, and without Ramified Network R 2 = 0. 9999 500 0 0 20 40 Pin 2 -Pout 2 60 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 (k. Pa) 18000 16; Pro-II 16; Analytical 18; Pro-II 18; Analytical 20; Pro-II 14000 12000 10000 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 d. P Pro-II MMSCFD d. P Model (k. Pa) 200 4975 5055 1. 62 300 7425 7326 1. 34 400 9950 9845 1. 05 Q NPS 18 (k. Pa) % Error

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 MMm 3/day 50 Variation in Demand as a Function of Time for Segment 3 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 24 730 0 0 0 Compressor 16, 700 Work (hp) 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 27, 000 HP C 2 30 km 81 km 25 km C 3 18. 24 Mm 3/day 2. 3% 2148. 2 Mm 3/day 3% C 1 57 km 80 km 134. 4 Mm 3/day C 4 38 km C 5 200 km 3617. 1 Mm 3/day 2. 6% C 6 C 7 384. 2 Mm 3/day 3. 7%

Model Cost Analysis (Ramified) Non Linear Model – Ramified Network Pipe Diameter (in) Compressor Work (hp) Pressure Drop (psi) Pipe S 1 -C 1 Pipe C 1 C 2 Pipe C 2 Pipe S 2 Pipe C 5 Pipe S 2 -S 4 Pipe C 5 -C 6 C 3 S 5 C 7 24 24 28 28 24 5, 010 0 0 8, 350 0 0 65 4, 190 4, 255 180 30 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 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