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SIMULATION OF UNSTEADY STATE FLOW OF NATURAL GAS IN PIPELINES USING FINITE VOLUME METHOD IN 2D CYLINDRICAL COORDINATES
ABSTRACT
Transient compressible natural gas flow through a pipeline was studied by the use of a finite volume method in 2D axisymmetric cylindrical coordinates. To account for turbulence within the pipeline system, the standard turbulence model was simulated together with the Navier Stokes System of equations via the Reynolds-Averaged method. The equation of state employed was the SoaveRedlich-Kwong equation. Implicit discretization was used for the temporal terms, whereas the central differencing scheme and the upwind differencing scheme were used in the discretization of the spatial diffusion terms and the spatial convection terms respectively. The Pressure Implicit with Splitting of Operators (PISO) algorithm was then used for calculating the pressure and velocities on a staggered grid. Computer simulation was carried out to determine variations in pressure, density, velocity and temperature within the pipeline system. Profiles for turbulence viscosity, turbulence kinetic energy and turbulence eddy dissipation along the pipeline were also obtained. To validate the model, data obtained from the following companies were used – Shell Petroleum Development Company, Port-Harcourt, Nigeria, Eroton Production and Exploration Company Limited, Nigeria and published data from the National Iranian Gas Company. Pressure validation was carried out with output pressure values obtained from the stated companies. Parametric analyses were also carried out in the work. This entailed ascertaining the effect of varied inlet temperature on some gas flow parameters. The temperature range considered was 290K – 330K with a temperature difference of 10K. In addition, a rupture that was assumed to have occurred at the middle of the pipe (18,000m long) was also analysed to determine pressure profile. For the purpose of comparison, simulations were carried out with the turbulence model and the turbulence model using the Shell data. The shapes of the profiles obtained from the results were in agreement with others obtained in validated literature results. Grid independence was also investigated. It was discovered that grid independence occurred at a value of 182,000 cells. This means that there was no change in the results obtained after the use of 182,000 cells. Output pressure values from the industries were: 3.19917MPa, 5.55MPa and 6MPa respectively for Shell, Eroton and the Iranian Companies respectively, while the simulated values were 3.153MPa, 5.5124MPa and 6.016MPa for the Shell, Eroton and Iranian Companies respectively. Percentage error between the Industry and simulated values gave, 1.44% for Shell data, 0.27% for Eroton data and 0.77% for National Iranian Gas Company data. These results prove accuracy of the steady state model. Percentage error for transient validation performed with the Iranian data was 0.3067%. There was also no significant difference between the pressure profiles obtained from the two turbulence models. The present method, therefore, can become an invaluable tool and template for use by the oil and gas industry for mitigating the consequences of pipeline perturbations such as vandalism, explosions and ruptures by its application in leak detection systems.
Keywords: Transient, compressible, cylindrical, axisymmetric, computer simulation, pipeline, pressure, velocity and turbulence
TABLE OF CONTENTS
| Cover Page | i |
| Copyright Page | ii |
| Certification | iii |
| Dedication | iv |
| Acknowledgements | v |
| Table of Contents | vi |
| List of Tables | xii |
| List of Figures | xiii |
| Nomenclature | xvii |
| Abstract
|
xix |
| CHAPTER ONE: INTRODUCTION | 1 |
| 1.1 Background Information | 1 |
| 1.2 Problem Statement | 2 |
| 1.3 Objectives of the Study | 2 |
| 1.4 Significance of the Study | 3 |
| 1.5 Scope of the Study | 4 |
TABLE OF CONTENTS
| CHAPTER TWO: LITERATURE REVIEW | 5 |
| 2.1 Computational Fluid Dynamics | 5 |
| 2.2 Discretisation Approaches | 5 |
| 2.2.1 The Finite Difference Method | 5 |
| 2.2.2 The Finite Volume Method | 15 |
| 2.2.3 The Finite Element Method | 20 |
| 2.2.4 The Method of Lines (Birken, 2012) | 27 |
| 2.2.5 The Method of Characteristics | 27 |
| 2.2.6 Matlab Simulink | 29 |
| 2.2.7 The Spectral Method | 30 |
| 2.2.8 Other Methods | 31 |
| 2.2.9 ANSYS FLUENT Software | 34 |
| 2.3 Important Appraisal of Literature Review
|
34 |
| CHAPTER THREE: MATERIALS AND METHODS | 35 |
| 3.1 Materials | 35 |
| 3.2 Methods | 36 |
| 3.2.1 The Conservation Equations (Bird et al, 2012) | 36 |
3.2.2 Equation of State 39
3.2.3 Boundary Conditions 40
3.2.4 Finite Volume Solution Scheme 41
3.2.5 Solution Method 57
3.2.6 The PISO Method 62
3.2.7 PISO Computational Solution Algorithm 69
3.2.8 Implementation of Boundary Conditions and Source Terms for Computation 71
3.2.9 Simulation by the Use of ANSYS FLUENT 77
3.2.9.1 Simulations for the 100m pipeline 77
3.2.9.2 Model Validation 77
3.2.9.3 Simulations following a rupture 78
3.2.9.4 Comparison of turbulence model with the turbulence model. 79
3.2.9.5 Comparison of pressure plots for standard k-epsilon, realizable k-epsilon and RNG
k-epsilon models. 79
3.2.9.6 Parametric Analysis Using Inlet Temperature 79
3.2.9.7 Comparison of results obtained from simulations performed with PISO, SIMPLE and
SIMPLEC algorithms 79
3.2.10 Confirmation of results obtained by the use of ANSYS FLUENT 80
3.2.11 Summary of Model Equation, Initial and Boundary Conditions 80
CHAPTER FOUR: RESULTS AND DISCUSSION 84
4.1 Results 84
4.1.1: Simulation results for 100m pipeline 84
4.1.2 Mass Balance, convergence plot and last 5 values of simulation convergence 84
4.1.3 Steady state and transient pressure distribution 85
4.1.4 Distribution of Steady State and Transient Temperature 86
4.1.5 Steady State and Transient Density variation 87
4.1.6 Steady State and Transient Velocity Distribution 88
4.1.7 Steady State and Transient Eddy Viscosity, Turbulence Kinetic Energy and Turbulence Eddy
Dissipation 89
4.1.8 Mach Number Distribution 92
4.1.9 Industrial Data Simulation Results 93
4.1.10 Steady state Pressure Validation 112
4.1.11 Simulations for Transient Validation of pressure 112
4.1.12 Simulations following a rupture 113
4.1.13 Comparison of pressure plots for turbulence model with turbulence model 114
4.1.14 Comparison of pressure plots for standard k-epsilon, realizable k-epsilon and RNG
4.2.2 Simulations for the 100m pipeline 125
| k-epsilon models. | 115 |
| 4.1.15 The effect of Varying Inlet Temperature on Some Flow Parameters | 116 |
| 4.1.16 Simulations for PISO, SIMPLE and SIMPLEC algorithms | 121 |
| 4.1.17 Simulation results from codes written in MATLAB (for convection-diffusion equation) | 123 |
| 4.2 Discussions | 124 |
| 4.2.1 Mass balance convergence plot (100m pipeline) | 124 |
4.2.3 Steady State Validation: Comparison with field data 129
4.2.4 Transient Validation: Comparison with field data 134
4.2.5 Simulations following a rupture in the pipeline 134
4.2.6 Comparison of pressure plots for turbulence model with turbulence model 134
4.2.7 Comparison of pressure plots for standard k-epsilon, realizable k-epsilon and RNG
k-epsilon models. 135
4.2.8 Parametric analyses 136
4.2.9 Comparison of PISO algorithm with SIMPLE and SIMPLEC algorithms 137
4.2.10 Confirmation of results obtained by the use of ANSYS FLUENT 137 CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS 139
5.1 Conclusion 139
5.2 Recommendations 140
5.3 Contribution to knowledge 140
REFERENCES 142
APPENDICES 152
APPENDIX A 152
APPENDIX B 154
APPENDIX C 156
APPENDIX D 158
APPENDIX E 249
APPENDIX F 253
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND INFORMATION
A gas distribution network is composed of pipe segments connected by simple junctions or other components (compressors stations, pressure regulators, valves, etc.), (Luongo, (1986). The assumption is that the mass of gas flowing through each of these components at any given time is negligible compared with the gas contained in the pipe segments which allows only a quasisteady state treatment of these components and leaves the pipe sections as the only distributed system requiring the solution of partial differential equations for its characterization.
Gas flow in pipelines can be steady (event free) or unsteady. Steady gas flow presents little or no problems unlike unsteady gas flow. Unsteady gas flow in pipelines occurs due to rapid and slow disturbances (Nouri-Borujerdi, 2011). Generally, slow disturbances are caused by mass flow and pressure fluctuations, whereas rapid disturbances arise from compression wave effects caused by sharp closure of a shut-off valve, system start-up or expansion wave related to the pipeline rupture. The unsteady flow of gas in a pipeline after an accidental rupture is of great interest to the natural gas industry due to the huge amount of combustible gas release and its possible dangers. Cases of pipeline failures have been reported in Achebe et al (2012) and Information Nigeria (2016). The correct prediction of outflow and its variation with time after pipeline rupture or (any other disturbance in the system) are therefore of tremendous importance since this information dictates all the major consequences associated with failures such as fire, system shut down, explosion and pollution of the environment (Mahgerefteh et al, 2006). Consequently, this study was focused on the modelling and prediction of unsteady compressible gas flow in 2D axisymmetric cylindrical coordinates. Computational Fluid Dynamics which can be defined as the field that applies computer resources to simulate flow related problems (Al Makky 2012) is the preferred tool to be employed in this work. To simulate a fluid flow problem, one has to use mathematical, physical and programming tools to solve the problem, and then data are generated and analyzed.
1.2 PROBLEM STATEMENT
Mitigating the consequences of pipeline perturbations has been a problem in the Oil/Gas
Industry. One way of doing this is by predicting flow along the pipeline by the use of
Computational Fluid Dynamics tools. Most published work in the area of numerical solution of fluid dynamics problems for prediction of flow properties have been centred on Cartesian coordinates. Furthermore some methods used for modelling in 2D or 3D cylindrical coordinates have presented results that require further improvement. The use of cylindrical coordinates has also not been greatly explored in predicting flow properties (including effect of turbulence using turbulence model) in pipelines. This work therefore presents the simulation of compressible flow in a pipeline system in 2D cylindrical coordinates by the use of a finite volume method for the purpose of predicting pressure, density, temperature, velocity, turbulence kinetic energy, turbulence dissipation rate and eddy viscosity distribution within the pipeline. These are the main parameters which govern the operation of gas pipelines in the petroleum industry.
1.3 OBJECTIVES OF THE STUDY
The main objective of this research is to simulate an unsteady state flow of natural gas in pipelines using finite volume method in 2D cylindrical (axisymmetric type) coordinates.
Specific objectives of the study are to:
- use an existing model to simulate unsteady state flow of natural gas through a pipeline in 2D cylindrical coordinates;
- adapt a simulation tool which enables the study of pressure distribution within the pipeline system and consequently predict velocity, temperature and density within the pipeline;
- use the k-ε turbulence model to predict turbulence kinetic energy, turbulence dissipation rate and eddy viscosity along the pipeline length with the simulation tool adapted.
- validate pressure model;
- investigate the effect of rupture on a pipeline using a rupture at the centre as a case study;
- compare some results obtained by the present method with those obtained by the use of such method as the turbulence model;
- perform a parametric analysis of the effect of inlet temperature on some flow parameters.
1.4 SIGNIFICANCE OF THE STUDY
Transient flow of natural gas involves change of certain flow variables such as pressure, velocity, density, temperature with respect to time as a result of disturbances in the system (which is the pipeline in this study). This work employs the use of mathematically efficient and accurate methods to predict downstream characteristics of gas flow that has been subjected to perturbations such as fire, system shut down, explosion, rupture, etc. Though some work had been done in the area of simulating gas flows, however, the need for elegant and user-friendly methods of solutions leading to accurate results is still required. That is precisely what this work has set out to accomplish. The result of the study can become an invaluable tool and template for use by the oil and gas industry to mitigate the consequences of pipeline perturbations.
1.5 SCOPE OF THE STUDY
The scope of this work includes:
1 Detailed study of the finite volume numerical method used in Computational Fluid
Dynamics for two – dimensional axisymmetric steady and transient compressible flows.
- The use of a model for describing the transient flow of natural gas through a pipeline in 2D axisymmetric cylindrical coordinates .
3 Use of a commercial code and implementation of user-defined code in ANSYS FLUENT for
simulation.
- Validation of the model by the use of field data.
- Investigation of the effect of rupture on a pipeline using a rupture at the centre as a case study. 6. Comparison some results obtained by the present method with those obtained by the use of such method as the turbulence model.
SIMULATION OF UNSTEADY STATE FLOW OF NATURAL GAS IN PIPELINES USING FINITE VOLUME METHOD IN 2D CYLINDRICAL COORDINATES
