Goals Design a pipeline network with economically optimized configurations under growing and uncertain gas demands at multiple locations Ramified Linear 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 fuels Economic growth Weather
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
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.
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-ft 2 ˚F Natural Gas Composition Used Natural Gas ComponentMole Fraction C1C1 0.949 C2C2 0.025 C3C3.002 N2N2 0.016 CO 2 0.007 C4C4 0.0003 iC 4 0.0003 C5C5 0.0001 iC 5 0.0001 O2O2 0.0002 Union Gas http://www.uniongas.com/aboutus/aboutng/composition.asp
Simulation set up In the Pro-II simulations, the compressor outlet pressure, P comp, was varied to give a downstream pressure of P 2 = 800 psi. The compressor inlet pressure P 1 was set to equal P 2 P 1 = 800 psig P comp P 2 = 800 psig L = 120 mi Q = 50 – 500 MMSCFD
Panhandle Versus Simulation 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
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 HP14,130 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.
Including Compressor Efficiency This examines the difference between using a constant compressor efficiency of 0.8 versus using a variable compressor efficiency
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 P 1 = 800 psig P2P2 P 5 = 800 psig L = 60 mi Q = 100 – 500 MMSCFD L = 60 mi P3P3 P4P4 Q = 50 MMSCFD
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
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
Optimizing Segment 1 first, Compared to Optimizing Segment 2 first Optimizing segment 2 first results in the optimum design
Overall Optimum & Relevance of Optimum 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 Diameters TAC per MCF Total Annual Cost (millions) 1P = 75018 & 18$ 0.631$ 66 2P = 85018 & 18$ 0.616$ 65 Both*P = 85018 & 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 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 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 Relaxed variables
Linear regression of simulation data used to find A = 67.826 and B = -2 x 10 7 / -∆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
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 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 Q MMSCFD dP Model (kPa) dP Pro-II (kPa) % Error 200497550551.62 300742573261.34 400995098451.05 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 1Pipe 2 Pipe Diameter (in)22 Compressor Work (hp)10,7400 Pressure Drop (psi)1,8301,490 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!
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 Pipe123457689 Pipe Diameter (in) 36 32 24 Compressor Work (hp) 16,7007300000000
Ramified Pipeline Network C2 23,000 HP C3 C4 C6 C7 18.24 Mm 3 /day 2.3% 30 km 80 km102 km 57 km 27,000 HP 2148.2 Mm 3 /day 3% 134.4 Mm 3 /day 81 km 25 km200 km 38 km 3617.1 Mm 3 /day 2.6% 384.2 Mm 3 /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 Network Pipe Pipe S1-C1Pipe C1-C2Pipe C2-C3Pipe S2-S4Pipe S2-S5Pipe C5-C6Pipe C5-C7 Pipe Diameter (in)24 28 24 Compressor Work (hp)5,010008,350 00 Pressure Drop (psi)654,1904,2551803010010
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