Exercise set
Chemical Process Safety and Hazard Control Exercises
Worked chemical engineering exercises for process safety and hazard control covering adiabatic temperature rise, safe hold time, blocked-in liquid expansion, relief capacity margin, secondary containment, corrosion remaining life, LOPA frequency, proof-test interval, bypass exposure, and incompatible-transfer risk ranking.
These exercises practise first-pass calculations used in chemical process safety and hazard control. They connect reaction heat, safe hold time, blocked-in liquid expansion, relief capacity, secondary containment, corrosion remaining life, protection-layer analysis, proof testing, bypass exposure, and failure-mode risk ranking.
Assume simplified nominal values unless an exercise states otherwise. Real process safety work requires site-specific chemistry, physical properties, relief design, consequence analysis, inspection records, functional safety review, emergency response planning, management of change, and independent competent review.
How to Use These Exercises
For each problem:
- define the hazardous scenario and operating mode;
- identify the initiating cause, consequence, and credited safeguards;
- keep heat, mass, pressure, time, frequency, and probability bases explicit;
- state which test, inspection, or operating record validates the safeguard;
- avoid counting the same sensor, utility, operator action, or procedure as two independent protection layers.
The most common mistake is treating a safeguard as real because it appears on a diagram. A safeguard is useful only when it is independent enough, fast enough, maintained, proof-tested, and valid for the specific scenario.
For each result, state whether it supports consequence screening, available response time, relief adequacy, containment readiness, inspection planning, protection-layer credit, bypass control, or residual-risk acceptance. A calculation should never imply risk acceptance unless the credited safeguards are auditable and scenario-specific.
Exercise 1: Adiabatic Temperature Rise
A batch reaction can consume 12{,}000\ \text{mol} of reactant during a runaway scenario. Heat of reaction is -75\ \text{kJ/mol}, meaning heat is released. The reacting mass is 4000\ \text{kg} and average heat capacity is 3.5\ \text{kJ/(kg K)}.
Estimate adiabatic temperature rise.
Solution
Heat released:
Thermal capacitance:
Adiabatic temperature rise:
Engineering Comment
A 64\ \text{K} adiabatic rise can move a process into decomposition, boiling, pressure rise, or loss of selectivity. Detailed review should include heat-release rate, accumulation, dosing, mixing, relief, and decomposition onset.
Exercise 2: Safe Hold Time After Cooling Loss
During an upset, a reactor generates heat at \dot{Q}=180\ \text{kW} after cooling is lost. The reacting mass and heat capacity are the same as Exercise 1, so mC_p=14{,}000\ \text{kJ/K}. The allowed temperature rise before emergency action is 15\ \text{K}.
Estimate safe hold time.
Solution
Allowable heat accumulation:
Use \dot{Q}=180\ \text{kJ/s}:
Convert to minutes:
Engineering Comment
Nineteen minutes is not a comfortable margin unless detection, diagnosis, operator action, emergency cooling, feed isolation, and escalation can occur reliably inside that time.
Exercise 3: Blocked-In Liquid Thermal Expansion
A blocked-in liquid segment contains V=2.0\ \text{m}^3 of liquid. Volumetric thermal expansion coefficient is \beta=7.0\times10^{-4}\ \text{K}^{-1}. The liquid can warm by 30\ \text{K}.
Estimate expansion volume.
Solution
Thermal expansion:
Engineering Comment
The liquid wants to expand by 42\ \text{L}. If the segment has no relief path or vapor space, pressure can rise rapidly. Thermal relief protection and isolation procedures should be verified.
Exercise 4: Relief Capacity Margin
A credible gas-generation scenario can produce vapor at 0.42\ \text{kg/s}. The installed relief path has verified capacity of 0.55\ \text{kg/s} for the same fluid basis and discharge condition.
Estimate relief capacity margin.
Solution
Absolute margin:
Relative margin:
Engineering Comment
The nominal margin is positive only if the scenario basis, fluid properties, backpressure, inlet losses, discharge path, and relief-device condition match the verification. Relief capacity is not transferable across different scenarios without review.
Exercise 5: Secondary Containment Capacity
A storage area must contain the largest tank release plus a transfer hose inventory and rainfall. The largest tank contains 25\ \text{m}^3, transfer inventory is 2\ \text{m}^3, rainfall allowance is 3\ \text{m}^3, and containment volume is 32\ \text{m}^3.
Check containment margin.
Solution
Required containment:
Margin:
Engineering Comment
The containment has only 2\ \text{m}^3 margin. The review should check drains, valves, foam or firewater, incompatible chemicals, liner condition, rainfall basis, inspection access, and whether the contained liquid can be safely recovered.
Exercise 6: Corrosion Remaining Life
A pressure vessel shell has measured wall thickness t_m=6.8\ \text{mm}. Minimum allowable thickness is t_{min}=5.5\ \text{mm}. Estimated corrosion rate is 0.35\ \text{mm/year}.
Estimate remaining life to minimum allowable thickness.
Solution
Remaining corrosion allowance:
Remaining life:
Engineering Comment
The calculated life depends on whether corrosion is uniform and whether the rate is stable. Localized corrosion, changed chemistry, inspection uncertainty, or startup/shutdown conditions can reduce the real margin.
Exercise 7: Simplified Layer of Protection Frequency
An initiating event frequency is 1.0\times10^{-2}\ \text{per year}. Credited independent protection layers have probability of failure on demand:
Estimate mitigated event frequency.
Solution
Mitigated frequency:
Engineering Comment
The calculation is only valid if the layers are genuinely independent and applicable to the scenario. Shared sensors, shared utilities, common operator action, or untested assumptions can invalidate the risk reduction.
Exercise 8: Proof-Test Interval Effect
A protective function has dangerous undetected failure rate \lambda=0.04\ \text{per year}. For a simplified low-demand approximation:
Estimate average probability of failure on demand for proof-test intervals of T=1.0\ \text{year} and T=0.5\ \text{year}.
Solution
Annual proof test:
Six-month proof test:
Engineering Comment
Shorter proof-test intervals reduce average undetected failure probability, but tests must verify the complete function. A test that confirms only the software bit does not prove the sensor, final valve, actuator, and field response.
Exercise 9: Bypass Exposure Fraction
A safety interlock was bypassed three times during a year for maintenance. Each bypass lasted 2.0\ \text{h}. Use 8760\ \text{h/year}.
Estimate annual bypass exposure fraction.
Solution
Total bypass time:
Exposure fraction:
Convert to percent:
Engineering Comment
The percentage is small, but bypass risk is scenario-dependent. A bypass during startup, maintenance, or abnormal operation can be much more important than the annual time fraction suggests.
Exercise 10: Incompatible Transfer Risk Ranking
A transfer system could send oxidizing material to a tank containing incompatible organic residue if line-up verification fails. Initial rankings are severity S=10, occurrence O=3, and detection D=4.
After keyed connections, independent line-up verification, batch ticket interlock, and operator training are added, occurrence is estimated at O=2 and detection at D=2. Compare traditional risk priority numbers.
Solution
Initial risk priority number:
Revised risk priority number:
Reduction:
Engineering Comment
The revised ranking is lower, but high-severity incompatible mixing deserves strict management of change, physical segregation where possible, clear labelling, batch records, interlock testing, and stop-work authority.
Process Safety Review Checklist
Before using these calculations in a hazard review, operating procedure, or management-of-change package, check:
- Is the hazardous scenario defined with initiating cause, consequence, operating mode, and affected equipment?
- Are temperature, pressure, inventory, reaction-rate, and relief assumptions valid for the worst credible case?
- Are emergency response times compared with detection delay, diagnosis time, actuator time, and escalation time?
- Are containment and relief margins checked against drains, firewater, backpressure, discharge routing, and incompatible materials?
- Are corrosion-life estimates tied to inspection uncertainty, damage mechanism, localized attack, and operating chemistry?
- Are credited protection layers independent, testable, maintained, and applicable to the exact scenario?
- Are bypasses controlled by permit, compensating measures, time limits, alarms, and shift handover?
- Is residual risk explicitly accepted, reduced by design, or escalated rather than hidden inside an RPN reduction?
Strong process safety engineering treats every number as a claim about a scenario, a safeguard, and a remaining risk. The calculation is useful only when those three elements stay connected.