Multi-Phase Flow Modelling for Haz Ass - Solomon Brown (University College London) - UKCCSRC Cranfield Biannual 21-22 April 2015

1. 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. 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

3. 3
CO2 pipeline transportation – hazards cont.

4. 4
P T3 P T3 P T3
P T3
12m 6m 12m6m50
High speed camera
HD camera
T 2F+T T T
CO2Quest experimental facilities

5. 5
Full bore rupture
Puncture release
Video recording during release

6. 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

7. 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
𝜕𝜌 𝑚𝑖𝑥 𝑧
𝜕𝑡
+
𝜕𝜌 𝑚𝑖𝑥 𝑢 𝑚𝑖𝑥 𝑧
𝜕𝑥
= 𝑆𝑧
𝜕𝜌 𝑚𝑖𝑥 𝑢 𝑚𝑖𝑥
𝜕𝑡
+
𝜕𝜌 𝑚𝑖𝑥 𝑢 𝑚𝑖𝑥
2
+ 𝑃
𝜕𝑥
= 𝑆 𝑢
𝜕𝜌 𝑚𝑖𝑥 𝐸 𝑚𝑖𝑥
𝜕𝑡
+
𝜕𝜌 𝑚𝑖𝑥 𝐻 𝑚𝑖𝑥
𝜕𝑥
= 𝑆 𝑒
𝜕𝜌 𝑚𝑖𝑥
𝜕𝑡
+
𝜕𝜌 𝑚𝑖𝑥 𝑢 𝑚𝑖𝑥
𝜕𝑥
= 𝑆𝜌
Balance equations:

8. 8
This works reasonably well…

9. 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
𝜕𝛼𝑖 𝜌𝑖
𝜕𝑡
+
𝜕𝛼𝑖 𝜌𝑖 𝑢𝑖
𝜕𝑥
= 𝑆𝜌
𝜕𝛼𝑖 𝜌𝑖 𝑢𝑖
𝜕𝑡
+
𝜕𝛼𝑖 𝜌𝑖 𝑢𝑖
2
+ 𝛼𝑖 𝑃𝑖
𝜕𝑥
= 𝑃𝑖
𝜕𝛼𝑖
𝜕𝑥
+ 𝑆 𝑢
𝜕𝛼𝑖 𝜌𝑖 𝐸𝑖
𝜕𝑡
+
𝜕𝛼𝑖 𝜌𝑖 𝐻𝑖
𝜕𝑥
= −𝑃𝑖 𝑢𝑖𝑛𝑡
𝜕𝛼𝑖
𝜕𝑥
+ 𝑆 𝑒
𝜕𝛼 𝑣
𝜕𝑡
+ 𝑢𝑖𝑛𝑡
𝜕𝛼 𝑣
𝜕𝑥
= 𝑆𝑖
Balance equations:

10. Inter-phase heat transfer model:
Inter-phase mass transfer model:
Inter-phase heat and mass transfer
𝑞 𝑣
𝑖 =
1
𝜏
𝐴𝑖𝑛𝑡 𝑇𝑠𝑎𝑡 − 𝑇𝑣
𝑞𝑙
𝑖
=
1
𝜏
𝐴𝑖𝑛𝑡 𝑇𝑠𝑎𝑡 − 𝑇𝑙
Γ𝑣 = −Γ𝑙 =
𝑞𝑙
𝑖
+ 𝑞 𝑣
𝑖
ℎ 𝑠𝑎𝑡,𝑣 − ℎ 𝑠𝑎𝑡,𝑙
These are both governed by the relaxation time scale 𝜏
Simple models for the heat and mass transfer are applied.

11. 11
Pressurised CO2
Rupture
plane: 1 atm
HRM Two-Fluid mode
Switching between the models

12. Coupled model results
0
2
4
6
8
10
12
14
0 5 10 15 20
Pressure(MPa)
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
Pressure(MPa)
Time (s)
Experimental
5x10⁻³
1x10⁻³
5x10⁻⁴
Liquid

13. 13CO2QUEST
Contact details
Solomon Brown
University College London
Gower Street, London,
United Kingdom
Tel: +44-2076793809
Thank you
Questions