The Pennsylvania State University. The Graduate School. Department of Energy and Mineral Engineering STEADY STATE FLOW STUDIES OF SECTIONS IN

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1 The Pennsylvania State University The Graduate School Department of Energy and Mineral Engineering STEADY STATE FLOW STUDIES OF SECTIONS IN NATURAL GAS PIPELINE NETWORKS A Thesis in Petroleum and Natural Gas Engineering by Kenneth C. Ken-Worgu 2008 Kenneth C. Ken-Worgu Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 2008

2 II The thesis of Kenneth C. Ken-Worgu was reviewed and approved by the following: Michael A. Adewumi Thesis Advisor Professor of Petroleum and Natural Gas Engineering Quentin E. and Louise L. Wood University Endowed Fellow Thaddeus Ityokumbul Associate Professor of Mineral Processing and Geo-Environmental Engr. Undergraduate program officer for Environmental Systems Engineering Turgay Ertekin Program Chair Professor of Petroleum and Natural Gas Engineering George E. Trimble Chair Head of Petroleum and Mineral Engineering *Signatures are on file in the Graduate School

3 III ABSTRACT Efficient transportation of natural gas is vital to the success of the economy of the US and the world, because of the various uses of natural gas and its components. Pipelines are the main form of transportation, transmission and distribution of natural gas. Pipelines networks are used to efficiently take the gas from the producer and deliver it to the consumer. There is a pressing need to improve the accuracy of the pressure and flow rate predictions in the pipes and at the nodes of these networks. An accurate correlation between the individual loops and sections in these networks would improve the accuracy of predictions and simulations of these networks. The equations used for a loop or section to predict the steady state values in the network has to be determined by a steady state study of the individual loops in the natural gas pipeline network. Using the initial field data of any network, the appropriate friction factor equation capable of accurate predictions of pressures and flow rates can be determined. In this work, the pipeline networks are analyzed. Loops consisting of different numbers of pipes are analyzed to study the accuracy of prediction by any particular friction factor equation for the particular segment of the gas pipeline network. The Newton-Raphson method was utilized for solving the networks. No equation currently available, is able to predict pressures and flow rates accurately for all cases. Over the years, several modifications have been proposed to improve the accuracy of the predictions. This work utilizes different friction factors

4 IV in different sections in the natural gas pipeline network to increase the accuracy of the predictions. This work also presents the effects of the different friction factor equations on predicted values of pressures and flow rate for several possible network configuration, sections and determines the optimum friction factor equation to use in the individual sections of the network.

5 V TABLE OF CONTENTS LIST OF FIGURES VIII LIST OF TABLES XII ACKNOWLEDGEMENTS XVII CHAPTER 1 INTRODUCTION 1 CHAPTER 2 LITERATURE REVIEW 6 CHAPTER 3 PROBLEM STATEMENT 9 CHAPTER 4 NUMERICAL MODEL Steady-state Analysis System of Equations Newton-Raphson Steady-state flow equations Network example Pipe, 4-Node Gas pipeline Network Statistical Analysis Analysis of Variance (ANOVA) 32 CHAPTERS 5 LOOP ANALYSIS : 3-Pipe, 4-Node open loop : 4-Pipe, 5-Node open loop : 2-Pipe, 2-Node closed loop : 3-Pipe, 3-Node closed loop : 4-Pipe, 4-Node closed loop : 5-Pipe, 5-Node closed loop : 6-Pipe, 6-Node closed loop : 7-Pipe, 7-Node closed loop : 8-Pipe, 8-Node closed loop : 9-Pipe, 9-Node closed loop : 10-Pipe, 10-Node closed loop : 11-Pipe, 11-Node closed loop : 12-Pipe, 12-Node closed loop 70 CHAPTERS 6 SECTIONAL ANALYSIS Pipe, 41-Node Natural Gas Pipeline Network Steady-State Analysis Sectional Analysis (Panhandle B data as the reference) 91

6 VI Section I Section II Section III Section IV Combination Sectional Analysis (Weymouth data as the reference) Section I Section II Section III Section IV Summary Pipe, 31-Node Natural Gas Pipeline Network Steady-State Analysis Sectional Analysis (Weymouth data as the reference) Section I Section II Section III Section IV Combination Summary 125 CHAPTERS 7 CONCLUSIONS AND RECOMMENDATIONS Conclusions Recommendations 128 BIBLIOGRAPHY 129 APPENDIX 132 A.1 Steady-State Analysis of a 21-Pipe, 16-Node Network 133 A.2 Loop Analysis 143 A.2.1 Loop Analysis of Section I 145 A.2.2 Loop Analysis of Section II 147 A.2.3 Loop Analysis of Section III 150 A.2.4 Loop Analysis of Section IV 153 A.2.5 Loop Analysis of Section V 156 A.2.6 Loop Analysis of Section VI 159 A.3 Steady-State Analysis of a section of the consumer power company s Gas transmission network serving Lower Michigan (combination) 160 B.1 Steady-State Analysis of Gas Distribution Grid in the Mexico Valley 167

7 VII B.1.1 Steady-State Analysis Technique 167 B.2 Loop Analysis 175 B.2.1 Loop Analysis of Section I 177 B.2.2 Loop Analysis of Section II 180 B.2.3 Loop Analysis of Section III 184 B.2.4 Loop Analysis of Section IV 187 B.2.5 Loop Analysis of Section V 191 B.3 Steady-State Analysis of Gas Distribution Grid in the Mexico Valley (Different friction factors for different loops in the same network) 193 C.1 Sectional Analysis of Gas Distribution Grid in the Mexico Valley 200 C.2 Sectional Analysis (Field data as the reference) 203 C.2.1 Section I 204 C.2.2 Section II 204 C.3 Steady-State Analysis of Gas Distribution Grid in the Mexico Valley (Different friction factors for different sections in the same network) 205

8 VIII LIST OF FIGURES Figure 4.1; A 5-pipe,4-node Gas pipeline Network, Ayala (2007) 21 Figure 4.2; Pressure curves for a 5-pipe,4-node Gas pipeline Network 27 Figure 4.3; Flow rate curves for a 5-pipe,4-node Gas pipeline Network 28 Figure 4.4; Weymouth Flow rate curves for a 5-pipe,4-node Network 29 Figure 4.5; Panhandle A Flow rate curves for a 5-pipe,4-node Network 30 Figure 4.6; Panhandle B Flow rate curves for a 5-pipe,4-node Network 31 Figure 5.1; A 3-Pipe, 4-Node open loop 35 Figure 5.2; Pressure curve 3-Pipe, 4-Node open loop 36 Figure 5.3; Flow rate curve 3-Pipe, 4-Node open loop 37 Figure 5.4; A 4-Pipe, 5-Node open loop 38 Figure 5.5; Pressure curve 4-Pipe, 5-Node open loop 39 Figure 5.6; Flow rate curve 5-Pipe, 5-Node open loop 39 Figure 5.7; 2-Pipe, 2-Node closed loop 41 Figure 5.8; Pressure curve; 2-Pipe, 2-Node closed loop 41 Figure 5.9; Flow rate curve; 2-Pipe, 2-Node closed loop 42 Figure 5.10; 3-Pipe, 3-Node closed loop 43 Figure 5.11; Pressure curve; 3-Pipe, 3-Node closed loop 44 Figure 5.12; Pressure change curve; 3-Pipe, 3-Node closed loop 44 Figure 5.13; Flow rate curve; 3-Pipe, 3-Node closed loop 45 Figure 5.14; 4-Pipe, 4-Node closed loop 46 Figure 5.15; Pressure curve; 4-Pipe, 4-Node closed loop 47 Figure 5.16; Pressure change curve; 4-Pipe, 4-node closed loop 47 Figure 5.17; Flow rate curve; 4-Pipe, 4-node closed loop 48 Figure 5.18; 5-Pipe, 5-Node closed loop 49 Figure 5.19; Pressure curve; 5-Pipe, 5-Node closed loop 50 Figure 5.20; Pressure change curve; 5-Pipe, 5-node closed loop 50 Figure 5.21; Flow rate curve; 5-Pipe, 5-Node closed loop 51 Figure 5.22; 6-Pipe, 6-Node closed loop 52 Figure 5.23; Pressure curve; 6-Pipe, 6-Node closed loop 53 Figure 5.24; Pressure change curve; 6-Pipe, 6-Node closed loop 53 Figure 5.25; Flow rate curve; 6-Pipe, 6-Node closed loop 54 Figure 5.26; 7-Pipe, 7-Node closed loop 55 Figure 5.27; Pressure curve; 7-Pipe, 7-Node closed loop 56 Figure 5.28; Pressure change curve; 7-Pipe, 7-Node closed loop 56 Figure 5.29; Flow rate curve; 7-Pipe, 7-Node closed loop 57 Figure 5.30; 8-Pipe, 8-Node closed loop 58 Figure 5.31; Pressure curve; 8-Pipe, 8-Node closed loop 59

9 Figure 5.32; Pressure change curve; 8-Pipe, 8-Node closed loop 59 Figure 5.33; Flow rate curve; 8-Pipe, 8-Node closed loop 60 Figure 5.34; 9-Pipe, 9-Node closed loop 61 Figure 5.35; Pressure curve; 9-Pipe, 9-Node closed loop 62 Figure 5.36; Pressure change curve; 9-Pipe, 9-Node closed loop 62 Figure 5.37; Flow rate curve; 9-Pipe, 9-Node closed loop 63 Figure 5.38; 10-Pipe, 10-Node closed loop 64 Figure 5.39; Pressure curve; 10-Pipe, 10-Node closed loop 65 Figure 5.40; Pressure change curve; 10-Pipe, 10-Node closed loop 66 Figure 5.41; Flow rate curve; 10-Pipe, 10-Node closed loop 66 Figure 5.42; 11-Pipe, 11-Node closed loop 68 Figure 5.43; Pressure curve; 11-Pipe, 11-Node closed loop 69 Figure 5.44; Pressure change curve; 11-Pipe, 11-Node closed loop 69 Figure 5.45; Flow rate curve; 11-Pipe, 11-Node closed loop 70 Figure 5.46; 12-Pipe, 12-Node closed loop 71 Figure 5.47; Pressure curve; 12-Pipe, 12-Node closed loop 72 Figure 5.48; Pressure change curve; 12-Pipe, 12-Node closed loop 73 Figure 5.49; Flow rate curve; 12-Pipe, 12-Node closed loop 73 Figure 6.1: Schematic of a 51-Pipe, 41-Node Gas Distribution Network 80 Figure 6.2: Steady State Pressure Analysis 83 Figure 6.3: Steady State Flow rate Analysis 84 Figure 6.4: schematic of the network divided into sections 85 Figure 6.5: Schematic of a 53-Pipe, 31-Node Gas Distribution Network 107 Figure 6.6: Steady State Pressure Analysis 111 Figure 6.7: Steady State Flow rate Analysis 111 Figure 6.8: schematic of the network divided into sections 113 Figure A.1: Schematic of a section of the consumer power company s gas transmission network serving Lower Michigan (Zhou et al., 1998) 136 Figure A.2: Steady State Pressure Using Weymouth Equation 139 Figure A.3: Steady State Pressure Using Panhandle A Equation 139 Figure A.4: Steady State Pressure Using Panhandle B Equation 140 Figure A.5: Steady State Flow rate Using Weymouth Equation 140 Figure A.6: Steady State Flow rate Using Panhandle A Equation 141 Figure A.7: Steady State Flow rate Using Panhandle B Equation 141 Figure A.8: Steady State Pressure analysis 142 Figure A.9: Steady State Flow rate analysis 142 Figure A.10: Schematic of the Gas Distribution Network divided into sections for loop analysis 144 Figure A.11: Schematic of section I of the Gas Distribution network 145 IX

10 Figure. A.12: Steady State Analysis for section I. 145 Figure A.13: Input data and results for steady state analysis of section I 146 Figure A.14: Schematic of section II of the Gas Distribution network 147 Figure. A.15: Steady State Analysis for section II 148 Figure A.16: Input data and results for steady state analysis of section II 149 Figure A.17: Schematic of section III of the Gas Distribution network 150 Figure. A.18: Steady State Analysis for section III 151 Figure A.19A: Input data and results for steady state analysis of section III 151 Figure A.19B: Deviation results for steady state analysis of section III 152 Figure A.20: Schematic of section IV of the Gas Distribution network 153 Figure A.21: Steady State Analysis for section IV 154 Figure A.22: Input data and results for steady state analysis of section IV 155 Figure A.23: Schematic of section V of the Gas Distribution network 156 Figure A.24: Steady State Analysis for section V 157 Figure A.25: Input data and results for steady state analysis of section V 158 Figure A.26: Schematic of section VI of the Gas Distribution network 159 Figure A.27: Steady State Analysis for section V 159 Figure A.28: Input data and results for steady state analysis of section V 160 Figure A.29: Schematic of a section of the consumer power company s gas transmission network serving Lower Michigan 161 Figure A.30: Steady state pressure Analysis; with the combination of friction factors for different loops 163 Figure B.1: Schematic of a Gas Distribution Network in the Mexico Valley, Nagoo (2003). 170 Figure B.2: Steady State Pressure Comparison between This Model s Predictions and Nagoo (2003). 173 Figure B.3: Steady State Flow rate Comparison between This Model s Predictions and Nagoo (2003). 173 Figure B.4: Steady State Pressure Analysis 174 Figure B.5: Steady State Flow rate Analysis 174 Figure B.6: Schematic of the Gas Distribution Network divided into sections for loop analysis 176 Figure B.5: Schematic of section I of the Gas Distribution Network divided into sections for loop analysis 177 Figure B.6: Steady State Pressure Analysis for Section I 178 Figure B.7: Input data and results of the Steady-state analysis of Section I 179 Figure B.8: Schematic of section II of the Gas Distribution Network divided into sections for loop analysis 180 Figure B.9: Steady State Pressure Analysis for Section II 181 X

11 Figure B.10A: Input data and results of the Steady-state analysis of Section II 182 Figure B.10B: Input data and results of the Steady-state analysis of Section II 183 Figure B.11: Schematic of section III of the Gas Distribution Network divided into sections for loop analysis 184 Figure B.12A: Steady State Pressure Analysis for Section III 185 Figure B.12B: Steady State Pressure Analysis for Section III 185 Figure B.13: Input data and results of the Steady-state analysis of Section III 186 Figure B.14: Schematic of section IV of the Gas Distribution Network divided into sections for loop analysis 187 Figure B.15: Steady State Pressure Analysis for Section IV 188 Figure B.16A: Input data and results of the Steady-state analysis of Section IV 189 Figure B.16B: Input data and results of the Steady-state analysis of Section IV 190 Figure B.16C: Input data and results of the Steady-state analysis of Section IV 191 Figure B.18: Steady State Pressure Analysis for Section V 192 Figure B.19: Input data and results of the Steady-state analysis of Section V 193 Figure B.20: Schematic of the Gas Distribution Network divided into sections and assigned to different friction factor equations for steady state analysis 194 Figure B.21: Steady State Pressure Analysis; with the combination of different friction factors for different loops 196 Figure C.1: schematic of the network divided into sections 200 Figure C.2: Schematic of Network divided into sections and assigned different friction factor equations for steady state analysis 206 Figure C.3: Steady state pressure Analysis; with the combination of friction factors for different Sections 209 XI

12 XII LIST OF TABLES Table 4.1: Input Parameters for a 5-pipe, 4-node Gas pipeline Network 22 Table 4.2: Nodal Loads for a 5-pipe, 4-node Gas pipeline Network 23 Table 4.3: Pressures at each node (Weymouth) 24 Table 4.4: Flow rates and Pressure changes for each pipe (Weymouth) 24 Table 4.5: Pressures at each node (Panhandle A) 25 Table 4.6: Flow rates and Pressure changes for each pipe (Panhandle A) 25 Table 4.7: Pressures at each node (Panhandle B) 26 Table 4.8: Flow rates and Pressure changes for each pipe (Panhandle B) 26 Table 5.1: Node Supply/Demand loads and Pipe parameters for a 3-Pipe, 4-Node open loop 36 Table 5.2: Node Supply/Demand loads and Pipe parameters for a 4-Pipe, 5-Node open loop 38 Table 5.3: Node Supply/Demand loads and Pipe parameters for a 2-Pipe, 2-Node closed loop 41 Table 5.4: Node Supply/Demand loads and Pipe parameters for a 3-Pipe, 3-Node closed loop 43 Table 5.5: Node Supply/Demand loads and Pipe parameters for a 4-Pipe, 4-Node closed loop 46 Table 5.6: Node Supply/Demand loads and Pipe parameters for a 5-Pipe, 5-Node closed loop 49 Table 5.7: Node Supply/Demand loads and Pipe parameters for a 6-Pipe, 6-Node closed loop 52 Table 5.8: Node Supply/Demand loads and Pipe parameters for a 7-Pipe, 7-Node closed loop 55 Table 5.9: Node Supply/Demand loads and Pipe parameters for a 8-Pipe, 8-Node closed loop 58 Table 5.10: Node Supply/Demand loads and Pipe parameters for a 9-Pipe, 9-Node closed loop 61 Table 5.11: Node Supply/Demand loads and Pipe parameters for a 10-Pipe, 10-Node closed loop 65 Table 5.12: Node Supply/Demand loads and Pipe parameters for a 11-Pipe, 11-Node closed loop 68 Table 5.13: Node Supply/Demand loads and Pipe parameters for a 12-Pipe, 12-Node closed loop 72 Table 6.1: Nodal Supply / Demand for 51-Pipe, 41-Node Natural gas pipeline network 78 Table 6.2: 51-Pipe, 41-Node Pipeline Network Characteristics 79

13 Table 6.3: Steady State results for 51-Pipe, 41-Node Pipeline Network (Pressures at each node) 81 Table 6.4: Steady State results for 51-Pipe, 41-Node Pipeline Network (Flow rate through each pipe) 82 Table 6.5A Pressure values for Section I 86 Table 6.5B Flow rate values for Section I 86 Table 6.6A Pressure values for Section II 87 Table 6.6B Flow rate values for Section II 87 Table 6.7A Pressure values for Section III 88 Table 6.7B Flow rate values for Section III 88 Table 6.8A Pressure values for Section IV 89 Table 6.8B Flow rate values for Section IV 90 Table 6.9: Statistical correlations for pressure values (Panhandle B data as the reference) 91 Table 6.10: Statistical correlations for flow rate values (Panhandle B data as the reference) 91 Table 6.11: Section I - Statistical correlations for pressure values (Panhandle B data as the reference) 92 Table 6.12: Section I - Statistical correlations for flow rate values (Panhandle B data as the reference) 92 Table 6.13: Section II - Statistical correlations for pressure values (Panhandle B data as the reference) 92 Table 6.14: Section II - Statistical correlations for flow rate values (Panhandle B data as the reference) 93 Table 6.15: Section III - Statistical correlations for pressure values (Panhandle B data as the reference) 93 Table 6.16: Section III - Statistical correlations for flow rate values (Panhandle B data as the reference) 93 Table 6.17: Section IV - Statistical correlations for pressure values (Panhandle B data as the reference) 94 Table 6.18: Section IV - Statistical correlations for flow rate values (Panhandle B data as the reference) 94 Table 6.19: Sections and their friction factor equations 95 Table 6.20: Steady State results for 51-Pipe, 41-Node Pipeline Network (Pressures at each node) 96 Table 6.21: Steady State results for 51-Pipe, 41-Node Pipeline Network (Flow rate through each pipe) 97 Table 6.22: Statistical correlations for pressure values (Panhandle B data as the reference) 98 XIII

14 Table 6.23: Statistical correlations for flow rate values (Panhandle B data as the reference) 98 Table 6.24: Statistical correlations for pressure values (Weymouth data as the reference) 99 Table 6.25: Statistical correlations for flow rate values (Weymouth data as the reference) 99 Table 6.26: Section I - Statistical correlations for pressure values (Weymouth data as the reference) 100 Table 6.27: Section I - Statistical correlations for flow rate values (Weymouth data as the reference) 100 Table 6.28: Section II - Statistical correlations for pressure values (Weymouth data as the reference) 100 Table 6.29: Section II - Statistical correlations for flow rate values (Weymouth data as the reference) 101 Table 6.30: Section III - Statistical correlations for pressure values (Weymouth data as the reference) 101 Table 6.31: Section III - Statistical correlations for flow rate values (Weymouth data as the reference) 101 Table 6.32: Section IV - Statistical correlations for pressure values (Weymouth data as the reference) 102 Table 6.33: Section IV - Statistical correlations for flow rate values (Weymouth data as the reference) 102 Table 6.34: Pressure Summary 103 Table 6.35: Flow rate Summary 103 Table 6.36: Nodal Supply / Demand for 53-Pipe, 31-Node Natural gas pipeline network 105 Table 6.37: 53-Pipe, 31-Node Pipeline Network Characteristics 106 Table 6.38: Steady State results for 53-Pipe, 31-Node Pipeline Network (Pressures at each node) 108 Table 6.39: Steady State results for 53-Pipe, 31-Node Pipeline Network (Flow rate through each pipe) 109 Table 6.40A Pressure values for Section I 114 Table 6.40B Flow rate values for Section I 114 Table 6.41A Pressure values for Section II 115 Table 6.41B Flow rate values for Section II 116 Table 6.42A Pressure values for Section III 117 Table 6.42B Flow rate values for Section III 117 Table 6.43A Pressure values for Section IV 118 Table 6.43B Flow rate values for Section IV 118 XIV

15 Table 6.44: Statistical correlations for pressure values (Weymouth data as the reference) 119 Table 6.45: Statistical correlations for flow rate values (Weymouth data as the reference) 120 Table 6.46: Section I - Statistical correlations for pressure values (Weymouth data as the reference) 120 Table 6.47: Section I - Statistical correlations for flow rate values (Weymouth data as the reference) 120 Table 6.48: Section II - Statistical correlations for pressure values (Weymouth data as the reference) 121 Table 6.49: Section II - Statistical correlations for flow rate values (Weymouth data as the reference) 121 Table 6.50: Section III - Statistical correlations for pressure values (Weymouth data as the reference) 122 Table 6.51: Section III - Statistical correlations for flow rate values (Weymouth data as the reference) 122 Table 6.52: Section IV - Statistical correlations for pressure values (Weymouth data as the reference) 122 Table 6.53: Section IV - Statistical correlations for flow rate values (Weymouth data as the reference) 123 Table 6.54: Sections and corresponding friction factor equations 123 Table 6.55: Steady State results for 53-Pipe, 31-Node Pipeline Network (Flow rate through each pipe) 124 Table 6.56: Statistical correlations for flow rate values (Weymouth data as the reference) 125 Table 6.57: Pressure Summary 126 Table 6.58: Flow rate Summary 126 Table A.1: Nodal Load for 21-Pipe, 16-Node Pipeline Network (Aina, 2006) 134 Table A.2: 21-Pipe, 16-Node Pipeline Network Characteristics (Aina, 2006) 135 Table A.3: Steady State results for 21-Pipe, 16-Node Pipeline Network (Pressures at each node) 137 Table A.4: Steady State results for 21-Pipe, 16-Node Pipeline Network (Flow rate through each pipe) 138 Table A.5: Steady State results for 21-Pipe, 22-Node Pipeline Network; with the combination of friction factors for different loops 162 Table A.6: Deviation analysis for 21-Pipe, 22-Node Pipeline Network; with the combination of friction factors for different loops 164 Table A.7: Percentage Deviation analysis for 21-Pipe, 22-Node Pipeline Network; combination of friction factors for different loops 165 XV

16 Table B.1: Nodal Supply / Demand for 25-Pipe, 22-Node Pipeline Network (Aina, 2006) 168 Table B.2: 25-Pipe, 22-Node Pipeline Network Characteristics, Aina ( 2006) 169 Table B.3: Steady State results for 25-Pipe, 22-Node Pipeline Network (Pressures at each node) 171 Table B.4: Steady State results for 25-Pipe, 22-NodePipeline Network (Flow rate through each pipe) 172 Table B.5: Steady State results for 25-Pipe, 22-Node Pipeline Network; with the combination of different friction factors for different loops (Pressures at each node) 195 Table B.6: Deviations analysis of the 25-Pipe, 22-Node Network (including the combination of friction factors) 197 Table B.7: Percentage Deviations analysis of the 25-Pipe, 22-Node Network (including the combination of friction factors) 198 Table B. 8: Statistical correlation for pressure values 198 Table C.1 Pressure values for Section I 201 Table C.2 Flow rate values for Section I 201 Table C.3A Pressure values for Section II 202 Table C.3B Flow rate values for Section II 203 Table C.4: Statistical correlations for pressure values 203 Table C.5: Section I - Statistical correlations for pressure values 204 Table C.6: Section II - Statistical correlations for pressure values 204 Table C.7: Sections and their friction factor equations 205 Table C.8: Steady State results (including sectional combination) 207 Table C.9: Statistical correlations for pressure values 208 XVI

17 XVII ACKNOWLEDGEMENTS First, I thank God, who has enabled me to succeed in all my life endeavors, especially the challenges of graduate work. This research is a part of my learning experience in Petroleum and Natural Gas. This process was facilitated, largely by the valuable counsel, support and guidance of my academic advisor, Dr. Michael Adewumi, to whom I am especially grateful. I would also like to thank Dr. Thaddeus Ityokumbul, Dr. Joel Haight and Dr. Turgay Ertekin for their valuable input in this project. I would also like to thank Dr. Luis Ayala, Dr. Zuleima Karpyn, and Dr. Yaw Yeboah for their input in my academic development. I am grateful for the constructive discussions of my research and class mates. I would not be where I am today without the love and support of my parents; Ken and Betty Worgu, my brother; Donald, my sisters; Victory and Winnie, the rest of my extended family and our family friend Raymond Kasper. I also appreciate my friends and loved ones, I have you all in my heart and I am thankful for your love, help and support.

18 1 CHAPTER 1 INTRODUCTION Natural gas as a vital component of the world s supply of energy is clean burning and we require it to heat our homes, cook and generate electricity (Wonmo et al., 1998). Natural gas is colorless, shapeless and odorless in its pure form, and consists mainly of methane; it can also include ethane, propane, butane and pentane (Ayala, 2007). Natural gas is produced at the well and transported to consumers by pipelines and pipeline networks. The transportation, distribution and transmission of natural gas through pipeline have been in practice for many decades. Approximately 95% crude oil and natural gas are transported through pipeline (Center for Energy, Canada, 2004). Gas is generally received from receipt points along the pipeline and delivered to sales stations at specific flows and pressures. Between these points, a pressure drop occurs due to gas expansion, friction loss, changes in elevation and changes in temperature (Mohitpour et al., 2003). A pipeline transmission network is a complex system that may consist of numerous nodes/ junctions, joining the pipes. The pressure drop along the pipe and the quantity of natural gas that flows through the pipe are the most important information required for design (Ouyang et al., 1995).The pressure and flow values in a pipeline network can be predicted using the mass, momentum and energy conservation equations.

19 2 These equations are modeled with the aid of sophisticated computer techniques. Recent advancements in technology has significantly increased the computational power, allowing more accurate modeling of the gas networks. The aim is to predict the unknowns; pressures at each node and flow rates through each pipe. The known data are inner pipe diameter, pipe length, demand and supply load at the nodes and the node orientation of the pipelines. During more than 100 years of gas production and transportation in pipes, dozens of flow equations (e.g., AGA, Weymouth, Panhandle, Modified Panhandle, Mueller, IGT, Cullender and Smith, Sukker and Cornell equations, etc.) have been proposed to relate the gas volume transmitted through pipes to various factors that influence this rate [Ouyang et al., 1995]. As far back as 1912, empirical gas flow equations have been used to model natural gas flow [Beggs, 2002]. The variations in these equations are the friction factor equation used to derive them. This factor accounts for most, if not all of the energy losses in pipeline flow [Aina, 2006]. The Mueller, IGT, Weymouth, Panhandle and Modified Panhandle equations are used in this work to model the steady state flow of natural gas through pipeline networks by solving for the pressures in each node and used to solve for the flow rates in each pipe. The following assumptions were made when developing the steady-state model for this work. -Newtonian fluid.

20 3 -Single phase flow. -Steady-state flow. -No heat transfer to and from the gas to the surroundings. -No mechanical work done on or by the fluid during its passage through the pipe (No shaft work or work of compression) The resulting general equation is the following form. P g g c udu fu dz 2 g Dg c 2 c dl 0 Eq. 1.1 In this work, isothermal flow and zero elevation is also assumed. The main objective of this work is to analyze pipeline networks and the relationship of the prediction accuracy of the model to the section (containing one or more loops) that make up the pipeline network under the assumption of steady state flow. The steady state analysis is done by setting up a system of mass conservation equations for each node. A system of equations is developed and a Jacobian matrix is formed, which is solved further on using the Newton-Raphson method. Every node and loop is taking into account when forming the Jacobian matrix.

21 4 J y1 y1... x1 xn.. ym y... x1 x m n Eq. 1.2A The solver gives a constant Dq and the flow rate is updated by: q new q old Dq Eq 1.2B q = Flow rate Dq= Constant The loop updates itself until Dqis less than the convergence value and converges. The Pressures are solved using: 2 2 n 1 P2 R q Eq. 1.3 P * P = Pressure The effects of the predicted values pressures and flow rate for a three pipe open loop, four pipe open loop, two pipe closed loop (digon), three pipe closed loop (trigon), four pipe closed loop(tetragon), five pipe closed loop (pentagon), six pipe closed loop (hexagon), seven pipe closed loop (heptagon), eight pipe closed loop (octagon), nine pipe closed loop (nonagon), ten pipe closed loop (decagon), eleven pipe closed loop (hendecagon) and twelve pipe closed loop (dodecagon) are investigated. The network can be divided into sections. This works leads to the determination of the best friction factor equation to use in each individual sections in the network. The use of different

22 5 equations for different sections in the same pipe network, is suggestive of a more accurate prediction of the pressures and flow rates.

23 6 CHAPTER 2 LITERATURE REVIEW This is a summary of the literature on the natural gas flow through pipeline networks. The following are reviews of existing research and developments. Natural occurring natural gas was discovered as early as 1626, when French explorers discovered natives igniting gases that were seeping into and around Lake Erie. The American natural gas industry got its beginning in 1859, when Colonel Edwin Drake dug his first well and hit oil and natural gas 69ft below the surface. One of the first lengthy pipelines was constructed in This pipeline was 120 miles long and carried natural gas from wells in central Indiana to the city of Chicago. After World War II, welding techniques, pipe rolling and metallurgical advances allowed for the construction of reliable pipelines. In steady state analysis, there is no time dependency; the gas supply and demand are usually specified. Steady state analyses of pipeline networks have been studied by Stoner (1969), Zhou-Adewumi (1998), Martinez-Romero et al. (2002), Nagoo (2003) and Aina (2006). Zhou-Adewumi (1998), proposed an analytical steady state pipeline flow equation without neglecting the kinetic energy term in the momentum equation. Matiniez-Romero et al. (2002) used the following empirical equations; Weymouth, Panhandle, Modified Panhandle, Clinedinst, Colebrook, IGT. These equations are set up for each pipe in the network and solved simultaneously. Software, GasNet was

24 7 developed as a powerful tool for design and optimization of Natural Gas pipeline networks. The optimization process in this work was performed with two criteria: the maximum operational permissible pressure and the gas from flow velocity. The Newton-Raphson method has been used by Martin et al. (1963), Shamir et al. (1968), Stoner (1969) and Matiniez et al (2002). The Hardy-Cross method, which is an iterative numerical protocol and an adaptation of the method of moment distribution, was suited for hand calculations in the 1960 s (Leanard 2001). The Linear Theory method was used by Zhou-Adewumi (1998) and Nagoo (2003). A one dimensional compressible fluid flow equation was used by Tian et al. (1994) to determined flow rates. Based on mass and momentum balance, a rigorous analytical equation is derived for compressible fluid flow in pipelines. This equation gives a functional relationship between flow rate, inlet pressure and outlet pressure. Costa et al. (1998) developed a steady-state gas pipeline simulator, where pipes and compressors were selected as the building elements of a compressible flow network. Conservation of energy and flow equations were solved in a coupled manner to investigate the differences between isothermal, adiabatic and polytrophic flow conditions. In the paper written by Lewandowski (1993), an algorithm for parallel simulation of a natural gas transmission system was presented with the assumption that there will be no major improvements in the performance and speed of the gas network simulators.

25 8 Nagoo (2003) captured the complexity, as it relates to the topology of a states or country s natural gas pipeline grid, for ease of application to fast and computationally robust modeling of steady and quasi steady natural gas flows within the various flow components of the system. His work addresses the complexity by creating one virtual test-bed or hub that mathematically models the integrated natural gas pipeline grid, schematically re-interpreted simply and solely from its geographically dispersed junction connections, with all flow components and junctions given in a topologically sorted order. He uses the linear theory method (LTM) to solve network equations based on the Topologically Sorted Spanning Tree (TSST) technique. Aina (2006) utilizes an algorithm especially suited for computer implementation for steady state analysis. The algorithm was able to define any network based on two parameters: length of pipelines and nodal orientation. These are used to obtain the shortest total path that connects all nodes without forming a geometric closure. Unsteady flow analysis was performed by solving the mass and momentum equations for each pipeline simultaneously. The need for iterations at every time step was eliminated and computational time was reduced by several orders of magnitude. There are no studies that investigate the effects of individual loops or the number of pipes in the loops or sections of the pipeline network and their correlation to friction factors or friction factor equations. Also there are no studies that delve into the use of different friction factors in the same natural gas networks to achieve more accurate predictions of pressures and flow rates.

26 9 CHAPTER 3 PROBLEM STATEMENT In steady state modeling, the demand at various nodes has to be properly accounted for. The pressure at each node and the flow rates in each of the pipes making up the network have to be accurately predicted with minimal error to allow for accurate monitoring of the system. Therefore, modeling the flow for more accurate predictions is very important. Previous studies at The Pennsylvania State University by( Nagoo, 2003 and Aina, 2006) focused on steady and transient flow in natural gas pipeline networks. In the present study, natural gas pipeline networks are split into different sections and modeled using different friction factor equations. The main focus of this work is to analyze whether using different friction factor equations for different sections of the transmission network results in better pressure and flow rate predictions for the overall network.

27 10 CHAPTER 4 NUMERICAL MODEL A steady-state model was used for the analysis of the natural gas pipeline network. The model employs empirical pipeline flow equations (Mueller, IGT distribution, Panhandle, Modified Panhandle, and Weymouth) to solve for flow rates through each pipe and pressure at each node in the natural gas pipeline network. For the pipeline network analysis, the basic information required is the inner diameter of the pipe, pipe length, node orientation and demand/supply loads at each node. These empirical equations mentioned above already have friction factors embedded in them. Most of the losses in the pipeline network are accounted for by these friction factors. This is one of the most important parameters in the analysis of natural gas pipeline networks and the prediction of flow rates across the pipes and the pressure in each node. The nodal known pressures are also specified. When the supply and demand at each node are specified, the unknowns are the flow rates through the pipes and the pressure at each node are then calculated.

28 Steady-State Analysis A steady state analysis of the gas pipeline network was carried out and any time change or accumulation was neglected. Total supply equals total demand at any point in time. The boundary conditions are not changing over time and the flow is assumed to be isothermal. For the analyses of the natural gas pipeline network, the unknowns in the system need to be established. The steps used in steady-state analysis would be buttressed using an 12-pipe and 9-node example presented later in this chapter. The composition of a network is made up of: Pipes = P = Pipelines, existing between nodes. Nodes = N = Junctions that connect two or more pipes. Loops = L = A closed network section of pipes. The following equations can be used to show the mathematical relationship between the parameters listed above; P L ( N 1) Eq. 4.1 There is always a need to simulate the network with equations equal in quantitative magnitude to that of the parameter P.

29 System of Equations The equations can be represented in the matrix form as: J. Q R Eq. 4.2 J J. J P J J J P J J J P1 P2. PP Q Q.. Q 1 2 P Re siduals Eq. 4.3 The matrix J in Eq. 4.2 is the Jacobian matrix and it is the square matrix in Eq. 4.3 with a magnitude of P. It consists of L loop equations and N-1 mass conservation equations. Q is the column vector of the unknown flow rates passing through the pipes. Dolan et al. (1993), established that the Kirchoff s laws can be applied to pipeline networks. The N-1 equations and the L equations are determined by Kirchoff s 1 st and 2 nd laws respectively. Kirchoff s First Law: States that the sum of currents entering a junction of an electric equals the sum of the currents leaving. This is applied to natural gas pipeline networks. This law leads to mass conservation equations as follows. ( Q i ) out ( Qi ) in 0 Eq. 4.4 Kirchoff s Second Law: Also known as Kirchoff s voltage law or loop rule states that the total voltage drop around a closed loop must be zero. This could also be applied to natural gas pipeline networks; Sum of momentum is zero.

30 13 ( P loop 2 ) 0 Eq. 4.5 n ( Rq ) 0 loop Eq. 4.6 Where, Q = Flow rate. P = Pressure. R = Resistance. q = Flow rate. The equation set representative of the network is obtained by determining the governing equations through Kirchoff s 1 st and 2 nd laws and taking the differential Newton-Raphson Method Any network model can be represented as a system of non-linear equations (Ayala, 2007). Below is a set of equations that describe the system. f1( q1, q2,... q p ) f ( q, q,... q p ) " P" Equations. f p ( q1, q2,... q p ) Eq. 4.7 The solution of this system is the combination of q 1, q2,... qp values that make up the functions = 0.

31 14 q s f q q q k p ' ),..., ( 2 1 Eq. 4.8 ) ( ) ( old l old old new q f q f q q Eq. 4.9 ) ( ) ( old l old q f q f q Eq f q f! Eq q are obtained by solving the system of equations p p p p p p f f f q q q q f q f q f q f q f q f q f q f Eq. 4.12

32 Steady State Flow Equations The flow of natural gas in steady state through a pipe can be described by the following: P * MW Eq Z * R * T Where; = density. P = Pressure. MW = molecular Weight. Z = compressibility facor. R = Reynolds number. T = Temperature. dp Vdv g c g * dz g c w losses 0 Generalized Flow equation Eq Where dp = Pressure energy. Vdv g c g * dz g c Kinetic energy. Potential energy.

33 16 w 0. f ( Frictionfa ctors ). losses Tb Q ( n 1)77.5 P b ( D 2 * WT) 2.5 P e 2 1 P G( h ZT GT LZf a 2 a h ) P 1 2 a 0.5 Eq Eq is another form of the general pipeline flow equation. Where; D = Pipe internal diameter (inches). e = Pipe efficiency (dimensionless). f = Friction factor (dimensionless). G = Gas specific gravity relative to air (dimensionless). h 1 = elevation (ft). h 2 = elevation (ft). L = Pipe length (miles). n = number of additional pipes in parallel (dimensionless). P 1 = Upstream node pressure (psia). P 2 = Downstream node pressure (psia). P a = Average pipeline pressure (psia). P b = Base pressure of the standard gas state (psia). Q = Flow rate (SCFD).

34 17 T a = T b = WT = Average gas flowing temperature for a pipe (R). Base temperature for the standard gas state (R). Wall thickness (inches). Z = Gas compressibility factor (dimensionless). For the analysis of gas networks, it is customary to express all pipe equations in the following form; 2 2 ( P P ) R* Eq n q sc Where; R = Pipe resistance. q sc = Flow rate at standard conditions. Several empirical equations were employing different friction factors have been proposed for the general pipeline flow equation. In this work, five friction factor equations were used; Mueller, panhandle, Modified Panhandle, Weymouth, and IGT distribution pipe equation. These equations are among the most common pipeline flow equations used presently in the industry (Coelho et al. 2007). Schroeder (2001) and Coelho et al. (2007) describes the friction factor equations as the following:

35 18 8 f u w 2 Darcy friction coefficient Eq Mueller pipe equation Re f Eq Q ( n 1) G D P e 2 1 P G( h ZT L 2 a h ) P 1 2 a Eq Where; Re = Reynolds number of gas flow (dimensionless) Panhandle (Panhandle A) pipe equation Re f Eq. 4.20

36 ) ( ) ( LZ T G ZT P h h G P P e D P T n Q a a a b b Eq Modified Panhandle (Panhandle B) pipe equation Re f Eq ) ( )737 ( LZ T G ZT P h h G P P e D P T n Q a a a b b Eq Weymouth pipe equation D f Eq. 4.24

37 ) ( ) ( LZ GT ZT P h h G P P e D P T n Q a a a b b Eq IGT distribution pipe equation Re f Eq ) ( )92.66 ( L T ZT P h h G P P e G D P T n Q a a a b b Eq Where; = Gas Absolute viscosity ( 2 sec/ ft Ib f )

38 Network example A 5-pipe, 4-node Gas pipeline Network Figure 4.1: A 5-pipe, 4-node Gas pipeline Network (Ayala, 2007) This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations.

39 22 Table 4.1: Input Parameters for a 5-pipe, 4-node Gas pipeline Network Diameter Pipe Diameter (inches) Length Pipe Length (miles)

40 23 Table 4.2: Nodal Loads for a 5-pipe, 4-node Gas pipeline Network Supply Node Supply (MMScf/D) Demand Node Demand (MMScf/D) Pressure Node Pressure (psia) 1 NA NA 4 NA

41 24 Table 4.3: Pressures at each node (Weymouth) Node Pressure Table 4.4: Flow rates and Pressure changes for each pipe (Weymouth) Pressure Change Pipe Leg Pressure Change Flow rate Pipe Flow rate Leg (scf/day)

42 25 Table 4.5: Pressures at each node (Panhandle A) Node Pressure Table 4.6: Flow rates and Pressure changes for each pipe (Panhandle A) Pressure Change Pipe Leg Pressure Change Flow rate Pipe Flow rate Leg (scf/day)

43 26 Table 4.7: Pressures at each node (Panhandle B) Node Pressure Table 4.8: Flow rates and Pressure changes for each pipe (Panhandle B) Pressure Change Pipe Leg Pressure Change Flow rate Pipe Flow rate Leg (scf/day)

44 Pressure (Psia) Pipe, 4-Node natural Gas pipeline Network Weymouth panhandle A Panhandle B Node Figure 4.2; Pressure curves for a 5-pipe,4-node Gas pipeline Network

45 Flow Rate (SCF/day) 28 5-Pipe, 4-Node natural Gas pipeline Network Weymouth panhandle A Panhandle B Pipe Figure 4.3; Flow rate curves for a 5-pipe,4-node Gas pipeline Network

46 Pressure Change (Psia) Pipe, 4-Node natural Gas pipeline Network Pipe Leg Figure 4.4; Weymouth pressure change curves for a 5-pipe,4-node Gas pipeline Network

47 Pressure Change (Psia) Pipe, 4-Node natural Gas pipeline Network Pipe Leg Figure 4.5; Panhandle A pressure change curves for a 5-pipe,4-node Gas pipeline Network

48 Pressure Change (Psia) Pipe, 4-Node natural Gas pipeline Network Pipe Leg Figure 4.6; Panhandle B pressure change curves for a 5-pipe,4-node Gas pipeline Network

49 Statistical Analysis The predicted data for the empirical natural gas pipeline flow equations were statistically analyzed. This analysis showed the equation that predicted values were in close agreement with those gotten from the field or experiment. The analysis of variance (ANOVA) method was used for this study Analysis of Variance (ANOVA) This is one of the most common methods used for correlating data (Zar, 1999). This is a statistical procedure for testing the significance of differences among several groups of data (Iversen et al, 1987). Analysis of variance is a technique for analyzing the way the mean of a variable is affected by different types and combination of factors. One-way analysis is the simplest form (Bewick et al., 2004). The ANOVA method that applied to this study is the Mean Deviation ; which is an average of the difference between the predicted and real values. The mean deviation measures how close the values predicted by the empirical pipeline flow equations are to the measured or field data. The standard deviation was also calculated; to measure the dispersion of the set of values. The set of data with the least value for the mean deviation is the best or nearest match to the field data. The following simple equations are used for this analysis D X field X predicted Eq. 4.28

50 33 MD / D / n Eq StDev 1 n 1 n i1 ( x i x) 2 Eq Where, D = Deviation X field = Data from the field X predicted = Data from the equations MD = Mean Deviation StDev = Standard Deviation n = Total number of values

51 34 CHAPTER 5 LOOP ANALYSIS The hypothesis of this project is that in any natural gas pipeline network, each loop in the network would correspond differently to different friction factor equations. Similar loops with the same number of sides may behave differently in different networks. In every network, the loops have certain characteristics based on the physical conditions of that network and would predict pressures at the nodes and flow rates through the pipes more efficiently when different friction factor equations are used effectively in the different loops in the same natural gas pipeline network. The loop analysis reveals the behavior of loops relative to their configuration and number of pipes in the loop. The pressure and flow rate curves show the behavior of the different friction factor equations used for this research; Mueller, Weymouth, Panhandle A, Panhandle B and IGT distribution pipeline flow equations. In this chapter, open loop and close loops would be examined and analyzed. The consistency of the magnitude differences in the five natural gas pipeline flow equations used in this study was also investigated. The consistency of the empirical equations show how the loops would behave when coupled together in a natural gas pipeline network.

52 35 5.1: 3-Pipe, 4-Node open loop This loop consists of three pipes connected in the shape of a cross by four nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.1; A 3-Pipe, 4-Node open loop

53 Presure (Psi) 36 Table 5.1: Node Supply/Demand loads and Pipe parameters for a 3-Pipe, 4-Node open loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in) Pipe, 4-Node open loop Mueller Pressure PanA Pressure PanB Pressure Weymonth Pressure IGT pressure Node Figure 5.2; Pressure curve 3-Pipe, 4-Node open loop

54 Flow Rate (MMSCF) 37 3-Pipe, 4-Node open loop Mueller PanA PanB Weymonth IGT Pipe Figure 5.3; Flow rate curve 3-Pipe, 4-Node open loop The 3-pipe, 4-node open loop shows that the Mueller pipeline flow equation predicts pressure values at the various nodes with the highest magnitude, followed by Panhandle A, then Panhandle B, Weymouth and the IGT distribution pipeline flow equation predicts pressure values with the lowest magnitude for the conditions specified. 5.2: 4-Pipe, 5-Node open loop This loop consists of four pipes connected in the shape of a cross by 5 nodes, with one center node. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth,

55 38 Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.4; A 4-Pipe, 5-Node open loop Table 5.2: Node Supply/Demand loads and Pipe parameters for a 4-Pipe, 5-Node open loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

56 Flow Rate (MMSCF) Presure (Psi) Pipe, 5-Node open loop Mueller Pressure PanA Pressure PanB Pressure Weymonth Pressure IGT pressure Node Figure 5.5; Pressure curve 4-Pipe, 5-Node open loop Pipe, 5-Node open loop Pipe Mueller PanA PanB Weymonth IGT Figure 5.6; Flow rate curve 4-Pipe, 5-Node open loop The 4-pipe, 5-node open loop shows that the Panhandle B pipeline flow equation predicts pressure values at the various nodes with the highest magnitude, followed by Mueller, then Panhandle A, IGT distribution and the Weymouth pipeline flow

57 40 equation predicts pressure values with the lowest magnitude for the conditions specified. From the above curves, it was observed that open loops behave very differently under similar conditions and pipeline physical parameters. If the 3-pipe, 4-node open loop and the 4-pipe, 5-node open loop were combined to make a simple natural gas pipeline network, each loop would correspond differently to any friction factor pipeline flow equation. To accurately model such a system, there is a need to separate the pipeline network into the individual loops and apply different equations to the loops and simultaneously solve the whole network to improve the accuracy of the model. When subsequent loops are closed; they behave differently from the open loop system. The behavior of these loops would facilitate proper understanding and improve future modeling of natural gas pipeline networks that contain these loops. 5.3: 2-Pipe, 2 Node closed loop This loop consists of two pipes connected and closed by two nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth,

58 Pressure (Psig) 41 Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.7; 2-Pipe, 2-Node closed loop Table 5.3: Node Supply/Demand loads and Pipe parameters for a 2-Pipe, 2-Node closed loop Node Supply/Demand (MMSCF) Pressure Pipe Length (miles) Inner Diameter (in) pipe_loop Mueller PanA PanB Weymouth IGT Node Figure 5.8; Pressure curve; 2-Pipe, 2-Node closed loop

59 Flow (MMSCF) 42 2pipe_loop Mueller PanA PanB Weymouth IGT Pipe Figure 5.9; Flow rate curve; 2-Pipe, 2-Node closed loop The 2-pipe, 2-node open loop shows that the Panhandle B pipeline flow equation predicts pressure values and the various nodes with the highest magnitude, followed by Mueller, then Panhandle A, Weymouth and the IGT distribution pipeline flow equation predicts pressure values with lowest magnitude for the conditions specified. 5.4: 3-Pipe, 3-Node closed loop This loop consists of three pipes connected in the shape of a triangle by three nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are

60 43 neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.10; 3-Pipe, 3-Node closed loop Table 5.4: Node Supply/Demand loads and Pipe parameters for a 3-Pipe, 3-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

61 Pressure Change (Psig) Pressure (Pisg) 44 3-Pipe, 3 node closed loop Mueller PanA PanB Weymouth IGT Node Figure 5.11; Pressure curve; 3-Pipe, 3-Node closed loop Pipe, 3 node closed loop Mueller PanA PanB Weymouth IGT -1.4 Pipe Figure 5.12; Pressure change curve; 3-Pipe, 3-Node closed loop

62 Flow (MMSCF) 45 3-Pipe, 3 node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.13; Flow rate curve; 3-Pipe, 3-Node closed loop From the 3-Pipe, 3-Node closed loop curves, the Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made pressure and flow rate predictions that were very close to each other. For the pressure change in the individual pipes, the modified Panhandle pipeline equation predicted pressure changes of the largest magnitude and IGT distribution equation predicted values with the lowest magnitude. 5.5: 4-Pipe, 4-Node closed loop This loop consists of four pipes connected in the shape of a quadrilateral by four nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility

63 46 of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.14; 4-Pipe, 4-Node closed loop Table 5.5: Node Supply/Demand loads and Pipe parameters for a 4-Pipe, 4-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

64 Pressure Change (Psig) Pressure (Psig) 47 4-Pipe, 4 node closed loop mueller PanA PanB Weymouth IGT Node Figure 5.15; Pressure curve; 4-Pipe, 4-Node closed loop 4-Pipe, 4 node closed loop Mueller PanA PanB Weymouth IGT -1.4 Pipe Figure 5.16; Pressure change curve; 4-Pipe, 4-node closed loop

65 Flow (MMSCF) Pipe, 4 node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.17; Flow rate curve; 4-Pipe, 4-node closed loop From the 4-Pipe, 4-node closed loop curves, the Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes of pressures and flow rates. For the pressure change in the individual pipes, the Modified Panhandle pipeline equation predicted pressure changes of the greatest magnitude and IGT distribution equation predicted values with the lowest magnitude. 5.6: 5-Pipe, 5-Node closed loop This loop consists of five pipes connected in the shape of a pentagon by five nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility

66 49 of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.18; 5-Pipe, 5-Node closed loop Table 5.6: Node Supply/Demand loads and Pipe parameters for a 5-Pipe, 5-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

67 Pressure Change (Psig) Pressure (Psia) 50 5-Pipe, 5 node closed loop Mueller PanA PanB Wymouth IGT Node Figure 5.19; Pressure curve; 5-Pipe, 5-Node closed loop 5-Pipe, 5 node closed loop Mueller PanA PanB Weymouth IGT -0.9 Pipe Figure 5.20; Pressure change curve; 5-Pipe, 5-node closed loop

68 Flow (MMSCF) Pipe, 5 node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.21; Flow rate curve; 5-Pipe, 5-Node closed loop From the 5-Pipe, 5-Node closed loop curves, the Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes of pressures and flow rates. For the pressure change in the individual pipes, the Modified Panhandle pipeline equation predicted pressure changes of the greatest magnitude and IGT distribution equation predicted values with the lowest magnitude. 5.7: 6-Pipe, 6-Node closed loop This loop consists of six pipes connected in the shape of a hexagon by six nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility

69 52 of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.22; 6-Pipe, 6-Node closed loop Table 5.7: Node Supply/Demand loads and Pipe parameters for a 6-Pipe, 6-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

70 Pressure Change (Psig) Pressure (Psig) Pipe, 6-Node closed loop Node Mueller PanA PanB Wymouth IGT Figure 5.23; Pressure curve; 6-Pipe, 6-Node closed loop 1 6-Pipe, 6-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.24; Pressure change curve; 6-Pipe, 6-Node closed loop

71 Flow (MMSCF) Pipe, 6-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.25; Flow rate curve; 6-Pipe, 6-Node closed loop From the curves, we observe that Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes of pressures and flow rates. For the pressure change in the individual pipes, the Modified Panhandle pipeline equation predicted pressure changes of the greatest magnitude and IGT distribution equation predicted values with the lowest magnitude. 5.8: 7-Pipe, 7-Node closed loop This loop consists of seven pipes connected in the shape of a heptagon by seven nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility

72 55 of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.26; 7-Pipe, 7-Node closed loop Table 5.8: Node Supply/Demand loads and Pipe parameters for a 7-Pipe, 7-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

73 Pressure Change (Psig) Pressure (Psig) 56 7-Pipe, 7-Node closed loop Mueller PanA PanB Weymouth IGT Node Figure 5.27; Pressure curve; 7-Pipe, 7-Node closed loop 7-Pipe, 7-Node closed loop Mueller PanA -1.5 PanB Weymouth -2 IGT -2.5 Pipe Figure 5.28; Pressure change curve; 7-Pipe, 7-Node closed loop

74 Flow (MMSCF) Pipe, 7-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.29; Flow rate curve; 7-Pipe, 7-Node closed loop From the 7-Pipe, 7-Node closed loop curves, the Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes of pressures and flow rates. For the pressure change in the individual pipes, the Modified Panhandle pipeline equation predicted pressure changes of the greatest magnitude and IGT distribution equation predicted values with the lowest magnitude. 5.9: 8-Pipe, 8-Node closed loop This loop consists of eight pipes connected in the shape of an octagon by eight nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility

75 58 of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.30; 8-Pipe, 8-Node closed loop Table 5.9: Node Supply/Demand loads and Pipe parameters for a 8-Pipe, 8-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

76 Pressure Change (Psig) Pressure (Psig) 59 8-Pipe, 8-Node closed loop Mueller PanA PanB Weymouth IGT Node Figure 5.31; Pressure curve; 8-Pipe, 8-Node closed loop 8-Pipe, 8-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.32; Pressure change curve; 8-Pipe, 8-Node closed loop

77 Flow (MMSCF) 60 8-Pipe, 8-Node closed loop Mueller PanA PanB Weymouth IGT -200 Pipe Figure 5.33; Flow rate curve; 8-Pipe, 8-Node closed loop From the 8-Pipe, 8-Node closed loop curves, the Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes for the flow rates in each pipe. For the pressure in each node and pressure change across each pipe, the Panhandle A pipeline equation predicted pressure changes of the greatest magnitude and IGT distribution equation predicted values with the lowest magnitude. 5.10: 9-Pipe, 9-Node closed loop This loop consists of nine pipes connected in the shape of a nonagon by nine nodes. This network has pipes with absolute roughness of ft, base pressure and

78 61 temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.34; 9-Pipe, 9-Node closed loop Table 5.10: Node Supply/Demand loads and Pipe parameters for a 9-Pipe, 9-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

79 Pressure Change (Psig) Pressure (Psig) 62 9-Pipe, 9-Node closed loop Node Mueller PanA PanB Weymouth IGT Figure 5.35; Pressure curve; 9-Pipe, 9-Node closed loop 9-Pipe, 9-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.36; Pressure change curve; 9-Pipe, 9-Node closed loop

80 Flow (MMSCF) Pipe, 9-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.37; Flow rate curve; 9-Pipe, 9-Node closed loop From the 9-Pipe, 9-Node closed loop curves, we observe that Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes for the flow rates in each pipe. For the pressure in each node and pressure change across each pipe, the Mueller pipeline equation predicted pressure changes of the greatest magnitude and the Weymouth equation predicted values with the lowest magnitude. 5.11: 10-Pipe, 10-Node closed loop This loop consists of ten pipes connected in the shape of a decagon by ten nodes. This network has pipe with absolute roughness of ft, Base pressure and

81 64 temperature are 14.7 psia and 60.0F respectively. Average gas compressibility of 0.86, Average gas gravity of 0.62 and Average temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.38; 10-Pipe, 10-Node closed loop

82 Pressure (Psig) 65 Table 5.11: Node Supply/Demand loads and Pipe parameters for a 10-Pipe, 10-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in) Pipe, 10-Node closed loop Node Mueller PanA PanB Weymouth IGT Figure 5.39; Pressure curve; 10-Pipe, 10-Node closed loop

83 Flow (MMSCF) Pressure Change (Psig) Pipe, 10-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.40; Pressure change curve; 10-Pipe, 10-Node closed loop Pipe, 10-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.41; Flow rate curve; 10-Pipe, 10-Node closed loop

84 67 From the curves, we observe that Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes for the flow rates in each pipe. For the pressure in each node and pressure change across each pipe, the Mueller pipeline equation predicted pressure changes of the greatest magnitude and the Weymouth equation predicted values with the lowest magnitude. 5.12: 11-Pipe, 11-Node closed loop This loop consists of eleven pipes connected in the shape of an undecagon by eleven nodes. This network has pipes with absolute roughness of ft, base pressure and temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop.

85 68 Figure 5.42; 11-Pipe, 11-Node closed loop Table 5.12: Node Supply/Demand loads and Pipe parameters for a 11-Pipe, 11-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in)

86 Pressure Change (Psig) Pressure (Psig) Pipe, 11-Node closed loop Mueller PanA PanB Weymouth IGT Node Figure 5.43; Pressure curve; 11-Pipe, 11-Node closed loop 11-Pipe, 11-Node closed loop Mueller PanA -15 PanB Weymouth -20 IGT -25 Pipe Figure 5.44; Pressure change curve; 11-Pipe, 11-Node closed loop

87 Flow (MMSCF) Pipe, 11-Node closed loop Pipe Mueller PanA PanB Weymouth IGT Figure 5.45; Flow rate curve; 11-Pipe, 11-Node closed loop From the curves, we observe that Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes for the flow rates in each pipe. For the pressure in each node and pressure change across each pipe, the Mueller pipeline equation predicted pressure changes of the greatest magnitude and the Weymouth equation predicted values with the lowest magnitude. 5.13: 12-Pipe, 12-Node closed loop This loop consists of twelve pipes connected in the shape of a dodecagon by twelve nodes. This network has pipes with absolute roughness of ft, base pressure and

88 71 temperature are 14.7 psia and 60.0F respectively, with an average gas compressibility of 0.86, gas specific gravity of 0.62 and temperature of 82.0F. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A and Panhandle B equations. Elevation changes are neglected. The calculations are performed for Weymouth, Panhandle A, Panhandle B, Mueller and IGT equations. Below is a pictorial view of the loop. Figure 5.46; 12-Pipe, 12-Node closed loop

89 Pressure (Psig) 72 Table 5.13: Node Supply/Demand loads and Pipe parameters for a 12-Pipe, 12-Node closed loop Node Supply/Demand (MMSCF) Pipe Length (miles) Inner Diameter (in) Pipe, 12-Node closed loop Node Mueller PanA PanB Weymouth IGT Figure 5.47; Pressure curve; 12-Pipe, 12-Node closed loop

90 Flow (MMSCF) Pressure Change (Psig) Pipe, 12-Node closed loop Mueller PanA PanB Weymouth IGT -30 Pipe Figure 5.48; Pressure change curve; 12-Pipe, 12-Node closed loop 12-Pipe, 12-Node closed loop Mueller PanA PanB Weymouth IGT -400 Pipe Figure 5.49; Flow rate curve; 12-Pipe, 12-Node closed loop

91 74 From the 12-Pipe, 12-Node closed loop curves, we observe that Mueller, Panhandle A, Panhandle B, Weymouth and the IGT distribution pipeline flow equations made predictions that were very close to each other in magnitudes for the flow rates in each pipe. For the pressure in each node and pressure change across each pipe, the Mueller pipeline equation predicted pressure changes of the greatest magnitude and the Weymouth equation predicted values with the lowest magnitude. In the case of the 3-Pipe, 4-Node open loop, the Mueller gas pipeline flow equation predicted the greatest values in magnitude of pressure for the specified conditions and the IGT distribution equation predicts the least. In the case of the 4-Pipe, 5-Node open loop, the Modified Panhandle equation predicts the highest pressures and Weymouth predicts the lowest. In the cases of the 2-Pipe, 2 node closed loop, 3-Pipe, 3-Node closed loop, 4-Pipe, 4-Node closed loop, 5-Pipe, 5-Node closed loop, 6-Pipe, 6-Node closed loop and 7-Pipe, 7-Node closed loop; the highest pressure values were predicted by the Modified Panhandle gas pipeline equation and the least were predicted by the IGT distribution gas pipeline equations. For the case of the 8-Pipe, 8-Node closed loop, the Panhandle equation predicted the greatest magnitude of pressures and the IGT equation predicted the least. And for the cases of the 9-Pipe, 9- Node closed loop, 10-Pipe, 10-Node closed loop, 11-Pipe, 11-Node closed loop and 12-Pipe, 12-Node closed loop; the Mueller gas pipeline equation predicted the highest pressures and the Weymouth equation predicted the least.

92 75 There are variations in the equations that predict the greatest and the least pressures for the different loops with different number of pipes. A Natural gas pipeline network, where there are numerous loops, configured in different orientations, can be modeled more accurately using different friction factor equations in different loops. The equations used for a loop to predict the steady and transient state values in the network has to be determined by a steady state study of the individual loops in the natural gas pipeline network. Using the initial field data of any network, the appropriate friction factor equation capable of efficient predictions of pressures and flow rates can be determined. The correlation values of the loop predicted values to field data can determine the best equation to use on a particular loop in a particular natural gas network.

93 76 CHAPTER 6 SECTIONAL ANALYSIS A natural gas pipeline network can be divided into sections; these sections could contain one or more open and closed loops. The main hypothesis is that in any natural gas pipeline network, each section in the network would respond in terms of accuracy, differently to the different friction factor equations. Each section would possess characteristics based on the physical configurations of the network. The predicted pressure and flow rate values are more accurate when different friction factor equations are used effectively for different sections in the same network. The section analysis shows the behavior of natural gas pipeline networks and their correlation to the different sections that make up the network. The pressure and flow rate curves show the behavior of the networks before and after they were divided into sections and analyzed. The pressure and flow rate curves also show the behavior of the Mueller, Weymouth, Panhandle A, Panhandle B and IGT distribution pipeline equations. In this chapter, the correlation of the accuracy of these equations is compared to reference data. The sections are divided based on these correlations. The equation that predicts the values closest to the reference data is used for that section. The combination of frictions factors for the sections are then used to calculate the entire network.

94 77 6.1: 51-Pipe, 41-Node Natural Gas Pipeline Network In this experimental case, the reference data is obtained from the Friction factor equations. Fig 6.1 is a schematic of the pipeline network. It consist of fifty one pipelines and forty one nodes. The supply network is 1000 psia at node number 1 and inlet temperature of 60.0F and the gas has a specific gravity of 0.6. This network would go through a steady state analysis to predict the gas flow rates of natural gas passing through each pipe and pressure values at each node Steady state analysis The steady state analysis is performed using Mueller, Panhandle A, Panhandle B, Weymouth and IGT distribution empirical pipeline flow equations. Input values are shown in Table 6.1 and Table 6.2 and the results of the steady state analysis are shown in the subsequent table

95 78 Table 6.1: Nodal Supply / Demand for 51-Pipe, 41-Node Natural gas pipeline network Node Supply/Demand (MMSCF) Pressure (Psig)

96 79 Table 6.2: 51-Pipe, 41-Node Pipeline Network Characteristics Pipe Length (miles) Diamter (in)

97 Figure 6.1: Schematic of a 51-Pipe, 41-Node Gas Distribution Network

98 81 Table 6.3: Steady State results for 51-Pipe, 41-Node Pipeline Network (Pressures at each node) IGT Weymouth Panhandle A Panhandle B Mueller Node Pressure (Psig) Pressure (Psig) Pressure (Psig) Pressure (Psig) Pressure (Psig)

99 82 Table 6.4: Steady State results for 51-Pipe, 41-Node Pipeline Network (Flow rate through each pipe) Pipe IGT Weymouth Panhandle A Panhandle B Mueller COMB_WE_F COMB_PB_F Flow (MMSCF/D) Flow (MMSCF/D) Flow (MMSCF/D) Flow (MMSCF/D) Flow (MMSCF/D) Flow (MMSCF/D) Flow (MMSCF/D)

100 Pressure (Psia) Pipe, 41-Node Network Node IGT Weymouth Panhandle A Panhandle B Mueller Figure 6.2: Steady State Pressure Analysis

101 Flow rate (MMScf) Pipe, 41-Node Network Pipe IGT Weymouth Panhandle A Panhandle B Mueller Figure 6.3: Steady State Flow rate Analysis The figures above show the prediction of the friction equation on the 51-Pipe, 41- Node pipeline network. The predictions made using Mueller, Panhandle A, Panhandle B, Weymouth and IGT distribution pipeline equations made predictions that were close to each other in magnitude. The sectional analysis is performed using the different equations as a reference. Figure 6.6 shows a schematic of the network divided into sections. In the event of bordering pipes in between two sections, the equation used for those pipe would be the one that has the closest values to the reference data for the entire natural gas pipeline network.

102 85 Figure 6.4: schematic of the network divided into sections Table 6.5 (A&B) shows the values for section I, Table 6.6 (A&B) shows the values for section II, Table 6.7 (A&B) shows the values for section III and Table 6.8 (A&B) shows the values for section IV.

103 86 Table 6.5A Pressure values for Section I Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig) Table 6.5B Flow rate values for Section I Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

104 87 Table 6.6A Pressure values for Section II Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig) Table 6.6B Flow rate values for Section II Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

105 88 Table 6.7A Pressure values for Section III Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig) Table 6.7B Flow rate values for Section III Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

106 Table 6.8A Pressure values for Section IV Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig)

107 90 Table 6.8B Flow rate values for Section IV Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

108 Sectional Analysis (Panhandle B data as the reference) The predicted values, gotten from the Panhandle B equation were used as the reference data. The following statistical correlations were obtained. Table 6.9: Statistical correlations for pressure values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth Table 6.10: Statistical correlations for flow rate values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth From the above data in Table 6.9 and Table 6.10, we can observe that for pressure value, Panhandle A is in better agreement with the reference data than the other equations and for flow rate values Panhandle A is the closest. The subsequent tables show the statistical correlations in the sections.

109 Section I Table 6.11: Section I - Statistical correlations for pressure values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth Table 6.12: Section I - Statistical correlations for flow rate values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth From table 6.11 and Table 6.12, the equation with the least deviation is Mueller for pressure values and Weymouth for Flow rates Section II Table 6.13: Section II - Statistical correlations for pressure values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth

110 93 Table 6.14: Section II - Statistical correlations for flow rate values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth From table 6.13 and Table 6.14, the equation with the least deviation is Panhandle A for pressure values and Flow rates Section III Table 6.15: Section III - Statistical correlations for pressure values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth Table 6.16: Section III - Statistical correlations for flow rate values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth From table 6.15 and Table 6.16, the equation with the least deviation is Panhandle A for pressure values and Flow rates.

111 Section IV Table 6.17: Section IV - Statistical correlations for pressure values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth Table 6.18: Section IV - Statistical correlations for flow rate values (Panhandle B data as the reference) Level N Mean St. Dev IGT Mueller Pan A Weymouth From table 6.17 and Table 6.18, the equation with the least deviation is Panhandle A for pressure values and Flow rates. In this case for the Pressure prediction, IGT would be the best equation and Panhandle B would produce the best results for flow rates Combination Based on the data from the sectional analyses, the ideal combination for the section of the network is shown in Table 6.19.

112 95 Table 6.19: Sections and their friction factor equations Section Pressure Flow I MU WE II PA PA III PA PA IV PA PA

113 96 Table 6.20: Steady State results for 51-Pipe, 41-Node Pipeline Network (Pressures at each node) Node IGT Weymouth Panhandle A Panhandle B Mueller COMB_PB_P Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) Pressure (Psig)

114 Table 6.21: Steady State results for 51-Pipe, 41-Node Pipeline Network (Flow rate through each pipe) Pipe IGT Weymouth Panhandle A Panhandle B Mueller COMB_PB_F Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) Flow (MMSCF/D)

115 Table 6.22: Statistical correlations for pressure values (Panhandle B data as the reference) Level N Mean St. Dev Meuller Pan A Pan B Weymouth COMB Table 6.23: Statistical correlations for flow rate values (Panhandle B data as the reference) Level N Mean St. Dev Meuller Pan A Pan B Weymouth COMB

116 Sectional Analysis (Weymouth data as the reference) The predicted values, gotten from the Weymouth equation were used as the reference data. The following statistical correlations were obtained. Table 6.24: Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB Table 6.25: Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB From the above data in Table 6.9 and Table 6.10, we can observe that for pressure value, IGT is closer to the reference data than the other equations and for flow rate values Panhandle B is the closest. The subsequent tables show the statistical correlations in the sections.

117 Section I Table 6.26: Section I - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB Table 6.27: Section I - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB From table 6.26 and Table 6.27, the equation with the least deviation is IGT for pressure values and Panhandle B for Flow rates Section II Table 6.28: Section II - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB

118 101 Table 6.29: Section II - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB From table 6.28 and Table 6.29, the equation with the least deviation is IGT for pressure values and IGT for Flow rates Section III Table 6.30: Section III - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB Table 6.31: Section III - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB From table 6.30 and Table 6.31, the equation with the least deviation is IGT for pressure values and Panhandle B for Flow rates.

119 Section IV Table 6.32: Section IV - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB Table 6.33: Section IV - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean St. Dev IGT Meuller Pan A PanB From table 6.32 and Table 6.33, the equation with the least deviation is IGT for pressure values and Panhandle B for Flow rates. In this case for the Pressure prediction, IGT would be the best equation and Panhandle B would produce the best results for flow rates.

120 Summary The Network can be summarized, based on the data predicted. The best combinations for the sections are given in Table 6.34 and Table 6.35, using different friction factor equations to generate the reference data. Table 6.34: Pressure Summary PRESSURE Section WE as ref IGT as ref PA as ref PB as ref MU as ref 1 IGT PA PB MU PB 2 IGT PA PB PA PB 3 IGT PA PB PA PB 4 IGT PA PB PA PB Table 6.35: Flow rate Summary FLOW Section WE as ref IGT as ref PA as ref PB as ref MU as ref 1 PB PA IGT WE IGT 2 PB PA IGT PA IGT 3 PB PA IGT PA IGT 4 PB PA IGT PA IGT

121 : 53-Pipe, 31-Node Natural Gas Pipeline Network In this experimental case, the reference data is obtained from friction factor equations. Fig 6.7 is a schematic of the pipeline network. It consists of fifty one pipelines and forty one nodes. The supply network is 1200 psia at node number 1 and inlet temperature of 60.0F and the gas has a specific gravity of 0.6. This network would go through a steady state analysis to predict the gas flow rates in each pipe and pressure values at each node Steady state analysis The steady state analysis is performed using Mueller, Panhandle A, Panhandle B, Weymouth and IGT distribution empirical pipeline flow equations. Input values are shown in Table 6.36 and Table 6.37 and the results of the steady state analysis are shown in the subsequent table

122 105 Table 6.36: Nodal Supply / Demand for 53-Pipe, 31-Node Natural gas pipeline network Node Supply/Demand (MMSCF) Pressure (Psig)

123 106 Table 6.37: 53-Pipe, 31-Node Pipeline Network Characteristics Pipe Diamter (in) Length (miles)

124 Figure 6.5: Schematic of a 53-Pipe, 31-Node Gas Distribution Network

125 108 Table 6.38: Steady State results for 53-Pipe, 31-Node Pipeline Network (Pressures at each node) Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig)

126 109 Table 6.39: Steady State results for 53-Pipe, 31-Node Pipeline Network (Flow rate through each pipe) Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

127

128 Flow rate (MMScf) Pressure (psia) Pipe, 31-Node Network Node IGT Weymouth Panhandle A Panhandle B Mueller Figure 6.6: Steady State Pressure Analysis 53-Pipe, 31-Node Network Pipe IGT Weymouth Panhandle A Panhandle B Mueller Figure 6.7: Steady State Flow rate Analysis The figures above show the prediction of the friction equation on the 53-Pipe, 31- Node pipeline network. The Mueller, Panhandle A, Panhandle B, Weymouth and

129 112 IGT distribution pipeline equations made predictions that were close to each other in magnitude. The sectional analysis is performed using the different equations as a reference. Figure 6.10 shows a schematic of the network divided into sections. In the event of bordering pipes in between two sections, the equation used for those pipes would be the one that has the closest values to the reference data for the entire natural gas pipeline network.

130 113 Figure 6.8: schematic of the network divided into sections Table 6.40 (A&B) shows the values for section I, Table 6.41 (A&B) shows the values for section II, Table 6.42 (A&B) shows the values for section III and Table 6.43 (A&B) shows the values for section IV.

131 114 Table 6.40A Pressure values for Section I Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig) Table 6.40B Flow rate values for Section I Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

132 115 Table 6.41A Pressure values for Section II Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig)

133 116 Table 6.41B Flow rate values for Section II Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

134 117 Table 6.42A Pressure values for Section III Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig) Table 6.42B Flow rate values for Section III Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

135 118 Table 6.43A Pressure values for Section IV Node IGT Pressure (Psig) Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Pressure (Psig) Mueller Pressure (Psig) Table 6.43B Flow rate values for Section IV Pipe IGT Weymouth Panhandle A Panhandle B Mueller Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D)

136 Sectional Analysis (Weymouth data as the reference) This section focuses on the flow rate values. The predicted values, gotten from the Weymouth equation were used as the reference data. The following statistical correlations were obtained. Table 6.44: Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB

137 120 Table 6.45: Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB From the above data in Table 6.44 and Table 6.45, we can observe that for pressure value, IGT is closer to the reference data than the other equations and for flow rate values Panhandle A is the closest. The subsequent tables show the statistical correlations in the sections Section I Table 6.46: Section I - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB Table 6.47: Section I - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB

138 121 From table 6.46 and Table 6.47, the equation with the least deviation is IGT for pressure values and Panhandle B for Flow rates Section II Table 6.48: Section II - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB Table 6.49: Section II - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB From table 6.48 and Table 6.49, the equation with the least deviation is IGT for pressure values and Panhandle A Flow rates.

139 Section III Table 6.50: Section III - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB Table 6.51: Section III - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB From table 6.50 and Table 6.51, the equation with the least deviation is IGT for pressure values and Panhandle B for Flow rates Section IV Table 6.52: Section IV - Statistical correlations for pressure values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB

140 123 Table 6.53: Section IV - Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean StDev IGT Mueller PanA PanB From table 6.52 and Table 6.53, the equation with the least deviation is IGT for pressure values and Panhandle A for Flow rates Combination Based on the data from the sectional analyses, the ideal combination for the section of the network is shown in Table Table 6.54: Sections and corresponding friction factor equations Section Pressure Flow I IGT PB II IGT PA III IGT PB IV IGT PA

141 124 Table 6.55: Steady State results for 53-Pipe, 31-Node Pipeline Network (Flow rate through each pipe) Pipe IGT Weymouth Panhandle A Panhandle B Mueller COMB_WE_F Flow Flow Flow Flow Flow (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) (MMSCF/D) Flow (MMSCF/D)

142 Table 6.56: Statistical correlations for flow rate values (Weymouth data as the reference) Level N Mean StDev COMB IGT Mueller PanA PanB Summary The Network can be summarized, based on the data predicted. The best combinations for the sections are given in Table 6.57 and Table 6.58, using different friction factor equations to generate the reference data.

143 126 Table 6.57: Pressure Summary PRESSURE Section WE as ref IGT as ref PA as ref PB as ref MU as ref 1 IGT WE MU MU PB 2 IGT WE MU MU PB 3 IGT WE MU MU PB 4 IGT WE MU MU PB Table 6.58: Flow rate Summary FLOW Section WE as ref IGT as ref PA as ref PB as ref MU as ref 1 PB PA IGT WE IGT 2 PA PA IGT PA IGT 3 PB PA IGT PA IGT 4 PA PA IGT PA IGT This section has demonstrated that the combination of friction factor equations based on the minimum correlation to the reference data in each section would produce data for the entire network with the least correlation to the reference data.

144 127 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS 7.1 Conclusions There is a pressing need for the calculations, modeling and simulation of natural gas pipeline networks to be as accurate as possible in accord with the current state of computational technology. Several equations are available for steady state analysis of natural gas pipelines. In design and simulations these equations are used and they may predict pressure and flow rate with varying degree of accuracy for natural gas pipeline networks. This study demonstrates that the combination of friction factor equations in a natural gas pipeline network can yield more accurate output values. The study also shows that the numerical solutions used for this project, applies the model to analyze different loop orientations and validates the work by performing sectional analysis on several natural gas pipeline networks. The combination of friction factors appropriately in the network resulted in reduced deviations of output values when compared to field data. This work can be applied to diverse cases and can be readily incorporated in industrial simulators and solvers. More complex networks can be broken down and isolated into various sections and analyzed to determine the best combination of friction factor equations needed for the most efficient and accurate simulation of the network.

145 Recommendations Several natural gas pipeline networks pass through areas of changing temperature. A good example would be pipelines that run from land to sea and vice versa. Changes in the total energy can be taken into consideration by incorporating energy balances. This work could be extended to study networks that are not assumed to be isothermal in nature. This work can be extended to other gases; beyond natural gas. The simulation of hydrocarbons in liquid phase through pipeline networks can be improved through this work. This work can also be extended to hydrocarbons that flow in multiple phases, in industrial transportation of chemicals and water supply. This study can be continued by exploring the relationship between pipeline length and friction factors.

146 129 BIBLIOGRAPHY Aina, I. O.: Steady-State and Transient flow studies in Natural Gas Pipeline Networks, The Pennsylvania State University, (2006). Ayala, l.f.: PNG 530 Class Notes, The Pennsylvania State University, University Park, PA,(2007). Beggs, H. D.: Gas production Operations. Oil and Gas Consultants International, Inc., October (2002). Bewick, V., Cheek, L., Ball, J.: Statistics review 9: One way analysis of variance, Biomed Central Ltd, March (2004). Center for Energy ( last accessed; May/12/2008. Coelho, P.M., Pinho, C.: Considerations about equations for steasy state flow in natural gas pipelines, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Volume 29, No. 3, (2007). Costa, A.L.H.: Steady State Modeling and Simulation of Pipeline Networks for Compressible Fluids, Brazilian Journal of Chemical Engineering, Volume 15, No. 4. (1998). Dolan, A., Aldous, J.: Networks and Algorithms; An Introductory Approach, John Wiley & Sons, (1993). Iversen, G.R., Norpoth, H.: Analysis of Variance, PP 10-20, Sage University paper, London, UK, (1987)

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149 132 APPENDIX THEORY VALIDATION Verification of the proposed theory; showing that it is accurate and reliable requires addressing the following considerations: - The accuracy of predictions by the individual friction factor equations. - The individual loops in the natural gas pipeline network behave differently and show variations in the equations that predict the highest and lowest pressures. -The use of different friction factor equation in different loops yield predictions that are closer to the field or experimental data than any of the equations used in the analysis. -A Visual comparison between calculated and field data for cases confirms and verifies the hypothesis. Statistical and quantitative measures, also present numeric validation of the project.

150 133 APPENDIX A A.1 Steady State Analysis of a 21-Pipe, 16-Node Network The field network example is represented by Fig A.1, which show a schematic drawing of a section of the consumer power company s gas transmission network serving lower Michigan (Stoner (1968), Wylie at al. (1971) & Zhou et al. (1998)). It is made up of 21 pipelines and 16 nodes. At initial measured nodal pressure at node #1 in the field network is 547 Psia. The average molecular weight of the gas is 17.5 Ibm/Ibm-mole; the average temperature of the gas in the network is 495 o R and an average compressibility factor of 0.9. A steady state analysis is performed on this network. The steady state analysis is performed using the Mueller, Panhandle, Modified Panhandle, Weymouth and IGT distribution empirical pipeline flow equations. Zhou et al. (1998) performed an extensive steady state analysis of this network. In their work Zhou and Adewumi did not neglect kinetic energy. The field network example was simulated using Zhou-Adewumi s analytical flow equation and the LTM steady state flow network scheme. Their results were compared with the Weymouth, Panhandle A and Panhandle B equations. Input values are shown in Table A.1 and Table A.2, while the results of the steady state analysis are shown in subsequent tables; Table A.3 shows the steady state pressure results, and Table A.4 shows the steady state flow rate results.

151 134 Table A.1: Nodal Load for 21-Pipe, 16-Node Pipeline Network (Aina, 2006) Node Supply/Demand ( MMCF/D )

152 135 Table A.2: 21-Pipe, 16-Node Pipeline Network Characteristics (Aina, 2006) Pipe Length (miles) Diamter (in) Upstream Node Downstream Node Pipe elevations

153 Figure A.1: Schematic of a section of the consumer power company s gas transmission network serving Lower Michigan (Zhou et al., 1998) 136

154 137 Table A.3: Steady State results for 21-Pipe, 16-Node Pipeline Network (Pressures at each node) Weymouth Panhandle A Panhandle B Mueller IGT Measured Node P (psia) P (psia) P (psia) P (psia) P (psia) P (psia)

155 138 Table A.4: Steady State results for 21-Pipe, 16-Node Pipeline Network (Flow rate through each pipe) Weymouth Panhandle A Panhandle B Mueller IGT Pipe (MMSCFD) (MMSCFD) (MMSCFD) (MMSCFD) (MMSCFD)

156 Pressure (Psig) Pressure (Psig) Lower Michigan Power Co. Zhou et al. (Weymouth) This Model (Weymouth) Node Figure A.2: Steady State Pressure Using Weymouth Equation Lower Michigan Power Co. Zhou et al. (Panhandle A) This Model (Panhandle A) Node Figure A.3: Steady State Pressure Using Panhandle A Equation

157 Abs. value of Flow Rate (MMSCF/D) Pressure (Psig) 140 Lower Michigan Power Co Node Zhou et al. (Panhandle B) This Model (Panhandle B) Figure A.4: Steady State Pressure Using Panhandle B Equation Lower Michigan Power Co Pipe Zhou et al. (Weymouth) This Model (Weymouth) Figure A.5: Steady State Flow rate Using Weymouth Equation

158 Abs. value of Flow Rate (MMSCF/D) Abs. value of Flow Rate (MMSCF/D) 141 Lower Michigan Power Co Pipe Zhou et al. (Panhandle A) This Model (Panhandle A) Figure A.6: Steady State Flow rate Using Panhandle A Equation Lower Michigan Power Co Pipe Zhou et al. (Panhandle B) This Model (Panhandle B) Figure A.7: Steady State Flow rate Using Panhandle B Equation

159 Abs. value of Flow Rate (MMSCF/D) Pressure (Psig) 142 Lower Michigan Power Co Node Mueller Pan A Pan B Weymouth IGT Measured Figure A.8: Steady State Pressure analysis Lower Michigan Power Co Pipe Mueller Pan A Pan B Weymouth IGT Figure A.9: Steady State Flow rate analysis

160 143 The figures above show the prediction of the friction factor equations on a section of the consumer power company s gas transmission network serving Lower Michigan. From the 21-Pipe, 16-Node natural gas pipeline curves, we observe that Mueller predicted the greatest values on average for pressures and Weymouth predicted the lowest magnitudes on average. The Mueller, Panhandle A, Panhandle B, Weymouth and IGT distribution pipeline flow equations made flow rate predictions that were very close to each other. A.2 Loop Analysis The section of the consumer power company s gas transmission network serving Lower Michigan can be divided into 6 sections; all closed loops. The loops are analyzed separately for the best friction factor calculation. The Figure A.10 shows a schematic of the gas distribution network divided into sections for loop analysis. Section I and II are 4-Pipe, 4-Node closed loops, section IV is a 5-Pipe, 5-Node closed loop, section III and V are 6-Pipe, 6-Node closed loops while Section VI is a 2-Pipe, 2-Node closed loop.

161 Figure A.10: Schematic of the Gas Distribution Network divided into sections for loop analysis. 144

162 Pressure (Psig) 145 A.2.1: Loop Analysis of section I Figure A.11: Schematic of section I of the Gas Distribution network. The graph, (Fig. A.12) shows that for the pressure in each node, the Panhandle B pipeline equation predicted pressures of the greatest magnitude and IGT predicted pressures with the least magnitude. Figure A.13 shows deviation analysis. The Weymouth equation has the lowest deviation; suggesting its use for this loop would yield accurate results. Lower Michigan Power Co. I Node Mueller PanA PanB Weymouth IGT Measures Figure. A.12: Steady State Analysis for section I.

163 146 Node Supply/Demand (MMcf/D) Pressure (Psig) Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) avg Deviation = Calc - Measured Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Abs. Deviation = Calc - Measured Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Figure A.13: Input data and results for steady state analysis of section I.

164 147 A.2.2: Loop Analysis of section II Figure A.14: Schematic of section II of the Gas Distribution network. The graph, (Fig.A.15) shows that for the pressure in each node, the Panhandle B pipeline equation predicted pressures of the greatest magnitude and IGT predicted pressures with the least magnitude. The Fig.A.16 shows deviation analysis. The IGT equation has the lowest deviation; therefore it is the most appropriate for this loop. These curves also show that the two 4-Pipe, 4-Node closed loops are similar.

165 Axis Title Axis Title Mueller PanA PanB Weymouth IGT Measured Figure. A.15: Steady State Analysis for section II.

166 149 Node Supply/Demand (MMcf/D) Pressure (Psig) Node Measured Pressure (Psig) Node Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) Average Node Deviation = Calc - Measured Panhandle Weymouth A Pressure Pressure (Psig) (Psig) Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) Average Node Abs. Deviation = Calc - Measured Panhandle Weymouth A Pressure Pressure (Psig) (Psig) Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) Average Figure A.16: Input data and results for steady state analysis of section II.

167 150 A.2.3: Loop Analysis of section III Figure A.17: Schematic of section III of the Gas Distribution network. The graph, (Fig.A.18) shows that for the pressure in each node, the Panhandle B pipeline equation predicted pressures of the greatest magnitude and IGT predicted pressures with the least magnitude. The Fig.A.19 shows deviation analysis. The Panhandle A equation has the lowest deviation; suggesting its use for this loop would yield accurate results.

168 Pressure (Psig) Lower Michigan Power Co. III Node Mueller PanA PanB Weymouth IGT Measured Figure A.18: Steady State Analysis for section III. Node Supply / Demand (MMcf/D) Pressure (Psig) Measured Pressure Node (Psig) Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Figure A.19A: Input data and results for steady state analysis of section III.

169 152 Deviation = Calc - Measured Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Abs. Deviation = Calc - Measured Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Figure A.19B: Deviation results for steady state analysis of section III.

170 153 A.2.4: Loop Analysis of section IV Figure A.20: Schematic of section IV of the Gas Distribution network. The graph, (Fig.A.21) shows that for the pressure in each node, the Panhandle B pipeline equation predicted pressures of the greatest magnitude and Weymouth predicted pressures with the least magnitude. The Fig.A.22 shows deviation analysis. The Weymouth equation has the lowest deviation; suggesting its use for this loop would yield accurate results.

171 Pressure (Psig) 154 Lower Michigan Power Co. IV Mueller PanA PanB Weymouth IGT Meaasured Node Figure A.21: Steady State Analysis for section IV.

172 155 Node Supply / Demand (MMcf/D) Pressure (Psig) Node Measured Pressure (Psig) Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Deviation = Calc - Measured Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Abs. Deviation = Calc - Measured Node Weymouth Panhandle A Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) (Psig) (Psig) Average Figure A.22: Input data and results for steady state analysis of section IV.

173 156 A.2.5: Loop Analysis of section V Figure A.23: Schematic of section V of the Gas Distribution network. The graph, (Fig.A.24) shows that for the pressure in each node, the Panhandle B pipeline equation predicted pressures of the greatest magnitude and IGT predicted pressures with the least magnitude. The Fig.A.25 shows deviation analysis. The Weymouth equation has the lowest deviation; suggesting its use for this loop would yield accurate results.

174 Pressure (psig) 157 Lower Michigan Power Co. V Mueller PanA PanB Weymouth IGT Measured Node Figure A.24: Steady State Analysis for section V.

175 158 Node Supply / Demand (MMcf/D) Pressure (Psig) Node Measured Pressure (Psig) Node Weymouth Pressure (Psig) Panhandle A Pressure (Psig) Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) Average Node Deviation = Calc - Measured Panhandle Weymouth A Pressure Pressure (Psig) (Psig) Panhandle B Mueller IGT Measured Pressure Pressure Pressure Pressure (Psig) (Psig) (Psig) (Psig) Average Figure A.25: Input data and results for steady state analysis of section V.

176 Pressure (Psig) 159 A.2.6: Loop Analysis of section VI Figure A.26: Schematic of section VI of the Gas Distribution network. The graph, (Fig.A.27) shows that for the pressure in each node, the Panhandle B pipeline equation predicted pressures of the greatest magnitude and IGT predicted pressures with the least magnitude. The Fig.A.28 shows deviation analysis. The Weymouth equation has the lowest deviation; suggesting its use for this loop would yield accurate results. Lower Michigan Power Co. VI Node Mueller PanA PanB Weymouth IGT Measured Figure A.27: Steady State Analysis for section V.