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Reliability Engineering

Reliability Engineering. The Protective Systems. The Protective Systems. Relief valves Rupture discs Alarms Trips, interlocks Reactor quench systems Sprinklers etc. Example – A Tank with Single Relief Valve. Example – A Tank with Two Relief Valves.

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Reliability Engineering

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  1. Reliability Engineering The Protective Systems

  2. The Protective Systems • Relief valves • Rupture discs • Alarms • Trips, interlocks • Reactor quench systems • Sprinklers • etc.

  3. Example – A Tank with Single Relief Valve

  4. Example – A Tank with Two Relief Valves

  5. Example – A Chlorination Reactor without Protective System Hydrocarbon Gas Chlorine from Vaporizer Reactor To next stage in process

  6. The Fault Tree without Protective System Run-away Reaction 13.21/yr OR 12.5/yr 0.71/yr OR OR flow control valve fails open High pressure in vaporizer fractured gas line low gas supply pressure gas flow control valve fails shut blockage in gas line 0.5/yr 0.01/yr 0.1/yr 0.5/yr 0.1/yr 12/yr low reliability!!! Need a protective system!

  7. Derivation of the Average Hazard Rate Definitions: • w(t):probability of system hazard per unit time at time t, or expected number of hazard per unit time at t; • U: life length of entire system; • S: life length of protective system; • T: inspectioninterval of the protective system; • W(0,T): expected number of hazards between 0 and T; • D: demand rate on the protective system; • A(t, t+dt]: hazardous event occurs in (t, t+dt], i.e. t<U<t+dt.

  8. Derivation (I) Assume that the protective system has n redundant devices in parallel and these devices obey exponential distribution with constant failure rate λ Note , we assume that the protective system is as good as new after testing .

  9. Derivation (II) From the definitions of unconditional failure intensity, w(t) From the definitions of U and A(t,t+dt], negligible 0 since S>U

  10. Derivation (III) Define Thus, The question now is: how to obtain an explicit expression for the integration term?

  11. Derivation (IV) Consider

  12. Derivation (V)

  13. Derivation (VI)

  14. Derivation (VII) Note,

  15. Derivation (VIII)

  16. Derivation (IX) THE AVEARGE HAZARD RATE OF A SYSTEM WITH n REDUNDANT PROTECTIVE DEVICES IN PARALLEL

  17. Special Cases of the Average Hazard rate (i) If λT<<1 and DT<<1, then Taylor series expansion:

  18. Example – Selecting a Trip System for the Chlorination Reactor The Chlorination is supervised by one process operator who spends 55 hr of his 2200 working hours per year near the reactor. At other times, the operator is out of the danger area. If the operator is near the unit when it detonates, there is a 0.1 chance of death. Choose, from the table in the following page, the most suitable flow-trip device which will reduce the hazard to the operator to a FAFR( fatal accident frequency rate ) of 1.25 ( per exposed-hours ).

  19. Note that two failure rates are given when the shut-down system has two redundant channels.

  20. Solution (1): The fatal accident frequency rate is Where = average hazard rate P = probability of the hazard resulting in death. To obtain P, we multiply the probability of death (0.1) by 55/2200, i.e P = (0.1)(55/2200)=0.0025. Assuming a monthly test interval(T=1/12 year) and D = 13.21/year,

  21. Solution (2): We now substitute values of n andλfor the various instruments listed in table and choose the most appropriate. With a Class II flow-ratio trip, n=2, and λ=0.6, so the FAFR is This $2,350 instrument is more than adequate.

  22. SAFETY VS. RELIABILITY IN SHUTDOWN SYSTEMS ONE OUT OF ONE SHUTDOWN TO SHUT DOWN SYSTEM Sensor 1 2 Safety DISTURBANCE NOT CORRECTED 1/3000 yrs AND SENSOR 1 INOPERATIVE DISTURBANCE IN STREAM 1 1/3yrs 1/10 yrs 4 days Reliability SPURIOUS SYSTEM SHUTDOWN 1/yr OR 1/yr SENSOR 1 SENDS SPURIOUS SIGNAL 1hr

  23. TWO OUT OF TWO SHUTDOWN TO SHUTDOWN SYSTEM 1 2 DISTURBANCE NOT CORRECTED SAFETY 1/1500 yrs AND OR DIST. IN STREAM 1 1/3 yrs S1 INOP. S2 INOP.

  24. RELIABILITY SPURIOUS SYSTEM SHUTDOWN AND S1 SENDS SPURIOUS SIGNAL 1/yr S2 SENDS SPURIOUS SIGNAL 1/yr

  25. TWO OUT OF THREE SHUTDOWN TO SHUTDOWN SYSTEM 1 2 SAFETY DISTURBANCE NOT CORRECTED AND OR DISTURBANCE ENTERS IN STREAM 1 1/3 yrs AND AND AND S1 S2 S1 S3 S2 S3 INOP. INOP. INOP. INOP. INOP. INOP.

  26. RELIABILITY SPURIOUS SYSTEM SHUTDOWN 1/20 yrs OR 1/60 yrs 1/60 yrs 1/60 yrs AND AND AND S1 SENDS SPURIOUS SIGNAL S2 SENDS SPURIOUS SIGNAL S1 SENDS SPURIOUS SIGNAL S3 SENDS SPURIOUS SIGNAL S2 SENDS SPURIOUS SIGNAL S3 SENDS SPURIOUS SIGNAL

  27. [ EMAMPLE ] SPURIOUS SYSTEM SHUTDOWN 1 OUT OF 3 TOP 2 OUT OF 3 TOP 2

  28. 3 OUT OF 3 TOP Where

  29. [ EXAMPLE ] DISTURBANCE NOT CORRECTED 1 OUT OF 3 TOP I 2 OUT OF 3 TOP 2 I

  30. 3 OUT OF 3 TOP I Where

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