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Fault tree (FTA) templates

Fault Tree — Batch Reactor Overpressure

A runaway exotherm meeting a failed relief path in a batch reactor: cooling loss, charging error or agitator stop on one side, relief valve and bursting disc in series-to-fail on the other, over a one-year campaign.

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Batch reactor overpressure with relief failureFault tree (IEC 61025) · 8 basic events · 5 gates · depth 3topReactor vesseloverpressure3.23e-5excursionRunaway exothermdevelops0.211876cooling_lostJacket cooling lost0.125154chiller_tripChiller trips onhigh head pressure0.06coolant_pumpCoolant circulationpump fails0.051203tcv_stuckTemperature controlvalve sticks shut0.019087charge_errorCatalyst overchargedduring addition0.008agitator_stopAgitator stopsduring the exotherm0.091863relief_failsRelief path does notprotect the vessel1.53e-4prv_failsRelief valve failsto open0.016958prv_stuckRelief valve stuckby polymer fouling0.014prv_undersizedRelief sizinginadequate for this…0.003disc_failsBursting disc failsto open at set…0.009Top event probability (exact)3.23e-5Minimal cut sets10Smallest cut set order3Single points of failurenoneMission time8760 hExact top-event probability 3.23e-5 · rare-event sum ΣP(cut set) 3.52e-5The usual approximation overstates this tree by 8.9% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {agitator_stop, prv_stuck, disc_fails} order 3 P 1.16e-5 35.8% of the top2. {chiller_trip, prv_stuck, disc_fails} order 3 P 7.56e-6 23.4% of the top3. {coolant_pump, prv_stuck, disc_fails} order 3 P 6.45e-6 20% of the top4. {agitator_stop, prv_undersized, disc_fails} order 3 P 2.48e-6 7.7% of the top5. {tcv_stuck, prv_stuck, disc_fails} order 3 P 2.41e-6 7.4% of the top6. {chiller_trip, prv_undersized, disc_fails} order 3 P 1.62e-6 5% of the top7. {coolant_pump, prv_undersized, disc_fails} order 3 P 1.38e-6 4.3% of the top8. {charge_error, prv_stuck, disc_fails} order 3 P 1.01e-6 3.1% of the top9. {tcv_stuck, prv_undersized, disc_fails} order 3 P 5.15e-7 1.6% of the top10. {charge_error, prv_undersized, disc_fails} order 3 P 2.16e-7 0.7% of the topImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)disc_fails — Bursting disc fails to open at set pressure q 0.009 FV 100% B 0.003593 CR 100%prv_stuck — Relief valve stuck by polymer fouling q 0.014 FV 82.6% B 0.001901 CR 82.3%agitator_stop — Agitator stops during the exotherm q 0.091863 FV 43.4% B 1.32e-4 CR 37.6%chiller_trip — Chiller trips on high head pressure q 0.06 FV 28.3% B 1.28e-4 CR 23.7%coolant_pump — Coolant circulation pump fails q 0.051203 FV 24.2% B 1.27e-4 CR 20.1%prv_undersized — Relief sizing inadequate for this recipe q 0.003 FV 17.7% B 0.00188 CR 17.4%tcv_stuck — Temperature control valve sticks shut q 0.019087 FV 9% B 1.23e-4 CR 7.2%charge_error — Catalyst overcharged during addition q 0.008 FV 3.8% B 1.21e-4 CR 3%Rectangle intermediate event · dome AND · shield OR · shield with k/n voting · hexagon INHIBIT with its oval condition · circle basic · diamond undeveloped · triangle transfer

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title "Batch reactor overpressure with relief failure"
mission 8760h

top "Reactor vessel overpressure" = AND(excursion, relief_fails)

gate excursion "Runaway exotherm develops" = OR(cooling_lost, charge_error, agitator_stop)
gate cooling_lost "Jacket cooling lost" = OR(chiller_trip, coolant_pump, tcv_stuck)
gate relief_fails "Relief path does not protect the vessel" = AND(prv_fails, disc_fails)
gate prv_fails "Relief valve fails to open" = OR(prv_stuck, prv_undersized)

event chiller_trip "Chiller trips on high head pressure" p=0.06
event coolant_pump "Coolant circulation pump fails" rate=6.0e-6
event tcv_stuck "Temperature control valve sticks shut" rate=2.2e-6
event charge_error "Catalyst overcharged during addition" p=0.008
event agitator_stop "Agitator stops during the exotherm" rate=1.1e-5
event prv_stuck "Relief valve stuck by polymer fouling" p=0.014
undeveloped prv_undersized "Relief sizing inadequate for this recipe" p=0.003
event disc_fails "Bursting disc fails to open at set pressure" p=0.009