CO2PipeHaz
CFD Modelling of Accidental Releases of Carbon Dioxide from PipelinesCarbon Dioxide from PipelinesRob Woolley, Mike Fairweather, Sam FalleU i i f L dUniversity of Leedshttp://www.co2pipehaz.eu/
CO2PipeHaz/COCATE Joint Meeting 22-23 March 2012, Birmingham, UK
Overview
1. Introduction – Aims, Objectives
2. CFD Code
3 C ibilit C ti3. Compressibility Correction
4. Non-ideal Equation of State for CO2/Air Mixturesq 2
5. Homogeneous Relaxation Model
6. INERIS Test Case
7. Liquid / Solid Particle Models
8. Work in Progress8. Work in Progress
1. Aims and Objectives
1. Aims and Objectives
Aims of Work Package 1.4 – Near-field Dispersion Model
Development and validation of mathematical models for predicting the near-fieldstructure of high pressure releases of supercritical and multi-phase CO2, includingmodels for the formation of liquid droplets and solid particles in order to providemodels for the formation of liquid droplets and solid particles in order to provideinput in to far-field dispersion models and to allow assessments of the near-fieldimpact of CO2 release.ObjectivesObjectives
Incorporate compressibility-corrected turbulence model into dispersioncode - Completecode. CompleteIncorporate non-ideal equation of state for CO2/Air mixtures. - CompleteIdentification of suitable liquid/solid particle models and incorporation intoturbulent code. - Completeturbulent code. CompleteValidation of all models against literature data and project data. -OngoingExtension of the model to three-dimensional cases. - Ongoingg g
2. CFD Code
Calculations of Multi-phase turbulent flow field.
Conservative, upwind, finite volume code solving the Reynolds-averagedNavier Stokes conservation equations for mass momentum totalNavier-Stokes conservation equations for mass, momentum, totalenergy, and mean of mixture fraction.
Adaptive Mesh Refinement with a hierarchyAdaptive Mesh Refinement with a hierarchyof grids – Solution computed on all grids.Mesh is refined where solution varies rapidly.
For shock calculations, we use an HLL(Harten, Lax, van Leer) Riemann solver.
Coordinates: axisymmetric cylindrical polar.Now working in three-dimensions also.
3. Compressibility Correction
k-ε turbulence model modified using the Sarkar correction for ibilicompressibility
Compressibility reduces mixing due to enhanced turbulence dissipation.
Corrections are introduced to the turbulence dissipation rate and turbulence viscosity as a function of Mach numberviscosity as a function of Mach number.
C ibl di i ti t 2MCompressible dissipation rate:
2k
2sMτε α ε=
Turbulence viscosity: and 2(1 )tkCMμ
τ
μ ρε
=+
0.09Cμ =
3. Compressibility Correction
Example of validation case: Seiner and Norum moderately underexpanded air jet pressure predictions with and without
corrections
Corrected model validated for cases of moderately and highly under-expanded jets
4. Non-ideal Equation of State
Peng-Robinson Equation of State for CO2 (1976)
( )( )
( ) ( )0.645a TRTP
v b v v b b v b= −
− + + −
This is satisfactory for the gas phase, but not for the condensed phase. It is not accurate for the vapour pressure below the triple point and it does not account for the discontinuity in properties at the triple point. In particular, there is no latent t e d sco t u ty p ope t es at t e t p e po t pa t cu a , t e e s o ate theat of fusion. Span and Wagner (1996) is valid for both the gas and liquid above the triple point, but it does not take account of experimental data below the triple point, norpoint, but it does not take account of experimental data below the triple point, nor does it give the properties of the solid. We have therefore constructed a composite equation of state in which the gas phase is computed from Peng-Robinson the liquid phase from Span and Wagnerphase is computed from Peng Robinson, the liquid phase from Span and Wagner and the latent heat of fusion and solid phase from the DIPPR tables given in the Knovel library (2011). Vapour pressures below the triple point are tabulated from Span and Wagner.Span and Wagner.
4. Non-ideal Equation of State
Saturation Pressure Liquid Density Gas Density
Good agreement between Peng-Robinson and Span-Peng Robinson and SpanWagner above the triple point.
4. Non-ideal Equation of State
x10 5
0.0
U
Gas Phase: Peng-Robinson Eqn of State
-4.0
-2.0 Liquid Phase:Span & Wagner
Eqn of StateLatent heat: DIPPR data
-6.0
4.0 q
100.0 150.0 200.0 250.0 300.0
-8.0
Solid phase: DIPPR data
Internal energy on the saturation line for the improved equation of state. The top curve is the vapour phase and the bottom curve the liquid/solid
T
phase.
5. Homogeneous Relaxation Model
Relaxation of condensed phase to equilibrium
The vapour will only be in equilibrium if the size of the liquid drops or solidparticles are sufficiently small. There are indications that this will not be true.
The full model requires the inclusion of drops and particles, but it is possible toderive a simple model for the relaxation to equilibrium in which one ignores thetemperature relaxation and simply assumes that the condensed phase masstemperature relaxation and simply assumes that the condensed phase massfraction is given by:
( ) ( )tu St αρα ρα μ α∂
+∇ −∇ ∇ =∂
i i( )v s
s
p pS
pα βτ−
=
5. Homogeneous Relaxation Model
Temperature and α along the axis for the Peng-Robinson equation of state(markers) and improved equation of state with τ = 10-3 (line).
5. Homogeneous Relaxation Model
Vapour pressure (line) and saturation pressure along the axis for the improved equation of state with τ = 10-3 (top) and τ = 0.1 (bottom).
6. INERIS Test Case
2 ‘’ tube, 1.65 m long inside2 m3 sphere (Φ 1.56 m)
orifice2 ‘’ tube, 6 to 40 m long in total (50 mm inner dia, 5 mm wall, very smooth)
orifice
6. INERIS Test Case
Release point
Modelled Region
1 m2 m
5 m
2 m3 vessel10m
20 m
2 m3 vessel
: Thermocouple K ± 0.25°C : O2 analyser ± 0.01% v/v: CO2 IR sensor
Test N° Ambiant T °C Air humidity % P reservoir (babs) Orifice (mm)
6 3 95 90 9
7 6 95 85 12
8 4 95 77 25
6. INERIS Test Case
Test 5 with 9 mm // 36 bar
6. INERIS Test Case
Temperature Predictions of INERIS Releases Using Peng-Robinson Derived Initial Conditions – Predominantly Liquid Release
300
Test 8x = 1m
200
220
240
260
280
Tem
pera
ture
/ K
Test 6x = 1m
Test 71 x = 1m
d = 40
160
180
T x = 1md = 112
x = 1md = 85
260
280
300
160
180
200
220
240
260
Tem
pera
ture
/ K
Test 6x = 2md = 225
Test 7x = 2md = 170
Test 8x = 2md = 80
240
260
280
300
atur
e / K
160
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
160
180
200
220
y / m
Tem
pera
Test 6x = 5md = 562
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
y / m
Test 7x = 5md = 424
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2y / m
Test 8x = 2md = 200
Pressure – 95 barOrifice – 9 mm
Pressure – 85 barOrifice – 12 mm
Pressure – 77 barOrifice – 12 mm
y / m y / m y / m
6. INERIS Test Case
Test 5 with 9 mm // 36 bar
Entraiment of air
Expansion zone
T/C (1 mm) @ 3 cm, 7 cmand 15 cm off axis
T
cm and 15 cm off axis
Steel rope
TT
10 20 30 40 50 cm
T T T Tsupport
PdDynamic pressureDynamic pressure
6. INERIS Test Case
Improvements made to the model performance:
Improvement on Peng-Robinson EoS below the triple point.
Inclusion of non-equilibrium effects close to the nozzle.
Improvements to be made to the model performance:
Eff t f ti l th t b l t fl fi ld d h k t tEffect of particles on the turbulent flow field and shock structure.
Application of a second-moment turbulence model.
7. Liquid / Solid Particle Models
S l ti l di t ib ti f ti f li id d l t d lid ti lSolve particle distribution function for liquid droplets and solid particles,together with particle equation of motion, giving number density of particles inspace with masses in chosen range.
Method applied for small droplets/particles to reduce model run times
For droplets/particles above certain size use Lagrangian particle trackingFor droplets/particles above certain size, use Lagrangian particle trackingalgorithm.
Both methods admit one way two way and four way coupling betweenBoth methods admit one-way, two-way and four-way coupling betweenparticles and flow, and force terms due to drag, gravity, buoyancy, lift, Bassetforce, pressure gradient and virtual mass.
Processes of formation/nucleation, condensation/growth, evaporation/sublimation and coagulation are accommodated.
7. Liquid / Solid Particle Models
Particle Tracker
No Relaxation – Particles follow fluid streamlines
Relaxation – Particles deviate from fluid streamlines
8. Work in Progress
• Prediction of initial distribution sizePrediction of initial distribution size
• Estimation Based Upon Frequency of Disturbance
• The Flash Evaporation Model – Heat Conduction Problemp
• Droplet Disintegration Due to Flash Evaporation• Droplet Disintegration Due to Flash Evaporation
• Particle Coagulation Models
8. Work in Progress
• The performance of the two-dimensional model with the newpcomposite non-ideal equation of state and particle relaxationmodel has been assessed, and is being validated using INERISdata as it becomes available.
• The Yokozeki model for three phases of CO2 developed atDemokritos is being incorporated into the solver.Demokritos is being incorporated into the solver.
• The code has been adapted to provide full three-dimensionalcapabilities and is currently being validatedcapabilities and is currently being validated.
• A second-moment Reynolds stress model is being incorporatedf finto the code and there is scope for further development and
collaboration.
Acknowledgements & Disclaimer
The research leading to the results described in this presentation has received funding from the Europeanpresentation has received funding from the European Union 7th Framework Programme FP7-ENERGY-2009-1 under grant agreement number 241346.
The presentation reflects only the authors’ views and the European Union is not liable for any use that may be made of the information contained thereinof the information contained therein.
