1. KOREA INSTITUTE OF MACHINERY & MATERIALS High-Order Perturbation Solutions To A LH 2 Spreading Model With Continuous Spill Sep 13, 2011 Myungbae Kim ICHS 2011

2. KOREA INSTITUTE OF MACHINERY & MATERIALS Introduction Formulation Results & Discussion Conclusions Contents

3. KOREA INSTITUTE OF MACHINERY & MATERIALS Introduction - 1 Leak of flammable liquid  Most common undesirable event in several plants, especially offshore production installations  Initiating event in almost all Event Tree Analysis  Top event of almost all Fault Tree Analysis  Makes a pool or a puddle The pool radius is important for determining a fire size.

4. KOREA INSTITUTE OF MACHINERY & MATERIALS Introduction - 2 Leak model  Instantaneous Release  Continuous Release Spread model  Simple Physical Model  Shallow Layer Model  Full Navier-Stokes Equation

5. KOREA INSTITUTE OF MACHINERY & MATERIALS Simple Physical Model - Briscoe & Shaw R(t) H(t) Hydrostatic Pressure Spill source rate,  Evaporation, E  Radius always tends to increase  Neglecting viscosity and surface tension

6. KOREA INSTITUTE OF MACHINERY & MATERIALS Formulation ▣ Governing Equations ▣ Initial Conditions and

7. KOREA INSTITUTE OF MACHINERY & MATERIALS Previous Results The 1 st order solution for the pool volume due to the non-uniform expansion by secular terms as time increases

8. KOREA INSTITUTE OF MACHINERY & MATERIALS Non-dimensionalization ▣ Characteristic Time & Length ▣ Dimensionless Variables

9. KOREA INSTITUTE OF MACHINERY & MATERIALS Dimensionless Governing Equations with Dimensionless evaporation rate ; an unique governing parameter

10. KOREA INSTITUTE OF MACHINERY & MATERIALS 3 rd Order Expansion for Solutions

11. KOREA INSTITUTE OF MACHINERY & MATERIALS Perturbation Equations Initial conditions; All variables is zero at t=0

12. KOREA INSTITUTE OF MACHINERY & MATERIALS Perturbation Solutions

13. KOREA INSTITUTE OF MACHINERY & MATERIALS Results and Discussion -1 LH 2 Spill on wax E=4.2  10 -4 m/s ( Verfondern & Dienhart )

14. KOREA INSTITUTE OF MACHINERY & MATERIALS Results and Discussion -2 LH 2 Spill on concrete E=4.2  10 -4 m/s

15. KOREA INSTITUTE OF MACHINERY & MATERIALS Conclusions  The unique governing parameter by non- dimensionalization.  For the pool volume, improvement of the 3 rd - order solutions is shown.  For the pool radius, the 3 rd -order and 2 nd - order solutions are nearly identical, and the improvement by high order solutions is not so large compared to 1 st -order solutions.

16. KOREA INSTITUTE OF MACHINERY & MATERIALS Thank you for your attention!!