multi-phase flow modelling for haz ass - solomon brown (university college london) - ukccsrc...
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Multiphase flow modelling for hazard
assessment of dense phase CO2
pipelines containing impurities
Dr Solomon Brown, Dr Sergey Martynov, Prof Haroun Mahgerefteh
Department of Chemical Engineering,
University College London, London, UK
UKCCSRC Biannual Meeting
21-22 April 2015, Cranfield
2
CO2 pipeline transportation – hazards
At concentrations higher than 10%, CO2 gas can cause severe injury or death due to asphyxiation.
In case the of accidental leakage/ release of CO2 from a pipeline:
• the CO2 gas can accumulate to potentially dangerous concentrations in low-lying areas,
• the released cloud could cover an area of several square kilometres.
Courtesy of Laurence Cusco, HSL
4
P T3 P T3 P T3 P T3
12m 6m 12m 6m50
High speed camera HD camera
T 2F+T T T
CO2Quest experimental facilities
6
Pressurised CO2
Rupture
plane: 1 atm
• At the rupture plane the fluid is exposed to ambient air
• Following the rupture, the rarefaction wave starts propagating along the
pipe
• The vapour phase emerges in the expansion wave
• Due to rapid cooling of the fluid in the decompression wave, the solid
phase may also be released from the pipe
Physics of decompression
Mathematical model -Pipeline discharge
where ρ, u, P, H, z and E are the density, velocity, pressure, total enthalpy, vapour quality and total energy of a two-phase fluid mixture as function of time t and space x.
Homogeneous Relaxation Model
Mixture
𝜕𝜌𝑚𝑖𝑥𝑧
𝜕𝑡+𝜕𝜌𝑚𝑖𝑥𝑢𝑚𝑖𝑥𝑧
𝜕𝑥= 𝑆𝑧
𝜕𝜌𝑚𝑖𝑥𝑢𝑚𝑖𝑥
𝜕𝑡+𝜕𝜌𝑚𝑖𝑥𝑢𝑚𝑖𝑥
2 + 𝑃
𝜕𝑥= 𝑆𝑢
𝜕𝜌𝑚𝑖𝑥𝐸𝑚𝑖𝑥
𝜕𝑡+𝜕𝜌𝑚𝑖𝑥𝐻𝑚𝑖𝑥
𝜕𝑥= 𝑆𝑒
𝜕𝜌𝑚𝑖𝑥
𝜕𝑡+𝜕𝜌𝑚𝑖𝑥𝑢𝑚𝑖𝑥
𝜕𝑥= 𝑆𝜌
Balance equations:
Mathematical model -Pipeline discharge
where α is the volume fraction as function of time t and space x.
Characterisation of these terms is difficult
Two-Fluid Model
Vapour
Liquid 𝜕𝛼𝑖𝜌𝑖𝜕𝑡
+𝜕𝛼𝑖𝜌𝑖𝑢𝑖𝜕𝑥
= 𝑆𝜌
𝜕𝛼𝑖𝜌𝑖𝑢𝑖𝜕𝑡
+𝜕𝛼𝑖𝜌𝑖𝑢𝑖
2 + 𝛼𝑖𝑃𝑖𝜕𝑥
= 𝑃𝑖𝜕𝛼𝑖𝜕𝑥
+ 𝑆𝑢
𝜕𝛼𝑖𝜌𝑖𝐸𝑖𝜕𝑡
+𝜕𝛼𝑖𝜌𝑖𝐻𝑖
𝜕𝑥= −𝑃𝑖𝑢𝑖𝑛𝑡
𝜕𝛼𝑖𝜕𝑥
+ 𝑆𝑒
𝜕𝛼𝑣𝜕𝑡
+ 𝑢𝑖𝑛𝑡𝜕𝛼𝑣𝜕𝑥
= 𝑆𝑖
Balance equations:
Inter-phase heat transfer model:
Inter-phase mass transfer model:
Inter-phase heat and mass transfer
𝑞𝑣𝑖 =
1
𝜏𝐴𝑖𝑛𝑡 𝑇𝑠𝑎𝑡 − 𝑇𝑣
𝑞𝑙𝑖 =
1
𝜏𝐴𝑖𝑛𝑡 𝑇𝑠𝑎𝑡 − 𝑇𝑙
Γ𝑣 = −Γ𝑙 =𝑞𝑙𝑖 + 𝑞𝑣
𝑖
ℎ𝑠𝑎𝑡,𝑣 − ℎ𝑠𝑎𝑡,𝑙
These are both governed by the relaxation time scale 𝜏
Simple models for the heat and mass transfer are applied.
11
Pressurised CO2
Rupture
plane: 1 atm
HRM Two-Fluid mode
Switching between the models
Coupled model results
0
2
4
6
8
10
12
14
0 5 10 15 20
Pre
ssu
re (
MP
a)
Time (s)
Experimental
5x10⁻³
1x10⁻³
5x10⁻⁴
Liquid
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20
Pre
ssu
re (
MP
a)
Time (s)
Experimental5x10⁻³ 1x10⁻³ 5x10⁻⁴
Liquid
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