Depressurization of CO2-rich mixtures in pipes: Two-phase flow modelling and comparison with experiments

We present and discuss two-phase flow models to simulate transient flow of CO2rich mixtures in pipes, which is of relevance for design, operation and safety. The model predictions are compared to data from five depressurization experiments from three facilities. Two flow-model formulations are considered. One is a homogeneous equilibrium model in which the phases travel at the same velocity. The other is a more complex two-fluid model in which the slip between the phases is modelled. The thermodynamic equilibrium of the multi-component mixture, constrained by energy and volume, is computed simultaneously with the flow equations. In general, good agreement with the experiments is obtained, including the dry-out point where the liquid in the pipe has evaporated. For the friction and heat-transfer models tested, the two-fluid model did not provide substantially better predictions than the homogeneous equilibrium model. The e ect of di erent heat-transfer models is also discussed. In our case, it is necessary to take the pipe heat capacity into account.

[1]  L. Friedel.  Improved Friction Pressure Drop Correlation for Horizontal and Vertical Two-Phase Pipe Flow , 1979 .

[2]  Steinar Evje,et al.  The multi‐stage centred‐scheme approach applied to a drift‐flux two‐phase flow model , 2006 .

[3]  Juma Yousuf Alaydi,et al.  Heat Transfer , 2018, A Concise Manual of Engineering Thermodynamics.

[4]  Steinar Evje,et al.  A MUSTA Scheme for a Nonconservative Two-Fluid Model , 2009, SIAM J. Sci. Comput..

[5]  Ivar Eskerud Smith,et al.  Simulating rapidly fluctuating CO2 flow into the Vedsted CO2 pipeline, injection well and reservoir , 2011 .

[6]  Jennifer X. Wen,et al.  A pipeline depressurization model for fast decompression and slow blowdown , 2014 .

[7]  Svend Tollak Munkejord,et al.  Solution of the Span–Wagner Equation of State Using a Density–Energy State Function for Fluid-Dynamic Simulation of Carbon Dioxide , 2012 .

[8]  Morten Hammer,et al.  A method for simulating two-phase pipe flow with real equations of state , 2014 .

[9]  J. X. Wen,et al.  Predicting the Decompression Characteristics of Carbon Dioxide Using Computational Fluid Dynamics , 2012 .

[10]  Svend Tollak Munkejord,et al.  CO2 Pipeline Integrity: Comparison of a Coupled Fluid-structure Model and Uncoupled Two-curve Methods , 2014 .

[11]  Eleuterio F. Toro,et al.  CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS , 2004 .

[12]  Svend Tollak Munkejord,et al.  Thermo- and fluid-dynamical modelling of two-phase multi-component carbon dioxide mixtures , 2010 .

[13]  Michael L. Michelsen,et al.  State function based flash specifications , 1999 .

[14]  D. Drew.  Mathematical Modeling of Two-Phase Flow , 1983 .

[15]  K. K. Botros,et al.  Measurements of Speed of Sound in Lean and Rich Natural Gas Mixtures at Pressures up to 37 MPa Using a Specialized Rupture Tube , 2010 .

[16]  F. Douglas Swesty,et al.  The Accuracy, Consistency, and Speed of an Electron-Positron Equation of State Based on Table Interpolation of the Helmholtz Free Energy , 2000 .

[17]  Aie,et al.  Energy Technology Perspectives 2012 , 2006 .

[18]  Howard J. M. Hanley,et al.  Prediction of transport properties. 2. Thermal conductivity of pure fluids and mixtures , 1983 .

[19]  Michael Locht Michelsen,et al.  Thermodynamic Modelling: Fundamentals and Computational Aspects , 2004 .

[20]  Matthias Kunicka,et al.  Fast Calculation of Thermodynamic Properties of Water and Steam in Process Modelling using Spline Interpolation , 2008 .

[21]  K. Gungor,et al.  Simplified general correlation for saturated flow boiling and comparisons of correlations with data , 1987 .

[22]  A. Morin,et al.  A Two-Fluid Four-Equation Model with Instantaneous Thermodynamical Equilibrium , 2016 .

[23]  Svend Tollak Munkejord,et al.  A new coupled fluid-structure modeling methodology for running ductile fracture , 2012 .

[24]  Svend Tollak Munkejord,et al.  Frictional Pressure Drop for Two-phase Flow of Carbon Dioxide in a Tube: Comparison between Models and Experimental Data☆ , 2014 .

[25]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[26]  Eleuterio F. Toro,et al.  MUSTA: a multi-stage numerical flux , 2006 .

[27]  Haroun Mahgerefteh,et al.  Modelling the non-equilibrium two-phase flow during depressurisation of CO2 pipelines , 2014 .

[28]  Martin Peter Breil,et al.  Thermodynamic Models: Fundamental & Computational Aspects , 2008 .

[29]  P. L. Spedding,et al.  Prediction in stratified gas-liquid co-current flow in horizontal pipelines , 1997 .

[30]  Hailong Li,et al.  PVTxy properties of CO2 mixtures relevant for CO2 capture, transport and storage: Review of available experimental data and theoretical models , 2011 .

[31]  Giacomo Bruno Azzurro Persico,et al.  Consistent look-up table interpolation method for real-gas flow simulations , 2015 .

[32]  W. Wagner,et al.  The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004 , 2012 .

[33]  Michael Fairweather,et al.  Validation of a model of gas and dense phase CO2 jet releases for carbon capture and storage application , 2014 .

[34]  Julian Barnett,et al.  The Decompression Behaviour of Carbon Dioxide in the Dense Phase , 2012 .

[35]  R. Stryjek,et al.  PRSV: An improved peng—Robinson equation of state for pure compounds and mixtures , 1986 .

[36]  Charles L. Merkle,et al.  Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations , 2007, J. Comput. Phys..

[37]  Howard J. M. Hanley,et al.  Prediction of transport properties. 1. Viscosity of fluids and mixtures , 1981 .

[38]  Jan Fredrik Helgaker,et al.  Validation of 1D flow model for high pressure offshore natural gas pipelines , 2014 .

[39]  H Mahgerefteh,et al.  Modelling the impact of stream impurities on ductile fractures in CO2 pipelines , 2012 .

[40]  F. Swesty,et al.  Thermodynamically Consistent Interpolation for Equation of State Tables , 1996 .

[41]  Eleuterio F. Toro,et al.  MUSTA schemes for multi‐dimensional hyperbolic systems: analysis and improvements , 2005 .

[42]  J. H. Stuhmiller,et al.  The influence of interfacial pressure forces on the character of two-phase flow model equations , 1977 .

[43]  Svend Tollak Munkejord.  Partially-reflecting boundary conditions for transient two-phase flow , 2006 .

[44]  Gelein de Koeijer,et al.  Experiments and modeling of two-phase transient flow during CO2 pipeline depressurization , 2009 .

[45]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[46]  Eleuterio F. Toro,et al.  Centred TVD schemes for hyperbolic conservation laws , 2000 .

[47]  Svend Tollak Munkejord,et al.  Combining Thermodynamic and Fluid Flow Modelling for CO2 Flow Assurance , 2013 .

[48]  Christophe Eric Corre,et al.  On the extension of the AUSM+ scheme to compressible two-fluid models , 2003 .

[49]  Svend Tollak Munkejord,et al.  Method Using a Density–Energy State Function with a Reference Equation of State for Fluid-Dynamics Simulation of Vapor–Liquid–Solid Carbon Dioxide , 2013 .

[50]  D. Bestion,et al.  The physical closure laws in the CATHARE code , 1990 .

[51]  Peder Aursand,et al.  Pipeline transport of CO2 mixtures: Models for transient simulation , 2013 .

[52]  Cheng Lu,et al.  Decompression wave speed in CO2 mixtures: CFD modelling with the GERG-2008 equation of state , 2015 .

[53]  Svend Tollak Munkejord,et al.  Experiments and modelling of two-phase transient flow during pipeline depressurization of CO2 with various N2 compositions , 2014 .

[54]  Jinyue Yan,et al.  Viscosities, thermal conductivities and diffusion coefficients of CO2 mixtures:Review of experimental data and theoretical models , 2011 .

[55]  Frøydis Aakenes,et al.  Frictional pressure-drop models for steady-state and transient two-phase flow of carbon dioxide , 2012 .

[56]  Julian Barnett,et al.  CO2 Transport Systems Development: Status of Three Large European CCS Demonstration Projects with EEPR Funding , 2014 .