ML18213A090
| ML18213A090 | |
| Person / Time | |
|---|---|
| Issue date: | 07/31/2018 |
| From: | Tammie Rivera NRC/RES/DRA/FRB, Electric Power Research Institute |
| To: | |
| Shared Package | |
| ML18213A072 | List: |
| References | |
| Download: ML18213A090 (16) | |
Text
Module III - Fire Analysis Special Topics in Detection and Suppression Analysis -
General Approach for Treatment of Progressive Damage States Joint EPRI/NRC-RES Fire PRA Workshop August 6-10, 2018 A Collaboration of the Electric Power Research Institute (EPRI) & U.S. NRC Office of Nuclear Regulatory Research (RES)
Common challenge: multiple fire PRA damage targets with some degree of spatial separation T2 T3 Three fire PRA targets of interest:
first tray, fourth tray, T1 hot gas layer.
Fire source 2
Damage state progresses in time Fire will damage closest tray first:
T2 T3 T1 Fire source 3
Damage state progresses in time As fire grows and spreads, it will progress through tray stack eventually reaching fourth tray:
T3 T2 T1 Fire source 4
Damage state progresses in time If fire is large enough, hot gas layer may form damaging final tray T2 T3 T1 Fire source 5
You can build an event tree to reflect a progressive damage state increasing with time The key is that the fire must burn long enough to cause the postulated damage, and the more extensive damage states take additional time
- t1 = time to damage for T1
- t2 = time to damage for T2
- t3 = time to damage for T3
- t1 < t2 < t3 The likelihood of successful fire suppression gets better and better with longer times
- Said another way - the probability of non-suppression gets smaller and smaller with longer time available before damage
We can reflect this credit through a modified suppression event tree:
6
A modified suppression event tree for a three-stage set of fire PRA targets Ignition Damage State 1 Damage State 2 Damage State 3 End State No damage tsuppression < t1 Only the ignition source is lost t=0 tsuppression < t2 Loss of T1 only T2 is protected tsuppression = t1 Loss of T1 Loss of T1+T2 tsuppression < t3 T3 is protected tsuppression = t1 Loss of T2 tsuppression = t1 Loss of T3 Loss of all targets (T1+T2+T3) 7
The key is to properly calculate the branch point split fractions Branch point values depend on time to damage and the applicable non-suppression probability curve, but The events are dependent
- You cant just pick numbers off suppression curve for each branch For example - the second split fraction, for damage to T2, is:
- the conditional probability that given the fire was not suppressed before time t=t1, the fire will remain unsuppressed through time t=t2
- Same goes for final split fraction The formal approach to calculate these conditional split fractions lies beyond the scope of our course
- You need to integrate the density function across time intervals We can, however, illustrate the concept with an even simpler example that we can solve by inspection 8
Reduce our problem to a two-stage damage state Step 1: build a simplified event tree and see what we know about answers Suppression by Suppression by Fire time = t1 time = t2 No Damage What is the final answer for this branch?
1 Target set 1 Target set 2 9
Two-stage example (cont.)
Step 2: What else do we know about answer?
Suppression by Suppression by Fire time = t1 time = t2 Probability of suppression within time t1:
No Damage Pr = PS(t1) = 1 - PNS(t1) 1 Target set 1 Target set 2 What is the final answer for this branch?
10
Two-stage example (cont.)
Step 3: Last branch has to be probability of non-suppression within time t2:
Suppression by Suppression by Fire time = t1 time = t2 No Damage Pr = 1 - PNS(t1) 1 Target set 1 So what does that leave for here?
Target set 2 Pr = PNS(t2) 11
Two-stage example (cont.)
Step 4: Middle branch has to be the residual left over from a total of 1 for all branches:
Suppression by Suppression by Fire time = t1 time = t2 No Damage Pr = 1 - PNS(t1) 1 Target set 1 Pr = 1 - [1 - PNS(t1)] - PNS(t2) = PNS(t1) - PNS(t2)
Target set 2 Pr = PNS(t2) 12
Two-stage example (cont.)
Step 5: What are branch point values that yeild the known end state probabilities? Fill in known branch points:
Suppression by Suppression by Fire time = t1 time = t2 No Damage Pr = 1 - PNS(t1) 1 - PNS(t1) 1 Target set 1 Pr = PNS(t1) - PNS(t2)
PNS(t1)
Target set 2 Pr = PNS(t2) 13
Two-stage example (cont.)
Next step is to fill in sencond branch point so end state probability matches when multiplied:
Suppression by Suppression by Fire time = t1 time = t2 No Damage Pr = 1 - PNS(t1) 1 - PNS(t1) 1 Target set 1 Pr = PNS(t1) - PNS(t2) 1 - [PNS(t2)/PNS(t1)]
PNS(t1)
Target set 2 Pr = PNS(t2)
PNS(t2)/PNS(t1) 14
Two-stage example (conclusion)
One final simplification is possible given the behavior of exponentials:
PNS(t) = e-t so PNS(t2)/PNS(t1) = e-t2/e-t1= e-(t2-t1) = PNS(t2-t1)
Suppression by Suppression by Fire time = t1 time = t2 No Damage Pr = 1 - PNS(t1) 1 - PNS(t1) 1 Target set 1 Pr = PNS(t1) - PNS(t2) 1- [PNS(t2-t1)]
PNS(t1)
Target set 2 Pr = PNS(t2)
PNS(t2-t1) 15
Summary - multi-stage damage states The multi-stage damage state approach is a powerful tool
- Any scenario with multiple targets threatened by the same fire source with discrete damage times
- The key is some degree of spatial separation between targets Tray stacks Above the fire versus away from the fire The more damage stages you develop the more complicated it gets
- You may need to seek the help of a good statistics person Two-to-three discrete states is relatively easy and works for many scenarios The event tree approach help
- Individual end states must be properly weighed
- Very easy to double count overlapping damage states 16