¹ NTNU - Norwegian University of Science and Technology ² Polytec R&D Institute ³ Gassco AS

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Bruno James
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June 2012 ¹ NTNU - Norwegian University of

1 Accuracy of 1D natural gas transmission models Jan Fredrik Helgaker ¹ T. Ytrehus ¹, A. Oosterkamp ², L. I. Langelandsvik ³, W. Postvoll ³ GERG Academic Network Event, 14th June 2012 ¹ NTNU - Norwegian University of Science and Technology ² Polytec R&D Institute ³ Gassco AS 1

2 Outline Motivation Improved models for long transmission pipelines Theory 1D compressible pipe flow Numerical scheme Results Model Validation Errors and uncertainties Future outlook Conclusions 2

3 Motivation 1D compressible flow models frequently used in the gas industry. Applications include: Design, monitor and operate natural gas pipelines Predict pipeline hydraulic capacity Leak detection systems Models need to be accurate, fast and efficient. 3

Pipeline hydraulic capacity 2008: Increased knowledge about the frictional pressure drop at large flow rates led to updated and increased capacity estimates for Gassco s pipelines in the range 0.

4 Pipeline hydraulic capacity 2008: Increased knowledge about the frictional pressure drop at large flow rates led to updated and increased capacity estimates for Gassco s pipelines in the range 0.2-1% [1]. Reliable data for sea bed temperature are required for further improvement of capacity estimates. [1] L.I. Langelandsvik, Modeling of natural gas transport and friction factor for large scale pipelines, PhD Thesis, Norwegian University of Science and Technology, 2008 Figure: Langelandsvik, Postvoll, Aarhus, Kaste, Accurate calculation of pipeline transport capacity, Proceedings to World Gas Conference

5 Motivation Modeled flow values found using existing commercial tools. m [MSm3/d] p [bar] Time Measured inlet mass flow Time Measured and modeled inlet pressure What is the reason behind the discrepancy in modeled and measured inlet pressure in transient periods? 5

6 Motivation Difference between modeled and measured outlet temperature. What is the reason for this seasonal variation? 6

7 Theory 1D compressible pipe flow Governing equations found by integrating 3D equations for mass, momentum and energy across the pipeline cross-section Continuity ρ ( ρu) t x 0 Momentum Energy 2 2 ( ρu) ( ρu p) fρu ρg sin t x 2D 3 T T p u f u 4 U c V u T ρ ρ ( T Ta ) t x T x 2D D ρ Equation of state p ρ ZRT 7

8 Theory Numerical scheme The governing equations form a system of hyperbolic partial differential equations and have to be solved using numerical techniques. The pipeline is divided into N sections. Each section is discretized in the following way: Time derivative: Y t Y Y Y Y 2 t n 1 n 1 n n i 1 i i 1 i Spatial derivative: Y x Y Y x n 1 n 1 i 1 i Individual terms: Y Y Y 2 n 1 n 1 i 1 i Get a system of algebraic equations. Non-linear terms are linearized about the previous time step to get a linear model. 8

9 Results - Validation Model validated using operational data from a 650 km offshore pipeline. Inlet mass flow and temperature and outlet pressure used as boundary 9 conditions.

10 Results - Validation Better agreement between modeled and measured pressure. What errors and uncertainty do we have in the model? 10

11 Errors and uncertainty in CFD Acknowledged error Physical modeling error Measurement uncertainty (uncertainty in boundary conditions) Computer round off error Discretization error Unacknowledged error Computer programming error Usage error 11

12 Errors and uncertainty Measurement uncertainty Measured flow values used as boundary conditions in the model. Uncertainty claimed to be % for pressure, 0.5% for mass flow and 0.04% for temperature. Discretization error Governing flow equations represented as algebraic expressions in discrete space and time. Select time step t and spatial length x. A consistent numerical method will approach continuum representation and zero discretization error when t 0 and x 0. An approximate value for the discretization error will be given in the following. 12

13 Discretization error Time discretization error for inlet pressure. t [s] Error [bar]

14 Spatial discretization error Nodes ( x [km]) Error [bar] 26 (26) (13) (6.5) (3.25) (1.625) (0.8125) Spatial discretization error for pressure Discretization errors for mass flow and temperature found to be of the same order of magnitude. Discretization errors in model are small. 14

15 Physical modeling error 1D approximation Governing equations transformed from a 3D to a 1D version. Distributed turbulence effects neglected in energy dissipation term [1]. Friction factor verified for steady flow only. Linearized model Governing equations are non-linear. Linearize about previous time step to get a system of linear equations which can be solved in an efficient way. This approximation determined to be valid [2]. [1] Helgaker, Ytrehus, Energy equation in 1D gas pipeline flow Effect of turbulent dissipation, International Gas Research Conference, 2011 [2] Helgaker, An implicit method for 1D unsteady flow in a high pressure transmission pipeline, Proceedings to first ECCOMAS Young Investigator Conference, Aveiro Portugal,

16 Sensitivity analysis Parameter Change Inlet pressure [bar] Outlet mass flow [MSm³/d] Sea temp +1 C U value * Z factor * f (friction) * Z/ T * Z/ p * Outlet temperature [ C] Sea bottom temperature, compressibility factor Z and friction factor f important physical parameters when modeling 1D pipe flow. 16

17 Heat transfer model Currently using a steady state heat transfer model. Chaczykowski [3] shows that an unsteady heat transfer model which accounts for heat accumulation in the surroundings of the pipeline is required. Figure: Chaczykowski [3] [3] M. Chaczykowski, Transient flow in natural gas pipeline The effect of pipeline thermal model, J. Applied Mathematical Modelling,

Will investigate heat accumulation in the

18 Outlook Fellow PhD student A. Oosterkamp has implemented a 2D unsteady heat transfer soil model This has been coupled with 1D model presented here. Will investigate heat accumulation in the ground where pipeline is buried Measuring sensors have been installed next to the pipeline by A. Oosterkamp. This will be used to validate modeled results. 18

19 Conclusions Accurate 1D compressible flow models important to predict the pipeline hydraulic capacity and allow for safe operation of the pipeline network. Previous models have given inaccurate results, especially during transient conditions. This work demonstrates that the uncertainties in the model are linked to physical modeling error and not to the numerical method used to solve the governing equations The most important parameters identified are the heat transfer model, ambient temperature, compressibility factor and friction factor. Unsteady heat transfer model will be investigated and compared to forthcoming experimental results. 19

20 20 Thank you for you attention

ESTIMATING RAPID FLOW TRANSIENTS USING EXTENDED KALMAN FILTER

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