December 2, 2020

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Problem 12-6. Modify the event tree of Figure 12-11 to determine the runaways per year if the

loss of cooling initiating event is reduced to 0.80 occurrences per year.

Solution to Problem 12-6. Notice that the bracked numbers are for 0.8 occurances/yr

Problem 12-7. A toxic liquid is pumped into a storage vessel. The vessel is equipped with a high level sensor to stop the

flow and sound an alarm if the level is too high. If the level sensor and alarm fails, the vessel will overflow and the

toxic material will be released into the operating environment. Use the LOPA method to determine if this system

requires additional safeguards. Assume a threshold quantity for the liquid of 5 lb. The pumping rate is 1 lb per

minute and it will take 20 minutes for the operator to notice the spill and stop the flow manually. Make suggestions

for improvement if additional safeguards are required.

Solution for Problem 12-7 (See Section 12-6)

Problem 12-8. A reactor experiences trouble once every 16 months. The protection

device fails once every 25 yr. Inspection takes place once every month. Calculate

the unavailability, the frequency of dangerous coincidences, and the MTBC.

Solution for Problem 12-8 (See Secton on Probability of Coincidence)

λ12

16 0.75 Per year τ1

12 0.083 Years

Problem 12-9. A starter is connected to a motor that is connected to a pump. The

starter fails once in 50 yr and requires 2 hr to repair. The motor fails once in

20 yr and requires 36 hr to repair. The pump fails once per 10 yr and requires

4 hr to repair. Determine the overall failure frequency, the probability that the

system will fail in the coming 2 yr, the reliability, and the unavailability for

this system.

Solution for Problem 12-9

Starter Motor Pump

Problem 12-10. If a regulator has a consequence frequency of 10

-1

failure/yr, what will be the

frequency if this regulator is given preventive maintenance once per month?

Solution to Problem 12-10

See in the section on Estmating the LOPA that the frequency for maintenance

reduces the frequency per year by dividing the frequency by the number of

maintenance given in a year. (See secton on estimating the LOPA Frequency).

Therefore:

Problem12-11. Draw an F-N curve using the following data:

Incident

OutcomeCase Frequency,F

i

(per

year)

Estimated

numberof

fatalities,N

1 1×10

‐6

20

2 1×10

‐4

5

3 1×10

‐5

7

4 1×10

‐5

3

5 1×10

‐4

2

Solution for Problem 12-11

Problem12-11. Draw an F-N curve using the following data:

Problem 12-12. The peak overpressure expected as a result of the explosion of a tank in

a plant is approximated by the following equation

log 6.0 1.8logPr

where P is the overpressure in psi and r is the distance from the blast in feet. The

plant employs 50 people who work in an area from 10 to 500 ft from the blast.

Assume that the population density is constant in the work area.

a. Estimate the fraction of fatalities at 10, 100, 250 and 500 ft using a probit

equation.

b. Calculate the individual risk at each location in part a in yr-1. Assume a

frequency of the initiating event of 10-4 per year.

c. Plot the risk contours.

Solution for Problem 12-12

See the summary of results in the table below the calculations.

The Probit (see Table 2-5) for fatalities due to lung hemorrihage is:

TABLE for Problem 12-12

Radius at

outer

boundary

(ft)

Area

between

boundaries

(ft

2

)

Radius at

center of

Area (ft)

People

in Area

Pressure

at center

of Area

(atm)

Probit at

center of

Area

Percent

effected

People

effected

(fatalities)

Risk

(f x fatalities)

1 2 3 4 5 6 7 8 9

End of Problems for Chapter 12

Problems and Solutions for Chapter 13

Problems

a

Problem 13-1

For a large semibatch polyether reactor (add ethylene and/or propylene oxide

to hydrocarbon alcohol) use the hierarchy concept to make recommendations

for improving the safety of this process.

Solution 13-1

Problem 13-2

For the polyether reactor described in Problem 13-1, list a few of the most

important safeguards that should be in place.

Solution 13-2

Problem 13-3

Human factors need to be addressed during all phases of operation. Expand

on the descriptions given in the section on Human Factors.

Solution 13-3

Problem 13-4

As shown in Table 13-1, operators make mistakes that are related to the

operators' environment. List the operator environment in an order of importance

for 1 error in every 1,000 times the operation is done.

Solution 13-4

Problem 13-5

Use the CSB Website to a) describe the T2 Laboratories Inc. incident on Dec.

19, 2007 and b) list the CSB recommendations.

Solution 13-5

Problem 13-6

Use the T2 incident of Problem 13-5 to list the most important elements of an

Incident Investigation; i.e. a) the underlying and root causes of the incident,

and b) the first and other recommendation layers.

Solution 13-6

Program and encourage participation.

Problem 13-7

As emphasized in this chapter, many incidents and grave consequences are

due to the failure to use codes, standards, and other Recognized and

Generally Accepted Good Engineering Practices (RAGAGEP). Read the West

Pharmaceutical Services Dust Explosion and Fire (2003) Incident (CSB report)

and a) describe the incident, b) list the major recommendations, and c) site

the RAGAGEP that is used most frequently.

Solution 13-7

a) Describe the incident: On January 29, 2003, an explosion and fire destroyed the

b) Recommendations:

1) Make compliance with NFPA 654, Standard for the Prevention of Fire and Dust